LMFDB - Embedded newform 5292.2.l.f.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			$0.500000 + 0.224437i$ of defining polynomial
Character	$\chi$	$=$	5292.361
Dual form			5292.2.l.f.3313.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.69963 q^{5} +O(q^{10})$	$q-1.69963 q^{5} -2.47710 q^{11} +(0.388736 - 0.673310i) q^{13} +(-1.40545 + 2.43430i) q^{17} +(-2.49381 - 4.31941i) q^{19} -0.712008 q^{23} -2.11126 q^{25} +(2.25526 + 3.90623i) q^{29} +(2.54944 + 4.41576i) q^{31} +(3.43818 + 5.95510i) q^{37} +(2.93818 - 5.08907i) q^{41} +(2.32691 + 4.03033i) q^{43} +(-6.49381 + 11.2476i) q^{47} +(0.944368 - 1.63569i) q^{53} +4.21015 q^{55} +(-7.14400 - 12.3738i) q^{59} +(7.15452 - 12.3920i) q^{61} +(-0.660706 + 1.14438i) q^{65} +(-3.99381 - 6.91748i) q^{67} +10.2632 q^{71} +(2.49381 - 4.31941i) q^{73} +(4.60507 - 7.97622i) q^{79} +(-4.40545 - 7.63046i) q^{83} +(2.38874 - 4.13741i) q^{85} +(-4.82691 - 8.36046i) q^{89} +(4.23855 + 7.34138i) q^{95} +(4.32072 + 7.48371i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.69963			−0.760097			−0.380048	−	0.924967i	$-0.624093\pi$
$5$	−1.69963			−0.760097			−0.380048	+	0.924967i	$0.624093\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.47710			−0.746874			−0.373437	−	0.927656i	$-0.621821\pi$
$11$	−2.47710			−0.746874			−0.373437	+	0.927656i	$0.621821\pi$
$12$		0			0
$13$	0.388736	−	0.673310i	0.107816	−	0.186743i	−0.807069	−	0.590457i	$-0.798948\pi$
$13$	0.388736	−	0.673310i	0.107816	−	0.186743i	0.914885	+	0.403714i	$0.132281\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.40545	+	2.43430i	−0.340871	+	0.590405i	−0.984595	−	0.174852i	$-0.944055\pi$
$17$	−1.40545	+	2.43430i	−0.340871	+	0.590405i	0.643724	+	0.765258i	$0.277389\pi$
$18$		0			0
$19$	−2.49381	−	4.31941i	−0.572119	−	0.990940i	−0.996348	−	0.0853846i	$-0.972788\pi$
$19$	−2.49381	−	4.31941i	−0.572119	−	0.990940i	0.424229	−	0.905555i	$-0.360545\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.712008			−0.148464			−0.0742320	−	0.997241i	$-0.523651\pi$
$23$	−0.712008			−0.148464			−0.0742320	+	0.997241i	$0.523651\pi$
$24$		0			0
$25$	−2.11126			−0.422253
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.25526	+	3.90623i	0.418791	+	0.725368i	0.995818	−	0.0913573i	$-0.0291205\pi$
$29$	2.25526	+	3.90623i	0.418791	+	0.725368i	−0.577027	+	0.816725i	$0.695787\pi$
$30$		0			0
$31$	2.54944	+	4.41576i	0.457893	+	0.793095i	0.998849	−	0.0479563i	$-0.0152708\pi$
$31$	2.54944	+	4.41576i	0.457893	+	0.793095i	−0.540956	+	0.841051i	$0.681937\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.43818	+	5.95510i	0.565233	+	0.979012i	0.997028	+	0.0770405i	$0.0245471\pi$
$37$	3.43818	+	5.95510i	0.565233	+	0.979012i	−0.431795	+	0.901972i	$0.642120\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.93818	−	5.08907i	0.458866	−	0.794780i	−0.540035	−	0.841643i	$-0.681589\pi$
$41$	2.93818	−	5.08907i	0.458866	−	0.794780i	0.998901	+	0.0468628i	$0.0149223\pi$
$42$		0			0
$43$	2.32691	+	4.03033i	0.354851	+	0.614620i	0.987092	−	0.160151i	$-0.0511982\pi$
$43$	2.32691	+	4.03033i	0.354851	+	0.614620i	−0.632241	+	0.774771i	$0.717865\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.49381	+	11.2476i	−0.947220	+	1.64063i	−0.195975	+	0.980609i	$0.562787\pi$
$47$	−6.49381	+	11.2476i	−0.947220	+	1.64063i	−0.751245	+	0.660023i	$0.770546\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.944368	−	1.63569i	0.129719	−	0.224680i	−0.793849	−	0.608115i	$-0.791926\pi$
$53$	0.944368	−	1.63569i	0.129719	−	0.224680i	0.923568	+	0.383436i	$0.125259\pi$
$54$		0			0
$55$	4.21015			0.567696
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−7.14400	−	12.3738i	−0.930069	−	1.61093i	−0.783199	−	0.621771i	$-0.786413\pi$
$59$	−7.14400	−	12.3738i	−0.930069	−	1.61093i	−0.146870	−	0.989156i	$-0.546920\pi$
$60$		0			0
$61$	7.15452	−	12.3920i	0.916042	−	1.58663i	0.110673	−	0.993857i	$-0.464699\pi$
$61$	7.15452	−	12.3920i	0.916042	−	1.58663i	0.805369	−	0.592774i	$-0.201967\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.660706	+	1.14438i	−0.0819505	+	0.141942i
$66$		0			0
$67$	−3.99381	−	6.91748i	−0.487922	−	0.845105i	0.511982	−	0.858996i	$-0.328911\pi$
$67$	−3.99381	−	6.91748i	−0.487922	−	0.845105i	−0.999904	+	0.0138913i	$0.995578\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	10.2632			1.21802			0.609011	−	0.793162i	$-0.291567\pi$
$71$	10.2632			1.21802			0.609011	+	0.793162i	$0.291567\pi$
$72$		0			0
$73$	2.49381	−	4.31941i	0.291878	−	0.505548i	−0.682376	−	0.731002i	$-0.739053\pi$
$73$	2.49381	−	4.31941i	0.291878	−	0.505548i	0.974254	+	0.225454i	$0.0723864\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	4.60507	−	7.97622i	0.518111	−	0.897395i	−0.481667	−	0.876354i	$-0.659969\pi$
$79$	4.60507	−	7.97622i	0.518111	−	0.897395i	0.999779	−	0.0210410i	$-0.00669805\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.40545	−	7.63046i	−0.483561	−	0.837551i	0.516261	−	0.856431i	$-0.327323\pi$
$83$	−4.40545	−	7.63046i	−0.483561	−	0.837551i	−0.999822	+	0.0188798i	$0.993990\pi$
$84$		0			0
$85$	2.38874	−	4.13741i	0.259095	−	0.448765i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.82691	−	8.36046i	−0.511652	−	0.886207i	−0.999909	−	0.0135071i	$-0.995700\pi$
$89$	−4.82691	−	8.36046i	−0.511652	−	0.886207i	0.488257	−	0.872700i	$-0.337633\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4.23855	+	7.34138i	0.434866	+	0.753210i
$96$		0			0
$97$	4.32072	+	7.48371i	0.438703	+	0.759856i	0.997590	−	0.0693880i	$-0.0221047\pi$
$97$	4.32072	+	7.48371i	0.438703	+	0.759856i	−0.558887	+	0.829244i	$0.688771\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.41164			0.239967			0.119983	−	0.992776i	$-0.461716\pi$
$101$	2.41164			0.239967			0.119983	+	0.992776i	$0.461716\pi$
$102$		0			0
$103$	4.33379			0.427021			0.213511	−	0.976941i	$-0.431510\pi$
$103$	4.33379			0.427021			0.213511	+	0.976941i	$0.431510\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.59888	+	16.6258i	0.927959	+	1.60727i	0.786732	+	0.617295i	$0.211772\pi$
$107$	9.59888	+	16.6258i	0.927959	+	1.60727i	0.141228	+	0.989977i	$0.454895\pi$
$108$		0			0
$109$	−9.48143	+	16.4223i	−0.908156	+	1.57297i	−0.0915329	+	0.995802i	$0.529177\pi$
$109$	−9.48143	+	16.4223i	−0.908156	+	1.57297i	−0.816623	+	0.577171i	$0.804157\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	6.46472	−	11.1972i	0.608150	−	1.05335i	−0.383395	−	0.923584i	$-0.625245\pi$
$113$	6.46472	−	11.1972i	0.608150	−	1.05335i	0.991545	−	0.129762i	$-0.0414213\pi$
$114$		0			0
$115$	1.21015			0.112847
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.86398			−0.442180
$122$		0			0
$123$		0			0
$124$		0			0
$125$	12.0865			1.08105
$126$		0			0
$127$	17.6291			1.56433			0.782163	−	0.623073i	$-0.214116\pi$
$127$	17.6291			1.56433			0.782163	+	0.623073i	$0.214116\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.68725			−0.496897			−0.248449	−	0.968645i	$-0.579921\pi$
$131$	−5.68725			−0.496897			−0.248449	+	0.968645i	$0.579921\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	19.4523			1.66193			0.830963	−	0.556328i	$-0.187790\pi$
$137$	19.4523			1.66193			0.830963	+	0.556328i	$0.187790\pi$
$138$		0			0
$139$	−1.49381	+	2.58736i	−0.126703	+	0.219457i	−0.922397	−	0.386242i	$-0.873773\pi$
$139$	−1.49381	+	2.58736i	−0.126703	+	0.219457i	0.795694	+	0.605699i	$0.207106\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.962937	+	1.66786i	−0.0805249	+	0.139473i
$144$		0			0
$145$	−3.83310	−	6.63913i	−0.318322	−	0.551350i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−8.09888			−0.663486			−0.331743	−	0.943370i	$-0.607637\pi$
$149$	−8.09888			−0.663486			−0.331743	+	0.943370i	$0.607637\pi$
$150$		0			0
$151$	−8.86398			−0.721340			−0.360670	−	0.932693i	$-0.617452\pi$
$151$	−8.86398			−0.721340			−0.360670	+	0.932693i	$0.617452\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−4.33310	−	7.50516i	−0.348043	−	0.602829i
$156$		0			0
$157$	−4.38255	−	7.59079i	−0.349765	−	0.605811i	0.636442	−	0.771324i	$-0.280405\pi$
$157$	−4.38255	−	7.59079i	−0.349765	−	0.605811i	−0.986208	+	0.165513i	$0.947072\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	0.993810	+	1.72133i	0.0778412	+	0.134825i	0.902318	−	0.431070i	$-0.141864\pi$
$163$	0.993810	+	1.72133i	0.0778412	+	0.134825i	−0.824477	+	0.565895i	$0.808531\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.31089	+	2.27053i	−0.101440	+	0.175699i	−0.912278	−	0.409571i	$-0.865678\pi$
$167$	−1.31089	+	2.27053i	−0.101440	+	0.175699i	0.810838	+	0.585270i	$0.199012\pi$
$168$		0			0
$169$	6.19777	+	10.7349i	0.476751	+	0.825758i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.61491	−	4.52915i	0.198808	−	0.344345i	−0.749334	−	0.662192i	$-0.769626\pi$
$173$	2.61491	−	4.52915i	0.198808	−	0.344345i	0.948142	+	0.317847i	$0.102960\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−2.38255	+	4.12669i	−0.178080	+	0.308443i	−0.941223	−	0.337786i	$-0.890322\pi$
$179$	−2.38255	+	4.12669i	−0.178080	+	0.308443i	0.763143	+	0.646230i	$0.223655\pi$
$180$		0			0
$181$	10.4313			0.775352			0.387676	−	0.921796i	$-0.373278\pi$
$181$	10.4313			0.775352			0.387676	+	0.921796i	$0.373278\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−5.84362	−	10.1215i	−0.429632	−	0.744144i
$186$		0			0
$187$	3.48143	−	6.03001i	0.254587	−	0.440958i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.66071	−	11.5367i	0.481952	−	0.834765i	−0.517834	−	0.855481i	$-0.673261\pi$
$191$	6.66071	−	11.5367i	0.481952	−	0.834765i	0.999785	+	0.0207164i	$0.00659470\pi$
$192$		0			0
$193$	7.32072	+	12.6799i	0.526957	+	0.912717i	0.999507	+	0.0314125i	$0.0100005\pi$
$193$	7.32072	+	12.6799i	0.526957	+	0.912717i	−0.472549	+	0.881304i	$0.656666\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	18.4858			1.31706			0.658528	−	0.752556i	$-0.271179\pi$
$197$	18.4858			1.31706			0.658528	+	0.752556i	$0.271179\pi$
$198$		0			0
$199$	11.8083	−	20.4527i	0.837071	−	1.44985i	−0.0552614	−	0.998472i	$-0.517599\pi$
$199$	11.8083	−	20.4527i	0.837071	−	1.44985i	0.892333	−	0.451378i	$-0.149067\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−4.99381	+	8.64953i	−0.348783	+	0.604110i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	6.17742	+	10.6996i	0.427301	+	0.740107i
$210$		0			0
$211$	7.27747	−	12.6050i	0.501002	−	0.867761i	−0.498998	−	0.866603i	$-0.666298\pi$
$211$	7.27747	−	12.6050i	0.501002	−	0.867761i	0.999999	−	0.00115718i	$-0.000368342\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.95489	−	6.85007i	−0.269721	−	0.467171i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.09269	+	1.89260i	0.0735026	+	0.127310i
$222$		0			0
$223$	4.72253	+	8.17966i	0.316244	+	0.547750i	0.979701	−	0.200464i	$-0.0642449\pi$
$223$	4.72253	+	8.17966i	0.316244	+	0.547750i	−0.663457	+	0.748214i	$0.730912\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	19.1113			1.26846			0.634230	−	0.773145i	$-0.281317\pi$
$227$	19.1113			1.26846			0.634230	+	0.773145i	$0.281317\pi$
$228$		0			0
$229$	−11.4451			−0.756311			−0.378155	−	0.925742i	$-0.623441\pi$
$229$	−11.4451			−0.756311			−0.378155	+	0.925742i	$0.623441\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.595243	−	1.03099i	−0.0389956	−	0.0675424i	0.845869	−	0.533391i	$-0.179083\pi$
$233$	−0.595243	−	1.03099i	−0.0389956	−	0.0675424i	−0.884865	+	0.465848i	$0.845749\pi$
$234$		0			0
$235$	11.0371	−	19.1168i	0.719979	−	1.24704i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	12.1414	−	21.0296i	0.785365	−	1.36029i	−0.143416	−	0.989663i	$-0.545809\pi$
$239$	12.1414	−	21.0296i	0.785365	−	1.36029i	0.928781	−	0.370630i	$-0.120858\pi$
$240$		0			0
$241$	21.4189			1.37971			0.689857	−	0.723946i	$-0.257673\pi$
$241$	21.4189			1.37971			0.689857	+	0.723946i	$0.257673\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−3.87773			−0.246734
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−2.67996			−0.169158			−0.0845789	−	0.996417i	$-0.526955\pi$
$251$	−2.67996			−0.169158			−0.0845789	+	0.996417i	$0.526955\pi$
$252$		0			0
$253$	1.76371			0.110884
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−11.0851			−0.691471			−0.345736	−	0.938332i	$-0.612371\pi$
$257$	−11.0851			−0.691471			−0.345736	+	0.938332i	$0.612371\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−13.4079			−0.826768			−0.413384	−	0.910557i	$-0.635653\pi$
$263$	−13.4079			−0.826768			−0.413384	+	0.910557i	$0.635653\pi$
$264$		0			0
$265$	−1.60507	+	2.78007i	−0.0985989	+	0.170778i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−2.04511	+	3.54224i	−0.124693	+	0.215974i	−0.921613	−	0.388111i	$-0.873128\pi$
$269$	−2.04511	+	3.54224i	−0.124693	+	0.215974i	0.796920	+	0.604085i	$0.206461\pi$
$270$		0			0
$271$	3.06182	+	5.30323i	0.185992	+	0.322148i	0.943910	−	0.330201i	$-0.107117\pi$
$271$	3.06182	+	5.30323i	0.185992	+	0.322148i	−0.757918	+	0.652350i	$0.773783\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	5.22981			0.315370
$276$		0			0
$277$	15.7651			0.947233			0.473616	−	0.880731i	$-0.342948\pi$
$277$	15.7651			0.947233			0.473616	+	0.880731i	$0.342948\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−10.5946	−	18.3503i	−0.632018	−	1.09469i	−0.987139	−	0.159867i	$-0.948893\pi$
$281$	−10.5946	−	18.3503i	−0.632018	−	1.09469i	0.355120	−	0.934821i	$-0.384440\pi$
$282$		0			0
$283$	3.43818	+	5.95510i	0.204378	+	0.353994i	0.949935	−	0.312449i	$-0.101149\pi$
$283$	3.43818	+	5.95510i	0.204378	+	0.353994i	−0.745556	+	0.666443i	$0.767816\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	4.54944	+	7.87987i	0.267614	+	0.463521i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	13.7534	−	23.8216i	0.803482	−	1.39167i	−0.113829	−	0.993500i	$-0.536311\pi$
$293$	13.7534	−	23.8216i	0.803482	−	1.39167i	0.917311	−	0.398172i	$-0.130355\pi$
$294$		0			0
$295$	12.1421	+	21.0308i	0.706943	+	1.22446i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.276783	+	0.479402i	−0.0160068	+	0.0277245i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−12.1600	+	21.0618i	−0.696281	+	1.20599i
$306$		0			0
$307$	21.5178			1.22809			0.614043	−	0.789273i	$-0.289542\pi$
$307$	21.5178			1.22809			0.614043	+	0.789273i	$0.289542\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.19275	−	15.9223i	−0.521273	−	0.902871i	−0.999694	−	0.0247407i	$-0.992124\pi$
$311$	−9.19275	−	15.9223i	−0.521273	−	0.902871i	0.478421	−	0.878131i	$-0.341209\pi$
$312$		0			0
$313$	−0.000688709		0.00119288i	−3.89281e−5		6.74255e-5i	−0.866045	−	0.499966i	$-0.833346\pi$
$313$	−0.000688709		0.00119288i	−3.89281e−5		6.74255e-5i	0.866006	+	0.500034i	$0.166679\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.04944	−	12.2100i	0.395936	−	0.685781i	−0.597284	−	0.802030i	$-0.703753\pi$
$317$	7.04944	−	12.2100i	0.395936	−	0.685781i	0.993220	+	0.116248i	$0.0370868\pi$
$318$		0			0
$319$	−5.58650	−	9.67611i	−0.312784	−	0.541758i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	14.0197			0.780075
$324$		0			0
$325$	−0.820724	+	1.42154i	−0.0455256	+	0.0788526i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−6.98143	+	12.0922i	−0.383734	+	0.664647i	−0.991593	−	0.129398i	$-0.958695\pi$
$331$	−6.98143	+	12.0922i	−0.383734	+	0.664647i	0.607859	+	0.794045i	$0.292029\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	6.78799	+	11.7571i	0.370868	+	0.642362i
$336$		0			0
$337$	−12.0982	+	20.9547i	−0.659031	+	1.14147i	0.321836	+	0.946795i	$0.395700\pi$
$337$	−12.0982	+	20.9547i	−0.659031	+	1.14147i	−0.980867	+	0.194679i	$0.937633\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−6.31522	−	10.9383i	−0.341988	−	0.592341i
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−16.3578	−	28.3325i	−0.878132	−	1.52097i	−0.853389	−	0.521275i	$-0.825456\pi$
$347$	−16.3578	−	28.3325i	−0.878132	−	1.52097i	−0.0247435	−	0.999694i	$-0.507877\pi$
$348$		0			0
$349$	−11.8887	−	20.5919i	−0.636389	−	1.10226i	−0.986219	−	0.165445i	$-0.947094\pi$
$349$	−11.8887	−	20.5919i	−0.636389	−	1.10226i	0.349830	−	0.936813i	$-0.386240\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	20.0617			1.06778			0.533889	−	0.845554i	$-0.320730\pi$
$353$	20.0617			1.06778			0.533889	+	0.845554i	$0.320730\pi$
$354$		0			0
$355$	−17.4437			−0.925814
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.15087	+	7.18953i	0.219075	+	0.379449i	0.954525	−	0.298130i	$-0.0963628\pi$
$359$	4.15087	+	7.18953i	0.219075	+	0.379449i	−0.735451	+	0.677578i	$0.763029\pi$
$360$		0			0
$361$	−2.93818	+	5.08907i	−0.154641	+	0.267846i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−4.23855	+	7.34138i	−0.221856	+	0.384266i
$366$		0			0
$367$	−11.5439			−0.602589			−0.301294	−	0.953531i	$-0.597419\pi$
$367$	−11.5439			−0.602589			−0.301294	+	0.953531i	$0.597419\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	2.85160			0.147650			0.0738250	−	0.997271i	$-0.476479\pi$
$373$	2.85160			0.147650			0.0738250	+	0.997271i	$0.476479\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.50680			0.180609
$378$		0			0
$379$	35.9519			1.84672			0.923361	−	0.383932i	$-0.125430\pi$
$379$	35.9519			1.84672			0.923361	+	0.383932i	$0.125430\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.83056			−0.0935370			−0.0467685	−	0.998906i	$-0.514892\pi$
$383$	−1.83056			−0.0935370			−0.0467685	+	0.998906i	$0.514892\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	11.3906			0.577526			0.288763	−	0.957401i	$-0.406756\pi$
$389$	11.3906			0.577526			0.288763	+	0.957401i	$0.406756\pi$
$390$		0			0
$391$	1.00069	−	1.73324i	0.0506070	−	0.0876539i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−7.82691	+	13.5566i	−0.393815	+	0.682107i
$396$		0			0
$397$	−5.21565	−	9.03377i	−0.261766	−	0.453392i	0.704945	−	0.709262i	$-0.250972\pi$
$397$	−5.21565	−	9.03377i	−0.261766	−	0.453392i	−0.966711	+	0.255870i	$0.917638\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	34.0741			1.70158			0.850790	−	0.525505i	$-0.176124\pi$
$401$	34.0741			1.70158			0.850790	+	0.525505i	$0.176124\pi$
$402$		0			0
$403$	3.96424			0.197473
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−8.51671	−	14.7514i	−0.422158	−	0.731199i
$408$		0			0
$409$	1.98762	+	3.44266i	0.0982815	+	0.170229i	0.910973	−	0.412465i	$-0.135332\pi$
$409$	1.98762	+	3.44266i	0.0982815	+	0.170229i	−0.812692	+	0.582694i	$0.801999\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	7.48762	+	12.9689i	0.367553	+	0.636620i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	4.72184	−	8.17847i	0.230677	−	0.399544i	−0.727331	−	0.686287i	$-0.759239\pi$
$419$	4.72184	−	8.17847i	0.230677	−	0.399544i	0.958008	+	0.286743i	$0.0925726\pi$
$420$		0			0
$421$	3.16002	+	5.47331i	0.154010	+	0.266753i	0.932698	−	0.360658i	$-0.117448\pi$
$421$	3.16002	+	5.47331i	0.154010	+	0.266753i	−0.778688	+	0.627411i	$0.784115\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.96727	−	5.13946i	0.143934	−	0.249300i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−13.8770	+	24.0357i	−0.668434	+	1.15776i	0.309908	+	0.950766i	$0.399702\pi$
$431$	−13.8770	+	24.0357i	−0.668434	+	1.15776i	−0.978342	+	0.206995i	$0.933632\pi$
$432$		0			0
$433$	−11.2473			−0.540510			−0.270255	−	0.962789i	$-0.587108\pi$
$433$	−11.2473			−0.540510			−0.270255	+	0.962789i	$0.587108\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.77561	+	3.07545i	0.0849391	+	0.147119i
$438$		0			0
$439$	−7.54325	+	13.0653i	−0.360020	+	0.623573i	−0.987964	−	0.154686i	$-0.950563\pi$
$439$	−7.54325	+	13.0653i	−0.360020	+	0.623573i	0.627944	+	0.778259i	$0.283897\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	3.96658	−	6.87032i	0.188458	−	0.326419i	−0.756278	−	0.654250i	$-0.772984\pi$
$443$	3.96658	−	6.87032i	0.188458	−	0.326419i	0.944736	+	0.327831i	$0.106318\pi$
$444$		0			0
$445$	8.20396	+	14.2097i	0.388905	+	0.673603i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	32.5636			1.53677			0.768386	−	0.639987i	$-0.221060\pi$
$449$	32.5636			1.53677			0.768386	+	0.639987i	$0.221060\pi$
$450$		0			0
$451$	−7.27816	+	12.6061i	−0.342715	+	0.593600i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−5.70396	+	9.87955i	−0.266820	+	0.462146i	−0.968039	−	0.250800i	$-0.919306\pi$
$457$	−5.70396	+	9.87955i	−0.266820	+	0.462146i	0.701219	+	0.712946i	$0.252640\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2.45853	−	4.25830i	−0.114505	−	0.198329i	0.803077	−	0.595876i	$-0.203195\pi$
$461$	−2.45853	−	4.25830i	−0.114505	−	0.198329i	−0.917582	+	0.397547i	$0.869862\pi$
$462$		0			0
$463$	−7.59957	+	13.1628i	−0.353182	+	0.611729i	−0.986805	−	0.161913i	$-0.948234\pi$
$463$	−7.59957	+	13.1628i	−0.353182	+	0.611729i	0.633623	+	0.773642i	$0.281567\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−11.8905	−	20.5950i	−0.550228	−	0.953022i	−0.998258	−	0.0590037i	$-0.981208\pi$
$467$	−11.8905	−	20.5950i	−0.550228	−	0.953022i	0.448030	−	0.894018i	$-0.352126\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−5.76400	−	9.98354i	−0.265029	−	0.459044i
$474$		0			0
$475$	5.26509	+	9.11941i	0.241579	+	0.418427i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	6.05818			0.276805			0.138403	−	0.990376i	$-0.455803\pi$
$479$	6.05818			0.276805			0.138403	+	0.990376i	$0.455803\pi$
$480$		0			0
$481$	5.34617			0.243764
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−7.34362	−	12.7195i	−0.333457	−	0.577564i
$486$		0			0
$487$	−0.568012	+	0.983825i	−0.0257391	+	0.0445814i	−0.878608	−	0.477544i	$-0.841527\pi$
$487$	−0.568012	+	0.983825i	−0.0257391	+	0.0445814i	0.852869	+	0.522125i	$0.174861\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−16.4382	+	28.4718i	−0.741845	+	1.28491i	0.209810	+	0.977742i	$0.432715\pi$
$491$	−16.4382	+	28.4718i	−0.741845	+	1.28491i	−0.951655	+	0.307170i	$0.900618\pi$
$492$		0			0
$493$	−12.6786			−0.571015
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	26.1978			1.17277			0.586387	−	0.810031i	$-0.300550\pi$
$499$	26.1978			1.17277			0.586387	+	0.810031i	$0.300550\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−25.8516			−1.15267			−0.576333	−	0.817215i	$-0.695517\pi$
$503$	−25.8516			−1.15267			−0.576333	+	0.817215i	$0.695517\pi$
$504$		0			0
$505$	−4.09888			−0.182398
$506$		0			0
$507$		0			0
$508$		0			0
$509$	35.1716			1.55896			0.779478	−	0.626430i	$-0.215485\pi$
$509$	35.1716			1.55896			0.779478	+	0.626430i	$0.215485\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−7.36584			−0.324578
$516$		0			0
$517$	16.0858	−	27.8615i	0.707453	−	1.22535i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	8.93130	−	15.4695i	0.391287	−	0.677730i	−0.601332	−	0.798999i	$-0.705363\pi$
$521$	8.93130	−	15.4695i	0.391287	−	0.677730i	0.992620	+	0.121270i	$0.0386965\pi$
$522$		0			0
$523$	−11.4320	−	19.8008i	−0.499886	−	0.865828i	0.500114	−	0.865960i	$-0.333291\pi$
$523$	−11.4320	−	19.8008i	−0.499886	−	0.865828i	−1.00000		0.000131698i	$0.999958\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−14.3324			−0.624330
$528$		0			0
$529$	−22.4930			−0.977958
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.28435	−	3.95661i	−0.0989462	−	0.171380i
$534$		0			0
$535$	−16.3145	−	28.2576i	−0.705339	−	1.22168i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−11.1538	−	19.3190i	−0.479541	−	0.830589i	0.520184	−	0.854054i	$-0.325863\pi$
$541$	−11.1538	−	19.3190i	−0.479541	−	0.830589i	−0.999725	+	0.0234656i	$0.992530\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	16.1149	−	27.9118i	0.690287	−	1.19561i
$546$		0			0
$547$	−10.8083	−	18.7206i	−0.462131	−	0.800435i	0.536936	−	0.843623i	$-0.319582\pi$
$547$	−10.8083	−	18.7206i	−0.462131	−	0.800435i	−0.999067	+	0.0431882i	$0.986249\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	11.2484	−	19.4828i	0.479197	−	0.829994i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.58768	−	2.74993i	0.0672720	−	0.116518i	−0.830428	−	0.557127i	$-0.811904\pi$
$557$	1.58768	−	2.74993i	0.0672720	−	0.116518i	0.897700	+	0.440608i	$0.145237\pi$
$558$		0			0
$559$	3.61822			0.153034
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−21.8814	−	37.8997i	−0.922190	−	1.59728i	−0.796019	−	0.605271i	$-0.793065\pi$
$563$	−21.8814	−	37.8997i	−0.922190	−	1.59728i	−0.126171	−	0.992009i	$-0.540269\pi$
$564$		0			0
$565$	−10.9876	+	19.0311i	−0.462253	+	0.800645i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−11.9313	+	20.6656i	−0.500186	+	0.866348i	0.499814	+	0.866133i	$0.333402\pi$
$569$	−11.9313	+	20.6656i	−0.500186	+	0.866348i	−1.00000		0.000214897i	$0.999932\pi$
$570$		0			0
$571$	−5.11058	−	8.85178i	−0.213871	−	0.370435i	0.739052	−	0.673649i	$-0.235274\pi$
$571$	−5.11058	−	8.85178i	−0.213871	−	0.370435i	−0.952923	+	0.303213i	$0.901941\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.50324			0.0626893
$576$		0			0
$577$	−18.0185	+	31.2089i	−0.750120	+	1.29925i	0.197645	+	0.980274i	$0.436671\pi$
$577$	−18.0185	+	31.2089i	−0.750120	+	1.29925i	−0.947764	+	0.318972i	$0.896663\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−2.33929	+	4.05178i	−0.0968836	+	0.167807i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	10.5142	+	18.2111i	0.433966	+	0.751651i	0.997211	−	0.0746391i	$-0.0237805\pi$
$587$	10.5142	+	18.2111i	0.433966	+	0.751651i	−0.563245	+	0.826290i	$0.690447\pi$
$588$		0			0
$589$	12.7156	−	22.0242i	0.523939	−	0.907489i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	12.5803	+	21.7897i	0.516612	+	0.894798i	0.999814	+	0.0192889i	$0.00614021\pi$
$593$	12.5803	+	21.7897i	0.516612	+	0.894798i	−0.483202	+	0.875509i	$0.660526\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.11126	−	1.92477i	−0.0454050	−	0.0786438i	0.842430	−	0.538806i	$-0.181125\pi$
$599$	−1.11126	−	1.92477i	−0.0454050	−	0.0786438i	−0.887835	+	0.460162i	$0.847791\pi$
$600$		0			0
$601$	14.0494	+	24.3343i	0.573089	+	0.992619i	0.996246	+	0.0865627i	$0.0275883\pi$
$601$	14.0494	+	24.3343i	0.573089	+	0.992619i	−0.423158	+	0.906056i	$0.639078\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	8.26695			0.336099
$606$		0			0
$607$	6.53018			0.265052			0.132526	−	0.991180i	$-0.457691\pi$
$607$	6.53018			0.265052			0.132526	+	0.991180i	$0.457691\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	5.04875	+	8.74470i	0.204251	+	0.353773i
$612$		0			0
$613$	−5.36398	+	9.29068i	−0.216649	+	0.375247i	−0.953781	−	0.300501i	$-0.902846\pi$
$613$	−5.36398	+	9.29068i	−0.216649	+	0.375247i	0.737132	+	0.675748i	$0.236179\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−15.5265	+	26.8928i	−0.625075	+	1.08266i	0.363451	+	0.931613i	$0.381598\pi$
$617$	−15.5265	+	26.8928i	−0.625075	+	1.08266i	−0.988526	+	0.151049i	$0.951735\pi$
$618$		0			0
$619$	1.44643			0.0581371			0.0290685	−	0.999577i	$-0.490746\pi$
$619$	1.44643			0.0581371			0.0290685	+	0.999577i	$0.490746\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−9.98624			−0.399450
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−19.3287			−0.770686
$630$		0			0
$631$	0.0741250			0.00295087			0.00147544	−	0.999999i	$-0.499530\pi$
$631$	0.0741250			0.00295087			0.00147544	+	0.999999i	$0.499530\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−29.9629			−1.18904
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	47.0407			1.85800			0.928998	−	0.370085i	$-0.120671\pi$
$641$	47.0407			1.85800			0.928998	+	0.370085i	$0.120671\pi$
$642$		0			0
$643$	−16.8647	+	29.2105i	−0.665077	+	1.15195i	0.314187	+	0.949361i	$0.398268\pi$
$643$	−16.8647	+	29.2105i	−0.665077	+	1.15195i	−0.979264	+	0.202587i	$0.935065\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−22.4814	+	38.9390i	−0.883836	+	1.53085i	−0.0367945	+	0.999323i	$0.511715\pi$
$647$	−22.4814	+	38.9390i	−0.883836	+	1.53085i	−0.847042	+	0.531526i	$0.821619\pi$
$648$		0			0
$649$	17.6964	+	30.6510i	0.694644	+	1.20316i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−41.7156			−1.63246			−0.816228	−	0.577730i	$-0.803939\pi$
$653$	−41.7156			−1.63246			−0.816228	+	0.577730i	$0.803939\pi$
$654$		0			0
$655$	9.66621			0.377690
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−10.5259	−	18.2313i	−0.410029	−	0.710191i	0.584863	−	0.811132i	$-0.301148\pi$
$659$	−10.5259	−	18.2313i	−0.410029	−	0.710191i	−0.994892	+	0.100941i	$0.967815\pi$
$660$		0			0
$661$	11.2218	+	19.4368i	0.436479	+	0.756004i	0.997415	−	0.0718553i	$-0.0228920\pi$
$661$	11.2218	+	19.4368i	0.436479	+	0.756004i	−0.560936	+	0.827859i	$0.689559\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1.60576	−	2.78126i	−0.0621754	−	0.107691i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−17.7225	+	30.6962i	−0.684168	+	1.18501i
$672$		0			0
$673$	5.83929	+	10.1140i	0.225088	+	0.389864i	0.956346	−	0.292237i	$-0.0943996\pi$
$673$	5.83929	+	10.1140i	0.225088	+	0.389864i	−0.731258	+	0.682101i	$0.761066\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−5.23422	+	9.06593i	−0.201167	+	0.348432i	−0.948905	−	0.315562i	$-0.897807\pi$
$677$	−5.23422	+	9.06593i	−0.201167	+	0.348432i	0.747737	+	0.663995i	$0.231140\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	16.4079	−	28.4193i	0.627832	−	1.08744i	−0.360154	−	0.932893i	$-0.617276\pi$
$683$	16.4079	−	28.4193i	0.627832	−	1.08744i	0.987986	−	0.154543i	$-0.0493906\pi$
$684$		0			0
$685$	−33.0617			−1.26322
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.734219	−	1.27171i	−0.0279715	−	0.0484481i
$690$		0			0
$691$	2.95056	−	5.11052i	0.112245	−	0.194413i	−0.804430	−	0.594047i	$-0.797529\pi$
$691$	2.95056	−	5.11052i	0.112245	−	0.194413i	0.916675	+	0.399634i	$0.130863\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.53892	−	4.39754i	0.0963068	−	0.166808i
$696$		0			0
$697$	8.25890	+	14.3048i	0.312828	+	0.541834i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	12.3782			0.467519			0.233759	−	0.972294i	$-0.424897\pi$
$701$	12.3782			0.467519			0.233759	+	0.972294i	$0.424897\pi$
$702$		0			0
$703$	17.1483	−	29.7018i	0.646761	−	1.12022i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	6.64145	−	11.5033i	0.249425	−	0.432016i	−0.713942	−	0.700205i	$-0.753092\pi$
$709$	6.64145	−	11.5033i	0.249425	−	0.432016i	0.963366	+	0.268189i	$0.0864251\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.81522	−	3.14406i	−0.0679806	−	0.117746i
$714$		0			0
$715$	1.63664	−	2.83474i	0.0612067	−	0.106013i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	12.1847	+	21.1045i	0.454413	+	0.787066i	0.998654	−	0.0518628i	$-0.0165158\pi$
$719$	12.1847	+	21.1045i	0.454413	+	0.787066i	−0.544242	+	0.838929i	$0.683183\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−4.76145	−	8.24707i	−0.176836	−	0.306289i
$726$		0			0
$727$	−7.99450	−	13.8469i	−0.296500	−	0.513552i	0.678833	−	0.734293i	$-0.262486\pi$
$727$	−7.99450	−	13.8469i	−0.296500	−	0.513552i	−0.975333	+	0.220740i	$0.929153\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−13.0814			−0.483833
$732$		0			0
$733$	42.2829			1.56175			0.780877	−	0.624685i	$-0.214772\pi$
$733$	42.2829			1.56175			0.780877	+	0.624685i	$0.214772\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	9.89307	+	17.1353i	0.364416	+	0.631187i
$738$		0			0
$739$	1.54325	−	2.67299i	0.0567695	−	0.0983276i	−0.836244	−	0.548357i	$-0.815253\pi$
$739$	1.54325	−	2.67299i	0.0567695	−	0.0983276i	0.893014	+	0.450030i	$0.148587\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	3.31522	−	5.74213i	0.121624	−	0.210658i	−0.798784	−	0.601617i	$-0.794523\pi$
$743$	3.31522	−	5.74213i	0.121624	−	0.210658i	0.920408	+	0.390959i	$0.127857\pi$
$744$		0			0
$745$	13.7651			0.504314
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−42.7403			−1.55962			−0.779808	−	0.626018i	$-0.784684\pi$
$751$	−42.7403			−1.55962			−0.779808	+	0.626018i	$0.784684\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	15.0655			0.548288
$756$		0			0
$757$	−31.0232			−1.12756			−0.563779	−	0.825926i	$-0.690653\pi$
$757$	−31.0232			−1.12756			−0.563779	+	0.825926i	$0.690653\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	23.6364			0.856817			0.428409	−	0.903585i	$-0.359074\pi$
$761$	23.6364			0.856817			0.428409	+	0.903585i	$0.359074\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−11.1085			−0.401105
$768$		0			0
$769$	−1.73422	+	3.00376i	−0.0625375	+	0.108318i	−0.895599	−	0.444862i	$-0.853253\pi$
$769$	−1.73422	+	3.00376i	−0.0625375	+	0.108318i	0.833061	+	0.553180i	$0.186586\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−17.2985	+	29.9619i	−0.622184	+	1.07765i	0.366894	+	0.930263i	$0.380421\pi$
$773$	−17.2985	+	29.9619i	−0.622184	+	1.07765i	−0.989078	+	0.147392i	$0.952912\pi$
$774$		0			0
$775$	−5.38255	−	9.32284i	−0.193347	−	0.334886i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−29.3090			−1.05011
$780$		0			0
$781$	−25.4231			−0.909708
$782$		0			0
$783$		0			0
$784$		0			0
$785$	7.44870	+	12.9015i	0.265855	+	0.460475i
$786$		0			0
$787$	−6.07963	−	10.5302i	−0.216715	−	0.375362i	0.737087	−	0.675798i	$-0.236201\pi$
$787$	−6.07963	−	10.5302i	−0.216715	−	0.375362i	−0.953802	+	0.300437i	$0.902868\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−5.56243	−	9.63442i	−0.197528	−	0.342128i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−2.89493	+	5.01416i	−0.102544	+	0.177611i	−0.912732	−	0.408559i	$-0.866031\pi$
$797$	−2.89493	+	5.01416i	−0.102544	+	0.177611i	0.810188	+	0.586170i	$0.199365\pi$
$798$		0			0
$799$	−18.2534	−	31.6158i	−0.645759	−	1.11849i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−6.17742	+	10.6996i	−0.217996	+	0.377581i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−24.5908	+	42.5926i	−0.864568	+	1.49748i	0.00290803	+	0.999996i	$0.499074\pi$
$809$	−24.5908	+	42.5926i	−0.864568	+	1.49748i	−0.867476	+	0.497479i	$0.834259\pi$
$810$		0			0
$811$	−40.7266			−1.43010			−0.715052	−	0.699072i	$-0.753597\pi$
$811$	−40.7266			−1.43010			−0.715052	+	0.699072i	$0.753597\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1.68911	−	2.92562i	−0.0591669	−	0.102480i
$816$		0			0
$817$	11.6058	−	20.1018i	0.406034	−	0.703272i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.54689	−	13.0716i	0.263388	−	0.456202i	−0.703752	−	0.710446i	$-0.748493\pi$
$821$	7.54689	−	13.0716i	0.263388	−	0.456202i	0.967140	+	0.254244i	$0.0818266\pi$
$822$		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
$827$	−35.2348			−1.22523			−0.612616	−	0.790381i	$-0.709883\pi$
$827$	−35.2348			−1.22523			−0.612616	+	0.790381i	$0.709883\pi$
$828$		0			0
$829$	−1.61745	+	2.80151i	−0.0561765	+	0.0973006i	−0.892746	−	0.450560i	$-0.851224\pi$
$829$	−1.61745	+	2.80151i	−0.0561765	+	0.0973006i	0.836570	+	0.547861i	$0.184558\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	2.22803	−	3.85906i	0.0771041	−	0.133548i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	15.5197	+	26.8808i	0.535798	+	0.928030i	0.999124	+	0.0418419i	$0.0133226\pi$
$839$	15.5197	+	26.8808i	0.535798	+	0.928030i	−0.463326	+	0.886188i	$0.653344\pi$
$840$		0			0
$841$	4.32760	−	7.49563i	0.149228	−	0.258470i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−10.5339	−	18.2453i	−0.362377	−	0.627656i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.44801	−	4.24008i	−0.0839167	−	0.145348i
$852$		0			0
$853$	−8.03637	−	13.9194i	−0.275160	−	0.476591i	0.695015	−	0.718995i	$-0.255398\pi$
$853$	−8.03637	−	13.9194i	−0.275160	−	0.476591i	−0.970176	+	0.242403i	$0.922064\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	19.2212			0.656582			0.328291	−	0.944577i	$-0.393527\pi$
$857$	19.2212			0.656582			0.328291	+	0.944577i	$0.393527\pi$
$858$		0			0
$859$	14.8022			0.505046			0.252523	−	0.967591i	$-0.418740\pi$
$859$	14.8022			0.505046			0.252523	+	0.967591i	$0.418740\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	7.38441	+	12.7902i	0.251368	+	0.435382i	0.963903	−	0.266255i	$-0.0857862\pi$
$863$	7.38441	+	12.7902i	0.251368	+	0.435382i	−0.712535	+	0.701637i	$0.752453\pi$
$864$		0			0
$865$	−4.44437	+	7.69787i	−0.151113	+	0.261735i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−11.4072	+	19.7579i	−0.386964	+	0.670241i
$870$		0			0
$871$	−6.21015			−0.210423
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	52.3832			1.76885			0.884427	−	0.466679i	$-0.154550\pi$
$877$	52.3832			1.76885			0.884427	+	0.466679i	$0.154550\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−31.3214			−1.05525			−0.527623	−	0.849479i	$-0.676916\pi$
$881$	−31.3214			−1.05525			−0.527623	+	0.849479i	$0.676916\pi$
$882$		0			0
$883$	−43.0494			−1.44873			−0.724363	−	0.689419i	$-0.757866\pi$
$883$	−43.0494			−1.44873			−0.724363	+	0.689419i	$0.757866\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−14.9766			−0.502866			−0.251433	−	0.967875i	$-0.580902\pi$
$887$	−14.9766			−0.502866			−0.251433	+	0.967875i	$0.580902\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	64.7773			2.16769
$894$		0			0
$895$	4.04944	−	7.01384i	0.135358	−	0.234447i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−11.4993	+	19.9174i	−0.383524	+	0.664282i
$900$		0			0
$901$	2.65452	+	4.59776i	0.0884348	+	0.153174i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−17.7293			−0.589343
$906$		0			0
$907$	30.4559			1.01127			0.505636	−	0.862747i	$-0.331258\pi$
$907$	30.4559			1.01127			0.505636	+	0.862747i	$0.331258\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−9.97593	−	17.2788i	−0.330517	−	0.572473i	0.652096	−	0.758136i	$-0.273890\pi$
$911$	−9.97593	−	17.2788i	−0.330517	−	0.572473i	−0.982613	+	0.185664i	$0.940557\pi$
$912$		0			0
$913$	10.9127	+	18.9014i	0.361159	+	0.625545i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−22.8145	−	39.5159i	−0.752582	−	1.30351i	−0.946567	−	0.322506i	$-0.895475\pi$
$919$	−22.8145	−	39.5159i	−0.752582	−	1.30351i	0.193985	−	0.981004i	$-0.437859\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	3.98969	−	6.91034i	0.131322	−	0.227457i
$924$		0			0
$925$	−7.25890	−	12.5728i	−0.238671	−	0.413391i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−28.1861	+	48.8197i	−0.924755	+	1.60172i	−0.132801	+	0.991143i	$0.542397\pi$
$929$	−28.1861	+	48.8197i	−0.924755	+	1.60172i	−0.791954	+	0.610580i	$0.790936\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−5.91714	+	10.2488i	−0.193511	+	0.335171i
$936$		0			0
$937$	36.8530			1.20393			0.601967	−	0.798521i	$-0.294384\pi$
$937$	36.8530			1.20393			0.601967	+	0.798521i	$0.294384\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	4.38000	+	7.58638i	0.142784	+	0.247309i	0.928544	−	0.371223i	$-0.121061\pi$
$941$	4.38000	+	7.58638i	0.142784	+	0.247309i	−0.785760	+	0.618531i	$0.787728\pi$
$942$		0			0
$943$	−2.09201	+	3.62346i	−0.0681251	+	0.117996i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	13.3226	−	23.0754i	0.432926	−	0.749849i	−0.564198	−	0.825640i	$-0.690815\pi$
$947$	13.3226	−	23.0754i	0.432926	−	0.749849i	0.997124	+	0.0757901i	$0.0241479\pi$
$948$		0			0
$949$	−1.93887	−	3.35822i	−0.0629383	−	0.109012i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−24.3039			−0.787282			−0.393641	−	0.919264i	$-0.628785\pi$
$953$	−24.3039			−0.787282			−0.393641	+	0.919264i	$0.628785\pi$
$954$		0			0
$955$	−11.3207	+	19.6081i	−0.366330	+	0.634502i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	2.50069	−	4.33132i	0.0806674	−	0.139720i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−12.4425	−	21.5511i	−0.400539	−	0.693753i
$966$		0			0
$967$	5.22872	−	9.05641i	0.168144	−	0.291234i	−0.769623	−	0.638498i	$-0.779556\pi$
$967$	5.22872	−	9.05641i	0.168144	−	0.291234i	0.937767	+	0.347264i	$0.112889\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	20.8578	+	36.1267i	0.669358	+	1.15936i	0.978084	+	0.208211i	$0.0667642\pi$
$971$	20.8578	+	36.1267i	0.669358	+	1.15936i	−0.308726	+	0.951151i	$0.599902\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	2.94506	+	5.10099i	0.0942207	+	0.163195i	0.909283	−	0.416178i	$-0.136631\pi$
$977$	2.94506	+	5.10099i	0.0942207	+	0.163195i	−0.815062	+	0.579373i	$0.803297\pi$
$978$		0			0
$979$	11.9567	+	20.7097i	0.382139	+	0.661885i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	41.8392			1.33446			0.667232	−	0.744850i	$-0.267479\pi$
$983$	41.8392			1.33446			0.667232	+	0.744850i	$0.267479\pi$
$984$		0			0
$985$	−31.4189			−1.00109
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.65678	−	2.86963i	−0.0526826	−	0.0912489i
$990$		0			0
$991$	27.3578	−	47.3851i	0.869049	−	1.50524i	0.00607865	−	0.999982i	$-0.498065\pi$
$991$	27.3578	−	47.3851i	0.869049	−	1.50524i	0.862970	−	0.505255i	$-0.168602\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−20.0698	+	34.7619i	−0.636255	+	1.10203i
$996$		0			0
$997$	18.0495			0.571634			0.285817	−	0.958284i	$-0.407735\pi$
$997$	18.0495			0.571634			0.285817	+	0.958284i	$0.407735\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5292.2.l.f.361.1		6
3.2	odd	2		1764.2.l.f.949.3		6
7.2	even	3		5292.2.i.e.1549.3		6
7.3	odd	6		756.2.j.b.253.1		6
7.4	even	3		5292.2.j.d.1765.3		6
7.5	odd	6		5292.2.i.f.1549.1		6
7.6	odd	2		5292.2.l.e.361.3		6
9.2	odd	6		1764.2.i.d.1537.3		6
9.7	even	3		5292.2.i.e.2125.3		6
21.2	odd	6		1764.2.i.d.373.3		6
21.5	even	6		1764.2.i.g.373.1		6
21.11	odd	6		1764.2.j.e.589.1		6
21.17	even	6		252.2.j.a.85.3	✓	6
21.20	even	2		1764.2.l.e.949.1		6
28.3	even	6		3024.2.r.j.1009.1		6
63.2	odd	6		1764.2.l.f.961.3		6
63.11	odd	6		1764.2.j.e.1177.1		6
63.16	even	3	inner	5292.2.l.f.3313.1		6
63.20	even	6		1764.2.i.g.1537.1		6
63.25	even	3		5292.2.j.d.3529.3		6
63.31	odd	6		2268.2.a.h.1.3		3
63.34	odd	6		5292.2.i.f.2125.1		6
63.38	even	6		252.2.j.a.169.3	yes	6
63.47	even	6		1764.2.l.e.961.1		6
63.52	odd	6		756.2.j.b.505.1		6
63.59	even	6		2268.2.a.i.1.1		3
63.61	odd	6		5292.2.l.e.3313.3		6
84.59	odd	6		1008.2.r.j.337.1		6
252.31	even	6		9072.2.a.bv.1.3		3
252.59	odd	6		9072.2.a.by.1.1		3
252.115	even	6		3024.2.r.j.2017.1		6
252.227	odd	6		1008.2.r.j.673.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.j.a.85.3	✓	6	21.17	even	6
252.2.j.a.169.3	yes	6	63.38	even	6
756.2.j.b.253.1		6	7.3	odd	6
756.2.j.b.505.1		6	63.52	odd	6
1008.2.r.j.337.1		6	84.59	odd	6
1008.2.r.j.673.1		6	252.227	odd	6
1764.2.i.d.373.3		6	21.2	odd	6
1764.2.i.d.1537.3		6	9.2	odd	6
1764.2.i.g.373.1		6	21.5	even	6
1764.2.i.g.1537.1		6	63.20	even	6
1764.2.j.e.589.1		6	21.11	odd	6
1764.2.j.e.1177.1		6	63.11	odd	6
1764.2.l.e.949.1		6	21.20	even	2
1764.2.l.e.961.1		6	63.47	even	6
1764.2.l.f.949.3		6	3.2	odd	2
1764.2.l.f.961.3		6	63.2	odd	6
2268.2.a.h.1.3		3	63.31	odd	6
2268.2.a.i.1.1		3	63.59	even	6
3024.2.r.j.1009.1		6	28.3	even	6
3024.2.r.j.2017.1		6	252.115	even	6
5292.2.i.e.1549.3		6	7.2	even	3
5292.2.i.e.2125.3		6	9.7	even	3
5292.2.i.f.1549.1		6	7.5	odd	6
5292.2.i.f.2125.1		6	63.34	odd	6
5292.2.j.d.1765.3		6	7.4	even	3
5292.2.j.d.3529.3		6	63.25	even	3
5292.2.l.e.361.3		6	7.6	odd	2
5292.2.l.e.3313.3		6	63.61	odd	6
5292.2.l.f.361.1		6	1.1	even	1	trivial
5292.2.l.f.3313.1		6	63.16	even	3	inner
9072.2.a.bv.1.3		3	252.31	even	6
9072.2.a.by.1.1		3	252.59	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:	\( N \)	\(=\)	\( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5292.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.69963 q^{5} +O(q^{10})\)	\(q-1.69963 q^{5} -2.47710 q^{11} +(0.388736 - 0.673310i) q^{13} +(-1.40545 + 2.43430i) q^{17} +(-2.49381 - 4.31941i) q^{19} -0.712008 q^{23} -2.11126 q^{25} +(2.25526 + 3.90623i) q^{29} +(2.54944 + 4.41576i) q^{31} +(3.43818 + 5.95510i) q^{37} +(2.93818 - 5.08907i) q^{41} +(2.32691 + 4.03033i) q^{43} +(-6.49381 + 11.2476i) q^{47} +(0.944368 - 1.63569i) q^{53} +4.21015 q^{55} +(-7.14400 - 12.3738i) q^{59} +(7.15452 - 12.3920i) q^{61} +(-0.660706 + 1.14438i) q^{65} +(-3.99381 - 6.91748i) q^{67} +10.2632 q^{71} +(2.49381 - 4.31941i) q^{73} +(4.60507 - 7.97622i) q^{79} +(-4.40545 - 7.63046i) q^{83} +(2.38874 - 4.13741i) q^{85} +(-4.82691 - 8.36046i) q^{89} +(4.23855 + 7.34138i) q^{95} +(4.32072 + 7.48371i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{5}+O(q^{10}) \) 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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