LMFDB - Embedded newform 3024.2.ca.e.2033.18

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			2033.18
Character	$\chi$	$=$	3024.2033
Dual form			3024.2.ca.e.2609.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.793002 - 1.37352i) q^{5} +(-2.62988 + 0.289398i) q^{7} +(3.42298 - 1.97626i) q^{11} +(-5.09214 + 2.93995i) q^{13} +(-3.19652 + 5.53653i) q^{17} +(6.37856 - 3.68267i) q^{19} +(2.10532 + 1.21551i) q^{23} +(1.24230 + 2.15172i) q^{25} +(-4.34058 - 2.50604i) q^{29} -0.987677i q^{31} +(-1.68800 + 3.84168i) q^{35} +(0.183332 + 0.317540i) q^{37} +(5.58681 + 9.67664i) q^{41} +(-1.26688 + 2.19430i) q^{43} -1.08656 q^{47} +(6.83250 - 1.52216i) q^{49} +(6.89030 + 3.97812i) q^{53} -6.26871i q^{55} -5.46840 q^{59} -14.4066i q^{61} +9.32554i q^{65} +11.4100 q^{67} +9.65277i q^{71} +(7.64694 + 4.41497i) q^{73} +(-8.43010 + 6.18792i) q^{77} +10.6131 q^{79} +(-2.96819 + 5.14105i) q^{83} +(5.06969 + 8.78096i) q^{85} +(4.70952 + 8.15712i) q^{89} +(12.5409 - 9.20535i) q^{91} -11.6814i q^{95} +(-10.4826 - 6.05213i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

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

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
$5$	0.793002	−	1.37352i	0.354641	−	0.614257i	−0.632415	−	0.774630i	$-0.717936\pi$
$5$	0.793002	−	1.37352i	0.354641	−	0.614257i	0.987057	+	0.160373i	$0.0512696\pi$
$6$		0			0
$7$	−2.62988	+	0.289398i	−0.994000	+	0.109382i
$7$	−2.62988	+	0.289398i	−0.994000	+	0.109382i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.42298	−	1.97626i	1.03207	−	0.595865i	0.114492	−	0.993424i	$-0.463476\pi$
$11$	3.42298	−	1.97626i	1.03207	−	0.595865i	0.917576	+	0.397559i	$0.130143\pi$
$12$		0			0
$13$	−5.09214	+	2.93995i	−1.41231	+	0.815395i	−0.995605	−	0.0936493i	$-0.970147\pi$
$13$	−5.09214	+	2.93995i	−1.41231	+	0.815395i	−0.416700	+	0.909044i	$0.636813\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.19652	+	5.53653i	−0.775269	+	1.34281i	0.159374	+	0.987218i	$0.449053\pi$
$17$	−3.19652	+	5.53653i	−0.775269	+	1.34281i	−0.934643	+	0.355588i	$0.884281\pi$
$18$		0			0
$19$	6.37856	−	3.68267i	1.46334	−	0.844862i	0.464179	−	0.885741i	$-0.346349\pi$
$19$	6.37856	−	3.68267i	1.46334	−	0.844862i	0.999164	+	0.0408799i	$0.0130161\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.10532	+	1.21551i	0.438990	+	0.253451i	0.703169	−	0.711022i	$-0.251768\pi$
$23$	2.10532	+	1.21551i	0.438990	+	0.253451i	−0.264179	+	0.964474i	$0.585101\pi$
$24$		0			0
$25$	1.24230	+	2.15172i	0.248459	+	0.430344i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.34058	−	2.50604i	−0.806026	−	0.465359i	0.0395477	−	0.999218i	$-0.487408\pi$
$29$	−4.34058	−	2.50604i	−0.806026	−	0.465359i	−0.845574	+	0.533858i	$0.820742\pi$
$30$		0			0
$31$		−	0.987677i		−	0.177392i	−0.996059	−	0.0886960i	$-0.971730\pi$
$31$		−	0.987677i		−	0.177392i	0.996059	−	0.0886960i	$-0.0282700\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.68800	+	3.84168i	−0.285325	+	0.649362i
$36$		0			0
$37$	0.183332	+	0.317540i	0.0301396	+	0.0522033i	0.880702	−	0.473671i	$-0.157071\pi$
$37$	0.183332	+	0.317540i	0.0301396	+	0.0522033i	−0.850562	+	0.525874i	$0.823738\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.58681	+	9.67664i	0.872513	+	1.51124i	0.859389	+	0.511323i	$0.170844\pi$
$41$	5.58681	+	9.67664i	0.872513	+	1.51124i	0.0131240	+	0.999914i	$0.495822\pi$
$42$		0			0
$43$	−1.26688	+	2.19430i	−0.193197	+	0.334627i	−0.946308	−	0.323266i	$-0.895219\pi$
$43$	−1.26688	+	2.19430i	−0.193197	+	0.334627i	0.753111	+	0.657894i	$0.228552\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.08656			−0.158491			−0.0792456	−	0.996855i	$-0.525251\pi$
$47$	−1.08656			−0.158491			−0.0792456	+	0.996855i	$0.525251\pi$
$48$		0			0
$49$	6.83250	−	1.52216i	0.976071	−	0.217451i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.89030	+	3.97812i	0.946455	+	0.546436i	0.891978	−	0.452079i	$-0.149317\pi$
$53$	6.89030	+	3.97812i	0.946455	+	0.546436i	0.0544773	+	0.998515i	$0.482651\pi$
$54$		0			0
$55$		−	6.26871i		−	0.845273i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5.46840			−0.711925			−0.355963	−	0.934500i	$-0.615847\pi$
$59$	−5.46840			−0.711925			−0.355963	+	0.934500i	$0.615847\pi$
$60$		0			0
$61$		−	14.4066i		−	1.84458i	−0.386503	−	0.922288i	$-0.626317\pi$
$61$		−	14.4066i		−	1.84458i	0.386503	−	0.922288i	$-0.373683\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			9.32554i			1.15669i
$66$		0			0
$67$	11.4100			1.39396			0.696978	−	0.717092i	$-0.254527\pi$
$67$	11.4100			1.39396			0.696978	+	0.717092i	$0.254527\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			9.65277i			1.14557i	0.819705	+	0.572787i	$0.194138\pi$
$71$			9.65277i			1.14557i	−0.819705	+	0.572787i	$0.805862\pi$
$72$		0			0
$73$	7.64694	+	4.41497i	0.895007	+	0.516733i	0.875577	−	0.483079i	$-0.160481\pi$
$73$	7.64694	+	4.41497i	0.895007	+	0.516733i	0.0194302	+	0.999811i	$0.493815\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−8.43010	+	6.18792i	−0.960699	+	0.705179i
$78$		0			0
$79$	10.6131			1.19406			0.597032	−	0.802217i	$-0.296346\pi$
$79$	10.6131			1.19406			0.597032	+	0.802217i	$0.296346\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−2.96819	+	5.14105i	−0.325801	+	0.564303i	−0.981674	−	0.190568i	$-0.938967\pi$
$83$	−2.96819	+	5.14105i	−0.325801	+	0.564303i	0.655873	+	0.754871i	$0.272301\pi$
$84$		0			0
$85$	5.06969	+	8.78096i	0.549885	+	0.952429i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.70952	+	8.15712i	0.499208	+	0.864653i	1.00000		0.000914461i	$-0.000291082\pi$
$89$	4.70952	+	8.15712i	0.499208	+	0.864653i	−0.500792	+	0.865568i	$0.666958\pi$
$90$		0			0
$91$	12.5409	−	9.20535i	1.31464	−	0.964983i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		−	11.6814i		−	1.19849i
$96$		0			0
$97$	−10.4826	−	6.05213i	−1.06435	−	0.614501i	−0.137715	−	0.990472i	$-0.543976\pi$
$97$	−10.4826	−	6.05213i	−1.06435	−	0.614501i	−0.926631	+	0.375971i	$0.877309\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.0121553	−	0.0210536i	−0.00120950	−	0.00209491i	0.865420	−	0.501047i	$-0.167052\pi$
$101$	−0.0121553	−	0.0210536i	−0.00120950	−	0.00209491i	−0.866630	+	0.498952i	$0.833718\pi$
$102$		0			0
$103$	1.23623	+	0.713737i	0.121809	+	0.0703266i	0.559667	−	0.828718i	$-0.310929\pi$
$103$	1.23623	+	0.713737i	0.121809	+	0.0703266i	−0.437857	+	0.899044i	$0.644263\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	10.9445	−	6.31880i	1.05804	−	0.610862i	0.133153	−	0.991095i	$-0.457490\pi$
$107$	10.9445	−	6.31880i	1.05804	−	0.610862i	0.924890	+	0.380234i	$0.124156\pi$
$108$		0			0
$109$	0.0726028	−	0.125752i	0.00695408	−	0.0120448i	−0.862527	−	0.506010i	$-0.831120\pi$
$109$	0.0726028	−	0.125752i	0.00695408	−	0.0120448i	0.869482	+	0.493965i	$0.164453\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	9.35867	−	5.40323i	0.880390	−	0.508293i	0.00960284	−	0.999954i	$-0.496943\pi$
$113$	9.35867	−	5.40323i	0.880390	−	0.508293i	0.870787	+	0.491661i	$0.163610\pi$
$114$		0			0
$115$	3.33905	−	1.92780i	0.311368	−	0.179769i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	6.80419	−	15.4855i	0.623739	−	1.41955i
$120$		0			0
$121$	2.31121	−	4.00313i	0.210110	−	0.363920i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.8706			1.06174
$126$		0			0
$127$	3.63647			0.322685			0.161342	−	0.986899i	$-0.448418\pi$
$127$	3.63647			0.322685			0.161342	+	0.986899i	$0.448418\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.50992	−	4.34731i	0.219293	−	0.379826i	−0.735299	−	0.677743i	$-0.762958\pi$
$131$	2.50992	−	4.34731i	0.219293	−	0.379826i	0.954592	+	0.297917i	$0.0962917\pi$
$132$		0			0
$133$	−15.7091	+	11.5309i	−1.36215	+	0.999856i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−8.06192	+	4.65455i	−0.688777	+	0.397665i	−0.803154	−	0.595772i	$-0.796846\pi$
$137$	−8.06192	+	4.65455i	−0.688777	+	0.397665i	0.114377	+	0.993437i	$0.463513\pi$
$138$		0			0
$139$	−3.82307	+	2.20725i	−0.324269	+	0.187217i	−0.653294	−	0.757105i	$-0.726613\pi$
$139$	−3.82307	+	2.20725i	−0.324269	+	0.187217i	0.329025	+	0.944321i	$0.393280\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−11.6202	+	20.1268i	−0.971730	+	1.68309i
$144$		0			0
$145$	−6.88418	+	3.97459i	−0.571700	+	0.330071i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	2.50691	+	1.44736i	0.205374	+	0.118573i	0.599160	−	0.800630i	$-0.295502\pi$
$149$	2.50691	+	1.44736i	0.205374	+	0.118573i	−0.393786	+	0.919202i	$0.628835\pi$
$150$		0			0
$151$	1.38558	+	2.39990i	0.112757	+	0.195301i	0.916881	−	0.399161i	$-0.130698\pi$
$151$	1.38558	+	2.39990i	0.112757	+	0.195301i	−0.804124	+	0.594462i	$0.797365\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.35659	−	0.783230i	−0.108964	−	0.0629105i
$156$		0			0
$157$			0.169009i			0.0134884i	0.999977	+	0.00674418i	$0.00214676\pi$
$157$			0.169009i			0.0134884i	−0.999977	+	0.00674418i	$0.997853\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−5.88851	−	2.58736i	−0.464079	−	0.203913i
$162$		0			0
$163$	3.55929	+	6.16487i	0.278785	+	0.482870i	0.971083	−	0.238742i	$-0.0767350\pi$
$163$	3.55929	+	6.16487i	0.278785	+	0.482870i	−0.692298	+	0.721612i	$0.743402\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.19494	−	2.06970i	−0.0924675	−	0.160158i	0.816081	−	0.577937i	$-0.196142\pi$
$167$	−1.19494	−	2.06970i	−0.0924675	−	0.160158i	−0.908549	+	0.417779i	$0.862809\pi$
$168$		0			0
$169$	10.7866	−	18.6829i	0.829737	−	1.43715i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.15941			0.544320			0.272160	−	0.962252i	$-0.412262\pi$
$173$	7.15941			0.544320			0.272160	+	0.962252i	$0.412262\pi$
$174$		0			0
$175$	−3.88979	−	5.29924i	−0.294040	−	0.400585i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	8.02286	+	4.63200i	0.599657	+	0.346212i	0.768906	−	0.639361i	$-0.220801\pi$
$179$	8.02286	+	4.63200i	0.599657	+	0.346212i	−0.169250	+	0.985573i	$0.554134\pi$
$180$		0			0
$181$			21.5541i			1.60210i	0.598595	+	0.801052i	$0.295726\pi$
$181$			21.5541i			1.60210i	−0.598595	+	0.801052i	$0.704274\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.581530			0.0427549
$186$		0			0
$187$			25.2686i			1.84782i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			3.36134i			0.243218i	0.992578	+	0.121609i	$0.0388054\pi$
$191$			3.36134i			0.243218i	−0.992578	+	0.121609i	$0.961195\pi$
$192$		0			0
$193$	8.35689			0.601542			0.300771	−	0.953696i	$-0.402756\pi$
$193$	8.35689			0.601542			0.300771	+	0.953696i	$0.402756\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			5.57159i			0.396959i	0.980105	+	0.198480i	$0.0636003\pi$
$197$			5.57159i			0.396959i	−0.980105	+	0.198480i	$0.936400\pi$
$198$		0			0
$199$	11.6605	+	6.73222i	0.826594	+	0.477234i	0.852685	−	0.522425i	$-0.174973\pi$
$199$	11.6605	+	6.73222i	0.826594	+	0.477234i	−0.0260910	+	0.999660i	$0.508306\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	12.1404	+	5.33441i	0.852092	+	0.374402i
$204$		0			0
$205$	17.7214			1.23772
$206$		0			0
$207$		0			0
$208$		0			0
$209$	14.5558	−	25.2114i	1.00685	−	1.74391i
$210$		0			0
$211$	−7.23362	−	12.5290i	−0.497983	−	0.862532i	0.502014	−	0.864859i	$-0.332592\pi$
$211$	−7.23362	−	12.5290i	−0.497983	−	0.862532i	−0.999997	+	0.00232753i	$0.999259\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.00928	+	3.48017i	0.137031	+	0.237345i
$216$		0			0
$217$	0.285831	+	2.59747i	0.0194035	+	0.176328i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		−	37.5904i		−	2.52860i
$222$		0			0
$223$	−18.3399	−	10.5885i	−1.22813	−	0.709060i	−0.261490	−	0.965206i	$-0.584214\pi$
$223$	−18.3399	−	10.5885i	−1.22813	−	0.709060i	−0.966638	+	0.256146i	$0.917547\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.23836	+	7.34106i	0.281310	+	0.487243i	0.971708	−	0.236187i	$-0.0758978\pi$
$227$	4.23836	+	7.34106i	0.281310	+	0.487243i	−0.690398	+	0.723430i	$0.742564\pi$
$228$		0			0
$229$	17.1285	+	9.88915i	1.13188	+	0.653494i	0.944408	−	0.328776i	$-0.106636\pi$
$229$	17.1285	+	9.88915i	1.13188	+	0.653494i	0.187476	+	0.982269i	$0.439969\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−23.7957	+	13.7385i	−1.55891	+	0.900037i	−0.561548	+	0.827444i	$0.689794\pi$
$233$	−23.7957	+	13.7385i	−1.55891	+	0.900037i	−0.997362	+	0.0725933i	$0.976873\pi$
$234$		0			0
$235$	−0.861645	+	1.49241i	−0.0562075	+	0.0973543i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.979306	−	0.565402i	0.0633460	−	0.0365728i	−0.467992	−	0.883732i	$-0.655023\pi$
$239$	0.979306	−	0.565402i	0.0633460	−	0.0365728i	0.531339	+	0.847160i	$0.321689\pi$
$240$		0			0
$241$	−1.26288	+	0.729123i	−0.0813491	+	0.0469669i	−0.540123	−	0.841586i	$-0.681622\pi$
$241$	−1.26288	+	0.729123i	−0.0813491	+	0.0469669i	0.458774	+	0.888553i	$0.348289\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.32747	−	10.5916i	0.212584	−	0.676676i
$246$		0			0
$247$	−21.6537	+	37.5053i	−1.37779	+	2.38640i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.61932			−0.102210			−0.0511052	−	0.998693i	$-0.516274\pi$
$251$	−1.61932			−0.102210			−0.0511052	+	0.998693i	$0.516274\pi$
$252$		0			0
$253$	9.60865			0.604091
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.47759	+	7.75542i	−0.279305	+	0.483770i	−0.971212	−	0.238216i	$-0.923437\pi$
$257$	−4.47759	+	7.75542i	−0.279305	+	0.483770i	0.691908	+	0.721986i	$0.256771\pi$
$258$		0			0
$259$	−0.574035	−	0.782035i	−0.0356688	−	0.0485933i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.35287	+	1.35843i	−0.145084	+	0.0837643i	−0.570785	−	0.821100i	$-0.693361\pi$
$263$	−2.35287	+	1.35843i	−0.145084	+	0.0837643i	0.425701	+	0.904864i	$0.360028\pi$
$264$		0			0
$265$	10.9280	−	6.30931i	0.671304	−	0.387578i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−8.87918	+	15.3792i	−0.541373	+	0.937686i	0.457452	+	0.889234i	$0.348762\pi$
$269$	−8.87918	+	15.3792i	−0.541373	+	0.937686i	−0.998826	+	0.0484519i	$0.984571\pi$
$270$		0			0
$271$	−2.76570	+	1.59678i	−0.168004	+	0.0969973i	−0.581644	−	0.813443i	$-0.697590\pi$
$271$	−2.76570	+	1.59678i	−0.168004	+	0.0969973i	0.413640	+	0.910440i	$0.364257\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	8.50471	+	4.91020i	0.512853	+	0.296096i
$276$		0			0
$277$	−3.31771	−	5.74644i	−0.199342	−	0.345270i	0.748973	−	0.662600i	$-0.230547\pi$
$277$	−3.31771	−	5.74644i	−0.199342	−	0.345270i	−0.948315	+	0.317330i	$0.897214\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.88306	+	3.97394i	0.410609	+	0.237065i	0.691051	−	0.722806i	$-0.257148\pi$
$281$	6.88306	+	3.97394i	0.410609	+	0.237065i	−0.280442	+	0.959871i	$0.590481\pi$
$282$		0			0
$283$		−	25.3795i		−	1.50866i	−0.656497	−	0.754328i	$-0.727963\pi$
$283$		−	25.3795i		−	1.50866i	0.656497	−	0.754328i	$-0.272037\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−17.4930	−	23.8315i	−1.03258	−	1.40673i
$288$		0			0
$289$	−11.9354	−	20.6728i	−0.702085	−	1.21605i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	4.29543	+	7.43990i	0.250942	+	0.434644i	0.963785	−	0.266679i	$-0.0859265\pi$
$293$	4.29543	+	7.43990i	0.250942	+	0.434644i	−0.712844	+	0.701323i	$0.752593\pi$
$294$		0			0
$295$	−4.33645	+	7.51096i	−0.252478	+	0.437305i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−14.2941			−0.826651
$300$		0			0
$301$	2.69671	−	6.13737i	0.155436	−	0.353752i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−19.7878	−	11.4245i	−1.13304	−	0.654163i
$306$		0			0
$307$		−	24.2144i		−	1.38199i	−0.722861	−	0.690994i	$-0.757173\pi$
$307$		−	24.2144i		−	1.38199i	0.722861	−	0.690994i	$-0.242827\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	25.4018			1.44040			0.720201	−	0.693766i	$-0.244050\pi$
$311$	25.4018			1.44040			0.720201	+	0.693766i	$0.244050\pi$
$312$		0			0
$313$			23.1410i			1.30800i	0.756493	+	0.654002i	$0.226911\pi$
$313$			23.1410i			1.30800i	−0.756493	+	0.654002i	$0.773089\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	6.02945i		−	0.338648i	−0.985560	−	0.169324i	$-0.945842\pi$
$317$		−	6.02945i		−	0.338648i	0.985560	−	0.169324i	$-0.0541584\pi$
$318$		0			0
$319$	−19.8103			−1.10917
$320$		0			0
$321$		0			0
$322$		0			0
$323$			47.0868i			2.61998i
$324$		0			0
$325$	−12.6519	−	7.30457i	−0.701800	−	0.405184i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	2.85752	−	0.314448i	0.157540	−	0.0173361i
$330$		0			0
$331$	17.4188			0.957424			0.478712	−	0.877972i	$-0.341104\pi$
$331$	17.4188			0.957424			0.478712	+	0.877972i	$0.341104\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	9.04818	−	15.6719i	0.494355	−	0.856247i
$336$		0			0
$337$	−0.760462	−	1.31716i	−0.0414250	−	0.0717502i	0.844570	−	0.535446i	$-0.179856\pi$
$337$	−0.760462	−	1.31716i	−0.0414250	−	0.0717502i	−0.885995	+	0.463696i	$0.846523\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.95191	−	3.38080i	−0.105702	−	0.183081i
$342$		0			0
$343$	−17.5281	+	5.98040i	−0.946429	+	0.322911i
$344$		0			0
$345$		0			0
$346$		0			0
$347$			21.9428i			1.17795i	0.808151	+	0.588975i	$0.200468\pi$
$347$			21.9428i			1.17795i	−0.808151	+	0.588975i	$0.799532\pi$
$348$		0			0
$349$	−4.95655	−	2.86167i	−0.265318	−	0.153182i	0.361440	−	0.932395i	$-0.382285\pi$
$349$	−4.95655	−	2.86167i	−0.265318	−	0.153182i	−0.626758	+	0.779214i	$0.715619\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.92270	−	3.33022i	−0.102335	−	0.177250i	0.810311	−	0.586000i	$-0.199298\pi$
$353$	−1.92270	−	3.33022i	−0.102335	−	0.177250i	−0.912646	+	0.408750i	$0.865965\pi$
$354$		0			0
$355$	13.2583	+	7.65467i	0.703676	+	0.406268i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.8763	−	6.27946i	0.574031	−	0.331417i	−0.184727	−	0.982790i	$-0.559140\pi$
$359$	10.8763	−	6.27946i	0.574031	−	0.331417i	0.758758	+	0.651373i	$0.225807\pi$
$360$		0			0
$361$	17.6241	−	30.5258i	0.927582	−	1.60662i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	12.1281	−	7.00215i	0.634813	−	0.366509i
$366$		0			0
$367$	1.05849	−	0.611122i	0.0552530	−	0.0319003i	−0.472119	−	0.881535i	$-0.656511\pi$
$367$	1.05849	−	0.611122i	0.0552530	−	0.0319003i	0.527372	+	0.849634i	$0.323177\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−19.2719	−	8.46792i	−1.00055	−	0.439632i
$372$		0			0
$373$	−6.57624	+	11.3904i	−0.340505	+	0.589772i	−0.984527	−	0.175235i	$-0.943931\pi$
$373$	−6.57624	+	11.3904i	−0.340505	+	0.589772i	0.644022	+	0.765007i	$0.277265\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	29.4705			1.51781
$378$		0			0
$379$	−22.9852			−1.18067			−0.590336	−	0.807157i	$-0.701005\pi$
$379$	−22.9852			−1.18067			−0.590336	+	0.807157i	$0.701005\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−13.9683	+	24.1938i	−0.713746	+	1.23625i	0.249695	+	0.968325i	$0.419670\pi$
$383$	−13.9683	+	24.1938i	−0.713746	+	1.23625i	−0.963441	+	0.267920i	$0.913664\pi$
$384$		0			0
$385$	1.81415	+	16.4859i	0.0924576	+	0.840201i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	12.3942	−	7.15580i	0.628412	−	0.362814i	−0.151725	−	0.988423i	$-0.548483\pi$
$389$	12.3942	−	7.15580i	0.628412	−	0.362814i	0.780137	+	0.625609i	$0.215150\pi$
$390$		0			0
$391$	−13.4594	+	7.77080i	−0.680672	+	0.392986i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	8.41619	−	14.5773i	0.423465	−	0.733462i
$396$		0			0
$397$	−3.97038	+	2.29230i	−0.199267	+	0.115047i	−0.596314	−	0.802751i	$-0.703369\pi$
$397$	−3.97038	+	2.29230i	−0.199267	+	0.115047i	0.397046	+	0.917799i	$0.370035\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.59026	−	5.53694i	−0.478915	−	0.276502i	0.241049	−	0.970513i	$-0.422508\pi$
$401$	−9.59026	−	5.53694i	−0.478915	−	0.276502i	−0.719964	+	0.694011i	$0.755842\pi$
$402$		0			0
$403$	2.90372	+	5.02939i	0.144645	+	0.250532i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.25508	+	0.724623i	0.0622122	+	0.0359182i
$408$		0			0
$409$			6.13944i			0.303576i	0.988413	+	0.151788i	$0.0485031\pi$
$409$			6.13944i			0.303576i	−0.988413	+	0.151788i	$0.951497\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	14.3812	−	1.58254i	0.707653	−	0.0778718i
$414$		0			0
$415$	4.70756	+	8.15372i	0.231085	+	0.400251i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	8.83059	+	15.2950i	0.431402	+	0.747211i	0.996994	−	0.0774744i	$-0.0246856\pi$
$419$	8.83059	+	15.2950i	0.431402	+	0.747211i	−0.565592	+	0.824685i	$0.691352\pi$
$420$		0			0
$421$	11.3569	−	19.6707i	0.553501	−	0.958693i	−0.444517	−	0.895770i	$-0.646625\pi$
$421$	11.3569	−	19.6707i	0.553501	−	0.958693i	0.998018	−	0.0629223i	$-0.0200420\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−15.8841			−0.770491
$426$		0			0
$427$	4.16923	+	37.8876i	0.201763	+	1.83351i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−18.4152	−	10.6320i	−0.887031	−	0.512128i	−0.0140610	−	0.999901i	$-0.504476\pi$
$431$	−18.4152	−	10.6320i	−0.887031	−	0.512128i	−0.872970	+	0.487773i	$0.837809\pi$
$432$		0			0
$433$			16.1075i			0.774079i	0.922063	+	0.387039i	$0.126502\pi$
$433$			16.1075i			0.774079i	−0.922063	+	0.387039i	$0.873498\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	17.9053			0.856525
$438$		0			0
$439$		−	12.9880i		−	0.619884i	−0.950755	−	0.309942i	$-0.899690\pi$
$439$		−	12.9880i		−	0.619884i	0.950755	−	0.309942i	$-0.100310\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			17.8237i			0.846828i	0.905936	+	0.423414i	$0.139168\pi$
$443$			17.8237i			0.846828i	−0.905936	+	0.423414i	$0.860832\pi$
$444$		0			0
$445$	14.9386			0.708159
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	5.71118i		−	0.269527i	−0.990878	−	0.134764i	$-0.956972\pi$
$449$		−	5.71118i		−	0.269527i	0.990878	−	0.134764i	$-0.0430275\pi$
$450$		0			0
$451$	38.2471	+	22.0820i	1.80099	+	1.03980i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.69879	−	24.5250i	−0.126521	−	1.14975i
$456$		0			0
$457$	−9.51768			−0.445218			−0.222609	−	0.974908i	$-0.571457\pi$
$457$	−9.51768			−0.445218			−0.222609	+	0.974908i	$0.571457\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−20.1348	+	34.8746i	−0.937773	+	1.62427i	−0.168160	+	0.985760i	$0.553782\pi$
$461$	−20.1348	+	34.8746i	−0.937773	+	1.62427i	−0.769613	+	0.638510i	$0.779551\pi$
$462$		0			0
$463$	−6.92014	−	11.9860i	−0.321606	−	0.557038i	0.659213	−	0.751956i	$-0.270889\pi$
$463$	−6.92014	−	11.9860i	−0.321606	−	0.557038i	−0.980820	+	0.194917i	$0.937556\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.5793	+	18.3238i	0.489549	+	0.847924i	0.999928	−	0.0120256i	$-0.00382796\pi$
$467$	10.5793	+	18.3238i	0.489549	+	0.847924i	−0.510378	+	0.859950i	$0.670495\pi$
$468$		0			0
$469$	−30.0070	+	3.30203i	−1.38559	+	0.152474i
$470$		0			0
$471$		0			0
$472$		0			0
$473$			10.0147i			0.460478i
$474$		0			0
$475$	15.8481	+	9.14992i	0.727162	+	0.419827i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−1.17063	−	2.02760i	−0.0534876	−	0.0926433i	0.838042	−	0.545606i	$-0.183700\pi$
$479$	−1.17063	−	2.02760i	−0.0534876	−	0.0926433i	−0.891530	+	0.452963i	$0.850367\pi$
$480$		0			0
$481$	−1.86710	−	1.07797i	−0.0851325	−	0.0491513i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−16.6254	+	9.59871i	−0.754923	+	0.435855i
$486$		0			0
$487$	8.83818	−	15.3082i	0.400496	−	0.693679i	−0.593290	−	0.804989i	$-0.702171\pi$
$487$	8.83818	−	15.3082i	0.400496	−	0.693679i	0.993786	+	0.111310i	$0.0355045\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	2.01875	−	1.16553i	0.0911051	−	0.0525995i	−0.453755	−	0.891126i	$-0.649916\pi$
$491$	2.01875	−	1.16553i	0.0911051	−	0.0525995i	0.544860	+	0.838527i	$0.316583\pi$
$492$		0			0
$493$	27.7495	−	16.0212i	1.24977	−	0.721558i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2.79349	−	25.3856i	−0.125305	−	1.13870i
$498$		0			0
$499$	15.8044	−	27.3740i	0.707501	−	1.22543i	−0.258280	−	0.966070i	$-0.583156\pi$
$499$	15.8044	−	27.3740i	0.707501	−	1.22543i	0.965781	−	0.259358i	$-0.0835109\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−38.9500			−1.73670			−0.868348	−	0.495956i	$-0.834818\pi$
$503$	−38.9500			−1.73670			−0.868348	+	0.495956i	$0.834818\pi$
$504$		0			0
$505$	−0.0385567			−0.00171575
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−6.89778	+	11.9473i	−0.305739	+	0.529555i	−0.977426	−	0.211280i	$-0.932237\pi$
$509$	−6.89778	+	11.9473i	−0.305739	+	0.529555i	0.671687	+	0.740835i	$0.265570\pi$
$510$		0			0
$511$	−21.3882	−	9.39781i	−0.946158	−	0.415734i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.96066	−	1.13199i	0.0863972	−	0.0498814i
$516$		0			0
$517$	−3.71928	+	2.14733i	−0.163574	+	0.0944393i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	2.27458	−	3.93969i	0.0996512	−	0.172601i	−0.811889	−	0.583812i	$-0.801561\pi$
$521$	2.27458	−	3.93969i	0.0996512	−	0.172601i	0.911540	+	0.411211i	$0.134894\pi$
$522$		0			0
$523$	−32.6301	+	18.8390i	−1.42681	+	0.823772i	−0.996868	−	0.0790830i	$-0.974801\pi$
$523$	−32.6301	+	18.8390i	−1.42681	+	0.823772i	−0.429946	+	0.902855i	$0.641467\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.46830	+	3.15713i	0.238203	+	0.137527i
$528$		0			0
$529$	−8.54507	−	14.8005i	−0.371525	−	0.643500i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−56.8976	−	32.8498i	−2.46451	−	1.42288i
$534$		0			0
$535$		−	20.0433i		−	0.866547i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	20.3793	−	18.7131i	0.877800	−	0.806031i
$540$		0			0
$541$	−1.53417	−	2.65727i	−0.0659593	−	0.114245i	0.831160	−	0.556034i	$-0.187677\pi$
$541$	−1.53417	−	2.65727i	−0.0659593	−	0.114245i	−0.897119	+	0.441789i	$0.854344\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.115148	−	0.199443i	−0.00493241	−	0.00854319i
$546$		0			0
$547$	7.22022	−	12.5058i	0.308714	−	0.534709i	−0.669367	−	0.742932i	$-0.733435\pi$
$547$	7.22022	−	12.5058i	0.308714	−	0.534709i	0.978081	+	0.208223i	$0.0667679\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−36.9156			−1.57266
$552$		0			0
$553$	−27.9111	+	3.07140i	−1.18690	+	0.130609i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	7.14024	+	4.12242i	0.302542	+	0.174672i	0.643584	−	0.765375i	$-0.277447\pi$
$557$	7.14024	+	4.12242i	0.302542	+	0.174672i	−0.341042	+	0.940048i	$0.610780\pi$
$558$		0			0
$559$		−	14.8982i		−	0.630128i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−9.37245			−0.395002			−0.197501	−	0.980303i	$-0.563283\pi$
$563$	−9.37245			−0.395002			−0.197501	+	0.980303i	$0.563283\pi$
$564$		0			0
$565$		−	17.1391i		−	0.721047i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			19.0614i			0.799098i	0.916712	+	0.399549i	$0.130833\pi$
$569$			19.0614i			0.799098i	−0.916712	+	0.399549i	$0.869167\pi$
$570$		0			0
$571$	10.0442			0.420335			0.210167	−	0.977665i	$-0.432599\pi$
$571$	10.0442			0.420335			0.210167	+	0.977665i	$0.432599\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			6.04009i			0.251889i
$576$		0			0
$577$	−10.1403	−	5.85453i	−0.422148	−	0.243727i	0.273848	−	0.961773i	$-0.411704\pi$
$577$	−10.1403	−	5.85453i	−0.422148	−	0.243727i	−0.695996	+	0.718046i	$0.745037\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	6.31815	−	14.3793i	0.262121	−	0.596554i
$582$		0			0
$583$	31.4472			1.30241
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.476262	−	0.824911i	0.0196575	−	0.0340477i	−0.856029	−	0.516927i	$-0.827076\pi$
$587$	0.476262	−	0.824911i	0.0196575	−	0.0340477i	0.875687	+	0.482880i	$0.160409\pi$
$588$		0			0
$589$	−3.63728	−	6.29996i	−0.149872	−	0.259585i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−15.4339	−	26.7323i	−0.633794	−	1.09776i	−0.986769	−	0.162130i	$-0.948164\pi$
$593$	−15.4339	−	26.7323i	−0.633794	−	1.09776i	0.352976	−	0.935632i	$-0.385170\pi$
$594$		0			0
$595$	−15.8738	−	21.6257i	−0.650764	−	0.886567i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	41.2112i		−	1.68384i	−0.539600	−	0.841921i	$-0.681425\pi$
$599$		−	41.2112i		−	1.68384i	0.539600	−	0.841921i	$-0.318575\pi$
$600$		0			0
$601$	14.3592	+	8.29029i	0.585724	+	0.338168i	0.763405	−	0.645920i	$-0.223526\pi$
$601$	14.3592	+	8.29029i	0.585724	+	0.338168i	−0.177681	+	0.984088i	$0.556859\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−3.66558	−	6.34897i	−0.149027	−	0.258122i
$606$		0			0
$607$	−41.1061	−	23.7326i	−1.66844	−	0.963277i	−0.968477	−	0.249102i	$-0.919864\pi$
$607$	−41.1061	−	23.7326i	−1.66844	−	0.963277i	−0.699968	−	0.714175i	$-0.746802\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	5.53292	−	3.19443i	0.223838	−	0.129233i
$612$		0			0
$613$	7.32074	−	12.6799i	0.295682	−	0.512136i	−0.679462	−	0.733711i	$-0.737787\pi$
$613$	7.32074	−	12.6799i	0.295682	−	0.512136i	0.975143	+	0.221575i	$0.0711199\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	40.1960	−	23.2072i	1.61823	−	0.934286i	0.630852	−	0.775903i	$-0.282705\pi$
$617$	40.1960	−	23.2072i	1.61823	−	0.934286i	0.987378	−	0.158383i	$-0.0506279\pi$
$618$		0			0
$619$	−6.70694	+	3.87225i	−0.269575	+	0.155639i	−0.628694	−	0.777653i	$-0.716410\pi$
$619$	−6.70694	+	3.87225i	−0.269575	+	0.155639i	0.359120	+	0.933292i	$0.383077\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−14.7461	−	20.0893i	−0.590790	−	0.804861i
$624$		0			0
$625$	3.20193	−	5.54590i	0.128077	−	0.221836i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2.34409			−0.0934651
$630$		0			0
$631$	−24.3088			−0.967718			−0.483859	−	0.875146i	$-0.660765\pi$
$631$	−24.3088			−0.967718			−0.483859	+	0.875146i	$0.660765\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	2.88373	−	4.99477i	0.114437	−	0.198211i
$636$		0			0
$637$	−30.3170	+	27.8382i	−1.20120	+	1.10299i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	15.1837	−	8.76629i	0.599718	−	0.346248i	−0.169212	−	0.985580i	$-0.554122\pi$
$641$	15.1837	−	8.76629i	0.599718	−	0.346248i	0.768931	+	0.639332i	$0.220789\pi$
$642$		0			0
$643$	−7.49992	+	4.33008i	−0.295768	+	0.170762i	−0.640540	−	0.767925i	$-0.721290\pi$
$643$	−7.49992	+	4.33008i	−0.295768	+	0.170762i	0.344772	+	0.938686i	$0.387956\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	13.3349	−	23.0967i	0.524249	−	0.908026i	−0.475352	−	0.879796i	$-0.657679\pi$
$647$	13.3349	−	23.0967i	0.524249	−	0.908026i	0.999601	−	0.0282305i	$-0.00898725\pi$
$648$		0			0
$649$	−18.7182	+	10.8070i	−0.734755	+	0.424211i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	37.9632	+	21.9181i	1.48562	+	0.857721i	0.999866	−	0.0163768i	$-0.00521313\pi$
$653$	37.9632	+	21.9181i	1.48562	+	0.857721i	0.485750	+	0.874098i	$0.338546\pi$
$654$		0			0
$655$	−3.98074	−	6.89485i	−0.155540	−	0.269404i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−39.3555	−	22.7219i	−1.53307	−	0.885120i	−0.999218	−	0.0395437i	$-0.987410\pi$
$659$	−39.3555	−	22.7219i	−1.53307	−	0.885120i	−0.533855	−	0.845576i	$-0.679257\pi$
$660$		0			0
$661$		−	40.3292i		−	1.56862i	−0.620367	−	0.784311i	$-0.713017\pi$
$661$		−	40.3292i		−	1.56862i	0.620367	−	0.784311i	$-0.286983\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	3.38058	+	30.7208i	0.131093	+	1.19130i
$666$		0			0
$667$	−6.09223	−	10.5520i	−0.235892	−	0.408577i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−28.4712	−	49.3135i	−1.09912	−	1.90373i
$672$		0			0
$673$	−3.85511	+	6.67724i	−0.148603	+	0.257389i	−0.930712	−	0.365754i	$-0.880811\pi$
$673$	−3.85511	+	6.67724i	−0.148603	+	0.257389i	0.782108	+	0.623143i	$0.214144\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−44.0576			−1.69327			−0.846635	−	0.532174i	$-0.821375\pi$
$677$	−44.0576			−1.69327			−0.846635	+	0.532174i	$0.821375\pi$
$678$		0			0
$679$	29.3194	+	12.8827i	1.12518	+	0.494393i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	3.75165	+	2.16602i	0.143553	+	0.0828804i	0.570056	−	0.821606i	$-0.306921\pi$
$683$	3.75165	+	2.16602i	0.143553	+	0.0828804i	−0.426503	+	0.904486i	$0.640255\pi$
$684$		0			0
$685$			14.7643i			0.564114i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−46.7818			−1.78225
$690$		0			0
$691$			8.08638i			0.307621i	0.988100	+	0.153810i	$0.0491545\pi$
$691$			8.08638i			0.307621i	−0.988100	+	0.153810i	$0.950846\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			7.00142i			0.265579i
$696$		0			0
$697$	−71.4333			−2.70573
$698$		0			0
$699$		0			0
$700$		0			0
$701$			41.8099i			1.57914i	0.613662	+	0.789569i	$0.289696\pi$
$701$			41.8099i			1.57914i	−0.613662	+	0.789569i	$0.710304\pi$
$702$		0			0
$703$	2.33879	+	1.35030i	0.0882091	+	0.0509275i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.0380598	+	0.0518506i	0.00143139	+	0.00195004i
$708$		0			0
$709$	−45.2940			−1.70105			−0.850526	−	0.525934i	$-0.823716\pi$
$709$	−45.2940			−1.70105			−0.850526	+	0.525934i	$0.823716\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.20053	−	2.07938i	0.0449602	−	0.0778734i
$714$		0			0
$715$	18.4297	+	31.9212i	0.689231	+	1.19378i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.73529	−	3.00561i	−0.0647155	−	0.112090i	0.831852	−	0.554997i	$-0.187281\pi$
$719$	−1.73529	−	3.00561i	−0.0647155	−	0.112090i	−0.896568	+	0.442907i	$0.853947\pi$
$720$		0			0
$721$	−3.45768	−	1.51928i	−0.128771	−	0.0565809i
$722$		0			0
$723$		0			0
$724$		0			0
$725$		−	12.4530i		−	0.462491i
$726$		0			0
$727$	−37.7189	−	21.7770i	−1.39892	−	0.807665i	−0.404638	−	0.914477i	$-0.632603\pi$
$727$	−37.7189	−	21.7770i	−1.39892	−	0.807665i	−0.994279	+	0.106811i	$0.965936\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−8.09920	−	14.0282i	−0.299560	−	0.518853i
$732$		0			0
$733$	−6.61431	−	3.81877i	−0.244305	−	0.141050i	0.372849	−	0.927892i	$-0.378381\pi$
$733$	−6.61431	−	3.81877i	−0.244305	−	0.141050i	−0.617154	+	0.786843i	$0.711714\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	39.0563	−	22.5492i	1.43866	−	0.830610i
$738$		0			0
$739$	−22.0809	+	38.2453i	−0.812260	+	1.40687i	0.0990195	+	0.995085i	$0.468429\pi$
$739$	−22.0809	+	38.2453i	−0.812260	+	1.40687i	−0.911279	+	0.411789i	$0.864904\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	10.8720	−	6.27693i	0.398853	−	0.230278i	−0.287136	−	0.957890i	$-0.592703\pi$
$743$	10.8720	−	6.27693i	0.398853	−	0.230278i	0.685989	+	0.727612i	$0.259370\pi$
$744$		0			0
$745$	3.97596	−	2.29552i	0.145668	−	0.0841015i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−26.9540	+	19.7850i	−0.984878	+	0.722927i
$750$		0			0
$751$	9.05749	−	15.6880i	0.330512	−	0.572464i	−0.652100	−	0.758133i	$-0.726112\pi$
$751$	9.05749	−	15.6880i	0.330512	−	0.572464i	0.982612	+	0.185669i	$0.0594451\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	4.39509			0.159954
$756$		0			0
$757$	39.8682			1.44903			0.724517	−	0.689257i	$-0.242063\pi$
$757$	39.8682			1.44903			0.724517	+	0.689257i	$0.242063\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−7.52844	+	13.0396i	−0.272906	+	0.472687i	−0.969605	−	0.244677i	$-0.921318\pi$
$761$	−7.52844	+	13.0396i	−0.272906	+	0.472687i	0.696699	+	0.717364i	$0.254651\pi$
$762$		0			0
$763$	−0.154544	+	0.351722i	−0.00559487	+	0.0127332i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	27.8459	−	16.0768i	1.00546	−	0.580500i
$768$		0			0
$769$	0.522559	−	0.301700i	0.0188440	−	0.0108796i	−0.490548	−	0.871414i	$-0.663204\pi$
$769$	0.522559	−	0.301700i	0.0188440	−	0.0108796i	0.509392	+	0.860534i	$0.329870\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1.56956	−	2.71856i	0.0564533	−	0.0977799i	−0.836418	−	0.548093i	$-0.815354\pi$
$773$	1.56956	−	2.71856i	0.0564533	−	0.0977799i	0.892871	+	0.450313i	$0.148687\pi$
$774$		0			0
$775$	2.12520	−	1.22699i	0.0763395	−	0.0440746i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	71.2716	+	41.1487i	2.55357	+	1.47431i
$780$		0			0
$781$	19.0764	+	33.0413i	0.682607	+	1.18231i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.232137	+	0.134024i	0.00828532	+	0.00478353i
$786$		0			0
$787$		−	18.4336i		−	0.657088i	−0.944489	−	0.328544i	$-0.893442\pi$
$787$		−	18.4336i		−	0.657088i	0.944489	−	0.328544i	$-0.106558\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−23.0485	+	16.9182i	−0.819509	+	0.601542i
$792$		0			0
$793$	42.3547	+	73.3604i	1.50406	+	2.60510i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−17.1802	−	29.7570i	−0.608554	−	1.05405i	−0.991479	−	0.130267i	$-0.958417\pi$
$797$	−17.1802	−	29.7570i	−0.608554	−	1.05405i	0.382925	−	0.923779i	$-0.374917\pi$
$798$		0			0
$799$	3.47321	−	6.01578i	0.122873	−	0.212823i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	34.9005			1.23161
$804$		0			0
$805$	−8.22340	+	6.03620i	−0.289837	+	0.212748i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−44.3399	−	25.5996i	−1.55891	−	0.900035i	−0.997362	−	0.0725881i	$-0.976874\pi$
$809$	−44.3399	−	25.5996i	−1.55891	−	0.900035i	−0.561544	−	0.827447i	$-0.689793\pi$
$810$		0			0
$811$		−	46.2446i		−	1.62387i	−0.583751	−	0.811933i	$-0.698415\pi$
$811$		−	46.2446i		−	1.62387i	0.583751	−	0.811933i	$-0.301585\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	11.2901			0.395475
$816$		0			0
$817$			18.6620i			0.652900i
$818$		0			0
$819$		0			0
$820$		0			0
$821$			8.46721i			0.295508i	0.989024	+	0.147754i	$0.0472044\pi$
$821$			8.46721i			0.295508i	−0.989024	+	0.147754i	$0.952796\pi$
$822$		0			0
$823$	25.3246			0.882759			0.441380	−	0.897321i	$-0.354489\pi$
$823$	25.3246			0.882759			0.441380	+	0.897321i	$0.354489\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	6.75531i		−	0.234905i	−0.993078	−	0.117453i	$-0.962527\pi$
$827$		−	6.75531i		−	0.234905i	0.993078	−	0.117453i	$-0.0374728\pi$
$828$		0			0
$829$	−17.0191	−	9.82599i	−0.591098	−	0.341271i	0.174434	−	0.984669i	$-0.444191\pi$
$829$	−17.0191	−	9.82599i	−0.591098	−	0.341271i	−0.765532	+	0.643398i	$0.777524\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−13.4127	+	42.6939i	−0.464723	+	1.47926i
$834$		0			0
$835$	−3.79037			−0.131171
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−16.6302	+	28.8044i	−0.574140	+	0.994439i	0.421995	+	0.906598i	$0.361330\pi$
$839$	−16.6302	+	28.8044i	−0.574140	+	0.994439i	−0.996135	+	0.0878410i	$0.972003\pi$
$840$		0			0
$841$	−1.93955	−	3.35940i	−0.0668811	−	0.115841i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−17.1076	−	29.6312i	−0.588518	−	1.01934i
$846$		0			0
$847$	−4.91969	+	11.1966i	−0.169043	+	0.384719i
$848$		0			0
$849$		0			0
$850$		0			0
$851$			0.891366i			0.0305556i
$852$		0			0
$853$	25.0891	+	14.4852i	0.859035	+	0.495964i	0.863689	−	0.504025i	$-0.168148\pi$
$853$	25.0891	+	14.4852i	0.859035	+	0.495964i	−0.00465409	+	0.999989i	$0.501481\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	23.3225	+	40.3957i	0.796680	+	1.37989i	0.921767	+	0.387744i	$0.126746\pi$
$857$	23.3225	+	40.3957i	0.796680	+	1.37989i	−0.125087	+	0.992146i	$0.539921\pi$
$858$		0			0
$859$	12.7591	+	7.36645i	0.435334	+	0.251340i	0.701616	−	0.712555i	$-0.252462\pi$
$859$	12.7591	+	7.36645i	0.435334	+	0.251340i	−0.266283	+	0.963895i	$0.585795\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−40.0533	+	23.1248i	−1.36343	+	0.787177i	−0.990079	−	0.140513i	$-0.955125\pi$
$863$	−40.0533	+	23.1248i	−1.36343	+	0.787177i	−0.373352	+	0.927690i	$0.621792\pi$
$864$		0			0
$865$	5.67743	−	9.83360i	0.193038	−	0.334352i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	36.3284	−	20.9742i	1.23236	−	0.711501i
$870$		0			0
$871$	−58.1014	+	33.5449i	−1.96869	+	1.13663i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−31.2182	+	3.43532i	−1.05537	+	0.116135i
$876$		0			0
$877$	23.9704	−	41.5179i	0.809422	−	1.40196i	−0.103843	−	0.994594i	$-0.533114\pi$
$877$	23.9704	−	41.5179i	0.809422	−	1.40196i	0.913265	−	0.407367i	$-0.133553\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	22.8464			0.769715			0.384857	−	0.922976i	$-0.374251\pi$
$881$	22.8464			0.769715			0.384857	+	0.922976i	$0.374251\pi$
$882$		0			0
$883$	9.97054			0.335535			0.167768	−	0.985827i	$-0.446344\pi$
$883$	9.97054			0.335535			0.167768	+	0.985827i	$0.446344\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	7.27637	−	12.6030i	0.244317	−	0.423169i	−0.717623	−	0.696432i	$-0.754770\pi$
$887$	7.27637	−	12.6030i	0.244317	−	0.423169i	0.961939	+	0.273263i	$0.0881031\pi$
$888$		0			0
$889$	−9.56347	+	1.05239i	−0.320748	+	0.0352959i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−6.93070	+	4.00144i	−0.231927	+	0.133903i
$894$		0			0
$895$	12.7243	−	7.34637i	0.425326	−	0.245562i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.47516	+	4.28709i	−0.0825510	+	0.142983i
$900$		0			0
$901$	−44.0499	+	25.4322i	−1.46752	+	0.847270i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	29.6050	+	17.0924i	0.984103	+	0.568172i
$906$		0			0
$907$	−10.9546	−	18.9739i	−0.363740	−	0.630017i	0.624833	−	0.780759i	$-0.285167\pi$
$907$	−10.9546	−	18.9739i	−0.363740	−	0.630017i	−0.988573	+	0.150742i	$0.951834\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	44.3072	+	25.5808i	1.46796	+	0.847529i	0.999356	−	0.0358768i	$-0.0114224\pi$
$911$	44.3072	+	25.5808i	1.46796	+	0.847529i	0.468608	+	0.883406i	$0.344756\pi$
$912$		0			0
$913$			23.4636i			0.776533i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−5.34268	+	12.1592i	−0.176431	+	0.401534i
$918$		0			0
$919$	28.4261	+	49.2355i	0.937691	+	1.62413i	0.769763	+	0.638329i	$0.220374\pi$
$919$	28.4261	+	49.2355i	0.937691	+	1.62413i	0.167928	+	0.985799i	$0.446293\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−28.3786	−	49.1533i	−0.934094	−	1.61790i
$924$		0			0
$925$	−0.455505	+	0.788957i	−0.0149769	+	0.0259407i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−10.3112			−0.338301			−0.169151	−	0.985590i	$-0.554102\pi$
$929$	−10.3112			−0.338301			−0.169151	+	0.985590i	$0.554102\pi$
$930$		0			0
$931$	37.9759	−	34.8710i	1.24461	−	1.14285i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	34.7069	+	20.0380i	1.13504	+	0.655314i
$936$		0			0
$937$		−	2.65580i		−	0.0867614i	−0.999059	−	0.0433807i	$-0.986187\pi$
$937$		−	2.65580i		−	0.0867614i	0.999059	−	0.0433807i	$-0.0138128\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−2.87329			−0.0936665			−0.0468333	−	0.998903i	$-0.514913\pi$
$941$	−2.87329			−0.0936665			−0.0468333	+	0.998903i	$0.514913\pi$
$942$		0			0
$943$			27.1633i			0.884558i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	9.27609i		−	0.301432i	−0.988577	−	0.150716i	$-0.951842\pi$
$947$		−	9.27609i		−	0.301432i	0.988577	−	0.150716i	$-0.0481579\pi$
$948$		0			0
$949$	−51.9191			−1.68536
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	52.9084i		−	1.71387i	−0.515425	−	0.856935i	$-0.672366\pi$
$953$		−	52.9084i		−	1.71387i	0.515425	−	0.856935i	$-0.327634\pi$
$954$		0			0
$955$	4.61686	+	2.66555i	0.149398	+	0.0862551i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	19.8548	−	14.5740i	0.641146	−	0.470619i
$960$		0			0
$961$	30.0245			0.968532
$962$		0			0
$963$		0			0
$964$		0			0
$965$	6.62703	−	11.4784i	0.213332	−	0.369501i
$966$		0			0
$967$	−5.65450	−	9.79388i	−0.181836	−	0.314950i	0.760669	−	0.649139i	$-0.224871\pi$
$967$	−5.65450	−	9.79388i	−0.181836	−	0.314950i	−0.942506	+	0.334189i	$0.891537\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−22.5860	−	39.1201i	−0.724819	−	1.25542i	−0.959048	−	0.283242i	$-0.908590\pi$
$971$	−22.5860	−	39.1201i	−0.724819	−	1.25542i	0.234230	−	0.972181i	$-0.424743\pi$
$972$		0			0
$973$	9.41544	−	6.91119i	0.301845	−	0.221563i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			17.6026i			0.563158i	0.959538	+	0.281579i	$0.0908582\pi$
$977$			17.6026i			0.563158i	−0.959538	+	0.281579i	$0.909142\pi$
$978$		0			0
$979$	32.2412	+	18.6145i	1.03043	+	0.594921i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−17.5420	−	30.3837i	−0.559504	−	0.969090i	−0.997538	−	0.0701312i	$-0.977658\pi$
$983$	−17.5420	−	30.3837i	−0.559504	−	0.969090i	0.438033	−	0.898959i	$-0.355675\pi$
$984$		0			0
$985$	7.65268	+	4.41828i	0.243835	+	0.140778i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−5.33438	+	3.07981i	−0.169624	+	0.0979322i
$990$		0			0
$991$	−16.9731	+	29.3982i	−0.539167	+	0.933865i	0.459782	+	0.888032i	$0.347928\pi$
$991$	−16.9731	+	29.3982i	−0.539167	+	0.933865i	−0.998949	+	0.0458331i	$0.985406\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	18.4937	−	10.6773i	0.586289	−	0.338494i
$996$		0			0
$997$	−22.1123	+	12.7666i	−0.700304	+	0.404321i	−0.807461	−	0.589921i	$-0.799159\pi$
$997$	−22.1123	+	12.7666i	−0.700304	+	0.404321i	0.107156	+	0.994242i	$0.465825\pi$
$998$		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.2033.18		48
3.2	odd	2		1008.2.ca.e.353.3		48
4.3	odd	2		1512.2.bs.a.521.18		48
7.5	odd	6		3024.2.df.e.1601.18		48
9.4	even	3		1008.2.df.e.689.7		48
9.5	odd	6		3024.2.df.e.17.18		48
12.11	even	2		504.2.bs.a.353.22	yes	48
21.5	even	6		1008.2.df.e.929.7		48
28.19	even	6		1512.2.cx.a.89.18		48
36.23	even	6		1512.2.cx.a.17.18		48
36.31	odd	6		504.2.cx.a.185.18	yes	48
63.5	even	6	inner	3024.2.ca.e.2609.18		48
63.40	odd	6		1008.2.ca.e.257.3		48
84.47	odd	6		504.2.cx.a.425.18	yes	48
252.103	even	6		504.2.bs.a.257.22	✓	48
252.131	odd	6		1512.2.bs.a.1097.18		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.22	✓	48	252.103	even	6
504.2.bs.a.353.22	yes	48	12.11	even	2
504.2.cx.a.185.18	yes	48	36.31	odd	6
504.2.cx.a.425.18	yes	48	84.47	odd	6
1008.2.ca.e.257.3		48	63.40	odd	6
1008.2.ca.e.353.3		48	3.2	odd	2
1008.2.df.e.689.7		48	9.4	even	3
1008.2.df.e.929.7		48	21.5	even	6
1512.2.bs.a.521.18		48	4.3	odd	2
1512.2.bs.a.1097.18		48	252.131	odd	6
1512.2.cx.a.17.18		48	36.23	even	6
1512.2.cx.a.89.18		48	28.19	even	6
3024.2.ca.e.2033.18		48	1.1	even	1	trivial
3024.2.ca.e.2609.18		48	63.5	even	6	inner
3024.2.df.e.17.18		48	9.5	odd	6
3024.2.df.e.1601.18		48	7.5	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)

\(f(q)\)	\(=\)	\(q+(0.793002 - 1.37352i) q^{5} +(-2.62988 + 0.289398i) q^{7} +(3.42298 - 1.97626i) q^{11} +(-5.09214 + 2.93995i) q^{13} +(-3.19652 + 5.53653i) q^{17} +(6.37856 - 3.68267i) q^{19} +(2.10532 + 1.21551i) q^{23} +(1.24230 + 2.15172i) q^{25} +(-4.34058 - 2.50604i) q^{29} -0.987677i q^{31} +(-1.68800 + 3.84168i) q^{35} +(0.183332 + 0.317540i) q^{37} +(5.58681 + 9.67664i) q^{41} +(-1.26688 + 2.19430i) q^{43} -1.08656 q^{47} +(6.83250 - 1.52216i) q^{49} +(6.89030 + 3.97812i) q^{53} -6.26871i q^{55} -5.46840 q^{59} -14.4066i q^{61} +9.32554i q^{65} +11.4100 q^{67} +9.65277i q^{71} +(7.64694 + 4.41497i) q^{73} +(-8.43010 + 6.18792i) q^{77} +10.6131 q^{79} +(-2.96819 + 5.14105i) q^{83} +(5.06969 + 8.78096i) q^{85} +(4.70952 + 8.15712i) q^{89} +(12.5409 - 9.20535i) q^{91} -11.6814i q^{95} +(-10.4826 - 6.05213i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{23} - 24 q^{25} - 18 q^{29} - 6 q^{41} + 6 q^{43} + 36 q^{47} + 6 q^{49} - 12 q^{53} + 36 q^{77} + 12 q^{79} - 18 q^{89} - 6 q^{91}+O(q^{100}) \) 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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