LMFDB - Embedded newform 162.8.c.q.109.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [162,8,Mod(55,162)] 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("162.55"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(162, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	162.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-32,0,-256,-528] 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:	$50.6063741284$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 518x^{5} + 53377x^{4} + 11940x^{3} + 3528x^{2} + 1563408x + 346406544 $ x^8 - 2x^7 + 2x^6 + 518x^5 + 53377x^4 + 11940x^3 + 3528x^2 + 1563408*x + 346406544
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{18} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.3
Root			$11.0098 + 11.0098i$ of defining polynomial
Character	$\chi$	$=$	162.109
Dual form			162.8.c.q.55.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.00000 - 6.92820i) q^{2} +(-32.0000 + 55.4256i) q^{4} +(-5.62316 + 9.73960i) q^{5} +(-719.735 - 1246.62i) q^{7} +512.000 q^{8} +89.9705 q^{10} +(-2216.31 - 3838.77i) q^{11} +(3615.49 - 6262.21i) q^{13} +(-5757.88 + 9972.94i) q^{14} +(-2048.00 - 3547.24i) q^{16} +13221.1 q^{17} +13506.6 q^{19} +(-359.882 - 623.334i) q^{20} +(-17730.5 + 30710.1i) q^{22} +(32869.3 - 56931.3i) q^{23} +(38999.3 + 67548.7i) q^{25} -57847.8 q^{26} +92126.0 q^{28} +(-74249.1 - 128603. i) q^{29} +(-69431.2 + 120258. i) q^{31} +(-16384.0 + 28377.9i) q^{32} +(-52884.4 - 91598.4i) q^{34} +16188.7 q^{35} -121532. q^{37} +(-54026.5 - 93576.6i) q^{38} +(-2879.06 + 4986.67i) q^{40} +(-26393.4 + 45714.8i) q^{41} +(-375862. - 651012. i) q^{43} +283688. q^{44} -525909. q^{46} +(-491796. - 851816. i) q^{47} +(-624264. + 1.08126e6i) q^{49} +(311994. - 540390. i) q^{50} +(231391. + 400781. i) q^{52} -621759. q^{53} +49850.7 q^{55} +(-368504. - 638268. i) q^{56} +(-593992. + 1.02883e6i) q^{58} +(-407108. + 705132. i) q^{59} +(1.23477e6 + 2.13868e6i) q^{61} +1.11090e6 q^{62} +262144. q^{64} +(40660.9 + 70426.8i) q^{65} +(-1.72741e6 + 2.99196e6i) q^{67} +(-423075. + 732788. i) q^{68} +(-64754.9 - 112159. i) q^{70} +3.64076e6 q^{71} -5.55060e6 q^{73} +(486126. + 841995. i) q^{74} +(-432212. + 748613. i) q^{76} +(-3.19032e6 + 5.52579e6i) q^{77} +(1.02318e6 + 1.77220e6i) q^{79} +46064.9 q^{80} +422295. q^{82} +(-5.13258e6 - 8.88989e6i) q^{83} +(-74344.3 + 128768. i) q^{85} +(-3.00690e6 + 5.20810e6i) q^{86} +(-1.13475e6 - 1.96545e6i) q^{88} +8.12374e6 q^{89} -1.04088e7 q^{91} +(2.10364e6 + 3.64360e6i) q^{92} +(-3.93437e6 + 6.81453e6i) q^{94} +(-75949.9 + 131549. i) q^{95} +(6.64660e6 + 1.15122e7i) q^{97} +9.98823e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 32 q^{2} - 256 q^{4} - 528 q^{5} - 560 q^{7} + 4096 q^{8} + 8448 q^{10} - 2160 q^{11} - 13460 q^{13} - 4480 q^{14} - 16384 q^{16} + 45120 q^{17} + 73408 q^{19} - 33792 q^{20} - 17280 q^{22} - 62640 q^{23}+ \cdots + 23190336 q^{98}+O(q^{100}) $ 8 * q - 32 * q^2 - 256 * q^4 - 528 * q^5 - 560 * q^7 + 4096 * q^8 + 8448 * q^10 - 2160 * q^11 - 13460 * q^13 - 4480 * q^14 - 16384 * q^16 + 45120 * q^17 + 73408 * q^19 - 33792 * q^20 - 17280 * q^22 - 62640 * q^23 - 94696 * q^25 + 215360 * q^26 + 71680 * q^28 - 68400 * q^29 - 227504 * q^31 - 131072 * q^32 - 180480 * q^34 - 126048 * q^35 + 1047160 * q^37 - 293632 * q^38 - 270336 * q^40 - 67200 * q^41 - 562640 * q^43 + 276480 * q^44 + 1002240 * q^46 - 515328 * q^47 - 1449396 * q^49 - 757568 * q^50 - 861440 * q^52 + 4996032 * q^53 + 2645568 * q^55 - 286720 * q^56 - 547200 * q^58 - 4155840 * q^59 - 2130764 * q^61 + 3640064 * q^62 + 2097152 * q^64 - 8966496 * q^65 + 1205440 * q^67 - 1443840 * q^68 + 504192 * q^70 + 24972960 * q^71 - 9641720 * q^73 - 4188640 * q^74 - 2349056 * q^76 - 18686592 * q^77 + 11471680 * q^79 + 4325376 * q^80 + 1075200 * q^82 - 16811232 * q^83 + 21006396 * q^85 - 4501120 * q^86 - 1105920 * q^88 + 33715200 * q^89 - 46401088 * q^91 - 4008960 * q^92 - 4122624 * q^94 - 14090160 * q^95 + 27078040 * q^97 + 23190336 * q^98

Character values

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

$n$	$83$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−4.00000	−	6.92820i	−0.353553	−	0.612372i
$2$	−4.00000	−	6.92820i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−32.0000	+	55.4256i	−0.250000	+	0.433013i
$5$	−5.62316	+	9.73960i	−0.0201180	+	0.0348454i	−0.875909	−	0.482476i	$-0.839738\pi$
$5$	−5.62316	+	9.73960i	−0.0201180	+	0.0348454i	0.855791	+	0.517322i	$0.173071\pi$
$6$		0			0
$7$	−719.735	−	1246.62i	−0.793102	−	1.37369i	−0.924037	−	0.382303i	$-0.875131\pi$
$7$	−719.735	−	1246.62i	−0.793102	−	1.37369i	0.130935	−	0.991391i	$-0.458202\pi$
$8$	512.000			0.353553
$9$		0			0
$10$	89.9705			0.0284512
$11$	−2216.31	−	3838.77i	−0.502061	−	0.869596i	−0.999997	−	0.00238204i	$-0.999242\pi$
$11$	−2216.31	−	3838.77i	−0.502061	−	0.869596i	0.497936	−	0.867214i	$-0.334092\pi$
$12$		0			0
$13$	3615.49	−	6262.21i	0.456420	−	0.790543i	−0.542348	−	0.840154i	$-0.682465\pi$
$13$	3615.49	−	6262.21i	0.456420	−	0.790543i	0.998769	+	0.0496105i	$0.0157980\pi$
$14$	−5757.88	+	9972.94i	−0.560808	+	0.971348i
$15$		0			0
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	13221.1			0.652674			0.326337	−	0.945254i	$-0.394186\pi$
$17$	13221.1			0.652674			0.326337	+	0.945254i	$0.394186\pi$
$18$		0			0
$19$	13506.6			0.451761			0.225881	−	0.974155i	$-0.427474\pi$
$19$	13506.6			0.451761			0.225881	+	0.974155i	$0.427474\pi$
$20$	−359.882	−	623.334i	−0.0100590	−	0.0174227i
$21$		0			0
$22$	−17730.5	+	30710.1i	−0.355011	+	0.614897i
$23$	32869.3	−	56931.3i	0.563304	−	0.975672i	−0.433901	−	0.900961i	$-0.642863\pi$
$23$	32869.3	−	56931.3i	0.563304	−	0.975672i	0.997205	−	0.0747111i	$-0.0238034\pi$
$24$		0			0
$25$	38999.3	+	67548.7i	0.499191	+	0.864623i
$26$	−57847.8			−0.645476
$27$		0			0
$28$	92126.0			0.793102
$29$	−74249.1	−	128603.i	−0.565325	−	0.979171i	−0.997019	−	0.0771513i	$-0.975418\pi$
$29$	−74249.1	−	128603.i	−0.565325	−	0.979171i	0.431695	−	0.902020i	$-0.357916\pi$
$30$		0			0
$31$	−69431.2	+	120258.i	−0.418590	+	0.725019i	−0.995798	−	0.0915783i	$-0.970809\pi$
$31$	−69431.2	+	120258.i	−0.418590	+	0.725019i	0.577208	+	0.816597i	$0.304142\pi$
$32$	−16384.0	+	28377.9i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−52884.4	−	91598.4i	−0.230755	−	0.399679i
$35$	16188.7			0.0638226
$36$		0			0
$37$	−121532.			−0.394442			−0.197221	−	0.980359i	$-0.563192\pi$
$37$	−121532.			−0.394442			−0.197221	+	0.980359i	$0.563192\pi$
$38$	−54026.5	−	93576.6i	−0.159722	−	0.276646i
$39$		0			0
$40$	−2879.06	+	4986.67i	−0.00711279	+	0.0123197i
$41$	−26393.4	+	45714.8i	−0.0598070	+	0.103589i	−0.894379	−	0.447311i	$-0.852382\pi$
$41$	−26393.4	+	45714.8i	−0.0598070	+	0.103589i	0.834572	+	0.550899i	$0.185715\pi$
$42$		0			0
$43$	−375862.	−	651012.i	−0.720923	−	1.24868i	−0.960630	−	0.277830i	$-0.910385\pi$
$43$	−375862.	−	651012.i	−0.720923	−	1.24868i	0.239707	−	0.970845i	$-0.422949\pi$
$44$	283688.			0.502061
$45$		0			0
$46$	−525909.			−0.796633
$47$	−491796.	−	851816.i	−0.690944	−	1.19675i	−0.971529	−	0.236921i	$-0.923862\pi$
$47$	−491796.	−	851816.i	−0.690944	−	1.19675i	0.280585	−	0.959829i	$-0.409472\pi$
$48$		0			0
$49$	−624264.	+	1.08126e6i	−0.758023	+	1.31293i
$50$	311994.	−	540390.i	0.352981	−	0.611381i
$51$		0			0
$52$	231391.	+	400781.i	0.228210	+	0.395272i
$53$	−621759.			−0.573663			−0.286831	−	0.957981i	$-0.592602\pi$
$53$	−621759.			−0.573663			−0.286831	+	0.957981i	$0.592602\pi$
$54$		0			0
$55$	49850.7			0.0404019
$56$	−368504.	−	638268.i	−0.280404	−	0.485674i
$57$		0			0
$58$	−593992.	+	1.02883e6i	−0.399745	+	0.692378i
$59$	−407108.	+	705132.i	−0.258064	+	0.446980i	−0.965723	−	0.259574i	$-0.916418\pi$
$59$	−407108.	+	705132.i	−0.258064	+	0.446980i	0.707659	+	0.706554i	$0.249751\pi$
$60$		0			0
$61$	1.23477e6	+	2.13868e6i	0.696514	+	1.20640i	0.969668	+	0.244428i	$0.0786001\pi$
$61$	1.23477e6	+	2.13868e6i	0.696514	+	1.20640i	−0.273153	+	0.961971i	$0.588067\pi$
$62$	1.11090e6			0.591975
$63$		0			0
$64$	262144.			0.125000
$65$	40660.9	+	70426.8i	0.0183646	+	0.0318083i
$66$		0			0
$67$	−1.72741e6	+	2.99196e6i	−0.701671	+	1.21533i	0.266209	+	0.963915i	$0.414229\pi$
$67$	−1.72741e6	+	2.99196e6i	−0.701671	+	1.21533i	−0.967880	+	0.251414i	$0.919105\pi$
$68$	−423075.	+	732788.i	−0.163168	+	0.282616i
$69$		0			0
$70$	−64754.9	−	112159.i	−0.0225647	−	0.0390832i
$71$	3.64076e6			1.20722			0.603612	−	0.797278i	$-0.293728\pi$
$71$	3.64076e6			1.20722			0.603612	+	0.797278i	$0.293728\pi$
$72$		0			0
$73$	−5.55060e6			−1.66997			−0.834987	−	0.550269i	$-0.814525\pi$
$73$	−5.55060e6			−1.66997			−0.834987	+	0.550269i	$0.814525\pi$
$74$	486126.	+	841995.i	0.139456	+	0.241545i
$75$		0			0
$76$	−432212.	+	748613.i	−0.112940	+	0.195618i
$77$	−3.19032e6	+	5.52579e6i	−0.796372	+	1.37936i
$78$		0			0
$79$	1.02318e6	+	1.77220e6i	0.233484	+	0.404407i	0.958831	−	0.283977i	$-0.0916539\pi$
$79$	1.02318e6	+	1.77220e6i	0.233484	+	0.404407i	−0.725347	+	0.688384i	$0.758321\pi$
$80$	46064.9			0.0100590
$81$		0			0
$82$	422295.			0.0845799
$83$	−5.13258e6	−	8.88989e6i	−0.985286	−	1.70657i	−0.640657	−	0.767827i	$-0.721338\pi$
$83$	−5.13258e6	−	8.88989e6i	−0.985286	−	1.70657i	−0.344630	−	0.938739i	$-0.611995\pi$
$84$		0			0
$85$	−74344.3	+	128768.i	−0.0131305	+	0.0227427i
$86$	−3.00690e6	+	5.20810e6i	−0.509770	+	0.882947i
$87$		0			0
$88$	−1.13475e6	−	1.96545e6i	−0.177506	−	0.307449i
$89$	8.12374e6			1.22149			0.610747	−	0.791826i	$-0.290869\pi$
$89$	8.12374e6			1.22149			0.610747	+	0.791826i	$0.290869\pi$
$90$		0			0
$91$	−1.04088e7			−1.44795
$92$	2.10364e6	+	3.64360e6i	0.281652	+	0.487836i
$93$		0			0
$94$	−3.93437e6	+	6.81453e6i	−0.488571	+	0.846230i
$95$	−75949.9	+	131549.i	−0.00908854	+	0.0157418i
$96$		0			0
$97$	6.64660e6	+	1.15122e7i	0.739432	+	1.28073i	0.952751	+	0.303752i	$0.0982394\pi$
$97$	6.64660e6	+	1.15122e7i	0.739432	+	1.28073i	−0.213319	+	0.976983i	$0.568427\pi$
$98$	9.98823e6			1.07201
$99$		0			0
$100$	−4.99191e6			−0.499191
$101$	6.68327e6	+	1.15758e7i	0.645452	+	1.11796i	0.984197	+	0.177078i	$0.0566644\pi$
$101$	6.68327e6	+	1.15758e7i	0.645452	+	1.11796i	−0.338745	+	0.940878i	$0.610002\pi$
$102$		0			0
$103$	−6.76614e6	+	1.17193e7i	−0.610114	+	1.05675i	0.381107	+	0.924531i	$0.375543\pi$
$103$	−6.76614e6	+	1.17193e7i	−0.610114	+	1.05675i	−0.991221	+	0.132217i	$0.957790\pi$
$104$	1.85113e6	−	3.20625e6i	0.161369	−	0.279499i
$105$		0			0
$106$	2.48704e6	+	4.30767e6i	0.202820	+	0.351295i
$107$	−1.89550e7			−1.49583			−0.747914	−	0.663796i	$-0.768944\pi$
$107$	−1.89550e7			−1.49583			−0.747914	+	0.663796i	$0.768944\pi$
$108$		0			0
$109$	−1.33257e7			−0.985589			−0.492794	−	0.870146i	$-0.664025\pi$
$109$	−1.33257e7			−0.985589			−0.492794	+	0.870146i	$0.664025\pi$
$110$	−199403.	−	345376.i	−0.0142842	−	0.0247410i
$111$		0			0
$112$	−2.94803e6	+	5.10614e6i	−0.198276	+	0.343423i
$113$	−1.02134e7	+	1.76901e7i	−0.665878	+	1.15333i	0.313168	+	0.949698i	$0.398610\pi$
$113$	−1.02134e7	+	1.76901e7i	−0.665878	+	1.15333i	−0.979046	+	0.203637i	$0.934724\pi$
$114$		0			0
$115$	369659.	+	640267.i	0.0226651	+	0.0392572i
$116$	9.50388e6			0.565325
$117$		0			0
$118$	6.51373e6			0.364958
$119$	−9.51568e6	−	1.64816e7i	−0.517637	−	0.896574i
$120$		0			0
$121$	−80510.7	+	139449.i	−0.00413147	+	0.00715592i
$122$	9.87812e6	−	1.71094e7i	0.492510	−	0.853052i
$123$		0			0
$124$	−4.44360e6	−	7.69653e6i	−0.209295	−	0.362509i
$125$	−1.75581e6			−0.0804069
$126$		0			0
$127$	1.13846e7			0.493178			0.246589	−	0.969120i	$-0.420690\pi$
$127$	1.13846e7			0.493178			0.246589	+	0.969120i	$0.420690\pi$
$128$	−1.04858e6	−	1.81619e6i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	325287.	−	563414.i	0.0129857	−	0.0224919i
$131$	−2.64090e6	+	4.57417e6i	−0.102636	+	0.177772i	−0.912770	−	0.408474i	$-0.866061\pi$
$131$	−2.64090e6	+	4.57417e6i	−0.102636	+	0.177772i	0.810134	+	0.586245i	$0.199395\pi$
$132$		0			0
$133$	−9.72118e6	−	1.68376e7i	−0.358293	−	0.620582i
$134$	2.76385e7			0.992312
$135$		0			0
$136$	6.76920e6			0.230755
$137$	−2.45057e7	−	4.24451e7i	−0.814226	−	1.41028i	−0.909882	−	0.414866i	$-0.863828\pi$
$137$	−2.45057e7	−	4.24451e7i	−0.814226	−	1.41028i	0.0956566	−	0.995414i	$-0.469505\pi$
$138$		0			0
$139$	9.43972e6	−	1.63501e7i	0.298131	−	0.516378i	−0.677577	−	0.735452i	$-0.736970\pi$
$139$	9.43972e6	−	1.63501e7i	0.298131	−	0.516378i	0.975708	+	0.219073i	$0.0703034\pi$
$140$	−518039.	+	897270.i	−0.0159557	+	0.0276360i
$141$		0			0
$142$	−1.45630e7	−	2.52239e7i	−0.426818	−	0.739270i
$143$	−3.20522e7			−0.916604
$144$		0			0
$145$	1.67006e6			0.0454929
$146$	2.22024e7	+	3.84557e7i	0.590425	+	1.02265i
$147$		0			0
$148$	3.88901e6	−	6.73596e6i	0.0986105	−	0.170798i
$149$	1.44249e7	−	2.49846e7i	0.357240	−	0.618758i	−0.630259	−	0.776385i	$-0.717051\pi$
$149$	1.44249e7	−	2.49846e7i	0.357240	−	0.618758i	0.987499	+	0.157627i	$0.0503845\pi$
$150$		0			0
$151$	1.79766e7	+	3.11364e7i	0.424902	+	0.735952i	0.996411	−	0.0846435i	$-0.0269751\pi$
$151$	1.79766e7	+	3.11364e7i	0.424902	+	0.735952i	−0.571509	+	0.820596i	$0.693642\pi$
$152$	6.91539e6			0.159722
$153$		0			0
$154$	5.10451e7			1.12624
$155$	−780845.	−	1.35246e6i	−0.0168424	−	0.0291719i
$156$		0			0
$157$	2.89045e7	−	5.00641e7i	0.596097	−	1.03247i	−0.397294	−	0.917691i	$-0.630051\pi$
$157$	2.89045e7	−	5.00641e7i	0.596097	−	1.03247i	0.993391	−	0.114779i	$-0.0366159\pi$
$158$	8.18545e6	−	1.41776e7i	0.165098	−	0.285959i
$159$		0			0
$160$	−184260.	−	319147.i	−0.00355640	−	0.00615986i
$161$	−9.46287e7			−1.78703
$162$		0			0
$163$	3.23536e7			0.585148			0.292574	−	0.956243i	$-0.405488\pi$
$163$	3.23536e7			0.585148			0.292574	+	0.956243i	$0.405488\pi$
$164$	−1.68918e6	−	2.92574e6i	−0.0299035	−	0.0517944i
$165$		0			0
$166$	−4.10606e7	+	7.11191e7i	−0.696703	+	1.20672i
$167$	4.33872e7	−	7.51489e7i	0.720866	−	1.24858i	−0.239788	−	0.970825i	$-0.577078\pi$
$167$	4.33872e7	−	7.51489e7i	0.720866	−	1.24858i	0.960653	−	0.277751i	$-0.0895889\pi$
$168$		0			0
$169$	5.23077e6	+	9.05996e6i	0.0833608	+	0.144385i
$170$	1.18951e6			0.0185693
$171$		0			0
$172$	4.81103e7			0.720923
$173$	5.38618e6	+	9.32914e6i	0.0790897	+	0.136987i	0.902857	−	0.429940i	$-0.141465\pi$
$173$	5.38618e6	+	9.32914e6i	0.0790897	+	0.136987i	−0.823768	+	0.566927i	$0.808132\pi$
$174$		0			0
$175$	5.61382e7	−	9.72343e7i	0.791818	−	1.37147i
$176$	−9.07802e6	+	1.57236e7i	−0.125515	+	0.217399i
$177$		0			0
$178$	−3.24950e7	−	5.62829e7i	−0.431863	−	0.748009i
$179$	−3.61175e7			−0.470687			−0.235343	−	0.971912i	$-0.575621\pi$
$179$	−3.61175e7			−0.470687			−0.235343	+	0.971912i	$0.575621\pi$
$180$		0			0
$181$	2.78118e7			0.348621			0.174310	−	0.984691i	$-0.444230\pi$
$181$	2.78118e7			0.348621			0.174310	+	0.984691i	$0.444230\pi$
$182$	4.16351e7	+	7.21140e7i	0.511928	+	0.886686i
$183$		0			0
$184$	1.68291e7	−	2.91488e7i	0.199158	−	0.344952i
$185$	683391.	−	1.18367e6i	0.00793539	−	0.0137445i
$186$		0			0
$187$	−2.93021e7	−	5.07527e7i	−0.327682	−	0.567563i
$188$	6.29499e7			0.690944
$189$		0			0
$190$	1.21520e6			0.0128531
$191$	4.73127e7	+	8.19480e7i	0.491316	+	0.850984i	0.999950	−	0.00999867i	$-0.00318273\pi$
$191$	4.73127e7	+	8.19480e7i	0.491316	+	0.850984i	−0.508634	+	0.860983i	$0.669849\pi$
$192$		0			0
$193$	6.11115e7	−	1.05848e8i	0.611889	−	1.05982i	−0.379033	−	0.925383i	$-0.623743\pi$
$193$	6.11115e7	−	1.05848e8i	0.611889	−	1.05982i	0.990922	−	0.134439i	$-0.0429234\pi$
$194$	5.31728e7	−	9.20980e7i	0.522858	−	0.905616i
$195$		0			0
$196$	−3.99529e7	−	6.92005e7i	−0.379011	−	0.656467i
$197$	−1.37768e8			−1.28385			−0.641926	−	0.766766i	$-0.721864\pi$
$197$	−1.37768e8			−1.28385			−0.641926	+	0.766766i	$0.721864\pi$
$198$		0			0
$199$	−1.62646e8			−1.46305			−0.731524	−	0.681815i	$-0.761191\pi$
$199$	−1.62646e8			−1.46305			−0.731524	+	0.681815i	$0.761191\pi$
$200$	1.99676e7	+	3.45849e7i	0.176491	+	0.305691i
$201$		0			0
$202$	5.34662e7	−	9.26061e7i	0.456404	−	0.790514i
$203$	−1.06879e8	+	1.85120e8i	−0.896721	+	1.55317i
$204$		0			0
$205$	−296829.	−	514123.i	−0.00240640	−	0.00416800i
$206$	1.08258e8			0.862831
$207$		0			0
$208$	−2.96181e7			−0.228210
$209$	−2.99349e7	−	5.18488e7i	−0.226812	−	0.392850i
$210$		0			0
$211$	7.77889e7	−	1.34734e8i	0.570071	−	0.987392i	−0.426487	−	0.904494i	$-0.640249\pi$
$211$	7.77889e7	−	1.34734e8i	0.570071	−	0.987392i	0.996558	−	0.0828986i	$-0.0264178\pi$
$212$	1.98963e7	−	3.44614e7i	0.143416	−	0.248403i
$213$		0			0
$214$	7.58202e7	+	1.31324e8i	0.528855	+	0.916003i
$215$	8.45413e6			0.0580142
$216$		0			0
$217$	1.99888e8			1.32794
$218$	5.33026e7	+	9.23228e7i	0.348458	+	0.603547i
$219$		0			0
$220$	−1.59522e6	+	2.76301e6i	−0.0101005	+	0.0174946i
$221$	4.78007e7	−	8.27932e7i	0.297894	−	0.515967i
$222$		0			0
$223$	6.19714e7	+	1.07338e8i	0.374218	+	0.648164i	0.990210	−	0.139588i	$-0.0445779\pi$
$223$	6.19714e7	+	1.07338e8i	0.374218	+	0.648164i	−0.615992	+	0.787752i	$0.711245\pi$
$224$	4.71685e7			0.280404
$225$		0			0
$226$	1.63414e8			0.941694
$227$	6.88520e7	+	1.19255e8i	0.390685	+	0.676685i	0.992540	−	0.121920i	$-0.0389050\pi$
$227$	6.88520e7	+	1.19255e8i	0.390685	+	0.676685i	−0.601855	+	0.798605i	$0.705572\pi$
$228$		0			0
$229$	−1.17560e8	+	2.03621e8i	−0.646899	+	1.12046i	0.336960	+	0.941519i	$0.390601\pi$
$229$	−1.17560e8	+	2.03621e8i	−0.646899	+	1.12046i	−0.983859	+	0.178944i	$0.942732\pi$
$230$	2.95727e6	−	5.12214e6i	0.0160267	−	0.0277590i
$231$		0			0
$232$	−3.80155e7	−	6.58448e7i	−0.199872	−	0.346189i
$233$	−1.44039e8			−0.745992			−0.372996	−	0.927833i	$-0.621670\pi$
$233$	−1.44039e8			−0.745992			−0.372996	+	0.927833i	$0.621670\pi$
$234$		0			0
$235$	1.10618e7			0.0556017
$236$	−2.60549e7	−	4.51284e7i	−0.129032	−	0.223490i
$237$		0			0
$238$	−7.61254e7	+	1.31853e8i	−0.366025	+	0.633974i
$239$	−3.65693e7	+	6.33399e7i	−0.173270	+	0.300113i	−0.939561	−	0.342381i	$-0.888767\pi$
$239$	−3.65693e7	+	6.33399e7i	−0.173270	+	0.300113i	0.766291	+	0.642494i	$0.222100\pi$
$240$		0			0
$241$	6.14199e7	+	1.06382e8i	0.282650	+	0.489564i	0.972037	−	0.234829i	$-0.0754531\pi$
$241$	6.14199e7	+	1.06382e8i	0.282650	+	0.489564i	−0.689386	+	0.724394i	$0.742120\pi$
$242$	1.28817e6			0.00584278
$243$		0			0
$244$	−1.58050e8			−0.696514
$245$	−7.02067e6	−	1.21602e7i	−0.0304998	−	0.0528273i
$246$		0			0
$247$	4.88330e7	−	8.45812e7i	0.206193	−	0.357137i
$248$	−3.55488e7	+	6.15723e7i	−0.147994	+	0.256333i
$249$		0			0
$250$	7.02326e6	+	1.21646e7i	0.0284281	+	0.0492390i
$251$	7.30348e7			0.291522			0.145761	−	0.989320i	$-0.453437\pi$
$251$	7.30348e7			0.291522			0.145761	+	0.989320i	$0.453437\pi$
$252$		0			0
$253$	−2.91395e8			−1.13125
$254$	−4.55383e7	−	7.88746e7i	−0.174365	−	0.302009i
$255$		0			0
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	−6.69979e7	+	1.16044e8i	−0.246204	+	0.426438i	−0.962469	−	0.271390i	$-0.912517\pi$
$257$	−6.69979e7	+	1.16044e8i	−0.246204	+	0.426438i	0.716265	+	0.697828i	$0.245850\pi$
$258$		0			0
$259$	8.74705e7	+	1.51503e8i	0.312833	+	0.541842i
$260$	−5.20460e6			−0.0183646
$261$		0			0
$262$	4.22543e7			0.145150
$263$	−1.90065e8	−	3.29202e8i	−0.644253	−	1.11588i	−0.984473	−	0.175534i	$-0.943835\pi$
$263$	−1.90065e8	−	3.29202e8i	−0.644253	−	1.11588i	0.340220	−	0.940346i	$-0.389498\pi$
$264$		0			0
$265$	3.49625e6	−	6.05568e6i	0.0115410	−	0.0199895i
$266$	−7.77695e7	+	1.34701e8i	−0.253351	+	0.438818i
$267$		0			0
$268$	−1.10554e8	−	1.91485e8i	−0.350835	−	0.607664i
$269$	5.57685e8			1.74685			0.873426	−	0.486958i	$-0.161893\pi$
$269$	5.57685e8			1.74685			0.873426	+	0.486958i	$0.161893\pi$
$270$		0			0
$271$	−9.65793e7			−0.294776			−0.147388	−	0.989079i	$-0.547087\pi$
$271$	−9.65793e7			−0.294776			−0.147388	+	0.989079i	$0.547087\pi$
$272$	−2.70768e7	−	4.68984e7i	−0.0815842	−	0.141308i
$273$		0			0
$274$	−1.96045e8	+	3.39561e8i	−0.575745	+	0.997219i
$275$	1.72869e8	−	2.99418e8i	0.501249	−	0.868188i
$276$		0			0
$277$	−2.82900e8	−	4.89997e8i	−0.799749	−	1.38521i	−0.919779	−	0.392436i	$-0.871633\pi$
$277$	−2.82900e8	−	4.89997e8i	−0.799749	−	1.38521i	0.120030	−	0.992770i	$-0.461701\pi$
$278$	−1.51035e8			−0.421621
$279$		0			0
$280$	8.28863e6			0.0225647
$281$	−1.99775e8	−	3.46020e8i	−0.537117	−	0.930314i	−0.999058	−	0.0434033i	$-0.986180\pi$
$281$	−1.99775e8	−	3.46020e8i	−0.537117	−	0.930314i	0.461940	−	0.886911i	$-0.347153\pi$
$282$		0			0
$283$	−3.39361e8	+	5.87791e8i	−0.890040	+	1.54160i	−0.0502152	+	0.998738i	$0.515991\pi$
$283$	−3.39361e8	+	5.87791e8i	−0.890040	+	1.54160i	−0.839825	+	0.542857i	$0.817343\pi$
$284$	−1.16504e8	+	2.01791e8i	−0.301806	+	0.522743i
$285$		0			0
$286$	1.28209e8	+	2.22064e8i	0.324069	+	0.561303i
$287$	7.59851e7			0.189732
$288$		0			0
$289$	−2.35541e8			−0.574017
$290$	−6.68023e6	−	1.15705e7i	−0.0160842	−	0.0278586i
$291$		0			0
$292$	1.77619e8	−	3.07645e8i	0.417494	−	0.723120i
$293$	−5.58695e7	+	9.67688e7i	−0.129759	+	0.224750i	−0.923583	−	0.383398i	$-0.874754\pi$
$293$	−5.58695e7	+	9.67688e7i	−0.129759	+	0.224750i	0.793824	+	0.608148i	$0.208087\pi$
$294$		0			0
$295$	−4.57847e6	−	7.93014e6i	−0.0103835	−	0.0179847i
$296$	−6.22242e7			−0.139456
$297$		0			0
$298$	−2.30798e8			−0.505214
$299$	−2.37677e8	−	4.11669e8i	−0.514207	−	0.890633i
$300$		0			0
$301$	−5.41042e8	+	9.37112e8i	−1.14353	+	1.98065i
$302$	1.43813e8	−	2.49092e8i	0.300451	−	0.520397i
$303$		0			0
$304$	−2.76616e7	−	4.79112e7i	−0.0564702	−	0.0978092i
$305$	−2.77731e7			−0.0560500
$306$		0			0
$307$	−1.53022e8			−0.301835			−0.150917	−	0.988546i	$-0.548223\pi$
$307$	−1.53022e8			−0.301835			−0.150917	+	0.988546i	$0.548223\pi$
$308$	−2.04180e8	−	3.53651e8i	−0.398186	−	0.689679i
$309$		0			0
$310$	−6.24676e6	+	1.08197e7i	−0.0119094	+	0.0206276i
$311$	1.14184e8	−	1.97772e8i	0.215250	−	0.372825i	−0.738100	−	0.674692i	$-0.764277\pi$
$311$	1.14184e8	−	1.97772e8i	0.215250	−	0.372825i	0.953350	+	0.301867i	$0.0976099\pi$
$312$		0			0
$313$	3.51372e8	+	6.08594e8i	0.647682	+	1.12182i	0.983675	+	0.179954i	$0.0575950\pi$
$313$	3.51372e8	+	6.08594e8i	0.647682	+	1.12182i	−0.335993	+	0.941865i	$0.609072\pi$
$314$	−4.62472e8			−0.843008
$315$		0			0
$316$	−1.30967e8			−0.233484
$317$	5.20588e8	+	9.01686e8i	0.917883	+	1.58982i	0.802625	+	0.596484i	$0.203436\pi$
$317$	5.20588e8	+	9.01686e8i	0.917883	+	1.58982i	0.115257	+	0.993336i	$0.463231\pi$
$318$		0			0
$319$	−3.29118e8	+	5.70050e8i	−0.567655	+	0.983208i
$320$	−1.47408e6	+	2.55318e6i	−0.00251475	+	0.00435568i
$321$		0			0
$322$	3.78515e8	+	6.55607e8i	0.631811	+	1.09433i
$323$	1.78572e8			0.294853
$324$		0			0
$325$	5.64005e8			0.911363
$326$	−1.29414e8	−	2.24152e8i	−0.206881	−	0.358328i
$327$		0			0
$328$	−1.35134e7	+	2.34060e7i	−0.0211450	+	0.0366242i
$329$	−7.07926e8	+	1.22616e9i	−1.09598	+	1.89829i
$330$		0			0
$331$	−1.60638e8	−	2.78233e8i	−0.243472	−	0.421706i	0.718229	−	0.695807i	$-0.244953\pi$
$331$	−1.60638e8	−	2.78233e8i	−0.243472	−	0.421706i	−0.961701	+	0.274101i	$0.911620\pi$
$332$	6.56970e8			0.985286
$333$		0			0
$334$	−6.94196e8			−1.01946
$335$	−1.94270e7	−	3.36485e7i	−0.0282324	−	0.0489000i
$336$		0			0
$337$	4.56823e8	−	7.91241e8i	0.650194	−	1.12617i	−0.332881	−	0.942969i	$-0.608021\pi$
$337$	4.56823e8	−	7.91241e8i	0.650194	−	1.12617i	0.983075	−	0.183201i	$-0.0586459\pi$
$338$	4.18462e7	−	7.24797e7i	0.0589450	−	0.102096i
$339$		0			0
$340$	−4.75804e6	−	8.24116e6i	−0.00656525	−	0.0113714i
$341$	6.15525e8			0.840631
$342$		0			0
$343$	6.11754e8			0.818554
$344$	−1.92441e8	−	3.33318e8i	−0.254885	−	0.441473i
$345$		0			0
$346$	4.30895e7	−	7.46331e7i	0.0559248	−	0.0968646i
$347$	2.98992e8	−	5.17869e8i	0.384155	−	0.665376i	−0.607497	−	0.794322i	$-0.707826\pi$
$347$	2.98992e8	−	5.17869e8i	0.384155	−	0.665376i	0.991652	+	0.128946i	$0.0411595\pi$
$348$		0			0
$349$	−3.25273e8	−	5.63390e8i	−0.409599	−	0.709447i	0.585245	−	0.810856i	$-0.300998\pi$
$349$	−3.25273e8	−	5.63390e8i	−0.409599	−	0.709447i	−0.994845	+	0.101409i	$0.967665\pi$
$350$	−8.98212e8			−1.11980
$351$		0			0
$352$	1.45248e8			0.177506
$353$	3.08623e7	+	5.34551e7i	0.0373437	+	0.0646811i	0.884093	−	0.467311i	$-0.154777\pi$
$353$	3.08623e7	+	5.34551e7i	0.0373437	+	0.0646811i	−0.846750	+	0.531992i	$0.821444\pi$
$354$		0			0
$355$	−2.04726e7	+	3.54595e7i	−0.0242869	+	0.0420662i
$356$	−2.59960e8	+	4.50264e8i	−0.305373	+	0.528922i
$357$		0			0
$358$	1.44470e8	+	2.50229e8i	0.166413	+	0.288235i
$359$	1.70542e9			1.94537			0.972683	−	0.232137i	$-0.0745719\pi$
$359$	1.70542e9			1.94537			0.972683	+	0.232137i	$0.0745719\pi$
$360$		0			0
$361$	−7.11443e8			−0.795912
$362$	−1.11247e8	−	1.92686e8i	−0.123256	−	0.213486i
$363$		0			0
$364$	3.33080e8	−	5.76912e8i	0.361988	−	0.626982i
$365$	3.12119e7	−	5.40606e7i	0.0335966	−	0.0581910i
$366$		0			0
$367$	−1.21509e8	−	2.10460e8i	−0.128315	−	0.222248i	0.794709	−	0.606991i	$-0.207624\pi$
$367$	−1.21509e8	−	2.10460e8i	−0.128315	−	0.222248i	−0.923024	+	0.384743i	$0.874290\pi$
$368$	−2.69265e8			−0.281652
$369$		0			0
$370$	−1.09343e7			−0.0112223
$371$	4.47501e8	+	7.75095e8i	0.454973	+	0.788037i
$372$		0			0
$373$	3.29270e8	−	5.70313e8i	0.328528	−	0.569026i	−0.653692	−	0.756760i	$-0.726781\pi$
$373$	3.29270e8	−	5.70313e8i	0.328528	−	0.569026i	0.982220	+	0.187734i	$0.0601143\pi$
$374$	−2.34417e8	+	4.06022e8i	−0.231706	+	0.401327i
$375$		0			0
$376$	−2.51800e8	−	4.36130e8i	−0.244286	−	0.423115i
$377$	−1.07379e9			−1.03210
$378$		0			0
$379$	1.55665e7			0.0146877			0.00734387	−	0.999973i	$-0.497662\pi$
$379$	1.55665e7			0.0146877			0.00734387	+	0.999973i	$0.497662\pi$
$380$	−4.86079e6	−	8.41914e6i	−0.00454427	−	0.00787091i
$381$		0			0
$382$	3.78501e8	−	6.55584e8i	0.347413	−	0.601737i
$383$	4.33940e8	−	7.51606e8i	0.394670	−	0.683588i	−0.598389	−	0.801206i	$-0.704192\pi$
$383$	4.33940e8	−	7.51606e8i	0.394670	−	0.683588i	0.993059	+	0.117617i	$0.0375256\pi$
$384$		0			0
$385$	−3.58793e7	−	6.21448e7i	−0.0320429	−	0.0554999i
$386$	−9.77784e8			−0.865342
$387$		0			0
$388$	−8.50765e8			−0.739432
$389$	8.92558e8	+	1.54596e9i	0.768799	+	1.33160i	0.938215	+	0.346054i	$0.112479\pi$
$389$	8.92558e8	+	1.54596e9i	0.768799	+	1.33160i	−0.169416	+	0.985545i	$0.554188\pi$
$390$		0			0
$391$	4.34568e8	−	7.52694e8i	0.367654	−	0.636795i
$392$	−3.19623e8	+	5.53604e8i	−0.268002	+	0.464192i
$393$		0			0
$394$	5.51070e8	+	9.54481e8i	0.453910	+	0.786196i
$395$	−2.30140e7			−0.0187890
$396$		0			0
$397$	1.49554e9			1.19958			0.599792	−	0.800156i	$-0.295250\pi$
$397$	1.49554e9			1.19958			0.599792	+	0.800156i	$0.295250\pi$
$398$	6.50586e8	+	1.12685e9i	0.517266	+	0.895931i
$399$		0			0
$400$	1.59741e8	−	2.76679e8i	0.124798	−	0.216156i
$401$	5.21084e8	−	9.02543e8i	0.403554	−	0.698977i	−0.590598	−	0.806966i	$-0.701108\pi$
$401$	5.21084e8	−	9.02543e8i	0.403554	−	0.698977i	0.994152	+	0.107989i	$0.0344413\pi$
$402$		0			0
$403$	5.02055e8	+	8.69585e8i	0.382106	+	0.661827i
$404$	−8.55458e8			−0.645452
$405$		0			0
$406$	1.71007e9			1.26815
$407$	2.69352e8	+	4.66532e8i	0.198034	+	0.343005i
$408$		0			0
$409$	−6.94223e8	+	1.20243e9i	−0.501727	+	0.869017i	0.498271	+	0.867021i	$0.333968\pi$
$409$	−6.94223e8	+	1.20243e9i	−0.501727	+	0.869017i	−0.999998	+	0.00199527i	$0.999365\pi$
$410$	−2.37463e6	+	4.11298e6i	−0.00170158	+	0.00294722i
$411$		0			0
$412$	−4.33033e8	−	7.50035e8i	−0.305057	−	0.528374i
$413$	1.17204e9			0.818685
$414$		0			0
$415$	1.15445e8			0.0792880
$416$	1.18472e8	+	2.05200e8i	0.0806845	+	0.139750i
$417$		0			0
$418$	−2.39479e8	+	4.14790e8i	−0.160380	+	0.277787i
$419$	5.35466e8	−	9.27454e8i	0.355617	−	0.615947i	−0.631606	−	0.775289i	$-0.717604\pi$
$419$	5.35466e8	−	9.27454e8i	0.355617	−	0.615947i	0.987223	+	0.159342i	$0.0509373\pi$
$420$		0			0
$421$	−3.33942e8	−	5.78405e8i	−0.218114	−	0.377785i	0.736117	−	0.676854i	$-0.236657\pi$
$421$	−3.33942e8	−	5.78405e8i	−0.218114	−	0.377785i	−0.954231	+	0.299069i	$0.903324\pi$
$422$	−1.24462e9			−0.806203
$423$		0			0
$424$	−3.18341e8			−0.202820
$425$	5.15613e8	+	8.93068e8i	0.325809	+	0.564317i
$426$		0			0
$427$	1.77741e9	−	3.07856e9i	1.10481	−	1.91359i
$428$	6.06561e8	−	1.05059e9i	0.373957	−	0.647712i
$429$		0			0
$430$	−3.38165e7	−	5.85719e7i	−0.0205111	−	0.0355263i
$431$	−8.88266e8			−0.534408			−0.267204	−	0.963640i	$-0.586100\pi$
$431$	−8.88266e8			−0.534408			−0.267204	+	0.963640i	$0.586100\pi$
$432$		0			0
$433$	1.04197e9			0.616806			0.308403	−	0.951256i	$-0.400205\pi$
$433$	1.04197e9			0.616806			0.308403	+	0.951256i	$0.400205\pi$
$434$	−7.99552e8	−	1.38487e9i	−0.469497	−	0.813193i
$435$		0			0
$436$	4.26421e8	−	7.38583e8i	0.246397	−	0.426772i
$437$	4.43953e8	−	7.68949e8i	0.254479	−	0.440771i
$438$		0			0
$439$	−1.36180e9	−	2.35870e9i	−0.768223	−	1.33060i	−0.938526	−	0.345209i	$-0.887808\pi$
$439$	−1.36180e9	−	2.35870e9i	−0.768223	−	1.33060i	0.170303	−	0.985392i	$-0.445525\pi$
$440$	2.55236e7			0.0142842
$441$		0			0
$442$	−7.64811e8			−0.421285
$443$	−7.09330e8	−	1.22860e9i	−0.387646	−	0.671422i	0.604487	−	0.796615i	$-0.293378\pi$
$443$	−7.09330e8	−	1.22860e9i	−0.387646	−	0.671422i	−0.992132	+	0.125193i	$0.960045\pi$
$444$		0			0
$445$	−4.56811e7	+	7.91220e7i	−0.0245740	+	0.0425635i
$446$	4.95771e8	−	8.58701e8i	0.264612	−	0.458321i
$447$		0			0
$448$	−1.88674e8	−	3.26793e8i	−0.0991378	−	0.171712i
$449$	−3.79133e9			−1.97665			−0.988324	−	0.152368i	$-0.951310\pi$
$449$	−3.79133e9			−1.97665			−0.988324	+	0.152368i	$0.951310\pi$
$450$		0			0
$451$	2.33984e8			0.120107
$452$	−6.53656e8	−	1.13217e9i	−0.332939	−	0.576667i
$453$		0			0
$454$	5.50816e8	−	9.54042e8i	0.276256	−	0.478489i
$455$	5.85301e7	−	1.01377e8i	0.0291299	−	0.0504545i
$456$		0			0
$457$	−9.36482e8	−	1.62204e9i	−0.458979	−	0.794975i	0.539928	−	0.841711i	$-0.318451\pi$
$457$	−9.36482e8	−	1.62204e9i	−0.458979	−	0.794975i	−0.998907	+	0.0467359i	$0.985118\pi$
$458$	1.88097e9			0.914854
$459$		0			0
$460$	−4.73163e7			−0.0226651
$461$	−2.73697e8	−	4.74057e8i	−0.130112	−	0.225360i	0.793608	−	0.608430i	$-0.208200\pi$
$461$	−2.73697e8	−	4.74057e8i	−0.130112	−	0.225360i	−0.923719	+	0.383070i	$0.874867\pi$
$462$		0			0
$463$	5.61388e8	−	9.72353e8i	0.262863	−	0.455292i	−0.704138	−	0.710063i	$-0.748667\pi$
$463$	5.61388e8	−	9.72353e8i	0.262863	−	0.455292i	0.967002	+	0.254770i	$0.0819999\pi$
$464$	−3.04124e8	+	5.26758e8i	−0.141331	+	0.244793i
$465$		0			0
$466$	5.76156e8	+	9.97931e8i	0.263748	+	0.456825i
$467$	2.32612e9			1.05687			0.528436	−	0.848973i	$-0.322779\pi$
$467$	2.32612e9			1.05687			0.528436	+	0.848973i	$0.322779\pi$
$468$		0			0
$469$	4.97310e9			2.22599
$470$	−4.42472e7	−	7.66384e7i	−0.0196582	−	0.0340489i
$471$		0			0
$472$	−2.08439e8	+	3.61028e8i	−0.0912395	+	0.158031i
$473$	−1.66606e9	+	2.88570e9i	−0.723895	+	1.25382i
$474$		0			0
$475$	5.26748e8	+	9.12355e8i	0.225515	+	0.390603i
$476$	1.21801e9			0.517637
$477$		0			0
$478$	5.85109e8			0.245041
$479$	8.84067e8	+	1.53125e9i	0.367545	+	0.636607i	0.989181	−	0.146699i	$-0.0468649\pi$
$479$	8.84067e8	+	1.53125e9i	0.367545	+	0.636607i	−0.621636	+	0.783306i	$0.713532\pi$
$480$		0			0
$481$	−4.39396e8	+	7.61056e8i	−0.180031	+	0.311823i
$482$	4.91359e8	−	8.51059e8i	0.199864	−	0.346174i
$483$		0			0
$484$	−5.15268e6	−	8.92471e6i	−0.00206573	−	0.00357796i
$485$	−1.49500e8			−0.0595037
$486$		0			0
$487$	−1.97414e9			−0.774509			−0.387254	−	0.921973i	$-0.626577\pi$
$487$	−1.97414e9			−0.774509			−0.387254	+	0.921973i	$0.626577\pi$
$488$	6.32200e8	+	1.09500e9i	0.246255	+	0.426526i
$489$		0			0
$490$	−5.61654e7	+	9.72813e7i	−0.0215666	+	0.0373545i
$491$	1.75190e9	−	3.03438e9i	0.667920	−	1.15687i	−0.310564	−	0.950552i	$-0.600518\pi$
$491$	1.75190e9	−	3.03438e9i	0.667920	−	1.15687i	0.978485	−	0.206320i	$-0.0661487\pi$
$492$		0			0
$493$	−9.81654e8	−	1.70027e9i	−0.368973	−	0.639079i
$494$	−7.81328e8			−0.291601
$495$		0			0
$496$	5.68780e8			0.209295
$497$	−2.62038e9	−	4.53863e9i	−0.957452	−	1.65836i
$498$		0			0
$499$	−4.37327e8	+	7.57473e8i	−0.157563	+	0.272907i	−0.933989	−	0.357301i	$-0.883697\pi$
$499$	−4.37327e8	+	7.57473e8i	−0.157563	+	0.272907i	0.776426	+	0.630208i	$0.217030\pi$
$500$	5.61861e7	−	9.73171e7i	0.0201017	−	0.0348172i
$501$		0			0
$502$	−2.92139e8	−	5.06000e8i	−0.103069	−	0.178520i
$503$	−2.61478e9			−0.916111			−0.458055	−	0.888924i	$-0.651454\pi$
$503$	−2.61478e9			−0.916111			−0.458055	+	0.888924i	$0.651454\pi$
$504$		0			0
$505$	−1.50324e8			−0.0519409
$506$	1.16558e9	+	2.01884e9i	0.399959	+	0.692748i
$507$		0			0
$508$	−3.64306e8	+	6.30997e8i	−0.123294	+	0.213552i
$509$	−4.26286e8	+	7.38349e8i	−0.143281	+	0.248170i	−0.928730	−	0.370756i	$-0.879099\pi$
$509$	−4.26286e8	+	7.38349e8i	−0.143281	+	0.248170i	0.785449	+	0.618926i	$0.212432\pi$
$510$		0			0
$511$	3.99496e9	+	6.91947e9i	1.32446	+	2.29403i
$512$	1.34218e8			0.0441942
$513$		0			0
$514$	1.07197e9			0.348185
$515$	−7.60942e7	−	1.31799e8i	−0.0245486	−	0.0425194i
$516$		0			0
$517$	−2.17995e9	+	3.77578e9i	−0.693793	+	1.20168i
$518$	6.99764e8	−	1.21203e9i	0.221206	−	0.383140i
$519$		0			0
$520$	2.08184e7	+	3.60585e7i	0.00649285	+	0.0112459i
$521$	−2.66940e9			−0.826954			−0.413477	−	0.910515i	$-0.635686\pi$
$521$	−2.66940e9			−0.826954			−0.413477	+	0.910515i	$0.635686\pi$
$522$		0			0
$523$	−4.41770e9			−1.35033			−0.675165	−	0.737667i	$-0.735928\pi$
$523$	−4.41770e9			−1.35033			−0.675165	+	0.737667i	$0.735928\pi$
$524$	−1.69017e8	−	2.92747e8i	−0.0513182	−	0.0888858i
$525$		0			0
$526$	−1.52052e9	+	2.63362e9i	−0.455556	+	0.789046i
$527$	−9.17956e8	+	1.58995e9i	−0.273203	+	0.473201i
$528$		0			0
$529$	−4.58369e8	−	7.93919e8i	−0.134623	−	0.233175i
$530$	−5.59400e7			−0.0163214
$531$		0			0
$532$	1.24431e9			0.358293
$533$	1.90850e8	+	3.30562e8i	0.0545943	+	0.0945601i
$534$		0			0
$535$	1.06587e8	−	1.84614e8i	0.0300931	−	0.0521228i
$536$	−8.84433e8	+	1.53188e9i	−0.248078	+	0.429684i
$537$		0			0
$538$	−2.23074e9	−	3.86375e9i	−0.617605	−	1.06972i
$539$	5.53426e9			1.52230
$540$		0			0
$541$	−3.86240e9			−1.04874			−0.524368	−	0.851492i	$-0.675699\pi$
$541$	−3.86240e9			−1.04874			−0.524368	+	0.851492i	$0.675699\pi$
$542$	3.86317e8	+	6.69121e8i	0.104219	+	0.180513i
$543$		0			0
$544$	−2.16614e8	+	3.75187e8i	−0.0576888	+	0.0999199i
$545$	7.49323e7	−	1.29786e8i	0.0198281	−	0.0343433i
$546$		0			0
$547$	1.08461e9	+	1.87859e9i	0.283346	+	0.490769i	0.972207	−	0.234124i	$-0.0752223\pi$
$547$	1.08461e9	+	1.87859e9i	0.283346	+	0.490769i	−0.688861	+	0.724894i	$0.741889\pi$
$548$	3.13673e9			0.814226
$549$		0			0
$550$	−2.76591e9			−0.708873
$551$	−1.00285e9	−	1.73699e9i	−0.255392	−	0.442352i
$552$		0			0
$553$	1.47284e9	−	2.55103e9i	0.370354	−	0.641472i
$554$	−2.26320e9	+	3.91998e9i	−0.565508	+	0.979489i
$555$		0			0
$556$	6.04142e8	+	1.04640e9i	0.149066	+	0.258189i
$557$	2.25645e8			0.0553265			0.0276632	−	0.999617i	$-0.491193\pi$
$557$	2.25645e8			0.0553265			0.0276632	+	0.999617i	$0.491193\pi$
$558$		0			0
$559$	−5.43570e9			−1.31618
$560$	−3.31545e7	−	5.74253e7i	−0.00797783	−	0.0138180i
$561$		0			0
$562$	−1.59820e9	+	2.76816e9i	−0.379799	+	0.657831i
$563$	−3.90401e8	+	6.76194e8i	−0.0922001	+	0.159695i	−0.908437	−	0.418023i	$-0.862723\pi$
$563$	−3.90401e8	+	6.76194e8i	−0.0922001	+	0.159695i	0.816237	+	0.577718i	$0.196057\pi$
$564$		0			0
$565$	−1.14863e8	−	1.98948e8i	−0.0267923	−	0.0464056i
$566$	5.42978e9			1.25871
$567$		0			0
$568$	1.86407e9			0.426818
$569$	3.34607e8	+	5.79557e8i	0.0761452	+	0.131887i	0.901584	−	0.432605i	$-0.142405\pi$
$569$	3.34607e8	+	5.79557e8i	0.0761452	+	0.131887i	−0.825439	+	0.564492i	$0.809072\pi$
$570$		0			0
$571$	6.68261e8	−	1.15746e9i	0.150217	−	0.260184i	−0.781090	−	0.624418i	$-0.785336\pi$
$571$	6.68261e8	−	1.15746e9i	0.150217	−	0.260184i	0.931307	+	0.364235i	$0.118669\pi$
$572$	1.02567e9	−	1.77651e9i	0.229151	−	0.396901i
$573$		0			0
$574$	−3.03940e8	−	5.26440e8i	−0.0670805	−	0.116187i
$575$	5.12751e9			1.12478
$576$		0			0
$577$	−7.13624e9			−1.54651			−0.773257	−	0.634092i	$-0.781374\pi$
$577$	−7.13624e9			−1.54651			−0.773257	+	0.634092i	$0.781374\pi$
$578$	9.42165e8	+	1.63188e9i	0.202946	+	0.351512i
$579$		0			0
$580$	−5.34418e7	+	9.25639e7i	−0.0113732	+	0.0196990i
$581$	−7.38819e9	+	1.27967e10i	−1.56287	+	2.70696i
$582$		0			0
$583$	1.37801e9	+	2.38679e9i	0.288014	+	0.498855i
$584$	−2.84191e9			−0.590425
$585$		0			0
$586$	8.93912e8			0.183507
$587$	−1.42735e9	−	2.47224e9i	−0.291271	−	0.504496i	0.682839	−	0.730568i	$-0.260745\pi$
$587$	−1.42735e9	−	2.47224e9i	−0.291271	−	0.504496i	−0.974111	+	0.226072i	$0.927411\pi$
$588$		0			0
$589$	−9.37781e8	+	1.62428e9i	−0.189103	+	0.327535i
$590$	−3.66277e7	+	6.34411e7i	−0.00734223	+	0.0127171i
$591$		0			0
$592$	2.48897e8	+	4.31102e8i	0.0493052	+	0.0853992i
$593$	−6.55017e9			−1.28991			−0.644957	−	0.764219i	$-0.723125\pi$
$593$	−6.55017e9			−1.28991			−0.644957	+	0.764219i	$0.723125\pi$
$594$		0			0
$595$	2.14033e8			0.0416553
$596$	9.23192e8	+	1.59902e9i	0.178620	+	0.309379i
$597$		0			0
$598$	−1.90142e9	+	3.29335e9i	−0.363599	+	0.629773i
$599$	3.75708e9	−	6.50744e9i	0.714259	−	1.23713i	−0.248985	−	0.968507i	$-0.580097\pi$
$599$	3.75708e9	−	6.50744e9i	0.714259	−	1.23713i	0.963244	−	0.268626i	$-0.0865697\pi$
$600$		0			0
$601$	1.70371e9	+	2.95092e9i	0.320137	+	0.554493i	0.980516	−	0.196439i	$-0.0629378\pi$
$601$	1.70371e9	+	2.95092e9i	0.320137	+	0.554493i	−0.660379	+	0.750932i	$0.729604\pi$
$602$	8.65667e9			1.61720
$603$		0			0
$604$	−2.30101e9			−0.424902
$605$	−905448.	−	1.56828e6i	−0.000166234	−	0.000287926i
$606$		0			0
$607$	−2.47151e9	+	4.28078e9i	−0.448540	+	0.776895i	−0.998291	−	0.0584338i	$-0.981389\pi$
$607$	−2.47151e9	+	4.28078e9i	−0.448540	+	0.776895i	0.549751	+	0.835329i	$0.314723\pi$
$608$	−2.21292e8	+	3.83290e8i	−0.0399304	+	0.0691616i
$609$		0			0
$610$	1.11093e8	+	1.92418e8i	0.0198167	+	0.0343235i
$611$	−7.11233e9			−1.26144
$612$		0			0
$613$	4.05250e9			0.710577			0.355288	−	0.934757i	$-0.384383\pi$
$613$	4.05250e9			0.710577			0.355288	+	0.934757i	$0.384383\pi$
$614$	6.12087e8	+	1.06017e9i	0.106715	+	0.184835i
$615$		0			0
$616$	−1.63344e9	+	2.82920e9i	−0.281560	+	0.487676i
$617$	−3.07794e9	+	5.33115e9i	−0.527549	+	0.913741i	0.471936	+	0.881633i	$0.343555\pi$
$617$	−3.07794e9	+	5.33115e9i	−0.527549	+	0.913741i	−0.999484	+	0.0321082i	$0.989778\pi$
$618$		0			0
$619$	−1.82063e8	−	3.15342e8i	−0.0308534	−	0.0534397i	0.850186	−	0.526482i	$-0.176489\pi$
$619$	−1.82063e8	−	3.15342e8i	−0.0308534	−	0.0534397i	−0.881040	+	0.473042i	$0.843156\pi$
$620$	9.99482e7			0.0168424
$621$		0			0
$622$	−1.82694e9			−0.304410
$623$	−5.84694e9	−	1.01272e10i	−0.968770	−	1.67796i
$624$		0			0
$625$	−3.03694e9	+	5.26014e9i	−0.497573	+	0.861822i
$626$	2.81098e9	−	4.86875e9i	0.457981	−	0.793246i
$627$		0			0
$628$	1.84989e9	+	3.20410e9i	0.298048	+	0.516235i
$629$	−1.60678e9			−0.257442
$630$		0			0
$631$	3.22087e9			0.510353			0.255177	−	0.966894i	$-0.417866\pi$
$631$	3.22087e9			0.510353			0.255177	+	0.966894i	$0.417866\pi$
$632$	5.23869e8	+	9.07368e8i	0.0825492	+	0.142979i
$633$		0			0
$634$	4.16471e9	−	7.21349e9i	0.649041	−	1.12417i
$635$	−6.40172e7	+	1.10881e8i	−0.00992176	+	0.0171850i
$636$		0			0
$637$	4.51404e9	+	7.81855e9i	0.691954	+	1.19850i
$638$	5.26590e9			0.802786
$639$		0			0
$640$	2.35852e7			0.00355640
$641$	6.22206e9	+	1.07769e10i	0.933106	+	1.61619i	0.777978	+	0.628292i	$0.216246\pi$
$641$	6.22206e9	+	1.07769e10i	0.933106	+	1.61619i	0.155128	+	0.987894i	$0.450421\pi$
$642$		0			0
$643$	2.41505e8	−	4.18298e8i	0.0358251	−	0.0620509i	−0.847557	−	0.530704i	$-0.821927\pi$
$643$	2.41505e8	−	4.18298e8i	0.0358251	−	0.0620509i	0.883382	+	0.468654i	$0.155261\pi$
$644$	3.02812e9	−	5.24485e9i	0.446758	−	0.773808i
$645$		0			0
$646$	−7.14289e8	−	1.23719e9i	−0.104246	−	0.180560i
$647$	4.60241e9			0.668068			0.334034	−	0.942561i	$-0.391590\pi$
$647$	4.60241e9			0.668068			0.334034	+	0.942561i	$0.391590\pi$
$648$		0			0
$649$	3.60912e9			0.518256
$650$	−2.25602e9	−	3.90754e9i	−0.322215	−	0.558094i
$651$		0			0
$652$	−1.03531e9	+	1.79322e9i	−0.146287	+	0.253376i
$653$	−2.84182e9	+	4.92218e9i	−0.399393	+	0.691769i	−0.993651	−	0.112505i	$-0.964113\pi$
$653$	−2.84182e9	+	4.92218e9i	−0.399393	+	0.691769i	0.594258	+	0.804275i	$0.297446\pi$
$654$		0			0
$655$	−2.97003e7	−	5.14425e7i	−0.00412969	−	0.00715282i
$656$	2.16215e8			0.0299035
$657$		0			0
$658$	1.13268e10			1.54995
$659$	−2.25571e9	−	3.90700e9i	−0.307032	−	0.531796i	0.670679	−	0.741747i	$-0.266003\pi$
$659$	−2.25571e9	−	3.90700e9i	−0.307032	−	0.531796i	−0.977712	+	0.209952i	$0.932669\pi$
$660$		0			0
$661$	−4.88093e8	+	8.45401e8i	−0.0657351	+	0.113856i	−0.897020	−	0.441990i	$-0.854273\pi$
$661$	−4.88093e8	+	8.45401e8i	−0.0657351	+	0.113856i	0.831285	+	0.555847i	$0.187606\pi$
$662$	−1.28510e9	+	2.22586e9i	−0.172161	+	0.298191i
$663$		0			0
$664$	−2.62788e9	−	4.55162e9i	−0.348351	−	0.603362i
$665$	2.18655e8			0.0288326
$666$		0			0
$667$	−9.76206e9			−1.27380
$668$	2.77678e9	+	4.80953e9i	0.360433	+	0.624288i
$669$		0			0
$670$	−1.55416e8	+	2.69188e8i	−0.0199634	+	0.0345775i
$671$	5.47326e9	−	9.47996e9i	0.699386	−	1.21137i
$672$		0			0
$673$	−6.26231e9	−	1.08466e10i	−0.791921	−	1.37165i	−0.924776	−	0.380513i	$-0.875748\pi$
$673$	−6.26231e9	−	1.08466e10i	−0.791921	−	1.37165i	0.132854	−	0.991136i	$-0.457586\pi$
$674$	−7.30917e9			−0.919514
$675$		0			0
$676$	−6.69539e8			−0.0833608
$677$	−5.22456e9	−	9.04920e9i	−0.647126	−	1.12086i	−0.983806	−	0.179237i	$-0.942637\pi$
$677$	−5.22456e9	−	9.04920e9i	−0.647126	−	1.12086i	0.336680	−	0.941619i	$-0.390696\pi$
$678$		0			0
$679$	9.56758e9	−	1.65715e10i	1.17289	−	2.03151i
$680$	−3.80643e7	+	6.59293e7i	−0.00464234	+	0.00804076i
$681$		0			0
$682$	−2.46210e9	−	4.26448e9i	−0.297208	−	0.514779i
$683$	1.12280e9			0.134844			0.0674218	−	0.997725i	$-0.478523\pi$
$683$	1.12280e9			0.134844			0.0674218	+	0.997725i	$0.478523\pi$
$684$		0			0
$685$	5.51197e8			0.0655225
$686$	−2.44702e9	−	4.23836e9i	−0.289403	−	0.501260i
$687$		0			0
$688$	−1.53953e9	+	2.66655e9i	−0.180231	+	0.312169i
$689$	−2.24796e9	+	3.89358e9i	−0.261831	+	0.453505i
$690$		0			0
$691$	−3.73022e9	−	6.46092e9i	−0.430091	−	0.744940i	0.566789	−	0.823863i	$-0.308185\pi$
$691$	−3.73022e9	−	6.46092e9i	−0.430091	−	0.744940i	−0.996881	+	0.0789226i	$0.974852\pi$
$692$	−6.89431e8			−0.0790897
$693$		0			0
$694$	−4.78387e9			−0.543277
$695$	1.06162e8	+	1.83878e8i	0.0119956	+	0.0207770i
$696$		0			0
$697$	−3.48950e8	+	6.04399e8i	−0.0390345	+	0.0676097i
$698$	−2.60219e9	+	4.50712e9i	−0.289631	+	0.501655i
$699$		0			0
$700$	3.59285e9	+	6.22299e9i	0.395909	+	0.685735i
$701$	−1.79013e10			−1.96278			−0.981392	−	0.192014i	$-0.938498\pi$
$701$	−1.79013e10			−1.96278			−0.981392	+	0.192014i	$0.938498\pi$
$702$		0			0
$703$	−1.64148e9			−0.178194
$704$	−5.80993e8	−	1.00631e9i	−0.0627577	−	0.108700i
$705$		0			0
$706$	2.46898e8	−	4.27641e8i	0.0264060	−	0.0457365i
$707$	9.62036e9	−	1.66630e10i	1.02382	−	1.77331i
$708$		0			0
$709$	−3.77521e9	−	6.53885e9i	−0.397813	−	0.689032i	0.595643	−	0.803249i	$-0.296897\pi$
$709$	−3.77521e9	−	6.53885e9i	−0.397813	−	0.689032i	−0.993456	+	0.114217i	$0.963564\pi$
$710$	3.27561e8			0.0343469
$711$		0			0
$712$	4.15936e9			0.431863
$713$	4.56431e9	+	7.90562e9i	0.471587	+	0.816812i
$714$		0			0
$715$	1.80235e8	−	3.12176e8i	0.0184403	−	0.0319395i
$716$	1.15576e9	−	2.00183e9i	0.117672	−	0.203813i
$717$		0			0
$718$	−6.82169e9	−	1.18155e10i	−0.687791	−	1.19129i
$719$	−3.79868e9			−0.381137			−0.190569	−	0.981674i	$-0.561033\pi$
$719$	−3.79868e9			−0.381137			−0.190569	+	0.981674i	$0.561033\pi$
$720$		0			0
$721$	1.94793e10			1.93553
$722$	2.84577e9	+	4.92902e9i	0.281397	+	0.487394i
$723$		0			0
$724$	−8.89976e8	+	1.54148e9i	−0.0871552	+	0.150957i
$725$	5.79132e9	−	1.00309e10i	0.564409	−	0.977586i
$726$		0			0
$727$	1.96762e9	+	3.40802e9i	0.189920	+	0.328952i	0.945224	−	0.326424i	$-0.105844\pi$
$727$	1.96762e9	+	3.40802e9i	0.189920	+	0.328952i	−0.755303	+	0.655376i	$0.772510\pi$
$728$	−5.32929e9			−0.511928
$729$		0			0
$730$	−4.99390e8			−0.0475127
$731$	−4.96931e9	−	8.60710e9i	−0.470528	−	0.814978i
$732$		0			0
$733$	5.67457e9	−	9.82865e9i	0.532193	−	0.921785i	−0.467100	−	0.884204i	$-0.654701\pi$
$733$	5.67457e9	−	9.82865e9i	0.532193	−	0.921785i	0.999294	−	0.0375812i	$-0.0119653\pi$
$734$	−9.72073e8	+	1.68368e9i	−0.0907325	+	0.157153i
$735$		0			0
$736$	1.07706e9	+	1.86552e9i	0.0995791	+	0.172476i
$737$	1.53139e10			1.40913
$738$		0			0
$739$	1.61420e10			1.47130			0.735652	−	0.677359i	$-0.236876\pi$
$739$	1.61420e10			1.47130			0.735652	+	0.677359i	$0.236876\pi$
$740$	4.37370e7	+	7.57548e7i	0.00396770	+	0.00687225i
$741$		0			0
$742$	3.58001e9	−	6.20076e9i	0.321715	−	0.557226i
$743$	2.96574e9	−	5.13681e9i	0.265260	−	0.459444i	−0.702371	−	0.711811i	$-0.747875\pi$
$743$	2.96574e9	−	5.13681e9i	0.265260	−	0.459444i	0.967632	+	0.252366i	$0.0812088\pi$
$744$		0			0
$745$	1.62227e8	+	2.80985e8i	0.0143739	+	0.0248964i
$746$	−5.26833e9			−0.464608
$747$		0			0
$748$	3.75067e9			0.327682
$749$	1.36426e10	+	2.36297e10i	1.18634	+	2.05481i
$750$		0			0
$751$	1.67463e9	−	2.90054e9i	0.144271	−	0.249885i	−0.784830	−	0.619711i	$-0.787250\pi$
$751$	1.67463e9	−	2.90054e9i	0.144271	−	0.249885i	0.929101	+	0.369827i	$0.120583\pi$
$752$	−2.01440e9	+	3.48904e9i	−0.172736	+	0.299187i
$753$		0			0
$754$	4.29514e9	+	7.43941e9i	0.364903	+	0.632031i
$755$	−4.04342e8			−0.0341928
$756$		0			0
$757$	−3.71611e9			−0.311353			−0.155677	−	0.987808i	$-0.549756\pi$
$757$	−3.71611e9			−0.311353			−0.155677	+	0.987808i	$0.549756\pi$
$758$	−6.22661e7	−	1.07848e8i	−0.00519290	−	0.00899436i
$759$		0			0
$760$	−3.88863e7	+	6.73531e7i	−0.00321329	+	0.00556557i
$761$	−7.21722e8	+	1.25006e9i	−0.0593641	+	0.102822i	−0.894180	−	0.447707i	$-0.852241\pi$
$761$	−7.21722e8	+	1.25006e9i	−0.0593641	+	0.102822i	0.834816	+	0.550529i	$0.185574\pi$
$762$		0			0
$763$	9.59093e9	+	1.66120e10i	0.781673	+	1.35390i
$764$	−6.05602e9			−0.491316
$765$		0			0
$766$	−6.94304e9			−0.558148
$767$	2.94379e9	+	5.09879e9i	0.235572	+	0.408022i
$768$		0			0
$769$	−5.12495e9	+	8.87668e9i	−0.406394	+	0.703895i	−0.994483	−	0.104901i	$-0.966547\pi$
$769$	−5.12495e9	+	8.87668e9i	−0.406394	+	0.703895i	0.588088	+	0.808797i	$0.299881\pi$
$770$	−2.87034e8	+	4.97158e8i	−0.0226577	+	0.0392443i
$771$		0			0
$772$	3.91114e9	+	6.77429e9i	0.305944	+	0.529911i
$773$	−2.47581e10			−1.92792			−0.963959	−	0.266049i	$-0.914282\pi$
$773$	−2.47581e10			−1.92792			−0.963959	+	0.266049i	$0.914282\pi$
$774$		0			0
$775$	−1.08311e10			−0.835824
$776$	3.40306e9	+	5.89427e9i	0.261429	+	0.452808i
$777$		0			0
$778$	7.14046e9	−	1.23676e10i	0.543623	−	0.941583i
$779$	−3.56486e8	+	6.17452e8i	−0.0270185	+	0.0467974i
$780$		0			0
$781$	−8.06906e9	−	1.39760e10i	−0.606100	−	1.04980i
$782$	−6.95309e9			−0.519941
$783$		0			0
$784$	5.11397e9			0.379011
$785$	3.25069e8	+	5.63036e8i	0.0239846	+	0.0415425i
$786$		0			0
$787$	1.04848e10	−	1.81603e10i	0.766744	−	1.32804i	−0.172575	−	0.984996i	$-0.555209\pi$
$787$	1.04848e10	−	1.81603e10i	0.766744	−	1.32804i	0.939319	−	0.343044i	$-0.111458\pi$
$788$	4.40856e9	−	7.63585e9i	0.320963	−	0.555924i
$789$		0			0
$790$	9.20562e7	+	1.59446e8i	0.00664291	+	0.0115059i
$791$	2.94037e10			2.11244
$792$		0			0
$793$	1.78571e10			1.27161
$794$	−5.98215e9	−	1.03614e10i	−0.424117	−	0.734592i
$795$		0			0
$796$	5.20469e9	−	9.01478e9i	0.365762	−	0.633519i
$797$	−8.17893e9	+	1.41663e10i	−0.572259	+	0.991181i	0.424075	+	0.905627i	$0.360599\pi$
$797$	−8.17893e9	+	1.41663e10i	−0.572259	+	0.991181i	−0.996334	+	0.0855541i	$0.972734\pi$
$798$		0			0
$799$	−6.50209e9	−	1.12619e10i	−0.450961	−	0.781087i
$800$	−2.55586e9			−0.176491
$801$		0			0
$802$	−8.33734e9			−0.570712
$803$	1.23019e10	+	2.13075e10i	0.838430	+	1.45220i
$804$		0			0
$805$	5.32112e8	−	9.21645e8i	0.0359515	−	0.0622699i
$806$	4.01644e9	−	6.95668e9i	0.270190	−	0.467982i
$807$		0			0
$808$	3.42183e9	+	5.92679e9i	0.228202	+	0.395257i
$809$	8.79414e9			0.583947			0.291974	−	0.956426i	$-0.405688\pi$
$809$	8.79414e9			0.583947			0.291974	+	0.956426i	$0.405688\pi$
$810$		0			0
$811$	8.84977e8			0.0582585			0.0291292	−	0.999576i	$-0.490727\pi$
$811$	8.84977e8			0.0582585			0.0291292	+	0.999576i	$0.490727\pi$
$812$	−6.84027e9	−	1.18477e10i	−0.448360	−	0.776583i
$813$		0			0
$814$	2.15482e9	−	3.73225e9i	0.140031	−	0.242541i
$815$	−1.81929e8	+	3.15111e8i	−0.0117720	+	0.0203897i
$816$		0			0
$817$	−5.07663e9	−	8.79297e9i	−0.325685	−	0.564103i
$818$	1.11076e10			0.709549
$819$		0			0
$820$	3.79941e7			0.00240640
$821$	−1.02524e10	−	1.77577e10i	−0.646584	−	1.11992i	−0.983933	−	0.178537i	$-0.942864\pi$
$821$	−1.02524e10	−	1.77577e10i	−0.646584	−	1.11992i	0.337349	−	0.941380i	$-0.390470\pi$
$822$		0			0
$823$	−2.42539e9	+	4.20090e9i	−0.151664	+	0.262690i	−0.931839	−	0.362871i	$-0.881797\pi$
$823$	−2.42539e9	+	4.20090e9i	−0.151664	+	0.262690i	0.780175	+	0.625561i	$0.215130\pi$
$824$	−3.46426e9	+	6.00028e9i	−0.215708	+	0.373617i
$825$		0			0
$826$	−4.68816e9	−	8.12013e9i	−0.289449	−	0.501340i
$827$	1.02887e10			0.632545			0.316272	−	0.948668i	$-0.397569\pi$
$827$	1.02887e10			0.632545			0.316272	+	0.948668i	$0.397569\pi$
$828$		0			0
$829$	3.17520e9			0.193566			0.0967832	−	0.995305i	$-0.469145\pi$
$829$	3.17520e9			0.193566			0.0967832	+	0.995305i	$0.469145\pi$
$830$	−4.61781e8	−	7.99828e8i	−0.0280326	−	0.0485538i
$831$		0			0
$832$	9.47778e8	−	1.64160e9i	0.0570525	−	0.0988179i
$833$	−8.25346e9	+	1.42954e10i	−0.494742	+	0.856918i
$834$		0			0
$835$	4.87947e8	+	8.45148e8i	0.0290048	+	0.0502378i
$836$	3.83167e9			0.226812
$837$		0			0
$838$	−8.56746e9			−0.502919
$839$	1.22074e10	+	2.11438e10i	0.713601	+	1.23599i	0.963497	+	0.267720i	$0.0862702\pi$
$839$	1.22074e10	+	2.11438e10i	0.713601	+	1.23599i	−0.249896	+	0.968273i	$0.580396\pi$
$840$		0			0
$841$	−2.40091e9	+	4.15849e9i	−0.139184	+	0.241074i
$842$	−2.67154e9	+	4.62724e9i	−0.154230	+	0.267134i
$843$		0			0
$844$	4.97849e9	+	8.62300e9i	0.285036	+	0.493696i
$845$	−1.17654e8			−0.00670822
$846$		0			0
$847$	2.31785e8			0.0131067
$848$	1.27336e9	+	2.20553e9i	0.0717078	+	0.124202i
$849$		0			0
$850$	4.12490e9	−	7.14454e9i	0.230381	−	0.399032i
$851$	−3.99466e9	+	6.91895e9i	−0.222191	+	0.384846i
$852$		0			0
$853$	1.05073e9	+	1.81991e9i	0.0579653	+	0.100399i	0.893552	−	0.448960i	$-0.148205\pi$
$853$	1.05073e9	+	1.81991e9i	0.0579653	+	0.100399i	−0.835587	+	0.549359i	$0.814872\pi$
$854$	−2.84385e10			−1.56244
$855$		0			0
$856$	−9.70498e9			−0.528855
$857$	2.16795e9	+	3.75500e9i	0.117657	+	0.203787i	0.918839	−	0.394634i	$-0.129128\pi$
$857$	2.16795e9	+	3.75500e9i	0.117657	+	0.203787i	−0.801182	+	0.598421i	$0.795795\pi$
$858$		0			0
$859$	−1.02072e10	+	1.76793e10i	−0.549451	+	0.951677i	0.448861	+	0.893602i	$0.351830\pi$
$859$	−1.02072e10	+	1.76793e10i	−0.549451	+	0.951677i	−0.998312	+	0.0580756i	$0.981504\pi$
$860$	−2.70532e8	+	4.68575e8i	−0.0145035	+	0.0251209i
$861$		0			0
$862$	3.55306e9	+	6.15409e9i	0.188942	+	0.327257i
$863$	7.33916e9			0.388695			0.194347	−	0.980933i	$-0.437741\pi$
$863$	7.33916e9			0.388695			0.194347	+	0.980933i	$0.437741\pi$
$864$		0			0
$865$	−1.21149e8			−0.00636451
$866$	−4.16789e9	−	7.21900e9i	−0.218074	−	0.377715i
$867$		0			0
$868$	−6.39642e9	+	1.10789e10i	−0.331985	+	0.575014i
$869$	4.53538e9	−	7.85551e9i	0.234447	−	0.406074i
$870$		0			0
$871$	1.24908e10	+	2.16348e10i	0.640513	+	1.10940i
$872$	−6.82273e9			−0.348458
$873$		0			0
$874$	−7.10325e9			−0.359888
$875$	1.26372e9	+	2.18883e9i	0.0637709	+	0.110455i
$876$		0			0
$877$	−3.82404e9	+	6.62343e9i	−0.191436	+	0.331577i	−0.945726	−	0.324964i	$-0.894648\pi$
$877$	−3.82404e9	+	6.62343e9i	−0.191436	+	0.331577i	0.754290	+	0.656541i	$0.227981\pi$
$878$	−1.08944e10	+	1.88696e10i	−0.543215	+	0.940877i
$879$		0			0
$880$	−1.02094e8	−	1.76833e8i	−0.00505024	−	0.00874728i
$881$	2.38502e9			0.117511			0.0587553	−	0.998272i	$-0.481287\pi$
$881$	2.38502e9			0.117511			0.0587553	+	0.998272i	$0.481287\pi$
$882$		0			0
$883$	−1.51552e10			−0.740797			−0.370399	−	0.928873i	$-0.620779\pi$
$883$	−1.51552e10			−0.740797			−0.370399	+	0.928873i	$0.620779\pi$
$884$	3.05924e9	+	5.29877e9i	0.148947	+	0.257983i
$885$		0			0
$886$	−5.67464e9	+	9.82876e9i	−0.274107	+	0.474767i
$887$	1.95358e10	−	3.38371e10i	0.939938	−	1.62802i	0.174357	−	0.984683i	$-0.444215\pi$
$887$	1.95358e10	−	3.38371e10i	0.939938	−	1.62802i	0.765582	−	0.643339i	$-0.222451\pi$
$888$		0			0
$889$	−8.19387e9	−	1.41922e10i	−0.391141	−	0.677475i
$890$	7.30898e8			0.0347529
$891$		0			0
$892$	−7.93234e9			−0.374218
$893$	−6.64251e9	−	1.15052e10i	−0.312142	−	0.540645i
$894$		0			0
$895$	2.03094e8	−	3.51770e8i	0.00946928	−	0.0164013i
$896$	−1.50939e9	+	2.61435e9i	−0.0701010	+	0.121419i
$897$		0			0
$898$	1.51653e10	+	2.62671e10i	0.698850	+	1.21044i
$899$	2.06208e10			0.946557
$900$		0			0
$901$	−8.22033e9			−0.374415
$902$	−9.35938e8	−	1.62109e9i	−0.0424643	−	0.0735504i
$903$		0			0
$904$	−5.22925e9	+	9.05732e9i	−0.235423	+	0.407765i
$905$	−1.56390e8	+	2.70875e8i	−0.00701356	+	0.0121478i
$906$		0			0
$907$	4.84063e9	+	8.38421e9i	0.215415	+	0.373110i	0.953401	−	0.301706i	$-0.0975562\pi$
$907$	4.84063e9	+	8.38421e9i	0.215415	+	0.373110i	−0.737986	+	0.674816i	$0.764223\pi$
$908$	−8.81306e9			−0.390685
$909$		0			0
$910$	−9.36482e8			−0.0411960
$911$	−1.61408e9	−	2.79567e9i	−0.0707312	−	0.122510i	0.828491	−	0.560003i	$-0.189200\pi$
$911$	−1.61408e9	−	2.79567e9i	−0.0707312	−	0.122510i	−0.899222	+	0.437493i	$0.855867\pi$
$912$		0			0
$913$	−2.27508e10	+	3.94056e10i	−0.989349	+	1.71360i
$914$	−7.49186e9	+	1.29763e10i	−0.324547	+	0.562132i
$915$		0			0
$916$	−7.52386e9	−	1.30317e10i	−0.323450	−	0.560231i
$917$	7.60298e9			0.325605
$918$		0			0
$919$	−2.75829e10			−1.17229			−0.586145	−	0.810206i	$-0.699355\pi$
$919$	−2.75829e10			−1.17229			−0.586145	+	0.810206i	$0.699355\pi$
$920$	1.89265e8	+	3.27817e8i	0.00801334	+	0.0138795i
$921$		0			0
$922$	−2.18958e9	+	3.79246e9i	−0.0920029	+	0.159354i
$923$	1.31631e10	−	2.27992e10i	0.551001	−	0.954362i
$924$		0			0
$925$	−4.73964e9	−	8.20930e9i	−0.196902	−	0.341044i
$926$	−8.98221e9			−0.371745
$927$		0			0
$928$	4.86599e9			0.199872
$929$	−1.30557e10	−	2.26132e10i	−0.534251	−	0.925350i	−0.999199	−	0.0400123i	$-0.987260\pi$
$929$	−1.30557e10	−	2.26132e10i	−0.534251	−	0.925350i	0.464948	−	0.885338i	$-0.346073\pi$
$930$		0			0
$931$	−8.43170e9	+	1.46041e10i	−0.342445	+	0.593133i
$932$	4.60925e9	−	7.98345e9i	0.186498	−	0.323024i
$933$		0			0
$934$	−9.30447e9	−	1.61158e10i	−0.373661	−	0.647199i
$935$	6.59081e8			0.0263693
$936$		0			0
$937$	2.33086e10			0.925608			0.462804	−	0.886461i	$-0.346843\pi$
$937$	2.33086e10			0.925608			0.462804	+	0.886461i	$0.346843\pi$
$938$	−1.98924e10	−	3.44547e10i	−0.787005	−	1.36313i
$939$		0			0
$940$	−3.53977e8	+	6.13107e8i	−0.0139004	+	0.0240762i
$941$	−1.17469e10	+	2.03462e10i	−0.459577	+	0.796011i	−0.998939	−	0.0460632i	$-0.985332\pi$
$941$	−1.17469e10	+	2.03462e10i	−0.459577	+	0.796011i	0.539361	+	0.842075i	$0.318666\pi$
$942$		0			0
$943$	1.73507e9	+	3.00522e9i	0.0673791	+	0.116704i
$944$	3.33503e9			0.129032
$945$		0			0
$946$	2.66569e10			1.02374
$947$	−1.67345e10	−	2.89850e10i	−0.640306	−	1.10904i	−0.985364	−	0.170462i	$-0.945474\pi$
$947$	−1.67345e10	−	2.89850e10i	−0.640306	−	1.10904i	0.345058	−	0.938581i	$-0.387859\pi$
$948$		0			0
$949$	−2.00681e10	+	3.47590e10i	−0.762210	+	1.32019i
$950$	4.21399e9	−	7.29884e9i	0.159463	−	0.276198i
$951$		0			0
$952$	−4.87203e9	−	8.43860e9i	−0.183012	−	0.316987i
$953$	3.61551e10			1.35315			0.676573	−	0.736375i	$-0.263464\pi$
$953$	3.61551e10			1.35315			0.676573	+	0.736375i	$0.263464\pi$
$954$		0			0
$955$	−1.06419e9			−0.0395372
$956$	−2.34044e9	−	4.05376e9i	−0.0866352	−	0.150057i
$957$		0			0
$958$	7.07254e9	−	1.22500e10i	0.259894	−	0.450149i
$959$	−3.52752e10	+	6.10984e10i	−1.29153	+	2.23699i
$960$		0			0
$961$	4.11493e9	+	7.12726e9i	0.149565	+	0.259054i
$962$	7.03033e9			0.254603
$963$		0			0
$964$	−7.86174e9			−0.282650
$965$	6.87280e8	+	1.19040e9i	0.0246200	+	0.0426431i
$966$		0			0
$967$	1.29346e10	−	2.24033e10i	0.460002	−	0.796746i	−0.538959	−	0.842332i	$-0.681182\pi$
$967$	1.29346e10	−	2.24033e10i	0.460002	−	0.796746i	0.998960	+	0.0455859i	$0.0145155\pi$
$968$	−4.12215e7	+	7.13977e7i	−0.00146070	+	0.00253000i
$969$		0			0
$970$	5.97998e8	+	1.03576e9i	0.0210377	+	0.0364384i
$971$	2.99112e10			1.04850			0.524248	−	0.851565i	$-0.324346\pi$
$971$	2.99112e10			1.04850			0.524248	+	0.851565i	$0.324346\pi$
$972$		0			0
$973$	−2.71764e10			−0.945794
$974$	7.89656e9	+	1.36772e10i	0.273830	+	0.474288i
$975$		0			0
$976$	5.05760e9	−	8.76002e9i	0.174129	−	0.301600i
$977$	1.47182e10	−	2.54927e10i	0.504921	−	0.874549i	−0.495063	−	0.868857i	$-0.664855\pi$
$977$	1.47182e10	−	2.54927e10i	0.504921	−	0.874549i	0.999984	−	0.00569161i	$-0.00181170\pi$
$978$		0			0
$979$	−1.80048e10	−	3.11852e10i	−0.613265	−	1.06221i
$980$	8.98646e8			0.0304998
$981$		0			0
$982$	−2.80304e10			−0.944582
$983$	−2.48687e10	−	4.30739e10i	−0.835057	−	1.44636i	−0.893984	−	0.448099i	$-0.852101\pi$
$983$	−2.48687e10	−	4.30739e10i	−0.835057	−	1.44636i	0.0589270	−	0.998262i	$-0.481232\pi$
$984$		0			0
$985$	7.74689e8	−	1.34180e9i	0.0258286	−	0.0447364i
$986$	−7.85323e9	+	1.36022e10i	−0.260903	+	0.451897i
$987$		0			0
$988$	3.12531e9	+	5.41320e9i	0.103097	+	0.178568i
$989$	−4.94173e10			−1.62440
$990$		0			0
$991$	3.46904e9			0.113227			0.0566137	−	0.998396i	$-0.481970\pi$
$991$	3.46904e9			0.113227			0.0566137	+	0.998396i	$0.481970\pi$
$992$	−2.27512e9	−	3.94063e9i	−0.0739969	−	0.128166i
$993$		0			0
$994$	−2.09630e10	+	3.63091e10i	−0.677021	+	1.17263i
$995$	9.14587e8	−	1.58411e9i	0.0294336	−	0.0509806i
$996$		0			0
$997$	1.71811e10	+	2.97586e10i	0.549058	+	0.950997i	0.998339	+	0.0576063i	$0.0183468\pi$
$997$	1.71811e10	+	2.97586e10i	0.549058	+	0.950997i	−0.449281	+	0.893390i	$0.648320\pi$
$998$	6.99723e9			0.222828
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.8.c.q.109.3		8
3.2	odd	2		162.8.c.r.109.2		8
9.2	odd	6		162.8.c.r.55.2		8
9.4	even	3		162.8.a.j.1.2	yes	4
9.5	odd	6		162.8.a.g.1.3	✓	4
9.7	even	3	inner	162.8.c.q.55.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.8.a.g.1.3	✓	4	9.5	odd	6
162.8.a.j.1.2	yes	4	9.4	even	3
162.8.c.q.55.3		8	9.7	even	3	inner
162.8.c.q.109.3		8	1.1	even	1	trivial
162.8.c.r.55.2		8	9.2	odd	6
162.8.c.r.109.2		8	3.2	odd	2

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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	162.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 - 6.92820i) q^{2} +(-32.0000 + 55.4256i) q^{4} +(-5.62316 + 9.73960i) q^{5} +(-719.735 - 1246.62i) q^{7} +512.000 q^{8} +89.9705 q^{10} +(-2216.31 - 3838.77i) q^{11} +(3615.49 - 6262.21i) q^{13} +(-5757.88 + 9972.94i) q^{14} +(-2048.00 - 3547.24i) q^{16} +13221.1 q^{17} +13506.6 q^{19} +(-359.882 - 623.334i) q^{20} +(-17730.5 + 30710.1i) q^{22} +(32869.3 - 56931.3i) q^{23} +(38999.3 + 67548.7i) q^{25} -57847.8 q^{26} +92126.0 q^{28} +(-74249.1 - 128603. i) q^{29} +(-69431.2 + 120258. i) q^{31} +(-16384.0 + 28377.9i) q^{32} +(-52884.4 - 91598.4i) q^{34} +16188.7 q^{35} -121532. q^{37} +(-54026.5 - 93576.6i) q^{38} +(-2879.06 + 4986.67i) q^{40} +(-26393.4 + 45714.8i) q^{41} +(-375862. - 651012. i) q^{43} +283688. q^{44} -525909. q^{46} +(-491796. - 851816. i) q^{47} +(-624264. + 1.08126e6i) q^{49} +(311994. - 540390. i) q^{50} +(231391. + 400781. i) q^{52} -621759. q^{53} +49850.7 q^{55} +(-368504. - 638268. i) q^{56} +(-593992. + 1.02883e6i) q^{58} +(-407108. + 705132. i) q^{59} +(1.23477e6 + 2.13868e6i) q^{61} +1.11090e6 q^{62} +262144. q^{64} +(40660.9 + 70426.8i) q^{65} +(-1.72741e6 + 2.99196e6i) q^{67} +(-423075. + 732788. i) q^{68} +(-64754.9 - 112159. i) q^{70} +3.64076e6 q^{71} -5.55060e6 q^{73} +(486126. + 841995. i) q^{74} +(-432212. + 748613. i) q^{76} +(-3.19032e6 + 5.52579e6i) q^{77} +(1.02318e6 + 1.77220e6i) q^{79} +46064.9 q^{80} +422295. q^{82} +(-5.13258e6 - 8.88989e6i) q^{83} +(-74344.3 + 128768. i) q^{85} +(-3.00690e6 + 5.20810e6i) q^{86} +(-1.13475e6 - 1.96545e6i) q^{88} +8.12374e6 q^{89} -1.04088e7 q^{91} +(2.10364e6 + 3.64360e6i) q^{92} +(-3.93437e6 + 6.81453e6i) q^{94} +(-75949.9 + 131549. i) q^{95} +(6.64660e6 + 1.15122e7i) q^{97} +9.98823e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{2} - 256 q^{4} - 528 q^{5} - 560 q^{7} + 4096 q^{8} + 8448 q^{10} - 2160 q^{11} - 13460 q^{13} - 4480 q^{14} - 16384 q^{16} + 45120 q^{17} + 73408 q^{19} - 33792 q^{20} - 17280 q^{22} - 62640 q^{23}+ \cdots + 23190336 q^{98}+O(q^{100}) \) 8 * q - 32 * q^2 - 256 * q^4 - 528 * q^5 - 560 * q^7 + 4096 * q^8 + 8448 * q^10 - 2160 * q^11 - 13460 * q^13 - 4480 * q^14 - 16384 * q^16 + 45120 * q^17 + 73408 * q^19 - 33792 * q^20 - 17280 * q^22 - 62640 * q^23 - 94696 * q^25 + 215360 * q^26 + 71680 * q^28 - 68400 * q^29 - 227504 * q^31 - 131072 * q^32 - 180480 * q^34 - 126048 * q^35 + 1047160 * q^37 - 293632 * q^38 - 270336 * q^40 - 67200 * q^41 - 562640 * q^43 + 276480 * q^44 + 1002240 * q^46 - 515328 * q^47 - 1449396 * q^49 - 757568 * q^50 - 861440 * q^52 + 4996032 * q^53 + 2645568 * q^55 - 286720 * q^56 - 547200 * q^58 - 4155840 * q^59 - 2130764 * q^61 + 3640064 * q^62 + 2097152 * q^64 - 8966496 * q^65 + 1205440 * q^67 - 1443840 * q^68 + 504192 * q^70 + 24972960 * q^71 - 9641720 * q^73 - 4188640 * q^74 - 2349056 * q^76 - 18686592 * q^77 + 11471680 * q^79 + 4325376 * q^80 + 1075200 * q^82 - 16811232 * q^83 + 21006396 * q^85 - 4501120 * q^86 - 1105920 * q^88 + 33715200 * q^89 - 46401088 * q^91 - 4008960 * q^92 - 4122624 * q^94 - 14090160 * q^95 + 27078040 * q^97 + 23190336 * q^98

Introduction

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