LMFDB - Embedded newform 5292.2.bm.b.2285.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5292,2,Mod(2285,5292)]

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, 5, 1]))

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

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

chi := DirichletCharacter("5292.2285");

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.bm (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$42.2568327497$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3x^{14} - 9x^{12} - 9x^{10} + 225x^{8} - 81x^{6} - 729x^{4} - 2187x^{2} + 6561 $ x^16 - 3x^14 - 9x^12 - 9x^10 + 225x^8 - 81x^6 - 729x^4 - 2187*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{37}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2285.3
Root			$-0.744857 + 1.56371i$ of defining polynomial
Character	$\chi$	$=$	5292.2285
Dual form			5292.2.bm.b.4625.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.553827 q^{5} +O(q^{10})$	$q-0.553827 q^{5} -4.65896i q^{11} +(-3.58265 - 2.06844i) q^{13} +(3.62264 - 6.27459i) q^{17} +(-5.81722 + 3.35857i) q^{19} -5.60371i q^{23} -4.69328 q^{25} +(-1.16599 + 0.673187i) q^{29} +(-0.830741 + 0.479629i) q^{31} +(3.53478 + 6.12241i) q^{37} +(-2.39152 + 4.14224i) q^{41} +(-1.02846 - 1.78135i) q^{43} +(-4.90301 + 8.49226i) q^{47} +(7.30235 + 4.21601i) q^{53} +2.58026i q^{55} +(3.89955 + 6.75422i) q^{59} +(-5.37336 - 3.10231i) q^{61} +(1.98417 + 1.14556i) q^{65} +(1.68814 + 2.92394i) q^{67} -0.407556i q^{71} +(7.47870 + 4.31783i) q^{73} +(-0.318176 + 0.551097i) q^{79} +(2.78840 + 4.82965i) q^{83} +(-2.00632 + 3.47504i) q^{85} +(3.46568 + 6.00274i) q^{89} +(3.22174 - 1.86007i) q^{95} +(-7.48798 + 4.32318i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 16 q^{25} + 12 q^{29} - 2 q^{37} + 4 q^{43} + 36 q^{53} - 24 q^{65} + 14 q^{67} + 20 q^{79} + 6 q^{85} - 60 q^{95}+O(q^{100}) $ 16 * q + 16 * q^25 + 12 * q^29 - 2 * q^37 + 4 * q^43 + 36 * q^53 - 24 * q^65 + 14 * q^67 + 20 * q^79 + 6 * q^85 - 60 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$	$2647$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.553827			−0.247679			−0.123840	−	0.992302i	$-0.539521\pi$
$5$	−0.553827			−0.247679			−0.123840	+	0.992302i	$0.539521\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	4.65896i		−	1.40473i	−0.711817	−	0.702365i	$-0.752128\pi$
$11$		−	4.65896i		−	1.40473i	0.711817	−	0.702365i	$-0.247872\pi$
$12$		0			0
$13$	−3.58265	−	2.06844i	−0.993648	−	0.573683i	−0.0872856	−	0.996183i	$-0.527819\pi$
$13$	−3.58265	−	2.06844i	−0.993648	−	0.573683i	−0.906363	+	0.422500i	$0.861153\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.62264	−	6.27459i	0.878619	−	1.52181i	0.0257612	−	0.999668i	$-0.491799\pi$
$17$	3.62264	−	6.27459i	0.878619	−	1.52181i	0.852857	−	0.522144i	$-0.174868\pi$
$18$		0			0
$19$	−5.81722	+	3.35857i	−1.33456	+	0.770510i	−0.985995	−	0.166774i	$-0.946665\pi$
$19$	−5.81722	+	3.35857i	−1.33456	+	0.770510i	−0.348567	+	0.937284i	$0.613332\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	5.60371i		−	1.16845i	−0.811590	−	0.584227i	$-0.801398\pi$
$23$		−	5.60371i		−	1.16845i	0.811590	−	0.584227i	$-0.198602\pi$
$24$		0			0
$25$	−4.69328			−0.938655
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.16599	+	0.673187i	−0.216520	+	0.125008i	−0.604338	−	0.796728i	$-0.706562\pi$
$29$	−1.16599	+	0.673187i	−0.216520	+	0.125008i	0.387818	+	0.921736i	$0.373229\pi$
$30$		0			0
$31$	−0.830741	+	0.479629i	−0.149206	+	0.0861438i	−0.572744	−	0.819734i	$-0.694121\pi$
$31$	−0.830741	+	0.479629i	−0.149206	+	0.0861438i	0.423539	+	0.905878i	$0.360788\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.53478	+	6.12241i	0.581114	+	1.00652i	0.995348	+	0.0963482i	$0.0307162\pi$
$37$	3.53478	+	6.12241i	0.581114	+	1.00652i	−0.414234	+	0.910170i	$0.635950\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.39152	+	4.14224i	−0.373493	+	0.646909i	−0.990100	−	0.140362i	$-0.955173\pi$
$41$	−2.39152	+	4.14224i	−0.373493	+	0.646909i	0.616607	+	0.787271i	$0.288507\pi$
$42$		0			0
$43$	−1.02846	−	1.78135i	−0.156839	−	0.271653i	0.776888	−	0.629639i	$-0.216797\pi$
$43$	−1.02846	−	1.78135i	−0.156839	−	0.271653i	−0.933727	+	0.357986i	$0.883464\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.90301	+	8.49226i	−0.715177	+	1.23872i	0.247714	+	0.968833i	$0.420321\pi$
$47$	−4.90301	+	8.49226i	−0.715177	+	1.23872i	−0.962891	+	0.269890i	$0.913013\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$	7.30235	+	4.21601i	1.00305	+	0.579114i	0.909151	−	0.416468i	$-0.136732\pi$
$53$	7.30235	+	4.21601i	1.00305	+	0.579114i	0.0939038	+	0.995581i	$0.470065\pi$
$54$		0			0
$55$			2.58026i			0.347922i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.89955	+	6.75422i	0.507678	+	0.879325i	0.999960	+	0.00888893i	$0.00282947\pi$
$59$	3.89955	+	6.75422i	0.507678	+	0.879325i	−0.492282	+	0.870436i	$0.663837\pi$
$60$		0			0
$61$	−5.37336	−	3.10231i	−0.687989	−	0.397211i	0.114869	−	0.993381i	$-0.463355\pi$
$61$	−5.37336	−	3.10231i	−0.687989	−	0.397211i	−0.802858	+	0.596170i	$0.796688\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.98417	+	1.14556i	0.246106	+	0.142089i
$66$		0			0
$67$	1.68814	+	2.92394i	0.206239	+	0.357217i	0.950527	−	0.310642i	$-0.100544\pi$
$67$	1.68814	+	2.92394i	0.206239	+	0.357217i	−0.744288	+	0.667859i	$0.767211\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	0.407556i		−	0.0483680i	−0.999708	−	0.0241840i	$-0.992301\pi$
$71$		−	0.407556i		−	0.0483680i	0.999708	−	0.0241840i	$-0.00769875\pi$
$72$		0			0
$73$	7.47870	+	4.31783i	0.875316	+	0.505364i	0.869111	−	0.494617i	$-0.164692\pi$
$73$	7.47870	+	4.31783i	0.875316	+	0.505364i	0.00620487	+	0.999981i	$0.498025\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.318176	+	0.551097i	−0.0357976	+	0.0620032i	−0.883369	−	0.468678i	$-0.844730\pi$
$79$	−0.318176	+	0.551097i	−0.0357976	+	0.0620032i	0.847572	+	0.530681i	$0.178064\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.78840	+	4.82965i	0.306066	+	0.530123i	0.977498	−	0.210944i	$-0.0676537\pi$
$83$	2.78840	+	4.82965i	0.306066	+	0.530123i	−0.671432	+	0.741066i	$0.734320\pi$
$84$		0			0
$85$	−2.00632	+	3.47504i	−0.217616	+	0.376921i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.46568	+	6.00274i	0.367362	+	0.636289i	0.989152	−	0.146895i	$-0.0469278\pi$
$89$	3.46568	+	6.00274i	0.367362	+	0.636289i	−0.621790	+	0.783184i	$0.713594\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.22174	−	1.86007i	0.330543	−	0.190839i
$96$		0			0
$97$	−7.48798	+	4.32318i	−0.760289	+	0.438953i	−0.829399	−	0.558656i	$-0.811317\pi$
$97$	−7.48798	+	4.32318i	−0.760289	+	0.438953i	0.0691107	+	0.997609i	$0.477984\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.68453			−0.466128			−0.233064	−	0.972461i	$-0.574875\pi$
$101$	−4.68453			−0.466128			−0.233064	+	0.972461i	$0.574875\pi$
$102$		0			0
$103$		−	7.39937i		−	0.729082i	−0.931187	−	0.364541i	$-0.881226\pi$
$103$		−	7.39937i		−	0.729082i	0.931187	−	0.364541i	$-0.118774\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.38260	+	2.53029i	−0.423682	+	0.244613i	−0.696651	−	0.717410i	$-0.745327\pi$
$107$	−4.38260	+	2.53029i	−0.423682	+	0.244613i	0.272970	+	0.962023i	$0.411994\pi$
$108$		0			0
$109$	−5.88142	+	10.1869i	−0.563337	+	0.975729i	0.433865	+	0.900978i	$0.357150\pi$
$109$	−5.88142	+	10.1869i	−0.563337	+	0.975729i	−0.997202	+	0.0747510i	$0.976184\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.51895	+	0.876965i	0.142891	+	0.0824979i	0.569741	−	0.821824i	$-0.307044\pi$
$113$	1.51895	+	0.876965i	0.142891	+	0.0824979i	−0.426850	+	0.904322i	$0.640377\pi$
$114$		0			0
$115$			3.10349i			0.289402i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−10.7059			−0.973264
$122$		0			0
$123$		0			0
$124$		0			0
$125$	5.36840			0.480164
$126$		0			0
$127$	11.0822			0.983385			0.491693	−	0.870769i	$-0.336378\pi$
$127$	11.0822			0.983385			0.491693	+	0.870769i	$0.336378\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−18.4729			−1.61398			−0.806990	−	0.590565i	$-0.798905\pi$
$131$	−18.4729			−1.61398			−0.806990	+	0.590565i	$0.798905\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	22.0013i		−	1.87970i	−0.341585	−	0.939851i	$-0.610964\pi$
$137$		−	22.0013i		−	1.87970i	0.341585	−	0.939851i	$-0.389036\pi$
$138$		0			0
$139$	8.55986	+	4.94204i	0.726038	+	0.419178i	0.816971	−	0.576679i	$-0.195652\pi$
$139$	8.55986	+	4.94204i	0.726038	+	0.419178i	−0.0909332	+	0.995857i	$0.528985\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−9.63680	+	16.6914i	−0.805870	+	1.39581i
$144$		0			0
$145$	0.645760	−	0.372830i	0.0536274	−	0.0309618i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	7.35171i		−	0.602275i	−0.953581	−	0.301138i	$-0.902634\pi$
$149$		−	7.35171i		−	0.602275i	0.953581	−	0.301138i	$-0.0973664\pi$
$150$		0			0
$151$	−4.33199			−0.352532			−0.176266	−	0.984343i	$-0.556402\pi$
$151$	−4.33199			−0.352532			−0.176266	+	0.984343i	$0.556402\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.460087	−	0.265632i	0.0369551	−	0.0213360i
$156$		0			0
$157$	−1.54152	+	0.889998i	−0.123027	+	0.0710296i	−0.560251	−	0.828323i	$-0.689295\pi$
$157$	−1.54152	+	0.889998i	−0.123027	+	0.0710296i	0.437224	+	0.899353i	$0.355962\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	2.81818	+	4.88122i	0.220737	+	0.382327i	0.955032	−	0.296503i	$-0.0958206\pi$
$163$	2.81818	+	4.88122i	0.220737	+	0.382327i	−0.734295	+	0.678830i	$0.762487\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.38803	+	4.13618i	−0.184791	+	0.320067i	−0.943506	−	0.331355i	$-0.892494\pi$
$167$	−2.38803	+	4.13618i	−0.184791	+	0.320067i	0.758715	+	0.651423i	$0.225827\pi$
$168$		0			0
$169$	2.05692	+	3.56270i	0.158225	+	0.274054i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.83766	+	4.91497i	−0.215743	+	0.373678i	−0.953502	−	0.301386i	$-0.902551\pi$
$173$	−2.83766	+	4.91497i	−0.215743	+	0.373678i	0.737759	+	0.675064i	$0.235884\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	10.9383	+	6.31525i	0.817570	+	0.472024i	0.849578	−	0.527463i	$-0.176857\pi$
$179$	10.9383	+	6.31525i	0.817570	+	0.472024i	−0.0320079	+	0.999488i	$0.510190\pi$
$180$		0			0
$181$			22.7424i			1.69043i	0.534426	+	0.845215i	$0.320528\pi$
$181$			22.7424i			1.69043i	−0.534426	+	0.845215i	$0.679472\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.95766	−	3.39076i	−0.143930	−	0.249294i
$186$		0			0
$187$	−29.2331	−	16.8777i	−2.13773	−	1.23422i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−10.0537	−	5.80452i	−0.727462	−	0.420000i	0.0900309	−	0.995939i	$-0.471303\pi$
$191$	−10.0537	−	5.80452i	−0.727462	−	0.420000i	−0.817493	+	0.575939i	$0.804637\pi$
$192$		0			0
$193$	−3.16599	−	5.48366i	−0.227893	−	0.394723i	0.729290	−	0.684204i	$-0.239850\pi$
$193$	−3.16599	−	5.48366i	−0.227893	−	0.394723i	−0.957184	+	0.289482i	$0.906517\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	3.10030i		−	0.220888i	−0.993882	−	0.110444i	$-0.964773\pi$
$197$		−	3.10030i		−	0.220888i	0.993882	−	0.110444i	$-0.0352272\pi$
$198$		0			0
$199$	−13.6198	−	7.86341i	−0.965484	−	0.557422i	−0.0676272	−	0.997711i	$-0.521543\pi$
$199$	−13.6198	−	7.86341i	−0.965484	−	0.557422i	−0.897856	+	0.440288i	$0.854876\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	1.32449	−	2.29409i	0.0925065	−	0.160226i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	15.6475	+	27.1022i	1.08236	+	1.87470i
$210$		0			0
$211$	3.51263	−	6.08406i	0.241820	−	0.418844i	−0.719413	−	0.694582i	$-0.755589\pi$
$211$	3.51263	−	6.08406i	0.241820	−	0.418844i	0.961233	+	0.275739i	$0.0889225\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.569590	+	0.986559i	0.0388457	+	0.0672828i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−25.9573	+	14.9864i	−1.74608	+	1.00810i
$222$		0			0
$223$	−21.3477	+	12.3251i	−1.42955	+	0.825350i	−0.997085	−	0.0763008i	$-0.975689\pi$
$223$	−21.3477	+	12.3251i	−1.42955	+	0.825350i	−0.432464	+	0.901651i	$0.642356\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	20.0743			1.33238			0.666190	−	0.745782i	$-0.267924\pi$
$227$	20.0743			1.33238			0.666190	+	0.745782i	$0.267924\pi$
$228$		0			0
$229$			7.80422i			0.515717i	0.966183	+	0.257859i	$0.0830169\pi$
$229$			7.80422i			0.515717i	−0.966183	+	0.257859i	$0.916983\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.89843	−	3.98281i	0.451931	−	0.260922i	−0.256714	−	0.966487i	$-0.582640\pi$
$233$	6.89843	−	3.98281i	0.451931	−	0.260922i	0.708645	+	0.705565i	$0.249307\pi$
$234$		0			0
$235$	2.71542	−	4.70325i	0.177135	−	0.306806i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−23.2059	−	13.3979i	−1.50107	−	0.866640i	−0.999999	−	0.00123146i	$-0.999608\pi$
$239$	−23.2059	−	13.3979i	−1.50107	−	0.866640i	−0.501066	−	0.865409i	$-0.667059\pi$
$240$		0			0
$241$		−	0.874407i		−	0.0563255i	−0.999603	−	0.0281628i	$-0.991034\pi$
$241$		−	0.874407i		−	0.0563255i	0.999603	−	0.0281628i	$-0.00896567\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	27.7881			1.76811
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−2.32082			−0.146489			−0.0732445	−	0.997314i	$-0.523335\pi$
$251$	−2.32082			−0.146489			−0.0732445	+	0.997314i	$0.523335\pi$
$252$		0			0
$253$	−26.1075			−1.64136
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−24.6035			−1.53472			−0.767361	−	0.641215i	$-0.778431\pi$
$257$	−24.6035			−1.53472			−0.767361	+	0.641215i	$0.778431\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$			23.7024i			1.46155i	0.682619	+	0.730775i	$0.260841\pi$
$263$			23.7024i			1.46155i	−0.682619	+	0.730775i	$0.739159\pi$
$264$		0			0
$265$	−4.04424	−	2.33494i	−0.248436	−	0.143434i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	10.3106	−	17.8585i	0.628648	−	1.08885i	−0.359176	−	0.933270i	$-0.616942\pi$
$269$	10.3106	−	17.8585i	0.628648	−	1.08885i	0.987823	−	0.155580i	$-0.0497245\pi$
$270$		0			0
$271$	−12.0771	+	6.97270i	−0.733630	+	0.423562i	−0.819749	−	0.572723i	$-0.805887\pi$
$271$	−12.0771	+	6.97270i	−0.733630	+	0.423562i	0.0861186	+	0.996285i	$0.472554\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			21.8658i			1.31856i
$276$		0			0
$277$	20.7881			1.24904			0.624518	−	0.781011i	$-0.285296\pi$
$277$	20.7881			1.24904			0.624518	+	0.781011i	$0.285296\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	20.3371	−	11.7416i	1.21321	−	0.700448i	0.249754	−	0.968309i	$-0.419650\pi$
$281$	20.3371	−	11.7416i	1.21321	−	0.700448i	0.963457	+	0.267862i	$0.0863170\pi$
$282$		0			0
$283$	−11.1906	+	6.46089i	−0.665211	+	0.384060i	−0.794260	−	0.607578i	$-0.792141\pi$
$283$	−11.1906	+	6.46089i	−0.665211	+	0.384060i	0.129048	+	0.991638i	$0.458808\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−17.7470	−	30.7387i	−1.04394	−	1.80816i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.99115	+	3.44878i	−0.116324	+	0.201480i	−0.918308	−	0.395866i	$-0.870445\pi$
$293$	−1.99115	+	3.44878i	−0.116324	+	0.201480i	0.801984	+	0.597346i	$0.203778\pi$
$294$		0			0
$295$	−2.15968	−	3.74067i	−0.125741	−	0.217790i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−11.5910	+	20.0761i	−0.670322	+	1.16103i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2.97592	+	1.71815i	0.170401	+	0.0983808i
$306$		0			0
$307$		−	22.3162i		−	1.27365i	−0.771008	−	0.636825i	$-0.780247\pi$
$307$		−	22.3162i		−	1.27365i	0.771008	−	0.636825i	$-0.219753\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−8.18371	−	14.1746i	−0.464056	−	0.803768i	0.535103	−	0.844787i	$-0.320273\pi$
$311$	−8.18371	−	14.1746i	−0.464056	−	0.803768i	−0.999158	+	0.0410190i	$0.986940\pi$
$312$		0			0
$313$	−16.5547	−	9.55785i	−0.935726	−	0.540242i	−0.0471079	−	0.998890i	$-0.515000\pi$
$313$	−16.5547	−	9.55785i	−0.935726	−	0.540242i	−0.888618	+	0.458648i	$0.848334\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	20.8798	+	12.0550i	1.17273	+	0.677074i	0.954321	−	0.298784i	$-0.0965811\pi$
$317$	20.8798	+	12.0550i	1.17273	+	0.677074i	0.218405	+	0.975858i	$0.429914\pi$
$318$		0			0
$319$	3.13635	+	5.43232i	0.175602	+	0.304152i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			48.6676i			2.70794i
$324$		0			0
$325$	16.8144	+	9.70778i	0.932693	+	0.538491i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−5.70077	+	9.87403i	−0.313343	+	0.542726i	−0.979084	−	0.203457i	$-0.934782\pi$
$331$	−5.70077	+	9.87403i	−0.313343	+	0.542726i	0.665741	+	0.746183i	$0.268116\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.934938	−	1.61936i	−0.0510811	−	0.0884751i
$336$		0			0
$337$	2.16599	−	3.75161i	0.117989	−	0.204363i	−0.800981	−	0.598689i	$-0.795689\pi$
$337$	2.16599	−	3.75161i	0.117989	−	0.204363i	0.918971	+	0.394326i	$0.129022\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2.23457	+	3.87039i	0.121009	+	0.209593i
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.62254	+	2.66882i	−0.248151	+	0.143270i	−0.618917	−	0.785456i	$-0.712428\pi$
$347$	−4.62254	+	2.66882i	−0.248151	+	0.143270i	0.370766	+	0.928726i	$0.379095\pi$
$348$		0			0
$349$	−8.78031	+	5.06931i	−0.469999	+	0.271354i	−0.716239	−	0.697855i	$-0.754138\pi$
$349$	−8.78031	+	5.06931i	−0.469999	+	0.271354i	0.246240	+	0.969209i	$0.420805\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	15.3513			0.817067			0.408533	−	0.912743i	$-0.366040\pi$
$353$	15.3513			0.817067			0.408533	+	0.912743i	$0.366040\pi$
$354$		0			0
$355$			0.225715i			0.0119797i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.51381	−	0.874000i	0.0798960	−	0.0461280i	−0.459520	−	0.888168i	$-0.651978\pi$
$359$	1.51381	−	0.874000i	0.0798960	−	0.0461280i	0.539416	+	0.842040i	$0.318645\pi$
$360$		0			0
$361$	13.0600	−	22.6207i	0.687371	−	1.19056i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−4.14191	−	2.39133i	−0.216798	−	0.125168i
$366$		0			0
$367$			12.9004i			0.673393i	0.941613	+	0.336697i	$0.109310\pi$
$367$			12.9004i			0.673393i	−0.941613	+	0.336697i	$0.890690\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−10.6956			−0.553799			−0.276900	−	0.960899i	$-0.589307\pi$
$373$	−10.6956			−0.553799			−0.276900	+	0.960899i	$0.589307\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	5.56980			0.286859
$378$		0			0
$379$	0.566797			0.0291144			0.0145572	−	0.999894i	$-0.495366\pi$
$379$	0.566797			0.0291144			0.0145572	+	0.999894i	$0.495366\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	18.8612			0.963761			0.481880	−	0.876237i	$-0.339954\pi$
$383$	18.8612			0.963761			0.481880	+	0.876237i	$0.339954\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	16.5332i		−	0.838267i	−0.907925	−	0.419133i	$-0.862334\pi$
$389$		−	16.5332i		−	0.838267i	0.907925	−	0.419133i	$-0.137666\pi$
$390$		0			0
$391$	−35.1610	−	20.3002i	−1.77817	−	1.02663i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.176215	−	0.305213i	0.00886632	−	0.0153569i
$396$		0			0
$397$	−29.5384	+	17.0540i	−1.48249	+	0.855917i	−0.999802	−	0.0198756i	$-0.993673\pi$
$397$	−29.5384	+	17.0540i	−1.48249	+	0.855917i	−0.482688	+	0.875792i	$0.660340\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			21.5230i			1.07481i	0.843325	+	0.537404i	$0.180595\pi$
$401$			21.5230i			1.07481i	−0.843325	+	0.537404i	$0.819405\pi$
$402$		0			0
$403$	3.96834			0.197677
$404$		0			0
$405$		0			0
$406$		0			0
$407$	28.5241	−	16.4684i	1.41389	−	0.816308i
$408$		0			0
$409$	19.2516	−	11.1149i	0.951933	−	0.549599i	0.0582520	−	0.998302i	$-0.481447\pi$
$409$	19.2516	−	11.1149i	0.951933	−	0.549599i	0.893681	+	0.448703i	$0.148114\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−1.54429	−	2.67479i	−0.0758063	−	0.131300i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−6.81490	+	11.8038i	−0.332930	+	0.576651i	−0.983085	−	0.183150i	$-0.941371\pi$
$419$	−6.81490	+	11.8038i	−0.332930	+	0.576651i	0.650155	+	0.759802i	$0.274704\pi$
$420$		0			0
$421$	13.7071	+	23.7414i	0.668043	+	1.15708i	0.978451	+	0.206480i	$0.0662009\pi$
$421$	13.7071	+	23.7414i	0.668043	+	1.15708i	−0.310408	+	0.950603i	$0.600466\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−17.0020	+	29.4484i	−0.824720	+	1.42846i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−30.1663	−	17.4165i	−1.45306	−	0.838925i	−0.454406	−	0.890795i	$-0.650149\pi$
$431$	−30.1663	−	17.4165i	−1.45306	−	0.838925i	−0.998654	+	0.0518699i	$0.983482\pi$
$432$		0			0
$433$			19.5648i			0.940223i	0.882607	+	0.470112i	$0.155786\pi$
$433$			19.5648i			0.940223i	−0.882607	+	0.470112i	$0.844214\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	18.8205	+	32.5980i	0.900305	+	1.55937i
$438$		0			0
$439$	24.7361	+	14.2814i	1.18059	+	0.681614i	0.956151	−	0.292874i	$-0.0946116\pi$
$439$	24.7361	+	14.2814i	1.18059	+	0.681614i	0.224439	+	0.974488i	$0.427945\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−21.8612	−	12.6216i	−1.03866	−	0.599669i	−0.119205	−	0.992870i	$-0.538034\pi$
$443$	−21.8612	−	12.6216i	−1.03866	−	0.599669i	−0.919453	+	0.393201i	$0.871368\pi$
$444$		0			0
$445$	−1.91939	−	3.32448i	−0.0909878	−	0.157596i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			15.1042i			0.712811i	0.934331	+	0.356405i	$0.115998\pi$
$449$			15.1042i			0.712811i	−0.934331	+	0.356405i	$0.884002\pi$
$450$		0			0
$451$	19.2985	+	11.1420i	0.908733	+	0.524657i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.75138	+	3.03348i	−0.0819261	+	0.141900i	−0.904077	−	0.427369i	$-0.859440\pi$
$457$	−1.75138	+	3.03348i	−0.0819261	+	0.141900i	0.822151	+	0.569269i	$0.192774\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.98765	+	3.44272i	0.0925743	+	0.160343i	0.908594	−	0.417681i	$-0.137157\pi$
$461$	1.98765	+	3.44272i	0.0925743	+	0.160343i	−0.816019	+	0.578025i	$0.803824\pi$
$462$		0			0
$463$	−5.18494	+	8.98058i	−0.240965	+	0.417363i	−0.960989	−	0.276585i	$-0.910797\pi$
$463$	−5.18494	+	8.98058i	−0.240965	+	0.417363i	0.720025	+	0.693948i	$0.244130\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	9.80952	+	16.9906i	0.453930	+	0.786230i	0.998626	−	0.0524035i	$-0.0166882\pi$
$467$	9.80952	+	16.9906i	0.453930	+	0.786230i	−0.544696	+	0.838634i	$0.683355\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−8.29923	+	4.79156i	−0.381599	+	0.220316i
$474$		0			0
$475$	27.3018	−	15.7627i	1.25269	−	0.723243i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−31.6474			−1.44600			−0.723002	−	0.690846i	$-0.757238\pi$
$479$	−31.6474			−1.44600			−0.723002	+	0.690846i	$0.757238\pi$
$480$		0			0
$481$		−	29.2460i		−	1.33350i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.14705	−	2.39430i	0.188308	−	0.108719i
$486$		0			0
$487$	9.72923	−	16.8515i	0.440874	−	0.763616i	−0.556881	−	0.830592i	$-0.688002\pi$
$487$	9.72923	−	16.8515i	0.440874	−	0.763616i	0.997755	+	0.0669768i	$0.0213353\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−23.9525	−	13.8290i	−1.08096	−	0.624094i	−0.149806	−	0.988715i	$-0.547865\pi$
$491$	−23.9525	−	13.8290i	−1.08096	−	0.624094i	−0.931156	+	0.364622i	$0.881198\pi$
$492$		0			0
$493$			9.75485i			0.439336i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−9.01263			−0.403461			−0.201730	−	0.979441i	$-0.564656\pi$
$499$	−9.01263			−0.403461			−0.201730	+	0.979441i	$0.564656\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−27.1572			−1.21088			−0.605440	−	0.795891i	$-0.707003\pi$
$503$	−27.1572			−1.21088			−0.605440	+	0.795891i	$0.707003\pi$
$504$		0			0
$505$	2.59442			0.115450
$506$		0			0
$507$		0			0
$508$		0			0
$509$	13.1360			0.582242			0.291121	−	0.956686i	$-0.405972\pi$
$509$	13.1360			0.582242			0.291121	+	0.956686i	$0.405972\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$			4.09797i			0.180578i
$516$		0			0
$517$	39.5651	+	22.8429i	1.74007	+	1.00463i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−2.01609	+	3.49198i	−0.0883266	+	0.152986i	−0.906804	−	0.421553i	$-0.861485\pi$
$521$	−2.01609	+	3.49198i	−0.0883266	+	0.152986i	0.818477	+	0.574539i	$0.194819\pi$
$522$		0			0
$523$	−0.516117	+	0.297980i	−0.0225682	+	0.0130298i	−0.511242	−	0.859437i	$-0.670814\pi$
$523$	−0.516117	+	0.297980i	−0.0225682	+	0.0130298i	0.488673	+	0.872467i	$0.337481\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			6.95008i			0.302750i
$528$		0			0
$529$	−8.40154			−0.365285
$530$		0			0
$531$		0			0
$532$		0			0
$533$	17.1360	−	9.89347i	0.742242	−	0.428534i
$534$		0			0
$535$	2.42720	−	1.40135i	0.104937	−	0.0605855i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	7.05061	+	12.2120i	0.303129	+	0.525035i	0.976843	−	0.213957i	$-0.0686353\pi$
$541$	7.05061	+	12.2120i	0.303129	+	0.525035i	−0.673714	+	0.738992i	$0.735302\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	3.25729	−	5.64179i	0.139527	−	0.241668i
$546$		0			0
$547$	−18.9921	−	32.8952i	−0.812042	−	1.40650i	−0.911433	−	0.411450i	$-0.865023\pi$
$547$	−18.9921	−	32.8952i	−0.812042	−	1.40650i	0.0993905	−	0.995049i	$-0.468311\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	4.52190	−	7.83216i	0.192639	−	0.333661i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	36.1181	+	20.8528i	1.53037	+	0.883562i	0.999344	+	0.0362098i	$0.0115285\pi$
$557$	36.1181	+	20.8528i	1.53037	+	0.883562i	0.531031	+	0.847353i	$0.321805\pi$
$558$		0			0
$559$			8.50926i			0.359903i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.938436	−	1.62542i	−0.0395504	−	0.0685033i	0.845573	−	0.533860i	$-0.179259\pi$
$563$	−0.938436	−	1.62542i	−0.0395504	−	0.0685033i	−0.885123	+	0.465357i	$0.845926\pi$
$564$		0			0
$565$	−0.841235	−	0.485687i	−0.0353910	−	0.0204330i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−20.6391	−	11.9160i	−0.865237	−	0.499545i	0.000525844	−	1.00000i	$-0.499833\pi$
$569$	−20.6391	−	11.9160i	−0.865237	−	0.499545i	−0.865762	+	0.500455i	$0.833166\pi$
$570$		0			0
$571$	−14.8719	−	25.7589i	−0.622370	−	1.07798i	−0.989043	−	0.147626i	$-0.952837\pi$
$571$	−14.8719	−	25.7589i	−0.622370	−	1.07798i	0.366674	−	0.930350i	$-0.380497\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			26.2997i			1.09678i
$576$		0			0
$577$	−12.6950	−	7.32947i	−0.528501	−	0.305130i	0.211905	−	0.977290i	$-0.432033\pi$
$577$	−12.6950	−	7.32947i	−0.528501	−	0.305130i	−0.740406	+	0.672160i	$0.765367\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	19.6422	−	34.0213i	0.813498	−	1.40902i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−22.2189	−	38.4843i	−0.917074	−	1.58842i	−0.803836	−	0.594851i	$-0.797211\pi$
$587$	−22.2189	−	38.4843i	−0.917074	−	1.58842i	−0.113238	−	0.993568i	$-0.536122\pi$
$588$		0			0
$589$	3.22174	−	5.58021i	0.132749	−	0.229929i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−18.5593	−	32.1457i	−0.762140	−	1.32006i	−0.941746	−	0.336326i	$-0.890816\pi$
$593$	−18.5593	−	32.1457i	−0.762140	−	1.32006i	0.179606	−	0.983739i	$-0.442518\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−12.0534	+	6.95901i	−0.492487	+	0.284338i	−0.725606	−	0.688111i	$-0.758440\pi$
$599$	−12.0534	+	6.95901i	−0.492487	+	0.284338i	0.233119	+	0.972448i	$0.425107\pi$
$600$		0			0
$601$	−0.377613	+	0.218015i	−0.0154032	+	0.00889301i	−0.507682	−	0.861545i	$-0.669497\pi$
$601$	−0.377613	+	0.218015i	−0.0154032	+	0.00889301i	0.492279	+	0.870438i	$0.336164\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	5.92923			0.241057
$606$		0			0
$607$			2.21837i			0.0900410i	0.998986	+	0.0450205i	$0.0143353\pi$
$607$			2.21837i			0.0900410i	−0.998986	+	0.0450205i	$0.985665\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	35.1315	−	20.2832i	1.42127	−	0.820570i
$612$		0			0
$613$	−19.1011	+	33.0841i	−0.771488	+	1.33626i	0.165260	+	0.986250i	$0.447154\pi$
$613$	−19.1011	+	33.0841i	−0.771488	+	1.33626i	−0.936748	+	0.350006i	$0.886180\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−21.1043	−	12.1846i	−0.849628	−	0.490533i	0.0108970	−	0.999941i	$-0.496531\pi$
$617$	−21.1043	−	12.1846i	−0.849628	−	0.490533i	−0.860525	+	0.509407i	$0.829865\pi$
$618$		0			0
$619$		−	29.3845i		−	1.18106i	−0.807015	−	0.590531i	$-0.798918\pi$
$619$		−	29.3845i		−	1.18106i	0.807015	−	0.590531i	$-0.201082\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	20.4932			0.819728
$626$		0			0
$627$		0			0
$628$		0			0
$629$	51.2209			2.04231
$630$		0			0
$631$	5.17077			0.205845			0.102923	−	0.994689i	$-0.467181\pi$
$631$	5.17077			0.205845			0.102923	+	0.994689i	$0.467181\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−6.13762			−0.243564
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$			6.14769i			0.242819i	0.992603	+	0.121410i	$0.0387414\pi$
$641$			6.14769i			0.242819i	−0.992603	+	0.121410i	$0.961259\pi$
$642$		0			0
$643$	−23.9599	−	13.8333i	−0.944886	−	0.545530i	−0.0533976	−	0.998573i	$-0.517005\pi$
$643$	−23.9599	−	13.8333i	−0.944886	−	0.545530i	−0.891489	+	0.453043i	$0.850338\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.40729	+	4.16954i	−0.0946402	+	0.163922i	−0.909458	−	0.415795i	$-0.863503\pi$
$647$	−2.40729	+	4.16954i	−0.0946402	+	0.163922i	0.814818	+	0.579717i	$0.196837\pi$
$648$		0			0
$649$	31.4676	−	18.1679i	1.23521	−	0.713151i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			24.4518i			0.956874i	0.878122	+	0.478437i	$0.158796\pi$
$653$			24.4518i			0.956874i	−0.878122	+	0.478437i	$0.841204\pi$
$654$		0			0
$655$	10.2308			0.399749
$656$		0			0
$657$		0			0
$658$		0			0
$659$	20.7514	−	11.9808i	0.808359	−	0.466706i	−0.0380267	−	0.999277i	$-0.512107\pi$
$659$	20.7514	−	11.9808i	0.808359	−	0.466706i	0.846386	+	0.532570i	$0.178774\pi$
$660$		0			0
$661$	−6.73275	+	3.88715i	−0.261874	+	0.151193i	−0.625189	−	0.780473i	$-0.714978\pi$
$661$	−6.73275	+	3.88715i	−0.261874	+	0.151193i	0.363315	+	0.931666i	$0.381645\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3.77234	+	6.53389i	0.146066	+	0.252993i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−14.4536	+	25.0343i	−0.557973	+	0.966438i
$672$		0			0
$673$	−14.7281	−	25.5097i	−0.567725	−	0.983328i	−0.996790	−	0.0800548i	$-0.974490\pi$
$673$	−14.7281	−	25.5097i	−0.567725	−	0.983328i	0.429066	−	0.903273i	$-0.358843\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	17.8293	−	30.8812i	0.685235	−	1.18686i	−0.288128	−	0.957592i	$-0.593033\pi$
$677$	17.8293	−	30.8812i	0.685235	−	1.18686i	0.973363	−	0.229270i	$-0.0736337\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	11.3423	+	6.54846i	0.433999	+	0.250570i	0.701049	−	0.713113i	$-0.252715\pi$
$683$	11.3423	+	6.54846i	0.433999	+	0.250570i	−0.267050	+	0.963683i	$0.586049\pi$
$684$		0			0
$685$			12.1850i			0.465563i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−17.4412	−	30.2090i	−0.664456	−	1.15087i
$690$		0			0
$691$	7.81992	+	4.51483i	0.297484	+	0.171752i	0.641312	−	0.767280i	$-0.278390\pi$
$691$	7.81992	+	4.51483i	0.297484	+	0.171752i	−0.343828	+	0.939033i	$0.611724\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.74068	−	2.73704i	−0.179824	−	0.103822i
$696$		0			0
$697$	17.3273	+	30.0117i	0.656316	+	1.13677i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			0.259274i			0.00979264i	0.999988	+	0.00489632i	$0.00155855\pi$
$701$			0.259274i			0.00979264i	−0.999988	+	0.00489632i	$0.998441\pi$
$702$		0			0
$703$	−41.1252	−	23.7436i	−1.55107	−	0.895508i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−3.08574	+	5.34467i	−0.115888	+	0.200723i	−0.918134	−	0.396270i	$-0.870305\pi$
$709$	−3.08574	+	5.34467i	−0.115888	+	0.200723i	0.802247	+	0.596993i	$0.203638\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	2.68770	+	4.65523i	0.100655	+	0.174340i
$714$		0			0
$715$	5.33712	−	9.24417i	0.199597	−	0.345712i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−9.76375	−	16.9113i	−0.364127	−	0.630686i	0.624509	−	0.781018i	$-0.285299\pi$
$719$	−9.76375	−	16.9113i	−0.364127	−	0.630686i	−0.988636	+	0.150332i	$0.951966\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$	5.47233	−	3.15945i	0.203237	−	0.117339i
$726$		0			0
$727$	−0.425312	+	0.245554i	−0.0157740	+	0.00910710i	−0.507866	−	0.861436i	$-0.669566\pi$
$727$	−0.425312	+	0.245554i	−0.0157740	+	0.00910710i	0.492092	+	0.870543i	$0.336232\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−14.9030			−0.551206
$732$		0			0
$733$			7.71829i			0.285082i	0.989789	+	0.142541i	$0.0455272\pi$
$733$			7.71829i			0.285082i	−0.989789	+	0.142541i	$0.954473\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	13.6225	−	7.86498i	0.501793	−	0.289710i
$738$		0			0
$739$	−5.45417	+	9.44690i	−0.200635	+	0.347510i	−0.948733	−	0.316078i	$-0.897634\pi$
$739$	−5.45417	+	9.44690i	−0.200635	+	0.347510i	0.748098	+	0.663588i	$0.230967\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−27.0051	−	15.5914i	−0.990722	−	0.571994i	−0.0852322	−	0.996361i	$-0.527163\pi$
$743$	−27.0051	−	15.5914i	−0.990722	−	0.571994i	−0.905490	+	0.424367i	$0.860497\pi$
$744$		0			0
$745$			4.07158i			0.149171i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−46.0734			−1.68124			−0.840622	−	0.541623i	$-0.817810\pi$
$751$	−46.0734			−1.68124			−0.840622	+	0.541623i	$0.817810\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	2.39917			0.0873149
$756$		0			0
$757$	40.6419			1.47715			0.738577	−	0.674169i	$-0.235498\pi$
$757$	40.6419			1.47715			0.738577	+	0.674169i	$0.235498\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−7.28380			−0.264037			−0.132019	−	0.991247i	$-0.542146\pi$
$761$	−7.28380			−0.264037			−0.132019	+	0.991247i	$0.542146\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	32.2640i		−	1.16499i
$768$		0			0
$769$	35.8261	+	20.6842i	1.29192	+	0.745892i	0.978995	−	0.203886i	$-0.0653570\pi$
$769$	35.8261	+	20.6842i	1.29192	+	0.745892i	0.312927	+	0.949777i	$0.398690\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−8.55914	+	14.8249i	−0.307851	+	0.533213i	−0.977892	−	0.209111i	$-0.932943\pi$
$773$	−8.55914	+	14.8249i	−0.307851	+	0.533213i	0.670041	+	0.742324i	$0.266276\pi$
$774$		0			0
$775$	3.89890	−	2.25103i	0.140053	−	0.0808594i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	32.1284i		−	1.15112i
$780$		0			0
$781$	−1.89879			−0.0679439
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.853737	−	0.492906i	0.0304712	−	0.0175926i
$786$		0			0
$787$	−25.7426	+	14.8625i	−0.917623	+	0.529790i	−0.882876	−	0.469606i	$-0.844396\pi$
$787$	−25.7426	+	14.8625i	−0.917623	+	0.529790i	−0.0347472	+	0.999396i	$0.511063\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	12.8339	+	22.2290i	0.455746	+	0.789375i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	20.6019	−	35.6836i	0.729757	−	1.26398i	−0.227229	−	0.973841i	$-0.572966\pi$
$797$	20.6019	−	35.6836i	0.729757	−	1.26398i	0.956986	−	0.290135i	$-0.0937002\pi$
$798$		0			0
$799$	35.5236	+	61.5288i	1.25674	+	2.17673i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	20.1166	−	34.8430i	0.709900	−	1.22958i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	10.7589	+	6.21165i	0.378262	+	0.218390i	0.677062	−	0.735926i	$-0.263253\pi$
$809$	10.7589	+	6.21165i	0.378262	+	0.218390i	−0.298800	+	0.954316i	$0.596586\pi$
$810$		0			0
$811$		−	32.8713i		−	1.15427i	−0.816650	−	0.577133i	$-0.804171\pi$
$811$		−	32.8713i		−	1.15427i	0.816650	−	0.577133i	$-0.195829\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1.56078	−	2.70336i	−0.0546719	−	0.0946944i
$816$		0			0
$817$	11.9656	+	6.90833i	0.418623	+	0.241692i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−11.7411	−	6.77873i	−0.409768	−	0.236579i	0.280922	−	0.959731i	$-0.409360\pi$
$821$	−11.7411	−	6.77873i	−0.409768	−	0.236579i	−0.690690	+	0.723151i	$0.742693\pi$
$822$		0			0
$823$	12.2565	+	21.2289i	0.427235	+	0.739993i	0.996626	−	0.0820737i	$-0.0261543\pi$
$823$	12.2565	+	21.2289i	0.427235	+	0.739993i	−0.569391	+	0.822067i	$0.692821\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			14.7323i			0.512292i	0.966638	+	0.256146i	$0.0824527\pi$
$827$			14.7323i			0.512292i	−0.966638	+	0.256146i	$0.917547\pi$
$828$		0			0
$829$	−11.7079	−	6.75957i	−0.406633	−	0.234770i	0.282709	−	0.959206i	$-0.408767\pi$
$829$	−11.7079	−	6.75957i	−0.406633	−	0.234770i	−0.689342	+	0.724436i	$0.742100\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.32255	−	2.29073i	0.0457689	−	0.0792740i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−0.511154	−	0.885345i	−0.0176470	−	0.0305655i	0.857067	−	0.515205i	$-0.172284\pi$
$839$	−0.511154	−	0.885345i	−0.0176470	−	0.0305655i	−0.874714	+	0.484639i	$0.838951\pi$
$840$		0			0
$841$	−13.5936	+	23.5449i	−0.468746	+	0.811892i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.13918	−	1.97312i	−0.0391890	−	0.0678773i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$	34.3082	−	19.8079i	1.17607	−	0.679005i
$852$		0			0
$853$	−8.70682	+	5.02689i	−0.298116	+	0.172117i	−0.641596	−	0.767043i	$-0.721727\pi$
$853$	−8.70682	+	5.02689i	−0.298116	+	0.172117i	0.343480	+	0.939160i	$0.388394\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	28.2543			0.965150			0.482575	−	0.875855i	$-0.339702\pi$
$857$	28.2543			0.965150			0.482575	+	0.875855i	$0.339702\pi$
$858$		0			0
$859$			31.1538i			1.06295i	0.847073	+	0.531476i	$0.178363\pi$
$859$			31.1538i			1.06295i	−0.847073	+	0.531476i	$0.821637\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−49.4703	+	28.5617i	−1.68399	+	0.972252i	−0.725026	+	0.688722i	$0.758172\pi$
$863$	−49.4703	+	28.5617i	−1.68399	+	0.972252i	−0.958963	+	0.283530i	$0.908495\pi$
$864$		0			0
$865$	1.57157	−	2.72204i	0.0534351	−	0.0925522i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2.56754	+	1.48237i	0.0870978	+	0.0502859i
$870$		0			0
$871$		−	13.9673i		−	0.473264i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−31.3382			−1.05822			−0.529108	−	0.848554i	$-0.677473\pi$
$877$	−31.3382			−1.05822			−0.529108	+	0.848554i	$0.677473\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	12.2822			0.413799			0.206900	−	0.978362i	$-0.433663\pi$
$881$	12.2822			0.413799			0.206900	+	0.978362i	$0.433663\pi$
$882$		0			0
$883$	3.61496			0.121653			0.0608266	−	0.998148i	$-0.480626\pi$
$883$	3.61496			0.121653			0.0608266	+	0.998148i	$0.480626\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	18.8853			0.634106			0.317053	−	0.948408i	$-0.397307\pi$
$887$	18.8853			0.634106			0.317053	+	0.948408i	$0.397307\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	65.8685i		−	2.20420i
$894$		0			0
$895$	−6.05795	−	3.49756i	−0.202495	−	0.116911i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.645760	−	1.11849i	0.0215373	−	0.0373037i
$900$		0			0
$901$	52.9075	−	30.5462i	1.76260	−	1.01764i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	12.5954i		−	0.418684i
$906$		0			0
$907$	−57.7603			−1.91790			−0.958950	−	0.283576i	$-0.908479\pi$
$907$	−57.7603			−1.91790			−0.958950	+	0.283576i	$0.908479\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	33.7810	−	19.5034i	1.11921	−	0.646178i	0.178013	−	0.984028i	$-0.443033\pi$
$911$	33.7810	−	19.5034i	1.11921	−	0.646178i	0.941200	+	0.337850i	$0.109700\pi$
$912$		0			0
$913$	22.5011	−	12.9910i	0.744679	−	0.429940i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	15.9047	+	27.5478i	0.524649	+	0.908719i	0.999588	+	0.0287001i	$0.00913677\pi$
$919$	15.9047	+	27.5478i	0.524649	+	0.908719i	−0.474939	+	0.880019i	$0.657530\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.843006	+	1.46013i	−0.0277479	+	0.0480607i
$924$		0			0
$925$	−16.5897	−	28.7342i	−0.545465	−	0.944774i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	19.0424	−	32.9825i	0.624762	−	1.08212i	−0.363824	−	0.931468i	$-0.618529\pi$
$929$	19.0424	−	32.9825i	0.624762	−	1.08212i	0.988587	−	0.150653i	$-0.0481375\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	16.1901	+	9.34735i	0.529472	+	0.305691i
$936$		0			0
$937$		−	37.6261i		−	1.22919i	−0.788842	−	0.614596i	$-0.789319\pi$
$937$		−	37.6261i		−	1.22919i	0.788842	−	0.614596i	$-0.210681\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.837737	−	1.45100i	−0.0273094	−	0.0473014i	0.852048	−	0.523464i	$-0.175361\pi$
$941$	−0.837737	−	1.45100i	−0.0273094	−	0.0473014i	−0.879357	+	0.476163i	$0.842027\pi$
$942$		0			0
$943$	23.2119	+	13.4014i	0.755884	+	0.436410i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	19.2331	+	11.1042i	0.624992	+	0.360839i	0.778810	−	0.627260i	$-0.215824\pi$
$947$	19.2331	+	11.1042i	0.624992	+	0.360839i	−0.153818	+	0.988099i	$0.549157\pi$
$948$		0			0
$949$	−17.8624	−	30.9386i	−0.579838	−	1.00431i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			27.1505i			0.879491i	0.898122	+	0.439746i	$0.144931\pi$
$953$			27.1505i			0.879491i	−0.898122	+	0.439746i	$0.855069\pi$
$954$		0			0
$955$	5.56803	+	3.21470i	0.180177	+	0.104025i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−15.0399	+	26.0499i	−0.485158	+	0.840319i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.75341	+	3.03700i	0.0564444	+	0.0977646i
$966$		0			0
$967$	−16.7553	+	29.0211i	−0.538815	+	0.933255i	0.460153	+	0.887840i	$0.347795\pi$
$967$	−16.7553	+	29.0211i	−0.538815	+	0.933255i	−0.998968	+	0.0454157i	$0.985539\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	17.8733	+	30.9574i	0.573580	+	0.993470i	0.996194	+	0.0871606i	$0.0277793\pi$
$971$	17.8733	+	30.9574i	0.573580	+	0.993470i	−0.422614	+	0.906310i	$0.638887\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−39.5696	+	22.8455i	−1.26594	+	0.730892i	−0.974218	−	0.225610i	$-0.927562\pi$
$977$	−39.5696	+	22.8455i	−1.26594	+	0.730892i	−0.291725	+	0.956502i	$0.594229\pi$
$978$		0			0
$979$	27.9665	−	16.1465i	0.893814	−	0.516044i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−18.6743			−0.595616			−0.297808	−	0.954626i	$-0.596256\pi$
$983$	−18.6743			−0.595616			−0.297808	+	0.954626i	$0.596256\pi$
$984$		0			0
$985$			1.71703i			0.0547092i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−9.98215	+	5.76320i	−0.317414	+	0.183259i
$990$		0			0
$991$	−24.2806	+	42.0552i	−0.771299	+	1.33593i	0.165553	+	0.986201i	$0.447059\pi$
$991$	−24.2806	+	42.0552i	−0.771299	+	1.33593i	−0.936851	+	0.349727i	$0.886274\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	7.54303	+	4.35497i	0.239130	+	0.138062i
$996$		0			0
$997$			52.1903i			1.65288i	0.563022	+	0.826442i	$0.309639\pi$
$997$			52.1903i			1.65288i	−0.563022	+	0.826442i	$0.690361\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5292.2.bm.b.2285.3		16
3.2	odd	2		1764.2.bm.b.1697.6		16
7.2	even	3		5292.2.w.a.1097.6		16
7.3	odd	6		756.2.x.a.125.3		16
7.4	even	3		756.2.x.a.125.6		16
7.5	odd	6		5292.2.w.a.1097.3		16
7.6	odd	2	inner	5292.2.bm.b.2285.6		16
9.2	odd	6		5292.2.w.a.521.3		16
9.7	even	3		1764.2.w.a.1109.3		16
21.2	odd	6		1764.2.w.a.509.6		16
21.5	even	6		1764.2.w.a.509.3		16
21.11	odd	6		252.2.x.a.41.1	✓	16
21.17	even	6		252.2.x.a.41.8	yes	16
21.20	even	2		1764.2.bm.b.1697.3		16
28.3	even	6		3024.2.cc.c.881.3		16
28.11	odd	6		3024.2.cc.c.881.6		16
63.2	odd	6	inner	5292.2.bm.b.4625.6		16
63.4	even	3		2268.2.f.b.1133.6		16
63.11	odd	6		756.2.x.a.629.3		16
63.16	even	3		1764.2.bm.b.1685.3		16
63.20	even	6		5292.2.w.a.521.6		16
63.25	even	3		252.2.x.a.209.8	yes	16
63.31	odd	6		2268.2.f.b.1133.11		16
63.32	odd	6		2268.2.f.b.1133.12		16
63.34	odd	6		1764.2.w.a.1109.6		16
63.38	even	6		756.2.x.a.629.6		16
63.47	even	6	inner	5292.2.bm.b.4625.3		16
63.52	odd	6		252.2.x.a.209.1	yes	16
63.59	even	6		2268.2.f.b.1133.5		16
63.61	odd	6		1764.2.bm.b.1685.6		16
84.11	even	6		1008.2.cc.c.545.8		16
84.59	odd	6		1008.2.cc.c.545.1		16
252.11	even	6		3024.2.cc.c.2897.3		16
252.115	even	6		1008.2.cc.c.209.8		16
252.151	odd	6		1008.2.cc.c.209.1		16
252.227	odd	6		3024.2.cc.c.2897.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.x.a.41.1	✓	16	21.11	odd	6
252.2.x.a.41.8	yes	16	21.17	even	6
252.2.x.a.209.1	yes	16	63.52	odd	6
252.2.x.a.209.8	yes	16	63.25	even	3
756.2.x.a.125.3		16	7.3	odd	6
756.2.x.a.125.6		16	7.4	even	3
756.2.x.a.629.3		16	63.11	odd	6
756.2.x.a.629.6		16	63.38	even	6
1008.2.cc.c.209.1		16	252.151	odd	6
1008.2.cc.c.209.8		16	252.115	even	6
1008.2.cc.c.545.1		16	84.59	odd	6
1008.2.cc.c.545.8		16	84.11	even	6
1764.2.w.a.509.3		16	21.5	even	6
1764.2.w.a.509.6		16	21.2	odd	6
1764.2.w.a.1109.3		16	9.7	even	3
1764.2.w.a.1109.6		16	63.34	odd	6
1764.2.bm.b.1685.3		16	63.16	even	3
1764.2.bm.b.1685.6		16	63.61	odd	6
1764.2.bm.b.1697.3		16	21.20	even	2
1764.2.bm.b.1697.6		16	3.2	odd	2
2268.2.f.b.1133.5		16	63.59	even	6
2268.2.f.b.1133.6		16	63.4	even	3
2268.2.f.b.1133.11		16	63.31	odd	6
2268.2.f.b.1133.12		16	63.32	odd	6
3024.2.cc.c.881.3		16	28.3	even	6
3024.2.cc.c.881.6		16	28.11	odd	6
3024.2.cc.c.2897.3		16	252.11	even	6
3024.2.cc.c.2897.6		16	252.227	odd	6
5292.2.w.a.521.3		16	9.2	odd	6
5292.2.w.a.521.6		16	63.20	even	6
5292.2.w.a.1097.3		16	7.5	odd	6
5292.2.w.a.1097.6		16	7.2	even	3
5292.2.bm.b.2285.3		16	1.1	even	1	trivial
5292.2.bm.b.2285.6		16	7.6	odd	2	inner
5292.2.bm.b.4625.3		16	63.47	even	6	inner
5292.2.bm.b.4625.6		16	63.2	odd	6	inner

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.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.553827 q^{5} +O(q^{10})\)	\(q-0.553827 q^{5} -4.65896i q^{11} +(-3.58265 - 2.06844i) q^{13} +(3.62264 - 6.27459i) q^{17} +(-5.81722 + 3.35857i) q^{19} -5.60371i q^{23} -4.69328 q^{25} +(-1.16599 + 0.673187i) q^{29} +(-0.830741 + 0.479629i) q^{31} +(3.53478 + 6.12241i) q^{37} +(-2.39152 + 4.14224i) q^{41} +(-1.02846 - 1.78135i) q^{43} +(-4.90301 + 8.49226i) q^{47} +(7.30235 + 4.21601i) q^{53} +2.58026i q^{55} +(3.89955 + 6.75422i) q^{59} +(-5.37336 - 3.10231i) q^{61} +(1.98417 + 1.14556i) q^{65} +(1.68814 + 2.92394i) q^{67} -0.407556i q^{71} +(7.47870 + 4.31783i) q^{73} +(-0.318176 + 0.551097i) q^{79} +(2.78840 + 4.82965i) q^{83} +(-2.00632 + 3.47504i) q^{85} +(3.46568 + 6.00274i) q^{89} +(3.22174 - 1.86007i) q^{95} +(-7.48798 + 4.32318i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 16 q^{25} + 12 q^{29} - 2 q^{37} + 4 q^{43} + 36 q^{53} - 24 q^{65} + 14 q^{67} + 20 q^{79} + 6 q^{85} - 60 q^{95}+O(q^{100}) \) 16 * q + 16 * q^25 + 12 * q^29 - 2 * q^37 + 4 * q^43 + 36 * q^53 - 24 * q^65 + 14 * q^67 + 20 * q^79 + 6 * q^85 - 60 * q^95

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