LMFDB - Embedded newform 1512.2.bs.a.521.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1512,2,Mod(521,1512)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1512, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1512.521"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.bs (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.6
Character	$\chi$	$=$	1512.521
Dual form			1512.2.bs.a.1097.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11415 + 1.92977i) q^{5} +(-0.553477 - 2.58721i) q^{7} +(-1.83714 + 1.06068i) q^{11} +(5.10339 - 2.94644i) q^{13} +(-2.34020 + 4.05335i) q^{17} +(-4.54550 + 2.62435i) q^{19} +(-3.77916 - 2.18190i) q^{23} +(0.0173374 + 0.0300292i) q^{25} +(2.25182 + 1.30009i) q^{29} +7.61221i q^{31} +(5.60937 + 1.81446i) q^{35} +(-1.80274 - 3.12244i) q^{37} +(0.0395039 + 0.0684228i) q^{41} +(-1.24922 + 2.16371i) q^{43} -3.79674 q^{47} +(-6.38733 + 2.86393i) q^{49} +(-4.08014 - 2.35567i) q^{53} -4.72701i q^{55} -13.1939 q^{59} +8.15939i q^{61} +13.1311i q^{65} -4.75228 q^{67} +10.0325i q^{71} +(-12.6610 - 7.30986i) q^{73} +(3.76101 + 4.16602i) q^{77} -14.5483 q^{79} +(6.41294 - 11.1075i) q^{83} +(-5.21468 - 9.03209i) q^{85} +(2.73464 + 4.73654i) q^{89} +(-10.4477 - 11.5728i) q^{91} -11.6957i q^{95} +(12.9290 + 7.46454i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{23} - 24 q^{25} - 18 q^{29} - 6 q^{41} - 6 q^{43} - 36 q^{47} + 6 q^{49} - 12 q^{53} + 36 q^{77} - 12 q^{79} - 18 q^{89} + 6 q^{91}+O(q^{100}) $ 48 * q + 12 * q^23 - 24 * q^25 - 18 * q^29 - 6 * q^41 - 6 * q^43 - 36 * q^47 + 6 * q^49 - 12 * q^53 + 36 * q^77 - 12 * q^79 - 18 * q^89 + 6 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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
$5$	−1.11415	+	1.92977i	−0.498263	+	0.863017i	−0.999998	−	0.00200427i	$-0.999362\pi$
$5$	−1.11415	+	1.92977i	−0.498263	+	0.863017i	0.501735	+	0.865022i	$0.332695\pi$
$6$		0			0
$7$	−0.553477	−	2.58721i	−0.209195	−	0.977874i
$7$	−0.553477	−	2.58721i	−0.209195	−	0.977874i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.83714	+	1.06068i	−0.553920	+	0.319806i	−0.750701	−	0.660642i	$-0.770284\pi$
$11$	−1.83714	+	1.06068i	−0.553920	+	0.319806i	0.196782	+	0.980447i	$0.436951\pi$
$12$		0			0
$13$	5.10339	−	2.94644i	1.41542	−	0.817196i	0.419533	−	0.907740i	$-0.362194\pi$
$13$	5.10339	−	2.94644i	1.41542	−	0.817196i	0.995892	+	0.0905443i	$0.0288607\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.34020	+	4.05335i	−0.567583	+	0.983082i	0.429222	+	0.903199i	$0.358788\pi$
$17$	−2.34020	+	4.05335i	−0.567583	+	0.983082i	−0.996804	+	0.0798828i	$0.974545\pi$
$18$		0			0
$19$	−4.54550	+	2.62435i	−1.04281	+	0.602066i	−0.920628	−	0.390442i	$-0.872322\pi$
$19$	−4.54550	+	2.62435i	−1.04281	+	0.602066i	−0.122181	+	0.992508i	$0.538989\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.77916	−	2.18190i	−0.788010	−	0.454958i	0.0512518	−	0.998686i	$-0.483679\pi$
$23$	−3.77916	−	2.18190i	−0.788010	−	0.454958i	−0.839261	+	0.543728i	$0.817012\pi$
$24$		0			0
$25$	0.0173374	+	0.0300292i	0.00346748	+	0.00600585i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.25182	+	1.30009i	0.418152	+	0.241420i	0.694286	−	0.719699i	$-0.255720\pi$
$29$	2.25182	+	1.30009i	0.418152	+	0.241420i	−0.276134	+	0.961119i	$0.589053\pi$
$30$		0			0
$31$			7.61221i			1.36719i	0.729860	+	0.683597i	$0.239585\pi$
$31$			7.61221i			1.36719i	−0.729860	+	0.683597i	$0.760415\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	5.60937	+	1.81446i	0.948156	+	0.306700i
$36$		0			0
$37$	−1.80274	−	3.12244i	−0.296369	−	0.513326i	0.678934	−	0.734200i	$-0.262442\pi$
$37$	−1.80274	−	3.12244i	−0.296369	−	0.513326i	−0.975302	+	0.220874i	$0.929109\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.0395039	+	0.0684228i	0.00616948	+	0.0106858i	0.869094	−	0.494648i	$-0.164703\pi$
$41$	0.0395039	+	0.0684228i	0.00616948	+	0.0106858i	−0.862924	+	0.505333i	$0.831370\pi$
$42$		0			0
$43$	−1.24922	+	2.16371i	−0.190504	+	0.329962i	−0.945417	−	0.325862i	$-0.894345\pi$
$43$	−1.24922	+	2.16371i	−0.190504	+	0.329962i	0.754914	+	0.655824i	$0.227679\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.79674			−0.553811			−0.276905	−	0.960897i	$-0.589309\pi$
$47$	−3.79674			−0.553811			−0.276905	+	0.960897i	$0.589309\pi$
$48$		0			0
$49$	−6.38733	+	2.86393i	−0.912475	+	0.409132i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.08014	−	2.35567i	−0.560451	−	0.323576i	0.192876	−	0.981223i	$-0.438219\pi$
$53$	−4.08014	−	2.35567i	−0.560451	−	0.323576i	−0.753326	+	0.657647i	$0.771552\pi$
$54$		0			0
$55$		−	4.72701i		−	0.637390i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−13.1939			−1.71770			−0.858849	−	0.512229i	$-0.828820\pi$
$59$	−13.1939			−1.71770			−0.858849	+	0.512229i	$0.828820\pi$
$60$		0			0
$61$			8.15939i			1.04470i	0.852730	+	0.522352i	$0.174945\pi$
$61$			8.15939i			1.04470i	−0.852730	+	0.522352i	$0.825055\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			13.1311i			1.62871i
$66$		0			0
$67$	−4.75228			−0.580583			−0.290292	−	0.956938i	$-0.593752\pi$
$67$	−4.75228			−0.580583			−0.290292	+	0.956938i	$0.593752\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			10.0325i			1.19064i	0.803490	+	0.595318i	$0.202974\pi$
$71$			10.0325i			1.19064i	−0.803490	+	0.595318i	$0.797026\pi$
$72$		0			0
$73$	−12.6610	−	7.30986i	−1.48186	−	0.855554i	−0.482075	−	0.876130i	$-0.660117\pi$
$73$	−12.6610	−	7.30986i	−1.48186	−	0.855554i	−0.999788	+	0.0205755i	$0.993450\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.76101	+	4.16602i	0.428607	+	0.474762i
$78$		0			0
$79$	−14.5483			−1.63681			−0.818405	−	0.574642i	$-0.805141\pi$
$79$	−14.5483			−1.63681			−0.818405	+	0.574642i	$0.805141\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.41294	−	11.1075i	0.703911	−	1.21921i	−0.263172	−	0.964749i	$-0.584769\pi$
$83$	6.41294	−	11.1075i	0.703911	−	1.21921i	0.967083	−	0.254461i	$-0.0818982\pi$
$84$		0			0
$85$	−5.21468	−	9.03209i	−0.565611	−	0.979667i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.73464	+	4.73654i	0.289871	+	0.502072i	0.973779	−	0.227497i	$-0.0730541\pi$
$89$	2.73464	+	4.73654i	0.289871	+	0.502072i	−0.683907	+	0.729569i	$0.739721\pi$
$90$		0			0
$91$	−10.4477	−	11.5728i	−1.09521	−	1.21315i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		−	11.6957i		−	1.19995i
$96$		0			0
$97$	12.9290	+	7.46454i	1.31274	+	0.757909i	0.982549	−	0.186006i	$-0.0595544\pi$
$97$	12.9290	+	7.46454i	1.31274	+	0.757909i	0.330188	+	0.943915i	$0.392888\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.63302	+	2.82847i	0.162492	+	0.281444i	0.935762	−	0.352633i	$-0.114714\pi$
$101$	1.63302	+	2.82847i	0.162492	+	0.281444i	−0.773270	+	0.634077i	$0.781380\pi$
$102$		0			0
$103$	4.12945	+	2.38414i	0.406887	+	0.234916i	0.689451	−	0.724332i	$-0.257852\pi$
$103$	4.12945	+	2.38414i	0.406887	+	0.234916i	−0.282564	+	0.959248i	$0.591185\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.39655	−	3.69305i	0.618378	−	0.357021i	−0.157859	−	0.987462i	$-0.550459\pi$
$107$	6.39655	−	3.69305i	0.618378	−	0.357021i	0.776237	+	0.630441i	$0.217126\pi$
$108$		0			0
$109$	−1.17349	+	2.03254i	−0.112400	+	0.194682i	−0.916737	−	0.399490i	$-0.869187\pi$
$109$	−1.17349	+	2.03254i	−0.112400	+	0.194682i	0.804338	+	0.594173i	$0.202520\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−11.8961	+	6.86824i	−1.11909	+	0.646109i	−0.941170	−	0.337935i	$-0.890272\pi$
$113$	−11.8961	+	6.86824i	−1.11909	+	0.646109i	−0.177925	+	0.984044i	$0.556938\pi$
$114$		0			0
$115$	8.42111	−	4.86193i	0.785272	−	0.453377i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	11.7821	+	3.81116i	1.08007	+	0.349369i
$120$		0			0
$121$	−3.24993	+	5.62905i	−0.295449	+	0.511732i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−11.2188			−1.00344
$126$		0			0
$127$	−5.97913			−0.530562			−0.265281	−	0.964171i	$-0.585465\pi$
$127$	−5.97913			−0.530562			−0.265281	+	0.964171i	$0.585465\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	10.4792	−	18.1506i	0.915576	−	1.58582i	0.109519	−	0.993985i	$-0.465069\pi$
$131$	10.4792	−	18.1506i	0.915576	−	1.58582i	0.806056	−	0.591839i	$-0.201598\pi$
$132$		0			0
$133$	9.30557	+	10.3077i	0.806895	+	0.893787i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.00063	−	1.73242i	0.256361	−	0.148010i	−0.366312	−	0.930492i	$-0.619380\pi$
$137$	3.00063	−	1.73242i	0.256361	−	0.148010i	0.622674	+	0.782482i	$0.286046\pi$
$138$		0			0
$139$	0.379607	−	0.219166i	0.0321979	−	0.0185895i	−0.483815	−	0.875170i	$-0.660749\pi$
$139$	0.379607	−	0.219166i	0.0321979	−	0.0185895i	0.516013	+	0.856581i	$0.327416\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−6.25044	+	10.8261i	−0.522688	+	0.905322i
$144$		0			0
$145$	−5.01773	+	2.89699i	−0.416700	+	0.240582i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	15.1560	+	8.75030i	1.24162	+	0.716852i	0.969425	−	0.245388i	$-0.0789154\pi$
$149$	15.1560	+	8.75030i	1.24162	+	0.716852i	0.272200	+	0.962241i	$0.412249\pi$
$150$		0			0
$151$	0.187420	+	0.324621i	0.0152520	+	0.0264172i	0.873551	−	0.486733i	$-0.161812\pi$
$151$	0.187420	+	0.324621i	0.0152520	+	0.0264172i	−0.858299	+	0.513150i	$0.828478\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−14.6898	−	8.48115i	−1.17991	−	0.681223i
$156$		0			0
$157$			20.3549i			1.62450i	0.583311	+	0.812249i	$0.301757\pi$
$157$			20.3549i			1.62450i	−0.583311	+	0.812249i	$0.698243\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−3.55336	+	10.9851i	−0.280044	+	0.865749i
$162$		0			0
$163$	−7.25400	−	12.5643i	−0.568177	−	0.984112i	−0.996746	−	0.0806027i	$-0.974316\pi$
$163$	−7.25400	−	12.5643i	−0.568177	−	0.984112i	0.428569	−	0.903509i	$-0.359018\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.62510	+	13.2071i	0.590048	+	1.02199i	0.994225	+	0.107313i	$0.0342246\pi$
$167$	7.62510	+	13.2071i	0.590048	+	1.02199i	−0.404177	+	0.914681i	$0.632442\pi$
$168$		0			0
$169$	10.8630	−	18.8153i	0.835619	−	1.44733i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.88136			−0.143037			−0.0715185	−	0.997439i	$-0.522785\pi$
$173$	−1.88136			−0.143037			−0.0715185	+	0.997439i	$0.522785\pi$
$174$		0			0
$175$	0.0680961	−	0.0614760i	0.00514758	−	0.00464715i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−8.64064	−	4.98867i	−0.645831	−	0.372871i	0.141026	−	0.990006i	$-0.454960\pi$
$179$	−8.64064	−	4.98867i	−0.645831	−	0.372871i	−0.786857	+	0.617135i	$0.788293\pi$
$180$		0			0
$181$			11.2828i			0.838641i	0.907838	+	0.419320i	$0.137732\pi$
$181$			11.2828i			0.838641i	−0.907838	+	0.419320i	$0.862268\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	8.03410			0.590679
$186$		0			0
$187$		−	9.92879i		−	0.726065i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			12.8654i			0.930907i	0.885072	+	0.465454i	$0.154109\pi$
$191$			12.8654i			0.930907i	−0.885072	+	0.465454i	$0.845891\pi$
$192$		0			0
$193$	−12.0372			−0.866458			−0.433229	−	0.901284i	$-0.642626\pi$
$193$	−12.0372			−0.866458			−0.433229	+	0.901284i	$0.642626\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	27.7262i		−	1.97541i	−0.156339	−	0.987703i	$-0.549969\pi$
$197$		−	27.7262i		−	1.97541i	0.156339	−	0.987703i	$-0.450031\pi$
$198$		0			0
$199$	0.382862	+	0.221045i	0.0271404	+	0.0156695i	0.513509	−	0.858084i	$-0.328345\pi$
$199$	0.382862	+	0.221045i	0.0271404	+	0.0156695i	−0.486368	+	0.873754i	$0.661679\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.11727	−	6.54550i	0.148603	−	0.459404i
$204$		0			0
$205$	−0.176053			−0.0122961
$206$		0			0
$207$		0			0
$208$		0			0
$209$	5.56716	−	9.64260i	0.385088	−	0.666993i
$210$		0			0
$211$	−0.219300	−	0.379839i	−0.0150972	−	0.0261492i	0.858378	−	0.513018i	$-0.171472\pi$
$211$	−0.219300	−	0.379839i	−0.0150972	−	0.0261492i	−0.873475	+	0.486868i	$0.838139\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2.78363	−	4.82139i	−0.189842	−	0.328816i
$216$		0			0
$217$	19.6944	−	4.21319i	1.33694	−	0.286010i
$218$		0			0
$219$		0			0
$220$		0			0
$221$			27.5811i			1.85531i
$222$		0			0
$223$	17.6417	+	10.1854i	1.18137	+	0.682066i	0.956332	−	0.292284i	$-0.0944151\pi$
$223$	17.6417	+	10.1854i	1.18137	+	0.682066i	0.225041	+	0.974349i	$0.427748\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.754935	−	1.30759i	−0.0501068	−	0.0867875i	0.839884	−	0.542766i	$-0.182623\pi$
$227$	−0.754935	−	1.30759i	−0.0501068	−	0.0867875i	−0.889991	+	0.455978i	$0.849290\pi$
$228$		0			0
$229$	18.3899	+	10.6174i	1.21524	+	0.701617i	0.963895	−	0.266281i	$-0.0857950\pi$
$229$	18.3899	+	10.6174i	1.21524	+	0.701617i	0.251341	+	0.967899i	$0.419128\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	9.85938	−	5.69231i	0.645909	−	0.372916i	−0.140978	−	0.990013i	$-0.545025\pi$
$233$	9.85938	−	5.69231i	0.645909	−	0.372916i	0.786887	+	0.617097i	$0.211691\pi$
$234$		0			0
$235$	4.23013	−	7.32681i	0.275944	−	0.477948i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−14.1401	+	8.16380i	−0.914648	+	0.528072i	−0.881924	−	0.471392i	$-0.843752\pi$
$239$	−14.1401	+	8.16380i	−0.914648	+	0.528072i	−0.0327241	+	0.999464i	$0.510418\pi$
$240$		0			0
$241$	20.7592	−	11.9853i	1.33722	−	0.772042i	0.350822	−	0.936442i	$-0.385902\pi$
$241$	20.7592	−	11.9853i	1.33722	−	0.772042i	0.986394	+	0.164400i	$0.0525688\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.58974	−	15.5169i	0.101564	−	0.991337i
$246$		0			0
$247$	−15.4650	+	26.7861i	−0.984012	+	1.70436i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	25.9828			1.64002			0.820009	−	0.572351i	$-0.193969\pi$
$251$	25.9828			1.64002			0.820009	+	0.572351i	$0.193969\pi$
$252$		0			0
$253$	9.25715			0.581992
$254$		0			0
$255$		0			0
$256$		0			0
$257$	0.979785	−	1.69704i	0.0611173	−	0.105858i	−0.833848	−	0.551994i	$-0.813867\pi$
$257$	0.979785	−	1.69704i	0.0611173	−	0.105858i	0.894965	+	0.446136i	$0.147200\pi$
$258$		0			0
$259$	−7.08063	+	6.39227i	−0.439969	+	0.397196i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	3.11722	−	1.79973i	0.192216	−	0.110976i	−0.400804	−	0.916164i	$-0.631269\pi$
$263$	3.11722	−	1.79973i	0.192216	−	0.110976i	0.593019	+	0.805188i	$0.297936\pi$
$264$		0			0
$265$	9.09179	−	5.24915i	0.558504	−	0.322453i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−4.06967	+	7.04888i	−0.248132	+	0.429778i	−0.963008	−	0.269474i	$-0.913150\pi$
$269$	−4.06967	+	7.04888i	−0.248132	+	0.429778i	0.714875	+	0.699252i	$0.246483\pi$
$270$		0			0
$271$	16.3378	−	9.43265i	0.992452	−	0.572992i	0.0864458	−	0.996257i	$-0.472449\pi$
$271$	16.3378	−	9.43265i	0.992452	−	0.572992i	0.906006	+	0.423264i	$0.139116\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.0637026	−	0.0367787i	−0.00384141	−	0.00221784i
$276$		0			0
$277$	−10.8340	−	18.7650i	−0.650950	−	1.12748i	−0.982893	−	0.184179i	$-0.941037\pi$
$277$	−10.8340	−	18.7650i	−0.650950	−	1.12748i	0.331943	−	0.943300i	$-0.392296\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−11.6851	−	6.74642i	−0.697077	−	0.402457i	0.109181	−	0.994022i	$-0.465177\pi$
$281$	−11.6851	−	6.74642i	−0.697077	−	0.402457i	−0.806258	+	0.591564i	$0.798511\pi$
$282$		0			0
$283$		−	2.03256i		−	0.120823i	−0.998174	−	0.0604115i	$-0.980759\pi$
$283$		−	2.03256i		−	0.120823i	0.998174	−	0.0604115i	$-0.0192413\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.155160	−	0.140075i	0.00915879	−	0.00826839i
$288$		0			0
$289$	−2.45310	−	4.24890i	−0.144300	−	0.249935i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−15.8661	−	27.4809i	−0.926908	−	1.60545i	−0.788463	−	0.615083i	$-0.789123\pi$
$293$	−15.8661	−	27.4809i	−0.926908	−	1.60545i	−0.138446	−	0.990370i	$-0.544211\pi$
$294$		0			0
$295$	14.7000	−	25.4611i	0.855866	−	1.48240i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−25.7154			−1.48716
$300$		0			0
$301$	6.28938	+	2.03442i	0.362514	+	0.117262i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−15.7457	−	9.09079i	−0.901597	−	0.520537i
$306$		0			0
$307$		−	0.266045i		−	0.0151840i	−0.999971	−	0.00759200i	$-0.997583\pi$
$307$		−	0.266045i		−	0.0151840i	0.999971	−	0.00759200i	$-0.00241663\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.36245			−0.247372			−0.123686	−	0.992321i	$-0.539472\pi$
$311$	−4.36245			−0.247372			−0.123686	+	0.992321i	$0.539472\pi$
$312$		0			0
$313$			15.4386i			0.872640i	0.899792	+	0.436320i	$0.143718\pi$
$313$			15.4386i			0.872640i	−0.899792	+	0.436320i	$0.856282\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	21.7248i		−	1.22019i	−0.792329	−	0.610094i	$-0.791132\pi$
$317$		−	21.7248i		−	1.22019i	0.792329	−	0.610094i	$-0.208868\pi$
$318$		0			0
$319$	−5.51589			−0.308831
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	24.5660i		−	1.36689i
$324$		0			0
$325$	0.176959	+	0.102167i	0.00981591	+	0.00566722i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	2.10141	+	9.82296i	0.115854	+	0.541557i
$330$		0			0
$331$	−15.1462			−0.832511			−0.416255	−	0.909248i	$-0.636658\pi$
$331$	−15.1462			−0.832511			−0.416255	+	0.909248i	$0.636658\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	5.29475	−	9.17078i	0.289283	−	0.501053i
$336$		0			0
$337$	3.75166	+	6.49807i	0.204366	+	0.353973i	0.949931	−	0.312461i	$-0.101153\pi$
$337$	3.75166	+	6.49807i	0.204366	+	0.353973i	−0.745564	+	0.666434i	$0.767820\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−8.07409	−	13.9847i	−0.437237	−	0.757316i
$342$		0			0
$343$	10.9448	+	14.9402i	0.590965	+	0.806697i
$344$		0			0
$345$		0			0
$346$		0			0
$347$			4.89571i			0.262816i	0.991328	+	0.131408i	$0.0419497\pi$
$347$			4.89571i			0.262816i	−0.991328	+	0.131408i	$0.958050\pi$
$348$		0			0
$349$	2.64213	+	1.52543i	0.141430	+	0.0816546i	0.569045	−	0.822306i	$-0.307313\pi$
$349$	2.64213	+	1.52543i	0.141430	+	0.0816546i	−0.427615	+	0.903961i	$0.640646\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	8.51890	+	14.7552i	0.453415	+	0.785338i	0.998596	−	0.0529806i	$-0.0168722\pi$
$353$	8.51890	+	14.7552i	0.453415	+	0.785338i	−0.545180	+	0.838319i	$0.683539\pi$
$354$		0			0
$355$	−19.3603	−	11.1777i	−1.02754	−	0.593250i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.27682	+	1.31452i	−0.120166	+	0.0693778i	−0.558878	−	0.829250i	$-0.688768\pi$
$359$	−2.27682	+	1.31452i	−0.120166	+	0.0693778i	0.438712	+	0.898628i	$0.355435\pi$
$360$		0			0
$361$	4.27438	−	7.40344i	0.224967	−	0.389655i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	28.2126	−	16.2886i	1.47672	−	0.852583i
$366$		0			0
$367$	16.2436	−	9.37824i	0.847908	−	0.489540i	−0.0120362	−	0.999928i	$-0.503831\pi$
$367$	16.2436	−	9.37824i	0.847908	−	0.489540i	0.859945	+	0.510387i	$0.170498\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−3.83635	+	11.8600i	−0.199174	+	0.615741i
$372$		0			0
$373$	−2.42980	+	4.20853i	−0.125810	+	0.217910i	−0.922049	−	0.387072i	$-0.873486\pi$
$373$	−2.42980	+	4.20853i	−0.125810	+	0.217910i	0.796239	+	0.604982i	$0.206820\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	15.3225			0.789151
$378$		0			0
$379$	−3.46902			−0.178192			−0.0890959	−	0.996023i	$-0.528398\pi$
$379$	−3.46902			−0.178192			−0.0890959	+	0.996023i	$0.528398\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	9.30298	−	16.1132i	0.475360	−	0.823348i	−0.524241	−	0.851570i	$-0.675651\pi$
$383$	9.30298	−	16.1132i	0.475360	−	0.823348i	0.999602	+	0.0282216i	$0.00898441\pi$
$384$		0			0
$385$	−12.2298	+	2.61629i	−0.623287	+	0.133339i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−13.4613	+	7.77186i	−0.682513	+	0.394049i	−0.800801	−	0.598930i	$-0.795593\pi$
$389$	−13.4613	+	7.77186i	−0.682513	+	0.394049i	0.118288	+	0.992979i	$0.462259\pi$
$390$		0			0
$391$	17.6880	−	10.2122i	0.894521	−	0.516452i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	16.2090	−	28.0748i	0.815562	−	1.41260i
$396$		0			0
$397$	−13.0507	+	7.53483i	−0.654996	+	0.378162i	−0.790368	−	0.612633i	$-0.790111\pi$
$397$	−13.0507	+	7.53483i	−0.654996	+	0.378162i	0.135371	+	0.990795i	$0.456777\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6.74463	+	3.89401i	0.336811	+	0.194458i	0.658861	−	0.752265i	$-0.271039\pi$
$401$	6.74463	+	3.89401i	0.336811	+	0.194458i	−0.322050	+	0.946723i	$0.604372\pi$
$402$		0			0
$403$	22.4289	+	38.8481i	1.11727	+	1.93516i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	6.62379	+	3.82425i	0.328329	+	0.189561i
$408$		0			0
$409$		−	8.99874i		−	0.444959i	−0.974937	−	0.222480i	$-0.928585\pi$
$409$		−	8.99874i		−	0.444959i	0.974937	−	0.222480i	$-0.0714151\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	7.30252	+	34.1354i	0.359334	+	1.67969i
$414$		0			0
$415$	14.2900	+	24.7509i	0.701466	+	1.21498i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−6.70022	−	11.6051i	−0.327327	−	0.566947i	0.654653	−	0.755929i	$-0.272815\pi$
$419$	−6.70022	−	11.6051i	−0.327327	−	0.566947i	−0.981981	+	0.188982i	$0.939481\pi$
$420$		0			0
$421$	9.44700	−	16.3627i	0.460419	−	0.797469i	−0.538563	−	0.842585i	$-0.681033\pi$
$421$	9.44700	−	16.3627i	0.460419	−	0.797469i	0.998982	+	0.0451166i	$0.0143659\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.162292			−0.00787232
$426$		0			0
$427$	21.1101	−	4.51604i	1.02159	−	0.218547i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	25.4056	+	14.6679i	1.22375	+	0.706530i	0.965714	−	0.259607i	$-0.0835931\pi$
$431$	25.4056	+	14.6679i	1.22375	+	0.706530i	0.258031	+	0.966137i	$0.416926\pi$
$432$		0			0
$433$			9.41744i			0.452573i	0.974061	+	0.226287i	$0.0726586\pi$
$433$			9.41744i			0.452573i	−0.974061	+	0.226287i	$0.927341\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	22.9042			1.09566
$438$		0			0
$439$		−	31.7980i		−	1.51764i	−0.651302	−	0.758819i	$-0.725777\pi$
$439$		−	31.7980i		−	1.51764i	0.651302	−	0.758819i	$-0.274223\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			37.0295i			1.75932i	0.475600	+	0.879662i	$0.342231\pi$
$443$			37.0295i			1.75932i	−0.475600	+	0.879662i	$0.657769\pi$
$444$		0			0
$445$	−12.1872			−0.577729
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	19.3840i		−	0.914789i	−0.889264	−	0.457394i	$-0.848783\pi$
$449$		−	19.3840i		−	0.914789i	0.889264	−	0.457394i	$-0.151217\pi$
$450$		0			0
$451$	−0.145149	−	0.0838017i	−0.00683479	−	0.00394607i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	33.9730	−	7.26778i	1.59268	−	0.340719i
$456$		0			0
$457$	10.5349			0.492803			0.246401	−	0.969168i	$-0.420752\pi$
$457$	10.5349			0.492803			0.246401	+	0.969168i	$0.420752\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	7.09138	−	12.2826i	0.330278	−	0.572059i	−0.652288	−	0.757971i	$-0.726191\pi$
$461$	7.09138	−	12.2826i	0.330278	−	0.572059i	0.982566	+	0.185912i	$0.0595240\pi$
$462$		0			0
$463$	5.05071	+	8.74808i	0.234726	+	0.406558i	0.959193	−	0.282752i	$-0.0912473\pi$
$463$	5.05071	+	8.74808i	0.234726	+	0.406558i	−0.724467	+	0.689310i	$0.757914\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	11.1047	+	19.2340i	0.513866	+	0.890042i	0.999871	+	0.0160858i	$0.00512048\pi$
$467$	11.1047	+	19.2340i	0.513866	+	0.890042i	−0.486005	+	0.873956i	$0.661546\pi$
$468$		0			0
$469$	2.63028	+	12.2951i	0.121455	+	0.567737i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		−	5.30005i		−	0.243697i
$474$		0			0
$475$	−0.157614	−	0.0909986i	−0.00723184	−	0.00417530i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	4.71275	+	8.16272i	0.215331	+	0.372964i	0.953375	−	0.301788i	$-0.0975836\pi$
$479$	4.71275	+	8.16272i	0.215331	+	0.372964i	−0.738044	+	0.674753i	$0.764250\pi$
$480$		0			0
$481$	−18.4002	−	10.6233i	−0.838975	−	0.484383i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−28.8096	+	16.6332i	−1.30818	+	0.755276i
$486$		0			0
$487$	14.6113	−	25.3076i	0.662103	−	1.14680i	−0.317959	−	0.948104i	$-0.602997\pi$
$487$	14.6113	−	25.3076i	0.662103	−	1.14680i	0.980062	−	0.198692i	$-0.0636692\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−6.31308	+	3.64486i	−0.284905	+	0.164490i	−0.635642	−	0.771984i	$-0.719265\pi$
$491$	−6.31308	+	3.64486i	−0.284905	+	0.164490i	0.350737	+	0.936474i	$0.385931\pi$
$492$		0			0
$493$	−10.5394	+	6.08494i	−0.474672	+	0.274052i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	25.9561	−	5.55275i	1.16429	−	0.249075i
$498$		0			0
$499$	−7.80996	+	13.5272i	−0.349622	+	0.605563i	−0.986182	−	0.165664i	$-0.947023\pi$
$499$	−7.80996	+	13.5272i	−0.349622	+	0.605563i	0.636561	+	0.771227i	$0.280357\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−6.09425			−0.271729			−0.135865	−	0.990727i	$-0.543381\pi$
$503$	−6.09425			−0.271729			−0.135865	+	0.990727i	$0.543381\pi$
$504$		0			0
$505$	−7.27772			−0.323854
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−14.1799	+	24.5604i	−0.628515	+	1.08862i	0.359335	+	0.933208i	$0.383003\pi$
$509$	−14.1799	+	24.5604i	−0.628515	+	1.08862i	−0.987850	+	0.155411i	$0.950330\pi$
$510$		0			0
$511$	−11.9045	+	36.8026i	−0.526626	+	1.62805i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−9.20167	+	5.31258i	−0.405474	+	0.234100i
$516$		0			0
$517$	6.97515	−	4.02710i	0.306767	−	0.177112i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	19.2896	−	33.4105i	0.845091	−	1.46374i	−0.0404517	−	0.999181i	$-0.512880\pi$
$521$	19.2896	−	33.4105i	0.845091	−	1.46374i	0.885542	−	0.464559i	$-0.153787\pi$
$522$		0			0
$523$	−24.1399	+	13.9372i	−1.05556	+	0.609429i	−0.924201	−	0.381905i	$-0.875268\pi$
$523$	−24.1399	+	13.9372i	−1.05556	+	0.609429i	−0.131361	+	0.991335i	$0.541935\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−30.8550	−	17.8141i	−1.34406	−	0.775996i
$528$		0			0
$529$	−1.97863	−	3.42708i	−0.0860273	−	0.149004i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.403208	+	0.232792i	0.0174649	+	0.0100833i
$534$		0			0
$535$			16.4585i			0.711561i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	8.69674	−	12.0363i	0.374595	−	0.518441i
$540$		0			0
$541$	−10.9182	−	18.9109i	−0.469410	−	0.813041i	0.529979	−	0.848011i	$-0.322200\pi$
$541$	−10.9182	−	18.9109i	−0.469410	−	0.813041i	−0.999388	+	0.0349697i	$0.988867\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2.61489	−	4.52912i	−0.112009	−	0.194006i
$546$		0			0
$547$	12.5173	−	21.6806i	0.535201	−	0.926995i	−0.463953	−	0.885860i	$-0.653569\pi$
$547$	12.5173	−	21.6806i	0.535201	−	0.926995i	0.999154	−	0.0411350i	$-0.0130974\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−13.6475			−0.581404
$552$		0			0
$553$	8.05215	+	37.6395i	0.342412	+	1.60059i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−11.1937	−	6.46267i	−0.474291	−	0.273832i	0.243743	−	0.969840i	$-0.421625\pi$
$557$	−11.1937	−	6.46267i	−0.474291	−	0.273832i	−0.718034	+	0.696008i	$0.754958\pi$
$558$		0			0
$559$			14.7230i			0.622715i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	15.6211			0.658352			0.329176	−	0.944269i	$-0.393229\pi$
$563$	15.6211			0.658352			0.329176	+	0.944269i	$0.393229\pi$
$564$		0			0
$565$		−	30.6090i		−	1.28773i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			42.6069i			1.78617i	0.449884	+	0.893087i	$0.351465\pi$
$569$			42.6069i			1.78617i	−0.449884	+	0.893087i	$0.648535\pi$
$570$		0			0
$571$	−19.7970			−0.828477			−0.414239	−	0.910168i	$-0.635952\pi$
$571$	−19.7970			−0.828477			−0.414239	+	0.910168i	$0.635952\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	0.151314i		−	0.00631022i
$576$		0			0
$577$	−40.6443	−	23.4660i	−1.69204	−	0.976902i	−0.952866	−	0.303391i	$-0.901881\pi$
$577$	−40.6443	−	23.4660i	−1.69204	−	0.976902i	−0.739178	−	0.673511i	$-0.764786\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−32.2870	−	10.4439i	−1.33949	−	0.433284i
$582$		0			0
$583$	9.99442			0.413927
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2.18063	−	3.77696i	0.0900041	−	0.155892i	−0.817509	−	0.575917i	$-0.804645\pi$
$587$	2.18063	−	3.77696i	0.0900041	−	0.155892i	0.907513	+	0.420025i	$0.137979\pi$
$588$		0			0
$589$	−19.9771	−	34.6013i	−0.823141	−	1.42572i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−2.31077	−	4.00236i	−0.0948918	−	0.164357i	0.814672	−	0.579922i	$-0.196917\pi$
$593$	−2.31077	−	4.00236i	−0.0948918	−	0.164357i	−0.909563	+	0.415565i	$0.863584\pi$
$594$		0			0
$595$	−20.4817	+	18.4905i	−0.839668	+	0.758038i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			25.5173i			1.04261i	0.853371	+	0.521304i	$0.174554\pi$
$599$			25.5173i			1.04261i	−0.853371	+	0.521304i	$0.825446\pi$
$600$		0			0
$601$	−22.6824	−	13.0957i	−0.925235	−	0.534185i	−0.0399336	−	0.999202i	$-0.512715\pi$
$601$	−22.6824	−	13.0957i	−0.925235	−	0.534185i	−0.885301	+	0.465018i	$0.846048\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−7.24183	−	12.5432i	−0.294422	−	0.509954i
$606$		0			0
$607$	−5.08757	−	2.93731i	−0.206498	−	0.119222i	0.393185	−	0.919459i	$-0.371373\pi$
$607$	−5.08757	−	2.93731i	−0.206498	−	0.119222i	−0.599683	+	0.800238i	$0.704707\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−19.3762	+	11.1869i	−0.783878	+	0.452572i
$612$		0			0
$613$	12.4511	−	21.5660i	0.502896	−	0.871041i	−0.497099	−	0.867694i	$-0.665601\pi$
$613$	12.4511	−	21.5660i	0.502896	−	0.871041i	0.999994	−	0.00334675i	$-0.00106531\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−26.1105	+	15.0749i	−1.05117	+	0.606894i	−0.922977	−	0.384855i	$-0.874251\pi$
$617$	−26.1105	+	15.0749i	−1.05117	+	0.606894i	−0.128194	+	0.991749i	$0.540918\pi$
$618$		0			0
$619$	−29.5953	+	17.0869i	−1.18954	+	0.686779i	−0.958201	−	0.286096i	$-0.907642\pi$
$619$	−29.5953	+	17.0869i	−1.18954	+	0.686779i	−0.231334	+	0.972874i	$0.574309\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	10.7409	−	9.69666i	0.430323	−	0.388489i
$624$		0			0
$625$	12.4127	−	21.4994i	0.496508	−	0.859978i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	16.8751			0.672855
$630$		0			0
$631$	8.55990			0.340764			0.170382	−	0.985378i	$-0.445500\pi$
$631$	8.55990			0.340764			0.170382	+	0.985378i	$0.445500\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	6.66165	−	11.5383i	0.264360	−	0.457884i
$636$		0			0
$637$	−24.1586	+	33.4356i	−0.957199	+	1.32477i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	35.0737	−	20.2498i	1.38533	−	0.799818i	0.392542	−	0.919734i	$-0.371596\pi$
$641$	35.0737	−	20.2498i	1.38533	−	0.799818i	0.992784	+	0.119916i	$0.0382624\pi$
$642$		0			0
$643$	31.8435	−	18.3849i	1.25579	−	0.725028i	0.283533	−	0.958963i	$-0.408493\pi$
$643$	31.8435	−	18.3849i	1.25579	−	0.725028i	0.972252	+	0.233935i	$0.0751602\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−23.5492	+	40.7884i	−0.925815	+	1.60356i	−0.135569	+	0.990768i	$0.543286\pi$
$647$	−23.5492	+	40.7884i	−0.925815	+	1.60356i	−0.790246	+	0.612790i	$0.790047\pi$
$648$		0			0
$649$	24.2391	−	13.9944i	0.951467	−	0.549330i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2.16748	+	1.25139i	0.0848199	+	0.0489708i	0.541810	−	0.840501i	$-0.317739\pi$
$653$	2.16748	+	1.25139i	0.0848199	+	0.0489708i	−0.456990	+	0.889472i	$0.651073\pi$
$654$		0			0
$655$	23.3509	+	40.4450i	0.912395	+	1.58032i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−36.2490	−	20.9284i	−1.41206	−	0.815254i	−0.416479	−	0.909146i	$-0.636736\pi$
$659$	−36.2490	−	20.9284i	−1.41206	−	0.815254i	−0.995582	+	0.0938917i	$0.970069\pi$
$660$		0			0
$661$			8.49304i			0.330341i	0.986265	+	0.165170i	$0.0528174\pi$
$661$			8.49304i			0.330341i	−0.986265	+	0.165170i	$0.947183\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−30.2592	+	6.47329i	−1.17340	+	0.251023i
$666$		0			0
$667$	−5.67333	−	9.82649i	−0.219672	−	0.380483i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−8.65447	−	14.9900i	−0.334102	−	0.578682i
$672$		0			0
$673$	−16.9974	+	29.4403i	−0.655201	+	1.13484i	0.326642	+	0.945148i	$0.394083\pi$
$673$	−16.9974	+	29.4403i	−0.655201	+	1.13484i	−0.981843	+	0.189694i	$0.939251\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	39.0351			1.50024			0.750121	−	0.661301i	$-0.229995\pi$
$677$	39.0351			1.50024			0.750121	+	0.661301i	$0.229995\pi$
$678$		0			0
$679$	12.1564	−	37.5814i	0.466522	−	1.44224i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.91400	+	1.10505i	0.0732373	+	0.0422836i	0.536171	−	0.844109i	$-0.319870\pi$
$683$	1.91400	+	1.10505i	0.0732373	+	0.0422836i	−0.462934	+	0.886393i	$0.653203\pi$
$684$		0			0
$685$			7.72069i			0.294992i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−27.7634			−1.05770
$690$		0			0
$691$		−	3.41836i		−	0.130041i	−0.997884	−	0.0650203i	$-0.979289\pi$
$691$		−	3.41836i		−	0.130041i	0.997884	−	0.0650203i	$-0.0207112\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			0.976737i			0.0370498i
$696$		0			0
$697$	−0.369789			−0.0140068
$698$		0			0
$699$		0			0
$700$		0			0
$701$			37.5732i			1.41912i	0.704645	+	0.709560i	$0.251106\pi$
$701$			37.5732i			1.41912i	−0.704645	+	0.709560i	$0.748894\pi$
$702$		0			0
$703$	16.3887	+	9.46203i	0.618112	+	0.356867i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.41402	−	5.79046i	0.241224	−	0.217773i
$708$		0			0
$709$	−26.8780			−1.00942			−0.504712	−	0.863288i	$-0.668401\pi$
$709$	−26.8780			−1.00942			−0.504712	+	0.863288i	$0.668401\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	16.6091	−	28.7678i	0.622015	−	1.07736i
$714$		0			0
$715$	−13.9279	−	24.1238i	−0.520872	−	0.902177i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.41278	−	2.44701i	−0.0526879	−	0.0912580i	0.838479	−	0.544935i	$-0.183446\pi$
$719$	−1.41278	−	2.44701i	−0.0526879	−	0.0912580i	−0.891166	+	0.453676i	$0.850112\pi$
$720$		0			0
$721$	3.88272	−	12.0033i	0.144600	−	0.447028i
$722$		0			0
$723$		0			0
$724$		0			0
$725$			0.0901606i			0.00334848i
$726$		0			0
$727$	−0.622076	−	0.359156i	−0.0230715	−	0.0133203i	0.488420	−	0.872609i	$-0.337573\pi$
$727$	−0.622076	−	0.359156i	−0.0230715	−	0.0133203i	−0.511491	+	0.859288i	$0.670907\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−5.84684	−	10.1270i	−0.216253	−	0.374561i
$732$		0			0
$733$	33.4490	+	19.3118i	1.23547	+	0.713297i	0.968164	−	0.250315i	$-0.0805343\pi$
$733$	33.4490	+	19.3118i	1.23547	+	0.713297i	0.267303	+	0.963613i	$0.413868\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	8.73062	−	5.04063i	0.321596	−	0.185674i
$738$		0			0
$739$	11.9491	−	20.6965i	0.439556	−	0.761334i	−0.558099	−	0.829775i	$-0.688469\pi$
$739$	11.9491	−	20.6965i	0.439556	−	0.761334i	0.997655	+	0.0684405i	$0.0218023\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−20.5325	+	11.8544i	−0.753264	+	0.434897i	−0.826872	−	0.562390i	$-0.809882\pi$
$743$	−20.5325	+	11.8544i	−0.753264	+	0.434897i	0.0736078	+	0.997287i	$0.476549\pi$
$744$		0			0
$745$	−33.7720	+	19.4983i	−1.23731	+	0.714362i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−13.0950	−	14.5052i	−0.478483	−	0.530009i
$750$		0			0
$751$	−6.89344	+	11.9398i	−0.251545	+	0.435689i	−0.963951	−	0.266078i	$-0.914272\pi$
$751$	−6.89344	+	11.9398i	−0.251545	+	0.435689i	0.712406	+	0.701767i	$0.247605\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−0.835255			−0.0303981
$756$		0			0
$757$	−19.6447			−0.714000			−0.357000	−	0.934104i	$-0.616200\pi$
$757$	−19.6447			−0.714000			−0.357000	+	0.934104i	$0.616200\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−26.4732	+	45.8529i	−0.959653	+	1.66217i	−0.236312	+	0.971677i	$0.575939\pi$
$761$	−26.4732	+	45.8529i	−0.959653	+	1.66217i	−0.723341	+	0.690491i	$0.757395\pi$
$762$		0			0
$763$	5.90812	+	1.91110i	0.213888	+	0.0691864i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−67.3335	+	38.8750i	−2.43127	+	1.40370i
$768$		0			0
$769$	−17.6774	+	10.2060i	−0.637462	+	0.368039i	−0.783636	−	0.621220i	$-0.786637\pi$
$769$	−17.6774	+	10.2060i	−0.637462	+	0.368039i	0.146174	+	0.989259i	$0.453304\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1.07789	−	1.86697i	0.0387692	−	0.0671501i	−0.845990	−	0.533199i	$-0.820990\pi$
$773$	1.07789	−	1.86697i	0.0387692	−	0.0671501i	0.884759	+	0.466049i	$0.154323\pi$
$774$		0			0
$775$	−0.228589	+	0.131976i	−0.00821116	+	0.00474072i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.359130	−	0.207344i	−0.0128672	−	0.00742887i
$780$		0			0
$781$	−10.6412	−	18.4311i	−0.380772	−	0.659517i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−39.2802	−	22.6784i	−1.40197	−	0.809428i
$786$		0			0
$787$			20.8939i			0.744786i	0.928075	+	0.372393i	$0.121463\pi$
$787$			20.8939i			0.744786i	−0.928075	+	0.372393i	$0.878537\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	24.3538	+	26.9764i	0.865922	+	0.959170i
$792$		0			0
$793$	24.0412	+	41.6405i	0.853727	+	1.47870i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	13.9964	+	24.2424i	0.495777	+	0.858710i	0.999988	−	0.00486976i	$-0.00155010\pi$
$797$	13.9964	+	24.2424i	0.495777	+	0.858710i	−0.504211	+	0.863580i	$0.668217\pi$
$798$		0			0
$799$	8.88513	−	15.3895i	0.314333	−	0.544441i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	31.0136			1.09444
$804$		0			0
$805$	−17.2397	−	19.0962i	−0.607621	−	0.673053i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−37.1345	−	21.4396i	−1.30558	−	0.753777i	−0.324225	−	0.945980i	$-0.605103\pi$
$809$	−37.1345	−	21.4396i	−1.30558	−	0.753777i	−0.981355	+	0.192203i	$0.938437\pi$
$810$		0			0
$811$			23.7421i			0.833699i	0.908976	+	0.416849i	$0.136866\pi$
$811$			23.7421i			0.833699i	−0.908976	+	0.416849i	$0.863134\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	32.3282			1.13241
$816$		0			0
$817$		−	13.1135i		−	0.458783i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		−	1.58699i		−	0.0553863i	−0.999616	−	0.0276932i	$-0.991184\pi$
$821$		−	1.58699i		−	0.0553863i	0.999616	−	0.0276932i	$-0.00881614\pi$
$822$		0			0
$823$	3.08203			0.107433			0.0537164	−	0.998556i	$-0.482893\pi$
$823$	3.08203			0.107433			0.0537164	+	0.998556i	$0.482893\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			20.7448i			0.721369i	0.932688	+	0.360685i	$0.117457\pi$
$827$			20.7448i			0.721369i	−0.932688	+	0.360685i	$0.882543\pi$
$828$		0			0
$829$	−0.917576	−	0.529763i	−0.0318687	−	0.0183994i	0.483981	−	0.875079i	$-0.339190\pi$
$829$	−0.917576	−	0.529763i	−0.0318687	−	0.0183994i	−0.515850	+	0.856679i	$0.672524\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	3.33914	−	32.5922i	0.115694	−	1.12925i
$834$		0			0
$835$	−33.9820			−1.17600
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−19.2137	+	33.2792i	−0.663332	+	1.14892i	0.316403	+	0.948625i	$0.397525\pi$
$839$	−19.2137	+	33.2792i	−0.663332	+	1.14892i	−0.979735	+	0.200299i	$0.935809\pi$
$840$		0			0
$841$	−11.1195	−	19.2596i	−0.383432	−	0.664124i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	24.2061	+	41.9262i	0.832716	+	1.44231i
$846$		0			0
$847$	16.3623	+	5.29271i	0.562216	+	0.181860i
$848$		0			0
$849$		0			0
$850$		0			0
$851$			15.7336i			0.539341i
$852$		0			0
$853$	12.0659	+	6.96626i	0.413129	+	0.238520i	0.692133	−	0.721770i	$-0.256671\pi$
$853$	12.0659	+	6.96626i	0.413129	+	0.238520i	−0.279004	+	0.960290i	$0.590004\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	13.4632	+	23.3189i	0.459894	+	0.796560i	0.998955	−	0.0457070i	$-0.0145541\pi$
$857$	13.4632	+	23.3189i	0.459894	+	0.796560i	−0.539061	+	0.842267i	$0.681221\pi$
$858$		0			0
$859$	−17.4938	−	10.1000i	−0.596880	−	0.344609i	0.170933	−	0.985283i	$-0.445322\pi$
$859$	−17.4938	−	10.1000i	−0.596880	−	0.344609i	−0.767813	+	0.640674i	$0.778655\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−38.1427	+	22.0217i	−1.29839	+	0.749627i	−0.980126	−	0.198374i	$-0.936434\pi$
$863$	−38.1427	+	22.0217i	−1.29839	+	0.749627i	−0.318266	+	0.948001i	$0.603101\pi$
$864$		0			0
$865$	2.09612	−	3.63058i	0.0712701	−	0.123443i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	26.7273	−	15.4310i	0.906662	−	0.523461i
$870$		0			0
$871$	−24.2527	+	14.0023i	−0.821772	+	0.474450i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	6.20934	+	29.0253i	0.209914	+	0.981235i
$876$		0			0
$877$	27.0436	−	46.8409i	0.913198	−	1.58170i	0.103678	−	0.994611i	$-0.466939\pi$
$877$	27.0436	−	46.8409i	0.913198	−	1.58170i	0.809519	−	0.587094i	$-0.199728\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	6.82593			0.229972			0.114986	−	0.993367i	$-0.463318\pi$
$881$	6.82593			0.229972			0.114986	+	0.993367i	$0.463318\pi$
$882$		0			0
$883$	−9.87685			−0.332382			−0.166191	−	0.986094i	$-0.553147\pi$
$883$	−9.87685			−0.332382			−0.166191	+	0.986094i	$0.553147\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−17.5412	+	30.3823i	−0.588977	+	1.02014i	0.405390	+	0.914144i	$0.367136\pi$
$887$	−17.5412	+	30.3823i	−0.588977	+	1.02014i	−0.994367	+	0.105994i	$0.966198\pi$
$888$		0			0
$889$	3.30931	+	15.4693i	0.110991	+	0.518823i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	17.2581	−	9.96395i	0.577519	−	0.333431i
$894$		0			0
$895$	19.2539	−	11.1163i	0.643588	−	0.371576i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−9.89655	+	17.1413i	−0.330069	+	0.571695i
$900$		0			0
$901$	19.0967	−	11.0255i	0.636204	−	0.367313i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−21.7731	−	12.5707i	−0.723761	−	0.417864i
$906$		0			0
$907$	−17.2231	−	29.8313i	−0.571885	−	0.990533i	−0.996372	−	0.0850994i	$-0.972879\pi$
$907$	−17.2231	−	29.8313i	−0.571885	−	0.990533i	0.424488	−	0.905434i	$-0.360454\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	45.9046	+	26.5030i	1.52089	+	0.878084i	0.999696	+	0.0246430i	$0.00784490\pi$
$911$	45.9046	+	26.5030i	1.52089	+	0.878084i	0.521190	+	0.853441i	$0.325488\pi$
$912$		0			0
$913$			27.2082i			0.900460i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−52.7594	−	17.0661i	−1.74227	−	0.563571i
$918$		0			0
$919$	5.73193	+	9.92799i	0.189079	+	0.327494i	0.944943	−	0.327234i	$-0.106116\pi$
$919$	5.73193	+	9.92799i	0.189079	+	0.327494i	−0.755865	+	0.654728i	$0.772783\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	29.5601	+	51.1996i	0.972983	+	1.68526i
$924$		0			0
$925$	0.0625096	−	0.108270i	0.00205530	−	0.00355989i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−34.7866			−1.14131			−0.570656	−	0.821189i	$-0.693311\pi$
$929$	−34.7866			−1.14131			−0.570656	+	0.821189i	$0.693311\pi$
$930$		0			0
$931$	21.5177	−	29.7805i	0.705213	−	0.976017i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	19.1602	+	11.0622i	0.626606	+	0.361771i
$936$		0			0
$937$			18.5180i			0.604956i	0.953156	+	0.302478i	$0.0978139\pi$
$937$			18.5180i			0.604956i	−0.953156	+	0.302478i	$0.902186\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	9.78447			0.318965			0.159482	−	0.987201i	$-0.449017\pi$
$941$	9.78447			0.318965			0.159482	+	0.987201i	$0.449017\pi$
$942$		0			0
$943$		−	0.344774i		−	0.0112274i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	33.5503i		−	1.09024i	−0.838359	−	0.545119i	$-0.816484\pi$
$947$		−	33.5503i		−	1.09024i	0.838359	−	0.545119i	$-0.183516\pi$
$948$		0			0
$949$	−86.1523			−2.79662
$950$		0			0
$951$		0			0
$952$		0			0
$953$			10.8871i			0.352668i	0.984330	+	0.176334i	$0.0564239\pi$
$953$			10.8871i			0.352668i	−0.984330	+	0.176334i	$0.943576\pi$
$954$		0			0
$955$	−24.8272	−	14.3340i	−0.803389	−	0.463837i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−6.14291	−	6.80442i	−0.198365	−	0.219726i
$960$		0			0
$961$	−26.9458			−0.869220
$962$		0			0
$963$		0			0
$964$		0			0
$965$	13.4113	−	23.2290i	0.431724	−	0.747768i
$966$		0			0
$967$	26.3931	+	45.7142i	0.848746	+	1.47007i	0.882328	+	0.470635i	$0.155975\pi$
$967$	26.3931	+	45.7142i	0.848746	+	1.47007i	−0.0335826	+	0.999436i	$0.510692\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−15.7931	−	27.3544i	−0.506824	−	0.877844i	−0.999969	−	0.00789735i	$-0.997486\pi$
$971$	−15.7931	−	27.3544i	−0.506824	−	0.877844i	0.493145	−	0.869947i	$-0.335847\pi$
$972$		0			0
$973$	−0.777134	−	0.860821i	−0.0249138	−	0.0275966i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	39.2654i		−	1.25621i	−0.778128	−	0.628106i	$-0.783831\pi$
$977$		−	39.2654i		−	1.25621i	0.778128	−	0.628106i	$-0.216169\pi$
$978$		0			0
$979$	−10.0479	−	5.80113i	−0.321131	−	0.185405i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	19.9170	+	34.4973i	0.635255	+	1.10029i	0.986461	+	0.163996i	$0.0524383\pi$
$983$	19.9170	+	34.4973i	0.635255	+	1.10029i	−0.351206	+	0.936298i	$0.614228\pi$
$984$		0			0
$985$	53.5050	+	30.8911i	1.70481	+	0.984273i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	9.44198	−	5.45133i	0.300237	−	0.173342i
$990$		0			0
$991$	−19.9472	+	34.5496i	−0.633645	+	1.09750i	0.353156	+	0.935565i	$0.385109\pi$
$991$	−19.9472	+	34.5496i	−0.633645	+	1.09750i	−0.986801	+	0.161940i	$0.948225\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−0.853132	+	0.492556i	−0.0270461	+	0.0156151i
$996$		0			0
$997$	25.6084	−	14.7850i	0.811026	−	0.468246i	−0.0362863	−	0.999341i	$-0.511553\pi$
$997$	25.6084	−	14.7850i	0.811026	−	0.468246i	0.847312	+	0.531096i	$0.178219\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.bs.a.521.6		48
3.2	odd	2		504.2.bs.a.353.14	yes	48
4.3	odd	2		3024.2.ca.e.2033.6		48
7.5	odd	6		1512.2.cx.a.89.6		48
9.4	even	3		504.2.cx.a.185.22	yes	48
9.5	odd	6		1512.2.cx.a.17.6		48
12.11	even	2		1008.2.ca.e.353.11		48
21.5	even	6		504.2.cx.a.425.22	yes	48
28.19	even	6		3024.2.df.e.1601.6		48
36.23	even	6		3024.2.df.e.17.6		48
36.31	odd	6		1008.2.df.e.689.3		48
63.5	even	6	inner	1512.2.bs.a.1097.6		48
63.40	odd	6		504.2.bs.a.257.14	✓	48
84.47	odd	6		1008.2.df.e.929.3		48
252.103	even	6		1008.2.ca.e.257.11		48
252.131	odd	6		3024.2.ca.e.2609.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.14	✓	48	63.40	odd	6
504.2.bs.a.353.14	yes	48	3.2	odd	2
504.2.cx.a.185.22	yes	48	9.4	even	3
504.2.cx.a.425.22	yes	48	21.5	even	6
1008.2.ca.e.257.11		48	252.103	even	6
1008.2.ca.e.353.11		48	12.11	even	2
1008.2.df.e.689.3		48	36.31	odd	6
1008.2.df.e.929.3		48	84.47	odd	6
1512.2.bs.a.521.6		48	1.1	even	1	trivial
1512.2.bs.a.1097.6		48	63.5	even	6	inner
1512.2.cx.a.17.6		48	9.5	odd	6
1512.2.cx.a.89.6		48	7.5	odd	6
3024.2.ca.e.2033.6		48	4.3	odd	2
3024.2.ca.e.2609.6		48	252.131	odd	6
3024.2.df.e.17.6		48	36.23	even	6
3024.2.df.e.1601.6		48	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.bs (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.11415 + 1.92977i) q^{5} +(-0.553477 - 2.58721i) q^{7} +(-1.83714 + 1.06068i) q^{11} +(5.10339 - 2.94644i) q^{13} +(-2.34020 + 4.05335i) q^{17} +(-4.54550 + 2.62435i) q^{19} +(-3.77916 - 2.18190i) q^{23} +(0.0173374 + 0.0300292i) q^{25} +(2.25182 + 1.30009i) q^{29} +7.61221i q^{31} +(5.60937 + 1.81446i) q^{35} +(-1.80274 - 3.12244i) q^{37} +(0.0395039 + 0.0684228i) q^{41} +(-1.24922 + 2.16371i) q^{43} -3.79674 q^{47} +(-6.38733 + 2.86393i) q^{49} +(-4.08014 - 2.35567i) q^{53} -4.72701i q^{55} -13.1939 q^{59} +8.15939i q^{61} +13.1311i q^{65} -4.75228 q^{67} +10.0325i q^{71} +(-12.6610 - 7.30986i) q^{73} +(3.76101 + 4.16602i) q^{77} -14.5483 q^{79} +(6.41294 - 11.1075i) q^{83} +(-5.21468 - 9.03209i) q^{85} +(2.73464 + 4.73654i) q^{89} +(-10.4477 - 11.5728i) q^{91} -11.6957i q^{95} +(12.9290 + 7.46454i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{23} - 24 q^{25} - 18 q^{29} - 6 q^{41} - 6 q^{43} - 36 q^{47} + 6 q^{49} - 12 q^{53} + 36 q^{77} - 12 q^{79} - 18 q^{89} + 6 q^{91}+O(q^{100}) \) 48 * q + 12 * q^23 - 24 * q^25 - 18 * q^29 - 6 * q^41 - 6 * q^43 - 36 * q^47 + 6 * q^49 - 12 * q^53 + 36 * q^77 - 12 * q^79 - 18 * q^89 + 6 * q^91

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