LMFDB - Embedded newform 162.13.d.h.107.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [162,13,Mod(53,162)] 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("162.53"); S:= CuspForms(chi, 13); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(162, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 13, names="a")

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	162.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,24576,0,0,220224] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$148.066998399$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.5
Character	$\chi$	$=$	162.107
Dual form			162.13.d.h.53.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-39.1918 - 22.6274i) q^{2} +(1024.00 + 1773.62i) q^{4} +(2889.58 - 1668.30i) q^{5} +(-92313.0 + 159891. i) q^{7} -92681.9i q^{8} -150997. q^{10} +(-1.91171e6 - 1.10373e6i) q^{11} +(-1.40859e6 - 2.43974e6i) q^{13} +(7.23583e6 - 4.17761e6i) q^{14} +(-2.09715e6 + 3.63237e6i) q^{16} -1.32044e7i q^{17} +7.60755e7 q^{19} +(5.91786e6 + 3.41668e6i) q^{20} +(4.99491e7 + 8.65143e7i) q^{22} +(1.23695e8 - 7.14156e7i) q^{23} +(-1.16504e8 + 2.01791e8i) q^{25} +1.27491e8i q^{26} -3.78114e8 q^{28} +(-3.12082e8 - 1.80181e8i) q^{29} +(8.09827e8 + 1.40266e9i) q^{31} +(1.64382e8 - 9.49063e7i) q^{32} +(-2.98782e8 + 5.17506e8i) q^{34} +6.16023e8i q^{35} +2.44691e9 q^{37} +(-2.98154e9 - 1.72139e9i) q^{38} +(-1.54621e8 - 2.67812e8i) q^{40} +(-3.31048e9 + 1.91130e9i) q^{41} +(-2.67503e9 + 4.63329e9i) q^{43} -4.52087e9i q^{44} -6.46380e9 q^{46} +(1.42950e10 + 8.25324e9i) q^{47} +(-1.01227e10 - 1.75331e10i) q^{49} +(9.13200e9 - 5.27236e9i) q^{50} +(2.88478e9 - 4.99659e9i) q^{52} -6.02729e9i q^{53} -7.36541e9 q^{55} +(1.48190e10 + 8.55574e9i) q^{56} +(8.15404e9 + 1.41232e10i) q^{58} +(-4.04063e10 + 2.33286e10i) q^{59} +(-1.65613e10 + 2.86850e10i) q^{61} -7.32972e10i q^{62} -8.58993e9 q^{64} +(-8.14044e9 - 4.69989e9i) q^{65} +(-1.39454e10 - 2.41541e10i) q^{67} +(2.34196e10 - 1.35213e10i) q^{68} +(1.39390e10 - 2.41431e10i) q^{70} +1.64440e11i q^{71} +2.51213e10 q^{73} +(-9.58988e10 - 5.53672e10i) q^{74} +(7.79013e10 + 1.34929e11i) q^{76} +(3.52952e11 - 2.03777e11i) q^{77} +(-9.88871e10 + 1.71277e11i) q^{79} +1.39947e10i q^{80} +1.72992e11 q^{82} +(2.97872e11 + 1.71976e11i) q^{83} +(-2.20290e10 - 3.81553e10i) q^{85} +(2.09679e11 - 1.21058e11i) q^{86} +(-1.02296e11 + 1.77181e11i) q^{88} -4.71252e11i q^{89} +5.20123e11 q^{91} +(2.53328e11 + 1.46259e11i) q^{92} +(-3.73499e11 - 6.46920e11i) q^{94} +(2.19826e11 - 1.26917e11i) q^{95} +(2.59322e11 - 4.49158e11i) q^{97} +9.16204e11i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24576 q^{4} + 220224 q^{7} + 758016 q^{10} + 2372808 q^{13} - 50331648 q^{16} + 285339360 q^{19} - 70253568 q^{22} + 727623852 q^{25} + 902037504 q^{28} - 577374720 q^{31} - 2238076800 q^{34} - 6056330712 q^{37}+ \cdots + 2570481096384 q^{97}+O(q^{100}) $ 24 * q + 24576 * q^4 + 220224 * q^7 + 758016 * q^10 + 2372808 * q^13 - 50331648 * q^16 + 285339360 * q^19 - 70253568 * q^22 + 727623852 * q^25 + 902037504 * q^28 - 577374720 * q^31 - 2238076800 * q^34 - 6056330712 * q^37 + 776208384 * q^40 - 33702957168 * q^43 - 49846440960 * q^46 - 72166762836 * q^49 - 4859510784 * q^52 - 316402444512 * q^55 + 21247000704 * q^58 - 213044029980 * q^61 - 206158430208 * q^64 - 70227468528 * q^67 + 251325402624 * q^70 + 99306462720 * q^73 + 292187504640 * q^76 + 696725200560 * q^79 + 1471123266048 * q^82 + 271807264548 * q^85 + 143879307264 * q^88 + 1458470433408 * q^91 - 1211537346048 * q^94 + 2570481096384 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−39.1918	−	22.6274i	−0.612372	−	0.353553i
$2$	−39.1918	−	22.6274i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	1024.00	+	1773.62i	0.250000	+	0.433013i
$5$	2889.58	−	1668.30i	0.184933	−	0.106771i	−0.404675	−	0.914460i	$-0.632615\pi$
$5$	2889.58	−	1668.30i	0.184933	−	0.106771i	0.589608	+	0.807689i	$0.299282\pi$
$6$		0			0
$7$	−92313.0	+	159891.i	−0.784647	+	1.35905i	0.144563	+	0.989496i	$0.453823\pi$
$7$	−92313.0	+	159891.i	−0.784647	+	1.35905i	−0.929210	+	0.369553i	$0.879511\pi$
$8$		−	92681.9i		−	0.353553i
$9$		0			0
$10$	−150997.			−0.150997
$11$	−1.91171e6	−	1.10373e6i	−1.07911	−	0.623026i	−0.148456	−	0.988919i	$-0.547430\pi$
$11$	−1.91171e6	−	1.10373e6i	−1.07911	−	0.623026i	−0.930657	+	0.365893i	$0.880764\pi$
$12$		0			0
$13$	−1.40859e6	−	2.43974e6i	−0.291825	−	0.505456i	0.682416	−	0.730964i	$-0.260929\pi$
$13$	−1.40859e6	−	2.43974e6i	−0.291825	−	0.505456i	−0.974241	+	0.225508i	$0.927596\pi$
$14$	7.23583e6	−	4.17761e6i	0.960993	−	0.554829i
$15$		0			0
$16$	−2.09715e6	+	3.63237e6i	−0.125000	+	0.216506i
$17$		−	1.32044e7i		−	0.547049i	−0.961865	−	0.273524i	$-0.911811\pi$
$17$		−	1.32044e7i		−	0.547049i	0.961865	−	0.273524i	$-0.0881894\pi$
$18$		0			0
$19$	7.60755e7			1.61705			0.808524	−	0.588463i	$-0.200267\pi$
$19$	7.60755e7			1.61705			0.808524	+	0.588463i	$0.200267\pi$
$20$	5.91786e6	+	3.41668e6i	0.0924666	+	0.0533856i
$21$		0			0
$22$	4.99491e7	+	8.65143e7i	0.440546	+	0.763048i
$23$	1.23695e8	−	7.14156e7i	0.835577	−	0.482421i	−0.0201814	−	0.999796i	$-0.506424\pi$
$23$	1.23695e8	−	7.14156e7i	0.835577	−	0.482421i	0.855758	+	0.517376i	$0.173091\pi$
$24$		0			0
$25$	−1.16504e8	+	2.01791e8i	−0.477200	+	0.826534i
$26$			1.27491e8i			0.412703i
$27$		0			0
$28$	−3.78114e8			−0.784647
$29$	−3.12082e8	−	1.80181e8i	−0.524663	−	0.302914i	0.214177	−	0.976795i	$-0.431293\pi$
$29$	−3.12082e8	−	1.80181e8i	−0.524663	−	0.302914i	−0.738840	+	0.673880i	$0.764626\pi$
$30$		0			0
$31$	8.09827e8	+	1.40266e9i	0.912477	+	1.58046i	0.810553	+	0.585665i	$0.199167\pi$
$31$	8.09827e8	+	1.40266e9i	0.912477	+	1.58046i	0.101924	+	0.994792i	$0.467500\pi$
$32$	1.64382e8	−	9.49063e7i	0.153093	−	0.0883883i
$33$		0			0
$34$	−2.98782e8	+	5.17506e8i	−0.193411	+	0.334998i
$35$			6.16023e8i			0.335111i
$36$		0			0
$37$	2.44691e9			0.953690			0.476845	−	0.878987i	$-0.341780\pi$
$37$	2.44691e9			0.953690			0.476845	+	0.878987i	$0.341780\pi$
$38$	−2.98154e9	−	1.72139e9i	−0.990236	−	0.571713i
$39$		0			0
$40$	−1.54621e8	−	2.67812e8i	−0.0377493	−	0.0653838i
$41$	−3.31048e9	+	1.91130e9i	−0.696927	+	0.402371i	−0.806202	−	0.591641i	$-0.798480\pi$
$41$	−3.31048e9	+	1.91130e9i	−0.696927	+	0.402371i	0.109275	+	0.994012i	$0.465147\pi$
$42$		0			0
$43$	−2.67503e9	+	4.63329e9i	−0.423173	+	0.732957i	−0.996248	−	0.0865458i	$-0.972417\pi$
$43$	−2.67503e9	+	4.63329e9i	−0.423173	+	0.732957i	0.573075	+	0.819503i	$0.305750\pi$
$44$		−	4.52087e9i		−	0.623026i
$45$		0			0
$46$	−6.46380e9			−0.682246
$47$	1.42950e10	+	8.25324e9i	1.32617	+	0.765663i	0.984705	−	0.174233i	$-0.0557445\pi$
$47$	1.42950e10	+	8.25324e9i	1.32617	+	0.765663i	0.341462	+	0.939895i	$0.389078\pi$
$48$		0			0
$49$	−1.01227e10	−	1.75331e10i	−0.731342	−	1.26672i
$50$	9.13200e9	−	5.27236e9i	0.584448	−	0.337431i
$51$		0			0
$52$	2.88478e9	−	4.99659e9i	0.145913	−	0.252728i
$53$		−	6.02729e9i		−	0.271936i	−0.990713	−	0.135968i	$-0.956586\pi$
$53$		−	6.02729e9i		−	0.271936i	0.990713	−	0.135968i	$-0.0434145\pi$
$54$		0			0
$55$	−7.36541e9			−0.266085
$56$	1.48190e10	+	8.55574e9i	0.480496	+	0.277415i
$57$		0			0
$58$	8.15404e9	+	1.41232e10i	0.214193	+	0.370993i
$59$	−4.04063e10	+	2.33286e10i	−0.957938	+	0.553066i	−0.895538	−	0.444985i	$-0.853209\pi$
$59$	−4.04063e10	+	2.33286e10i	−0.957938	+	0.553066i	−0.0624003	+	0.998051i	$0.519876\pi$
$60$		0			0
$61$	−1.65613e10	+	2.86850e10i	−0.321451	+	0.556769i	−0.980788	−	0.195079i	$-0.937504\pi$
$61$	−1.65613e10	+	2.86850e10i	−0.321451	+	0.556769i	0.659337	+	0.751848i	$0.270837\pi$
$62$		−	7.32972e10i		−	1.29044i
$63$		0			0
$64$	−8.58993e9			−0.125000
$65$	−8.14044e9	−	4.69989e9i	−0.107936	−	0.0623171i
$66$		0			0
$67$	−1.39454e10	−	2.41541e10i	−0.154163	−	0.267019i	0.778591	−	0.627532i	$-0.215935\pi$
$67$	−1.39454e10	−	2.41541e10i	−0.154163	−	0.267019i	−0.932754	+	0.360513i	$0.882602\pi$
$68$	2.34196e10	−	1.35213e10i	0.236879	−	0.136762i
$69$		0			0
$70$	1.39390e10	−	2.41431e10i	0.118480	−	0.205213i
$71$			1.64440e11i			1.28368i	0.766838	+	0.641841i	$0.221829\pi$
$71$			1.64440e11i			1.28368i	−0.766838	+	0.641841i	$0.778171\pi$
$72$		0			0
$73$	2.51213e10			0.165999			0.0829995	−	0.996550i	$-0.473550\pi$
$73$	2.51213e10			0.165999			0.0829995	+	0.996550i	$0.473550\pi$
$74$	−9.58988e10	−	5.53672e10i	−0.584013	−	0.337180i
$75$		0			0
$76$	7.79013e10	+	1.34929e11i	0.404262	+	0.700203i
$77$	3.52952e11	−	2.03777e11i	1.69345	−	0.977712i
$78$		0			0
$79$	−9.88871e10	+	1.71277e11i	−0.406796	+	0.704592i	−0.994529	−	0.104463i	$-0.966687\pi$
$79$	−9.88871e10	+	1.71277e11i	−0.406796	+	0.704592i	0.587732	+	0.809055i	$0.300021\pi$
$80$			1.39947e10i			0.0533856i
$81$		0			0
$82$	1.72992e11			0.569039
$83$	2.97872e11	+	1.71976e11i	0.911089	+	0.526017i	0.880781	−	0.473523i	$-0.157018\pi$
$83$	2.97872e11	+	1.71976e11i	0.911089	+	0.526017i	0.0303075	+	0.999541i	$0.490351\pi$
$84$		0			0
$85$	−2.20290e10	−	3.81553e10i	−0.0584091	−	0.101167i
$86$	2.09679e11	−	1.21058e11i	0.518279	−	0.299229i
$87$		0			0
$88$	−1.02296e11	+	1.77181e11i	−0.220273	+	0.381524i
$89$		−	4.71252e11i		−	0.948229i	−0.880463	−	0.474115i	$-0.842768\pi$
$89$		−	4.71252e11i		−	0.948229i	0.880463	−	0.474115i	$-0.157232\pi$
$90$		0			0
$91$	5.20123e11			0.915920
$92$	2.53328e11	+	1.46259e11i	0.417788	+	0.241210i
$93$		0			0
$94$	−3.73499e11	−	6.46920e11i	−0.541405	−	0.937742i
$95$	2.19826e11	−	1.26917e11i	0.299046	−	0.172654i
$96$		0			0
$97$	2.59322e11	−	4.49158e11i	0.311321	−	0.539224i	−0.667328	−	0.744764i	$-0.732562\pi$
$97$	2.59322e11	−	4.49158e11i	0.311321	−	0.539224i	0.978649	+	0.205541i	$0.0658953\pi$
$98$			9.16204e11i			1.03427i
$99$		0			0
$100$	−4.77200e11			−0.477200
$101$	−6.21489e11	−	3.58817e11i	−0.585471	−	0.338022i	0.177834	−	0.984061i	$-0.443091\pi$
$101$	−6.21489e11	−	3.58817e11i	−0.585471	−	0.338022i	−0.763304	+	0.646039i	$0.776424\pi$
$102$		0			0
$103$	−9.38604e11	−	1.62571e12i	−0.786066	−	1.36151i	−0.928360	−	0.371682i	$-0.878781\pi$
$103$	−9.38604e11	−	1.62571e12i	−0.786066	−	1.36151i	0.142294	−	0.989825i	$-0.454552\pi$
$104$	−2.26120e11	+	1.30550e11i	−0.178706	+	0.103176i
$105$		0			0
$106$	−1.36382e11	+	2.36221e11i	−0.0961440	+	0.166526i
$107$		−	1.81018e12i		−	1.20620i	−0.797666	−	0.603099i	$-0.793932\pi$
$107$		−	1.81018e12i		−	1.20620i	0.797666	−	0.603099i	$-0.206068\pi$
$108$		0			0
$109$	−9.59875e11			−0.572342			−0.286171	−	0.958179i	$-0.592383\pi$
$109$	−9.59875e11			−0.572342			−0.286171	+	0.958179i	$0.592383\pi$
$110$	2.88664e11	+	1.66660e11i	0.162943	+	0.0940753i
$111$		0			0
$112$	−3.87189e11	−	6.70630e11i	−0.196162	−	0.339762i
$113$	2.02470e12	−	1.16896e12i	0.972499	−	0.561473i	0.0725021	−	0.997368i	$-0.476902\pi$
$113$	2.02470e12	−	1.16896e12i	0.972499	−	0.561473i	0.899997	+	0.435896i	$0.143568\pi$
$114$		0			0
$115$	2.38285e11	−	4.12722e11i	0.103017	−	0.178431i
$116$		−	7.38020e11i		−	0.302914i
$117$		0			0
$118$	2.11146e12			0.782153
$119$	2.11127e12	+	1.21894e12i	0.743466	+	0.429240i
$120$		0			0
$121$	8.67221e11	+	1.50207e12i	0.276323	+	0.478606i
$122$	1.29813e12	−	7.49477e11i	0.393695	−	0.227300i
$123$		0			0
$124$	−1.65853e12	+	2.87265e12i	−0.456239	+	0.790229i
$125$			1.59205e12i			0.417347i
$126$		0			0
$127$	−3.00898e12			−0.717129			−0.358565	−	0.933505i	$-0.616734\pi$
$127$	−3.00898e12			−0.717129			−0.358565	+	0.933505i	$0.616734\pi$
$128$	3.36655e11	+	1.94368e11i	0.0765466	+	0.0441942i
$129$		0			0
$130$	2.12693e11	+	3.68394e11i	0.0440648	+	0.0763226i
$131$	7.01478e12	−	4.04999e12i	1.38799	−	0.801356i	0.394901	−	0.918724i	$-0.370779\pi$
$131$	7.01478e12	−	4.04999e12i	1.38799	−	0.801356i	0.993089	+	0.117367i	$0.0374455\pi$
$132$		0			0
$133$	−7.02275e12	+	1.21638e13i	−1.26881	+	2.19765i
$134$			1.26219e12i			0.218020i
$135$		0			0
$136$	−1.22381e12			−0.193411
$137$	−6.50098e12	−	3.75334e12i	−0.983231	−	0.567669i	−0.0799872	−	0.996796i	$-0.525488\pi$
$137$	−6.50098e12	−	3.75334e12i	−0.983231	−	0.567669i	−0.903244	+	0.429127i	$0.858821\pi$
$138$		0			0
$139$	−2.29616e12	−	3.97706e12i	−0.318356	−	0.551408i	0.661789	−	0.749690i	$-0.269797\pi$
$139$	−2.29616e12	−	3.97706e12i	−0.318356	−	0.551408i	−0.980145	+	0.198282i	$0.936464\pi$
$140$	−1.09259e12	+	6.30808e11i	−0.145107	+	0.0837777i
$141$		0			0
$142$	3.72085e12	−	6.44471e12i	0.453850	−	0.786091i
$143$			6.21879e12i			0.727259i
$144$		0			0
$145$	−1.20238e12			−0.129370
$146$	−9.84551e11	−	5.68431e11i	−0.101653	−	0.0586895i
$147$		0			0
$148$	2.50563e12	+	4.33988e12i	0.238422	+	0.412960i
$149$	−9.65857e12	+	5.57638e12i	−0.882664	+	0.509606i	−0.871536	−	0.490332i	$-0.836876\pi$
$149$	−9.65857e12	+	5.57638e12i	−0.882664	+	0.509606i	−0.0111279	+	0.999938i	$0.503542\pi$
$150$		0			0
$151$	7.99257e11	−	1.38435e12i	0.0674256	−	0.116785i	−0.830342	−	0.557254i	$-0.811855\pi$
$151$	7.99257e11	−	1.38435e12i	0.0674256	−	0.116785i	0.897767	+	0.440470i	$0.145188\pi$
$152$		−	7.05082e12i		−	0.571713i
$153$		0			0
$154$	−1.84438e13			−1.38269
$155$	4.68012e12	+	2.70207e12i	0.337495	+	0.194853i
$156$		0			0
$157$	−4.70133e12	−	8.14294e12i	−0.313923	−	0.543730i	0.665285	−	0.746589i	$-0.268310\pi$
$157$	−4.70133e12	−	8.14294e12i	−0.313923	−	0.543730i	−0.979208	+	0.202859i	$0.934977\pi$
$158$	7.75113e12	−	4.47512e12i	0.498222	−	0.287648i
$159$		0			0
$160$	3.16664e11	−	5.48479e11i	0.0188747	−	0.0326919i
$161$			2.63703e13i			1.51412i
$162$		0			0
$163$	−2.99231e13			−1.59544			−0.797722	−	0.603026i	$-0.793962\pi$
$163$	−2.99231e13			−1.59544			−0.797722	+	0.603026i	$0.793962\pi$
$164$	−6.77986e12	−	3.91435e12i	−0.348464	−	0.201186i
$165$		0			0
$166$	−7.78276e12	−	1.34801e13i	−0.371950	−	0.644237i
$167$	8.44299e10	−	4.87456e10i	0.00389222	−	0.00224717i	−0.498053	−	0.867147i	$-0.665951\pi$
$167$	8.44299e10	−	4.87456e10i	0.00389222	−	0.00224717i	0.501945	+	0.864900i	$0.332618\pi$
$168$		0			0
$169$	7.68082e12	−	1.33036e13i	0.329676	−	0.571015i
$170$			1.99383e12i			0.0826029i
$171$		0			0
$172$	−1.09569e13			−0.423173
$173$	−2.09435e13	−	1.20917e13i	−0.781219	−	0.451037i	0.0556432	−	0.998451i	$-0.482279\pi$
$173$	−2.09435e13	−	1.20917e13i	−0.781219	−	0.451037i	−0.836862	+	0.547414i	$0.815612\pi$
$174$		0			0
$175$	−2.15096e13	−	3.72558e13i	−0.748867	−	1.29708i
$176$	8.01831e12	−	4.62937e12i	0.269778	−	0.155757i
$177$		0			0
$178$	−1.06632e13	+	1.84692e13i	−0.335250	+	0.580670i
$179$		−	1.51765e13i		−	0.461374i	−0.973028	−	0.230687i	$-0.925903\pi$
$179$		−	1.51765e13i		−	0.461374i	0.973028	−	0.230687i	$-0.0740974\pi$
$180$		0			0
$181$	−3.27365e13			−0.931024			−0.465512	−	0.885041i	$-0.654130\pi$
$181$	−3.27365e13			−0.931024			−0.465512	+	0.885041i	$0.654130\pi$
$182$	−2.03846e13	−	1.17690e13i	−0.560884	−	0.323827i
$183$		0			0
$184$	−6.61893e12	−	1.14643e13i	−0.170561	−	0.295421i
$185$	7.07054e12	−	4.08218e12i	0.176369	−	0.101827i
$186$		0			0
$187$	−1.45741e13	+	2.52431e13i	−0.340826	+	0.590327i
$188$			3.38053e13i			0.765663i
$189$		0			0
$190$	−1.14872e13			−0.244170
$191$	−7.79605e13	−	4.50105e13i	−1.60574	−	0.927072i	−0.990309	−	0.138879i	$-0.955650\pi$
$191$	−7.79605e13	−	4.50105e13i	−1.60574	−	0.927072i	−0.615427	−	0.788194i	$-0.711016\pi$
$192$		0			0
$193$	3.50970e13	+	6.07898e13i	0.679088	+	1.17621i	0.975256	+	0.221079i	$0.0709578\pi$
$193$	3.50970e13	+	6.07898e13i	0.679088	+	1.17621i	−0.296168	+	0.955136i	$0.595709\pi$
$194$	−2.03266e13	+	1.17356e13i	−0.381289	+	0.220137i
$195$		0			0
$196$	2.07313e13	−	3.59077e13i	0.365671	−	0.633361i
$197$			1.05814e14i			1.81028i	0.425113	+	0.905140i	$0.360234\pi$
$197$			1.05814e14i			1.81028i	−0.425113	+	0.905140i	$0.639766\pi$
$198$		0			0
$199$	−7.56441e13			−1.21803			−0.609013	−	0.793160i	$-0.708434\pi$
$199$	−7.56441e13			−1.21803			−0.609013	+	0.793160i	$0.708434\pi$
$200$	1.87023e13	+	1.07978e13i	0.292224	+	0.168716i
$201$		0			0
$202$	1.62382e13	+	2.81254e13i	0.239017	+	0.413990i
$203$	5.76184e13	−	3.32660e13i	0.823351	−	0.475362i
$204$		0			0
$205$	−6.37726e12	+	1.10457e13i	−0.0859233	+	0.148824i
$206$			8.49528e13i			1.11167i
$207$		0			0
$208$	1.18161e13			0.145913
$209$	−1.45435e14	−	8.39667e13i	−1.74498	−	1.00746i
$210$		0			0
$211$	−5.76009e13	−	9.97676e13i	−0.652731	−	1.13056i	−0.982457	−	0.186487i	$-0.940290\pi$
$211$	−5.76009e13	−	9.97676e13i	−0.652731	−	1.13056i	0.329726	−	0.944077i	$-0.393044\pi$
$212$	1.06901e13	−	6.17195e12i	0.117752	−	0.0679840i
$213$		0			0
$214$	−4.09597e13	+	7.09442e13i	−0.426455	+	0.738643i
$215$			1.78510e13i			0.180731i
$216$		0			0
$217$	−2.99030e14			−2.86389
$218$	3.76193e13	+	2.17195e13i	0.350486	+	0.202353i
$219$		0			0
$220$	−7.54218e12	−	1.30634e13i	−0.0665213	−	0.115218i
$221$	−3.22154e13	+	1.85996e13i	−0.276509	+	0.159643i
$222$		0			0
$223$	−7.21303e13	+	1.24933e14i	−0.586528	+	1.01590i	0.408155	+	0.912913i	$0.366172\pi$
$223$	−7.21303e13	+	1.24933e14i	−0.586528	+	1.01590i	−0.994683	+	0.102984i	$0.967161\pi$
$224$			3.50443e13i			0.277415i
$225$		0			0
$226$	−1.05802e14			−0.794042
$227$	1.35494e14	+	7.82272e13i	0.990292	+	0.571746i	0.905362	−	0.424641i	$-0.139600\pi$
$227$	1.35494e14	+	7.82272e13i	0.990292	+	0.571746i	0.0849307	+	0.996387i	$0.472933\pi$
$228$		0			0
$229$	−8.40086e13	−	1.45507e14i	−0.582520	−	1.00895i	−0.995180	−	0.0980690i	$-0.968733\pi$
$229$	−8.40086e13	−	1.45507e14i	−0.582520	−	1.00895i	0.412660	−	0.910885i	$-0.364600\pi$
$230$	−1.86777e13	+	1.07836e13i	−0.126170	+	0.0728442i
$231$		0			0
$232$	−1.66995e13	+	2.89243e13i	−0.107096	+	0.185496i
$233$		−	1.95254e14i		−	1.22029i	−0.792288	−	0.610147i	$-0.791110\pi$
$233$		−	1.95254e14i		−	1.22029i	0.792288	−	0.610147i	$-0.208890\pi$
$234$		0			0
$235$	5.50756e13			0.327003
$236$	−8.27522e13	−	4.77770e13i	−0.478969	−	0.276533i
$237$		0			0
$238$	−5.51629e13	−	9.55449e13i	−0.303519	−	0.525710i
$239$	3.02644e14	−	1.74732e14i	1.62385	−	0.937528i	0.637968	−	0.770063i	$-0.279775\pi$
$239$	3.02644e14	−	1.74732e14i	1.62385	−	0.937528i	0.985878	−	0.167465i	$-0.0535581\pi$
$240$		0			0
$241$	4.22734e13	−	7.32196e13i	0.215757	−	0.373702i	−0.737750	−	0.675075i	$-0.764111\pi$
$241$	4.22734e13	−	7.32196e13i	0.215757	−	0.373702i	0.953506	+	0.301373i	$0.0974448\pi$
$242$		−	7.84919e13i		−	0.390780i
$243$		0			0
$244$	−6.78349e13			−0.321451
$245$	−5.85008e13	−	3.37755e13i	−0.270499	−	0.156173i
$246$		0			0
$247$	−1.07159e14	−	1.85604e14i	−0.471896	−	0.817348i
$248$	1.30001e14	−	7.50563e13i	0.558776	−	0.322609i
$249$		0			0
$250$	3.60241e13	−	6.23955e13i	0.147555	−	0.255572i
$251$			2.55320e14i			1.02104i	0.859866	+	0.510519i	$0.170547\pi$
$251$			2.55320e14i			1.02104i	−0.859866	+	0.510519i	$0.829453\pi$
$252$		0			0
$253$	−3.15294e14			−1.20224
$254$	1.17928e14	+	6.80855e13i	0.439150	+	0.253544i
$255$		0			0
$256$	−8.79609e12	−	1.52353e13i	−0.0312500	−	0.0541266i
$257$	−3.68477e14	+	2.12741e14i	−1.27883	+	0.738332i	−0.976633	−	0.214915i	$-0.931053\pi$
$257$	−3.68477e14	+	2.12741e14i	−1.27883	+	0.738332i	−0.302195	+	0.953246i	$0.597719\pi$
$258$		0			0
$259$	−2.25881e14	+	3.91238e14i	−0.748310	+	1.29611i
$260$		−	1.92507e13i		−	0.0623171i
$261$		0			0
$262$	−3.66563e14			−1.13329
$263$	−2.39578e14	−	1.38320e14i	−0.723955	−	0.417976i	0.0922514	−	0.995736i	$-0.470594\pi$
$263$	−2.39578e14	−	1.38320e14i	−0.723955	−	0.417976i	−0.816207	+	0.577760i	$0.803927\pi$
$264$		0			0
$265$	−1.00553e13	−	1.74164e13i	−0.0290350	−	0.0502900i
$266$	5.50469e14	−	3.17813e14i	1.55397	−	0.897186i
$267$		0			0
$268$	2.85601e13	−	4.94676e13i	0.0770817	−	0.133509i
$269$			4.10640e14i			1.08380i	0.840444	+	0.541898i	$0.182294\pi$
$269$			4.10640e14i			1.08380i	−0.840444	+	0.541898i	$0.817706\pi$
$270$		0			0
$271$	6.95801e14			1.75659			0.878293	−	0.478123i	$-0.158683\pi$
$271$	6.95801e14			1.75659			0.878293	+	0.478123i	$0.158683\pi$
$272$	4.79634e13	+	2.76917e13i	0.118440	+	0.0683811i
$273$		0			0
$274$	1.69857e14	+	2.94201e14i	0.401403	+	0.695250i
$275$	4.45444e14	−	2.57177e14i	1.02991	−	0.594616i
$276$		0			0
$277$	−2.19300e14	+	3.79840e14i	−0.485468	+	0.840856i	−0.999861	−	0.0166992i	$-0.994684\pi$
$277$	−2.19300e14	+	3.79840e14i	−0.485468	+	0.840856i	0.514392	+	0.857555i	$0.328018\pi$
$278$			2.07824e14i			0.450223i
$279$		0			0
$280$	5.70942e13			0.118480
$281$	−9.98393e13	−	5.76422e13i	−0.202798	−	0.117085i	0.395162	−	0.918611i	$-0.370688\pi$
$281$	−9.98393e13	−	5.76422e13i	−0.202798	−	0.117085i	−0.597960	+	0.801526i	$0.704022\pi$
$282$		0			0
$283$	−8.74311e13	−	1.51435e14i	−0.170195	−	0.294787i	0.768293	−	0.640099i	$-0.221107\pi$
$283$	−8.74311e13	−	1.51435e14i	−0.170195	−	0.294787i	−0.938488	+	0.345312i	$0.887773\pi$
$284$	−2.91654e14	+	1.68387e14i	−0.555851	+	0.320920i
$285$		0			0
$286$	1.40715e14	−	2.43726e14i	0.257125	−	0.445354i
$287$		−	7.05753e14i		−	1.26288i
$288$		0			0
$289$	4.08265e14			0.700738
$290$	4.71235e13	+	2.72068e13i	0.0792227	+	0.0457393i
$291$		0			0
$292$	2.57242e13	+	4.45557e13i	0.0414997	+	0.0718797i
$293$	4.88527e14	−	2.82051e14i	0.772117	−	0.445782i	−0.0615123	−	0.998106i	$-0.519592\pi$
$293$	4.88527e14	−	2.82051e14i	0.772117	−	0.445782i	0.833629	+	0.552324i	$0.186259\pi$
$294$		0			0
$295$	−7.78383e13	+	1.34820e14i	−0.118103	+	0.204560i
$296$		−	2.26784e14i		−	0.337180i
$297$		0			0
$298$	5.04716e14			0.720692
$299$	−3.48471e14	−	2.01190e14i	−0.487685	−	0.281565i
$300$		0			0
$301$	−4.93880e14	−	8.55425e14i	−0.664083	−	1.15023i
$302$	−6.26487e13	+	3.61702e13i	−0.0825792	+	0.0476771i
$303$		0			0
$304$	−1.59542e14	+	2.76335e14i	−0.202131	+	0.350101i
$305$			1.10517e14i			0.137287i
$306$		0			0
$307$	−5.14957e14			−0.615093			−0.307546	−	0.951533i	$-0.599508\pi$
$307$	−5.14957e14			−0.615093			−0.307546	+	0.951533i	$0.599508\pi$
$308$	7.22846e14	+	4.17335e14i	0.846723	+	0.488856i
$309$		0			0
$310$	−1.22282e14	−	2.11798e14i	−0.137782	−	0.238645i
$311$	2.15069e14	−	1.24170e14i	0.237692	−	0.137232i	−0.376423	−	0.926448i	$-0.622846\pi$
$311$	2.15069e14	−	1.24170e14i	0.237692	−	0.137232i	0.614116	+	0.789216i	$0.289513\pi$
$312$		0			0
$313$	4.00338e14	−	6.93405e14i	0.425756	−	0.737430i	−0.570735	−	0.821134i	$-0.693342\pi$
$313$	4.00338e14	−	6.93405e14i	0.425756	−	0.737430i	0.996491	+	0.0837040i	$0.0266750\pi$
$314$			4.25516e14i			0.443954i
$315$		0			0
$316$	−4.05041e14			−0.406796
$317$	2.02358e14	+	1.16831e14i	0.199418	+	0.115134i	0.596384	−	0.802699i	$-0.296604\pi$
$317$	2.02358e14	+	1.16831e14i	0.199418	+	0.115134i	−0.396966	+	0.917833i	$0.629937\pi$
$318$		0			0
$319$	3.97741e14	+	6.88908e14i	0.377447	+	0.653758i
$320$	−2.48213e13	+	1.43306e13i	−0.0231167	+	0.0133464i
$321$		0			0
$322$	5.96692e14	−	1.03350e15i	0.535322	−	0.927205i
$323$		−	1.00453e15i		−	0.884604i
$324$		0			0
$325$	6.56422e14			0.557036
$326$	1.17274e15	+	6.77083e14i	0.977006	+	0.564075i
$327$		0			0
$328$	1.77143e14	+	3.06821e14i	0.142260	+	0.246401i
$329$	−2.63923e15	+	1.52376e15i	−2.08115	+	1.20155i
$330$		0			0
$331$	7.06479e14	−	1.22366e15i	0.537194	−	0.930448i	−0.461860	−	0.886953i	$-0.652818\pi$
$331$	7.06479e14	−	1.22366e15i	0.537194	−	0.930448i	0.999054	−	0.0434945i	$-0.0138491\pi$
$332$			7.04415e14i			0.526017i
$333$		0			0
$334$	−4.41195e12			−0.00317798
$335$	−8.05926e13	−	4.65301e13i	−0.0570199	−	0.0329204i
$336$		0			0
$337$	8.01102e14	+	1.38755e15i	0.546901	+	0.947260i	0.998485	+	0.0550311i	$0.0175258\pi$
$337$	8.01102e14	+	1.38755e15i	0.546901	+	0.947260i	−0.451584	+	0.892229i	$0.649141\pi$
$338$	−6.02051e14	+	3.47594e14i	−0.403769	+	0.233116i
$339$		0			0
$340$	4.51153e13	−	7.81420e13i	0.0292045	−	0.0505837i
$341$		−	3.57532e15i		−	2.27399i
$342$		0			0
$343$	1.18237e15			0.726088
$344$	4.29422e14	+	2.47927e14i	0.259140	+	0.149614i
$345$		0			0
$346$	5.47210e14	+	9.47795e14i	0.318931	+	0.552405i
$347$	−2.11489e15	+	1.22103e15i	−1.21147	+	0.699441i	−0.963079	−	0.269220i	$-0.913234\pi$
$347$	−2.11489e15	+	1.22103e15i	−1.21147	+	0.699441i	−0.248388	+	0.968661i	$0.579901\pi$
$348$		0			0
$349$	−7.30058e14	+	1.26450e15i	−0.404022	+	0.699787i	−0.994207	−	0.107481i	$-0.965721\pi$
$349$	−7.30058e14	+	1.26450e15i	−0.404022	+	0.699787i	0.590185	+	0.807268i	$0.299055\pi$
$350$			1.94683e15i			1.05906i
$351$		0			0
$352$	−4.19003e14			−0.220273
$353$	−2.39612e15	−	1.38340e15i	−1.23840	−	0.714990i	−0.269633	−	0.962963i	$-0.586902\pi$
$353$	−2.39612e15	−	1.38340e15i	−1.23840	−	0.714990i	−0.968767	+	0.247973i	$0.920236\pi$
$354$		0			0
$355$	2.74335e14	+	4.75163e14i	0.137060	+	0.237395i
$356$	8.35822e14	−	4.82562e14i	0.410595	−	0.237057i
$357$		0			0
$358$	−3.43405e14	+	5.94795e14i	−0.163121	+	0.282533i
$359$			4.80862e13i			0.0224623i	0.999937	+	0.0112311i	$0.00357505\pi$
$359$			4.80862e13i			0.0224623i	−0.999937	+	0.0112311i	$0.996425\pi$
$360$		0			0
$361$	3.57416e15			1.61485
$362$	1.28300e15	+	7.40743e14i	0.570134	+	0.329167i
$363$		0			0
$364$	5.32606e14	+	9.22500e14i	0.228980	+	0.396605i
$365$	7.25901e13	−	4.19099e13i	0.0306987	−	0.0177239i
$366$		0			0
$367$	−2.95086e14	+	5.11104e14i	−0.120768	+	0.209176i	−0.920071	−	0.391752i	$-0.871869\pi$
$367$	−2.95086e14	+	5.11104e14i	−0.120768	+	0.209176i	0.799303	+	0.600929i	$0.205202\pi$
$368$			5.99077e14i			0.241210i
$369$		0			0
$370$	−3.69476e14			−0.144005
$371$	9.63708e14	+	5.56397e14i	0.369575	+	0.213374i
$372$		0			0
$373$	1.72365e15	+	2.98545e15i	0.640024	+	1.10855i	0.985427	+	0.170100i	$0.0544090\pi$
$373$	1.72365e15	+	2.98545e15i	0.640024	+	1.10855i	−0.345403	+	0.938455i	$0.612258\pi$
$374$	1.14237e15	−	6.59549e14i	0.417424	−	0.241000i
$375$		0			0
$376$	7.64926e14	−	1.32489e15i	0.270703	−	0.468871i
$377$			1.01520e15i			0.353592i
$378$		0			0
$379$	3.82658e15			1.29115			0.645573	−	0.763699i	$-0.276619\pi$
$379$	3.82658e15			1.29115			0.645573	+	0.763699i	$0.276619\pi$
$380$	4.50204e14	+	2.59926e14i	0.149523	+	0.0863272i
$381$		0			0
$382$	2.03694e15	+	3.52809e15i	0.655539	+	1.13543i
$383$	−4.48792e15	+	2.59110e15i	−1.42185	+	0.820904i	−0.996457	−	0.0841065i	$-0.973196\pi$
$383$	−4.48792e15	+	2.59110e15i	−1.42185	+	0.820904i	−0.425390	+	0.905010i	$0.639863\pi$
$384$		0			0
$385$	6.79922e14	−	1.17766e15i	0.208783	−	0.361623i
$386$		−	3.17662e15i		−	0.960375i
$387$		0			0
$388$	1.06218e15			0.311321
$389$	3.54008e14	+	2.04386e14i	0.102168	+	0.0589868i	0.550213	−	0.835024i	$-0.314546\pi$
$389$	3.54008e14	+	2.04386e14i	0.102168	+	0.0589868i	−0.448045	+	0.894011i	$0.647880\pi$
$390$		0			0
$391$	−9.43001e14	−	1.63333e15i	−0.263908	−	0.457101i
$392$	−1.62500e15	+	9.38193e14i	−0.447854	+	0.258569i
$393$		0			0
$394$	2.39430e15	−	4.14705e15i	0.640031	−	1.10857i
$395$			6.59894e14i			0.173737i
$396$		0			0
$397$	3.85065e15			0.983538			0.491769	−	0.870726i	$-0.336350\pi$
$397$	3.85065e15			0.983538			0.491769	+	0.870726i	$0.336350\pi$
$398$	2.96463e15	+	1.71163e15i	0.745885	+	0.430637i
$399$		0			0
$400$	−4.88653e14	−	8.46371e14i	−0.119300	−	0.206634i
$401$	−8.64960e14	+	4.99385e14i	−0.208032	+	0.120107i	−0.600396	−	0.799703i	$-0.704991\pi$
$401$	−8.64960e14	+	4.99385e14i	−0.208032	+	0.120107i	0.392365	+	0.919810i	$0.371657\pi$
$402$		0			0
$403$	2.28142e15	−	3.95154e15i	0.532568	−	0.922435i
$404$		−	1.46971e15i		−	0.338022i
$405$		0			0
$406$	−3.01089e15			−0.672263
$407$	−4.67779e15	−	2.70072e15i	−1.02914	−	0.594174i
$408$		0			0
$409$	−2.34043e15	−	4.05375e15i	−0.499984	−	0.865998i	0.500016	−	0.866016i	$-0.333328\pi$
$409$	−2.34043e15	−	4.05375e15i	−0.499984	−	0.865998i	−1.00000		1.80625e-5i	$0.999994\pi$
$410$	4.99873e14	−	2.88602e14i	0.105234	−	0.0607570i
$411$		0			0
$412$	1.92226e15	−	3.32946e15i	0.393033	−	0.680753i
$413$		−	8.61413e15i		−	1.73585i
$414$		0			0
$415$	1.14763e15			0.224654
$416$	−4.63093e14	−	2.67367e14i	−0.0893529	−	0.0515879i
$417$		0			0
$418$	3.79990e15	+	6.58162e15i	0.712384	+	1.23389i
$419$	−8.45507e15	+	4.88154e15i	−1.56255	+	0.902137i	−0.565549	+	0.824715i	$0.691336\pi$
$419$	−8.45507e15	+	4.88154e15i	−1.56255	+	0.902137i	−0.996998	+	0.0774225i	$0.975331\pi$
$420$		0			0
$421$	−4.23445e15	+	7.33428e15i	−0.760509	+	1.31724i	0.182080	+	0.983284i	$0.441717\pi$
$421$	−4.23445e15	+	7.33428e15i	−0.760509	+	1.31724i	−0.942589	+	0.333956i	$0.891616\pi$
$422$			5.21344e15i			0.923101i
$423$		0			0
$424$	−5.58621e14			−0.0961440
$425$	2.66453e15	+	1.53837e15i	0.452154	+	0.261052i
$426$		0			0
$427$	−3.05764e15	−	5.29598e15i	−0.504451	−	0.873735i
$428$	3.21057e15	−	1.85362e15i	0.522299	−	0.301550i
$429$		0			0
$430$	4.03923e14	−	6.99614e14i	0.0638980	−	0.110675i
$431$		−	3.87111e15i		−	0.603910i	−0.953322	−	0.301955i	$-0.902361\pi$
$431$		−	3.87111e15i		−	0.603910i	0.953322	−	0.301955i	$-0.0976392\pi$
$432$		0			0
$433$	3.92711e15			0.595862			0.297931	−	0.954587i	$-0.403704\pi$
$433$	3.92711e15			0.595862			0.297931	+	0.954587i	$0.403704\pi$
$434$	1.17195e16	+	6.76628e15i	1.75377	+	1.01254i
$435$		0			0
$436$	−9.82912e14	−	1.70245e15i	−0.143086	−	0.247831i
$437$	9.41018e15	−	5.43297e15i	1.35117	−	0.780098i
$438$		0			0
$439$	1.92127e15	−	3.32773e15i	0.268411	−	0.464902i	−0.700040	−	0.714103i	$-0.746835\pi$
$439$	1.92127e15	−	3.32773e15i	0.268411	−	0.464902i	0.968452	+	0.249201i	$0.0801680\pi$
$440$			6.82640e14i			0.0940753i
$441$		0			0
$442$	1.68344e15			0.225769
$443$	−8.49242e15	−	4.90310e15i	−1.12359	−	0.648707i	−0.181277	−	0.983432i	$-0.558023\pi$
$443$	−8.49242e15	−	4.90310e15i	−1.12359	−	0.648707i	−0.942316	+	0.334725i	$0.891356\pi$
$444$		0			0
$445$	−7.86190e14	−	1.36172e15i	−0.101244	−	0.175359i
$446$	5.65384e15	−	3.26425e15i	0.718347	−	0.414738i
$447$		0			0
$448$	7.92962e14	−	1.37345e15i	0.0980809	−	0.169881i
$449$			2.99959e15i			0.366087i	0.983105	+	0.183043i	$0.0585949\pi$
$449$			2.99959e15i			0.366087i	−0.983105	+	0.183043i	$0.941405\pi$
$450$		0			0
$451$	8.43825e15			1.00275
$452$	4.14658e15	+	2.39403e15i	0.486250	+	0.280736i
$453$		0			0
$454$	−3.54016e15	−	6.13174e15i	−0.404285	−	0.700242i
$455$	1.50294e15	−	8.67721e14i	0.169384	−	0.0977939i
$456$		0			0
$457$	−2.28935e15	+	3.96527e15i	−0.251313	+	0.435287i	−0.963888	−	0.266309i	$-0.914196\pi$
$457$	−2.28935e15	+	3.96527e15i	−0.251313	+	0.435287i	0.712575	+	0.701596i	$0.247529\pi$
$458$			7.60359e15i			0.823808i
$459$		0			0
$460$	9.76016e14			0.103017
$461$	5.14296e15	+	2.96929e15i	0.535806	+	0.309348i	0.743378	−	0.668872i	$-0.233223\pi$
$461$	5.14296e15	+	2.96929e15i	0.535806	+	0.309348i	−0.207571	+	0.978220i	$0.566556\pi$
$462$		0			0
$463$	8.85971e15	+	1.53455e16i	0.899360	+	1.55774i	0.828314	+	0.560264i	$0.189300\pi$
$463$	8.85971e15	+	1.53455e16i	0.899360	+	1.55774i	0.0710452	+	0.997473i	$0.477367\pi$
$464$	1.30897e15	−	7.55732e14i	0.131166	−	0.0757286i
$465$		0			0
$466$	−4.41810e15	+	7.65237e15i	−0.431439	+	0.747275i
$467$		−	9.97819e15i		−	0.961945i	−0.876736	−	0.480973i	$-0.840284\pi$
$467$		−	9.97819e15i		−	0.961945i	0.876736	−	0.480973i	$-0.159716\pi$
$468$		0			0
$469$	5.14935e15			0.483856
$470$	−2.15851e15	−	1.24622e15i	−0.200248	−	0.115613i
$471$		0			0
$472$	2.16214e15	+	3.74494e15i	0.195538	+	0.338682i
$473$	1.02278e16	−	5.90502e15i	0.913303	−	0.527296i
$474$		0			0
$475$	−8.86309e15	+	1.53513e16i	−0.771655	+	1.33655i
$476$			4.99278e15i			0.429240i
$477$		0			0
$478$	−1.58149e16			−1.32586
$479$	−4.43460e15	−	2.56032e15i	−0.367148	−	0.211973i	0.305063	−	0.952332i	$-0.401322\pi$
$479$	−4.43460e15	−	2.56032e15i	−0.367148	−	0.211973i	−0.672212	+	0.740359i	$0.734656\pi$
$480$		0			0
$481$	−3.44668e15	−	5.96982e15i	−0.278311	−	0.482049i
$482$	−3.31354e15	+	1.91307e15i	−0.264247	+	0.152563i
$483$		0			0
$484$	−1.77607e15	+	3.07624e15i	−0.138162	+	0.239303i
$485$		−	1.73051e15i		−	0.132960i
$486$		0			0
$487$	−2.02291e16			−1.51636			−0.758182	−	0.652043i	$-0.773912\pi$
$487$	−2.02291e16			−1.51636			−0.758182	+	0.652043i	$0.773912\pi$
$488$	2.65858e15	+	1.53493e15i	0.196848	+	0.113650i
$489$		0			0
$490$	1.52850e15	+	2.64745e15i	0.110431	+	0.191272i
$491$	4.67595e15	−	2.69966e15i	0.333719	−	0.192673i	−0.323772	−	0.946135i	$-0.604951\pi$
$491$	4.67595e15	−	2.69966e15i	0.333719	−	0.192673i	0.657491	+	0.753462i	$0.271618\pi$
$492$		0			0
$493$	−2.37918e15	+	4.12086e15i	−0.165709	+	0.287016i
$494$			9.69891e15i			0.667361i
$495$		0			0
$496$	−6.79332e15			−0.456239
$497$	−2.62924e16	−	1.51799e16i	−1.74459	−	1.00724i
$498$		0			0
$499$	−9.51227e15	−	1.64757e16i	−0.616142	−	1.06719i	−0.990183	−	0.139777i	$-0.955361\pi$
$499$	−9.51227e15	−	1.64757e16i	−0.616142	−	1.06719i	0.374041	−	0.927412i	$-0.377972\pi$
$500$	−2.82370e15	+	1.63026e15i	−0.180717	+	0.104337i
$501$		0			0
$502$	5.77723e15	−	1.00064e16i	0.360992	−	0.625256i
$503$		−	6.76009e15i		−	0.417393i	−0.977980	−	0.208696i	$-0.933078\pi$
$503$		−	6.76009e15i		−	0.417393i	0.977980	−	0.208696i	$-0.0669220\pi$
$504$		0			0
$505$	−2.39446e15			−0.144364
$506$	1.23569e16	+	7.13428e15i	0.736220	+	0.425057i
$507$		0			0
$508$	−3.08120e15	−	5.33679e15i	−0.179282	−	0.310526i
$509$	−1.82512e16	+	1.05373e16i	−1.04950	+	0.605931i	−0.922510	−	0.385973i	$-0.873866\pi$
$509$	−1.82512e16	+	1.05373e16i	−1.04950	+	0.605931i	−0.126993	+	0.991904i	$0.540533\pi$
$510$		0			0
$511$	−2.31902e15	+	4.01667e15i	−0.130251	+	0.225601i
$512$			7.96131e14i			0.0441942i
$513$		0			0
$514$	1.92551e16			1.04416
$515$	−5.42435e15	−	3.13175e15i	−0.290740	−	0.167859i
$516$		0			0
$517$	−1.82187e16	−	3.15557e16i	−0.954056	−	1.65247i
$518$	1.77054e16	−	1.02222e16i	0.916489	−	0.529135i
$519$		0			0
$520$	−4.35594e14	+	7.54472e14i	−0.0220324	+	0.0381613i
$521$		−	1.40350e16i		−	0.701754i	−0.936422	−	0.350877i	$-0.885884\pi$
$521$		−	1.40350e16i		−	0.701754i	0.936422	−	0.350877i	$-0.114116\pi$
$522$		0			0
$523$	−2.07647e16			−1.01465			−0.507324	−	0.861756i	$-0.669365\pi$
$523$	−2.07647e16			−1.01465			−0.507324	+	0.861756i	$0.669365\pi$
$524$	1.43663e16	+	8.29437e15i	0.693995	+	0.400678i
$525$		0			0
$526$	6.25966e15	+	1.08420e16i	0.295554	+	0.511914i
$527$	1.85213e16	−	1.06933e16i	0.864587	−	0.499170i
$528$		0			0
$529$	−7.56949e14	+	1.31107e15i	−0.0345408	+	0.0598265i
$530$			9.10105e14i			0.0410616i
$531$		0			0
$532$	−2.87652e16			−1.26881
$533$	9.32618e15	+	5.38447e15i	0.406762	+	0.234844i
$534$		0			0
$535$	−3.01992e15	−	5.23066e15i	−0.128787	−	0.223066i
$536$	−2.23865e15	+	1.29248e15i	−0.0944054	+	0.0545050i
$537$		0			0
$538$	9.29172e15	−	1.60937e16i	0.383180	−	0.663687i
$539$			4.46910e16i			1.82258i
$540$		0			0
$541$	−3.78898e16			−1.51126			−0.755629	−	0.655000i	$-0.772669\pi$
$541$	−3.78898e16			−1.51126			−0.755629	+	0.655000i	$0.772669\pi$
$542$	−2.72697e16	−	1.57442e16i	−1.07568	−	0.621047i
$543$		0			0
$544$	−1.25318e15	−	2.17058e15i	−0.0483527	−	0.0837494i
$545$	−2.77364e15	+	1.60136e15i	−0.105845	+	0.0611097i
$546$		0			0
$547$	−1.02049e16	+	1.76754e16i	−0.380965	+	0.659850i	−0.991200	−	0.132370i	$-0.957741\pi$
$547$	−1.02049e16	+	1.76754e16i	−0.380965	+	0.659850i	0.610236	+	0.792220i	$0.291075\pi$
$548$		−	1.53737e16i		−	0.567669i
$549$		0			0
$550$	−2.32770e16			−0.840914
$551$	−2.37418e16	−	1.37073e16i	−0.848406	−	0.489827i
$552$		0			0
$553$	−1.82571e16	−	3.16223e16i	−0.638383	−	1.10571i
$554$	1.71896e16	−	9.92441e15i	0.594575	−	0.343278i
$555$		0			0
$556$	4.70253e15	−	8.14502e15i	0.159178	−	0.275704i
$557$			4.87428e16i			1.63222i	0.577894	+	0.816112i	$0.303875\pi$
$557$			4.87428e16i			1.63222i	−0.577894	+	0.816112i	$0.696125\pi$
$558$		0			0
$559$	1.50720e16			0.493970
$560$	−2.23763e15	−	1.29189e15i	−0.0725537	−	0.0418889i
$561$		0			0
$562$	2.60859e15	+	4.51821e15i	0.0827919	+	0.143400i
$563$	8.03130e15	−	4.63688e15i	0.252195	−	0.145605i	−0.368574	−	0.929598i	$-0.620154\pi$
$563$	8.03130e15	−	4.63688e15i	0.252195	−	0.145605i	0.620769	+	0.783994i	$0.286821\pi$
$564$		0			0
$565$	3.90035e15	−	6.75561e15i	0.119898	−	0.207670i
$566$			7.91336e15i			0.240692i
$567$		0			0
$568$	1.52406e16			0.453850
$569$	−3.87453e16	−	2.23696e16i	−1.14168	−	0.659151i	−0.194836	−	0.980836i	$-0.562417\pi$
$569$	−3.87453e16	−	2.23696e16i	−1.14168	−	0.659151i	−0.946847	+	0.321685i	$0.895751\pi$
$570$		0			0
$571$	6.29906e15	+	1.09103e16i	0.181744	+	0.314789i	0.942474	−	0.334278i	$-0.108493\pi$
$571$	6.29906e15	+	1.09103e16i	0.181744	+	0.314789i	−0.760731	+	0.649068i	$0.775159\pi$
$572$	−1.10298e16	+	6.36804e15i	−0.314913	+	0.181815i
$573$		0			0
$574$	−1.59694e16	+	2.76597e16i	−0.446494	+	0.773351i
$575$			3.32808e16i			0.920844i
$576$		0			0
$577$	−2.31146e16			−0.626372			−0.313186	−	0.949692i	$-0.601396\pi$
$577$	−2.31146e16			−0.626372			−0.313186	+	0.949692i	$0.601396\pi$
$578$	−1.60007e16	−	9.23799e15i	−0.429112	−	0.247748i
$579$		0			0
$580$	−1.23124e15	−	2.13257e15i	−0.0323425	−	0.0560189i
$581$	−5.49948e16	+	3.17513e16i	−1.42977	+	0.825476i
$582$		0			0
$583$	−6.65250e15	+	1.15225e16i	−0.169423	+	0.293450i
$584$		−	2.32829e15i		−	0.0586895i
$585$		0			0
$586$	−2.55284e16			−0.630431
$587$	−1.03955e16	−	6.00185e15i	−0.254107	−	0.146709i	0.367536	−	0.930009i	$-0.380201\pi$
$587$	−1.03955e16	−	6.00185e15i	−0.254107	−	0.146709i	−0.621643	+	0.783300i	$0.713535\pi$
$588$		0			0
$589$	6.16080e16	+	1.06708e17i	1.47552	+	2.55568i
$590$	6.10125e15	−	3.52256e15i	0.144646	−	0.0835115i
$591$		0			0
$592$	−5.13154e15	+	8.88808e15i	−0.119211	+	0.206480i
$593$			3.54452e15i			0.0815134i	0.999169	+	0.0407567i	$0.0129769\pi$
$593$			3.54452e15i			0.0815134i	−0.999169	+	0.0407567i	$0.987023\pi$
$594$		0			0
$595$	8.13423e15			0.183322
$596$	−1.97808e16	−	1.14204e16i	−0.441332	−	0.254803i
$597$		0			0
$598$	9.10481e15	+	1.57700e16i	0.199097	+	0.344845i
$599$	4.92806e15	−	2.84522e15i	0.106688	−	0.0615963i	−0.445707	−	0.895179i	$-0.647048\pi$
$599$	4.92806e15	−	2.84522e15i	0.106688	−	0.0615963i	0.552395	+	0.833583i	$0.313714\pi$
$600$		0			0
$601$	2.85544e16	−	4.94577e16i	0.605935	−	1.04951i	−0.385968	−	0.922512i	$-0.626132\pi$
$601$	2.85544e16	−	4.94577e16i	0.605935	−	1.04951i	0.991903	−	0.126998i	$-0.0405342\pi$
$602$			4.47009e16i			0.939155i
$603$		0			0
$604$	3.27376e15			0.0674256
$605$	5.01181e15	+	2.89357e15i	0.102203	+	0.0590068i
$606$		0			0
$607$	−4.01459e16	−	6.95348e16i	−0.802619	−	1.39018i	−0.917887	−	0.396842i	$-0.870106\pi$
$607$	−4.01459e16	−	6.95348e16i	−0.802619	−	1.39018i	0.115268	−	0.993334i	$-0.463227\pi$
$608$	1.25055e16	−	7.22004e15i	0.247559	−	0.142928i
$609$		0			0
$610$	2.50071e15	−	4.33135e15i	0.0485382	−	0.0840706i
$611$		−	4.65016e16i		−	0.893759i
$612$		0			0
$613$	−6.59117e16			−1.24222			−0.621112	−	0.783722i	$-0.713319\pi$
$613$	−6.59117e16			−1.24222			−0.621112	+	0.783722i	$0.713319\pi$
$614$	2.01821e16	+	1.16521e16i	0.376666	+	0.217468i
$615$		0			0
$616$	−1.88864e16	−	3.27123e16i	−0.345673	−	0.598724i
$617$	8.02056e16	−	4.63067e16i	1.45376	−	0.839330i	0.455070	−	0.890456i	$-0.349614\pi$
$617$	8.02056e16	−	4.63067e16i	1.45376	−	0.839330i	0.998692	+	0.0511254i	$0.0162808\pi$
$618$		0			0
$619$	3.57047e14	−	6.18424e14i	0.00634719	−	0.0109937i	−0.862834	−	0.505487i	$-0.831313\pi$
$619$	3.57047e14	−	6.18424e14i	0.00634719	−	0.0109937i	0.869182	+	0.494493i	$0.164646\pi$
$620$			1.10677e16i			0.194853i
$621$		0			0
$622$	−1.12386e16			−0.194075
$623$	7.53489e16	+	4.35027e16i	1.28869	+	0.744025i
$624$		0			0
$625$	−2.57873e16	−	4.46649e16i	−0.432639	−	0.749353i
$626$	−3.13799e16	+	1.81172e16i	−0.521442	+	0.301055i
$627$		0			0
$628$	9.62832e15	−	1.66767e16i	0.156961	−	0.271865i
$629$		−	3.23100e16i		−	0.521715i
$630$		0			0
$631$	−3.14094e16			−0.497603			−0.248802	−	0.968554i	$-0.580037\pi$
$631$	−3.14094e16			−0.497603			−0.248802	+	0.968554i	$0.580037\pi$
$632$	1.58743e16	+	9.16504e15i	0.249111	+	0.143824i
$633$		0			0
$634$	−5.28718e15	−	9.15766e15i	−0.0814120	−	0.141010i
$635$	−8.69470e15	+	5.01989e15i	−0.132621	+	0.0765688i
$636$		0			0
$637$	−2.85174e16	+	4.93936e16i	−0.426848	+	0.739323i
$638$		−	3.59994e16i		−	0.533791i
$639$		0			0
$640$	1.29706e15			0.0188747
$641$	−6.58373e16	−	3.80112e16i	−0.949126	−	0.547978i	−0.0563164	−	0.998413i	$-0.517936\pi$
$641$	−6.58373e16	−	3.80112e16i	−0.949126	−	0.547978i	−0.892809	+	0.450435i	$0.851269\pi$
$642$		0			0
$643$	1.72928e16	+	2.99520e16i	0.244680	+	0.423799i	0.962042	−	0.272902i	$-0.0879836\pi$
$643$	1.72928e16	+	2.99520e16i	0.244680	+	0.423799i	−0.717361	+	0.696701i	$0.754650\pi$
$644$	−4.67709e16	+	2.70032e16i	−0.655633	+	0.378530i
$645$		0			0
$646$	−2.27300e16	+	3.93695e16i	−0.312755	+	0.541707i
$647$		−	9.23429e16i		−	1.25886i	−0.777057	−	0.629430i	$-0.783288\pi$
$647$		−	9.23429e16i		−	1.25886i	0.777057	−	0.629430i	$-0.216712\pi$
$648$		0			0
$649$	1.02994e17			1.37830
$650$	−2.57264e16	−	1.48531e16i	−0.341113	−	0.196942i
$651$		0			0
$652$	−3.06413e16	−	5.30723e16i	−0.398861	−	0.690847i
$653$	−6.24454e16	+	3.60529e16i	−0.805418	+	0.465009i	−0.845362	−	0.534193i	$-0.820615\pi$
$653$	−6.24454e16	+	3.60529e16i	−0.805418	+	0.465009i	0.0399438	+	0.999202i	$0.487282\pi$
$654$		0			0
$655$	1.35132e16	−	2.34055e16i	0.171124	−	0.296395i
$656$		−	1.60332e16i		−	0.201186i
$657$		0			0
$658$	1.37915e17			1.69925
$659$	1.28407e17	+	7.41358e16i	1.56775	+	0.905140i	0.996431	+	0.0844103i	$0.0269007\pi$
$659$	1.28407e17	+	7.41358e16i	1.56775	+	0.905140i	0.571317	+	0.820729i	$0.306433\pi$
$660$		0			0
$661$	3.02344e16	+	5.23676e16i	0.362488	+	0.627847i	0.988370	−	0.152071i	$-0.0485941\pi$
$661$	3.02344e16	+	5.23676e16i	0.362488	+	0.627847i	−0.625882	+	0.779918i	$0.715261\pi$
$662$	−5.53764e16	+	3.19716e16i	−0.657926	+	0.379854i
$663$		0			0
$664$	1.59391e16	−	2.76073e16i	0.185975	−	0.322119i
$665$			4.68642e16i			0.541891i
$666$		0			0
$667$	−5.14708e16			−0.584529
$668$	1.72912e14	+	9.98310e13i	0.00194611	+	0.00112359i
$669$		0			0
$670$	2.10571e15	+	3.64720e15i	0.0232783	+	0.0403191i
$671$	6.33208e16	−	3.65583e16i	0.693763	−	0.400545i
$672$		0			0
$673$	2.98978e16	−	5.17846e16i	0.321773	−	0.557327i	−0.659081	−	0.752072i	$-0.729055\pi$
$673$	2.98978e16	−	5.17846e16i	0.321773	−	0.557327i	0.980854	+	0.194745i	$0.0623879\pi$
$674$		−	7.25075e16i		−	0.773434i
$675$		0			0
$676$	3.14606e16			0.329676
$677$	6.03626e16	+	3.48503e16i	0.626954	+	0.361972i	0.779571	−	0.626313i	$-0.215437\pi$
$677$	6.03626e16	+	3.48503e16i	0.626954	+	0.361972i	−0.152618	+	0.988285i	$0.548770\pi$
$678$		0			0
$679$	4.78775e16	+	8.29262e16i	0.488554	+	0.846201i
$680$	−3.53630e15	+	2.04168e15i	−0.0357681	+	0.0206507i
$681$		0			0
$682$	−8.09002e16	+	1.40123e17i	−0.803977	+	1.39253i
$683$			2.15676e16i			0.212460i	0.994342	+	0.106230i	$0.0338780\pi$
$683$			2.15676e16i			0.212460i	−0.994342	+	0.106230i	$0.966122\pi$
$684$		0			0
$685$	−2.50468e16			−0.242443
$686$	−4.63393e16	−	2.67540e16i	−0.444636	−	0.256711i
$687$		0			0
$688$	−1.12199e16	−	1.94334e16i	−0.105793	−	0.183239i
$689$	−1.47050e16	+	8.48995e15i	−0.137452	+	0.0793579i
$690$		0			0
$691$	2.00241e16	−	3.46827e16i	0.183944	−	0.318599i	−0.759277	−	0.650768i	$-0.774447\pi$
$691$	2.00241e16	−	3.46827e16i	0.183944	−	0.318599i	0.943220	+	0.332169i	$0.107780\pi$
$692$		−	4.95278e16i		−	0.451037i
$693$		0			0
$694$	1.10515e17			0.989159
$695$	−1.32699e16	−	7.66136e15i	−0.117749	−	0.0679825i
$696$		0			0
$697$	2.52377e16	+	4.37129e16i	0.220117	+	0.381253i
$698$	5.72246e16	−	3.30387e16i	0.494824	−	0.285687i
$699$		0			0
$700$	4.40517e16	−	7.62998e16i	0.374433	−	0.648538i
$701$			1.58484e17i			1.33561i	0.744338	+	0.667803i	$0.232765\pi$
$701$			1.58484e17i			1.33561i	−0.744338	+	0.667803i	$0.767235\pi$
$702$		0			0
$703$	1.86150e17			1.54216
$704$	1.64215e16	+	9.48096e15i	0.134889	+	0.0778783i
$705$		0			0
$706$	6.26056e16	+	1.08436e17i	0.505575	+	0.875681i
$707$	1.14743e17	−	6.62469e16i	0.918776	−	0.530455i
$708$		0			0
$709$	2.10660e16	−	3.64874e16i	0.165846	−	0.287254i	−0.771109	−	0.636703i	$-0.780298\pi$
$709$	2.10660e16	−	3.64874e16i	0.165846	−	0.287254i	0.936955	+	0.349449i	$0.113631\pi$
$710$		−	2.48300e16i		−	0.193833i
$711$		0			0
$712$	−4.36766e16			−0.335250
$713$	2.00344e17	+	1.15668e17i	1.52489	+	0.880396i
$714$		0			0
$715$	1.03748e16	+	1.79697e16i	0.0776504	+	0.134494i
$716$	2.69174e16	−	1.55407e16i	0.199781	−	0.115344i
$717$		0			0
$718$	1.08807e15	−	1.88458e15i	0.00794161	−	0.0137553i
$719$		−	1.96385e17i		−	1.42146i	−0.703465	−	0.710729i	$-0.748365\pi$
$719$		−	1.96385e17i		−	1.42146i	0.703465	−	0.710729i	$-0.251635\pi$
$720$		0			0
$721$	3.46581e17			2.46714
$722$	−1.40078e17	−	8.08741e16i	−0.988888	−	0.570935i
$723$		0			0
$724$	−3.35222e16	−	5.80622e16i	−0.232756	−	0.403145i
$725$	7.27175e16	−	4.19835e16i	0.500738	−	0.289101i
$726$		0			0
$727$	1.99296e16	−	3.45191e16i	0.134987	−	0.233805i	−0.790605	−	0.612326i	$-0.790234\pi$
$727$	1.99296e16	−	3.45191e16i	0.134987	−	0.233805i	0.925593	+	0.378521i	$0.123567\pi$
$728$		−	4.82060e16i		−	0.323827i
$729$		0			0
$730$	−3.79325e15			−0.0250654
$731$	6.11799e16	+	3.53222e16i	0.400963	+	0.231496i
$732$		0			0
$733$	7.94129e16	+	1.37547e17i	0.511997	+	0.886804i	0.999903	+	0.0139084i	$0.00442733\pi$
$733$	7.94129e16	+	1.37547e17i	0.511997	+	0.886804i	−0.487907	+	0.872896i	$0.662239\pi$
$734$	2.31299e16	−	1.33541e16i	0.147910	−	0.0853959i
$735$		0			0
$736$	1.35556e16	−	2.34789e16i	0.0852807	−	0.147711i
$737$			6.15676e16i			0.384191i
$738$		0			0
$739$	2.58667e17			1.58808			0.794042	−	0.607863i	$-0.207973\pi$
$739$	2.58667e17			1.58808			0.794042	+	0.607863i	$0.207973\pi$
$740$	1.44805e16	+	8.36030e15i	0.0881845	+	0.0509133i
$741$		0			0
$742$	−2.51797e16	−	4.36124e16i	−0.150878	−	0.261329i
$743$	−1.30130e17	+	7.51307e16i	−0.773473	+	0.446565i	−0.834112	−	0.551595i	$-0.814019\pi$
$743$	−1.30130e17	+	7.51307e16i	−0.773473	+	0.446565i	0.0606391	+	0.998160i	$0.480686\pi$
$744$		0			0
$745$	−1.86062e16	+	3.22268e16i	−0.108823	+	0.188486i
$746$		−	1.56007e17i		−	0.905131i
$747$		0			0
$748$	−5.96955e16			−0.340826
$749$	2.89431e17	+	1.67103e17i	1.63928	+	0.946440i
$750$		0			0
$751$	−3.97341e16	−	6.88215e16i	−0.221475	−	0.383605i	0.733781	−	0.679386i	$-0.237754\pi$
$751$	−3.97341e16	−	6.88215e16i	−0.221475	−	0.383605i	−0.955256	+	0.295780i	$0.904420\pi$
$752$	−5.99577e16	+	3.46166e16i	−0.331542	+	0.191416i
$753$		0			0
$754$	2.29713e16	−	3.97875e16i	0.125014	−	0.216530i
$755$		−	5.33360e15i		−	0.0287965i
$756$		0			0
$757$	−2.15875e17			−1.14717			−0.573585	−	0.819146i	$-0.694448\pi$
$757$	−2.15875e17			−1.14717			−0.573585	+	0.819146i	$0.694448\pi$
$758$	−1.49971e17	−	8.65855e16i	−0.790662	−	0.456489i
$759$		0			0
$760$	−1.17629e16	−	2.03739e16i	−0.0610425	−	0.105729i
$761$	−1.66987e17	+	9.64098e16i	−0.859753	+	0.496379i	−0.863930	−	0.503613i	$-0.832004\pi$
$761$	−1.66987e17	+	9.64098e16i	−0.859753	+	0.496379i	0.00417657	+	0.999991i	$0.498671\pi$
$762$		0			0
$763$	8.86089e16	−	1.53475e17i	0.449087	−	0.777841i
$764$		−	1.84363e17i		−	0.927072i
$765$		0			0
$766$	2.34520e17			1.16093
$767$	1.13832e17	+	6.57207e16i	0.559101	+	0.322797i
$768$		0			0
$769$	−2.59182e16	−	4.48916e16i	−0.125327	−	0.217074i	0.796533	−	0.604594i	$-0.206665\pi$
$769$	−2.59182e16	−	4.48916e16i	−0.125327	−	0.217074i	−0.921861	+	0.387521i	$0.873331\pi$
$770$	−5.32948e16	+	3.07698e16i	−0.255706	+	0.147632i
$771$		0			0
$772$	−7.18786e16	+	1.24497e17i	−0.339544	+	0.588107i
$773$		−	1.40956e17i		−	0.660701i	−0.943858	−	0.330351i	$-0.892833\pi$
$773$		−	1.40956e17i		−	0.660701i	0.943858	−	0.330351i	$-0.107167\pi$
$774$		0			0
$775$	−3.77392e17			−1.74174
$776$	−4.16288e16	−	2.40344e16i	−0.190644	−	0.110069i
$777$		0			0
$778$	−9.24948e15	−	1.60206e16i	−0.0417099	−	0.0722437i
$779$	−2.51846e17	+	1.45403e17i	−1.12697	+	0.650654i
$780$		0			0
$781$	1.81497e17	−	3.14362e17i	0.799768	−	1.38524i
$782$			8.53507e16i			0.373222i
$783$		0			0
$784$	8.49155e16			0.365671
$785$	−2.71697e16	−	1.56865e16i	−0.116109	−	0.0670358i
$786$		0			0
$787$	1.03935e17	+	1.80020e17i	0.437434	+	0.757658i	0.997491	−	0.0707960i	$-0.0225539\pi$
$787$	1.03935e17	+	1.80020e17i	0.437434	+	0.757658i	−0.560057	+	0.828454i	$0.689221\pi$
$788$	−1.87674e17	+	1.08354e17i	−0.783874	+	0.452570i
$789$		0			0
$790$	1.49317e16	−	2.58624e16i	0.0614252	−	0.106392i
$791$			4.31640e17i			1.76223i
$792$		0			0
$793$	9.33118e16			0.375230
$794$	−1.50914e17	−	8.71303e16i	−0.602292	−	0.347733i
$795$		0			0
$796$	−7.74595e16	−	1.34164e17i	−0.304506	−	0.527421i
$797$	3.65398e17	−	2.10963e17i	1.42566	−	0.823106i	0.428887	−	0.903358i	$-0.358906\pi$
$797$	3.65398e17	−	2.10963e17i	1.42566	−	0.823106i	0.996775	+	0.0802520i	$0.0255725\pi$
$798$		0			0
$799$	1.08979e17	−	1.88758e17i	0.418855	−	0.725478i
$800$			4.42278e16i			0.168716i
$801$		0			0
$802$	4.51992e16			0.169857
$803$	−4.80248e16	−	2.77271e16i	−0.179132	−	0.103422i
$804$		0			0
$805$	4.39936e16	+	7.61992e16i	0.161664	+	0.280011i
$806$	−1.78826e17	+	1.03245e17i	−0.652260	+	0.376582i
$807$		0			0
$808$	−3.32558e16	+	5.76008e16i	−0.119509	+	0.206995i
$809$		−	4.35540e17i		−	1.55359i	−0.629753	−	0.776795i	$-0.716844\pi$
$809$		−	4.35540e17i		−	1.55359i	0.629753	−	0.776795i	$-0.283156\pi$
$810$		0			0
$811$	−3.84562e16			−0.135158			−0.0675789	−	0.997714i	$-0.521527\pi$
$811$	−3.84562e16			−0.135158			−0.0675789	+	0.997714i	$0.521527\pi$
$812$	1.18002e17	+	6.81288e16i	0.411675	+	0.237681i
$813$		0			0
$814$	1.22221e17	+	2.11693e17i	0.420144	+	0.727711i
$815$	−8.64653e16	+	4.99208e16i	−0.295051	+	0.170348i
$816$		0			0
$817$	−2.03504e17	+	3.52480e17i	−0.684291	+	1.18523i
$818$			2.11832e17i			0.707085i
$819$		0			0
$820$	−2.61213e16			−0.0859233
$821$	2.20631e17	+	1.27382e17i	0.720457	+	0.415956i	0.814921	−	0.579572i	$-0.196780\pi$
$821$	2.20631e17	+	1.27382e17i	0.720457	+	0.415956i	−0.0944636	+	0.995528i	$0.530114\pi$
$822$		0			0
$823$	1.95863e17	+	3.39245e17i	0.630309	+	1.09173i	0.987488	+	0.157692i	$0.0504052\pi$
$823$	1.95863e17	+	3.39245e17i	0.630309	+	1.09173i	−0.357179	+	0.934036i	$0.616261\pi$
$824$	−1.50674e17	+	8.69916e16i	−0.481365	+	0.277916i
$825$		0			0
$826$	−1.94916e17	+	3.37604e17i	−0.613714	+	1.06298i
$827$			3.37953e17i			1.05639i	0.849124	+	0.528193i	$0.177130\pi$
$827$			3.37953e17i			1.05639i	−0.849124	+	0.528193i	$0.822870\pi$
$828$		0			0
$829$	−1.78746e17			−0.550694			−0.275347	−	0.961345i	$-0.588793\pi$
$829$	−1.78746e17			−0.550694			−0.275347	+	0.961345i	$0.588793\pi$
$830$	−4.49778e16	−	2.59680e16i	−0.137572	−	0.0794272i
$831$		0			0
$832$	1.20997e16	+	2.09572e16i	0.0364782	+	0.0631820i
$833$	−2.31514e17	+	1.33665e17i	−0.692959	+	0.400080i
$834$		0			0
$835$	1.62645e14	−	2.81709e14i	0.000479867	−	0.000831154i
$836$		−	3.43928e17i		−	1.00746i
$837$		0			0
$838$	4.41826e17			1.27581
$839$	−3.50927e17	−	2.02608e17i	−1.00611	−	0.580877i	−0.0960581	−	0.995376i	$-0.530623\pi$
$839$	−3.50927e17	−	2.02608e17i	−1.00611	−	0.580877i	−0.910050	+	0.414499i	$0.863957\pi$
$840$		0			0
$841$	−1.11977e17	−	1.93950e17i	−0.316486	−	0.548169i
$842$	3.31912e17	−	1.91629e17i	0.931429	−	0.537761i
$843$		0			0
$844$	1.17967e17	−	2.04324e17i	0.326366	−	0.565282i
$845$		−	5.12557e16i		−	0.140800i
$846$		0			0
$847$	−3.20223e17			−0.867265
$848$	2.18934e16	+	1.26401e16i	0.0588759	+	0.0339920i
$849$		0			0
$850$	−6.96185e16	−	1.20583e17i	−0.184591	−	0.319722i
$851$	3.02671e17	−	1.74747e17i	0.796881	−	0.460080i
$852$		0			0
$853$	−1.20950e17	+	2.09492e17i	−0.313987	+	0.543842i	−0.979222	−	0.202792i	$-0.934998\pi$
$853$	−1.20950e17	+	2.09492e17i	−0.313987	+	0.543842i	0.665234	+	0.746635i	$0.268332\pi$
$854$			2.76746e17i			0.713401i
$855$		0			0
$856$	−1.67771e17			−0.426455
$857$	−6.60499e17	−	3.81339e17i	−1.66720	−	0.962557i	−0.969139	−	0.246516i	$-0.920714\pi$
$857$	−6.60499e17	−	3.81339e17i	−1.66720	−	0.962557i	−0.698059	−	0.716041i	$-0.745952\pi$
$858$		0			0
$859$	3.06401e17	+	5.30702e17i	0.762660	+	1.32097i	0.941475	+	0.337083i	$0.109440\pi$
$859$	3.06401e17	+	5.30702e17i	0.762660	+	1.32097i	−0.178815	+	0.983883i	$0.557226\pi$
$860$	−3.16609e16	+	1.82794e16i	−0.0782588	+	0.0451827i
$861$		0			0
$862$	−8.75932e16	+	1.51716e17i	−0.213514	+	0.369818i
$863$			2.66976e17i			0.646260i	0.946355	+	0.323130i	$0.104735\pi$
$863$			2.66976e17i			0.646260i	−0.946355	+	0.323130i	$0.895265\pi$
$864$		0			0
$865$	−8.06906e16			−0.192631
$866$	−1.53911e17	−	8.88603e16i	−0.364889	−	0.210669i
$867$		0			0
$868$	−3.06207e17	−	5.30366e17i	−0.715973	−	1.24010i
$869$	3.78088e17	−	2.18289e17i	0.877958	−	0.506890i
$870$		0			0
$871$	−3.92865e16	+	6.80462e16i	−0.0899776	+	0.155846i
$872$			8.89630e16i			0.202353i
$873$		0			0
$874$	−4.91737e17			−1.10322
$875$	−2.54555e17	−	1.46967e17i	−0.567195	−	0.327470i
$876$		0			0
$877$	−2.38478e17	−	4.13057e17i	−0.524145	−	0.907846i	−0.999605	−	0.0281083i	$-0.991052\pi$
$877$	−2.38478e17	−	4.13057e17i	−0.524145	−	0.907846i	0.475460	−	0.879737i	$-0.342282\pi$
$878$	−1.50596e17	+	8.69467e16i	−0.328735	+	0.189795i
$879$		0			0
$880$	1.54464e16	−	2.67539e16i	0.0332606	−	0.0576091i
$881$			2.01145e17i			0.430184i	0.976594	+	0.215092i	$0.0690051\pi$
$881$			2.01145e17i			0.430184i	−0.976594	+	0.215092i	$0.930995\pi$
$882$		0			0
$883$	−8.37188e17			−1.76628			−0.883138	−	0.469113i	$-0.844574\pi$
$883$	−8.37188e17			−1.76628			−0.883138	+	0.469113i	$0.844574\pi$
$884$	−6.59771e16	−	3.80919e16i	−0.138255	−	0.0798213i
$885$		0			0
$886$	2.21889e17	+	3.84323e17i	0.458705	+	0.794500i
$887$	−2.76310e17	+	1.59528e17i	−0.567356	+	0.327563i	−0.756093	−	0.654465i	$-0.772894\pi$
$887$	−2.76310e17	+	1.59528e17i	−0.567356	+	0.327563i	0.188737	+	0.982028i	$0.439561\pi$
$888$		0			0
$889$	2.77768e17	−	4.81109e17i	0.562693	−	0.974614i
$890$			7.11578e16i			0.143180i
$891$		0			0
$892$	−2.95446e17			−0.586528
$893$	1.08750e18	+	6.27870e17i	2.14448	+	1.23811i
$894$		0			0
$895$	−2.53190e16	−	4.38537e16i	−0.0492615	−	0.0853235i
$896$	−6.21553e16	+	3.58854e16i	−0.120124	+	0.0693537i
$897$		0			0
$898$	6.78730e16	−	1.17560e17i	0.129431	−	0.224182i
$899$		−	5.83660e17i		−	1.10561i
$900$		0			0
$901$	−7.95869e16			−0.148762
$902$	−3.30710e17	−	1.90936e17i	−0.614057	−	0.354526i
$903$		0			0
$904$	−1.08341e17	−	1.87653e17i	−0.198511	−	0.343830i
$905$	−9.45948e16	+	5.46144e16i	−0.172177	+	0.0994066i
$906$		0			0
$907$	2.16598e17	−	3.75159e17i	0.389055	−	0.673864i	−0.603267	−	0.797539i	$-0.706135\pi$
$907$	2.16598e17	−	3.75159e17i	0.389055	−	0.673864i	0.992323	+	0.123675i	$0.0394682\pi$
$908$			3.20419e17i			0.571746i
$909$		0			0
$910$	−7.85371e16			−0.138301
$911$	5.69666e17	+	3.28897e17i	0.996576	+	0.575373i	0.907233	−	0.420628i	$-0.138190\pi$
$911$	5.69666e17	+	3.28897e17i	0.996576	+	0.575373i	0.0893423	+	0.996001i	$0.471523\pi$
$912$		0			0
$913$	−3.79630e17	−	6.57539e17i	−0.655445	−	1.13526i
$914$	1.79448e17	−	1.03604e17i	0.307794	−	0.177705i
$915$		0			0
$916$	1.72050e17	−	2.97999e17i	0.291260	−	0.504477i
$917$			1.49546e18i			2.51513i
$918$		0			0
$919$	8.09467e17			1.34371			0.671856	−	0.740682i	$-0.265497\pi$
$919$	8.09467e17			1.34371			0.671856	+	0.740682i	$0.265497\pi$
$920$	−3.82519e16	−	2.20847e16i	−0.0630849	−	0.0364221i
$921$		0			0
$922$	−1.34375e17	−	2.32744e17i	−0.218742	−	0.378872i
$923$	4.01191e17	−	2.31628e17i	0.648845	−	0.374611i
$924$		0			0
$925$	−2.85074e17	+	4.93763e17i	−0.455101	+	0.788257i
$926$		−	8.01889e17i		−	1.27189i
$927$		0			0
$928$	−6.84011e16			−0.107096
$929$	−9.09682e17	−	5.25205e17i	−1.41513	−	0.817024i	−0.419261	−	0.907866i	$-0.637711\pi$
$929$	−9.09682e17	−	5.25205e17i	−1.41513	−	0.817024i	−0.995865	+	0.0908421i	$0.971044\pi$
$930$		0			0
$931$	−7.70091e17	−	1.33384e18i	−1.18262	−	2.04835i
$932$	3.46307e17	−	1.99940e17i	0.528403	−	0.305074i
$933$		0			0
$934$	−2.25781e17	+	3.91063e17i	−0.340099	+	0.589069i
$935$			9.72560e16i			0.145562i
$936$		0			0
$937$	−7.47499e17			−1.10452			−0.552260	−	0.833672i	$-0.686234\pi$
$937$	−7.47499e17			−1.10452			−0.552260	+	0.833672i	$0.686234\pi$
$938$	−2.01813e17	−	1.16517e17i	−0.296300	−	0.171069i
$939$		0			0
$940$	5.63974e16	+	9.76831e16i	0.0817508	+	0.141596i
$941$	1.24067e17	−	7.16301e16i	0.178697	−	0.103171i	−0.407983	−	0.912989i	$-0.633768\pi$
$941$	1.24067e17	−	7.16301e16i	0.178697	−	0.103171i	0.586681	+	0.809818i	$0.300434\pi$
$942$		0			0
$943$	−2.72994e17	+	4.72839e17i	−0.388224	+	0.672424i
$944$		−	1.95695e17i		−	0.276533i
$945$		0			0
$946$	−5.34461e17			−0.745709
$947$	−9.43123e17	−	5.44512e17i	−1.30758	−	0.754932i	−0.325888	−	0.945408i	$-0.605663\pi$
$947$	−9.43123e17	−	5.44512e17i	−1.30758	−	0.754932i	−0.981692	+	0.190477i	$0.938997\pi$
$948$		0			0
$949$	−3.53855e16	−	6.12895e16i	−0.0484427	−	0.0839052i
$950$	6.94721e17	−	4.01098e17i	0.945081	−	0.545643i
$951$		0			0
$952$	1.12974e17	−	1.95676e17i	0.151759	−	0.262855i
$953$		−	8.26064e16i		−	0.110270i	−0.998479	−	0.0551349i	$-0.982441\pi$
$953$		−	8.26064e16i		−	0.110270i	0.998479	−	0.0551349i	$-0.0175589\pi$
$954$		0			0
$955$	−3.00364e17			−0.395939
$956$	6.19815e17	+	3.57850e17i	0.811923	+	0.468764i
$957$		0			0
$958$	1.15867e17	+	2.00687e17i	0.149888	+	0.259613i
$959$	1.20025e18	−	6.92965e17i	1.54298	−	0.890840i
$960$		0			0
$961$	−9.17808e17	+	1.58969e18i	−1.16523	+	2.01824i
$962$			3.11958e17i			0.393591i
$963$		0			0
$964$	1.73152e17			0.215757
$965$	2.02831e17	+	1.17105e17i	0.251172	+	0.145014i
$966$		0			0
$967$	−2.02220e17	−	3.50255e17i	−0.247323	−	0.428376i	0.715459	−	0.698655i	$-0.246218\pi$
$967$	−2.02220e17	−	3.50255e17i	−0.247323	−	0.428376i	−0.962782	+	0.270278i	$0.912884\pi$
$968$	1.39215e17	−	8.03757e16i	0.169213	−	0.0976951i
$969$		0			0
$970$	−3.91569e16	+	6.78217e16i	−0.0470086	+	0.0814213i
$971$		−	6.92814e17i		−	0.826611i	−0.910592	−	0.413306i	$-0.864374\pi$
$971$		−	6.92814e17i		−	0.826611i	0.910592	−	0.413306i	$-0.135626\pi$
$972$		0			0
$973$	8.47860e17			0.999188
$974$	7.92817e17	+	4.57733e17i	0.928580	+	0.536116i
$975$		0			0
$976$	−6.94630e16	−	1.20313e17i	−0.0803627	−	0.139192i
$977$	−1.15465e17	+	6.66636e16i	−0.132765	+	0.0766517i	−0.564911	−	0.825152i	$-0.691090\pi$
$977$	−1.15465e17	+	6.66636e16i	−0.132765	+	0.0766517i	0.432147	+	0.901803i	$0.357756\pi$
$978$		0			0
$979$	−5.20135e17	+	9.00900e17i	−0.590772	+	1.02325i
$980$		−	1.38344e17i		−	0.156173i
$981$		0			0
$982$	−2.44345e17			−0.272480
$983$	−4.47986e17	−	2.58645e17i	−0.496527	−	0.286670i	0.230751	−	0.973013i	$-0.425882\pi$
$983$	−4.47986e17	−	2.58645e17i	−0.496527	−	0.286670i	−0.727278	+	0.686343i	$0.759215\pi$
$984$		0			0
$985$	1.76530e17	+	3.05758e17i	0.193286	+	0.334781i
$986$	1.86489e17	−	1.07669e17i	0.202951	−	0.117174i
$987$		0			0
$988$	2.19461e17	−	3.80118e17i	0.235948	−	0.408674i
$989$			7.64155e17i			0.816590i
$990$		0			0
$991$	−1.12883e18			−1.19175			−0.595876	−	0.803077i	$-0.703195\pi$
$991$	−1.12883e18			−1.19175			−0.595876	+	0.803077i	$0.703195\pi$
$992$	2.66243e17	+	1.53715e17i	0.279388	+	0.161305i
$993$		0			0
$994$	6.86966e17	+	1.18986e18i	0.712224	+	1.23361i
$995$	−2.18580e17	+	1.26197e17i	−0.225253	+	0.130050i
$996$		0			0
$997$	4.58065e17	−	7.93392e17i	0.466398	−	0.807825i	−0.532866	−	0.846200i	$-0.678885\pi$
$997$	4.58065e17	−	7.93392e17i	0.466398	−	0.807825i	0.999263	+	0.0383752i	$0.0122182\pi$
$998$			8.60952e17i			0.871356i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.13.d.h.107.5		24
3.2	odd	2	inner	162.13.d.h.107.8		24
9.2	odd	6		162.13.b.a.161.3	✓	12
9.4	even	3	inner	162.13.d.h.53.8		24
9.5	odd	6	inner	162.13.d.h.53.5		24
9.7	even	3		162.13.b.a.161.10	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.13.b.a.161.3	✓	12	9.2	odd	6
162.13.b.a.161.10	yes	12	9.7	even	3
162.13.d.h.53.5		24	9.5	odd	6	inner
162.13.d.h.53.8		24	9.4	even	3	inner
162.13.d.h.107.5		24	1.1	even	1	trivial
162.13.d.h.107.8		24	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	162.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-39.1918 - 22.6274i) q^{2} +(1024.00 + 1773.62i) q^{4} +(2889.58 - 1668.30i) q^{5} +(-92313.0 + 159891. i) q^{7} -92681.9i q^{8} -150997. q^{10} +(-1.91171e6 - 1.10373e6i) q^{11} +(-1.40859e6 - 2.43974e6i) q^{13} +(7.23583e6 - 4.17761e6i) q^{14} +(-2.09715e6 + 3.63237e6i) q^{16} -1.32044e7i q^{17} +7.60755e7 q^{19} +(5.91786e6 + 3.41668e6i) q^{20} +(4.99491e7 + 8.65143e7i) q^{22} +(1.23695e8 - 7.14156e7i) q^{23} +(-1.16504e8 + 2.01791e8i) q^{25} +1.27491e8i q^{26} -3.78114e8 q^{28} +(-3.12082e8 - 1.80181e8i) q^{29} +(8.09827e8 + 1.40266e9i) q^{31} +(1.64382e8 - 9.49063e7i) q^{32} +(-2.98782e8 + 5.17506e8i) q^{34} +6.16023e8i q^{35} +2.44691e9 q^{37} +(-2.98154e9 - 1.72139e9i) q^{38} +(-1.54621e8 - 2.67812e8i) q^{40} +(-3.31048e9 + 1.91130e9i) q^{41} +(-2.67503e9 + 4.63329e9i) q^{43} -4.52087e9i q^{44} -6.46380e9 q^{46} +(1.42950e10 + 8.25324e9i) q^{47} +(-1.01227e10 - 1.75331e10i) q^{49} +(9.13200e9 - 5.27236e9i) q^{50} +(2.88478e9 - 4.99659e9i) q^{52} -6.02729e9i q^{53} -7.36541e9 q^{55} +(1.48190e10 + 8.55574e9i) q^{56} +(8.15404e9 + 1.41232e10i) q^{58} +(-4.04063e10 + 2.33286e10i) q^{59} +(-1.65613e10 + 2.86850e10i) q^{61} -7.32972e10i q^{62} -8.58993e9 q^{64} +(-8.14044e9 - 4.69989e9i) q^{65} +(-1.39454e10 - 2.41541e10i) q^{67} +(2.34196e10 - 1.35213e10i) q^{68} +(1.39390e10 - 2.41431e10i) q^{70} +1.64440e11i q^{71} +2.51213e10 q^{73} +(-9.58988e10 - 5.53672e10i) q^{74} +(7.79013e10 + 1.34929e11i) q^{76} +(3.52952e11 - 2.03777e11i) q^{77} +(-9.88871e10 + 1.71277e11i) q^{79} +1.39947e10i q^{80} +1.72992e11 q^{82} +(2.97872e11 + 1.71976e11i) q^{83} +(-2.20290e10 - 3.81553e10i) q^{85} +(2.09679e11 - 1.21058e11i) q^{86} +(-1.02296e11 + 1.77181e11i) q^{88} -4.71252e11i q^{89} +5.20123e11 q^{91} +(2.53328e11 + 1.46259e11i) q^{92} +(-3.73499e11 - 6.46920e11i) q^{94} +(2.19826e11 - 1.26917e11i) q^{95} +(2.59322e11 - 4.49158e11i) q^{97} +9.16204e11i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24576 q^{4} + 220224 q^{7} + 758016 q^{10} + 2372808 q^{13} - 50331648 q^{16} + 285339360 q^{19} - 70253568 q^{22} + 727623852 q^{25} + 902037504 q^{28} - 577374720 q^{31} - 2238076800 q^{34} - 6056330712 q^{37}+ \cdots + 2570481096384 q^{97}+O(q^{100}) \) 24 * q + 24576 * q^4 + 220224 * q^7 + 758016 * q^10 + 2372808 * q^13 - 50331648 * q^16 + 285339360 * q^19 - 70253568 * q^22 + 727623852 * q^25 + 902037504 * q^28 - 577374720 * q^31 - 2238076800 * q^34 - 6056330712 * q^37 + 776208384 * q^40 - 33702957168 * q^43 - 49846440960 * q^46 - 72166762836 * q^49 - 4859510784 * q^52 - 316402444512 * q^55 + 21247000704 * q^58 - 213044029980 * q^61 - 206158430208 * q^64 - 70227468528 * q^67 + 251325402624 * q^70 + 99306462720 * q^73 + 292187504640 * q^76 + 696725200560 * q^79 + 1471123266048 * q^82 + 271807264548 * q^85 + 143879307264 * q^88 + 1458470433408 * q^91 - 1211537346048 * q^94 + 2570481096384 * q^97

Introduction

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