LMFDB - Embedded newform 5292.2.j.h.3529.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5292,2,Mod(1765,5292)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5292.1765"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5292, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5292.j (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$42.2568327497$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 3^{8} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3529.5
Root			$-1.73040 - 0.0755709i$ of defining polynomial
Character	$\chi$	$=$	5292.3529
Dual form			5292.2.j.h.1765.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.483929 + 0.838189i) q^{5} +(0.364122 - 0.630678i) q^{11} +(1.81066 + 3.13615i) q^{13} +6.99897 q^{17} +0.696101 q^{19} +(3.21898 + 5.57544i) q^{23} +(2.03163 - 3.51888i) q^{25} +(-3.34727 + 5.79764i) q^{29} +(-4.58310 - 7.93816i) q^{31} -1.70901 q^{37} +(3.62444 + 6.27771i) q^{41} +(-0.348050 + 0.602841i) q^{43} +(3.83120 - 6.63583i) q^{47} +4.11275 q^{53} +0.704836 q^{55} +(-2.38809 - 4.13629i) q^{59} +(-2.46287 + 4.26582i) q^{61} +(-1.75246 + 3.03535i) q^{65} +(2.91035 + 5.04087i) q^{67} -0.304424 q^{71} -10.6776 q^{73} +(1.61945 - 2.80497i) q^{79} +(-0.618759 + 1.07172i) q^{83} +(3.38700 + 5.86646i) q^{85} -11.5736 q^{89} +(0.336863 + 0.583464i) q^{95} +(1.32933 - 2.30247i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{5} - 2 q^{11} + 2 q^{13} + 4 q^{17} - 14 q^{19} - 11 q^{23} - 9 q^{25} - q^{29} - q^{31} - 20 q^{37} + 33 q^{41} + 7 q^{43} + 3 q^{47} - 30 q^{53} - 28 q^{55} + 14 q^{59} - 10 q^{61} - 15 q^{65}+ \cdots - 18 q^{97}+O(q^{100}) $ 14 * q + 2 * q^5 - 2 * q^11 + 2 * q^13 + 4 * q^17 - 14 * q^19 - 11 * q^23 - 9 * q^25 - q^29 - q^31 - 20 * q^37 + 33 * q^41 + 7 * q^43 + 3 * q^47 - 30 * q^53 - 28 * q^55 + 14 * q^59 - 10 * q^61 - 15 * q^65 + 6 * q^67 - 2 * q^71 - 42 * q^73 - 10 * q^79 + 25 * q^83 + 8 * q^85 - 12 * q^89 + 28 * q^95 - 18 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5292\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$	$2647$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$5$	0.483929	+	0.838189i	0.216419	+	0.374850i	0.953711	−	0.300725i	$-0.0972288\pi$
$5$	0.483929	+	0.838189i	0.216419	+	0.374850i	−0.737291	+	0.675575i	$0.763895\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.364122	−	0.630678i	0.109787	−	0.190156i	−0.805897	−	0.592056i	$-0.798317\pi$
$11$	0.364122	−	0.630678i	0.109787	−	0.190156i	0.915684	+	0.401899i	$0.131650\pi$
$12$		0			0
$13$	1.81066	+	3.13615i	0.502187	+	0.869813i	0.999997	+	0.00252677i	$0.000804296\pi$
$13$	1.81066	+	3.13615i	0.502187	+	0.869813i	−0.497810	+	0.867286i	$0.665862\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	6.99897			1.69750			0.848749	−	0.528795i	$-0.177356\pi$
$17$	6.99897			1.69750			0.848749	+	0.528795i	$0.177356\pi$
$18$		0			0
$19$	0.696101			0.159697			0.0798483	−	0.996807i	$-0.474556\pi$
$19$	0.696101			0.159697			0.0798483	+	0.996807i	$0.474556\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.21898	+	5.57544i	0.671204	+	1.16256i	0.977563	+	0.210643i	$0.0675557\pi$
$23$	3.21898	+	5.57544i	0.671204	+	1.16256i	−0.306359	+	0.951916i	$0.599111\pi$
$24$		0			0
$25$	2.03163	−	3.51888i	0.406325	−	0.703776i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.34727	+	5.79764i	−0.621573	+	1.07660i	0.367620	+	0.929976i	$0.380173\pi$
$29$	−3.34727	+	5.79764i	−0.621573	+	1.07660i	−0.989193	+	0.146619i	$0.953161\pi$
$30$		0			0
$31$	−4.58310	−	7.93816i	−0.823149	−	1.42574i	−0.903326	−	0.428956i	$-0.858882\pi$
$31$	−4.58310	−	7.93816i	−0.823149	−	1.42574i	0.0801762	−	0.996781i	$-0.474452\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.70901			−0.280960			−0.140480	−	0.990084i	$-0.544865\pi$
$37$	−1.70901			−0.280960			−0.140480	+	0.990084i	$0.544865\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.62444	+	6.27771i	0.566042	+	0.980413i	0.996952	+	0.0780185i	$0.0248593\pi$
$41$	3.62444	+	6.27771i	0.566042	+	0.980413i	−0.430910	+	0.902395i	$0.641807\pi$
$42$		0			0
$43$	−0.348050	+	0.602841i	−0.0530772	+	0.0919324i	−0.891343	−	0.453329i	$-0.850236\pi$
$43$	−0.348050	+	0.602841i	−0.0530772	+	0.0919324i	0.838266	+	0.545261i	$0.183570\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.83120	−	6.63583i	0.558838	−	0.967936i	−0.438756	−	0.898606i	$-0.644581\pi$
$47$	3.83120	−	6.63583i	0.558838	−	0.967936i	0.997594	−	0.0693294i	$-0.0220860\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.11275			0.564929			0.282465	−	0.959278i	$-0.408848\pi$
$53$	4.11275			0.564929			0.282465	+	0.959278i	$0.408848\pi$
$54$		0			0
$55$	0.704836			0.0950401
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.38809	−	4.13629i	−0.310903	−	0.538500i	0.667655	−	0.744471i	$-0.267298\pi$
$59$	−2.38809	−	4.13629i	−0.310903	−	0.538500i	−0.978558	+	0.205971i	$0.933965\pi$
$60$		0			0
$61$	−2.46287	+	4.26582i	−0.315338	+	0.546182i	−0.979509	−	0.201399i	$-0.935451\pi$
$61$	−2.46287	+	4.26582i	−0.315338	+	0.546182i	0.664171	+	0.747581i	$0.268785\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.75246	+	3.03535i	−0.217366	+	0.376489i
$66$		0			0
$67$	2.91035	+	5.04087i	0.355556	+	0.615841i	0.987213	−	0.159407i	$-0.0509583\pi$
$67$	2.91035	+	5.04087i	0.355556	+	0.615841i	−0.631657	+	0.775248i	$0.717625\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.304424			−0.0361285			−0.0180642	−	0.999837i	$-0.505750\pi$
$71$	−0.304424			−0.0361285			−0.0180642	+	0.999837i	$0.505750\pi$
$72$		0			0
$73$	−10.6776			−1.24972			−0.624858	−	0.780739i	$-0.714843\pi$
$73$	−10.6776			−1.24972			−0.624858	+	0.780739i	$0.714843\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	1.61945	−	2.80497i	0.182203	−	0.315584i	−0.760428	−	0.649423i	$-0.775011\pi$
$79$	1.61945	−	2.80497i	0.182203	−	0.315584i	0.942630	+	0.333839i	$0.108344\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.618759	+	1.07172i	−0.0679176	+	0.117637i	−0.897985	−	0.440027i	$-0.854969\pi$
$83$	−0.618759	+	1.07172i	−0.0679176	+	0.117637i	0.830067	+	0.557664i	$0.188302\pi$
$84$		0			0
$85$	3.38700	+	5.86646i	0.367372	+	0.636307i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−11.5736			−1.22680			−0.613399	−	0.789773i	$-0.710198\pi$
$89$	−11.5736			−1.22680			−0.613399	+	0.789773i	$0.710198\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.336863	+	0.583464i	0.0345614	+	0.0598622i
$96$		0			0
$97$	1.32933	−	2.30247i	0.134973	−	0.233780i	−0.790614	−	0.612315i	$-0.790238\pi$
$97$	1.32933	−	2.30247i	0.134973	−	0.233780i	0.925587	+	0.378534i	$0.123572\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	0.806969	−	1.39771i	0.0802964	−	0.139077i	−0.823081	−	0.567924i	$-0.807747\pi$
$101$	0.806969	−	1.39771i	0.0802964	−	0.139077i	0.903377	+	0.428847i	$0.141080\pi$
$102$		0			0
$103$	−5.42007	−	9.38783i	−0.534055	−	0.925010i	−0.999208	−	0.0397803i	$-0.987334\pi$
$103$	−5.42007	−	9.38783i	−0.534055	−	0.925010i	0.465153	−	0.885230i	$-0.345999\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.95259			0.962153			0.481077	−	0.876679i	$-0.340246\pi$
$107$	9.95259			0.962153			0.481077	+	0.876679i	$0.340246\pi$
$108$		0			0
$109$	18.5567			1.77741			0.888705	−	0.458480i	$-0.151606\pi$
$109$	18.5567			1.77741			0.888705	+	0.458480i	$0.151606\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.75824	−	9.97356i	−0.541689	−	0.938234i	−0.998807	−	0.0488275i	$-0.984452\pi$
$113$	−5.75824	−	9.97356i	−0.541689	−	0.938234i	0.457118	−	0.889406i	$-0.348882\pi$
$114$		0			0
$115$	−3.11551	+	5.39623i	−0.290523	+	0.503201i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.23483	+	9.06699i	0.475894	+	0.824272i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	8.77193			0.784586
$126$		0			0
$127$	9.06977			0.804812			0.402406	−	0.915461i	$-0.368174\pi$
$127$	9.06977			0.804812			0.402406	+	0.915461i	$0.368174\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.54255	+	11.3320i	0.571625	+	0.990084i	0.996399	+	0.0847847i	$0.0270202\pi$
$131$	6.54255	+	11.3320i	0.571625	+	0.990084i	−0.424774	+	0.905299i	$0.639646\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−10.0382	+	17.3867i	−0.857623	+	1.48545i	0.0165668	+	0.999863i	$0.494726\pi$
$137$	−10.0382	+	17.3867i	−0.857623	+	1.48545i	−0.874190	+	0.485584i	$0.838607\pi$
$138$		0			0
$139$	0.337832	+	0.585143i	0.0286546	+	0.0496312i	0.879997	−	0.474979i	$-0.157544\pi$
$139$	0.337832	+	0.585143i	0.0286546	+	0.0496312i	−0.851343	+	0.524610i	$0.824211\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.63720			0.220534
$144$		0			0
$145$	−6.47936			−0.538082
$146$		0			0
$147$		0			0
$148$		0			0
$149$	10.7544	+	18.6271i	0.881034	+	1.52599i	0.850193	+	0.526471i	$0.176485\pi$
$149$	10.7544	+	18.6271i	0.881034	+	1.52599i	0.0308402	+	0.999524i	$0.490182\pi$
$150$		0			0
$151$	−7.08523	+	12.2720i	−0.576588	+	0.998680i	0.419279	+	0.907857i	$0.362283\pi$
$151$	−7.08523	+	12.2720i	−0.576588	+	0.998680i	−0.995867	+	0.0908223i	$0.971050\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.43579	−	7.68301i	0.356291	−	0.617114i
$156$		0			0
$157$	7.99845	+	13.8537i	0.638346	+	1.10565i	0.985796	+	0.167949i	$0.0537143\pi$
$157$	7.99845	+	13.8537i	0.638346	+	1.10565i	−0.347450	+	0.937699i	$0.612952\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	20.1808			1.58068			0.790340	−	0.612669i	$-0.209904\pi$
$163$	20.1808			1.58068			0.790340	+	0.612669i	$0.209904\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12.2299	+	21.1828i	0.946378	+	1.63917i	0.752968	+	0.658057i	$0.228621\pi$
$167$	12.2299	+	21.1828i	0.946378	+	1.63917i	0.193410	+	0.981118i	$0.438045\pi$
$168$		0			0
$169$	−0.0569772	+	0.0986874i	−0.00438286	+	0.00759134i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	9.87800	−	17.1092i	0.751010	−	1.30079i	−0.196323	−	0.980539i	$-0.562900\pi$
$173$	9.87800	−	17.1092i	0.751010	−	1.30079i	0.947333	−	0.320249i	$-0.103767\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−12.6488			−0.945415			−0.472707	−	0.881219i	$-0.656723\pi$
$179$	−12.6488			−0.945415			−0.472707	+	0.881219i	$0.656723\pi$
$180$		0			0
$181$	12.5654			0.933975			0.466988	−	0.884264i	$-0.345339\pi$
$181$	12.5654			0.933975			0.466988	+	0.884264i	$0.345339\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.827040	−	1.43248i	−0.0608052	−	0.105318i
$186$		0			0
$187$	2.54848	−	4.41409i	0.186363	−	0.322790i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.70316	+	6.41407i	−0.267951	+	0.464105i	−0.968333	−	0.249663i	$-0.919680\pi$
$191$	−3.70316	+	6.41407i	−0.267951	+	0.464105i	0.700381	+	0.713769i	$0.253013\pi$
$192$		0			0
$193$	0.813937	+	1.40978i	0.0585885	+	0.101478i	0.893832	−	0.448402i	$-0.148007\pi$
$193$	0.813937	+	1.40978i	0.0585885	+	0.101478i	−0.835244	+	0.549880i	$0.814673\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.27125			0.589302			0.294651	−	0.955605i	$-0.404797\pi$
$197$	8.27125			0.589302			0.294651	+	0.955605i	$0.404797\pi$
$198$		0			0
$199$	−10.6882			−0.757667			−0.378834	−	0.925465i	$-0.623675\pi$
$199$	−10.6882			−0.757667			−0.378834	+	0.925465i	$0.623675\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−3.50794	+	6.07593i	−0.245005	+	0.424361i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.253466	−	0.439015i	0.0175326	−	0.0303673i
$210$		0			0
$211$	−11.2725	−	19.5246i	−0.776034	−	1.34413i	−0.934211	−	0.356720i	$-0.883895\pi$
$211$	−11.2725	−	19.5246i	−0.776034	−	1.34413i	0.158178	−	0.987411i	$-0.449438\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.673726			−0.0459478
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$	12.6727	+	21.9498i	0.852461	+	1.47651i
$222$		0			0
$223$	3.70093	−	6.41020i	0.247832	−	0.429258i	−0.715092	−	0.699031i	$-0.753615\pi$
$223$	3.70093	−	6.41020i	0.247832	−	0.429258i	0.962924	+	0.269772i	$0.0869484\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.299086	+	0.518033i	−0.0198511	+	0.0343831i	−0.875780	−	0.482710i	$-0.839653\pi$
$227$	−0.299086	+	0.518033i	−0.0198511	+	0.0343831i	0.855929	+	0.517093i	$0.172986\pi$
$228$		0			0
$229$	2.01858	+	3.49629i	0.133392	+	0.231041i	0.924982	−	0.380011i	$-0.124080\pi$
$229$	2.01858	+	3.49629i	0.133392	+	0.231041i	−0.791590	+	0.611052i	$0.790747\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−11.1951			−0.733414			−0.366707	−	0.930336i	$-0.619515\pi$
$233$	−11.1951			−0.733414			−0.366707	+	0.930336i	$0.619515\pi$
$234$		0			0
$235$	7.41611			0.483774
$236$		0			0
$237$		0			0
$238$		0			0
$239$	12.8171	+	22.1999i	0.829069	+	1.43599i	0.898769	+	0.438421i	$0.144462\pi$
$239$	12.8171	+	22.1999i	0.829069	+	1.43599i	−0.0697006	+	0.997568i	$0.522204\pi$
$240$		0			0
$241$	3.29590	−	5.70866i	0.212307	−	0.367727i	−0.740129	−	0.672465i	$-0.765236\pi$
$241$	3.29590	−	5.70866i	0.212307	−	0.367727i	0.952436	+	0.304738i	$0.0985688\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.26040	+	2.18308i	0.0801975	+	0.138906i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−25.0438			−1.58075			−0.790374	−	0.612624i	$-0.790114\pi$
$251$	−25.0438			−1.58075			−0.790374	+	0.612624i	$0.790114\pi$
$252$		0			0
$253$	4.68840			0.294757
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.07036	−	15.7103i	−0.565794	−	0.979984i	−0.996975	−	0.0777184i	$-0.975236\pi$
$257$	−9.07036	−	15.7103i	−0.565794	−	0.979984i	0.431182	−	0.902265i	$-0.358097\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	6.40438	−	11.0927i	0.394911	−	0.684006i	−0.598179	−	0.801363i	$-0.704109\pi$
$263$	6.40438	−	11.0927i	0.394911	−	0.684006i	0.993090	+	0.117357i	$0.0374421\pi$
$264$		0			0
$265$	1.99028	+	3.44726i	0.122262	+	0.211763i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−28.8825			−1.76099			−0.880497	−	0.474052i	$-0.842791\pi$
$269$	−28.8825			−1.76099			−0.880497	+	0.474052i	$0.842791\pi$
$270$		0			0
$271$	−9.19159			−0.558349			−0.279175	−	0.960240i	$-0.590061\pi$
$271$	−9.19159			−0.558349			−0.279175	+	0.960240i	$0.590061\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.47952	−	2.56260i	−0.0892183	−	0.154531i
$276$		0			0
$277$	1.95778	−	3.39098i	0.117632	−	0.203744i	−0.801197	−	0.598401i	$-0.795803\pi$
$277$	1.95778	−	3.39098i	0.117632	−	0.203744i	0.918829	+	0.394656i	$0.129136\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−7.64654	+	13.2442i	−0.456154	+	0.790082i	−0.998754	−	0.0499093i	$-0.984107\pi$
$281$	−7.64654	+	13.2442i	−0.456154	+	0.790082i	0.542600	+	0.839991i	$0.317440\pi$
$282$		0			0
$283$	−12.4890	−	21.6315i	−0.742392	−	1.28586i	−0.951403	−	0.307947i	$-0.900358\pi$
$283$	−12.4890	−	21.6315i	−0.742392	−	1.28586i	0.209011	−	0.977913i	$-0.432975\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	31.9855			1.88150
$290$		0			0
$291$		0			0
$292$		0			0
$293$	4.08092	+	7.06835i	0.238410	+	0.412938i	0.960258	−	0.279114i	$-0.0900406\pi$
$293$	4.08092	+	7.06835i	0.238410	+	0.412938i	−0.721848	+	0.692051i	$0.756707\pi$
$294$		0			0
$295$	2.31133	−	4.00334i	0.134571	−	0.233084i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−11.6570	+	20.1904i	−0.674139	+	1.16764i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−4.76742			−0.272981
$306$		0			0
$307$	18.0692			1.03126			0.515631	−	0.856811i	$-0.327558\pi$
$307$	18.0692			1.03126			0.515631	+	0.856811i	$0.327558\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.00384	−	8.66691i	−0.283742	−	0.491456i	0.688561	−	0.725178i	$-0.258243\pi$
$311$	−5.00384	−	8.66691i	−0.283742	−	0.491456i	−0.972303	+	0.233723i	$0.924909\pi$
$312$		0			0
$313$	−1.49532	+	2.58998i	−0.0845207	+	0.146394i	−0.905187	−	0.425014i	$-0.860269\pi$
$313$	−1.49532	+	2.58998i	−0.0845207	+	0.146394i	0.820666	+	0.571408i	$0.193603\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−11.9246	+	20.6541i	−0.669754	+	1.16005i	0.308219	+	0.951315i	$0.400267\pi$
$317$	−11.9246	+	20.6541i	−0.669754	+	1.16005i	−0.977973	+	0.208732i	$0.933066\pi$
$318$		0			0
$319$	2.43763	+	4.22210i	0.136481	+	0.236392i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	4.87199			0.271085
$324$		0			0
$325$	14.7143			0.816204
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	8.01886	−	13.8891i	0.440757	−	0.763413i	−0.556989	−	0.830520i	$-0.688044\pi$
$331$	8.01886	−	13.8891i	0.440757	−	0.763413i	0.997746	+	0.0671069i	$0.0213768\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2.81680	+	4.87884i	−0.153898	+	0.266560i
$336$		0			0
$337$	16.8985	+	29.2691i	0.920520	+	1.59439i	0.798613	+	0.601845i	$0.205568\pi$
$337$	16.8985	+	29.2691i	0.920520	+	1.59439i	0.121907	+	0.992542i	$0.461099\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−6.67523			−0.361484
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	17.6637	+	30.5944i	0.948237	+	1.64240i	0.749136	+	0.662417i	$0.230469\pi$
$347$	17.6637	+	30.5944i	0.948237	+	1.64240i	0.199102	+	0.979979i	$0.436198\pi$
$348$		0			0
$349$	−5.75344	+	9.96526i	−0.307975	+	0.533428i	−0.977919	−	0.208983i	$-0.932985\pi$
$349$	−5.75344	+	9.96526i	−0.307975	+	0.533428i	0.669944	+	0.742411i	$0.266318\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	12.4432	−	21.5522i	0.662283	−	1.14711i	−0.317732	−	0.948181i	$-0.602921\pi$
$353$	12.4432	−	21.5522i	0.662283	−	1.14711i	0.980014	−	0.198926i	$-0.0637455\pi$
$354$		0			0
$355$	−0.147320	−	0.255165i	−0.00781891	−	0.0135427i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	18.4536			0.973944			0.486972	−	0.873417i	$-0.338101\pi$
$359$	18.4536			0.973944			0.486972	+	0.873417i	$0.338101\pi$
$360$		0			0
$361$	−18.5154			−0.974497
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−5.16718	−	8.94982i	−0.270463	−	0.468455i
$366$		0			0
$367$	9.10688	−	15.7736i	0.475375	−	0.823374i	−0.524227	−	0.851579i	$-0.675646\pi$
$367$	9.10688	−	15.7736i	0.475375	−	0.823374i	0.999602	+	0.0282046i	$0.00897899\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	9.09995	+	15.7616i	0.471177	+	0.816103i	0.999456	−	0.0329676i	$-0.0104958\pi$
$373$	9.09995	+	15.7616i	0.471177	+	0.816103i	−0.528279	+	0.849071i	$0.677162\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−24.2431			−1.24858
$378$		0			0
$379$	−24.1061			−1.23825			−0.619124	−	0.785293i	$-0.712512\pi$
$379$	−24.1061			−1.23825			−0.619124	+	0.785293i	$0.712512\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.21847	−	5.57455i	−0.164456	−	0.284846i	0.772006	−	0.635615i	$-0.219254\pi$
$383$	−3.21847	−	5.57455i	−0.164456	−	0.284846i	−0.936462	+	0.350769i	$0.885920\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	16.9299	−	29.3234i	0.858379	−	1.48676i	−0.0150964	−	0.999886i	$-0.504806\pi$
$389$	16.9299	−	29.3234i	0.858379	−	1.48676i	0.873475	−	0.486869i	$-0.161861\pi$
$390$		0			0
$391$	22.5295	+	39.0223i	1.13937	+	1.97344i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	3.13480			0.157729
$396$		0			0
$397$	1.61726			0.0811679			0.0405840	−	0.999176i	$-0.487078\pi$
$397$	1.61726			0.0811679			0.0405840	+	0.999176i	$0.487078\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	2.87691	+	4.98296i	0.143666	+	0.248837i	0.928874	−	0.370395i	$-0.120778\pi$
$401$	2.87691	+	4.98296i	0.143666	+	0.248837i	−0.785208	+	0.619232i	$0.787444\pi$
$402$		0			0
$403$	16.5969	−	28.7466i	0.826749	−	1.43197i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.622289	+	1.07784i	−0.0308457	+	0.0534263i
$408$		0			0
$409$	2.88631	+	4.99923i	0.142719	+	0.247196i	0.928520	−	0.371284i	$-0.121082\pi$
$409$	2.88631	+	4.99923i	0.142719	+	0.247196i	−0.785801	+	0.618480i	$0.787749\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−1.19774			−0.0587948
$416$		0			0
$417$		0			0
$418$		0			0
$419$	9.29032	+	16.0913i	0.453862	+	0.786111i	0.998622	−	0.0524804i	$-0.0167127\pi$
$419$	9.29032	+	16.0913i	0.453862	+	0.786111i	−0.544760	+	0.838592i	$0.683379\pi$
$420$		0			0
$421$	−8.05788	+	13.9567i	−0.392717	+	0.680206i	−0.992807	−	0.119727i	$-0.961798\pi$
$421$	−8.05788	+	13.9567i	−0.392717	+	0.680206i	0.600090	+	0.799933i	$0.295131\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	14.2193	−	24.6285i	0.689737	−	1.19466i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	3.65327			0.175972			0.0879860	−	0.996122i	$-0.471957\pi$
$431$	3.65327			0.175972			0.0879860	+	0.996122i	$0.471957\pi$
$432$		0			0
$433$	12.6697			0.608865			0.304432	−	0.952534i	$-0.401533\pi$
$433$	12.6697			0.608865			0.304432	+	0.952534i	$0.401533\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.24073	+	3.88107i	0.107189	+	0.185657i
$438$		0			0
$439$	−5.85810	+	10.1465i	−0.279592	+	0.484267i	−0.971283	−	0.237926i	$-0.923532\pi$
$439$	−5.85810	+	10.1465i	−0.279592	+	0.484267i	0.691692	+	0.722193i	$0.256866\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−14.8735	+	25.7617i	−0.706661	+	1.22397i	0.259428	+	0.965763i	$0.416466\pi$
$443$	−14.8735	+	25.7617i	−0.706661	+	1.22397i	−0.966089	+	0.258210i	$0.916867\pi$
$444$		0			0
$445$	−5.60079	−	9.70085i	−0.265503	−	0.459865i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−11.0193			−0.520034			−0.260017	−	0.965604i	$-0.583728\pi$
$449$	−11.0193			−0.520034			−0.260017	+	0.965604i	$0.583728\pi$
$450$		0			0
$451$	5.27895			0.248576
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.258224	+	0.447257i	−0.0120792	+	0.0209218i	−0.872002	−	0.489503i	$-0.837178\pi$
$457$	−0.258224	+	0.447257i	−0.0120792	+	0.0209218i	0.859923	+	0.510424i	$0.170512\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	3.54962	−	6.14813i	0.165322	−	0.286347i	−0.771447	−	0.636293i	$-0.780467\pi$
$461$	3.54962	−	6.14813i	0.165322	−	0.286347i	0.936770	+	0.349946i	$0.113800\pi$
$462$		0			0
$463$	−4.91148	−	8.50693i	−0.228256	−	0.395351i	0.729035	−	0.684476i	$-0.239969\pi$
$463$	−4.91148	−	8.50693i	−0.228256	−	0.395351i	−0.957291	+	0.289125i	$0.906636\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.59208			−0.443868			−0.221934	−	0.975062i	$-0.571237\pi$
$467$	−9.59208			−0.443868			−0.221934	+	0.975062i	$0.571237\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.253466	+	0.439015i	0.0116544	+	0.0201859i
$474$		0			0
$475$	1.41422	−	2.44950i	0.0648887	−	0.112391i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	8.13621	−	14.0923i	0.371753	−	0.643895i	−0.618082	−	0.786113i	$-0.712090\pi$
$479$	8.13621	−	14.0923i	0.371753	−	0.643895i	0.989835	+	0.142218i	$0.0454235\pi$
$480$		0			0
$481$	−3.09444	−	5.35973i	−0.141094	−	0.244383i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.57321			0.116843
$486$		0			0
$487$	19.0102			0.861436			0.430718	−	0.902487i	$-0.358260\pi$
$487$	19.0102			0.861436			0.430718	+	0.902487i	$0.358260\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−2.55413	−	4.42387i	−0.115266	−	0.199647i	0.802620	−	0.596491i	$-0.203439\pi$
$491$	−2.55413	−	4.42387i	−0.115266	−	0.199647i	−0.917886	+	0.396844i	$0.870105\pi$
$492$		0			0
$493$	−23.4274	+	40.5775i	−1.05512	+	1.82752i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	14.2638	+	24.7056i	0.638536	+	1.10598i	0.985754	+	0.168192i	$0.0537928\pi$
$499$	14.2638	+	24.7056i	0.638536	+	1.10598i	−0.347219	+	0.937784i	$0.612874\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−4.05885			−0.180975			−0.0904877	−	0.995898i	$-0.528843\pi$
$503$	−4.05885			−0.180975			−0.0904877	+	0.995898i	$0.528843\pi$
$504$		0			0
$505$	1.56206			0.0695108
$506$		0			0
$507$		0			0
$508$		0			0
$509$	8.63023	+	14.9480i	0.382528	+	0.662558i	0.991423	−	0.130693i	$-0.0417202\pi$
$509$	8.63023	+	14.9480i	0.382528	+	0.662558i	−0.608895	+	0.793251i	$0.708387\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	5.24585	−	9.08608i	0.231160	−	0.400380i
$516$		0			0
$517$	−2.79005	−	4.83250i	−0.122706	−	0.212533i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−34.1050			−1.49417			−0.747083	−	0.664730i	$-0.768546\pi$
$521$	−34.1050			−1.49417			−0.747083	+	0.664730i	$0.768546\pi$
$522$		0			0
$523$	18.8969			0.826306			0.413153	−	0.910662i	$-0.364428\pi$
$523$	18.8969			0.826306			0.413153	+	0.910662i	$0.364428\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−32.0770	−	55.5589i	−1.39729	−	2.42019i
$528$		0			0
$529$	−9.22366	+	15.9758i	−0.401029	+	0.694602i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−13.1252	+	22.7336i	−0.568517	+	0.984701i
$534$		0			0
$535$	4.81634	+	8.34215i	0.208229	+	0.360663i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−1.12823			−0.0485066			−0.0242533	−	0.999706i	$-0.507721\pi$
$541$	−1.12823			−0.0485066			−0.0242533	+	0.999706i	$0.507721\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	8.98012	+	15.5540i	0.384666	+	0.666261i
$546$		0			0
$547$	15.8427	−	27.4404i	0.677386	−	1.17327i	−0.298380	−	0.954447i	$-0.596446\pi$
$547$	15.8427	−	27.4404i	0.677386	−	1.17327i	0.975765	−	0.218819i	$-0.0702205\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.33004	+	4.03575i	−0.0992630	+	0.171929i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−27.6271			−1.17060			−0.585298	−	0.810818i	$-0.699023\pi$
$557$	−27.6271			−1.17060			−0.585298	+	0.810818i	$0.699023\pi$
$558$		0			0
$559$	−2.52080			−0.106619
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.920685	+	1.59467i	0.0388022	+	0.0672074i	0.884774	−	0.466020i	$-0.154312\pi$
$563$	0.920685	+	1.59467i	0.0388022	+	0.0672074i	−0.845972	+	0.533227i	$0.820979\pi$
$564$		0			0
$565$	5.57315	−	9.65298i	0.234464	−	0.406104i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.75524	+	9.96837i	−0.241272	+	0.417896i	−0.961077	−	0.276281i	$-0.910898\pi$
$569$	−5.75524	+	9.96837i	−0.241272	+	0.417896i	0.719805	+	0.694177i	$0.244231\pi$
$570$		0			0
$571$	4.35262	+	7.53896i	0.182152	+	0.315496i	0.942613	−	0.333887i	$-0.108361\pi$
$571$	4.35262	+	7.53896i	0.182152	+	0.315496i	−0.760461	+	0.649383i	$0.775027\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	26.1591			1.09091
$576$		0			0
$577$	14.4872			0.603108			0.301554	−	0.953449i	$-0.402495\pi$
$577$	14.4872			0.603108			0.301554	+	0.953449i	$0.402495\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1.49754	−	2.59382i	0.0620218	−	0.107425i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	14.3695	−	24.8886i	0.593091	−	1.02726i	−0.400722	−	0.916200i	$-0.631241\pi$
$587$	14.3695	−	24.8886i	0.593091	−	1.02726i	0.993813	−	0.111065i	$-0.0354261\pi$
$588$		0			0
$589$	−3.19030	−	5.52576i	−0.131454	−	0.227685i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	13.6466			0.560397			0.280199	−	0.959942i	$-0.409600\pi$
$593$	13.6466			0.560397			0.280199	+	0.959942i	$0.409600\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	2.64585	+	4.58275i	0.108106	+	0.187246i	0.915003	−	0.403447i	$-0.132188\pi$
$599$	2.64585	+	4.58275i	0.108106	+	0.187246i	−0.806897	+	0.590693i	$0.798855\pi$
$600$		0			0
$601$	17.0522	−	29.5353i	0.695574	−	1.20477i	−0.274412	−	0.961612i	$-0.588483\pi$
$601$	17.0522	−	29.5353i	0.695574	−	1.20477i	0.969987	−	0.243158i	$-0.0781834\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−5.06657	+	8.77555i	−0.205985	+	0.356777i
$606$		0			0
$607$	4.52232	+	7.83289i	0.183555	+	0.317927i	0.943089	−	0.332541i	$-0.107906\pi$
$607$	4.52232	+	7.83289i	0.183555	+	0.317927i	−0.759533	+	0.650468i	$0.774573\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	27.7480			1.12256
$612$		0			0
$613$	−11.9578			−0.482970			−0.241485	−	0.970405i	$-0.577634\pi$
$613$	−11.9578			−0.482970			−0.241485	+	0.970405i	$0.577634\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.13220	−	8.88923i	−0.206615	−	0.357867i	0.744031	−	0.668145i	$-0.232911\pi$
$617$	−5.13220	−	8.88923i	−0.206615	−	0.357867i	−0.950646	+	0.310278i	$0.899578\pi$
$618$		0			0
$619$	21.7803	−	37.7245i	0.875423	−	1.51628i	0.0191114	−	0.999817i	$-0.493916\pi$
$619$	21.7803	−	37.7245i	0.875423	−	1.51628i	0.856312	−	0.516460i	$-0.172750\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−5.91314	−	10.2419i	−0.236526	−	0.409674i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−11.9613			−0.476929
$630$		0			0
$631$	19.3703			0.771119			0.385559	−	0.922683i	$-0.374008\pi$
$631$	19.3703			0.771119			0.385559	+	0.922683i	$0.374008\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	4.38912	+	7.60218i	0.174177	+	0.301684i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	2.25008	−	3.89725i	0.0888728	−	0.153932i	−0.818162	−	0.574988i	$-0.805007\pi$
$641$	2.25008	−	3.89725i	0.0888728	−	0.153932i	0.907035	+	0.421055i	$0.138340\pi$
$642$		0			0
$643$	−20.9045	−	36.2077i	−0.824394	−	1.42789i	−0.902381	−	0.430939i	$-0.858183\pi$
$643$	−20.9045	−	36.2077i	−0.824394	−	1.42789i	0.0779869	−	0.996954i	$-0.475151\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	23.8761			0.938667			0.469334	−	0.883021i	$-0.344494\pi$
$647$	23.8761			0.938667			0.469334	+	0.883021i	$0.344494\pi$
$648$		0			0
$649$	−3.47822			−0.136532
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.16674	−	7.21700i	−0.163057	−	0.282423i	0.772907	−	0.634520i	$-0.218802\pi$
$653$	−4.16674	−	7.21700i	−0.163057	−	0.282423i	−0.935964	+	0.352097i	$0.885469\pi$
$654$		0			0
$655$	−6.33226	+	10.9678i	−0.247422	+	0.428547i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	20.2488	−	35.0719i	0.788781	−	1.36621i	−0.137933	−	0.990442i	$-0.544046\pi$
$659$	20.2488	−	35.0719i	0.788781	−	1.36621i	0.926714	−	0.375767i	$-0.122621\pi$
$660$		0			0
$661$	3.88559	+	6.73004i	0.151132	+	0.261768i	0.931644	−	0.363373i	$-0.118375\pi$
$661$	3.88559	+	6.73004i	0.151132	+	0.261768i	−0.780512	+	0.625141i	$0.785042\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−43.0992			−1.66881
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1.79357	+	3.10656i	0.0692400	+	0.119927i
$672$		0			0
$673$	−22.7830	+	39.4614i	−0.878221	+	1.52112i	−0.0249302	+	0.999689i	$0.507936\pi$
$673$	−22.7830	+	39.4614i	−0.878221	+	1.52112i	−0.853291	+	0.521435i	$0.825397\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	6.54521	−	11.3366i	0.251553	−	0.435702i	−0.712401	−	0.701773i	$-0.752392\pi$
$677$	6.54521	−	11.3366i	0.251553	−	0.435702i	0.963954	+	0.266071i	$0.0857254\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−25.3011			−0.968121			−0.484060	−	0.875035i	$-0.660839\pi$
$683$	−25.3011			−0.968121			−0.484060	+	0.875035i	$0.660839\pi$
$684$		0			0
$685$	−19.4311			−0.742425
$686$		0			0
$687$		0			0
$688$		0			0
$689$	7.44679	+	12.8982i	0.283700	+	0.491383i
$690$		0			0
$691$	12.2016	−	21.1337i	0.464170	−	0.803965i	−0.534994	−	0.844856i	$-0.679686\pi$
$691$	12.2016	−	21.1337i	0.464170	−	0.803965i	0.999164	+	0.0408905i	$0.0130195\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.326974	+	0.566335i	−0.0124028	+	0.0214823i
$696$		0			0
$697$	25.3673	+	43.9375i	0.960855	+	1.66425i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	18.4137			0.695476			0.347738	−	0.937592i	$-0.386950\pi$
$701$	18.4137			0.695476			0.347738	+	0.937592i	$0.386950\pi$
$702$		0			0
$703$	−1.18965			−0.0448683
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	6.66501	−	11.5441i	0.250310	−	0.433549i	−0.713301	−	0.700858i	$-0.752801\pi$
$709$	6.66501	−	11.5441i	0.250310	−	0.433549i	0.963611	+	0.267308i	$0.0861342\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	29.5058	−	51.1056i	1.10500	−	1.91392i
$714$		0			0
$715$	1.27622	+	2.21047i	0.0477278	+	0.0826671i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−15.6941			−0.585291			−0.292646	−	0.956221i	$-0.594536\pi$
$719$	−15.6941			−0.585291			−0.292646	+	0.956221i	$0.594536\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$	13.6008	+	23.5573i	0.505121	+	0.874896i
$726$		0			0
$727$	−12.8388	+	22.2374i	−0.476163	+	0.824739i	−0.999627	−	0.0273090i	$-0.991306\pi$
$727$	−12.8388	+	22.2374i	−0.476163	+	0.824739i	0.523464	+	0.852048i	$0.324640\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−2.43599	+	4.21926i	−0.0900985	+	0.156055i
$732$		0			0
$733$	−0.586541	−	1.01592i	−0.0216644	−	0.0375238i	0.854990	−	0.518645i	$-0.173563\pi$
$733$	−0.586541	−	1.01592i	−0.0216644	−	0.0375238i	−0.876654	+	0.481121i	$0.840230\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.23889			0.156141
$738$		0			0
$739$	−23.2229			−0.854266			−0.427133	−	0.904189i	$-0.640476\pi$
$739$	−23.2229			−0.854266			−0.427133	+	0.904189i	$0.640476\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−11.7846	−	20.4115i	−0.432335	−	0.748826i	0.564739	−	0.825269i	$-0.308977\pi$
$743$	−11.7846	−	20.4115i	−0.432335	−	0.748826i	−0.997074	+	0.0764439i	$0.975643\pi$
$744$		0			0
$745$	−10.4087	+	18.0284i	−0.381346	+	0.660510i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−22.0531	−	38.1971i	−0.804728	−	1.39383i	−0.916474	−	0.400093i	$-0.868978\pi$
$751$	−22.0531	−	38.1971i	−0.804728	−	1.39383i	0.111746	−	0.993737i	$-0.464356\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−13.7150			−0.499139
$756$		0			0
$757$	−2.71020			−0.0985040			−0.0492520	−	0.998786i	$-0.515684\pi$
$757$	−2.71020			−0.0985040			−0.0492520	+	0.998786i	$0.515684\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	14.5248	+	25.1577i	0.526524	+	0.911966i	0.999522	+	0.0309029i	$0.00983826\pi$
$761$	14.5248	+	25.1577i	0.526524	+	0.911966i	−0.472999	+	0.881063i	$0.656828\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	8.64804	−	14.9788i	0.312263	−	0.540855i
$768$		0			0
$769$	−5.25175	−	9.09629i	−0.189383	−	0.328021i	0.755662	−	0.654962i	$-0.227315\pi$
$769$	−5.25175	−	9.09629i	−0.189383	−	0.328021i	−0.945045	+	0.326941i	$0.893982\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−23.8460			−0.857682			−0.428841	−	0.903380i	$-0.641078\pi$
$773$	−23.8460			−0.857682			−0.428841	+	0.903380i	$0.641078\pi$
$774$		0			0
$775$	−37.2446			−1.33787
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.52297	+	4.36992i	0.0903949	+	0.156569i
$780$		0			0
$781$	−0.110847	+	0.191993i	−0.00396643	+	0.00687007i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−7.74136	+	13.4084i	−0.276301	+	0.478567i
$786$		0			0
$787$	2.19788	+	3.80684i	0.0783460	+	0.135699i	0.902536	−	0.430613i	$-0.141703\pi$
$787$	2.19788	+	3.80684i	0.0783460	+	0.135699i	−0.824190	+	0.566313i	$0.808369\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−17.8377			−0.633435
$794$		0			0
$795$		0			0
$796$		0			0
$797$	2.56236	+	4.43813i	0.0907633	+	0.157207i	0.907833	−	0.419333i	$-0.137736\pi$
$797$	2.56236	+	4.43813i	0.0907633	+	0.157207i	−0.817069	+	0.576540i	$0.804403\pi$
$798$		0			0
$799$	26.8144	−	46.4440i	0.948627	−	1.64307i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.88794	+	6.73410i	−0.137202	+	0.237641i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−32.9223			−1.15749			−0.578744	−	0.815510i	$-0.696457\pi$
$809$	−32.9223			−1.15749			−0.578744	+	0.815510i	$0.696457\pi$
$810$		0			0
$811$	−31.8830			−1.11956			−0.559781	−	0.828640i	$-0.689115\pi$
$811$	−31.8830			−1.11956			−0.559781	+	0.828640i	$0.689115\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	9.76605	+	16.9153i	0.342090	+	0.592517i
$816$		0			0
$817$	−0.242278	+	0.419638i	−0.00847624	+	0.0146813i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	17.1139	−	29.6421i	0.597278	−	1.03452i	−0.395943	−	0.918275i	$-0.629582\pi$
$821$	17.1139	−	29.6421i	0.597278	−	1.03452i	0.993221	−	0.116241i	$-0.0370844\pi$
$822$		0			0
$823$	−19.1866	−	33.2321i	−0.668802	−	1.15840i	−0.978239	−	0.207480i	$-0.933474\pi$
$823$	−19.1866	−	33.2321i	−0.668802	−	1.15840i	0.309437	−	0.950920i	$-0.399859\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−9.23903			−0.321273			−0.160636	−	0.987014i	$-0.551355\pi$
$827$	−9.23903			−0.321273			−0.160636	+	0.987014i	$0.551355\pi$
$828$		0			0
$829$	−41.6448			−1.44638			−0.723191	−	0.690648i	$-0.757326\pi$
$829$	−41.6448			−1.44638			−0.723191	+	0.690648i	$0.757326\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−11.8368	+	20.5019i	−0.409629	+	0.709499i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	15.4241	−	26.7154i	0.532500	−	0.922318i	−0.466780	−	0.884374i	$-0.654586\pi$
$839$	15.4241	−	26.7154i	0.532500	−	0.922318i	0.999280	−	0.0379439i	$-0.0120808\pi$
$840$		0			0
$841$	−7.90845	−	13.6978i	−0.272705	−	0.472339i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.110292			−0.00379415
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−5.50128	−	9.52849i	−0.188581	−	0.326632i
$852$		0			0
$853$	−11.4171	+	19.7750i	−0.390913	+	0.677082i	−0.992570	−	0.121673i	$-0.961174\pi$
$853$	−11.4171	+	19.7750i	−0.390913	+	0.677082i	0.601657	+	0.798755i	$0.294507\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−26.6720	+	46.1973i	−0.911100	+	1.57807i	−0.0985862	+	0.995129i	$0.531432\pi$
$857$	−26.6720	+	46.1973i	−0.911100	+	1.57807i	−0.812513	+	0.582942i	$0.801901\pi$
$858$		0			0
$859$	11.5878	+	20.0707i	0.395372	+	0.684804i	0.993149	−	0.116859i	$-0.0372825\pi$
$859$	11.5878	+	20.0707i	0.395372	+	0.684804i	−0.597777	+	0.801663i	$0.703949\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9.16911			0.312120			0.156060	−	0.987748i	$-0.450121\pi$
$863$	9.16911			0.312120			0.156060	+	0.987748i	$0.450121\pi$
$864$		0			0
$865$	19.1210			0.650133
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.17936	−	2.04270i	−0.0400069	−	0.0692940i
$870$		0			0
$871$	−10.5393	+	18.2546i	−0.357111	+	0.618534i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−18.6190	−	32.2490i	−0.628718	−	1.08897i	−0.987809	−	0.155670i	$-0.950247\pi$
$877$	−18.6190	−	32.2490i	−0.628718	−	1.08897i	0.359091	−	0.933303i	$-0.383087\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−7.15345			−0.241006			−0.120503	−	0.992713i	$-0.538451\pi$
$881$	−7.15345			−0.241006			−0.120503	+	0.992713i	$0.538451\pi$
$882$		0			0
$883$	−39.8688			−1.34169			−0.670846	−	0.741596i	$-0.734069\pi$
$883$	−39.8688			−1.34169			−0.670846	+	0.741596i	$0.734069\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−10.6755	−	18.4904i	−0.358447	−	0.620848i	0.629255	−	0.777199i	$-0.283360\pi$
$887$	−10.6755	−	18.4904i	−0.358447	−	0.620848i	−0.987702	+	0.156351i	$0.950027\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	2.66690	−	4.61921i	0.0892445	−	0.154576i
$894$		0			0
$895$	−6.12111	−	10.6021i	−0.204606	−	0.354388i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	61.3635			2.04659
$900$		0			0
$901$	28.7850			0.958967
$902$		0			0
$903$		0			0
$904$		0			0
$905$	6.08073	+	10.5321i	0.202130	+	0.350100i
$906$		0			0
$907$	11.3012	−	19.5742i	0.375250	−	0.649951i	−0.615115	−	0.788438i	$-0.710890\pi$
$907$	11.3012	−	19.5742i	0.375250	−	0.649951i	0.990364	+	0.138486i	$0.0442237\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−12.7594	+	22.0999i	−0.422738	+	0.732203i	−0.996206	−	0.0870243i	$-0.972264\pi$
$911$	−12.7594	+	22.0999i	−0.422738	+	0.732203i	0.573468	+	0.819228i	$0.305598\pi$
$912$		0			0
$913$	0.450607	+	0.780475i	0.0149129	+	0.0258300i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−11.4265			−0.376926			−0.188463	−	0.982080i	$-0.560351\pi$
$919$	−11.4265			−0.376926			−0.188463	+	0.982080i	$0.560351\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.551208	−	0.954721i	−0.0181432	−	0.0314250i
$924$		0			0
$925$	−3.47207	+	6.01381i	−0.114161	+	0.197733i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	6.79851	−	11.7754i	0.223052	−	0.386337i	−0.732681	−	0.680572i	$-0.761731\pi$
$929$	6.79851	−	11.7754i	0.223052	−	0.386337i	0.955733	+	0.294235i	$0.0950648\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	4.93312			0.161330
$936$		0			0
$937$	−11.1455			−0.364109			−0.182054	−	0.983288i	$-0.558275\pi$
$937$	−11.1455			−0.364109			−0.182054	+	0.983288i	$0.558275\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	20.7310	+	35.9072i	0.675813	+	1.17054i	0.976231	+	0.216734i	$0.0695405\pi$
$941$	20.7310	+	35.9072i	0.675813	+	1.17054i	−0.300418	+	0.953808i	$0.597126\pi$
$942$		0			0
$943$	−23.3340	+	40.4156i	−0.759859	+	1.31611i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	21.2784	−	36.8552i	0.691454	−	1.19763i	−0.279908	−	0.960027i	$-0.590304\pi$
$947$	21.2784	−	36.8552i	0.691454	−	1.19763i	0.971362	−	0.237606i	$-0.0763627\pi$
$948$		0			0
$949$	−19.3335	−	33.4865i	−0.627590	−	1.08702i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−21.2114			−0.687106			−0.343553	−	0.939133i	$-0.611630\pi$
$953$	−21.2114			−0.687106			−0.343553	+	0.939133i	$0.611630\pi$
$954$		0			0
$955$	−7.16826			−0.231960
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−26.5096	+	45.9160i	−0.855150	+	1.48116i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.787775	+	1.36447i	−0.0253594	+	0.0439237i
$966$		0			0
$967$	−9.83257	−	17.0305i	−0.316194	−	0.547664i	0.663496	−	0.748179i	$-0.269072\pi$
$967$	−9.83257	−	17.0305i	−0.316194	−	0.547664i	−0.979691	+	0.200515i	$0.935738\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−24.5784			−0.788757			−0.394379	−	0.918948i	$-0.629040\pi$
$971$	−24.5784			−0.788757			−0.394379	+	0.918948i	$0.629040\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−23.7359	−	41.1117i	−0.759378	−	1.31528i	−0.943168	−	0.332316i	$-0.892170\pi$
$977$	−23.7359	−	41.1117i	−0.759378	−	1.31528i	0.183790	−	0.982966i	$-0.441163\pi$
$978$		0			0
$979$	−4.21420	+	7.29920i	−0.134686	+	0.233284i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	13.7720	−	23.8538i	0.439258	−	0.760817i	−0.558374	−	0.829589i	$-0.688575\pi$
$983$	13.7720	−	23.8538i	0.439258	−	0.760817i	0.997632	+	0.0687719i	$0.0219081\pi$
$984$		0			0
$985$	4.00269	+	6.93287i	0.127536	+	0.220900i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.48147			−0.142502
$990$		0			0
$991$	−38.4671			−1.22195			−0.610973	−	0.791651i	$-0.709222\pi$
$991$	−38.4671			−1.22195			−0.610973	+	0.791651i	$0.709222\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−5.17233	−	8.95874i	−0.163974	−	0.284011i
$996$		0			0
$997$	16.2272	−	28.1064i	0.513921	−	0.890138i	−0.485948	−	0.873988i	$-0.661526\pi$
$997$	16.2272	−	28.1064i	0.513921	−	0.890138i	0.999870	−	0.0161503i	$-0.00514103\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5292.2.j.h.3529.5		14
3.2	odd	2		1764.2.j.g.1177.6		14
7.2	even	3		756.2.i.b.613.5		14
7.3	odd	6		5292.2.l.i.3313.5		14
7.4	even	3		756.2.l.b.289.3		14
7.5	odd	6		5292.2.i.i.2125.3		14
7.6	odd	2		5292.2.j.g.3529.3		14
9.4	even	3	inner	5292.2.j.h.1765.5		14
9.5	odd	6		1764.2.j.g.589.6		14
21.2	odd	6		252.2.i.b.25.5	✓	14
21.5	even	6		1764.2.i.i.1537.3		14
21.11	odd	6		252.2.l.b.205.1	yes	14
21.17	even	6		1764.2.l.i.961.7		14
21.20	even	2		1764.2.j.h.1177.2		14
28.11	odd	6		3024.2.t.j.289.3		14
28.23	odd	6		3024.2.q.j.2881.5		14
63.2	odd	6		2268.2.k.e.1621.3		14
63.4	even	3		756.2.i.b.37.5		14
63.5	even	6		1764.2.l.i.949.7		14
63.11	odd	6		2268.2.k.e.1297.3		14
63.13	odd	6		5292.2.j.g.1765.3		14
63.16	even	3		2268.2.k.f.1621.5		14
63.23	odd	6		252.2.l.b.193.1	yes	14
63.25	even	3		2268.2.k.f.1297.5		14
63.31	odd	6		5292.2.i.i.1549.3		14
63.32	odd	6		252.2.i.b.121.5	yes	14
63.40	odd	6		5292.2.l.i.361.5		14
63.41	even	6		1764.2.j.h.589.2		14
63.58	even	3		756.2.l.b.361.3		14
63.59	even	6		1764.2.i.i.373.3		14
84.11	even	6		1008.2.t.j.961.7		14
84.23	even	6		1008.2.q.j.529.3		14
252.23	even	6		1008.2.t.j.193.7		14
252.67	odd	6		3024.2.q.j.2305.5		14
252.95	even	6		1008.2.q.j.625.3		14
252.247	odd	6		3024.2.t.j.1873.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.5	✓	14	21.2	odd	6
252.2.i.b.121.5	yes	14	63.32	odd	6
252.2.l.b.193.1	yes	14	63.23	odd	6
252.2.l.b.205.1	yes	14	21.11	odd	6
756.2.i.b.37.5		14	63.4	even	3
756.2.i.b.613.5		14	7.2	even	3
756.2.l.b.289.3		14	7.4	even	3
756.2.l.b.361.3		14	63.58	even	3
1008.2.q.j.529.3		14	84.23	even	6
1008.2.q.j.625.3		14	252.95	even	6
1008.2.t.j.193.7		14	252.23	even	6
1008.2.t.j.961.7		14	84.11	even	6
1764.2.i.i.373.3		14	63.59	even	6
1764.2.i.i.1537.3		14	21.5	even	6
1764.2.j.g.589.6		14	9.5	odd	6
1764.2.j.g.1177.6		14	3.2	odd	2
1764.2.j.h.589.2		14	63.41	even	6
1764.2.j.h.1177.2		14	21.20	even	2
1764.2.l.i.949.7		14	63.5	even	6
1764.2.l.i.961.7		14	21.17	even	6
2268.2.k.e.1297.3		14	63.11	odd	6
2268.2.k.e.1621.3		14	63.2	odd	6
2268.2.k.f.1297.5		14	63.25	even	3
2268.2.k.f.1621.5		14	63.16	even	3
3024.2.q.j.2305.5		14	252.67	odd	6
3024.2.q.j.2881.5		14	28.23	odd	6
3024.2.t.j.289.3		14	28.11	odd	6
3024.2.t.j.1873.3		14	252.247	odd	6
5292.2.i.i.1549.3		14	63.31	odd	6
5292.2.i.i.2125.3		14	7.5	odd	6
5292.2.j.g.1765.3		14	63.13	odd	6
5292.2.j.g.3529.3		14	7.6	odd	2
5292.2.j.h.1765.5		14	9.4	even	3	inner
5292.2.j.h.3529.5		14	1.1	even	1	trivial
5292.2.l.i.361.5		14	63.40	odd	6
5292.2.l.i.3313.5		14	7.3	odd	6

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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:	\( N \)	\(=\)	\( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5292.j (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.483929 + 0.838189i) q^{5} +(0.364122 - 0.630678i) q^{11} +(1.81066 + 3.13615i) q^{13} +6.99897 q^{17} +0.696101 q^{19} +(3.21898 + 5.57544i) q^{23} +(2.03163 - 3.51888i) q^{25} +(-3.34727 + 5.79764i) q^{29} +(-4.58310 - 7.93816i) q^{31} -1.70901 q^{37} +(3.62444 + 6.27771i) q^{41} +(-0.348050 + 0.602841i) q^{43} +(3.83120 - 6.63583i) q^{47} +4.11275 q^{53} +0.704836 q^{55} +(-2.38809 - 4.13629i) q^{59} +(-2.46287 + 4.26582i) q^{61} +(-1.75246 + 3.03535i) q^{65} +(2.91035 + 5.04087i) q^{67} -0.304424 q^{71} -10.6776 q^{73} +(1.61945 - 2.80497i) q^{79} +(-0.618759 + 1.07172i) q^{83} +(3.38700 + 5.86646i) q^{85} -11.5736 q^{89} +(0.336863 + 0.583464i) q^{95} +(1.32933 - 2.30247i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{5} - 2 q^{11} + 2 q^{13} + 4 q^{17} - 14 q^{19} - 11 q^{23} - 9 q^{25} - q^{29} - q^{31} - 20 q^{37} + 33 q^{41} + 7 q^{43} + 3 q^{47} - 30 q^{53} - 28 q^{55} + 14 q^{59} - 10 q^{61} - 15 q^{65}+ \cdots - 18 q^{97}+O(q^{100}) \) 14 * q + 2 * q^5 - 2 * q^11 + 2 * q^13 + 4 * q^17 - 14 * q^19 - 11 * q^23 - 9 * q^25 - q^29 - q^31 - 20 * q^37 + 33 * q^41 + 7 * q^43 + 3 * q^47 - 30 * q^53 - 28 * q^55 + 14 * q^59 - 10 * q^61 - 15 * q^65 + 6 * q^67 - 2 * q^71 - 42 * q^73 - 10 * q^79 + 25 * q^83 + 8 * q^85 - 12 * q^89 + 28 * q^95 - 18 * q^97

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