LMFDB - Embedded newform 1512.2.bs.a.1097.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			1097.18
Character	$\chi$	$=$	1512.1097
Dual form			1512.2.bs.a.521.18

$q$-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 $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.793002	+	1.37352i	0.354641	+	0.614257i	0.987057	−	0.160373i	$-0.0512696\pi$
$5$	0.793002	+	1.37352i	0.354641	+	0.614257i	−0.632415	+	0.774630i	$0.717936\pi$
$6$		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	$-0.536524\pi$
$11$	−3.42298	−	1.97626i	−1.03207	−	0.595865i	−0.917576	+	0.397559i	$0.869857\pi$
$12$		0			0
$13$	−5.09214	−	2.93995i	−1.41231	−	0.815395i	−0.416700	−	0.909044i	$-0.636813\pi$
$13$	−5.09214	−	2.93995i	−1.41231	−	0.815395i	−0.995605	+	0.0936493i	$0.970147\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.19652	−	5.53653i	−0.775269	−	1.34281i	−0.934643	−	0.355588i	$-0.884281\pi$
$17$	−3.19652	−	5.53653i	−0.775269	−	1.34281i	0.159374	−	0.987218i	$-0.449053\pi$
$18$		0			0
$19$	−6.37856	−	3.68267i	−1.46334	−	0.844862i	−0.464179	−	0.885741i	$-0.653651\pi$
$19$	−6.37856	−	3.68267i	−1.46334	−	0.844862i	−0.999164	+	0.0408799i	$0.986984\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.10532	+	1.21551i	−0.438990	+	0.253451i	−0.703169	−	0.711022i	$-0.748232\pi$
$23$	−2.10532	+	1.21551i	−0.438990	+	0.253451i	0.264179	+	0.964474i	$0.414899\pi$
$24$		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	−0.845574	−	0.533858i	$-0.820742\pi$
$29$	−4.34058	+	2.50604i	−0.806026	+	0.465359i	0.0395477	+	0.999218i	$0.487408\pi$
$30$		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	−0.850562	−	0.525874i	$-0.823738\pi$
$37$	0.183332	−	0.317540i	0.0301396	−	0.0522033i	0.880702	+	0.473671i	$0.157071\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.58681	−	9.67664i	0.872513	−	1.51124i	0.0131240	−	0.999914i	$-0.495822\pi$
$41$	5.58681	−	9.67664i	0.872513	−	1.51124i	0.859389	−	0.511323i	$-0.170844\pi$
$42$		0			0
$43$	1.26688	+	2.19430i	0.193197	+	0.334627i	0.946308	−	0.323266i	$-0.104781\pi$
$43$	1.26688	+	2.19430i	0.193197	+	0.334627i	−0.753111	+	0.657894i	$0.771448\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.08656			0.158491			0.0792456	−	0.996855i	$-0.474749\pi$
$47$	1.08656			0.158491			0.0792456	+	0.996855i	$0.474749\pi$
$48$		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	0.0544773	−	0.998515i	$-0.482651\pi$
$53$	6.89030	−	3.97812i	0.946455	−	0.546436i	0.891978	+	0.452079i	$0.149317\pi$
$54$		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	$-0.384153\pi$
$59$	5.46840			0.711925			0.355963	+	0.934500i	$0.384153\pi$
$60$		0			0
$61$			14.4066i			1.84458i	0.386503	+	0.922288i	$0.373683\pi$
$61$			14.4066i			1.84458i	−0.386503	+	0.922288i	$0.626317\pi$
$62$		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	$-0.745473\pi$
$67$	−11.4100			−1.39396			−0.696978	+	0.717092i	$0.745473\pi$
$68$		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	0.0194302	−	0.999811i	$-0.493815\pi$
$73$	7.64694	−	4.41497i	0.895007	−	0.516733i	0.875577	+	0.483079i	$0.160481\pi$
$74$		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	$-0.703654\pi$
$79$	−10.6131			−1.19406			−0.597032	+	0.802217i	$0.703654\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.96819	+	5.14105i	0.325801	+	0.564303i	0.981674	−	0.190568i	$-0.0610328\pi$
$83$	2.96819	+	5.14105i	0.325801	+	0.564303i	−0.655873	+	0.754871i	$0.727699\pi$
$84$		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	−0.500792	−	0.865568i	$-0.666958\pi$
$89$	4.70952	−	8.15712i	0.499208	−	0.864653i	1.00000		0.000914461i	$0.000291082\pi$
$90$		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	−0.926631	−	0.375971i	$-0.877309\pi$
$97$	−10.4826	+	6.05213i	−1.06435	+	0.614501i	−0.137715	+	0.990472i	$0.543976\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.0121553	+	0.0210536i	−0.00120950	+	0.00209491i	−0.866630	−	0.498952i	$-0.833718\pi$
$101$	−0.0121553	+	0.0210536i	−0.00120950	+	0.00209491i	0.865420	+	0.501047i	$0.167052\pi$
$102$		0			0
$103$	−1.23623	+	0.713737i	−0.121809	+	0.0703266i	−0.559667	−	0.828718i	$-0.689071\pi$
$103$	−1.23623	+	0.713737i	−0.121809	+	0.0703266i	0.437857	+	0.899044i	$0.355737\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−10.9445	−	6.31880i	−1.05804	−	0.610862i	−0.133153	−	0.991095i	$-0.542510\pi$
$107$	−10.9445	−	6.31880i	−1.05804	−	0.610862i	−0.924890	+	0.380234i	$0.875844\pi$
$108$		0			0
$109$	0.0726028	+	0.125752i	0.00695408	+	0.0120448i	0.869482	−	0.493965i	$-0.164453\pi$
$109$	0.0726028	+	0.125752i	0.00695408	+	0.0120448i	−0.862527	+	0.506010i	$0.831120\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	9.35867	+	5.40323i	0.880390	+	0.508293i	0.870787	−	0.491661i	$-0.163610\pi$
$113$	9.35867	+	5.40323i	0.880390	+	0.508293i	0.00960284	+	0.999954i	$0.496943\pi$
$114$		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	$-0.551582\pi$
$127$	−3.63647			−0.322685			−0.161342	+	0.986899i	$0.551582\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.50992	−	4.34731i	−0.219293	−	0.379826i	0.735299	−	0.677743i	$-0.237042\pi$
$131$	−2.50992	−	4.34731i	−0.219293	−	0.379826i	−0.954592	+	0.297917i	$0.903708\pi$
$132$		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	0.114377	−	0.993437i	$-0.463513\pi$
$137$	−8.06192	−	4.65455i	−0.688777	−	0.397665i	−0.803154	+	0.595772i	$0.796846\pi$
$138$		0			0
$139$	3.82307	+	2.20725i	0.324269	+	0.187217i	0.653294	−	0.757105i	$-0.273387\pi$
$139$	3.82307	+	2.20725i	0.324269	+	0.187217i	−0.329025	+	0.944321i	$0.606720\pi$
$140$		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	−0.393786	−	0.919202i	$-0.628835\pi$
$149$	2.50691	−	1.44736i	0.205374	−	0.118573i	0.599160	+	0.800630i	$0.295502\pi$
$150$		0			0
$151$	−1.38558	+	2.39990i	−0.112757	+	0.195301i	−0.916881	−	0.399161i	$-0.869302\pi$
$151$	−1.38558	+	2.39990i	−0.112757	+	0.195301i	0.804124	+	0.594462i	$0.202635\pi$
$152$		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	$-0.997853\pi$
$157$		−	0.169009i		−	0.0134884i	0.999977	−	0.00674418i	$-0.00214676\pi$
$158$		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	$-0.923265\pi$
$163$	−3.55929	+	6.16487i	−0.278785	+	0.482870i	0.692298	+	0.721612i	$0.256598\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.19494	−	2.06970i	0.0924675	−	0.160158i	−0.816081	−	0.577937i	$-0.803858\pi$
$167$	1.19494	−	2.06970i	0.0924675	−	0.160158i	0.908549	+	0.417779i	$0.137191\pi$
$168$		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	$-0.779199\pi$
$179$	−8.02286	+	4.63200i	−0.599657	+	0.346212i	0.169250	+	0.985573i	$0.445866\pi$
$180$		0			0
$181$		−	21.5541i		−	1.60210i	−0.598595	−	0.801052i	$-0.704274\pi$
$181$		−	21.5541i		−	1.60210i	0.598595	−	0.801052i	$-0.295726\pi$
$182$		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	$-0.936400\pi$
$197$		−	5.57159i		−	0.396959i	0.980105	−	0.198480i	$-0.0636003\pi$
$198$		0			0
$199$	−11.6605	+	6.73222i	−0.826594	+	0.477234i	−0.852685	−	0.522425i	$-0.825027\pi$
$199$	−11.6605	+	6.73222i	−0.826594	+	0.477234i	0.0260910	+	0.999660i	$0.491694\pi$
$200$		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	$-0.667408\pi$
$211$	7.23362	−	12.5290i	0.497983	−	0.862532i	0.999997	+	0.00232753i	$0.000740875\pi$
$212$		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	$-0.415786\pi$
$223$	18.3399	−	10.5885i	1.22813	−	0.709060i	0.966638	+	0.256146i	$0.0824529\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.23836	+	7.34106i	−0.281310	+	0.487243i	−0.971708	−	0.236187i	$-0.924102\pi$
$227$	−4.23836	+	7.34106i	−0.281310	+	0.487243i	0.690398	+	0.723430i	$0.257436\pi$
$228$		0			0
$229$	17.1285	−	9.88915i	1.13188	−	0.653494i	0.187476	−	0.982269i	$-0.439969\pi$
$229$	17.1285	−	9.88915i	1.13188	−	0.653494i	0.944408	+	0.328776i	$0.106636\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−23.7957	−	13.7385i	−1.55891	−	0.900037i	−0.997362	−	0.0725933i	$-0.976873\pi$
$233$	−23.7957	−	13.7385i	−1.55891	−	0.900037i	−0.561548	−	0.827444i	$-0.689794\pi$
$234$		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	$-0.344977\pi$
$239$	−0.979306	−	0.565402i	−0.0633460	−	0.0365728i	−0.531339	+	0.847160i	$0.678311\pi$
$240$		0			0
$241$	−1.26288	−	0.729123i	−0.0813491	−	0.0469669i	0.458774	−	0.888553i	$-0.348289\pi$
$241$	−1.26288	−	0.729123i	−0.0813491	−	0.0469669i	−0.540123	+	0.841586i	$0.681622\pi$
$242$		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	$-0.483726\pi$
$251$	1.61932			0.102210			0.0511052	+	0.998693i	$0.483726\pi$
$252$		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	0.691908	−	0.721986i	$-0.256771\pi$
$257$	−4.47759	−	7.75542i	−0.279305	−	0.483770i	−0.971212	+	0.238216i	$0.923437\pi$
$258$		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	$-0.306639\pi$
$263$	2.35287	+	1.35843i	0.145084	+	0.0837643i	−0.425701	+	0.904864i	$0.639972\pi$
$264$		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	−0.998826	−	0.0484519i	$-0.984571\pi$
$269$	−8.87918	−	15.3792i	−0.541373	−	0.937686i	0.457452	−	0.889234i	$-0.348762\pi$
$270$		0			0
$271$	2.76570	+	1.59678i	0.168004	+	0.0969973i	0.581644	−	0.813443i	$-0.302410\pi$
$271$	2.76570	+	1.59678i	0.168004	+	0.0969973i	−0.413640	+	0.910440i	$0.635743\pi$
$272$		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	−0.948315	−	0.317330i	$-0.897214\pi$
$277$	−3.31771	+	5.74644i	−0.199342	+	0.345270i	0.748973	+	0.662600i	$0.230547\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.88306	−	3.97394i	0.410609	−	0.237065i	−0.280442	−	0.959871i	$-0.590481\pi$
$281$	6.88306	−	3.97394i	0.410609	−	0.237065i	0.691051	+	0.722806i	$0.257148\pi$
$282$		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	−0.712844	−	0.701323i	$-0.752593\pi$
$293$	4.29543	−	7.43990i	0.250942	−	0.434644i	0.963785	+	0.266679i	$0.0859265\pi$
$294$		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	$-0.755950\pi$
$311$	−25.4018			−1.44040			−0.720201	+	0.693766i	$0.755950\pi$
$312$		0			0
$313$		−	23.1410i		−	1.30800i	−0.756493	−	0.654002i	$-0.773089\pi$
$313$		−	23.1410i		−	1.30800i	0.756493	−	0.654002i	$-0.226911\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			6.02945i			0.338648i	0.985560	+	0.169324i	$0.0541584\pi$
$317$			6.02945i			0.338648i	−0.985560	+	0.169324i	$0.945842\pi$
$318$		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	$-0.658896\pi$
$331$	−17.4188			−0.957424			−0.478712	+	0.877972i	$0.658896\pi$
$332$		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	−0.885995	−	0.463696i	$-0.846523\pi$
$337$	−0.760462	+	1.31716i	−0.0414250	+	0.0717502i	0.844570	+	0.535446i	$0.179856\pi$
$338$		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	−0.626758	−	0.779214i	$-0.715619\pi$
$349$	−4.95655	+	2.86167i	−0.265318	+	0.153182i	0.361440	+	0.932395i	$0.382285\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.92270	+	3.33022i	−0.102335	+	0.177250i	−0.912646	−	0.408750i	$-0.865965\pi$
$353$	−1.92270	+	3.33022i	−0.102335	+	0.177250i	0.810311	+	0.586000i	$0.199298\pi$
$354$		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	$-0.440860\pi$
$359$	−10.8763	−	6.27946i	−0.574031	−	0.331417i	−0.758758	+	0.651373i	$0.774193\pi$
$360$		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	$-0.343489\pi$
$367$	−1.05849	−	0.611122i	−0.0552530	−	0.0319003i	−0.527372	+	0.849634i	$0.676823\pi$
$368$		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	0.644022	−	0.765007i	$-0.277265\pi$
$373$	−6.57624	−	11.3904i	−0.340505	−	0.589772i	−0.984527	+	0.175235i	$0.943931\pi$
$374$		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	$-0.298995\pi$
$379$	22.9852			1.18067			0.590336	+	0.807157i	$0.298995\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	13.9683	+	24.1938i	0.713746	+	1.23625i	0.963441	+	0.267920i	$0.0863364\pi$
$383$	13.9683	+	24.1938i	0.713746	+	1.23625i	−0.249695	+	0.968325i	$0.580330\pi$
$384$		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	0.780137	−	0.625609i	$-0.215150\pi$
$389$	12.3942	+	7.15580i	0.628412	+	0.362814i	−0.151725	+	0.988423i	$0.548483\pi$
$390$		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	0.397046	−	0.917799i	$-0.370035\pi$
$397$	−3.97038	−	2.29230i	−0.199267	−	0.115047i	−0.596314	+	0.802751i	$0.703369\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.59026	+	5.53694i	−0.478915	+	0.276502i	−0.719964	−	0.694011i	$-0.755842\pi$
$401$	−9.59026	+	5.53694i	−0.478915	+	0.276502i	0.241049	+	0.970513i	$0.422508\pi$
$402$		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	$-0.951497\pi$
$409$		−	6.13944i		−	0.303576i	0.988413	−	0.151788i	$-0.0485031\pi$
$410$		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	$-0.975314\pi$
$419$	−8.83059	+	15.2950i	−0.431402	+	0.747211i	0.565592	+	0.824685i	$0.308648\pi$
$420$		0			0
$421$	11.3569	+	19.6707i	0.553501	+	0.958693i	0.998018	+	0.0629223i	$0.0200420\pi$
$421$	11.3569	+	19.6707i	0.553501	+	0.958693i	−0.444517	+	0.895770i	$0.646625\pi$
$422$		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	$-0.495524\pi$
$431$	18.4152	−	10.6320i	0.887031	−	0.512128i	0.872970	+	0.487773i	$0.162191\pi$
$432$		0			0
$433$		−	16.1075i		−	0.774079i	−0.922063	−	0.387039i	$-0.873498\pi$
$433$		−	16.1075i		−	0.774079i	0.922063	−	0.387039i	$-0.126502\pi$
$434$		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	$0.0430275\pi$
$449$			5.71118i			0.269527i	−0.990878	+	0.134764i	$0.956972\pi$
$450$		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	−0.769613	−	0.638510i	$-0.779551\pi$
$461$	−20.1348	−	34.8746i	−0.937773	−	1.62427i	−0.168160	−	0.985760i	$-0.553782\pi$
$462$		0			0
$463$	6.92014	−	11.9860i	0.321606	−	0.557038i	−0.659213	−	0.751956i	$-0.729111\pi$
$463$	6.92014	−	11.9860i	0.321606	−	0.557038i	0.980820	+	0.194917i	$0.0624439\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−10.5793	+	18.3238i	−0.489549	+	0.847924i	−0.999928	−	0.0120256i	$-0.996172\pi$
$467$	−10.5793	+	18.3238i	−0.489549	+	0.847924i	0.510378	+	0.859950i	$0.329505\pi$
$468$		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	$-0.816300\pi$
$479$	1.17063	−	2.02760i	0.0534876	−	0.0926433i	0.891530	+	0.452963i	$0.149633\pi$
$480$		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	$-0.297829\pi$
$487$	−8.83818	−	15.3082i	−0.400496	−	0.693679i	−0.993786	+	0.111310i	$0.964495\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−2.01875	−	1.16553i	−0.0911051	−	0.0525995i	0.453755	−	0.891126i	$-0.350084\pi$
$491$	−2.01875	−	1.16553i	−0.0911051	−	0.0525995i	−0.544860	+	0.838527i	$0.683417\pi$
$492$		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	−0.965781	−	0.259358i	$-0.916489\pi$
$499$	−15.8044	−	27.3740i	−0.707501	−	1.22543i	0.258280	−	0.966070i	$-0.416844\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	38.9500			1.73670			0.868348	−	0.495956i	$-0.165182\pi$
$503$	38.9500			1.73670			0.868348	+	0.495956i	$0.165182\pi$
$504$		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	0.671687	−	0.740835i	$-0.265570\pi$
$509$	−6.89778	−	11.9473i	−0.305739	−	0.529555i	−0.977426	+	0.211280i	$0.932237\pi$
$510$		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	0.911540	−	0.411211i	$-0.134894\pi$
$521$	2.27458	+	3.93969i	0.0996512	+	0.172601i	−0.811889	+	0.583812i	$0.801561\pi$
$522$		0			0
$523$	32.6301	+	18.8390i	1.42681	+	0.823772i	0.996868	−	0.0790830i	$-0.0251992\pi$
$523$	32.6301	+	18.8390i	1.42681	+	0.823772i	0.429946	+	0.902855i	$0.358533\pi$
$524$		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	−0.897119	−	0.441789i	$-0.854344\pi$
$541$	−1.53417	+	2.65727i	−0.0659593	+	0.114245i	0.831160	+	0.556034i	$0.187677\pi$
$542$		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	$-0.266565\pi$
$547$	−7.22022	−	12.5058i	−0.308714	−	0.534709i	−0.978081	+	0.208223i	$0.933232\pi$
$548$		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	−0.341042	−	0.940048i	$-0.610780\pi$
$557$	7.14024	−	4.12242i	0.302542	−	0.174672i	0.643584	+	0.765375i	$0.277447\pi$
$558$		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	$-0.436717\pi$
$563$	9.37245			0.395002			0.197501	+	0.980303i	$0.436717\pi$
$564$		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	$-0.869167\pi$
$569$		−	19.0614i		−	0.799098i	0.916712	−	0.399549i	$-0.130833\pi$
$570$		0			0
$571$	−10.0442			−0.420335			−0.210167	−	0.977665i	$-0.567401\pi$
$571$	−10.0442			−0.420335			−0.210167	+	0.977665i	$0.567401\pi$
$572$		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	−0.695996	−	0.718046i	$-0.745037\pi$
$577$	−10.1403	+	5.85453i	−0.422148	+	0.243727i	0.273848	+	0.961773i	$0.411704\pi$
$578$		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	$-0.172924\pi$
$587$	−0.476262	−	0.824911i	−0.0196575	−	0.0340477i	−0.875687	+	0.482880i	$0.839591\pi$
$588$		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	0.352976	+	0.935632i	$0.385170\pi$
$593$	−15.4339	+	26.7323i	−0.633794	+	1.09776i	−0.986769	+	0.162130i	$0.948164\pi$
$594$		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	−0.177681	−	0.984088i	$-0.556859\pi$
$601$	14.3592	−	8.29029i	0.585724	−	0.338168i	0.763405	+	0.645920i	$0.223526\pi$
$602$		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	0.699968	−	0.714175i	$-0.253198\pi$
$607$	41.1061	−	23.7326i	1.66844	−	0.963277i	0.968477	−	0.249102i	$-0.0801356\pi$
$608$		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	0.975143	−	0.221575i	$-0.0711199\pi$
$613$	7.32074	+	12.6799i	0.295682	+	0.512136i	−0.679462	+	0.733711i	$0.737787\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	40.1960	+	23.2072i	1.61823	+	0.934286i	0.987378	+	0.158383i	$0.0506279\pi$
$617$	40.1960	+	23.2072i	1.61823	+	0.934286i	0.630852	+	0.775903i	$0.282705\pi$
$618$		0			0
$619$	6.70694	+	3.87225i	0.269575	+	0.155639i	0.628694	−	0.777653i	$-0.283590\pi$
$619$	6.70694	+	3.87225i	0.269575	+	0.155639i	−0.359120	+	0.933292i	$0.616923\pi$
$620$		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	$-0.339235\pi$
$631$	24.3088			0.967718			0.483859	+	0.875146i	$0.339235\pi$
$632$		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	0.768931	−	0.639332i	$-0.220789\pi$
$641$	15.1837	+	8.76629i	0.599718	+	0.346248i	−0.169212	+	0.985580i	$0.554122\pi$
$642$		0			0
$643$	7.49992	+	4.33008i	0.295768	+	0.170762i	0.640540	−	0.767925i	$-0.278710\pi$
$643$	7.49992	+	4.33008i	0.295768	+	0.170762i	−0.344772	+	0.938686i	$0.612044\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−13.3349	−	23.0967i	−0.524249	−	0.908026i	−0.999601	−	0.0282305i	$-0.991013\pi$
$647$	−13.3349	−	23.0967i	−0.524249	−	0.908026i	0.475352	−	0.879796i	$-0.342321\pi$
$648$		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	0.485750	−	0.874098i	$-0.338546\pi$
$653$	37.9632	−	21.9181i	1.48562	−	0.857721i	0.999866	+	0.0163768i	$0.00521313\pi$
$654$		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	0.533855	−	0.845576i	$-0.320743\pi$
$659$	39.3555	−	22.7219i	1.53307	−	0.885120i	0.999218	−	0.0395437i	$-0.0125904\pi$
$660$		0			0
$661$			40.3292i			1.56862i	0.620367	+	0.784311i	$0.286983\pi$
$661$			40.3292i			1.56862i	−0.620367	+	0.784311i	$0.713017\pi$
$662$		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	0.782108	−	0.623143i	$-0.214144\pi$
$673$	−3.85511	−	6.67724i	−0.148603	−	0.257389i	−0.930712	+	0.365754i	$0.880811\pi$
$674$		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	$-0.693079\pi$
$683$	−3.75165	+	2.16602i	−0.143553	+	0.0828804i	0.426503	+	0.904486i	$0.359745\pi$
$684$		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	$-0.710304\pi$
$701$		−	41.8099i		−	1.57914i	0.613662	−	0.789569i	$-0.289696\pi$
$702$		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	$-0.812719\pi$
$719$	1.73529	−	3.00561i	0.0647155	−	0.112090i	0.896568	+	0.442907i	$0.146053\pi$
$720$		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	$-0.367397\pi$
$727$	37.7189	−	21.7770i	1.39892	−	0.807665i	0.994279	+	0.106811i	$0.0340641\pi$
$728$		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	−0.617154	−	0.786843i	$-0.711714\pi$
$733$	−6.61431	+	3.81877i	−0.244305	+	0.141050i	0.372849	+	0.927892i	$0.378381\pi$
$734$		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	0.911279	+	0.411789i	$0.135096\pi$
$739$	22.0809	+	38.2453i	0.812260	+	1.40687i	−0.0990195	+	0.995085i	$0.531571\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−10.8720	−	6.27693i	−0.398853	−	0.230278i	0.287136	−	0.957890i	$-0.407297\pi$
$743$	−10.8720	−	6.27693i	−0.398853	−	0.230278i	−0.685989	+	0.727612i	$0.740630\pi$
$744$		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	$-0.273888\pi$
$751$	−9.05749	−	15.6880i	−0.330512	−	0.572464i	−0.982612	+	0.185669i	$0.940555\pi$
$752$		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	0.696699	−	0.717364i	$-0.254651\pi$
$761$	−7.52844	−	13.0396i	−0.272906	−	0.472687i	−0.969605	+	0.244677i	$0.921318\pi$
$762$		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	0.509392	−	0.860534i	$-0.329870\pi$
$769$	0.522559	+	0.301700i	0.0188440	+	0.0108796i	−0.490548	+	0.871414i	$0.663204\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1.56956	+	2.71856i	0.0564533	+	0.0977799i	0.892871	−	0.450313i	$-0.148687\pi$
$773$	1.56956	+	2.71856i	0.0564533	+	0.0977799i	−0.836418	+	0.548093i	$0.815354\pi$
$774$		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	0.382925	+	0.923779i	$0.374917\pi$
$797$	−17.1802	+	29.7570i	−0.608554	+	1.05405i	−0.991479	+	0.130267i	$0.958417\pi$
$798$		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	−0.561544	+	0.827447i	$0.689793\pi$
$809$	−44.3399	+	25.5996i	−1.55891	+	0.900035i	−0.997362	+	0.0725881i	$0.976874\pi$
$810$		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	$-0.952796\pi$
$821$		−	8.46721i		−	0.295508i	0.989024	−	0.147754i	$-0.0472044\pi$
$822$		0			0
$823$	−25.3246			−0.882759			−0.441380	−	0.897321i	$-0.645511\pi$
$823$	−25.3246			−0.882759			−0.441380	+	0.897321i	$0.645511\pi$
$824$		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	−0.765532	−	0.643398i	$-0.777524\pi$
$829$	−17.0191	+	9.82599i	−0.591098	+	0.341271i	0.174434	+	0.984669i	$0.444191\pi$
$830$		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	0.996135	+	0.0878410i	$0.0279967\pi$
$839$	16.6302	+	28.8044i	0.574140	+	0.994439i	−0.421995	+	0.906598i	$0.638670\pi$
$840$		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	−0.00465409	−	0.999989i	$-0.501481\pi$
$853$	25.0891	−	14.4852i	0.859035	−	0.495964i	0.863689	+	0.504025i	$0.168148\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	23.3225	−	40.3957i	0.796680	−	1.37989i	−0.125087	−	0.992146i	$-0.539921\pi$
$857$	23.3225	−	40.3957i	0.796680	−	1.37989i	0.921767	−	0.387744i	$-0.126746\pi$
$858$		0			0
$859$	−12.7591	+	7.36645i	−0.435334	+	0.251340i	−0.701616	−	0.712555i	$-0.747538\pi$
$859$	−12.7591	+	7.36645i	−0.435334	+	0.251340i	0.266283	+	0.963895i	$0.414205\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	40.0533	+	23.1248i	1.36343	+	0.787177i	0.990079	−	0.140513i	$-0.0448751\pi$
$863$	40.0533	+	23.1248i	1.36343	+	0.787177i	0.373352	+	0.927690i	$0.378208\pi$
$864$		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	0.913265	+	0.407367i	$0.133553\pi$
$877$	23.9704	+	41.5179i	0.809422	+	1.40196i	−0.103843	+	0.994594i	$0.533114\pi$
$878$		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	$-0.553656\pi$
$883$	−9.97054			−0.335535			−0.167768	+	0.985827i	$0.553656\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−7.27637	−	12.6030i	−0.244317	−	0.423169i	0.717623	−	0.696432i	$-0.245230\pi$
$887$	−7.27637	−	12.6030i	−0.244317	−	0.423169i	−0.961939	+	0.273263i	$0.911897\pi$
$888$		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	$-0.714833\pi$
$907$	10.9546	−	18.9739i	0.363740	−	0.630017i	0.988573	+	0.150742i	$0.0481662\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−44.3072	+	25.5808i	−1.46796	+	0.847529i	−0.999356	−	0.0358768i	$-0.988578\pi$
$911$	−44.3072	+	25.5808i	−1.46796	+	0.847529i	−0.468608	+	0.883406i	$0.655244\pi$
$912$		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	−0.167928	+	0.985799i	$0.553707\pi$
$919$	−28.4261	+	49.2355i	−0.937691	+	1.62413i	−0.769763	+	0.638329i	$0.779626\pi$
$920$		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	$0.0138128\pi$
$937$			2.65580i			0.0867614i	−0.999059	+	0.0433807i	$0.986187\pi$
$938$		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	$0.327634\pi$
$953$			52.9084i			1.71387i	−0.515425	+	0.856935i	$0.672366\pi$
$954$		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	$-0.775129\pi$
$967$	5.65450	−	9.79388i	0.181836	−	0.314950i	0.942506	+	0.334189i	$0.108463\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	22.5860	−	39.1201i	0.724819	−	1.25542i	−0.234230	−	0.972181i	$-0.575257\pi$
$971$	22.5860	−	39.1201i	0.724819	−	1.25542i	0.959048	−	0.283242i	$-0.0914099\pi$
$972$		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	$-0.909142\pi$
$977$		−	17.6026i		−	0.563158i	0.959538	−	0.281579i	$-0.0908582\pi$
$978$		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	−0.438033	−	0.898959i	$-0.644325\pi$
$983$	17.5420	−	30.3837i	0.559504	−	0.969090i	0.997538	−	0.0701312i	$-0.0223418\pi$
$984$		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	0.998949	+	0.0458331i	$0.0145942\pi$
$991$	16.9731	+	29.3982i	0.539167	+	0.933865i	−0.459782	+	0.888032i	$0.652072\pi$
$992$		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	0.107156	−	0.994242i	$-0.465825\pi$
$997$	−22.1123	−	12.7666i	−0.700304	−	0.404321i	−0.807461	+	0.589921i	$0.799159\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.bs.a.1097.18		48
3.2	odd	2		504.2.bs.a.257.22	✓	48
4.3	odd	2		3024.2.ca.e.2609.18		48
7.3	odd	6		1512.2.cx.a.17.18		48
9.2	odd	6		1512.2.cx.a.89.18		48
9.7	even	3		504.2.cx.a.425.18	yes	48
12.11	even	2		1008.2.ca.e.257.3		48
21.17	even	6		504.2.cx.a.185.18	yes	48
28.3	even	6		3024.2.df.e.17.18		48
36.7	odd	6		1008.2.df.e.929.7		48
36.11	even	6		3024.2.df.e.1601.18		48
63.38	even	6	inner	1512.2.bs.a.521.18		48
63.52	odd	6		504.2.bs.a.353.22	yes	48
84.59	odd	6		1008.2.df.e.689.7		48
252.115	even	6		1008.2.ca.e.353.3		48
252.227	odd	6		3024.2.ca.e.2033.18		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.22	✓	48	3.2	odd	2
504.2.bs.a.353.22	yes	48	63.52	odd	6
504.2.cx.a.185.18	yes	48	21.17	even	6
504.2.cx.a.425.18	yes	48	9.7	even	3
1008.2.ca.e.257.3		48	12.11	even	2
1008.2.ca.e.353.3		48	252.115	even	6
1008.2.df.e.689.7		48	84.59	odd	6
1008.2.df.e.929.7		48	36.7	odd	6
1512.2.bs.a.521.18		48	63.38	even	6	inner
1512.2.bs.a.1097.18		48	1.1	even	1	trivial
1512.2.cx.a.17.18		48	7.3	odd	6
1512.2.cx.a.89.18		48	9.2	odd	6
3024.2.ca.e.2033.18		48	252.227	odd	6
3024.2.ca.e.2609.18		48	4.3	odd	2
3024.2.df.e.17.18		48	28.3	even	6
3024.2.df.e.1601.18		48	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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