LMFDB - Embedded newform 5292.2.l.e.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5292,2,Mod(361,5292)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5292, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("5292.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5292.l (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:	$42.2568327497$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 - 2.05195i$ of defining polynomial
Character	$\chi$	$=$	5292.361
Dual form			5292.2.l.e.3313.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46050 q^{5} +O(q^{10})$	$q-2.46050 q^{5} -4.64766 q^{11} +(-3.55408 + 6.15585i) q^{13} +(-2.25729 + 3.90975i) q^{17} +(-2.16372 - 3.74766i) q^{19} -5.86693 q^{23} +1.05408 q^{25} +(-3.48755 - 6.04061i) q^{29} +(3.69076 + 6.39258i) q^{31} +(0.363327 + 0.629301i) q^{37} +(0.136673 - 0.236725i) q^{41} +(2.41741 + 4.18708i) q^{43} +(1.83628 - 3.18054i) q^{47} +(2.52704 - 4.37697i) q^{53} +11.4356 q^{55} +(4.56654 + 7.90947i) q^{59} +(6.90856 - 11.9660i) q^{61} +(8.74484 - 15.1465i) q^{65} +(0.663715 + 1.14959i) q^{67} -13.5218 q^{71} +(2.16372 - 3.74766i) q^{73} +(-3.21780 + 5.57339i) q^{79} +(0.742705 + 1.28640i) q^{83} +(5.55408 - 9.61996i) q^{85} +(4.91741 + 8.51721i) q^{89} +(5.32383 + 9.22115i) q^{95} +(0.246304 + 0.426611i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{5}+O(q^{10}) $ 6 * q - 2 * q^5	$ 6 q - 2 q^{5} - 4 q^{11} - 3 q^{13} + 2 q^{17} - 3 q^{19} - 28 q^{23} - 12 q^{25} + q^{29} + 3 q^{31} + 3 q^{37} - 3 q^{43} + 21 q^{47} + 6 q^{53} + 12 q^{55} + 31 q^{59} - 6 q^{61} + 15 q^{65} - 6 q^{67} - 34 q^{71} + 3 q^{73} + 9 q^{79} + 20 q^{83} + 15 q^{85} + 12 q^{89} + 20 q^{95} + 9 q^{97}+O(q^{100}) $ 6 * q - 2 * q^5 - 4 * q^11 - 3 * q^13 + 2 * q^17 - 3 * q^19 - 28 * q^23 - 12 * q^25 + q^29 + 3 * q^31 + 3 * q^37 - 3 * q^43 + 21 * q^47 + 6 * q^53 + 12 * q^55 + 31 * q^59 - 6 * q^61 + 15 * q^65 - 6 * q^67 - 34 * q^71 + 3 * q^73 + 9 * q^79 + 20 * q^83 + 15 * q^85 + 12 * q^89 + 20 * q^95 + 9 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5292\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$	$2647$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	−2.46050			−1.10037			−0.550186	−	0.835042i	$-0.685443\pi$
$5$	−2.46050			−1.10037			−0.550186	+	0.835042i	$0.685443\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.64766			−1.40132			−0.700662	−	0.713494i	$-0.747112\pi$
$11$	−4.64766			−1.40132			−0.700662	+	0.713494i	$0.747112\pi$
$12$		0			0
$13$	−3.55408	+	6.15585i	−0.985726	+	1.70733i	−0.347059	+	0.937843i	$0.612820\pi$
$13$	−3.55408	+	6.15585i	−0.985726	+	1.70733i	−0.638667	+	0.769484i	$0.720514\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.25729	+	3.90975i	−0.547474	+	0.948253i	0.450972	+	0.892538i	$0.351077\pi$
$17$	−2.25729	+	3.90975i	−0.547474	+	0.948253i	−0.998447	+	0.0557155i	$0.982256\pi$
$18$		0			0
$19$	−2.16372	−	3.74766i	−0.496390	−	0.859773i	0.503601	−	0.863936i	$-0.332008\pi$
$19$	−2.16372	−	3.74766i	−0.496390	−	0.859773i	−0.999991	+	0.00416311i	$0.998675\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−5.86693			−1.22334			−0.611669	−	0.791114i	$-0.709502\pi$
$23$	−5.86693			−1.22334			−0.611669	+	0.791114i	$0.709502\pi$
$24$		0			0
$25$	1.05408			0.210817
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.48755	−	6.04061i	−0.647621	−	1.12171i	−0.983689	−	0.179875i	$-0.942431\pi$
$29$	−3.48755	−	6.04061i	−0.647621	−	1.12171i	0.336068	−	0.941838i	$-0.390903\pi$
$30$		0			0
$31$	3.69076	+	6.39258i	0.662880	+	1.14814i	0.979856	+	0.199708i	$0.0639992\pi$
$31$	3.69076	+	6.39258i	0.662880	+	1.14814i	−0.316976	+	0.948434i	$0.602667\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.363327	+	0.629301i	0.0597306	+	0.103456i	0.894344	−	0.447379i	$-0.147643\pi$
$37$	0.363327	+	0.629301i	0.0597306	+	0.103456i	−0.834614	+	0.550835i	$0.814309\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.136673	−	0.236725i	0.0213448	−	0.0369702i	−0.855156	−	0.518371i	$-0.826539\pi$
$41$	0.136673	−	0.236725i	0.0213448	−	0.0369702i	0.876500	+	0.481401i	$0.159872\pi$
$42$		0			0
$43$	2.41741	+	4.18708i	0.368652	+	0.638524i	0.989355	−	0.145522i	$-0.0464862\pi$
$43$	2.41741	+	4.18708i	0.368652	+	0.638524i	−0.620703	+	0.784046i	$0.713153\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.83628	−	3.18054i	0.267850	−	0.463929i	−0.700457	−	0.713695i	$-0.747020\pi$
$47$	1.83628	−	3.18054i	0.267850	−	0.463929i	0.968306	+	0.249766i	$0.0803536\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.52704	−	4.37697i	0.347116	−	0.601222i	−0.638620	−	0.769522i	$-0.720494\pi$
$53$	2.52704	−	4.37697i	0.347116	−	0.601222i	0.985736	+	0.168300i	$0.0538277\pi$
$54$		0			0
$55$	11.4356			1.54198
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.56654	+	7.90947i	0.594513	+	1.02973i	0.993615	+	0.112820i	$0.0359883\pi$
$59$	4.56654	+	7.90947i	0.594513	+	1.02973i	−0.399103	+	0.916906i	$0.630678\pi$
$60$		0			0
$61$	6.90856	−	11.9660i	0.884550	−	1.53209i	0.0383215	−	0.999265i	$-0.487799\pi$
$61$	6.90856	−	11.9660i	0.884550	−	1.53209i	0.846228	−	0.532820i	$-0.178868\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	8.74484	−	15.1465i	1.08466	−	1.87869i
$66$		0			0
$67$	0.663715	+	1.14959i	0.0810857	+	0.140445i	0.903717	−	0.428131i	$-0.140828\pi$
$67$	0.663715	+	1.14959i	0.0810857	+	0.140445i	−0.822631	+	0.568576i	$0.807495\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−13.5218			−1.60474			−0.802370	−	0.596826i	$-0.796428\pi$
$71$	−13.5218			−1.60474			−0.802370	+	0.596826i	$0.796428\pi$
$72$		0			0
$73$	2.16372	−	3.74766i	0.253244	−	0.438631i	−0.711173	−	0.703017i	$-0.751836\pi$
$73$	2.16372	−	3.74766i	0.253244	−	0.438631i	0.964417	+	0.264386i	$0.0851692\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−3.21780	+	5.57339i	−0.362031	+	0.627056i	−0.988295	−	0.152555i	$-0.951250\pi$
$79$	−3.21780	+	5.57339i	−0.362031	+	0.627056i	0.626264	+	0.779611i	$0.284583\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.742705	+	1.28640i	0.0815225	+	0.141201i	0.903904	−	0.427735i	$-0.140688\pi$
$83$	0.742705	+	1.28640i	0.0815225	+	0.141201i	−0.822382	+	0.568936i	$0.807355\pi$
$84$		0			0
$85$	5.55408	−	9.61996i	0.602425	−	1.04343i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.91741	+	8.51721i	0.521245	+	0.902822i	0.999695	+	0.0247073i	$0.00786539\pi$
$89$	4.91741	+	8.51721i	0.521245	+	0.902822i	−0.478450	+	0.878115i	$0.658801\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	5.32383	+	9.22115i	0.546214	+	0.946070i
$96$		0			0
$97$	0.246304	+	0.426611i	0.0250084	+	0.0433158i	0.878259	−	0.478186i	$-0.158705\pi$
$97$	0.246304	+	0.426611i	0.0250084	+	0.0433158i	−0.853250	+	0.521502i	$0.825372\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.40642			−0.338952			−0.169476	−	0.985534i	$-0.554207\pi$
$101$	−3.40642			−0.338952			−0.169476	+	0.985534i	$0.554207\pi$
$102$		0			0
$103$	5.16225			0.508652			0.254326	−	0.967119i	$-0.418146\pi$
$103$	5.16225			0.508652			0.254326	+	0.967119i	$0.418146\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.88151	−	4.99093i	−0.278567	−	0.482491i	0.692462	−	0.721454i	$-0.256526\pi$
$107$	−2.88151	−	4.99093i	−0.278567	−	0.482491i	−0.971029	+	0.238963i	$0.923193\pi$
$108$		0			0
$109$	4.49115	−	7.77889i	0.430174	−	0.745083i	−0.566714	−	0.823914i	$-0.691786\pi$
$109$	4.49115	−	7.77889i	0.430174	−	0.745083i	0.996888	+	0.0788317i	$0.0251190\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.679767	+	1.17739i	−0.0639471	+	0.110760i	−0.896226	−	0.443597i	$-0.853702\pi$
$113$	−0.679767	+	1.17739i	−0.0639471	+	0.110760i	0.832279	+	0.554356i	$0.187036\pi$
$114$		0			0
$115$	14.4356			1.34613
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	10.6008			0.963707
$122$		0			0
$123$		0			0
$124$		0			0
$125$	9.70895			0.868394
$126$		0			0
$127$	−0.820039			−0.0727667			−0.0363833	−	0.999338i	$-0.511584\pi$
$127$	−0.820039			−0.0727667			−0.0363833	+	0.999338i	$0.511584\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.78794			−0.680435			−0.340218	−	0.940347i	$-0.610501\pi$
$131$	−7.78794			−0.680435			−0.340218	+	0.940347i	$0.610501\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.99280			0.255692			0.127846	−	0.991794i	$-0.459194\pi$
$137$	2.99280			0.255692			0.127846	+	0.991794i	$0.459194\pi$
$138$		0			0
$139$	−3.16372	+	5.47972i	−0.268343	+	0.464783i	−0.968434	−	0.249270i	$-0.919809\pi$
$139$	−3.16372	+	5.47972i	−0.268343	+	0.464783i	0.700091	+	0.714053i	$0.253143\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	16.5182	−	28.6103i	1.38132	−	2.39252i
$144$		0			0
$145$	8.58113	+	14.8629i	0.712624	+	1.23430i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.38151			0.358948			0.179474	−	0.983763i	$-0.442560\pi$
$149$	4.38151			0.358948			0.179474	+	0.983763i	$0.442560\pi$
$150$		0			0
$151$	6.60078			0.537164			0.268582	−	0.963257i	$-0.413445\pi$
$151$	6.60078			0.537164			0.268582	+	0.963257i	$0.413445\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−9.08113	−	15.7290i	−0.729414	−	1.26338i
$156$		0			0
$157$	2.89037	+	5.00627i	0.230677	+	0.399544i	0.958007	−	0.286743i	$-0.0925727\pi$
$157$	2.89037	+	5.00627i	0.230677	+	0.399544i	−0.727331	+	0.686287i	$0.759239\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−3.66372	−	6.34574i	−0.286964	−	0.497037i	0.686119	−	0.727489i	$-0.259313\pi$
$163$	−3.66372	−	6.34574i	−0.286964	−	0.497037i	−0.973084	+	0.230452i	$0.925979\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.01459	+	10.4176i	−0.465423	+	0.806136i	−0.999221	−	0.0394762i	$-0.987431\pi$
$167$	−6.01459	+	10.4176i	−0.465423	+	0.806136i	0.533798	+	0.845612i	$0.320764\pi$
$168$		0			0
$169$	−18.7630	−	32.4985i	−1.44331	−	2.49989i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.44951	−	4.24268i	0.186233	−	0.322565i	−0.757758	−	0.652535i	$-0.773705\pi$
$173$	2.44951	−	4.24268i	0.186233	−	0.322565i	0.943991	+	0.329970i	$0.107039\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.890369	+	1.54216i	−0.0665493	+	0.115267i	−0.897380	−	0.441258i	$-0.854532\pi$
$179$	−0.890369	+	1.54216i	−0.0665493	+	0.115267i	0.830831	+	0.556525i	$0.187866\pi$
$180$		0			0
$181$	−16.9430			−1.25936			−0.629681	−	0.776854i	$-0.716815\pi$
$181$	−16.9430			−1.25936			−0.629681	+	0.776854i	$0.716815\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.893968	−	1.54840i	−0.0657258	−	0.113840i
$186$		0			0
$187$	10.4911	−	18.1712i	0.767189	−	1.32881i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.74484	+	4.75420i	−0.198610	+	0.344002i	−0.948078	−	0.318038i	$-0.896976\pi$
$191$	−2.74484	+	4.75420i	−0.198610	+	0.344002i	0.749468	+	0.662040i	$0.230309\pi$
$192$		0			0
$193$	2.75370	+	4.76954i	0.198215	+	0.343319i	0.947950	−	0.318420i	$-0.103152\pi$
$193$	2.75370	+	4.76954i	0.198215	+	0.343319i	−0.749734	+	0.661739i	$0.769819\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−11.6300			−0.828600			−0.414300	−	0.910140i	$-0.635974\pi$
$197$	−11.6300			−0.828600			−0.414300	+	0.910140i	$0.635974\pi$
$198$		0			0
$199$	2.07373	−	3.59181i	0.147003	−	0.254617i	−0.783115	−	0.621876i	$-0.786371\pi$
$199$	2.07373	−	3.59181i	0.147003	−	0.254617i	0.930118	+	0.367260i	$0.119704\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−0.336285	+	0.582462i	−0.0234871	+	0.0406809i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	10.0562	+	17.4179i	0.695603	+	1.20482i
$210$		0			0
$211$	13.6082	−	23.5700i	0.936825	−	1.62263i	0.165478	−	0.986213i	$-0.447083\pi$
$211$	13.6082	−	23.5700i	0.936825	−	1.62263i	0.771347	−	0.636415i	$-0.219583\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−5.94805	−	10.3023i	−0.405654	−	0.702613i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−16.0452	−	27.7912i	−1.07932	−	1.86944i
$222$		0			0
$223$	1.60817	+	2.78543i	0.107691	+	0.186526i	0.914834	−	0.403829i	$-0.132321\pi$
$223$	1.60817	+	2.78543i	0.107691	+	0.186526i	−0.807144	+	0.590355i	$0.798988\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−15.9459			−1.05837			−0.529184	−	0.848507i	$-0.677502\pi$
$227$	−15.9459			−1.05837			−0.529184	+	0.848507i	$0.677502\pi$
$228$		0			0
$229$	−1.21634			−0.0803778			−0.0401889	−	0.999192i	$-0.512796\pi$
$229$	−1.21634			−0.0803778			−0.0401889	+	0.999192i	$0.512796\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	9.98608	+	17.2964i	0.654210	+	1.13313i	0.982091	+	0.188406i	$0.0603321\pi$
$233$	9.98608	+	17.2964i	0.654210	+	1.13313i	−0.327881	+	0.944719i	$0.606335\pi$
$234$		0			0
$235$	−4.51819	+	7.82573i	−0.294734	+	0.510494i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	3.00739	−	5.20896i	0.194532	−	0.336939i	−0.752215	−	0.658918i	$-0.771015\pi$
$239$	3.00739	−	5.20896i	0.194532	−	0.336939i	0.946747	+	0.321978i	$0.104348\pi$
$240$		0			0
$241$	−18.6156			−1.19913			−0.599567	−	0.800325i	$-0.704660\pi$
$241$	−18.6156			−1.19913			−0.599567	+	0.800325i	$0.704660\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	30.7601			1.95722
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−6.99707			−0.441651			−0.220826	−	0.975313i	$-0.570875\pi$
$251$	−6.99707			−0.441651			−0.220826	+	0.975313i	$0.570875\pi$
$252$		0			0
$253$	27.2675			1.71429
$254$		0			0
$255$		0			0
$256$		0			0
$257$	17.7778			1.10895			0.554475	−	0.832201i	$-0.312919\pi$
$257$	17.7778			1.10895			0.554475	+	0.832201i	$0.312919\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	27.1986			1.67714			0.838570	−	0.544794i	$-0.183392\pi$
$263$	27.1986			1.67714			0.838570	+	0.544794i	$0.183392\pi$
$264$		0			0
$265$	−6.21780	+	10.7695i	−0.381956	+	0.661568i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	11.9481	−	20.6946i	0.728486	−	1.26177i	−0.229038	−	0.973418i	$-0.573558\pi$
$269$	11.9481	−	20.6946i	0.728486	−	1.26177i	0.957523	−	0.288356i	$-0.0931088\pi$
$270$		0			0
$271$	−6.13667	−	10.6290i	−0.372776	−	0.645668i	0.617215	−	0.786794i	$-0.288261\pi$
$271$	−6.13667	−	10.6290i	−0.372776	−	0.645668i	−0.989992	+	0.141127i	$0.954927\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.89903			−0.295423
$276$		0			0
$277$	12.7807			0.767920			0.383960	−	0.923350i	$-0.374560\pi$
$277$	12.7807			0.767920			0.383960	+	0.923350i	$0.374560\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−14.2573	−	24.6944i	−0.850519	−	1.47314i	−0.880741	−	0.473599i	$-0.842955\pi$
$281$	−14.2573	−	24.6944i	−0.850519	−	1.47314i	0.0302219	−	0.999543i	$-0.490379\pi$
$282$		0			0
$283$	−0.363327	−	0.629301i	−0.0215975	−	0.0374080i	0.855025	−	0.518587i	$-0.173542\pi$
$283$	−0.363327	−	0.629301i	−0.0215975	−	0.0374080i	−0.876622	+	0.481179i	$0.840209\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−1.69076	−	2.92848i	−0.0994563	−	0.172263i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	12.7901	−	22.1531i	0.747204	−	1.29420i	−0.201954	−	0.979395i	$-0.564729\pi$
$293$	12.7901	−	22.1531i	0.747204	−	1.29420i	0.949158	−	0.314800i	$-0.101938\pi$
$294$		0			0
$295$	−11.2360	−	19.4613i	−0.654184	−	1.13308i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	20.8515	−	36.1159i	1.20588	−	2.08864i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−16.9985	+	29.4423i	−0.973333	+	1.68586i
$306$		0			0
$307$	−6.23405			−0.355796			−0.177898	−	0.984049i	$-0.556930\pi$
$307$	−6.23405			−0.355796			−0.177898	+	0.984049i	$0.556930\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	14.6192	+	25.3211i	0.828976	+	1.43583i	0.898842	+	0.438273i	$0.144410\pi$
$311$	14.6192	+	25.3211i	0.828976	+	1.43583i	−0.0698655	+	0.997556i	$0.522257\pi$
$312$		0			0
$313$	−14.2434	+	24.6703i	−0.805083	+	1.39445i	0.111151	+	0.993803i	$0.464546\pi$
$313$	−14.2434	+	24.6703i	−0.805083	+	1.39445i	−0.916235	+	0.400642i	$0.868787\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.809243	−	1.40165i	0.0454516	−	0.0787245i	−0.842405	−	0.538846i	$-0.818861\pi$
$317$	0.809243	−	1.40165i	0.0454516	−	0.0787245i	0.887856	+	0.460121i	$0.152194\pi$
$318$		0			0
$319$	16.2089	+	28.0747i	0.907527	+	1.57188i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	19.5366			1.08704
$324$		0			0
$325$	−3.74630	+	6.48879i	−0.207808	+	0.359933i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	6.99115	−	12.1090i	0.384268	−	0.665572i	−0.607399	−	0.794397i	$-0.707787\pi$
$331$	6.99115	−	12.1090i	0.384268	−	0.665572i	0.991667	+	0.128825i	$0.0411205\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−1.63307	−	2.82857i	−0.0892244	−	0.154541i
$336$		0			0
$337$	−13.8619	+	24.0095i	−0.755104	+	1.30788i	0.190219	+	0.981742i	$0.439080\pi$
$337$	−13.8619	+	24.0095i	−0.755104	+	1.30788i	−0.945323	+	0.326137i	$0.894253\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−17.1534	−	29.7106i	−0.928909	−	1.60892i
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	3.76449	+	6.52029i	0.202089	+	0.350028i	0.949201	−	0.314670i	$-0.101894\pi$
$347$	3.76449	+	6.52029i	0.202089	+	0.350028i	−0.747113	+	0.664697i	$0.768560\pi$
$348$		0			0
$349$	15.0541	+	26.0744i	0.805827	+	1.39573i	0.915732	+	0.401791i	$0.131612\pi$
$349$	15.0541	+	26.0744i	0.805827	+	1.39573i	−0.109905	+	0.993942i	$0.535055\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	20.3638			1.08386			0.541928	−	0.840425i	$-0.317695\pi$
$353$	20.3638			1.08386			0.541928	+	0.840425i	$0.317695\pi$
$354$		0			0
$355$	33.2704			1.76581
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−8.01313	−	13.8791i	−0.422917	−	0.732513i	0.573307	−	0.819341i	$-0.305660\pi$
$359$	−8.01313	−	13.8791i	−0.422917	−	0.732513i	−0.996223	+	0.0868277i	$0.972327\pi$
$360$		0			0
$361$	0.136673	−	0.236725i	0.00719332	−	0.0124592i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−5.32383	+	9.22115i	−0.278662	+	0.482657i
$366$		0			0
$367$	−13.5979			−0.709802			−0.354901	−	0.934904i	$-0.615485\pi$
$367$	−13.5979			−0.709802			−0.354901	+	0.934904i	$0.615485\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−21.9282			−1.13540			−0.567700	−	0.823236i	$-0.692167\pi$
$373$	−21.9282			−1.13540			−0.567700	+	0.823236i	$0.692167\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	49.5801			2.55351
$378$		0			0
$379$	−29.7965			−1.53054			−0.765271	−	0.643708i	$-0.777395\pi$
$379$	−29.7965			−1.53054			−0.765271	+	0.643708i	$0.777395\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.0219809			0.00112317			0.000561587	−	1.00000i	$-0.499821\pi$
$383$	0.0219809			0.00112317			0.000561587		1.00000i	$0.499821\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	35.3566			1.79265			0.896326	−	0.443396i	$-0.146227\pi$
$389$	35.3566			1.79265			0.896326	+	0.443396i	$0.146227\pi$
$390$		0			0
$391$	13.2434	−	22.9382i	0.669746	−	1.16003i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	7.91741	−	13.7134i	0.398368	−	0.689994i
$396$		0			0
$397$	8.47150	+	14.6731i	0.425172	+	0.736420i	0.996436	−	0.0843464i	$-0.0268802\pi$
$397$	8.47150	+	14.6731i	0.425172	+	0.736420i	−0.571264	+	0.820766i	$0.693547\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	2.96362			0.147996			0.0739982	−	0.997258i	$-0.476424\pi$
$401$	2.96362			0.147996			0.0739982	+	0.997258i	$0.476424\pi$
$402$		0			0
$403$	−52.4690			−2.61367
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.68862	−	2.92478i	−0.0837018	−	0.144976i
$408$		0			0
$409$	7.32743	+	12.6915i	0.362318	+	0.627553i	0.988342	−	0.152251i	$-0.0486521\pi$
$409$	7.32743	+	12.6915i	0.362318	+	0.627553i	−0.626024	+	0.779804i	$0.715319\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−1.82743	−	3.16520i	−0.0897050	−	0.155374i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−12.6352	+	21.8848i	−0.617270	+	1.06914i	0.372711	+	0.927947i	$0.378428\pi$
$419$	−12.6352	+	21.8848i	−0.617270	+	1.06914i	−0.989982	+	0.141196i	$0.954905\pi$
$420$		0			0
$421$	7.99854	+	13.8539i	0.389825	+	0.675196i	0.992426	−	0.122846i	$-0.0392022\pi$
$421$	7.99854	+	13.8539i	0.389825	+	0.675196i	−0.602601	+	0.798043i	$0.705869\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.37938	+	4.12120i	−0.115417	+	0.199908i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	6.51673	−	11.2873i	0.313900	−	0.543690i	−0.665303	−	0.746573i	$-0.731698\pi$
$431$	6.51673	−	11.2873i	0.313900	−	0.543690i	0.979203	+	0.202883i	$0.0650311\pi$
$432$		0			0
$433$	23.5467			1.13158			0.565791	−	0.824549i	$-0.308571\pi$
$433$	23.5467			1.13158			0.565791	+	0.824549i	$0.308571\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	12.6944	+	21.9873i	0.607253	+	1.05179i
$438$		0			0
$439$	−3.35447	+	5.81012i	−0.160100	+	0.277302i	−0.934904	−	0.354900i	$-0.884515\pi$
$439$	−3.35447	+	5.81012i	−0.160100	+	0.277302i	0.774804	+	0.632201i	$0.217848\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	17.6228	−	30.5235i	0.837282	−	1.45022i	−0.0548760	−	0.998493i	$-0.517476\pi$
$443$	17.6228	−	30.5235i	0.837282	−	1.45022i	0.892158	−	0.451723i	$-0.149190\pi$
$444$		0			0
$445$	−12.0993	−	20.9566i	−0.573562	−	0.993439i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	12.9387			0.610616			0.305308	−	0.952254i	$-0.401241\pi$
$449$	12.9387			0.610616			0.305308	+	0.952254i	$0.401241\pi$
$450$		0			0
$451$	−0.635211	+	1.10022i	−0.0299109	+	0.0518072i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	14.5993	−	25.2868i	0.682927	−	1.18286i	−0.291156	−	0.956675i	$-0.594040\pi$
$457$	14.5993	−	25.2868i	0.682927	−	1.18286i	0.974083	−	0.226189i	$-0.0726267\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−9.34348	−	16.1834i	−0.435169	−	0.753735i	0.562140	−	0.827042i	$-0.309978\pi$
$461$	−9.34348	−	16.1834i	−0.435169	−	0.753735i	−0.997309	+	0.0733066i	$0.976645\pi$
$462$		0			0
$463$	19.1249	−	33.1253i	0.888809	−	1.53946i	0.0475247	−	0.998870i	$-0.484867\pi$
$463$	19.1249	−	33.1253i	0.888809	−	1.53946i	0.841285	−	0.540593i	$-0.181800\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.64387	−	13.2396i	−0.353716	−	0.612654i	0.633181	−	0.774004i	$-0.281749\pi$
$467$	−7.64387	−	13.2396i	−0.353716	−	0.612654i	−0.986897	+	0.161349i	$0.948415\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−11.2353	−	19.4601i	−0.516600	−	0.894778i
$474$		0			0
$475$	−2.28074	−	3.95035i	−0.104647	−	0.181255i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−11.0321			−0.504070			−0.252035	−	0.967718i	$-0.581100\pi$
$479$	−11.0321			−0.504070			−0.252035	+	0.967718i	$0.581100\pi$
$480$		0			0
$481$	−5.16518			−0.235512
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.606032	−	1.04968i	−0.0275185	−	0.0476635i
$486$		0			0
$487$	−8.30039	+	14.3767i	−0.376126	+	0.651470i	−0.990495	−	0.137549i	$-0.956078\pi$
$487$	−8.30039	+	14.3767i	−0.376126	+	0.651470i	0.614368	+	0.789019i	$0.289411\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−13.3633	+	23.1460i	−0.603079	+	1.04456i	0.389273	+	0.921122i	$0.372726\pi$
$491$	−13.3633	+	23.1460i	−0.603079	+	1.04456i	−0.992352	+	0.123440i	$0.960607\pi$
$492$		0			0
$493$	31.4897			1.41822
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	1.23697			0.0553744			0.0276872	−	0.999617i	$-0.491186\pi$
$499$	1.23697			0.0553744			0.0276872	+	0.999617i	$0.491186\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	1.07179			0.0477889			0.0238944	−	0.999714i	$-0.492393\pi$
$503$	1.07179			0.0477889			0.0238944	+	0.999714i	$0.492393\pi$
$504$		0			0
$505$	8.38151			0.372973
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−20.0689			−0.889537			−0.444768	−	0.895646i	$-0.646714\pi$
$509$	−20.0689			−0.889537			−0.444768	+	0.895646i	$0.646714\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−12.7017			−0.559706
$516$		0			0
$517$	−8.53443	+	14.7821i	−0.375344	+	0.650115i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−15.4430	+	26.7480i	−0.676570	+	1.17185i	0.299438	+	0.954116i	$0.403201\pi$
$521$	−15.4430	+	26.7480i	−0.676570	+	1.17185i	−0.976007	+	0.217737i	$0.930132\pi$
$522$		0			0
$523$	3.69961	+	6.40792i	0.161773	+	0.280199i	0.935505	−	0.353315i	$-0.114946\pi$
$523$	3.69961	+	6.40792i	0.161773	+	0.280199i	−0.773732	+	0.633513i	$0.781612\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−33.3245			−1.45164
$528$		0			0
$529$	11.4208			0.496557
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.971495	+	1.68268i	0.0420801	+	0.0728849i
$534$		0			0
$535$	7.08998	+	12.2802i	0.306527	+	0.530920i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−11.3348	−	19.6325i	−0.487322	−	0.844067i	0.512572	−	0.858644i	$-0.328693\pi$
$541$	−11.3348	−	19.6325i	−0.487322	−	0.844067i	−0.999894	+	0.0145779i	$0.995360\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−11.0505	+	19.1400i	−0.473351	+	0.819868i
$546$		0			0
$547$	3.07373	+	5.32386i	0.131423	+	0.227632i	0.924225	−	0.381847i	$-0.124712\pi$
$547$	3.07373	+	5.32386i	0.131423	+	0.227632i	−0.792802	+	0.609479i	$0.791379\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−15.0921	+	26.1403i	−0.642946	+	1.11361i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.8370	−	25.6984i	0.628662	−	1.08887i	−0.359158	−	0.933277i	$-0.616936\pi$
$557$	14.8370	−	25.6984i	0.628662	−	1.08887i	0.987820	−	0.155598i	$-0.0497305\pi$
$558$		0			0
$559$	−34.3667			−1.45356
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−14.6555	−	25.3841i	−0.617657	−	1.06981i	−0.989912	−	0.141683i	$-0.954749\pi$
$563$	−14.6555	−	25.3841i	−0.617657	−	1.06981i	0.372255	−	0.928131i	$-0.378585\pi$
$564$		0			0
$565$	1.67257	−	2.89698i	0.0703655	−	0.121877i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−18.4430	+	31.9442i	−0.773170	+	1.33917i	0.162647	+	0.986684i	$0.447997\pi$
$569$	−18.4430	+	31.9442i	−0.773170	+	1.33917i	−0.935817	+	0.352486i	$0.885336\pi$
$570$		0			0
$571$	−16.1893	−	28.0407i	−0.677501	−	1.17347i	−0.975731	−	0.218972i	$-0.929730\pi$
$571$	−16.1893	−	28.0407i	−0.677501	−	1.17347i	0.298230	−	0.954494i	$-0.403604\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−6.18423			−0.257900
$576$		0			0
$577$	−11.5093	+	19.9348i	−0.479140	+	0.829895i	−0.999714	−	0.0239220i	$-0.992385\pi$
$577$	−11.5093	+	19.9348i	−0.479140	+	0.829895i	0.520574	+	0.853817i	$0.325718\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−11.7448	+	20.3427i	−0.486422	+	0.842507i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2.87052	+	4.97189i	0.118479	+	0.205212i	0.919165	−	0.393872i	$-0.128865\pi$
$587$	2.87052	+	4.97189i	0.118479	+	0.205212i	−0.800686	+	0.599084i	$0.795531\pi$
$588$		0			0
$589$	15.9715	−	27.6634i	0.658094	−	1.13985i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	13.8727	+	24.0282i	0.569682	+	0.986718i	0.996597	+	0.0824263i	$0.0262669\pi$
$593$	13.8727	+	24.0282i	0.569682	+	0.986718i	−0.426915	+	0.904292i	$0.640400\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	2.05408	+	3.55778i	0.0839276	+	0.145367i	0.904934	−	0.425552i	$-0.139920\pi$
$599$	2.05408	+	3.55778i	0.0839276	+	0.145367i	−0.821006	+	0.570919i	$0.806587\pi$
$600$		0			0
$601$	−7.80924	−	13.5260i	−0.318546	−	0.551737i	0.661639	−	0.749822i	$-0.269861\pi$
$601$	−7.80924	−	13.5260i	−0.318546	−	0.551737i	−0.980185	+	0.198085i	$0.936528\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−26.0833			−1.06044
$606$		0			0
$607$	−0.561476			−0.0227896			−0.0113948	−	0.999935i	$-0.503627\pi$
$607$	−0.561476			−0.0227896			−0.0113948	+	0.999935i	$0.503627\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	13.0526	+	22.6078i	0.528053	+	0.914614i
$612$		0			0
$613$	10.1008	−	17.4951i	0.407967	−	0.706619i	−0.586695	−	0.809808i	$-0.699571\pi$
$613$	10.1008	−	17.4951i	0.407967	−	0.706619i	0.994662	+	0.103189i	$0.0329047\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−11.4569	+	19.8439i	−0.461238	+	0.798887i	−0.999023	−	0.0441948i	$-0.985928\pi$
$617$	−11.4569	+	19.8439i	−0.461238	+	0.798887i	0.537785	+	0.843082i	$0.319261\pi$
$618$		0			0
$619$	39.7031			1.59580			0.797901	−	0.602788i	$-0.205944\pi$
$619$	39.7031			1.59580			0.797901	+	0.602788i	$0.205944\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−29.1593			−1.16637
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−3.28054			−0.130804
$630$		0			0
$631$	−31.0364			−1.23554			−0.617769	−	0.786359i	$-0.711963\pi$
$631$	−31.0364			−1.23554			−0.617769	+	0.786359i	$0.711963\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	2.01771			0.0800703
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	29.5864			1.16859			0.584296	−	0.811541i	$-0.301371\pi$
$641$	29.5864			1.16859			0.584296	+	0.811541i	$0.301371\pi$
$642$		0			0
$643$	−12.8442	+	22.2467i	−0.506524	+	0.877325i	0.493447	+	0.869776i	$0.335737\pi$
$643$	−12.8442	+	22.2467i	−0.506524	+	0.877325i	−0.999972	+	0.00754978i	$0.997597\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	8.50885	−	14.7378i	0.334518	−	0.579401i	−0.648874	−	0.760895i	$-0.724760\pi$
$647$	8.50885	−	14.7378i	0.334518	−	0.579401i	0.983392	+	0.181494i	$0.0580933\pi$
$648$		0			0
$649$	−21.2237	−	36.7606i	−0.833104	−	1.44298i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.47102			−0.0575653			−0.0287827	−	0.999586i	$-0.509163\pi$
$653$	−1.47102			−0.0575653			−0.0287827	+	0.999586i	$0.509163\pi$
$654$		0			0
$655$	19.1623			0.748731
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−20.7003	−	35.8539i	−0.806369	−	1.39667i	−0.915363	−	0.402629i	$-0.868096\pi$
$659$	−20.7003	−	35.8539i	−0.806369	−	1.39667i	0.108995	−	0.994042i	$-0.465237\pi$
$660$		0			0
$661$	−19.1352	−	33.1432i	−0.744273	−	1.28912i	−0.950533	−	0.310622i	$-0.899463\pi$
$661$	−19.1352	−	33.1432i	−0.744273	−	1.28912i	0.206260	−	0.978497i	$-0.433871\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	20.4612	+	35.4398i	0.792260	+	1.37223i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−32.1086	+	55.6138i	−1.23954	+	2.14695i
$672$		0			0
$673$	15.2448	+	26.4048i	0.587645	+	1.01783i	0.994540	+	0.104357i	$0.0332783\pi$
$673$	15.2448	+	26.4048i	0.587645	+	1.01783i	−0.406894	+	0.913475i	$0.633388\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	22.4626	−	38.9064i	0.863309	−	1.49530i	−0.00540665	−	0.999985i	$-0.501721\pi$
$677$	22.4626	−	38.9064i	0.863309	−	1.49530i	0.868716	−	0.495310i	$-0.164946\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−24.1986	+	41.9133i	−0.925935	+	1.60377i	−0.135884	+	0.990725i	$0.543387\pi$
$683$	−24.1986	+	41.9133i	−0.925935	+	1.60377i	−0.790051	+	0.613041i	$0.789946\pi$
$684$		0			0
$685$	−7.36381			−0.281357
$686$		0			0
$687$		0			0
$688$		0			0
$689$	17.9626	+	31.1122i	0.684322	+	1.18528i
$690$		0			0
$691$	−9.19076	+	15.9189i	−0.349633	+	0.605582i	−0.986184	−	0.165652i	$-0.947027\pi$
$691$	−9.19076	+	15.9189i	−0.349633	+	0.605582i	0.636551	+	0.771234i	$0.280360\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	7.78434	−	13.4829i	0.295277	−	0.511434i
$696$		0			0
$697$	0.617023	+	1.06871i	0.0233714	+	0.0404805i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	27.0292			1.02088			0.510439	−	0.859914i	$-0.329483\pi$
$701$	27.0292			1.02088			0.510439	+	0.859914i	$0.329483\pi$
$702$		0			0
$703$	1.57227	−	2.72325i	0.0592994	−	0.102710i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−2.49261	+	4.31732i	−0.0936119	+	0.162141i	−0.909028	−	0.416734i	$-0.863175\pi$
$709$	−2.49261	+	4.31732i	−0.0936119	+	0.162141i	0.815417	+	0.578875i	$0.196508\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−21.6534	−	37.5048i	−0.810926	−	1.40457i
$714$		0			0
$715$	−40.6431	+	70.3959i	−1.51997	+	2.63266i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	7.84708	+	13.5915i	0.292647	+	0.506879i	0.974435	−	0.224671i	$-0.0721307\pi$
$719$	7.84708	+	13.5915i	0.292647	+	0.506879i	−0.681788	+	0.731550i	$0.738797\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−3.67617	−	6.36731i	−0.136529	−	0.236476i
$726$		0			0
$727$	−10.9071	−	18.8916i	−0.404522	−	0.700652i	0.589744	−	0.807590i	$-0.299229\pi$
$727$	−10.9071	−	18.8916i	−0.404522	−	0.700652i	−0.994266	+	0.106938i	$0.965895\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−21.8272			−0.807309
$732$		0			0
$733$	−24.0148			−0.887006			−0.443503	−	0.896273i	$-0.646264\pi$
$733$	−24.0148			−0.887006			−0.443503	+	0.896273i	$0.646264\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.08472	−	5.34290i	−0.113627	−	0.196808i
$738$		0			0
$739$	−9.35447	+	16.2024i	−0.344110	+	0.596016i	−0.985192	−	0.171457i	$-0.945153\pi$
$739$	−9.35447	+	16.2024i	−0.344110	+	0.596016i	0.641082	+	0.767473i	$0.278486\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−20.1534	+	34.9067i	−0.739356	+	1.28060i	0.213429	+	0.976959i	$0.431537\pi$
$743$	−20.1534	+	34.9067i	−0.739356	+	1.28060i	−0.952785	+	0.303644i	$0.901797\pi$
$744$		0			0
$745$	−10.7807			−0.394976
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−21.1259			−0.770894			−0.385447	−	0.922730i	$-0.625953\pi$
$751$	−21.1259			−0.770894			−0.385447	+	0.922730i	$0.625953\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−16.2412			−0.591079
$756$		0			0
$757$	8.85934			0.321998			0.160999	−	0.986955i	$-0.448528\pi$
$757$	8.85934			0.321998			0.160999	+	0.986955i	$0.448528\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1.38910			−0.0503549			−0.0251774	−	0.999683i	$-0.508015\pi$
$761$	−1.38910			−0.0503549			−0.0251774	+	0.999683i	$0.508015\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−64.9194			−2.34410
$768$		0			0
$769$	18.9626	−	32.8443i	0.683810	−	1.18439i	−0.289999	−	0.957027i	$-0.593655\pi$
$769$	18.9626	−	32.8443i	0.683810	−	1.18439i	0.973809	−	0.227367i	$-0.0730118\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	0.657981	−	1.13966i	0.0236659	−	0.0409906i	−0.853950	−	0.520355i	$-0.825800\pi$
$773$	0.657981	−	1.13966i	0.0236659	−	0.0409906i	0.877616	+	0.479365i	$0.159133\pi$
$774$		0			0
$775$	3.89037	+	6.73832i	0.139746	+	0.242047i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.18289			−0.0423813
$780$		0			0
$781$	62.8447			2.24876
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−7.11177	−	12.3179i	−0.253830	−	0.439646i
$786$		0			0
$787$	−6.12928	−	10.6162i	−0.218485	−	0.378428i	0.735860	−	0.677134i	$-0.236778\pi$
$787$	−6.12928	−	10.6162i	−0.218485	−	0.378428i	−0.954345	+	0.298706i	$0.903445\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	49.1072	+	85.0561i	1.74385	+	3.02043i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	10.7178	−	18.5638i	0.379644	−	0.657563i	−0.611366	−	0.791348i	$-0.709380\pi$
$797$	10.7178	−	18.5638i	0.379644	−	0.657563i	0.991010	+	0.133785i	$0.0427132\pi$
$798$		0			0
$799$	8.29007	+	14.3588i	0.293282	+	0.507979i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−10.0562	+	17.4179i	−0.354876	+	0.614664i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	13.3478	−	23.1190i	0.469282	−	0.812820i	−0.530101	−	0.847934i	$-0.677846\pi$
$809$	13.3478	−	23.1190i	0.469282	−	0.812820i	0.999383	+	0.0351140i	$0.0111794\pi$
$810$		0			0
$811$	38.2852			1.34438			0.672188	−	0.740381i	$-0.265355\pi$
$811$	38.2852			1.34438			0.672188	+	0.740381i	$0.265355\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	9.01459	+	15.6137i	0.315767	+	0.546925i
$816$		0			0
$817$	10.4612	−	18.1193i	0.365990	−	0.633914i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5.24990	+	9.09310i	−0.183223	+	0.317351i	−0.942976	−	0.332860i	$-0.891986\pi$
$821$	−5.24990	+	9.09310i	−0.183223	+	0.317351i	0.759753	+	0.650211i	$0.225320\pi$
$822$		0			0
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	0.692240	−	0.721668i	$-0.256624\pi$
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	−0.971102	+	0.238664i	$0.923291\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	48.7817			1.69631			0.848153	−	0.529752i	$-0.177715\pi$
$827$	48.7817			1.69631			0.848153	+	0.529752i	$0.177715\pi$
$828$		0			0
$829$	3.10963	−	5.38604i	0.108002	−	0.187065i	−0.806959	−	0.590608i	$-0.798888\pi$
$829$	3.10963	−	5.38604i	0.108002	−	0.187065i	0.914961	+	0.403543i	$0.132221\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	14.7989	−	25.6325i	0.512138	−	0.887049i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−21.0366	−	36.4364i	−0.726263	−	1.25792i	−0.958452	−	0.285254i	$-0.907922\pi$
$839$	−21.0366	−	36.4364i	−0.726263	−	1.25792i	0.232189	−	0.972671i	$-0.425411\pi$
$840$		0			0
$841$	−9.82597	+	17.0191i	−0.338826	+	0.586865i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	46.1665	+	79.9628i	1.58818	+	2.75080i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.13161	−	3.69206i	−0.0730707	−	0.126562i
$852$		0			0
$853$	6.72519	+	11.6484i	0.230266	+	0.398833i	0.957886	−	0.287147i	$-0.0927070\pi$
$853$	6.72519	+	11.6484i	0.230266	+	0.398833i	−0.727620	+	0.685980i	$0.759374\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−41.3786			−1.41347			−0.706733	−	0.707481i	$-0.749832\pi$
$857$	−41.3786			−1.41347			−0.706733	+	0.707481i	$0.749832\pi$
$858$		0			0
$859$	−39.7630			−1.35670			−0.678349	−	0.734740i	$-0.737304\pi$
$859$	−39.7630			−1.35670			−0.678349	+	0.734740i	$0.737304\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	26.6929	+	46.2334i	0.908637	+	1.57380i	0.815960	+	0.578109i	$0.196209\pi$
$863$	26.6929	+	46.2334i	0.908637	+	1.57380i	0.0926768	+	0.995696i	$0.470458\pi$
$864$		0			0
$865$	−6.02704	+	10.4391i	−0.204926	+	0.354942i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	14.9552	−	25.9033i	0.507322	−	0.878708i
$870$		0			0
$871$	−9.43560			−0.319713
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−6.85349			−0.231426			−0.115713	−	0.993283i	$-0.536915\pi$
$877$	−6.85349			−0.231426			−0.115713	+	0.993283i	$0.536915\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	12.5103			0.421483			0.210742	−	0.977542i	$-0.432412\pi$
$881$	12.5103			0.421483			0.210742	+	0.977542i	$0.432412\pi$
$882$		0			0
$883$	6.69124			0.225178			0.112589	−	0.993642i	$-0.464086\pi$
$883$	6.69124			0.225178			0.112589	+	0.993642i	$0.464086\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−32.1416			−1.07921			−0.539605	−	0.841918i	$-0.681426\pi$
$887$	−32.1416			−1.07921			−0.539605	+	0.841918i	$0.681426\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−15.8928			−0.531832
$894$		0			0
$895$	2.19076	−	3.79450i	0.0732289	−	0.126836i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	25.7434	−	44.5888i	0.858590	−	1.48712i
$900$		0			0
$901$	11.4086	+	19.7602i	0.380074	+	0.658308i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	41.6883			1.38577
$906$		0			0
$907$	−31.4031			−1.04272			−0.521362	−	0.853336i	$-0.674576\pi$
$907$	−31.4031			−1.04272			−0.521362	+	0.853336i	$0.674576\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	22.8982	+	39.6609i	0.758653	+	1.31402i	0.943538	+	0.331265i	$0.107475\pi$
$911$	22.8982	+	39.6609i	0.758653	+	1.31402i	−0.184885	+	0.982760i	$0.559191\pi$
$912$		0			0
$913$	−3.45185	−	5.97877i	−0.114239	−	0.197868i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−13.5900	−	23.5385i	−0.448292	−	0.776465i	0.549983	−	0.835176i	$-0.314634\pi$
$919$	−13.5900	−	23.5385i	−0.448292	−	0.776465i	−0.998275	+	0.0587112i	$0.981301\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	48.0576	−	83.2381i	1.58183	−	2.73982i
$924$		0			0
$925$	0.382977	+	0.663336i	0.0125922	+	0.0218104i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−20.3338	+	35.2192i	−0.667132	+	1.15551i	0.311571	+	0.950223i	$0.399145\pi$
$929$	−20.3338	+	35.2192i	−0.667132	+	1.15551i	−0.978703	+	0.205283i	$0.934189\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−25.8135	+	44.7103i	−0.844192	+	1.46218i
$936$		0			0
$937$	16.4150			0.536254			0.268127	−	0.963384i	$-0.413595\pi$
$937$	16.4150			0.536254			0.268127	+	0.963384i	$0.413595\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	3.66878	+	6.35451i	0.119599	+	0.207151i	0.919609	−	0.392836i	$-0.128506\pi$
$941$	3.66878	+	6.35451i	0.119599	+	0.207151i	−0.800010	+	0.599987i	$0.795173\pi$
$942$		0			0
$943$	−0.801851	+	1.38885i	−0.0261119	+	0.0452271i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	29.5562	−	51.1929i	0.960448	−	1.66354i	0.239071	−	0.971002i	$-0.423157\pi$
$947$	29.5562	−	51.1929i	0.960448	−	1.66354i	0.721377	−	0.692543i	$-0.243510\pi$
$948$		0			0
$949$	15.3801	+	26.6390i	0.499258	+	0.864740i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	16.9354			0.548592			0.274296	−	0.961645i	$-0.411555\pi$
$953$	16.9354			0.548592			0.274296	+	0.961645i	$0.411555\pi$
$954$		0			0
$955$	6.75370	−	11.6977i	0.218544	−	0.378530i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−11.7434	+	20.3401i	−0.378819	+	0.656133i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−6.77548	−	11.7355i	−0.218110	−	0.377778i
$966$		0			0
$967$	3.55555	−	6.15839i	0.114339	−	0.198040i	−0.803177	−	0.595741i	$-0.796858\pi$
$967$	3.55555	−	6.15839i	0.114339	−	0.198040i	0.917515	+	0.397701i	$0.130192\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−0.735508	−	1.27394i	−0.0236036	−	0.0408826i	0.853982	−	0.520302i	$-0.174181\pi$
$971$	−0.735508	−	1.27394i	−0.0236036	−	0.0408826i	−0.877586	+	0.479419i	$0.840847\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−9.71634	−	16.8292i	−0.310853	−	0.538413i	0.667694	−	0.744436i	$-0.267281\pi$
$977$	−9.71634	−	16.8292i	−0.310853	−	0.538413i	−0.978547	+	0.206022i	$0.933948\pi$
$978$		0			0
$979$	−22.8545	−	39.5851i	−0.730432	−	1.26515i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−7.74436			−0.247007			−0.123503	−	0.992344i	$-0.539413\pi$
$983$	−7.74436			−0.247007			−0.123503	+	0.992344i	$0.539413\pi$
$984$		0			0
$985$	28.6156			0.911768
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−14.1828	−	24.5653i	−0.450986	−	0.781130i
$990$		0			0
$991$	7.23551	−	12.5323i	0.229843	−	0.398101i	−0.727918	−	0.685664i	$-0.759512\pi$
$991$	7.23551	−	12.5323i	0.229843	−	0.398101i	0.957762	+	0.287563i	$0.0928452\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−5.10243	+	8.83767i	−0.161758	+	0.280173i
$996$		0			0
$997$	−55.3097			−1.75168			−0.875838	−	0.482605i	$-0.839691\pi$
$997$	−55.3097			−1.75168			−0.875838	+	0.482605i	$0.839691\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5292.2.l.e.361.1		6
3.2	odd	2		1764.2.l.e.949.2		6
7.2	even	3		5292.2.i.f.1549.3		6
7.3	odd	6		5292.2.j.d.1765.1		6
7.4	even	3		756.2.j.b.253.3		6
7.5	odd	6		5292.2.i.e.1549.1		6
7.6	odd	2		5292.2.l.f.361.3		6
9.2	odd	6		1764.2.i.g.1537.3		6
9.7	even	3		5292.2.i.f.2125.3		6
21.2	odd	6		1764.2.i.g.373.3		6
21.5	even	6		1764.2.i.d.373.1		6
21.11	odd	6		252.2.j.a.85.2	✓	6
21.17	even	6		1764.2.j.e.589.2		6
21.20	even	2		1764.2.l.f.949.2		6
28.11	odd	6		3024.2.r.j.1009.3		6
63.2	odd	6		1764.2.l.e.961.2		6
63.4	even	3		2268.2.a.h.1.1		3
63.11	odd	6		252.2.j.a.169.2	yes	6
63.16	even	3	inner	5292.2.l.e.3313.1		6
63.20	even	6		1764.2.i.d.1537.1		6
63.25	even	3		756.2.j.b.505.3		6
63.32	odd	6		2268.2.a.i.1.3		3
63.34	odd	6		5292.2.i.e.2125.1		6
63.38	even	6		1764.2.j.e.1177.2		6
63.47	even	6		1764.2.l.f.961.2		6
63.52	odd	6		5292.2.j.d.3529.1		6
63.61	odd	6		5292.2.l.f.3313.3		6
84.11	even	6		1008.2.r.j.337.2		6
252.11	even	6		1008.2.r.j.673.2		6
252.67	odd	6		9072.2.a.bv.1.1		3
252.95	even	6		9072.2.a.by.1.3		3
252.151	odd	6		3024.2.r.j.2017.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.j.a.85.2	✓	6	21.11	odd	6
252.2.j.a.169.2	yes	6	63.11	odd	6
756.2.j.b.253.3		6	7.4	even	3
756.2.j.b.505.3		6	63.25	even	3
1008.2.r.j.337.2		6	84.11	even	6
1008.2.r.j.673.2		6	252.11	even	6
1764.2.i.d.373.1		6	21.5	even	6
1764.2.i.d.1537.1		6	63.20	even	6
1764.2.i.g.373.3		6	21.2	odd	6
1764.2.i.g.1537.3		6	9.2	odd	6
1764.2.j.e.589.2		6	21.17	even	6
1764.2.j.e.1177.2		6	63.38	even	6
1764.2.l.e.949.2		6	3.2	odd	2
1764.2.l.e.961.2		6	63.2	odd	6
1764.2.l.f.949.2		6	21.20	even	2
1764.2.l.f.961.2		6	63.47	even	6
2268.2.a.h.1.1		3	63.4	even	3
2268.2.a.i.1.3		3	63.32	odd	6
3024.2.r.j.1009.3		6	28.11	odd	6
3024.2.r.j.2017.3		6	252.151	odd	6
5292.2.i.e.1549.1		6	7.5	odd	6
5292.2.i.e.2125.1		6	63.34	odd	6
5292.2.i.f.1549.3		6	7.2	even	3
5292.2.i.f.2125.3		6	9.7	even	3
5292.2.j.d.1765.1		6	7.3	odd	6
5292.2.j.d.3529.1		6	63.52	odd	6
5292.2.l.e.361.1		6	1.1	even	1	trivial
5292.2.l.e.3313.1		6	63.16	even	3	inner
5292.2.l.f.361.3		6	7.6	odd	2
5292.2.l.f.3313.3		6	63.61	odd	6
9072.2.a.bv.1.1		3	252.67	odd	6
9072.2.a.by.1.3		3	252.95	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5292.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.46050 q^{5} +O(q^{10})\)	\(q-2.46050 q^{5} -4.64766 q^{11} +(-3.55408 + 6.15585i) q^{13} +(-2.25729 + 3.90975i) q^{17} +(-2.16372 - 3.74766i) q^{19} -5.86693 q^{23} +1.05408 q^{25} +(-3.48755 - 6.04061i) q^{29} +(3.69076 + 6.39258i) q^{31} +(0.363327 + 0.629301i) q^{37} +(0.136673 - 0.236725i) q^{41} +(2.41741 + 4.18708i) q^{43} +(1.83628 - 3.18054i) q^{47} +(2.52704 - 4.37697i) q^{53} +11.4356 q^{55} +(4.56654 + 7.90947i) q^{59} +(6.90856 - 11.9660i) q^{61} +(8.74484 - 15.1465i) q^{65} +(0.663715 + 1.14959i) q^{67} -13.5218 q^{71} +(2.16372 - 3.74766i) q^{73} +(-3.21780 + 5.57339i) q^{79} +(0.742705 + 1.28640i) q^{83} +(5.55408 - 9.61996i) q^{85} +(4.91741 + 8.51721i) q^{89} +(5.32383 + 9.22115i) q^{95} +(0.246304 + 0.426611i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{5}+O(q^{10}) \) 6 * q - 2 * q^5	\( 6 q - 2 q^{5} - 4 q^{11} - 3 q^{13} + 2 q^{17} - 3 q^{19} - 28 q^{23} - 12 q^{25} + q^{29} + 3 q^{31} + 3 q^{37} - 3 q^{43} + 21 q^{47} + 6 q^{53} + 12 q^{55} + 31 q^{59} - 6 q^{61} + 15 q^{65} - 6 q^{67} - 34 q^{71} + 3 q^{73} + 9 q^{79} + 20 q^{83} + 15 q^{85} + 12 q^{89} + 20 q^{95} + 9 q^{97}+O(q^{100}) \) 6 * q - 2 * q^5 - 4 * q^11 - 3 * q^13 + 2 * q^17 - 3 * q^19 - 28 * q^23 - 12 * q^25 + q^29 + 3 * q^31 + 3 * q^37 - 3 * q^43 + 21 * q^47 + 6 * q^53 + 12 * q^55 + 31 * q^59 - 6 * q^61 + 15 * q^65 - 6 * q^67 - 34 * q^71 + 3 * q^73 + 9 * q^79 + 20 * q^83 + 15 * q^85 + 12 * q^89 + 20 * q^95 + 9 * q^97

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