LMFDB - Embedded newform 3024.2.ca.e.2609.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(2033,3024)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3024, 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("3024.2033"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.ca (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$24.1467615712$
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			2609.16
Character	$\chi$	$=$	3024.2609
Dual form			3024.2.ca.e.2033.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.537427 + 0.930850i) q^{5} +(1.37797 + 2.25858i) q^{7} +(3.55011 + 2.04966i) q^{11} +(3.69867 + 2.13543i) q^{13} +(0.717607 + 1.24293i) q^{17} +(-6.41973 - 3.70644i) q^{19} +(5.43530 - 3.13807i) q^{23} +(1.92235 - 3.32960i) q^{25} +(8.09846 - 4.67565i) q^{29} +6.88527i q^{31} +(-1.36185 + 2.49651i) q^{35} +(-0.453413 + 0.785334i) q^{37} +(3.88978 - 6.73730i) q^{41} +(6.32181 + 10.9497i) q^{43} -8.43528 q^{47} +(-3.20241 + 6.22451i) q^{49} +(1.50593 - 0.869452i) q^{53} +4.40616i q^{55} -6.10146 q^{59} -2.72573i q^{61} +4.59055i q^{65} -12.0391 q^{67} -0.783113i q^{71} +(-1.95868 + 1.13085i) q^{73} +(0.262612 + 10.8426i) q^{77} -1.63543 q^{79} +(-4.48646 - 7.77077i) q^{83} +(-0.771322 + 1.33597i) q^{85} +(1.71834 - 2.97625i) q^{89} +(0.273602 + 11.2963i) q^{91} -7.96775i q^{95} +(-5.05015 + 2.91570i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.537427	+	0.930850i	0.240345	+	0.416289i	0.960812	−	0.277199i	$-0.0894063\pi$
$5$	0.537427	+	0.930850i	0.240345	+	0.416289i	−0.720468	+	0.693488i	$0.756073\pi$
$6$		0			0
$7$	1.37797	+	2.25858i	0.520823	+	0.853665i
$7$	1.37797	+	2.25858i	0.520823	+	0.853665i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.55011	+	2.04966i	1.07040	+	0.617994i	0.928290	−	0.371857i	$-0.121279\pi$
$11$	3.55011	+	2.04966i	1.07040	+	0.617994i	0.142108	+	0.989851i	$0.454612\pi$
$12$		0			0
$13$	3.69867	+	2.13543i	1.02583	+	0.592262i	0.915787	−	0.401665i	$-0.131568\pi$
$13$	3.69867	+	2.13543i	1.02583	+	0.592262i	0.110041	+	0.993927i	$0.464902\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.717607	+	1.24293i	0.174045	+	0.301455i	0.939830	−	0.341641i	$-0.110983\pi$
$17$	0.717607	+	1.24293i	0.174045	+	0.301455i	−0.765785	+	0.643096i	$0.777649\pi$
$18$		0			0
$19$	−6.41973	−	3.70644i	−1.47279	−	0.850315i	−0.473257	−	0.880925i	$-0.656922\pi$
$19$	−6.41973	−	3.70644i	−1.47279	−	0.850315i	−0.999531	+	0.0306101i	$0.990255\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	5.43530	−	3.13807i	1.13334	−	0.654334i	0.188567	−	0.982060i	$-0.439616\pi$
$23$	5.43530	−	3.13807i	1.13334	−	0.654334i	0.944773	+	0.327727i	$0.106283\pi$
$24$		0			0
$25$	1.92235	−	3.32960i	0.384469	−	0.665920i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	8.09846	−	4.67565i	1.50385	−	0.868246i	0.503856	−	0.863788i	$-0.331914\pi$
$29$	8.09846	−	4.67565i	1.50385	−	0.868246i	0.999990	−	0.00445828i	$-0.00141912\pi$
$30$		0			0
$31$			6.88527i			1.23663i	0.785930	+	0.618316i	$0.212185\pi$
$31$			6.88527i			1.23663i	−0.785930	+	0.618316i	$0.787815\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.36185	+	2.49651i	−0.230194	+	0.421986i
$36$		0			0
$37$	−0.453413	+	0.785334i	−0.0745406	+	0.129108i	−0.900886	−	0.434055i	$-0.857082\pi$
$37$	−0.453413	+	0.785334i	−0.0745406	+	0.129108i	0.826346	+	0.563163i	$0.190416\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.88978	−	6.73730i	0.607482	−	1.05219i	−0.384172	−	0.923262i	$-0.625513\pi$
$41$	3.88978	−	6.73730i	0.607482	−	1.05219i	0.991654	−	0.128928i	$-0.0411537\pi$
$42$		0			0
$43$	6.32181	+	10.9497i	0.964067	+	1.66981i	0.712102	+	0.702076i	$0.247743\pi$
$43$	6.32181	+	10.9497i	0.964067	+	1.66981i	0.251965	+	0.967736i	$0.418923\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−8.43528			−1.23041			−0.615206	−	0.788366i	$-0.710927\pi$
$47$	−8.43528			−1.23041			−0.615206	+	0.788366i	$0.710927\pi$
$48$		0			0
$49$	−3.20241	+	6.22451i	−0.457487	+	0.889216i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.50593	−	0.869452i	0.206856	−	0.119428i	−0.392993	−	0.919541i	$-0.628560\pi$
$53$	1.50593	−	0.869452i	0.206856	−	0.119428i	0.599849	+	0.800113i	$0.295227\pi$
$54$		0			0
$55$			4.40616i			0.594126i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.10146			−0.794342			−0.397171	−	0.917745i	$-0.630008\pi$
$59$	−6.10146			−0.794342			−0.397171	+	0.917745i	$0.630008\pi$
$60$		0			0
$61$		−	2.72573i		−	0.348994i	−0.984658	−	0.174497i	$-0.944170\pi$
$61$		−	2.72573i		−	0.348994i	0.984658	−	0.174497i	$-0.0558299\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			4.59055i			0.569388i
$66$		0			0
$67$	−12.0391			−1.47081			−0.735403	−	0.677630i	$-0.763007\pi$
$67$	−12.0391			−1.47081			−0.735403	+	0.677630i	$0.763007\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	0.783113i		−	0.0929385i	−0.998920	−	0.0464692i	$-0.985203\pi$
$71$		−	0.783113i		−	0.0929385i	0.998920	−	0.0464692i	$-0.0147969\pi$
$72$		0			0
$73$	−1.95868	+	1.13085i	−0.229247	+	0.132356i	−0.610224	−	0.792229i	$-0.708921\pi$
$73$	−1.95868	+	1.13085i	−0.229247	+	0.132356i	0.380978	+	0.924584i	$0.375587\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.262612	+	10.8426i	0.0299274	+	1.23563i
$78$		0			0
$79$	−1.63543			−0.184000			−0.0919999	−	0.995759i	$-0.529326\pi$
$79$	−1.63543			−0.184000			−0.0919999	+	0.995759i	$0.529326\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.48646	−	7.77077i	−0.492452	−	0.852953i	0.507510	−	0.861646i	$-0.330566\pi$
$83$	−4.48646	−	7.77077i	−0.492452	−	0.852953i	−0.999962	+	0.00869330i	$0.997233\pi$
$84$		0			0
$85$	−0.771322	+	1.33597i	−0.0836616	+	0.144906i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.71834	−	2.97625i	0.182144	−	0.315482i	−0.760467	−	0.649377i	$-0.775030\pi$
$89$	1.71834	−	2.97625i	0.182144	−	0.315482i	0.942610	+	0.333895i	$0.108363\pi$
$90$		0			0
$91$	0.273602	+	11.2963i	0.0286813	+	1.18418i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		−	7.96775i		−	0.817474i
$96$		0			0
$97$	−5.05015	+	2.91570i	−0.512765	+	0.296045i	−0.733969	−	0.679182i	$-0.762334\pi$
$97$	−5.05015	+	2.91570i	−0.512765	+	0.296045i	0.221205	+	0.975227i	$0.429001\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.31220	−	4.00485i	0.230073	−	0.398497i	−0.727757	−	0.685835i	$-0.759437\pi$
$101$	2.31220	−	4.00485i	0.230073	−	0.398497i	0.957829	+	0.287338i	$0.0927703\pi$
$102$		0			0
$103$	3.68450	−	2.12724i	0.363044	−	0.209604i	−0.307371	−	0.951590i	$-0.599449\pi$
$103$	3.68450	−	2.12724i	0.363044	−	0.209604i	0.670415	+	0.741986i	$0.266116\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.73964	+	5.04583i	0.844893	+	0.487799i	0.858924	−	0.512102i	$-0.171133\pi$
$107$	8.73964	+	5.04583i	0.844893	+	0.487799i	−0.0140314	+	0.999902i	$0.504466\pi$
$108$		0			0
$109$	0.548395	+	0.949848i	0.0525267	+	0.0909790i	0.891093	−	0.453820i	$-0.149939\pi$
$109$	0.548395	+	0.949848i	0.0525267	+	0.0909790i	−0.838567	+	0.544799i	$0.816606\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	8.51839	+	4.91809i	0.801343	+	0.462655i	0.843940	−	0.536437i	$-0.180230\pi$
$113$	8.51839	+	4.91809i	0.801343	+	0.462655i	−0.0425979	+	0.999092i	$0.513563\pi$
$114$		0			0
$115$	5.84215	+	3.37297i	0.544784	+	0.314531i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.81843	+	3.33350i	−0.166695	+	0.305581i
$120$		0			0
$121$	2.90217	+	5.02671i	0.263834	+	0.456974i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	9.50674			0.850309
$126$		0			0
$127$	−15.2201			−1.35056			−0.675282	−	0.737559i	$-0.735978\pi$
$127$	−15.2201			−1.35056			−0.675282	+	0.737559i	$0.735978\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.45441	+	7.71526i	0.389184	+	0.674086i	0.992340	−	0.123537i	$-0.0394238\pi$
$131$	4.45441	+	7.71526i	0.389184	+	0.674086i	−0.603156	+	0.797623i	$0.706090\pi$
$132$		0			0
$133$	−0.474887	−	19.6069i	−0.0411779	−	1.70013i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.76339	+	5.63689i	0.834143	+	0.481592i	0.855269	−	0.518184i	$-0.173392\pi$
$137$	9.76339	+	5.63689i	0.834143	+	0.481592i	−0.0211264	+	0.999777i	$0.506725\pi$
$138$		0			0
$139$	12.0468	+	6.95522i	1.02180	+	0.589934i	0.914624	−	0.404306i	$-0.132487\pi$
$139$	12.0468	+	6.95522i	1.02180	+	0.589934i	0.107172	+	0.994240i	$0.465820\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	8.75380	+	15.1620i	0.732029	+	1.26791i
$144$		0			0
$145$	8.70466	+	5.02564i	0.722882	+	0.417356i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.09504	+	1.78692i	−0.253555	+	0.146390i	−0.621391	−	0.783501i	$-0.713432\pi$
$149$	−3.09504	+	1.78692i	−0.253555	+	0.146390i	0.367836	+	0.929891i	$0.380099\pi$
$150$		0			0
$151$	3.30180	−	5.71888i	0.268696	−	0.465396i	−0.699829	−	0.714310i	$-0.746741\pi$
$151$	3.30180	−	5.71888i	0.268696	−	0.465396i	0.968525	+	0.248915i	$0.0800739\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.40916	+	3.70033i	−0.514796	+	0.297217i
$156$		0			0
$157$			9.19553i			0.733883i	0.930244	+	0.366942i	$0.119595\pi$
$157$			9.19553i			0.733883i	−0.930244	+	0.366942i	$0.880405\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	14.5773	+	7.95193i	1.14885	+	0.626700i
$162$		0			0
$163$	−3.64872	+	6.31976i	−0.285790	+	0.495002i	−0.972800	−	0.231645i	$-0.925589\pi$
$163$	−3.64872	+	6.31976i	−0.285790	+	0.495002i	0.687011	+	0.726647i	$0.258923\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.07118	+	12.2476i	−0.547184	+	0.947751i	0.451282	+	0.892382i	$0.350967\pi$
$167$	−7.07118	+	12.2476i	−0.547184	+	0.947751i	−0.998466	+	0.0553694i	$0.982366\pi$
$168$		0			0
$169$	2.62013	+	4.53820i	0.201549	+	0.349092i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−13.4985			−1.02627			−0.513134	−	0.858308i	$-0.671516\pi$
$173$	−13.4985			−1.02627			−0.513134	+	0.858308i	$0.671516\pi$
$174$		0			0
$175$	10.1691	−	0.246300i	0.768713	−	0.0186186i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.97036	−	2.29229i	0.296759	−	0.171334i	−0.344227	−	0.938886i	$-0.611859\pi$
$179$	3.97036	−	2.29229i	0.296759	−	0.171334i	0.640986	+	0.767553i	$0.278526\pi$
$180$		0			0
$181$		−	2.22901i		−	0.165681i	−0.996563	−	0.0828405i	$-0.973601\pi$
$181$		−	2.22901i		−	0.165681i	0.996563	−	0.0828405i	$-0.0263992\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.974704			−0.0716617
$186$		0			0
$187$			5.88339i			0.430236i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	21.0351i		−	1.52204i	−0.648726	−	0.761022i	$-0.724698\pi$
$191$		−	21.0351i		−	1.52204i	0.648726	−	0.761022i	$-0.275302\pi$
$192$		0			0
$193$	−11.2043			−0.806500			−0.403250	−	0.915090i	$-0.632119\pi$
$193$	−11.2043			−0.806500			−0.403250	+	0.915090i	$0.632119\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			20.8945i			1.48867i	0.667805	+	0.744336i	$0.267234\pi$
$197$			20.8945i			1.48867i	−0.667805	+	0.744336i	$0.732766\pi$
$198$		0			0
$199$	15.8521	−	9.15222i	1.12373	−	0.648784i	0.181377	−	0.983414i	$-0.441945\pi$
$199$	15.8521	−	9.15222i	1.12373	−	0.648784i	0.942350	+	0.334630i	$0.108611\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	21.7198	+	11.8482i	1.52443	+	0.831578i
$204$		0			0
$205$	8.36189			0.584020
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−15.1938	−	26.3165i	−1.05098	−	1.82035i
$210$		0			0
$211$	−5.93845	+	10.2857i	−0.408820	+	0.708096i	−0.994758	−	0.102260i	$-0.967393\pi$
$211$	−5.93845	+	10.2857i	−0.408820	+	0.708096i	0.585938	+	0.810356i	$0.300726\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−6.79502	+	11.7693i	−0.463416	+	0.802660i
$216$		0			0
$217$	−15.5510	+	9.48768i	−1.05567	+	0.644066i
$218$		0			0
$219$		0			0
$220$		0			0
$221$			6.12960i			0.412321i
$222$		0			0
$223$	4.19957	−	2.42462i	0.281224	−	0.162365i	−0.352754	−	0.935716i	$-0.614755\pi$
$223$	4.19957	−	2.42462i	0.281224	−	0.162365i	0.633977	+	0.773352i	$0.281421\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.43645	−	2.48801i	0.0953408	−	0.165135i	−0.814410	−	0.580290i	$-0.802939\pi$
$227$	1.43645	−	2.48801i	0.0953408	−	0.165135i	0.909751	+	0.415155i	$0.136273\pi$
$228$		0			0
$229$	3.74833	−	2.16410i	0.247697	−	0.143008i	−0.371013	−	0.928628i	$-0.620989\pi$
$229$	3.74833	−	2.16410i	0.247697	−	0.143008i	0.618709	+	0.785620i	$0.287656\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−11.9136	−	6.87834i	−0.780488	−	0.450615i	0.0561154	−	0.998424i	$-0.482129\pi$
$233$	−11.9136	−	6.87834i	−0.780488	−	0.450615i	−0.836603	+	0.547809i	$0.815462\pi$
$234$		0			0
$235$	−4.53335	−	7.85198i	−0.295723	−	0.512207i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−15.6571	−	9.03963i	−1.01277	−	0.584725i	−0.100771	−	0.994910i	$-0.532131\pi$
$239$	−15.6571	−	9.03963i	−1.01277	−	0.584725i	−0.912003	+	0.410184i	$0.865464\pi$
$240$		0			0
$241$	−5.17659	−	2.98871i	−0.333454	−	0.192520i	0.323920	−	0.946085i	$-0.394999\pi$
$241$	−5.17659	−	2.98871i	−0.333454	−	0.192520i	−0.657373	+	0.753565i	$0.728333\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.51515	+	0.364254i	−0.480125	+	0.0232713i
$246$		0			0
$247$	−15.8297	−	27.4178i	−1.00722	−	1.74455i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	11.0004			0.694337			0.347169	−	0.937803i	$-0.387143\pi$
$251$	11.0004			0.694337			0.347169	+	0.937803i	$0.387143\pi$
$252$		0			0
$253$	25.7279			1.61750
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.74280	−	8.21477i	−0.295848	−	0.512423i	0.679334	−	0.733829i	$-0.262269\pi$
$257$	−4.74280	−	8.21477i	−0.295848	−	0.512423i	−0.975182	+	0.221406i	$0.928935\pi$
$258$		0			0
$259$	−2.39853	+	0.0580935i	−0.149037	+	0.00360975i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	16.3241	+	9.42470i	1.00658	+	0.581152i	0.910190	−	0.414192i	$-0.135936\pi$
$263$	16.3241	+	9.42470i	1.00658	+	0.581152i	0.0963945	+	0.995343i	$0.469269\pi$
$264$		0			0
$265$	1.61866	+	0.934533i	0.0994334	+	0.0574079i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	10.0233	+	17.3609i	0.611133	+	1.05851i	0.991050	+	0.133493i	$0.0426194\pi$
$269$	10.0233	+	17.3609i	0.611133	+	1.05851i	−0.379916	+	0.925021i	$0.624047\pi$
$270$		0			0
$271$	−17.3369	−	10.0095i	−1.05314	−	0.608032i	−0.129615	−	0.991564i	$-0.541374\pi$
$271$	−17.3369	−	10.0095i	−1.05314	−	0.608032i	−0.923528	+	0.383532i	$0.874708\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	13.6491	−	7.88029i	0.823069	−	0.475199i
$276$		0			0
$277$	1.70372	−	2.95093i	0.102367	−	0.177304i	−0.810293	−	0.586026i	$-0.800692\pi$
$277$	1.70372	−	2.95093i	0.102367	−	0.177304i	0.912659	+	0.408721i	$0.134025\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−16.0313	+	9.25568i	−0.956347	+	0.552147i	−0.895047	−	0.445972i	$-0.852858\pi$
$281$	−16.0313	+	9.25568i	−0.956347	+	0.552147i	−0.0613004	+	0.998119i	$0.519525\pi$
$282$		0			0
$283$		−	25.1116i		−	1.49273i	−0.665535	−	0.746366i	$-0.731797\pi$
$283$		−	25.1116i		−	1.49273i	0.665535	−	0.746366i	$-0.268203\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	20.5768	−	0.498378i	1.21461	−	0.0294183i
$288$		0			0
$289$	7.47008	−	12.9386i	0.439417	−	0.761092i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.11299	−	1.92775i	0.0650214	−	0.112620i	−0.831682	−	0.555252i	$-0.812622\pi$
$293$	1.11299	−	1.92775i	0.0650214	−	0.112620i	0.896703	+	0.442632i	$0.145955\pi$
$294$		0			0
$295$	−3.27909	−	5.67955i	−0.190916	−	0.330676i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	26.8046			1.55015
$300$		0			0
$301$	−16.0196	+	29.3667i	−0.923352	+	1.69267i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2.53725	−	1.46488i	0.145282	−	0.0838788i
$306$		0			0
$307$			24.2535i			1.38422i	0.721791	+	0.692111i	$0.243319\pi$
$307$			24.2535i			1.38422i	−0.721791	+	0.692111i	$0.756681\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−19.6300			−1.11312			−0.556559	−	0.830808i	$-0.687879\pi$
$311$	−19.6300			−1.11312			−0.556559	+	0.830808i	$0.687879\pi$
$312$		0			0
$313$			17.1547i			0.969643i	0.874613	+	0.484822i	$0.161115\pi$
$313$			17.1547i			0.969643i	−0.874613	+	0.484822i	$0.838885\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	12.4507i		−	0.699300i	−0.936880	−	0.349650i	$-0.886301\pi$
$317$		−	12.4507i		−	0.699300i	0.936880	−	0.349650i	$-0.113699\pi$
$318$		0			0
$319$	38.3339			2.14628
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	10.6391i		−	0.591973i
$324$		0			0
$325$	14.2203	−	8.21007i	0.788798	−	0.455413i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−11.6235	−	19.0518i	−0.640827	−	1.05036i
$330$		0			0
$331$	30.9175			1.69938			0.849691	−	0.527281i	$-0.176789\pi$
$331$	30.9175			1.69938			0.849691	+	0.527281i	$0.176789\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−6.47011	−	11.2066i	−0.353500	−	0.612280i
$336$		0			0
$337$	−1.06492	+	1.84450i	−0.0580099	+	0.100476i	−0.893572	−	0.448920i	$-0.851809\pi$
$337$	−1.06492	+	1.84450i	−0.0580099	+	0.100476i	0.835562	+	0.549396i	$0.185142\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−14.1124	+	24.4434i	−0.764231	+	1.32369i
$342$		0			0
$343$	−18.4714	+	1.34426i	−0.997362	+	0.0725832i
$344$		0			0
$345$		0			0
$346$		0			0
$347$			23.0026i			1.23485i	0.786631	+	0.617423i	$0.211823\pi$
$347$			23.0026i			1.23485i	−0.786631	+	0.617423i	$0.788177\pi$
$348$		0			0
$349$	−21.3306	+	12.3152i	−1.14180	+	0.659219i	−0.946876	−	0.321599i	$-0.895780\pi$
$349$	−21.3306	+	12.3152i	−1.14180	+	0.659219i	−0.194925	+	0.980818i	$0.562446\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.62190	+	2.80921i	−0.0863248	+	0.149519i	−0.905955	−	0.423374i	$-0.860846\pi$
$353$	−1.62190	+	2.80921i	−0.0863248	+	0.149519i	0.819630	+	0.572893i	$0.194179\pi$
$354$		0			0
$355$	0.728961	−	0.420866i	0.0386892	−	0.0223372i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.88399	+	2.81977i	0.257767	+	0.148822i	0.623316	−	0.781970i	$-0.285785\pi$
$359$	4.88399	+	2.81977i	0.257767	+	0.148822i	−0.365548	+	0.930792i	$0.619119\pi$
$360$		0			0
$361$	17.9753	+	31.1342i	0.946070	+	1.63864i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.10530	−	1.21549i	−0.110196	−	0.0636219i
$366$		0			0
$367$	−10.8668	−	6.27396i	−0.567243	−	0.327498i	0.188804	−	0.982015i	$-0.439539\pi$
$367$	−10.8668	−	6.27396i	−0.567243	−	0.327498i	−0.756048	+	0.654517i	$0.772872\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	4.03886	+	2.20320i	0.209687	+	0.114385i
$372$		0			0
$373$	6.58770	+	11.4102i	0.341098	+	0.590799i	0.984637	−	0.174614i	$-0.0558678\pi$
$373$	6.58770	+	11.4102i	0.341098	+	0.590799i	−0.643539	+	0.765414i	$0.722534\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	39.9381			2.05692
$378$		0			0
$379$	6.80285			0.349439			0.174720	−	0.984618i	$-0.444098\pi$
$379$	6.80285			0.349439			0.174720	+	0.984618i	$0.444098\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−9.82982	−	17.0257i	−0.502280	−	0.869975i	−0.999997	−	0.00263511i	$-0.999161\pi$
$383$	−9.82982	−	17.0257i	−0.502280	−	0.869975i	0.497716	−	0.867340i	$-0.334172\pi$
$384$		0			0
$385$	−9.95168	+	6.07154i	−0.507185	+	0.309434i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	15.8135	+	9.12995i	0.801778	+	0.462907i	0.844092	−	0.536198i	$-0.180140\pi$
$389$	15.8135	+	9.12995i	0.801778	+	0.462907i	−0.0423145	+	0.999104i	$0.513473\pi$
$390$		0			0
$391$	7.80082	+	4.50381i	0.394504	+	0.227767i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.878921	−	1.52234i	−0.0442233	−	0.0765970i
$396$		0			0
$397$	−31.8395	−	18.3825i	−1.59798	−	0.922593i	−0.991876	−	0.127206i	$-0.959399\pi$
$397$	−31.8395	−	18.3825i	−1.59798	−	0.922593i	−0.606101	−	0.795387i	$-0.707267\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−13.8175	+	7.97753i	−0.690012	+	0.398379i	−0.803617	−	0.595147i	$-0.797094\pi$
$401$	−13.8175	+	7.97753i	−0.690012	+	0.398379i	0.113604	+	0.993526i	$0.463760\pi$
$402$		0			0
$403$	−14.7030	+	25.4664i	−0.732410	+	1.26857i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.21933	+	1.85868i	−0.159576	+	0.0921313i
$408$		0			0
$409$		−	9.84803i		−	0.486954i	−0.969907	−	0.243477i	$-0.921712\pi$
$409$		−	9.84803i		−	0.486954i	0.969907	−	0.243477i	$-0.0782880\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−8.40761	−	13.7807i	−0.413712	−	0.678102i
$414$		0			0
$415$	4.82228	−	8.35244i	0.236716	−	0.410005i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−19.4482	+	33.6853i	−0.950106	+	1.64563i	−0.204917	+	0.978779i	$0.565692\pi$
$419$	−19.4482	+	33.6853i	−0.950106	+	1.64563i	−0.745189	+	0.666853i	$0.767641\pi$
$420$		0			0
$421$	−8.99598	−	15.5815i	−0.438437	−	0.759396i	0.559132	−	0.829079i	$-0.311135\pi$
$421$	−8.99598	−	15.5815i	−0.438437	−	0.759396i	−0.997569	+	0.0696829i	$0.977801\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	5.51795			0.267660
$426$		0			0
$427$	6.15629	−	3.75597i	0.297924	−	0.181764i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	6.23236	−	3.59826i	0.300202	−	0.173322i	−0.342331	−	0.939579i	$-0.611217\pi$
$431$	6.23236	−	3.59826i	0.300202	−	0.173322i	0.642534	+	0.766257i	$0.277883\pi$
$432$		0			0
$433$		−	26.5567i		−	1.27623i	−0.769939	−	0.638117i	$-0.779714\pi$
$433$		−	26.5567i		−	1.27623i	0.769939	−	0.638117i	$-0.220286\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−46.5243			−2.22556
$438$		0			0
$439$		−	26.6825i		−	1.27349i	−0.771076	−	0.636744i	$-0.780281\pi$
$439$		−	26.6825i		−	1.27349i	0.771076	−	0.636744i	$-0.219719\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	38.1169i		−	1.81099i	−0.424359	−	0.905494i	$-0.639501\pi$
$443$		−	38.1169i		−	1.81099i	0.424359	−	0.905494i	$-0.360499\pi$
$444$		0			0
$445$	3.69392			0.175109
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	21.5864i		−	1.01872i	−0.860552	−	0.509362i	$-0.829881\pi$
$449$		−	21.5864i		−	1.01872i	0.860552	−	0.509362i	$-0.170119\pi$
$450$		0			0
$451$	27.6183	−	15.9454i	1.30049	−	0.750841i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−10.3681	+	6.32563i	−0.486066	+	0.296550i
$456$		0			0
$457$	2.85522			0.133562			0.0667809	−	0.997768i	$-0.478727\pi$
$457$	2.85522			0.133562			0.0667809	+	0.997768i	$0.478727\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−13.3315	−	23.0909i	−0.620911	−	1.07545i	−0.989316	−	0.145784i	$-0.953429\pi$
$461$	−13.3315	−	23.0909i	−0.620911	−	1.07545i	0.368405	−	0.929665i	$-0.379904\pi$
$462$		0			0
$463$	3.63687	−	6.29925i	0.169020	−	0.292751i	−0.769056	−	0.639182i	$-0.779273\pi$
$463$	3.63687	−	6.29925i	0.169020	−	0.292751i	0.938076	+	0.346431i	$0.112606\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.37755	−	4.11804i	0.110020	−	0.190560i	−0.805758	−	0.592245i	$-0.798242\pi$
$467$	2.37755	−	4.11804i	0.110020	−	0.190560i	0.915778	+	0.401685i	$0.131575\pi$
$468$		0			0
$469$	−16.5894	−	27.1912i	−0.766029	−	1.25557i
$470$		0			0
$471$		0			0
$472$		0			0
$473$			51.8301i			2.38315i
$474$		0			0
$475$	−24.6819	+	14.2501i	−1.13248	+	0.653839i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	9.90097	−	17.1490i	0.452387	−	0.783557i	−0.546147	−	0.837689i	$-0.683906\pi$
$479$	9.90097	−	17.1490i	0.452387	−	0.783557i	0.998534	+	0.0541324i	$0.0172393\pi$
$480$		0			0
$481$	−3.35405	+	1.93646i	−0.152932	+	0.0882951i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−5.42817	−	3.13395i	−0.246480	−	0.142306i
$486$		0			0
$487$	−17.0806	−	29.5845i	−0.773996	−	1.34060i	−0.935357	−	0.353704i	$-0.884922\pi$
$487$	−17.0806	−	29.5845i	−0.773996	−	1.34060i	0.161362	−	0.986895i	$-0.448411\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−9.91208	−	5.72274i	−0.447326	−	0.258264i	0.259374	−	0.965777i	$-0.416484\pi$
$491$	−9.91208	−	5.72274i	−0.447326	−	0.258264i	−0.706700	+	0.707513i	$0.749817\pi$
$492$		0			0
$493$	11.6230	+	6.71055i	0.523474	+	0.302228i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.76873	−	1.07910i	0.0793383	−	0.0484045i
$498$		0			0
$499$	3.88151	+	6.72298i	0.173760	+	0.300962i	0.939732	−	0.341913i	$-0.111075\pi$
$499$	3.88151	+	6.72298i	0.173760	+	0.300962i	−0.765971	+	0.642875i	$0.777742\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	2.92995			0.130640			0.0653200	−	0.997864i	$-0.479193\pi$
$503$	2.92995			0.130640			0.0653200	+	0.997864i	$0.479193\pi$
$504$		0			0
$505$	4.97055			0.221187
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−5.81338	−	10.0691i	−0.257673	−	0.446303i	0.707945	−	0.706268i	$-0.249623\pi$
$509$	−5.81338	−	10.0691i	−0.257673	−	0.446303i	−0.965618	+	0.259964i	$0.916289\pi$
$510$		0			0
$511$	−5.25312	−	2.86558i	−0.232384	−	0.126766i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.96029	+	2.28648i	0.174511	+	0.100754i
$516$		0			0
$517$	−29.9462	−	17.2894i	−1.31703	−	0.760388i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−12.7515	−	22.0863i	−0.558655	−	0.967619i	−0.997609	−	0.0691093i	$-0.977984\pi$
$521$	−12.7515	−	22.0863i	−0.558655	−	0.967619i	0.438954	−	0.898509i	$-0.355349\pi$
$522$		0			0
$523$	−0.781452	−	0.451172i	−0.0341705	−	0.0197284i	0.482817	−	0.875721i	$-0.339613\pi$
$523$	−0.781452	−	0.451172i	−0.0341705	−	0.0197284i	−0.516988	+	0.855993i	$0.672947\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−8.55792	+	4.94092i	−0.372789	+	0.215230i
$528$		0			0
$529$	8.19501	−	14.1942i	0.356305	−	0.617138i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	28.7741	−	16.6127i	1.24634	−	0.719577i
$534$		0			0
$535$			10.8471i			0.468959i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−24.1270	+	15.5339i	−1.03922	+	0.669090i
$540$		0			0
$541$	−17.2460	+	29.8710i	−0.741464	+	1.28425i	0.210365	+	0.977623i	$0.432535\pi$
$541$	−17.2460	+	29.8710i	−0.741464	+	1.28425i	−0.951829	+	0.306630i	$0.900799\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.589444	+	1.02095i	−0.0252490	+	0.0437326i
$546$		0			0
$547$	−3.68664	−	6.38545i	−0.157629	−	0.273022i	0.776384	−	0.630260i	$-0.217052\pi$
$547$	−3.68664	−	6.38545i	−0.157629	−	0.273022i	−0.934013	+	0.357238i	$0.883718\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−69.3199			−2.95313
$552$		0			0
$553$	−2.25356	−	3.69375i	−0.0958312	−	0.157074i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	18.6335	−	10.7581i	0.789528	−	0.455834i	−0.0502687	−	0.998736i	$-0.516008\pi$
$557$	18.6335	−	10.7581i	0.789528	−	0.455834i	0.839796	+	0.542902i	$0.182674\pi$
$558$		0			0
$559$			53.9991i			2.28392i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	31.5550			1.32988			0.664942	−	0.746895i	$-0.268456\pi$
$563$	31.5550			1.32988			0.664942	+	0.746895i	$0.268456\pi$
$564$		0			0
$565$			10.5725i			0.444787i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	23.5719i		−	0.988184i	−0.869410	−	0.494092i	$-0.835501\pi$
$569$		−	23.5719i		−	0.988184i	0.869410	−	0.494092i	$-0.164499\pi$
$570$		0			0
$571$	−15.6689			−0.655723			−0.327861	−	0.944726i	$-0.606328\pi$
$571$	−15.6689			−0.655723			−0.327861	+	0.944726i	$0.606328\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	24.1298i		−	1.00628i
$576$		0			0
$577$	0.137448	−	0.0793554i	0.00572202	−	0.00330361i	−0.497136	−	0.867672i	$-0.665615\pi$
$577$	0.137448	−	0.0793554i	0.00572202	−	0.00330361i	0.502858	+	0.864369i	$0.332282\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	11.3688	−	20.8409i	0.471655	−	0.864627i
$582$		0			0
$583$	7.12831			0.295224
$584$		0			0
$585$		0			0
$586$		0			0
$587$	15.9041	+	27.5467i	0.656432	+	1.13697i	0.981533	+	0.191294i	$0.0612683\pi$
$587$	15.9041	+	27.5467i	0.656432	+	1.13697i	−0.325101	+	0.945679i	$0.605398\pi$
$588$		0			0
$589$	25.5198	−	44.2016i	1.05153	−	1.82130i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−15.8934	+	27.5283i	−0.652666	+	1.13045i	0.329808	+	0.944048i	$0.393016\pi$
$593$	−15.8934	+	27.5283i	−0.652666	+	1.13045i	−0.982474	+	0.186402i	$0.940317\pi$
$594$		0			0
$595$	−4.08026	+	0.0988256i	−0.167274	+	0.00405145i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	12.1844i		−	0.497842i	−0.968524	−	0.248921i	$-0.919924\pi$
$599$		−	12.1844i		−	0.497842i	0.968524	−	0.248921i	$-0.0800760\pi$
$600$		0			0
$601$	13.6048	−	7.85473i	0.554951	−	0.320401i	−0.196165	−	0.980571i	$-0.562849\pi$
$601$	13.6048	−	7.85473i	0.554951	−	0.320401i	0.751117	+	0.660170i	$0.229516\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−3.11941	+	5.40298i	−0.126822	+	0.219662i
$606$		0			0
$607$	−10.9361	+	6.31398i	−0.443884	+	0.256277i	−0.705244	−	0.708965i	$-0.749162\pi$
$607$	−10.9361	+	6.31398i	−0.443884	+	0.256277i	0.261360	+	0.965241i	$0.415829\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−31.1994	−	18.0130i	−1.26219	−	0.728727i
$612$		0			0
$613$	11.3476	+	19.6546i	0.458325	+	0.793842i	0.998873	−	0.0474711i	$-0.0151162\pi$
$613$	11.3476	+	19.6546i	0.458325	+	0.793842i	−0.540547	+	0.841314i	$0.681783\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	32.6259	+	18.8366i	1.31347	+	0.758333i	0.982669	−	0.185368i	$-0.0593476\pi$
$617$	32.6259	+	18.8366i	1.31347	+	0.758333i	0.330801	+	0.943700i	$0.392681\pi$
$618$		0			0
$619$	−4.50897	−	2.60326i	−0.181231	−	0.104634i	0.406640	−	0.913588i	$-0.366700\pi$
$619$	−4.50897	−	2.60326i	−0.181231	−	0.104634i	−0.587871	+	0.808955i	$0.700034\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	9.08993	−	0.220162i	0.364180	−	0.00882061i
$624$		0			0
$625$	−4.50255	−	7.79864i	−0.180102	−	0.311946i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−1.30149			−0.0518937
$630$		0			0
$631$	5.73635			0.228361			0.114180	−	0.993460i	$-0.463576\pi$
$631$	5.73635			0.228361			0.114180	+	0.993460i	$0.463576\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−8.17968	−	14.1676i	−0.324601	−	0.562225i
$636$		0			0
$637$	−25.1367	+	16.1839i	−0.995952	+	0.641230i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−23.0328	−	13.2980i	−0.909743	−	0.525240i	−0.0293943	−	0.999568i	$-0.509358\pi$
$641$	−23.0328	−	13.2980i	−0.909743	−	0.525240i	−0.880348	+	0.474328i	$0.842691\pi$
$642$		0			0
$643$	−22.7885	−	13.1569i	−0.898689	−	0.518858i	−0.0219144	−	0.999760i	$-0.506976\pi$
$643$	−22.7885	−	13.1569i	−0.898689	−	0.518858i	−0.876775	+	0.480901i	$0.840309\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−23.8420	−	41.2955i	−0.937324	−	1.62349i	−0.770436	−	0.637517i	$-0.779961\pi$
$647$	−23.8420	−	41.2955i	−0.937324	−	1.62349i	−0.166888	−	0.985976i	$-0.553372\pi$
$648$		0			0
$649$	−21.6608	−	12.5059i	−0.850262	−	0.490899i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−28.3370	+	16.3604i	−1.10891	+	0.640231i	−0.938548	−	0.345149i	$-0.887828\pi$
$653$	−28.3370	+	16.3604i	−1.10891	+	0.640231i	−0.170366	+	0.985381i	$0.554495\pi$
$654$		0			0
$655$	−4.78784	+	8.29278i	−0.187076	+	0.324026i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	26.5499	−	15.3286i	1.03424	−	0.597118i	0.116043	−	0.993244i	$-0.462979\pi$
$659$	26.5499	−	15.3286i	1.03424	−	0.597118i	0.918196	+	0.396126i	$0.129646\pi$
$660$		0			0
$661$		−	10.8025i		−	0.420167i	−0.977683	−	0.210084i	$-0.932626\pi$
$661$		−	10.8025i		−	0.420167i	0.977683	−	0.210084i	$-0.0673736\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	17.9958	−	10.9793i	0.697849	−	0.425759i
$666$		0			0
$667$	29.3451	−	50.8271i	1.13624	−	1.96803i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.58681	−	9.67663i	0.215676	−	0.373562i
$672$		0			0
$673$	19.4199	+	33.6363i	0.748583	+	1.29658i	0.948502	+	0.316771i	$0.102599\pi$
$673$	19.4199	+	33.6363i	0.748583	+	1.29658i	−0.199919	+	0.979812i	$0.564068\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	18.8638			0.724996			0.362498	−	0.931984i	$-0.381924\pi$
$677$	18.8638			0.724996			0.362498	+	0.931984i	$0.381924\pi$
$678$		0			0
$679$	−13.5443	−	7.38844i	−0.519783	−	0.283542i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	29.7510	−	17.1768i	1.13839	−	0.657251i	0.192360	−	0.981325i	$-0.438386\pi$
$683$	29.7510	−	17.1768i	1.13839	−	0.657251i	0.946032	+	0.324074i	$0.105053\pi$
$684$		0			0
$685$			12.1177i			0.462992i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	7.42662			0.282932
$690$		0			0
$691$			25.5640i			0.972502i	0.873819	+	0.486251i	$0.161636\pi$
$691$			25.5640i			0.972502i	−0.873819	+	0.486251i	$0.838364\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			14.9517i			0.567150i
$696$		0			0
$697$	11.1653			0.422917
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	32.3485i		−	1.22178i	−0.791714	−	0.610892i	$-0.790811\pi$
$701$		−	32.3485i		−	1.22178i	0.791714	−	0.610892i	$-0.209189\pi$
$702$		0			0
$703$	5.82158	−	3.36109i	0.219565	−	0.126766i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	12.2314	−	0.296250i	0.460010	−	0.0111416i
$708$		0			0
$709$	2.60238			0.0977344			0.0488672	−	0.998805i	$-0.484439\pi$
$709$	2.60238			0.0977344			0.0488672	+	0.998805i	$0.484439\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	21.6065	+	37.4235i	0.809169	+	1.40152i
$714$		0			0
$715$	−9.40905	+	16.2969i	−0.351878	+	0.609471i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−8.42868	+	14.5989i	−0.314337	+	0.544447i	−0.979296	−	0.202432i	$-0.935115\pi$
$719$	−8.42868	+	14.5989i	−0.314337	+	0.544447i	0.664960	+	0.746879i	$0.268449\pi$
$720$		0			0
$721$	9.88168	+	5.39047i	0.368013	+	0.200752i
$722$		0			0
$723$		0			0
$724$		0			0
$725$		−	35.9528i		−	1.33525i
$726$		0			0
$727$	36.1005	−	20.8426i	1.33889	−	0.773009i	0.352249	−	0.935906i	$-0.385417\pi$
$727$	36.1005	−	20.8426i	1.33889	−	0.773009i	0.986643	+	0.162897i	$0.0520838\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−9.07314	+	15.7151i	−0.335582	+	0.581246i
$732$		0			0
$733$	31.2134	−	18.0211i	1.15289	−	0.665623i	0.203303	−	0.979116i	$-0.434832\pi$
$733$	31.2134	−	18.0211i	1.15289	−	0.665623i	0.949591	+	0.313492i	$0.101499\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−42.7400	−	24.6759i	−1.57435	−	0.908949i
$738$		0			0
$739$	14.1322	+	24.4777i	0.519861	+	0.900426i	0.999733	+	0.0230879i	$0.00734977\pi$
$739$	14.1322	+	24.4777i	0.519861	+	0.900426i	−0.479872	+	0.877339i	$0.659317\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−28.7161	−	16.5793i	−1.05349	−	0.608234i	−0.129867	−	0.991531i	$-0.541455\pi$
$743$	−28.7161	−	16.5793i	−1.05349	−	0.608234i	−0.923625	+	0.383298i	$0.874788\pi$
$744$		0			0
$745$	−3.32671	−	1.92068i	−0.121881	−	0.0703682i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	0.646497	+	26.6922i	0.0236225	+	0.975312i
$750$		0			0
$751$	−21.6155	−	37.4391i	−0.788761	−	1.36617i	−0.926726	−	0.375737i	$-0.877390\pi$
$751$	−21.6155	−	37.4391i	−0.788761	−	1.36617i	0.137965	−	0.990437i	$-0.455944\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	7.09789			0.258319
$756$		0			0
$757$	33.2085			1.20698			0.603492	−	0.797369i	$-0.293776\pi$
$757$	33.2085			1.20698			0.603492	+	0.797369i	$0.293776\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	2.15969	+	3.74069i	0.0782887	+	0.135600i	0.902512	−	0.430665i	$-0.141721\pi$
$761$	2.15969	+	3.74069i	0.0782887	+	0.135600i	−0.824223	+	0.566265i	$0.808388\pi$
$762$		0			0
$763$	−1.38964	+	2.54746i	−0.0503084	+	0.0922241i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−22.5673	−	13.0292i	−0.814859	−	0.470459i
$768$		0			0
$769$	16.1845	+	9.34412i	0.583628	+	0.336958i	0.762574	−	0.646901i	$-0.223935\pi$
$769$	16.1845	+	9.34412i	0.583628	+	0.336958i	−0.178946	+	0.983859i	$0.557269\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−4.91482	−	8.51272i	−0.176774	−	0.306181i	0.764000	−	0.645216i	$-0.223233\pi$
$773$	−4.91482	−	8.51272i	−0.176774	−	0.306181i	−0.940774	+	0.339035i	$0.889899\pi$
$774$		0			0
$775$	22.9252	+	13.2359i	0.823497	+	0.475446i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−49.9427	+	28.8345i	−1.78938	+	1.03310i
$780$		0			0
$781$	1.60511	−	2.78014i	0.0574354	−	0.0994811i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−8.55966	+	4.94192i	−0.305507	+	0.176385i
$786$		0			0
$787$			45.4273i			1.61931i	0.586908	+	0.809654i	$0.300345\pi$
$787$			45.4273i			1.61931i	−0.586908	+	0.809654i	$0.699655\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.630130	+	26.0165i	0.0224049	+	0.925039i
$792$		0			0
$793$	5.82061	−	10.0816i	0.206696	−	0.358008i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−7.67140	+	13.2872i	−0.271735	+	0.470658i	−0.969306	−	0.245857i	$-0.920931\pi$
$797$	−7.67140	+	13.2872i	−0.271735	+	0.470658i	0.697571	+	0.716515i	$0.254264\pi$
$798$		0			0
$799$	−6.05322	−	10.4845i	−0.214147	−	0.370914i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−9.27139			−0.327180
$804$		0			0
$805$	0.432161	+	17.8428i	0.0152317	+	0.628878i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.785783	+	0.453672i	−0.0276267	+	0.0159503i	−0.513750	−	0.857940i	$-0.671744\pi$
$809$	−0.785783	+	0.453672i	−0.0276267	+	0.0159503i	0.486123	+	0.873890i	$0.338411\pi$
$810$		0			0
$811$		−	7.95121i		−	0.279205i	−0.990208	−	0.139602i	$-0.955418\pi$
$811$		−	7.95121i		−	0.279205i	0.990208	−	0.139602i	$-0.0445824\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−7.84367			−0.274752
$816$		0			0
$817$		−	93.7255i		−	3.27904i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		−	46.8699i		−	1.63577i	−0.575380	−	0.817886i	$-0.695146\pi$
$821$		−	46.8699i		−	1.63577i	0.575380	−	0.817886i	$-0.304854\pi$
$822$		0			0
$823$	−20.9899			−0.731661			−0.365831	−	0.930681i	$-0.619215\pi$
$823$	−20.9899			−0.731661			−0.365831	+	0.930681i	$0.619215\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			12.6370i			0.439430i	0.975564	+	0.219715i	$0.0705127\pi$
$827$			12.6370i			0.439430i	−0.975564	+	0.219715i	$0.929487\pi$
$828$		0			0
$829$	3.12273	−	1.80291i	0.108457	−	0.0626177i	−0.444790	−	0.895635i	$-0.646722\pi$
$829$	3.12273	−	1.80291i	0.108457	−	0.0626177i	0.553247	+	0.833017i	$0.313388\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−10.0347	+	0.486376i	−0.347682	+	0.0168519i
$834$		0			0
$835$	−15.2010			−0.526051
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−0.287256	−	0.497541i	−0.00991716	−	0.0171770i	0.861024	−	0.508564i	$-0.169823\pi$
$839$	−0.287256	−	0.497541i	−0.00991716	−	0.0171770i	−0.870941	+	0.491387i	$0.836490\pi$
$840$		0			0
$841$	29.2234	−	50.6163i	1.00770	−	1.74539i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−2.81626	+	4.87790i	−0.0968822	+	0.167805i
$846$		0			0
$847$	−7.35416	+	13.4815i	−0.252692	+	0.463228i
$848$		0			0
$849$		0			0
$850$		0			0
$851$			5.69137i			0.195098i
$852$		0			0
$853$	5.62283	−	3.24634i	0.192522	−	0.111153i	−0.400641	−	0.916235i	$-0.631212\pi$
$853$	5.62283	−	3.24634i	0.192522	−	0.111153i	0.593163	+	0.805083i	$0.297879\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.15768	−	2.00517i	0.0395457	−	0.0684952i	−0.845575	−	0.533857i	$-0.820742\pi$
$857$	1.15768	−	2.00517i	0.0395457	−	0.0684952i	0.885121	+	0.465361i	$0.154076\pi$
$858$		0			0
$859$	−48.1991	+	27.8278i	−1.64453	+	0.949471i	−0.665338	+	0.746542i	$0.731713\pi$
$859$	−48.1991	+	27.8278i	−1.64453	+	0.949471i	−0.979194	+	0.202929i	$0.934954\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	7.50527	+	4.33317i	0.255482	+	0.147503i	0.622272	−	0.782801i	$-0.286210\pi$
$863$	7.50527	+	4.33317i	0.255482	+	0.147503i	−0.366790	+	0.930304i	$0.619543\pi$
$864$		0			0
$865$	−7.25443	−	12.5650i	−0.246658	−	0.427224i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−5.80593	−	3.35206i	−0.196953	−	0.113711i
$870$		0			0
$871$	−44.5286	−	25.7086i	−1.50879	−	0.871102i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	13.1000	+	21.4718i	0.442860	+	0.725879i
$876$		0			0
$877$	−17.8315	−	30.8850i	−0.602126	−	1.04291i	−0.992499	−	0.122255i	$-0.960987\pi$
$877$	−17.8315	−	30.8850i	−0.602126	−	1.04291i	0.390373	−	0.920657i	$-0.372346\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	7.57740			0.255289			0.127644	−	0.991820i	$-0.459258\pi$
$881$	7.57740			0.255289			0.127644	+	0.991820i	$0.459258\pi$
$882$		0			0
$883$	5.35854			0.180329			0.0901646	−	0.995927i	$-0.471261\pi$
$883$	5.35854			0.180329			0.0901646	+	0.995927i	$0.471261\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−11.7952	−	20.4299i	−0.396045	−	0.685970i	0.597189	−	0.802100i	$-0.296284\pi$
$887$	−11.7952	−	20.4299i	−0.396045	−	0.685970i	−0.993234	+	0.116131i	$0.962951\pi$
$888$		0			0
$889$	−20.9728	−	34.3759i	−0.703405	−	1.15293i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	54.1523	+	31.2648i	1.81214	+	1.04624i
$894$		0			0
$895$	4.26755	+	2.46387i	0.142649	+	0.0823582i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	32.1931	+	55.7601i	1.07370	+	1.85970i
$900$		0			0
$901$	2.16134	+	1.24785i	0.0720046	+	0.0415719i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.07487	−	1.19793i	0.0689711	−	0.0398205i
$906$		0			0
$907$	−7.13516	+	12.3585i	−0.236919	+	0.410356i	−0.959829	−	0.280587i	$-0.909471\pi$
$907$	−7.13516	+	12.3585i	−0.236919	+	0.410356i	0.722910	+	0.690943i	$0.242804\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−40.0156	+	23.1030i	−1.32578	+	0.765437i	−0.984643	−	0.174578i	$-0.944144\pi$
$911$	−40.0156	+	23.1030i	−1.32578	+	0.765437i	−0.341133	+	0.940015i	$0.610811\pi$
$912$		0			0
$913$		−	36.7828i		−	1.21733i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−11.2875	+	20.6920i	−0.372748	+	0.683312i
$918$		0			0
$919$	16.8957	−	29.2643i	0.557339	−	0.965339i	−0.440379	−	0.897812i	$-0.645156\pi$
$919$	16.8957	−	29.2643i	0.557339	−	0.965339i	0.997717	−	0.0675269i	$-0.0215109\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.67228	−	2.89648i	0.0550439	−	0.0953389i
$924$		0			0
$925$	1.74323	+	3.01936i	0.0573171	+	0.0992761i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−34.9369			−1.14624			−0.573121	−	0.819471i	$-0.694267\pi$
$929$	−34.9369			−1.14624			−0.573121	+	0.819471i	$0.694267\pi$
$930$		0			0
$931$	43.6294	−	28.0902i	1.42990	−	0.920619i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−5.47655	+	3.16189i	−0.179102	+	0.103405i
$936$		0			0
$937$		−	11.6175i		−	0.379528i	−0.981830	−	0.189764i	$-0.939228\pi$
$937$		−	11.6175i		−	0.379528i	0.981830	−	0.189764i	$-0.0607723\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	9.55030			0.311331			0.155665	−	0.987810i	$-0.450248\pi$
$941$	9.55030			0.311331			0.155665	+	0.987810i	$0.450248\pi$
$942$		0			0
$943$		−	48.8257i		−	1.58998i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	36.6873i		−	1.19218i	−0.802919	−	0.596088i	$-0.796721\pi$
$947$		−	36.6873i		−	1.19218i	0.802919	−	0.596088i	$-0.203279\pi$
$948$		0			0
$949$	−9.65938			−0.313557
$950$		0			0
$951$		0			0
$952$		0			0
$953$			17.1813i			0.556556i	0.960501	+	0.278278i	$0.0897636\pi$
$953$			17.1813i			0.556556i	−0.960501	+	0.278278i	$0.910236\pi$
$954$		0			0
$955$	19.5805	−	11.3048i	0.633610	−	0.365815i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	0.722227	+	29.8189i	0.0233219	+	0.962902i
$960$		0			0
$961$	−16.4069			−0.529256
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−6.02146	−	10.4295i	−0.193838	−	0.335737i
$966$		0			0
$967$	2.43550	−	4.21841i	0.0783204	−	0.135655i	−0.824205	−	0.566292i	$-0.808378\pi$
$967$	2.43550	−	4.21841i	0.0783204	−	0.135655i	0.902525	+	0.430637i	$0.141711\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−14.0544	+	24.3429i	−0.451026	+	0.781200i	−0.998450	−	0.0556556i	$-0.982275\pi$
$971$	−14.0544	+	24.3429i	−0.451026	+	0.781200i	0.547424	+	0.836855i	$0.315608\pi$
$972$		0			0
$973$	0.891137	+	36.7928i	0.0285686	+	1.17952i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			30.5582i			0.977643i	0.872384	+	0.488822i	$0.162573\pi$
$977$			30.5582i			0.977643i	−0.872384	+	0.488822i	$0.837427\pi$
$978$		0			0
$979$	12.2006	−	7.04401i	0.389932	−	0.225127i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	5.98556	−	10.3673i	0.190910	−	0.330665i	−0.754642	−	0.656137i	$-0.772190\pi$
$983$	5.98556	−	10.3673i	0.190910	−	0.330665i	0.945552	+	0.325471i	$0.105523\pi$
$984$		0			0
$985$	−19.4497	+	11.2293i	−0.619718	+	0.357794i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	68.7219	+	39.6766i	2.18523	+	1.26164i
$990$		0			0
$991$	3.32513	+	5.75929i	0.105626	+	0.182950i	0.913994	−	0.405728i	$-0.132982\pi$
$991$	3.32513	+	5.75929i	0.105626	+	0.182950i	−0.808368	+	0.588678i	$0.799649\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	17.0387	+	9.83730i	0.540163	+	0.311863i
$996$		0			0
$997$	47.6751	+	27.5252i	1.50989	+	0.871733i	0.999934	+	0.0115298i	$0.00367014\pi$
$997$	47.6751	+	27.5252i	1.50989	+	0.871733i	0.509952	+	0.860203i	$0.329663\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.ca.e.2609.16		48
3.2	odd	2		1008.2.ca.e.257.4		48
4.3	odd	2		1512.2.bs.a.1097.16		48
7.3	odd	6		3024.2.df.e.17.16		48
9.2	odd	6		3024.2.df.e.1601.16		48
9.7	even	3		1008.2.df.e.929.13		48
12.11	even	2		504.2.bs.a.257.21	✓	48
21.17	even	6		1008.2.df.e.689.13		48
28.3	even	6		1512.2.cx.a.17.16		48
36.7	odd	6		504.2.cx.a.425.12	yes	48
36.11	even	6		1512.2.cx.a.89.16		48
63.38	even	6	inner	3024.2.ca.e.2033.16		48
63.52	odd	6		1008.2.ca.e.353.4		48
84.59	odd	6		504.2.cx.a.185.12	yes	48
252.115	even	6		504.2.bs.a.353.21	yes	48
252.227	odd	6		1512.2.bs.a.521.16		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.21	✓	48	12.11	even	2
504.2.bs.a.353.21	yes	48	252.115	even	6
504.2.cx.a.185.12	yes	48	84.59	odd	6
504.2.cx.a.425.12	yes	48	36.7	odd	6
1008.2.ca.e.257.4		48	3.2	odd	2
1008.2.ca.e.353.4		48	63.52	odd	6
1008.2.df.e.689.13		48	21.17	even	6
1008.2.df.e.929.13		48	9.7	even	3
1512.2.bs.a.521.16		48	252.227	odd	6
1512.2.bs.a.1097.16		48	4.3	odd	2
1512.2.cx.a.17.16		48	28.3	even	6
1512.2.cx.a.89.16		48	36.11	even	6
3024.2.ca.e.2033.16		48	63.38	even	6	inner
3024.2.ca.e.2609.16		48	1.1	even	1	trivial
3024.2.df.e.17.16		48	7.3	odd	6
3024.2.df.e.1601.16		48	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.ca (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.537427 + 0.930850i) q^{5} +(1.37797 + 2.25858i) q^{7} +(3.55011 + 2.04966i) q^{11} +(3.69867 + 2.13543i) q^{13} +(0.717607 + 1.24293i) q^{17} +(-6.41973 - 3.70644i) q^{19} +(5.43530 - 3.13807i) q^{23} +(1.92235 - 3.32960i) q^{25} +(8.09846 - 4.67565i) q^{29} +6.88527i q^{31} +(-1.36185 + 2.49651i) q^{35} +(-0.453413 + 0.785334i) q^{37} +(3.88978 - 6.73730i) q^{41} +(6.32181 + 10.9497i) q^{43} -8.43528 q^{47} +(-3.20241 + 6.22451i) q^{49} +(1.50593 - 0.869452i) q^{53} +4.40616i q^{55} -6.10146 q^{59} -2.72573i q^{61} +4.59055i q^{65} -12.0391 q^{67} -0.783113i q^{71} +(-1.95868 + 1.13085i) q^{73} +(0.262612 + 10.8426i) q^{77} -1.63543 q^{79} +(-4.48646 - 7.77077i) q^{83} +(-0.771322 + 1.33597i) q^{85} +(1.71834 - 2.97625i) q^{89} +(0.273602 + 11.2963i) q^{91} -7.96775i q^{95} +(-5.05015 + 2.91570i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{23} - 24 q^{25} - 18 q^{29} - 6 q^{41} + 6 q^{43} + 36 q^{47} + 6 q^{49} - 12 q^{53} + 36 q^{77} + 12 q^{79} - 18 q^{89} - 6 q^{91}+O(q^{100}) \) 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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