LMFDB - Embedded newform 1512.2.bs.a.521.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			521.12
Character	$\chi$	$=$	1512.521
Dual form			1512.2.bs.a.1097.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.103514 - 0.179292i) q^{5} +(2.64517 + 0.0556151i) q^{7} +(1.31380 - 0.758523i) q^{11} +(3.39130 - 1.95797i) q^{13} +(-0.873421 + 1.51281i) q^{17} +(-0.968573 + 0.559206i) q^{19} +(1.25201 + 0.722851i) q^{23} +(2.47857 + 4.29301i) q^{25} +(-1.99711 - 1.15303i) q^{29} -5.95518i q^{31} +(0.283783 - 0.468499i) q^{35} +(-2.13573 - 3.69920i) q^{37} +(-2.91134 - 5.04260i) q^{41} +(-0.213489 + 0.369774i) q^{43} +8.26814 q^{47} +(6.99381 + 0.294222i) q^{49} +(8.16638 + 4.71486i) q^{53} -0.314071i q^{55} -3.26809 q^{59} +12.1526i q^{61} -0.810709i q^{65} -6.48982 q^{67} -7.10884i q^{71} +(10.6188 + 6.13075i) q^{73} +(3.51741 - 1.93335i) q^{77} +5.15612 q^{79} +(8.36457 - 14.4879i) q^{83} +(0.180823 + 0.313194i) q^{85} +(1.96290 + 3.39984i) q^{89} +(9.07945 - 4.99055i) q^{91} +0.231543i q^{95} +(13.1184 + 7.57392i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{23} - 24 q^{25} - 18 q^{29} - 6 q^{41} - 6 q^{43} - 36 q^{47} + 6 q^{49} - 12 q^{53} + 36 q^{77} - 12 q^{79} - 18 q^{89} + 6 q^{91}+O(q^{100}) $ 48 * q + 12 * q^23 - 24 * q^25 - 18 * q^29 - 6 * q^41 - 6 * q^43 - 36 * q^47 + 6 * q^49 - 12 * q^53 + 36 * q^77 - 12 * q^79 - 18 * q^89 + 6 * q^91

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.103514	−	0.179292i	0.0462929	−	0.0801816i	−0.841951	−	0.539555i	$-0.818593\pi$
$5$	0.103514	−	0.179292i	0.0462929	−	0.0801816i	0.888243	+	0.459373i	$0.151926\pi$
$6$		0			0
$7$	2.64517	+	0.0556151i	0.999779	+	0.0210205i
$7$	2.64517	+	0.0556151i	0.999779	+	0.0210205i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.31380	−	0.758523i	0.396126	−	0.228703i	−0.288685	−	0.957424i	$-0.593218\pi$
$11$	1.31380	−	0.758523i	0.396126	−	0.228703i	0.684811	+	0.728721i	$0.259885\pi$
$12$		0			0
$13$	3.39130	−	1.95797i	0.940578	−	0.543043i	0.0504364	−	0.998727i	$-0.483939\pi$
$13$	3.39130	−	1.95797i	0.940578	−	0.543043i	0.890141	+	0.455684i	$0.150605\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.873421	+	1.51281i	−0.211836	+	0.366910i	−0.952289	−	0.305198i	$-0.901277\pi$
$17$	−0.873421	+	1.51281i	−0.211836	+	0.366910i	0.740453	+	0.672108i	$0.234611\pi$
$18$		0			0
$19$	−0.968573	+	0.559206i	−0.222206	+	0.128291i	−0.606971	−	0.794724i	$-0.707616\pi$
$19$	−0.968573	+	0.559206i	−0.222206	+	0.128291i	0.384765	+	0.923014i	$0.374282\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.25201	+	0.722851i	0.261063	+	0.150725i	0.624819	−	0.780769i	$-0.285173\pi$
$23$	1.25201	+	0.722851i	0.261063	+	0.150725i	−0.363756	+	0.931494i	$0.618506\pi$
$24$		0			0
$25$	2.47857	+	4.29301i	0.495714	+	0.858602i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.99711	−	1.15303i	−0.370853	−	0.214112i	0.302978	−	0.952998i	$-0.402019\pi$
$29$	−1.99711	−	1.15303i	−0.370853	−	0.214112i	−0.673831	+	0.738885i	$0.735352\pi$
$30$		0			0
$31$		−	5.95518i		−	1.06958i	−0.844985	−	0.534791i	$-0.820390\pi$
$31$		−	5.95518i		−	1.06958i	0.844985	−	0.534791i	$-0.179610\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.283783	−	0.468499i	0.0479681	−	0.0791908i
$36$		0			0
$37$	−2.13573	−	3.69920i	−0.351113	−	0.608145i	0.635332	−	0.772239i	$-0.280863\pi$
$37$	−2.13573	−	3.69920i	−0.351113	−	0.608145i	−0.986445	+	0.164094i	$0.947530\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.91134	−	5.04260i	−0.454676	−	0.787521i	0.543994	−	0.839089i	$-0.316911\pi$
$41$	−2.91134	−	5.04260i	−0.454676	−	0.787521i	−0.998669	+	0.0515680i	$0.983578\pi$
$42$		0			0
$43$	−0.213489	+	0.369774i	−0.0325568	+	0.0563900i	−0.881845	−	0.471540i	$-0.843698\pi$
$43$	−0.213489	+	0.369774i	−0.0325568	+	0.0563900i	0.849288	+	0.527930i	$0.177032\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	8.26814			1.20603			0.603016	−	0.797729i	$-0.293966\pi$
$47$	8.26814			1.20603			0.603016	+	0.797729i	$0.293966\pi$
$48$		0			0
$49$	6.99381	+	0.294222i	0.999116	+	0.0420318i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	8.16638	+	4.71486i	1.12174	+	0.647636i	0.941844	−	0.336050i	$-0.109091\pi$
$53$	8.16638	+	4.71486i	1.12174	+	0.647636i	0.179894	+	0.983686i	$0.442424\pi$
$54$		0			0
$55$		−	0.314071i		−	0.0423494i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.26809			−0.425469			−0.212735	−	0.977110i	$-0.568237\pi$
$59$	−3.26809			−0.425469			−0.212735	+	0.977110i	$0.568237\pi$
$60$		0			0
$61$			12.1526i			1.55598i	0.628277	+	0.777990i	$0.283760\pi$
$61$			12.1526i			1.55598i	−0.628277	+	0.777990i	$0.716240\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	0.810709i		−	0.100556i
$66$		0			0
$67$	−6.48982			−0.792858			−0.396429	−	0.918065i	$-0.629751\pi$
$67$	−6.48982			−0.792858			−0.396429	+	0.918065i	$0.629751\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	7.10884i		−	0.843665i	−0.906674	−	0.421832i	$-0.861387\pi$
$71$		−	7.10884i		−	0.843665i	0.906674	−	0.421832i	$-0.138613\pi$
$72$		0			0
$73$	10.6188	+	6.13075i	1.24283	+	0.717549i	0.969670	−	0.244419i	$-0.0785971\pi$
$73$	10.6188	+	6.13075i	1.24283	+	0.717549i	0.273162	+	0.961968i	$0.411930\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.51741	−	1.93335i	0.400846	−	0.220326i
$78$		0			0
$79$	5.15612			0.580109			0.290054	−	0.957010i	$-0.406327\pi$
$79$	5.15612			0.580109			0.290054	+	0.957010i	$0.406327\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	8.36457	−	14.4879i	0.918131	−	1.59025i	0.115879	−	0.993263i	$-0.463031\pi$
$83$	8.36457	−	14.4879i	0.918131	−	1.59025i	0.802252	−	0.596986i	$-0.203635\pi$
$84$		0			0
$85$	0.180823	+	0.313194i	0.0196130	+	0.0339707i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.96290	+	3.39984i	0.208067	+	0.360382i	0.951105	−	0.308866i	$-0.0999496\pi$
$89$	1.96290	+	3.39984i	0.208067	+	0.360382i	−0.743039	+	0.669248i	$0.766616\pi$
$90$		0			0
$91$	9.07945	−	4.99055i	0.951785	−	0.523151i
$92$		0			0
$93$		0			0
$94$		0			0
$95$			0.231543i			0.0237558i
$96$		0			0
$97$	13.1184	+	7.57392i	1.33197	+	0.769016i	0.985602	−	0.169082i	$-0.0540802\pi$
$97$	13.1184	+	7.57392i	1.33197	+	0.769016i	0.346372	+	0.938097i	$0.387414\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5.13315	−	8.89088i	−0.510767	−	0.884675i	−0.999922	−	0.0124781i	$-0.996028\pi$
$101$	−5.13315	−	8.89088i	−0.510767	−	0.884675i	0.489155	−	0.872197i	$-0.337305\pi$
$102$		0			0
$103$	−9.74935	−	5.62879i	−0.960632	−	0.554621i	−0.0642646	−	0.997933i	$-0.520470\pi$
$103$	−9.74935	−	5.62879i	−0.960632	−	0.554621i	−0.896368	+	0.443312i	$0.853804\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.87450	−	5.70104i	0.954604	−	0.551141i	0.0600957	−	0.998193i	$-0.480859\pi$
$107$	9.87450	−	5.70104i	0.954604	−	0.551141i	0.894508	+	0.447052i	$0.147526\pi$
$108$		0			0
$109$	1.50422	−	2.60538i	0.144078	−	0.249550i	−0.784951	−	0.619558i	$-0.787312\pi$
$109$	1.50422	−	2.60538i	0.144078	−	0.249550i	0.929029	+	0.370008i	$0.120645\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−14.2634	+	8.23500i	−1.34179	+	0.774683i	−0.987070	−	0.160289i	$-0.948757\pi$
$113$	−14.2634	+	8.23500i	−1.34179	+	0.774683i	−0.354721	+	0.934972i	$0.615424\pi$
$114$		0			0
$115$	0.259202	−	0.149650i	0.0241707	−	0.0139550i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.39448	+	3.95306i	−0.219502	+	0.362376i
$120$		0			0
$121$	−4.34928	+	7.53318i	−0.395390	+	0.684835i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	2.06141			0.184378
$126$		0			0
$127$	−8.52680			−0.756631			−0.378316	−	0.925677i	$-0.623497\pi$
$127$	−8.52680			−0.756631			−0.378316	+	0.925677i	$0.623497\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	7.27730	−	12.6047i	0.635821	−	1.10127i	−0.350520	−	0.936555i	$-0.613995\pi$
$131$	7.27730	−	12.6047i	0.635821	−	1.10127i	0.986341	−	0.164719i	$-0.0526716\pi$
$132$		0			0
$133$	−2.59314	+	1.42533i	−0.224853	+	0.123591i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.25263	−	5.34201i	0.790505	−	0.456398i	−0.0496351	−	0.998767i	$-0.515806\pi$
$137$	9.25263	−	5.34201i	0.790505	−	0.456398i	0.840140	+	0.542369i	$0.182473\pi$
$138$		0			0
$139$	−7.46448	+	4.30962i	−0.633129	+	0.365537i	−0.781963	−	0.623325i	$-0.785781\pi$
$139$	−7.46448	+	4.30962i	−0.633129	+	0.365537i	0.148834	+	0.988862i	$0.452448\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.97033	−	5.14476i	0.248391	−	0.430227i
$144$		0			0
$145$	−0.413457	+	0.238709i	−0.0343357	+	0.0198237i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	19.0951	+	11.0245i	1.56433	+	0.903166i	0.996811	+	0.0798049i	$0.0254297\pi$
$149$	19.0951	+	11.0245i	1.56433	+	0.903166i	0.567518	+	0.823361i	$0.307904\pi$
$150$		0			0
$151$	4.40064	+	7.62212i	0.358119	+	0.620280i	0.987647	−	0.156698i	$-0.0500850\pi$
$151$	4.40064	+	7.62212i	0.358119	+	0.620280i	−0.629528	+	0.776978i	$0.716752\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.06771	−	0.616444i	−0.0857608	−	0.0495140i
$156$		0			0
$157$			10.5531i			0.842228i	0.907008	+	0.421114i	$0.138361\pi$
$157$			10.5531i			0.842228i	−0.907008	+	0.421114i	$0.861639\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	3.27159	+	1.98169i	0.257837	+	0.156179i
$162$		0			0
$163$	−4.64731	−	8.04937i	−0.364005	−	0.630475i	0.624611	−	0.780936i	$-0.285258\pi$
$163$	−4.64731	−	8.04937i	−0.364005	−	0.630475i	−0.988616	+	0.150461i	$0.951924\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.44458	−	7.69824i	−0.343932	−	0.595707i	0.641227	−	0.767351i	$-0.278426\pi$
$167$	−4.44458	−	7.69824i	−0.343932	−	0.595707i	−0.985159	+	0.171644i	$0.945092\pi$
$168$		0			0
$169$	1.16728	−	2.02179i	0.0897910	−	0.155523i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.79940			−0.745034			−0.372517	−	0.928025i	$-0.621505\pi$
$173$	−9.79940			−0.745034			−0.372517	+	0.928025i	$0.621505\pi$
$174$		0			0
$175$	6.31747	+	11.4936i	0.477556	+	0.868832i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−14.3141	−	8.26425i	−1.06989	−	0.617699i	−0.141735	−	0.989905i	$-0.545268\pi$
$179$	−14.3141	−	8.26425i	−1.06989	−	0.617699i	−0.928150	+	0.372206i	$0.878602\pi$
$180$		0			0
$181$		−	23.8542i		−	1.77307i	−0.462664	−	0.886534i	$-0.653106\pi$
$181$		−	23.8542i		−	1.77307i	0.462664	−	0.886534i	$-0.346894\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.884314			−0.0650161
$186$		0			0
$187$			2.65004i			0.193790i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			22.3601i			1.61792i	0.587864	+	0.808960i	$0.299969\pi$
$191$			22.3601i			1.61792i	−0.587864	+	0.808960i	$0.700031\pi$
$192$		0			0
$193$	−8.65700			−0.623145			−0.311572	−	0.950222i	$-0.600856\pi$
$193$	−8.65700			−0.623145			−0.311572	+	0.950222i	$0.600856\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			23.2821i			1.65878i	0.558668	+	0.829391i	$0.311313\pi$
$197$			23.2821i			1.65878i	−0.558668	+	0.829391i	$0.688687\pi$
$198$		0			0
$199$	8.80893	+	5.08584i	0.624449	+	0.360526i	0.778599	−	0.627522i	$-0.215931\pi$
$199$	8.80893	+	5.08584i	0.624449	+	0.360526i	−0.154150	+	0.988047i	$0.549264\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−5.21855	−	3.16102i	−0.366270	−	0.221860i
$204$		0			0
$205$	−1.20546			−0.0841930
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.848341	+	1.46937i	−0.0586810	+	0.101638i
$210$		0			0
$211$	−13.2184	−	22.8949i	−0.909991	−	1.57615i	−0.814073	−	0.580762i	$-0.802755\pi$
$211$	−13.2184	−	22.8949i	−0.909991	−	1.57615i	−0.0959178	−	0.995389i	$-0.530579\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.0441983	+	0.0765537i	0.00301430	+	0.00522092i
$216$		0			0
$217$	0.331198	−	15.7524i	0.0224832	−	1.06935i
$218$		0			0
$219$		0			0
$220$		0			0
$221$			6.84052i			0.460143i
$222$		0			0
$223$	14.4887	+	8.36504i	0.970233	+	0.560164i	0.899307	−	0.437317i	$-0.144071\pi$
$223$	14.4887	+	8.36504i	0.970233	+	0.560164i	0.0709258	+	0.997482i	$0.477405\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.44461	+	7.69828i	0.294999	+	0.510953i	0.974985	−	0.222272i	$-0.0713474\pi$
$227$	4.44461	+	7.69828i	0.294999	+	0.510953i	−0.679986	+	0.733225i	$0.738014\pi$
$228$		0			0
$229$	−14.6822	−	8.47679i	−0.970229	−	0.560162i	−0.0709229	−	0.997482i	$-0.522594\pi$
$229$	−14.6822	−	8.47679i	−0.970229	−	0.560162i	−0.899306	+	0.437320i	$0.855928\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−17.3861	+	10.0379i	−1.13900	+	0.657602i	−0.946183	−	0.323633i	$-0.895096\pi$
$233$	−17.3861	+	10.0379i	−1.13900	+	0.657602i	−0.192817	+	0.981235i	$0.561762\pi$
$234$		0			0
$235$	0.855868	−	1.48241i	0.0558307	−	0.0967016i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−11.5629	+	6.67585i	−0.747943	+	0.431825i	−0.824950	−	0.565206i	$-0.808797\pi$
$239$	−11.5629	+	6.67585i	−0.747943	+	0.431825i	0.0770074	+	0.997031i	$0.475464\pi$
$240$		0			0
$241$	−11.0568	+	6.38367i	−0.712234	+	0.411209i	−0.811888	−	0.583814i	$-0.801560\pi$
$241$	−11.0568	+	6.38367i	−0.712234	+	0.411209i	0.0996536	+	0.995022i	$0.468227\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.776709	−	1.22348i	0.0496221	−	0.0781650i
$246$		0			0
$247$	−2.18981	+	3.79287i	−0.139335	+	0.241335i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−17.8367			−1.12584			−0.562921	−	0.826511i	$-0.690322\pi$
$251$	−17.8367			−1.12584			−0.562921	+	0.826511i	$0.690322\pi$
$252$		0			0
$253$	2.19320			0.137885
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.818588	+	1.41784i	−0.0510621	+	0.0884421i	−0.890427	−	0.455127i	$-0.849594\pi$
$257$	−0.818588	+	1.41784i	−0.0510621	+	0.0884421i	0.839365	+	0.543569i	$0.182927\pi$
$258$		0			0
$259$	−5.44364	−	9.90378i	−0.338251	−	0.615391i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−26.6087	+	15.3626i	−1.64077	+	0.947296i	−0.660203	+	0.751087i	$0.729530\pi$
$263$	−26.6087	+	15.3626i	−1.64077	+	0.947296i	−0.980562	+	0.196210i	$0.937137\pi$
$264$		0			0
$265$	1.69067	−	0.976108i	0.103857	−	0.0599619i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.491194	−	0.850773i	0.0299486	−	0.0518726i	−0.850663	−	0.525712i	$-0.823799\pi$
$269$	0.491194	−	0.850773i	0.0299486	−	0.0518726i	0.880611	+	0.473839i	$0.157132\pi$
$270$		0			0
$271$	−0.707412	+	0.408425i	−0.0429722	+	0.0248100i	−0.521332	−	0.853354i	$-0.674565\pi$
$271$	−0.707412	+	0.408425i	−0.0429722	+	0.0248100i	0.478360	+	0.878164i	$0.341231\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.51269	+	3.76011i	0.392730	+	0.226743i
$276$		0			0
$277$	−5.30188	−	9.18313i	−0.318559	−	0.551761i	0.661629	−	0.749832i	$-0.269866\pi$
$277$	−5.30188	−	9.18313i	−0.318559	−	0.551761i	−0.980188	+	0.198071i	$0.936532\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−14.1764	−	8.18477i	−0.845695	−	0.488262i	0.0135009	−	0.999909i	$-0.495702\pi$
$281$	−14.1764	−	8.18477i	−0.845695	−	0.488262i	−0.859196	+	0.511647i	$0.829036\pi$
$282$		0			0
$283$		−	6.55510i		−	0.389660i	−0.980837	−	0.194830i	$-0.937584\pi$
$283$		−	6.55510i		−	0.389660i	0.980837	−	0.194830i	$-0.0624156\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−7.42055	−	13.5004i	−0.438021	−	0.796905i
$288$		0			0
$289$	6.97427	+	12.0798i	0.410251	+	0.710576i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−7.02441	−	12.1666i	−0.410370	−	0.710782i	0.584560	−	0.811351i	$-0.301267\pi$
$293$	−7.02441	−	12.1666i	−0.410370	−	0.710782i	−0.994930	+	0.100568i	$0.967934\pi$
$294$		0			0
$295$	−0.338293	+	0.585941i	−0.0196962	+	0.0341148i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	5.66128			0.327400
$300$		0			0
$301$	−0.585280	+	0.966241i	−0.0337350	+	0.0556932i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2.17886	+	1.25796i	0.124761	+	0.0720308i
$306$		0			0
$307$		−	17.4335i		−	0.994982i	−0.867469	−	0.497491i	$-0.834255\pi$
$307$		−	17.4335i		−	0.994982i	0.867469	−	0.497491i	$-0.165745\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	15.5963			0.884382			0.442191	−	0.896921i	$-0.354201\pi$
$311$	15.5963			0.884382			0.442191	+	0.896921i	$0.354201\pi$
$312$		0			0
$313$			2.22985i			0.126039i	0.998012	+	0.0630193i	$0.0200730\pi$
$313$			2.22985i			0.126039i	−0.998012	+	0.0630193i	$0.979927\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			34.3250i			1.92789i	0.266109	+	0.963943i	$0.414262\pi$
$317$			34.3250i			1.92789i	−0.266109	+	0.963943i	$0.585738\pi$
$318$		0			0
$319$	−3.49840			−0.195873
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	1.95369i		−	0.108706i
$324$		0			0
$325$	16.8112	+	9.70592i	0.932515	+	0.538388i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	21.8706	+	0.459833i	1.20577	+	0.0253514i
$330$		0			0
$331$	−22.5403			−1.23893			−0.619463	−	0.785026i	$-0.712650\pi$
$331$	−22.5403			−1.23893			−0.619463	+	0.785026i	$0.712650\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.671787	+	1.16357i	−0.0367037	+	0.0635726i
$336$		0			0
$337$	−11.3776	−	19.7065i	−0.619776	−	1.07348i	−0.989526	−	0.144353i	$-0.953890\pi$
$337$	−11.3776	−	19.7065i	−0.619776	−	1.07348i	0.369750	−	0.929131i	$-0.379443\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−4.51714	−	7.82392i	−0.244617	−	0.423689i
$342$		0			0
$343$	18.4834	+	1.16723i	0.998012	+	0.0630244i
$344$		0			0
$345$		0			0
$346$		0			0
$347$			7.47007i			0.401015i	0.979692	+	0.200507i	$0.0642590\pi$
$347$			7.47007i			0.401015i	−0.979692	+	0.200507i	$0.935741\pi$
$348$		0			0
$349$	−7.60969	−	4.39346i	−0.407337	−	0.235176i	0.282308	−	0.959324i	$-0.408900\pi$
$349$	−7.60969	−	4.39346i	−0.407337	−	0.235176i	−0.689645	+	0.724148i	$0.742233\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−3.66305	−	6.34459i	−0.194965	−	0.337689i	0.751924	−	0.659249i	$-0.229126\pi$
$353$	−3.66305	−	6.34459i	−0.194965	−	0.337689i	−0.946889	+	0.321561i	$0.895793\pi$
$354$		0			0
$355$	−1.27456	−	0.735865i	−0.0676464	−	0.0390557i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	11.0036	−	6.35295i	0.580749	−	0.335296i	−0.180682	−	0.983542i	$-0.557830\pi$
$359$	11.0036	−	6.35295i	0.580749	−	0.335296i	0.761431	+	0.648246i	$0.224497\pi$
$360$		0			0
$361$	−8.87458	+	15.3712i	−0.467083	+	0.809012i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.19838	−	1.26924i	0.115069	−	0.0664349i
$366$		0			0
$367$	−14.0927	+	8.13641i	−0.735632	+	0.424717i	−0.820479	−	0.571677i	$-0.806293\pi$
$367$	−14.0927	+	8.13641i	−0.735632	+	0.424717i	0.0848471	+	0.996394i	$0.472960\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	21.3392	+	12.9258i	1.10788	+	0.671072i
$372$		0			0
$373$	−7.94015	+	13.7527i	−0.411126	+	0.712090i	−0.995013	−	0.0997442i	$-0.968198\pi$
$373$	−7.94015	+	13.7527i	−0.411126	+	0.712090i	0.583888	+	0.811835i	$0.301531\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−9.03038			−0.465088
$378$		0			0
$379$	−0.0882488			−0.00453304			−0.00226652	−	0.999997i	$-0.500721\pi$
$379$	−0.0882488			−0.00453304			−0.00226652	+	0.999997i	$0.500721\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−16.9637	+	29.3819i	−0.866802	+	1.50135i	−0.00155547	+	0.999999i	$0.500495\pi$
$383$	−16.9637	+	29.3819i	−0.866802	+	1.50135i	−0.865247	+	0.501346i	$0.832838\pi$
$384$		0			0
$385$	0.0174671	−	0.830771i	0.000890205	−	0.0423400i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−9.87060	+	5.69879i	−0.500459	+	0.288940i	−0.728903	−	0.684617i	$-0.759970\pi$
$389$	−9.87060	+	5.69879i	−0.500459	+	0.288940i	0.228444	+	0.973557i	$0.426636\pi$
$390$		0			0
$391$	−2.18707	+	1.26271i	−0.110605	+	0.0638578i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.533731	−	0.924449i	0.0268549	−	0.0465141i
$396$		0			0
$397$	−3.81168	+	2.20068i	−0.191303	+	0.110449i	−0.592592	−	0.805503i	$-0.701895\pi$
$397$	−3.81168	+	2.20068i	−0.191303	+	0.110449i	0.401289	+	0.915951i	$0.368562\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.34606	+	4.24125i	0.366845	+	0.211798i	0.672079	−	0.740479i	$-0.265401\pi$
$401$	7.34606	+	4.24125i	0.366845	+	0.211798i	−0.305234	+	0.952277i	$0.598735\pi$
$402$		0			0
$403$	−11.6601	−	20.1958i	−0.580828	−	1.00602i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.61186	−	3.24001i	−0.278170	−	0.160601i
$408$		0			0
$409$			11.5764i			0.572415i	0.958168	+	0.286207i	$0.0923946\pi$
$409$			11.5764i			0.572415i	−0.958168	+	0.286207i	$0.907605\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−8.64465	−	0.181755i	−0.425375	−	0.00894359i
$414$		0			0
$415$	−1.73170	−	2.99939i	−0.0850059	−	0.147234i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−11.3173	−	19.6021i	−0.552885	−	0.957625i	−0.998065	−	0.0621839i	$-0.980193\pi$
$419$	−11.3173	−	19.6021i	−0.552885	−	0.957625i	0.445180	−	0.895441i	$-0.353140\pi$
$420$		0			0
$421$	−3.51429	+	6.08693i	−0.171276	+	0.296659i	−0.938866	−	0.344282i	$-0.888122\pi$
$421$	−3.51429	+	6.08693i	−0.171276	+	0.296659i	0.767590	+	0.640941i	$0.221456\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−8.65934			−0.420040
$426$		0			0
$427$	−0.675867	+	32.1456i	−0.0327075	+	1.55564i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.267173	+	0.154252i	0.0128693	+	0.00743007i	0.506421	−	0.862286i	$-0.330968\pi$
$431$	0.267173	+	0.154252i	0.0128693	+	0.00743007i	−0.493552	+	0.869717i	$0.664302\pi$
$432$		0			0
$433$		−	32.8376i		−	1.57807i	−0.614347	−	0.789036i	$-0.710580\pi$
$433$		−	32.8376i		−	1.57807i	0.614347	−	0.789036i	$-0.289420\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.61689			−0.0773463
$438$		0			0
$439$		−	3.36313i		−	0.160514i	−0.996774	−	0.0802568i	$-0.974426\pi$
$439$		−	3.36313i		−	0.160514i	0.996774	−	0.0802568i	$-0.0255740\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	35.9108i		−	1.70617i	−0.521768	−	0.853087i	$-0.674727\pi$
$443$		−	35.9108i		−	1.70617i	0.521768	−	0.853087i	$-0.325273\pi$
$444$		0			0
$445$	0.812749			0.0385280
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	13.9993i		−	0.660668i	−0.943864	−	0.330334i	$-0.892839\pi$
$449$		−	13.9993i		−	0.660668i	0.943864	−	0.330334i	$-0.107161\pi$
$450$		0			0
$451$	−7.64985	−	4.41664i	−0.360217	−	0.207972i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.0450876	−	2.14446i	0.00211374	−	0.100534i
$456$		0			0
$457$	7.94102			0.371465			0.185733	−	0.982600i	$-0.440534\pi$
$457$	7.94102			0.371465			0.185733	+	0.982600i	$0.440534\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2.12627	−	3.68281i	0.0990304	−	0.171526i	−0.812253	−	0.583305i	$-0.801759\pi$
$461$	2.12627	−	3.68281i	0.0990304	−	0.171526i	0.911284	+	0.411779i	$0.135093\pi$
$462$		0			0
$463$	−10.2557	−	17.7634i	−0.476622	−	0.825534i	0.523019	−	0.852321i	$-0.324806\pi$
$463$	−10.2557	−	17.7634i	−0.476622	−	0.825534i	−0.999641	+	0.0267869i	$0.991472\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	13.8842	+	24.0481i	0.642484	+	1.11281i	0.984877	+	0.173257i	$0.0554292\pi$
$467$	13.8842	+	24.0481i	0.642484	+	1.11281i	−0.342393	+	0.939557i	$0.611237\pi$
$468$		0			0
$469$	−17.1667	−	0.360932i	−0.792682	−	0.0166663i
$470$		0			0
$471$		0			0
$472$		0			0
$473$			0.647746i			0.0297834i
$474$		0			0
$475$	−4.80135	−	2.77206i	−0.220301	−	0.127191i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	15.7064	+	27.2042i	0.717643	+	1.24299i	0.961931	+	0.273291i	$0.0881123\pi$
$479$	15.7064	+	27.2042i	0.717643	+	1.24299i	−0.244289	+	0.969703i	$0.578554\pi$
$480$		0			0
$481$	−14.4858	−	8.36340i	−0.660497	−	0.381338i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.71588	−	1.56801i	0.123322	−	0.0711999i
$486$		0			0
$487$	−16.1798	+	28.0242i	−0.733176	+	1.26990i	0.222343	+	0.974968i	$0.428629\pi$
$487$	−16.1798	+	28.0242i	−0.733176	+	1.26990i	−0.955519	+	0.294929i	$0.904704\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−33.6617	+	19.4346i	−1.51913	+	0.877071i	−0.519385	+	0.854540i	$0.673839\pi$
$491$	−33.6617	+	19.4346i	−1.51913	+	0.877071i	−0.999746	+	0.0225309i	$0.992828\pi$
$492$		0			0
$493$	3.48863	−	2.01416i	0.157120	−	0.0907132i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.395359	−	18.8041i	0.0177343	−	0.843478i
$498$		0			0
$499$	−19.8770	+	34.4280i	−0.889816	+	1.54121i	−0.0497240	+	0.998763i	$0.515834\pi$
$499$	−19.8770	+	34.4280i	−0.889816	+	1.54121i	−0.840092	+	0.542444i	$0.817499\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−4.45463			−0.198622			−0.0993110	−	0.995056i	$-0.531664\pi$
$503$	−4.45463			−0.198622			−0.0993110	+	0.995056i	$0.531664\pi$
$504$		0			0
$505$	−2.12541			−0.0945796
$506$		0			0
$507$		0			0
$508$		0			0
$509$	9.92165	−	17.1848i	0.439769	−	0.761703i	−0.557902	−	0.829907i	$-0.688394\pi$
$509$	9.92165	−	17.1848i	0.439769	−	0.761703i	0.997671	+	0.0682040i	$0.0217269\pi$
$510$		0			0
$511$	27.7474	+	16.8074i	1.22747	+	0.743516i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.01839	+	1.16532i	−0.0889409	+	0.0513500i
$516$		0			0
$517$	10.8627	−	6.27157i	0.477740	−	0.275824i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−6.51527	+	11.2848i	−0.285439	+	0.494395i	−0.972716	−	0.232001i	$-0.925473\pi$
$521$	−6.51527	+	11.2848i	−0.285439	+	0.494395i	0.687277	+	0.726396i	$0.258806\pi$
$522$		0			0
$523$	28.6981	−	16.5688i	1.25488	−	0.724505i	0.282805	−	0.959177i	$-0.408735\pi$
$523$	28.6981	−	16.5688i	1.25488	−	0.724505i	0.972075	+	0.234672i	$0.0754017\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	9.00905	+	5.20138i	0.392440	+	0.226575i
$528$		0			0
$529$	−10.4550	−	18.1085i	−0.454564	−	0.787328i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−19.7465	−	11.4006i	−0.855315	−	0.493817i
$534$		0			0
$535$		−	2.36055i		−	0.102056i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	9.41165	−	4.91842i	0.405389	−	0.211851i
$540$		0			0
$541$	13.3022	+	23.0402i	0.571908	+	0.990574i	0.996370	+	0.0851281i	$0.0271300\pi$
$541$	13.3022	+	23.0402i	0.571908	+	0.990574i	−0.424462	+	0.905446i	$0.639537\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.311415	−	0.539387i	−0.0133396	−	0.0231048i
$546$		0			0
$547$	−4.32361	+	7.48870i	−0.184864	+	0.320194i	−0.943531	−	0.331285i	$-0.892518\pi$
$547$	−4.32361	+	7.48870i	−0.184864	+	0.320194i	0.758667	+	0.651479i	$0.225851\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	2.57912			0.109874
$552$		0			0
$553$	13.6388	+	0.286758i	0.579981	+	0.0121942i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	19.1707	+	11.0682i	0.812289	+	0.468975i	0.847750	−	0.530396i	$-0.177957\pi$
$557$	19.1707	+	11.0682i	0.812289	+	0.468975i	−0.0354610	+	0.999371i	$0.511290\pi$
$558$		0			0
$559$			1.67202i			0.0707190i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−12.2055			−0.514400			−0.257200	−	0.966358i	$-0.582800\pi$
$563$	−12.2055			−0.514400			−0.257200	+	0.966358i	$0.582800\pi$
$564$		0			0
$565$			3.40975i			0.143449i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			9.42392i			0.395071i	0.980296	+	0.197536i	$0.0632938\pi$
$569$			9.42392i			0.395071i	−0.980296	+	0.197536i	$0.936706\pi$
$570$		0			0
$571$	15.4716			0.647465			0.323733	−	0.946149i	$-0.395062\pi$
$571$	15.4716			0.647465			0.323733	+	0.946149i	$0.395062\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			7.16655i			0.298866i
$576$		0			0
$577$	−8.48608	−	4.89944i	−0.353280	−	0.203966i	0.312849	−	0.949803i	$-0.398717\pi$
$577$	−8.48608	−	4.89944i	−0.353280	−	0.203966i	−0.666129	+	0.745836i	$0.732050\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	22.9314	−	37.8576i	0.951356	−	1.57060i
$582$		0			0
$583$	14.3053			0.592466
$584$		0			0
$585$		0			0
$586$		0			0
$587$	12.4297	−	21.5289i	0.513028	−	0.888591i	−0.486858	−	0.873481i	$-0.661857\pi$
$587$	12.4297	−	21.5289i	0.513028	−	0.888591i	0.999886	−	0.0151097i	$-0.00480974\pi$
$588$		0			0
$589$	3.33017	+	5.76802i	0.137217	+	0.237667i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−20.9831	−	36.3438i	−0.861673	−	1.49246i	−0.870313	−	0.492500i	$-0.836083\pi$
$593$	−20.9831	−	36.3438i	−0.861673	−	1.49246i	0.00863918	−	0.999963i	$-0.497250\pi$
$594$		0			0
$595$	0.460888	+	0.838507i	0.0188946	+	0.0343754i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			30.3196i			1.23882i	0.785066	+	0.619412i	$0.212629\pi$
$599$			30.3196i			1.23882i	−0.785066	+	0.619412i	$0.787371\pi$
$600$		0			0
$601$	2.71173	+	1.56562i	0.110614	+	0.0638628i	0.554286	−	0.832326i	$-0.312991\pi$
$601$	2.71173	+	1.56562i	0.110614	+	0.0638628i	−0.443673	+	0.896189i	$0.646325\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.900424	+	1.55958i	0.0366074	+	0.0634060i
$606$		0			0
$607$	12.4592	+	7.19329i	0.505701	+	0.291967i	0.731065	−	0.682308i	$-0.239024\pi$
$607$	12.4592	+	7.19329i	0.505701	+	0.291967i	−0.225364	+	0.974275i	$0.572357\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	28.0397	−	16.1888i	1.13437	−	0.654927i
$612$		0			0
$613$	−4.36863	+	7.56669i	−0.176447	+	0.305616i	−0.940661	−	0.339347i	$-0.889794\pi$
$613$	−4.36863	+	7.56669i	−0.176447	+	0.305616i	0.764214	+	0.644963i	$0.223127\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	25.9444	−	14.9790i	1.04448	−	0.603033i	0.123384	−	0.992359i	$-0.460625\pi$
$617$	25.9444	−	14.9790i	1.04448	−	0.603033i	0.921100	+	0.389326i	$0.127292\pi$
$618$		0			0
$619$	−2.27825	+	1.31535i	−0.0915706	+	0.0528683i	−0.545086	−	0.838380i	$-0.683503\pi$
$619$	−2.27825	+	1.31535i	−0.0915706	+	0.0528683i	0.453515	+	0.891248i	$0.350170\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	5.00311	+	9.10230i	0.200445	+	0.364676i
$624$		0			0
$625$	−12.1795	+	21.0955i	−0.487179	+	0.843818i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	7.46158			0.297513
$630$		0			0
$631$	−18.0872			−0.720039			−0.360019	−	0.932945i	$-0.617230\pi$
$631$	−18.0872			−0.720039			−0.360019	+	0.932945i	$0.617230\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.882644	+	1.52878i	−0.0350266	+	0.0606679i
$636$		0			0
$637$	24.2942	−	12.6959i	0.962572	−	0.503029i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	35.6571	−	20.5867i	1.40837	−	0.813124i	0.413141	−	0.910667i	$-0.364432\pi$
$641$	35.6571	−	20.5867i	1.40837	−	0.813124i	0.995231	+	0.0975432i	$0.0310984\pi$
$642$		0			0
$643$	31.3046	−	18.0737i	1.23453	−	0.712758i	0.266561	−	0.963818i	$-0.414113\pi$
$643$	31.3046	−	18.0737i	1.23453	−	0.712758i	0.967971	+	0.251060i	$0.0807792\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.09812	−	7.09815i	0.161114	−	0.279057i	−0.774155	−	0.632996i	$-0.781825\pi$
$647$	4.09812	−	7.09815i	0.161114	−	0.279057i	0.935268	+	0.353939i	$0.115158\pi$
$648$		0			0
$649$	−4.29362	+	2.47892i	−0.168539	+	0.0973063i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−23.3611	−	13.4875i	−0.914190	−	0.527808i	−0.0324129	−	0.999475i	$-0.510319\pi$
$653$	−23.3611	−	13.4875i	−0.914190	−	0.527808i	−0.881777	+	0.471667i	$0.843652\pi$
$654$		0			0
$655$	−1.50661	−	2.60952i	−0.0588680	−	0.101962i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	2.60125	+	1.50183i	0.101330	+	0.0585032i	0.549809	−	0.835291i	$-0.314701\pi$
$659$	2.60125	+	1.50183i	0.101330	+	0.0585032i	−0.448478	+	0.893794i	$0.648034\pi$
$660$		0			0
$661$		−	36.0755i		−	1.40317i	−0.712585	−	0.701586i	$-0.752476\pi$
$661$		−	36.0755i		−	1.40317i	0.712585	−	0.701586i	$-0.247524\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.0128773	+	0.612469i	−0.000499359	+	0.0237505i
$666$		0			0
$667$	−1.66694	−	2.88722i	−0.0645441	−	0.111794i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	9.21802	+	15.9661i	0.355858	+	0.616364i
$672$		0			0
$673$	3.20540	−	5.55191i	0.123559	−	0.214010i	−0.797610	−	0.603174i	$-0.793903\pi$
$673$	3.20540	−	5.55191i	0.123559	−	0.214010i	0.921169	+	0.389163i	$0.127236\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−34.4498			−1.32401			−0.662007	−	0.749498i	$-0.730295\pi$
$677$	−34.4498			−1.32401			−0.662007	+	0.749498i	$0.730295\pi$
$678$		0			0
$679$	34.2792	+	20.7639i	1.31551	+	0.796844i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	2.53802	+	1.46533i	0.0971148	+	0.0560693i	0.547771	−	0.836628i	$-0.315477\pi$
$683$	2.53802	+	1.46533i	0.0971148	+	0.0560693i	−0.450656	+	0.892698i	$0.648810\pi$
$684$		0			0
$685$		−	2.21189i		−	0.0845120i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	36.9262			1.40678
$690$		0			0
$691$			3.80337i			0.144687i	0.997380	+	0.0723434i	$0.0230478\pi$
$691$			3.80337i			0.144687i	−0.997380	+	0.0723434i	$0.976952\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			1.78443i			0.0676871i
$696$		0			0
$697$	10.1713			0.385266
$698$		0			0
$699$		0			0
$700$		0			0
$701$			36.7042i			1.38630i	0.720795	+	0.693149i	$0.243777\pi$
$701$			36.7042i			1.38630i	−0.720795	+	0.693149i	$0.756223\pi$
$702$		0			0
$703$	4.13723	+	2.38863i	0.156039	+	0.0900889i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−13.0836	−	23.8033i	−0.492058	−	0.895216i
$708$		0			0
$709$	20.8080			0.781460			0.390730	−	0.920505i	$-0.372223\pi$
$709$	20.8080			0.781460			0.390730	+	0.920505i	$0.372223\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	4.30471	−	7.45597i	0.161213	−	0.279228i
$714$		0			0
$715$	−0.614942	−	1.06511i	−0.0229975	−	0.0398329i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	15.1577	+	26.2540i	0.565288	+	0.979108i	0.997023	+	0.0771074i	$0.0245684\pi$
$719$	15.1577	+	26.2540i	0.565288	+	0.979108i	−0.431734	+	0.902001i	$0.642098\pi$
$720$		0			0
$721$	−25.4756	−	15.4313i	−0.948761	−	0.574692i
$722$		0			0
$723$		0			0
$724$		0			0
$725$		−	11.4315i		−	0.424554i
$726$		0			0
$727$	29.7259	+	17.1622i	1.10247	+	0.636512i	0.936869	−	0.349680i	$-0.113710\pi$
$727$	29.7259	+	17.1622i	1.10247	+	0.636512i	0.165602	+	0.986193i	$0.447043\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.372932	−	0.645937i	−0.0137934	−	0.0238908i
$732$		0			0
$733$	−5.35388	−	3.09106i	−0.197750	−	0.114171i	0.397855	−	0.917448i	$-0.369755\pi$
$733$	−5.35388	−	3.09106i	−0.197750	−	0.114171i	−0.595606	+	0.803277i	$0.703088\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−8.52633	+	4.92268i	−0.314071	+	0.181329i
$738$		0			0
$739$	−13.5892	+	23.5372i	−0.499887	+	0.865829i	−1.00000		0.000131035i	$-0.999958\pi$
$739$	−13.5892	+	23.5372i	−0.499887	+	0.865829i	0.500113	+	0.865960i	$0.333292\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−24.3213	+	14.0419i	−0.892262	+	0.515148i	−0.874682	−	0.484698i	$-0.838930\pi$
$743$	−24.3213	+	14.0419i	−0.892262	+	0.515148i	−0.0175804	+	0.999845i	$0.505596\pi$
$744$		0			0
$745$	3.95321	−	2.28239i	0.144835	−	0.0836203i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	26.4368	−	14.5310i	0.965978	−	0.530953i
$750$		0			0
$751$	21.0921	−	36.5326i	0.769661	−	1.33309i	−0.168086	−	0.985772i	$-0.553759\pi$
$751$	21.0921	−	36.5326i	0.769661	−	1.33309i	0.937747	−	0.347320i	$-0.112908\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1.82211			0.0663134
$756$		0			0
$757$	−32.6771			−1.18767			−0.593835	−	0.804587i	$-0.702387\pi$
$757$	−32.6771			−1.18767			−0.593835	+	0.804587i	$0.702387\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−15.8783	+	27.5021i	−0.575589	+	0.996949i	0.420388	+	0.907344i	$0.361894\pi$
$761$	−15.8783	+	27.5021i	−0.575589	+	0.996949i	−0.995977	+	0.0896051i	$0.971440\pi$
$762$		0			0
$763$	4.12380	−	6.80801i	0.149292	−	0.246466i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−11.0831	+	6.39882i	−0.400187	+	0.231048i
$768$		0			0
$769$	30.8593	−	17.8166i	1.11281	−	0.642484i	0.173258	−	0.984877i	$-0.444571\pi$
$769$	30.8593	−	17.8166i	1.11281	−	0.642484i	0.939557	+	0.342393i	$0.111237\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	6.44721	−	11.1669i	0.231890	−	0.401645i	−0.726474	−	0.687194i	$-0.758842\pi$
$773$	6.44721	−	11.1669i	0.231890	−	0.401645i	0.958364	+	0.285548i	$0.0921757\pi$
$774$		0			0
$775$	25.5656	−	14.7603i	0.918344	−	0.530206i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	5.63970	+	3.25608i	0.202063	+	0.116661i
$780$		0			0
$781$	−5.39222	−	9.33961i	−0.192949	−	0.334197i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1.89208	+	1.09239i	0.0675312	+	0.0389892i
$786$		0			0
$787$		−	17.6852i		−	0.630409i	−0.949024	−	0.315205i	$-0.897927\pi$
$787$		−	17.6852i		−	0.630409i	0.949024	−	0.315205i	$-0.102073\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−38.1871	+	20.9897i	−1.35778	+	0.746307i
$792$		0			0
$793$	23.7944	+	41.2131i	0.844963	+	1.46352i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−22.8391	−	39.5585i	−0.809003	−	1.40123i	−0.913555	−	0.406714i	$-0.866674\pi$
$797$	−22.8391	−	39.5585i	−0.809003	−	1.40123i	0.104553	−	0.994519i	$-0.466659\pi$
$798$		0			0
$799$	−7.22156	+	12.5081i	−0.255481	+	0.442505i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	18.6013			0.656424
$804$		0			0
$805$	0.693956	−	0.381435i	0.0244587	−	0.0134438i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−10.8291	−	6.25218i	−0.380731	−	0.219815i	0.297405	−	0.954751i	$-0.403879\pi$
$809$	−10.8291	−	6.25218i	−0.380731	−	0.219815i	−0.678136	+	0.734936i	$0.737212\pi$
$810$		0			0
$811$		−	9.57778i		−	0.336322i	−0.985760	−	0.168161i	$-0.946217\pi$
$811$		−	9.57778i		−	0.336322i	0.985760	−	0.168161i	$-0.0537828\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1.92425			−0.0674034
$816$		0			0
$817$		−	0.477538i		−	0.0167069i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		−	27.8721i		−	0.972742i	−0.873752	−	0.486371i	$-0.838320\pi$
$821$		−	27.8721i		−	0.972742i	0.873752	−	0.486371i	$-0.161680\pi$
$822$		0			0
$823$	47.2766			1.64796			0.823980	−	0.566619i	$-0.191749\pi$
$823$	47.2766			1.64796			0.823980	+	0.566619i	$0.191749\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	24.1672i		−	0.840377i	−0.907437	−	0.420188i	$-0.861964\pi$
$827$		−	24.1672i		−	0.840377i	0.907437	−	0.420188i	$-0.138036\pi$
$828$		0			0
$829$	23.0216	+	13.2915i	0.799572	+	0.461633i	0.843322	−	0.537409i	$-0.180597\pi$
$829$	23.0216	+	13.2915i	0.799572	+	0.461633i	−0.0437494	+	0.999043i	$0.513930\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−6.55365	+	10.3233i	−0.227070	+	0.357682i
$834$		0			0
$835$	−1.84030			−0.0636864
$836$		0			0
$837$		0			0
$838$		0			0
$839$	4.03255	−	6.98459i	0.139219	−	0.241135i	−0.787982	−	0.615698i	$-0.788874\pi$
$839$	4.03255	−	6.98459i	0.139219	−	0.241135i	0.927201	+	0.374563i	$0.122207\pi$
$840$		0			0
$841$	−11.8410	−	20.5093i	−0.408312	−	0.707217i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.241660	−	0.418568i	−0.00831337	−	0.0143992i
$846$		0			0
$847$	−11.9235	+	19.6846i	−0.409698	+	0.676372i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		−	6.17527i		−	0.211686i
$852$		0			0
$853$	11.6046	+	6.69994i	0.397335	+	0.229402i	0.685334	−	0.728229i	$-0.259656\pi$
$853$	11.6046	+	6.69994i	0.397335	+	0.229402i	−0.287998	+	0.957631i	$0.592990\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	22.3340	+	38.6836i	0.762914	+	1.32141i	0.941343	+	0.337452i	$0.109565\pi$
$857$	22.3340	+	38.6836i	0.762914	+	1.32141i	−0.178429	+	0.983953i	$0.557101\pi$
$858$		0			0
$859$	43.7433	+	25.2552i	1.49250	+	0.861696i	0.999963	−	0.00859547i	$-0.00273606\pi$
$859$	43.7433	+	25.2552i	1.49250	+	0.861696i	0.492538	+	0.870291i	$0.336069\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.227203	−	0.131176i	0.00773408	−	0.00446528i	−0.496128	−	0.868249i	$-0.665245\pi$
$863$	0.227203	−	0.131176i	0.00773408	−	0.00446528i	0.503862	+	0.863784i	$0.331912\pi$
$864$		0			0
$865$	−1.01438	+	1.75695i	−0.0344898	+	0.0597381i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	6.77412	−	3.91104i	0.229796	−	0.132673i
$870$		0			0
$871$	−22.0089	+	12.7069i	−0.745744	+	0.430556i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	5.45277	+	0.114645i	0.184337	+	0.00387572i
$876$		0			0
$877$	4.63303	−	8.02465i	0.156446	−	0.270973i	−0.777138	−	0.629330i	$-0.783329\pi$
$877$	4.63303	−	8.02465i	0.156446	−	0.270973i	0.933585	+	0.358357i	$0.116663\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	41.5555			1.40004			0.700021	−	0.714122i	$-0.253174\pi$
$881$	41.5555			1.40004			0.700021	+	0.714122i	$0.253174\pi$
$882$		0			0
$883$	−29.4547			−0.991231			−0.495615	−	0.868542i	$-0.665057\pi$
$883$	−29.4547			−0.991231			−0.495615	+	0.868542i	$0.665057\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−7.79122	+	13.4948i	−0.261603	+	0.453111i	−0.966668	−	0.256032i	$-0.917585\pi$
$887$	−7.79122	+	13.4948i	−0.261603	+	0.453111i	0.705065	+	0.709143i	$0.250918\pi$
$888$		0			0
$889$	−22.5548	−	0.474219i	−0.756464	−	0.0159048i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−8.00829	+	4.62359i	−0.267987	+	0.154723i
$894$		0			0
$895$	−2.96342	+	1.71093i	−0.0990562	+	0.0571901i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−6.86649	+	11.8931i	−0.229010	+	0.396658i
$900$		0			0
$901$	−14.2654	+	8.23612i	−0.475248	+	0.274385i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−4.27685	−	2.46924i	−0.142167	−	0.0820804i
$906$		0			0
$907$	−10.2604	−	17.7716i	−0.340692	−	0.590095i	0.643870	−	0.765135i	$-0.277328\pi$
$907$	−10.2604	−	17.7716i	−0.340692	−	0.590095i	−0.984561	+	0.175040i	$0.943995\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	15.0554	+	8.69226i	0.498809	+	0.287987i	0.728222	−	0.685342i	$-0.240347\pi$
$911$	15.0554	+	8.69226i	0.498809	+	0.287987i	−0.229413	+	0.973329i	$0.573681\pi$
$912$		0			0
$913$		−	25.3789i		−	0.839919i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	19.9507	−	32.9367i	0.658830	−	1.08767i
$918$		0			0
$919$	17.1002	+	29.6183i	0.564082	+	0.977019i	0.997134	+	0.0756501i	$0.0241032\pi$
$919$	17.1002	+	29.6183i	0.564082	+	0.977019i	−0.433052	+	0.901369i	$0.642563\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−13.9189	−	24.1082i	−0.458146	−	0.793532i
$924$		0			0
$925$	10.5871	−	18.3375i	0.348103	−	0.602932i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	2.99192			0.0981617			0.0490808	−	0.998795i	$-0.484371\pi$
$929$	2.99192			0.0981617			0.0490808	+	0.998795i	$0.484371\pi$
$930$		0			0
$931$	−6.93855	+	3.62600i	−0.227402	+	0.118838i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.475130	+	0.274316i	0.0155384	+	0.00897110i
$936$		0			0
$937$		−	10.9928i		−	0.359120i	−0.983747	−	0.179560i	$-0.942533\pi$
$937$		−	10.9928i		−	0.359120i	0.983747	−	0.179560i	$-0.0574674\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	9.90600			0.322926			0.161463	−	0.986879i	$-0.448379\pi$
$941$	9.90600			0.322926			0.161463	+	0.986879i	$0.448379\pi$
$942$		0			0
$943$		−	8.41787i		−	0.274124i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	27.0453i		−	0.878854i	−0.898278	−	0.439427i	$-0.855181\pi$
$947$		−	27.0453i		−	0.878854i	0.898278	−	0.439427i	$-0.144819\pi$
$948$		0			0
$949$	48.0152			1.55864
$950$		0			0
$951$		0			0
$952$		0			0
$953$			51.9958i			1.68431i	0.539236	+	0.842155i	$0.318713\pi$
$953$			51.9958i			1.68431i	−0.539236	+	0.842155i	$0.681287\pi$
$954$		0			0
$955$	4.00898	+	2.31458i	0.129727	+	0.0748982i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	24.7718	−	13.6159i	0.799924	−	0.439681i
$960$		0			0
$961$	−4.46414			−0.144004
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.896121	+	1.55213i	−0.0288472	+	0.0499648i
$966$		0			0
$967$	8.23005	+	14.2549i	0.264660	+	0.458405i	0.967475	−	0.252968i	$-0.0814068\pi$
$967$	8.23005	+	14.2549i	0.264660	+	0.458405i	−0.702814	+	0.711374i	$0.748073\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−6.09724	−	10.5607i	−0.195670	−	0.338910i	0.751450	−	0.659790i	$-0.229355\pi$
$971$	−6.09724	−	10.5607i	−0.195670	−	0.338910i	−0.947120	+	0.320880i	$0.896021\pi$
$972$		0			0
$973$	−19.9845	+	10.9845i	−0.640673	+	0.352148i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			21.7574i			0.696081i	0.937480	+	0.348040i	$0.113153\pi$
$977$			21.7574i			0.696081i	−0.937480	+	0.348040i	$0.886847\pi$
$978$		0			0
$979$	5.15771	+	2.97781i	0.164841	+	0.0951711i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−31.2373	−	54.1046i	−0.996316	−	1.72567i	−0.572430	−	0.819954i	$-0.693999\pi$
$983$	−31.2373	−	54.1046i	−0.996316	−	1.72567i	−0.423886	−	0.905716i	$-0.639334\pi$
$984$		0			0
$985$	4.17429	+	2.41003i	0.133004	+	0.0767898i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.534583	+	0.308642i	−0.0169988	+	0.00981424i
$990$		0			0
$991$	−27.5362	+	47.6942i	−0.874717	+	1.51505i	−0.0176535	+	0.999844i	$0.505620\pi$
$991$	−27.5362	+	47.6942i	−0.874717	+	1.51505i	−0.857064	+	0.515210i	$0.827714\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.82370	−	1.05291i	0.0578151	−	0.0333795i
$996$		0			0
$997$	−20.6726	+	11.9353i	−0.654707	+	0.377995i	−0.790257	−	0.612775i	$-0.790053\pi$
$997$	−20.6726	+	11.9353i	−0.654707	+	0.377995i	0.135550	+	0.990770i	$0.456720\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.bs.a.521.12		48
3.2	odd	2		504.2.bs.a.353.19	yes	48
4.3	odd	2		3024.2.ca.e.2033.12		48
7.5	odd	6		1512.2.cx.a.89.12		48
9.4	even	3		504.2.cx.a.185.10	yes	48
9.5	odd	6		1512.2.cx.a.17.12		48
12.11	even	2		1008.2.ca.e.353.6		48
21.5	even	6		504.2.cx.a.425.10	yes	48
28.19	even	6		3024.2.df.e.1601.12		48
36.23	even	6		3024.2.df.e.17.12		48
36.31	odd	6		1008.2.df.e.689.15		48
63.5	even	6	inner	1512.2.bs.a.1097.12		48
63.40	odd	6		504.2.bs.a.257.19	✓	48
84.47	odd	6		1008.2.df.e.929.15		48
252.103	even	6		1008.2.ca.e.257.6		48
252.131	odd	6		3024.2.ca.e.2609.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.19	✓	48	63.40	odd	6
504.2.bs.a.353.19	yes	48	3.2	odd	2
504.2.cx.a.185.10	yes	48	9.4	even	3
504.2.cx.a.425.10	yes	48	21.5	even	6
1008.2.ca.e.257.6		48	252.103	even	6
1008.2.ca.e.353.6		48	12.11	even	2
1008.2.df.e.689.15		48	36.31	odd	6
1008.2.df.e.929.15		48	84.47	odd	6
1512.2.bs.a.521.12		48	1.1	even	1	trivial
1512.2.bs.a.1097.12		48	63.5	even	6	inner
1512.2.cx.a.17.12		48	9.5	odd	6
1512.2.cx.a.89.12		48	7.5	odd	6
3024.2.ca.e.2033.12		48	4.3	odd	2
3024.2.ca.e.2609.12		48	252.131	odd	6
3024.2.df.e.17.12		48	36.23	even	6
3024.2.df.e.1601.12		48	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.103514 - 0.179292i) q^{5} +(2.64517 + 0.0556151i) q^{7} +(1.31380 - 0.758523i) q^{11} +(3.39130 - 1.95797i) q^{13} +(-0.873421 + 1.51281i) q^{17} +(-0.968573 + 0.559206i) q^{19} +(1.25201 + 0.722851i) q^{23} +(2.47857 + 4.29301i) q^{25} +(-1.99711 - 1.15303i) q^{29} -5.95518i q^{31} +(0.283783 - 0.468499i) q^{35} +(-2.13573 - 3.69920i) q^{37} +(-2.91134 - 5.04260i) q^{41} +(-0.213489 + 0.369774i) q^{43} +8.26814 q^{47} +(6.99381 + 0.294222i) q^{49} +(8.16638 + 4.71486i) q^{53} -0.314071i q^{55} -3.26809 q^{59} +12.1526i q^{61} -0.810709i q^{65} -6.48982 q^{67} -7.10884i q^{71} +(10.6188 + 6.13075i) q^{73} +(3.51741 - 1.93335i) q^{77} +5.15612 q^{79} +(8.36457 - 14.4879i) q^{83} +(0.180823 + 0.313194i) q^{85} +(1.96290 + 3.39984i) q^{89} +(9.07945 - 4.99055i) q^{91} +0.231543i q^{95} +(13.1184 + 7.57392i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{23} - 24 q^{25} - 18 q^{29} - 6 q^{41} - 6 q^{43} - 36 q^{47} + 6 q^{49} - 12 q^{53} + 36 q^{77} - 12 q^{79} - 18 q^{89} + 6 q^{91}+O(q^{100}) \) 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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