LMFDB - Embedded newform 54.8.c.b.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,8,Mod(19,54)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("54.19");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	54.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$16.8687913761$
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} + 1336x^{6} + 633664x^{4} + 125389995x^{2} + 8783438400 $ x^8 + 1336x^6 + 633664x^4 + 125389995*x^2 + 8783438400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{18} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.3
Root			$22.3446i$ of defining polynomial
Character	$\chi$	$=$	54.37
Dual form			54.8.c.b.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.00000 - 6.92820i) q^{2} +(-32.0000 + 55.4256i) q^{4} +(47.1766 - 81.7123i) q^{5} +(-101.366 - 175.572i) q^{7} +512.000 q^{8} -754.826 q^{10} +(-1560.90 - 2703.55i) q^{11} +(-1560.70 + 2703.22i) q^{13} +(-810.932 + 1404.57i) q^{14} +(-2048.00 - 3547.24i) q^{16} -34230.3 q^{17} +19665.3 q^{19} +(3019.30 + 5229.59i) q^{20} +(-12487.2 + 21628.4i) q^{22} +(-46889.1 + 81214.4i) q^{23} +(34611.2 + 59948.4i) q^{25} +24971.2 q^{26} +12974.9 q^{28} +(-9197.41 - 15930.4i) q^{29} +(-158690. + 274859. i) q^{31} +(-16384.0 + 28377.9i) q^{32} +(136921. + 237155. i) q^{34} -19128.5 q^{35} -128628. q^{37} +(-78661.1 - 136245. i) q^{38} +(24154.4 - 41836.7i) q^{40} +(-301188. + 521673. i) q^{41} +(-342153. - 592626. i) q^{43} +199795. q^{44} +750226. q^{46} +(-182693. - 316433. i) q^{47} +(391221. - 677615. i) q^{49} +(276890. - 479587. i) q^{50} +(-99884.9 - 173006. i) q^{52} -82663.8 q^{53} -294552. q^{55} +(-51899.6 - 89892.8i) q^{56} +(-73579.2 + 127443. i) q^{58} +(440225. - 762493. i) q^{59} +(-1.44867e6 - 2.50917e6i) q^{61} +2.53904e6 q^{62} +262144. q^{64} +(147257. + 255057. i) q^{65} +(-1.32111e6 + 2.28823e6i) q^{67} +(1.09537e6 - 1.89724e6i) q^{68} +(76514.0 + 132526. i) q^{70} +213917. q^{71} +3.73155e6 q^{73} +(514510. + 891158. i) q^{74} +(-629289. + 1.08996e6i) q^{76} +(-316445. + 548099. i) q^{77} +(-1.78704e6 - 3.09524e6i) q^{79} -386471. q^{80} +4.81901e6 q^{82} +(1.71280e6 + 2.96666e6i) q^{83} +(-1.61487e6 + 2.79704e6i) q^{85} +(-2.73722e6 + 4.74100e6i) q^{86} +(-799180. - 1.38422e6i) q^{88} -1.01749e7 q^{89} +632811. q^{91} +(-3.00091e6 - 5.19772e6i) q^{92} +(-1.46154e6 + 2.53146e6i) q^{94} +(927742. - 1.60690e6i) q^{95} +(1.07912e6 + 1.86909e6i) q^{97} -6.25954e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 32 q^{2} - 256 q^{4} - 54 q^{5} - 44 q^{7} + 4096 q^{8} + 864 q^{10} - 2172 q^{11} - 6398 q^{13} - 352 q^{14} - 16384 q^{16} + 51972 q^{17} + 90712 q^{19} - 3456 q^{20} - 17376 q^{22} + 2028 q^{23}+ \cdots + 20368608 q^{98}+O(q^{100}) $ 8 * q - 32 * q^2 - 256 * q^4 - 54 * q^5 - 44 * q^7 + 4096 * q^8 + 864 * q^10 - 2172 * q^11 - 6398 * q^13 - 352 * q^14 - 16384 * q^16 + 51972 * q^17 + 90712 * q^19 - 3456 * q^20 - 17376 * q^22 + 2028 * q^23 - 173446 * q^25 + 102368 * q^26 + 5632 * q^28 - 283098 * q^29 - 812 * q^31 - 131072 * q^32 - 207888 * q^34 + 1492992 * q^35 + 441688 * q^37 - 362848 * q^38 - 27648 * q^40 - 610704 * q^41 - 84380 * q^43 + 278016 * q^44 - 32448 * q^46 - 855708 * q^47 - 1273038 * q^49 - 1387568 * q^50 - 409472 * q^52 + 1842600 * q^53 + 7016760 * q^55 - 22528 * q^56 - 2264784 * q^58 - 380796 * q^59 - 3151130 * q^61 + 12992 * q^62 + 2097152 * q^64 + 326538 * q^65 - 9961580 * q^67 - 1663104 * q^68 - 5971968 * q^70 - 8970384 * q^71 + 29234932 * q^73 - 1766752 * q^74 - 2902784 * q^76 + 5954826 * q^77 - 17309396 * q^79 + 442368 * q^80 + 9771264 * q^82 + 11520192 * q^83 - 14675148 * q^85 - 675040 * q^86 - 1112064 * q^88 - 26066064 * q^89 + 26231936 * q^91 + 129792 * q^92 - 6845664 * q^94 + 31016952 * q^95 - 22003112 * q^97 + 20368608 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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
$5$	47.1766	−	81.7123i	0.168784	−	0.292343i	−0.769208	−	0.638998i	$-0.779349\pi$
$5$	47.1766	−	81.7123i	0.168784	−	0.292343i	0.937993	+	0.346655i	$0.112683\pi$
$6$		0			0
$7$	−101.366	−	175.572i	−0.111699	−	0.193469i	0.804756	−	0.593606i	$-0.202296\pi$
$7$	−101.366	−	175.572i	−0.111699	−	0.193469i	−0.916456	+	0.400136i	$0.868963\pi$
$8$	512.000			0.353553
$9$		0			0
$10$	−754.826			−0.238697
$11$	−1560.90	−	2703.55i	−0.353590	−	0.612436i	0.633286	−	0.773918i	$-0.281706\pi$
$11$	−1560.90	−	2703.55i	−0.353590	−	0.612436i	−0.986876	+	0.161482i	$0.948373\pi$
$12$		0			0
$13$	−1560.70	+	2703.22i	−0.197024	+	0.341255i	−0.947562	−	0.319572i	$-0.896461\pi$
$13$	−1560.70	+	2703.22i	−0.197024	+	0.341255i	0.750538	+	0.660827i	$0.229794\pi$
$14$	−810.932	+	1404.57i	−0.0789835	+	0.136803i
$15$		0			0
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	−34230.3			−1.68982			−0.844909	−	0.534910i	$-0.820345\pi$
$17$	−34230.3			−1.68982			−0.844909	+	0.534910i	$0.820345\pi$
$18$		0			0
$19$	19665.3			0.657753			0.328876	−	0.944373i	$-0.393330\pi$
$19$	19665.3			0.657753			0.328876	+	0.944373i	$0.393330\pi$
$20$	3019.30	+	5229.59i	0.0843921	+	0.146171i
$21$		0			0
$22$	−12487.2	+	21628.4i	−0.250026	+	0.433058i
$23$	−46889.1	+	81214.4i	−0.803572	+	1.39183i	0.113679	+	0.993518i	$0.463737\pi$
$23$	−46889.1	+	81214.4i	−0.803572	+	1.39183i	−0.917251	+	0.398310i	$0.869597\pi$
$24$		0			0
$25$	34611.2	+	59948.4i	0.443024	+	0.767340i
$26$	24971.2			0.278633
$27$		0			0
$28$	12974.9			0.111699
$29$	−9197.41	−	15930.4i	−0.0700281	−	0.121292i	0.828885	−	0.559419i	$-0.188976\pi$
$29$	−9197.41	−	15930.4i	−0.0700281	−	0.121292i	−0.898913	+	0.438126i	$0.855642\pi$
$30$		0			0
$31$	−158690.	+	274859.i	−0.956716	+	1.65708i	−0.226324	+	0.974052i	$0.572671\pi$
$31$	−158690.	+	274859.i	−0.956716	+	1.65708i	−0.730392	+	0.683028i	$0.760662\pi$
$32$	−16384.0	+	28377.9i	−0.0883883	+	0.153093i
$33$		0			0
$34$	136921.	+	237155.i	0.597441	+	1.03480i
$35$	−19128.5			−0.0754124
$36$		0			0
$37$	−128628.			−0.417473			−0.208736	−	0.977972i	$-0.566935\pi$
$37$	−128628.			−0.417473			−0.208736	+	0.977972i	$0.566935\pi$
$38$	−78661.1	−	136245.i	−0.232551	−	0.402790i
$39$		0			0
$40$	24154.4	−	41836.7i	0.0596742	−	0.103359i
$41$	−301188.	+	521673.i	−0.682487	+	1.18210i	0.291732	+	0.956500i	$0.405768\pi$
$41$	−301188.	+	521673.i	−0.682487	+	1.18210i	−0.974219	+	0.225602i	$0.927565\pi$
$42$		0			0
$43$	−342153.	−	592626.i	−0.656266	−	1.13669i	−0.981575	−	0.191079i	$-0.938801\pi$
$43$	−342153.	−	592626.i	−0.656266	−	1.13669i	0.325308	−	0.945608i	$-0.394532\pi$
$44$	199795.			0.353590
$45$		0			0
$46$	750226.			1.13642
$47$	−182693.	−	316433.i	−0.256672	−	0.444569i	0.708676	−	0.705534i	$-0.249293\pi$
$47$	−182693.	−	316433.i	−0.256672	−	0.444569i	−0.965348	+	0.260965i	$0.915959\pi$
$48$		0			0
$49$	391221.	−	677615.i	0.475046	−	0.822805i
$50$	276890.	−	479587.i	0.313265	−	0.542591i
$51$		0			0
$52$	−99884.9	−	173006.i	−0.0985118	−	0.170627i
$53$	−82663.8			−0.0762693			−0.0381346	−	0.999273i	$-0.512142\pi$
$53$	−82663.8			−0.0762693			−0.0381346	+	0.999273i	$0.512142\pi$
$54$		0			0
$55$	−294552.			−0.238722
$56$	−51899.6	−	89892.8i	−0.0394917	−	0.0684017i
$57$		0			0
$58$	−73579.2	+	127443.i	−0.0495173	+	0.0857666i
$59$	440225.	−	762493.i	0.279057	−	0.483341i	−0.692094	−	0.721808i	$-0.743311\pi$
$59$	440225.	−	762493.i	0.279057	−	0.483341i	0.971151	+	0.238467i	$0.0766448\pi$
$60$		0			0
$61$	−1.44867e6	−	2.50917e6i	−0.817176	−	1.41539i	−0.907755	−	0.419501i	$-0.862205\pi$
$61$	−1.44867e6	−	2.50917e6i	−0.817176	−	1.41539i	0.0905789	−	0.995889i	$-0.471128\pi$
$62$	2.53904e6			1.35300
$63$		0			0
$64$	262144.			0.125000
$65$	147257.	+	255057.i	0.0665090	+	0.115197i
$66$		0			0
$67$	−1.32111e6	+	2.28823e6i	−0.536634	+	0.929477i	0.462449	+	0.886646i	$0.346971\pi$
$67$	−1.32111e6	+	2.28823e6i	−0.536634	+	0.929477i	−0.999082	+	0.0428308i	$0.986362\pi$
$68$	1.09537e6	−	1.89724e6i	0.422454	−	0.731713i
$69$		0			0
$70$	76514.0	+	132526.i	0.0266623	+	0.0461805i
$71$	213917.			0.0709317			0.0354658	−	0.999371i	$-0.488709\pi$
$71$	213917.			0.0709317			0.0354658	+	0.999371i	$0.488709\pi$
$72$		0			0
$73$	3.73155e6			1.12269			0.561344	−	0.827583i	$-0.310285\pi$
$73$	3.73155e6			1.12269			0.561344	+	0.827583i	$0.310285\pi$
$74$	514510.	+	891158.i	0.147599	+	0.255649i
$75$		0			0
$76$	−629289.	+	1.08996e6i	−0.164438	+	0.284815i
$77$	−316445.	+	548099.i	−0.0789917	+	0.136818i
$78$		0			0
$79$	−1.78704e6	−	3.09524e6i	−0.407793	−	0.706317i	0.586850	−	0.809696i	$-0.300368\pi$
$79$	−1.78704e6	−	3.09524e6i	−0.407793	−	0.706317i	−0.994642	+	0.103379i	$0.967035\pi$
$80$	−386471.			−0.0843921
$81$		0			0
$82$	4.81901e6			0.965182
$83$	1.71280e6	+	2.96666e6i	0.328802	+	0.569501i	0.982274	−	0.187449i	$-0.0600219\pi$
$83$	1.71280e6	+	2.96666e6i	0.328802	+	0.569501i	−0.653473	+	0.756950i	$0.726689\pi$
$84$		0			0
$85$	−1.61487e6	+	2.79704e6i	−0.285215	+	0.494006i
$86$	−2.73722e6	+	4.74100e6i	−0.464050	+	0.803759i
$87$		0			0
$88$	−799180.	−	1.38422e6i	−0.125013	−	0.216529i
$89$	−1.01749e7			−1.52990			−0.764950	−	0.644089i	$-0.777236\pi$
$89$	−1.01749e7			−1.52990			−0.764950	+	0.644089i	$0.777236\pi$
$90$		0			0
$91$	632811.			0.0880298
$92$	−3.00091e6	−	5.19772e6i	−0.401786	−	0.695914i
$93$		0			0
$94$	−1.46154e6	+	2.53146e6i	−0.181494	+	0.314358i
$95$	927742.	−	1.60690e6i	0.111018	−	0.192289i
$96$		0			0
$97$	1.07912e6	+	1.86909e6i	0.120052	+	0.207936i	0.919788	−	0.392416i	$-0.128361\pi$
$97$	1.07912e6	+	1.86909e6i	0.120052	+	0.207936i	−0.799736	+	0.600352i	$0.795027\pi$
$98$	−6.25954e6			−0.671817
$99$		0			0
$100$	−4.43024e6			−0.443024
$101$	2.04374e6	+	3.53986e6i	0.197379	+	0.341870i	0.947678	−	0.319229i	$-0.103424\pi$
$101$	2.04374e6	+	3.53986e6i	0.197379	+	0.341870i	−0.750299	+	0.661099i	$0.770090\pi$
$102$		0			0
$103$	−7.81646e6	+	1.35385e7i	−0.704822	+	1.22079i	0.261933	+	0.965086i	$0.415640\pi$
$103$	−7.81646e6	+	1.35385e7i	−0.704822	+	1.22079i	−0.966756	+	0.255702i	$0.917693\pi$
$104$	−799080.	+	1.38405e6i	−0.0696584	+	0.120652i
$105$		0			0
$106$	330655.	+	572711.i	0.0269653	+	0.0467052i
$107$	−284943.			−0.0224861			−0.0112431	−	0.999937i	$-0.503579\pi$
$107$	−284943.			−0.0224861			−0.0112431	+	0.999937i	$0.503579\pi$
$108$		0			0
$109$	1.18746e7			0.878265			0.439132	−	0.898422i	$-0.355286\pi$
$109$	1.18746e7			0.878265			0.439132	+	0.898422i	$0.355286\pi$
$110$	1.17821e6	+	2.04071e6i	0.0844009	+	0.146187i
$111$		0			0
$112$	−415197.	+	719142.i	−0.0279249	+	0.0483673i
$113$	6.55768e6	−	1.13582e7i	0.427539	−	0.740519i	−0.569115	−	0.822258i	$-0.692714\pi$
$113$	6.55768e6	−	1.13582e7i	0.427539	−	0.740519i	0.996654	+	0.0817392i	$0.0260475\pi$
$114$		0			0
$115$	4.42414e6	+	7.66284e6i	0.271261	+	0.469837i
$116$	1.17727e6			0.0700281
$117$		0			0
$118$	−7.04361e6			−0.394646
$119$	3.46981e6	+	6.00988e6i	0.188752	+	0.326928i
$120$		0			0
$121$	4.87078e6	−	8.43644e6i	0.249948	−	0.432923i
$122$	−1.15894e7	+	2.00734e7i	−0.577831	+	1.00083i
$123$		0			0
$124$	−1.01561e7	−	1.75910e7i	−0.478358	−	0.828540i
$125$	1.39027e7			0.636670
$126$		0			0
$127$	1.84235e7			0.798102			0.399051	−	0.916929i	$-0.369340\pi$
$127$	1.84235e7			0.798102			0.399051	+	0.916929i	$0.369340\pi$
$128$	−1.04858e6	−	1.81619e6i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	1.17806e6	−	2.04046e6i	0.0470289	−	0.0814565i
$131$	2.44448e6	−	4.23397e6i	0.0950031	−	0.164550i	−0.814607	−	0.580014i	$-0.803047\pi$
$131$	2.44448e6	−	4.23397e6i	0.0950031	−	0.164550i	0.909610	+	0.415463i	$0.136381\pi$
$132$		0			0
$133$	−1.99340e6	−	3.45267e6i	−0.0734706	−	0.127255i
$134$	2.11378e7			0.758915
$135$		0			0
$136$	−1.75259e7			−0.597441
$137$	−6.85934e6	−	1.18807e7i	−0.227908	−	0.394749i	0.729280	−	0.684216i	$-0.239855\pi$
$137$	−6.85934e6	−	1.18807e7i	−0.227908	−	0.394749i	−0.957188	+	0.289467i	$0.906522\pi$
$138$		0			0
$139$	7.60628e6	−	1.31745e7i	0.240226	−	0.416084i	−0.720552	−	0.693400i	$-0.756112\pi$
$139$	7.60628e6	−	1.31745e7i	0.240226	−	0.416084i	0.960779	+	0.277317i	$0.0894451\pi$
$140$	612112.	−	1.06021e6i	0.0188531	−	0.0326545i
$141$		0			0
$142$	−855666.	−	1.48206e6i	−0.0250781	−	0.0434366i
$143$	9.74439e6			0.278662
$144$		0			0
$145$	−1.73561e6			−0.0472785
$146$	−1.49262e7	−	2.58529e7i	−0.396930	−	0.687503i
$147$		0			0
$148$	4.11608e6	−	7.12926e6i	0.104368	−	0.180771i
$149$	3.54711e7	−	6.14377e7i	0.878461	−	1.52154i	0.0254308	−	0.999677i	$-0.491904\pi$
$149$	3.54711e7	−	6.14377e7i	0.878461	−	1.52154i	0.853030	−	0.521862i	$-0.174762\pi$
$150$		0			0
$151$	−1.44987e7	−	2.51124e7i	−0.342696	−	0.593567i	0.642236	−	0.766507i	$-0.278007\pi$
$151$	−1.44987e7	−	2.51124e7i	−0.342696	−	0.593567i	−0.984932	+	0.172940i	$0.944673\pi$
$152$	1.00686e7			0.232551
$153$		0			0
$154$	5.06313e6			0.111711
$155$	1.49729e7	+	2.59338e7i	0.322957	+	0.559378i
$156$		0			0
$157$	2.01208e7	−	3.48503e7i	0.414951	−	0.718716i	−0.580472	−	0.814280i	$-0.697132\pi$
$157$	2.01208e7	−	3.48503e7i	0.414951	−	0.718716i	0.995423	+	0.0955638i	$0.0304654\pi$
$158$	−1.42963e7	+	2.47619e7i	−0.288353	+	0.499442i
$159$		0			0
$160$	1.54588e6	+	2.67755e6i	0.0298371	+	0.0516794i
$161$	1.90119e7			0.359034
$162$		0			0
$163$	−8.72763e7			−1.57848			−0.789241	−	0.614084i	$-0.789526\pi$
$163$	−8.72763e7			−1.57848			−0.789241	+	0.614084i	$0.789526\pi$
$164$	−1.92760e7	−	3.33871e7i	−0.341244	−	0.591051i
$165$		0			0
$166$	1.37024e7	−	2.37333e7i	0.232498	−	0.402698i
$167$	−3.76355e7	+	6.51866e7i	−0.625302	+	1.08305i	0.363180	+	0.931719i	$0.381691\pi$
$167$	−3.76355e7	+	6.51866e7i	−0.625302	+	1.08305i	−0.988482	+	0.151336i	$0.951642\pi$
$168$		0			0
$169$	2.65027e7	+	4.59040e7i	0.422363	+	0.731555i
$170$	2.58379e7			0.403354
$171$		0			0
$172$	4.37955e7			0.656266
$173$	−1.33635e7	−	2.31463e7i	−0.196227	−	0.339875i	0.751075	−	0.660217i	$-0.229536\pi$
$173$	−1.33635e7	−	2.31463e7i	−0.196227	−	0.339875i	−0.947302	+	0.320341i	$0.896202\pi$
$174$		0			0
$175$	7.01684e6	−	1.21535e7i	0.0989711	−	0.171423i
$176$	−6.39344e6	+	1.10738e7i	−0.0883975	+	0.153109i
$177$		0			0
$178$	4.06994e7	+	7.04935e7i	0.540902	+	0.936869i
$179$	−1.38513e8			−1.80511			−0.902557	−	0.430571i	$-0.858312\pi$
$179$	−1.38513e8			−1.80511			−0.902557	+	0.430571i	$0.858312\pi$
$180$		0			0
$181$	−4.41336e7			−0.553216			−0.276608	−	0.960983i	$-0.589210\pi$
$181$	−4.41336e7			−0.553216			−0.276608	+	0.960983i	$0.589210\pi$
$182$	−2.53125e6	−	4.38425e6i	−0.0311232	−	0.0539070i
$183$		0			0
$184$	−2.40072e7	+	4.15818e7i	−0.284106	+	0.492085i
$185$	−6.06821e6	+	1.05105e7i	−0.0704628	+	0.122045i
$186$		0			0
$187$	5.34300e7	+	9.25436e7i	0.597503	+	1.03491i
$188$	2.33846e7			0.256672
$189$		0			0
$190$	−1.48439e7			−0.157004
$191$	8.99835e7	+	1.55856e8i	0.934429	+	1.61848i	0.775649	+	0.631164i	$0.217423\pi$
$191$	8.99835e7	+	1.55856e8i	0.934429	+	1.61848i	0.158780	+	0.987314i	$0.449244\pi$
$192$		0			0
$193$	1.05609e7	−	1.82920e7i	0.105743	−	0.183152i	−0.808299	−	0.588773i	$-0.799611\pi$
$193$	1.05609e7	−	1.82920e7i	0.105743	−	0.183152i	0.914041	+	0.405621i	$0.132945\pi$
$194$	8.63298e6	−	1.49528e7i	0.0848896	−	0.147033i
$195$		0			0
$196$	2.50382e7	+	4.33674e7i	0.237523	+	0.411402i
$197$	−1.37374e8			−1.28018			−0.640091	−	0.768299i	$-0.721103\pi$
$197$	−1.37374e8			−1.28018			−0.640091	+	0.768299i	$0.721103\pi$
$198$		0			0
$199$	−9.69789e7			−0.872351			−0.436176	−	0.899862i	$-0.643667\pi$
$199$	−9.69789e7			−0.872351			−0.436176	+	0.899862i	$0.643667\pi$
$200$	1.77210e7	+	3.06936e7i	0.156633	+	0.271296i
$201$		0			0
$202$	1.63499e7	−	2.83189e7i	0.139568	−	0.241739i
$203$	−1.86462e6	+	3.22961e6i	−0.0156442	+	0.0270966i
$204$		0			0
$205$	2.84181e7	+	4.92216e7i	0.230386	+	0.399040i
$206$	1.25063e8			0.996769
$207$		0			0
$208$	1.27853e7			0.0985118
$209$	−3.06955e7	−	5.31662e7i	−0.232575	−	0.402831i
$210$		0			0
$211$	−7.89721e7	+	1.36784e8i	−0.578742	+	1.00241i	0.416882	+	0.908961i	$0.363123\pi$
$211$	−7.89721e7	+	1.36784e8i	−0.578742	+	1.00241i	−0.995624	+	0.0934499i	$0.970211\pi$
$212$	2.64524e6	−	4.58169e6i	0.0190673	−	0.0330256i
$213$		0			0
$214$	1.13977e6	+	1.97414e6i	0.00795005	+	0.0137699i
$215$	−6.45664e7			−0.443070
$216$		0			0
$217$	6.43433e7			0.427459
$218$	−4.74983e7	−	8.22695e7i	−0.310513	−	0.537825i
$219$		0			0
$220$	9.42565e6	−	1.63257e7i	0.0596804	−	0.103370i
$221$	5.34234e7	−	9.25320e7i	0.332934	−	0.576659i
$222$		0			0
$223$	−5.69079e7	−	9.85673e7i	−0.343641	−	0.595204i	0.641465	−	0.767153i	$-0.278327\pi$
$223$	−5.69079e7	−	9.85673e7i	−0.343641	−	0.595204i	−0.985106	+	0.171948i	$0.944994\pi$
$224$	6.64315e6			0.0394917
$225$		0			0
$226$	−1.04923e8			−0.604631
$227$	1.40643e7	+	2.43601e7i	0.0798046	+	0.138226i	0.903166	−	0.429292i	$-0.141237\pi$
$227$	1.40643e7	+	2.43601e7i	0.0798046	+	0.138226i	−0.823361	+	0.567518i	$0.807904\pi$
$228$		0			0
$229$	1.53057e8	−	2.65103e8i	0.842227	−	1.45878i	−0.0457801	−	0.998952i	$-0.514577\pi$
$229$	1.53057e8	−	2.65103e8i	0.842227	−	1.45878i	0.888007	−	0.459829i	$-0.152089\pi$
$230$	3.53931e7	−	6.13027e7i	0.191810	−	0.332225i
$231$		0			0
$232$	−4.70907e6	−	8.15635e6i	−0.0247587	−	0.0428833i
$233$	−2.62576e7			−0.135991			−0.0679955	−	0.997686i	$-0.521660\pi$
$233$	−2.62576e7			−0.135991			−0.0679955	+	0.997686i	$0.521660\pi$
$234$		0			0
$235$	−3.44753e7			−0.173289
$236$	2.81744e7	+	4.87995e7i	0.139529	+	0.241671i
$237$		0			0
$238$	2.77585e7	−	4.80791e7i	0.133468	−	0.231173i
$239$	−8.30493e6	+	1.43846e7i	−0.0393499	+	0.0681560i	−0.885030	−	0.465535i	$-0.845862\pi$
$239$	−8.30493e6	+	1.43846e7i	−0.0393499	+	0.0681560i	0.845680	+	0.533691i	$0.179195\pi$
$240$		0			0
$241$	−1.70901e8	−	2.96010e8i	−0.786477	−	1.36222i	−0.928113	−	0.372299i	$-0.878570\pi$
$241$	−1.70901e8	−	2.96010e8i	−0.786477	−	1.36222i	0.141636	−	0.989919i	$-0.454764\pi$
$242$	−7.79325e7			−0.353480
$243$		0			0
$244$	1.85430e8			0.817176
$245$	−3.69130e7	−	6.39352e7i	−0.160361	−	0.277753i
$246$		0			0
$247$	−3.06917e7	+	5.31595e7i	−0.129593	+	0.224461i
$248$	−8.12492e7	+	1.40728e8i	−0.338250	+	0.585866i
$249$		0			0
$250$	−5.56108e7	−	9.63208e7i	−0.225097	−	0.389879i
$251$	3.56672e8			1.42368			0.711838	−	0.702344i	$-0.247863\pi$
$251$	3.56672e8			1.42368			0.711838	+	0.702344i	$0.247863\pi$
$252$		0			0
$253$	2.92757e8			1.13654
$254$	−7.36939e7	−	1.27642e8i	−0.282172	−	0.488736i
$255$		0			0
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	1.48578e8	−	2.57345e8i	0.545996	−	0.945693i	−0.452548	−	0.891740i	$-0.649485\pi$
$257$	1.48578e8	−	2.57345e8i	0.545996	−	0.945693i	0.998544	−	0.0539525i	$-0.0171820\pi$
$258$		0			0
$259$	1.30385e7	+	2.25834e7i	0.0466315	+	0.0807681i
$260$	−1.88489e7			−0.0665090
$261$		0			0
$262$	−3.91117e7			−0.134355
$263$	1.29033e8	+	2.23491e8i	0.437376	+	0.757558i	0.997486	−	0.0708605i	$-0.0225745\pi$
$263$	1.29033e8	+	2.23491e8i	0.437376	+	0.757558i	−0.560110	+	0.828418i	$0.689241\pi$
$264$		0			0
$265$	−3.89980e6	+	6.75465e6i	−0.0128730	+	0.0222968i
$266$	−1.59472e7	+	2.76214e7i	−0.0519516	+	0.0899828i
$267$		0			0
$268$	−8.45512e7	−	1.46447e8i	−0.268317	−	0.464738i
$269$	3.07369e8			0.962779			0.481389	−	0.876507i	$-0.340132\pi$
$269$	3.07369e8			0.962779			0.481389	+	0.876507i	$0.340132\pi$
$270$		0			0
$271$	−2.93409e8			−0.895531			−0.447766	−	0.894151i	$-0.647780\pi$
$271$	−2.93409e8			−0.895531			−0.447766	+	0.894151i	$0.647780\pi$
$272$	7.01037e7	+	1.21423e8i	0.211227	+	0.365856i
$273$		0			0
$274$	−5.48747e7	+	9.50458e7i	−0.161156	+	0.279130i
$275$	1.08049e8	−	1.87147e8i	0.313298	−	0.542647i
$276$		0			0
$277$	1.51779e8	+	2.62889e8i	0.429074	+	0.743178i	0.996791	−	0.0800459i	$-0.0255067\pi$
$277$	1.51779e8	+	2.62889e8i	0.429074	+	0.743178i	−0.567717	+	0.823224i	$0.692173\pi$
$278$	−1.21700e8			−0.339731
$279$		0			0
$280$	−9.79380e6			−0.0266623
$281$	−1.11756e8	−	1.93566e8i	−0.300467	−	0.520424i	0.675775	−	0.737108i	$-0.263809\pi$
$281$	−1.11756e8	−	1.93566e8i	−0.300467	−	0.520424i	−0.976242	+	0.216684i	$0.930476\pi$
$282$		0			0
$283$	−2.77546e8	+	4.80724e8i	−0.727918	+	1.26079i	0.229844	+	0.973228i	$0.426179\pi$
$283$	−2.77546e8	+	4.80724e8i	−0.727918	+	1.26079i	−0.957762	+	0.287563i	$0.907155\pi$
$284$	−6.84533e6	+	1.18565e7i	−0.0177329	+	0.0307143i
$285$		0			0
$286$	−3.89775e7	−	6.75111e7i	−0.0985220	−	0.170645i
$287$	1.22122e8			0.304934
$288$		0			0
$289$	7.61377e8			1.85548
$290$	6.94244e6	+	1.20247e7i	0.0167155	+	0.0289521i
$291$		0			0
$292$	−1.19409e8	+	2.06823e8i	−0.280672	+	0.486138i
$293$	−2.60121e8	+	4.50543e8i	−0.604142	+	1.04640i	0.388045	+	0.921641i	$0.373151\pi$
$293$	−2.60121e8	+	4.50543e8i	−0.604142	+	1.04640i	−0.992186	+	0.124764i	$0.960183\pi$
$294$		0			0
$295$	−4.15367e7	−	7.19437e7i	−0.0942009	−	0.163161i
$296$	−6.58573e7			−0.147599
$297$		0			0
$298$	−5.67537e8			−1.24233
$299$	−1.46360e8	−	2.53503e8i	−0.316645	−	0.548446i
$300$		0			0
$301$	−6.93656e7	+	1.20145e8i	−0.146609	+	0.253935i
$302$	−1.15989e8	+	2.00899e8i	−0.242323	+	0.419715i
$303$		0			0
$304$	−4.02745e7	−	6.97575e7i	−0.0822191	−	0.142408i
$305$	−2.73374e8			−0.551706
$306$		0			0
$307$	5.16023e8			1.01785			0.508926	−	0.860810i	$-0.330043\pi$
$307$	5.16023e8			1.01785			0.508926	+	0.860810i	$0.330043\pi$
$308$	−2.02525e7	−	3.50784e7i	−0.0394958	−	0.0684088i
$309$		0			0
$310$	1.19783e8	−	2.07470e8i	0.228365	−	0.395540i
$311$	−3.58607e8	+	6.21125e8i	−0.676017	+	1.17089i	0.300154	+	0.953891i	$0.402962\pi$
$311$	−3.58607e8	+	6.21125e8i	−0.676017	+	1.17089i	−0.976171	+	0.217004i	$0.930371\pi$
$312$		0			0
$313$	−1.17928e7	−	2.04257e7i	−0.0217375	−	0.0376505i	0.854952	−	0.518707i	$-0.173586\pi$
$313$	−1.17928e7	−	2.04257e7i	−0.0217375	−	0.0376505i	−0.876690	+	0.481057i	$0.840253\pi$
$314$	−3.21933e8			−0.586829
$315$		0			0
$316$	2.28741e8			0.407793
$317$	−3.08327e8	−	5.34038e8i	−0.543631	−	0.941597i	−0.998692	−	0.0511365i	$-0.983716\pi$
$317$	−3.08327e8	−	5.34038e8i	−0.543631	−	0.941597i	0.455060	−	0.890461i	$-0.349618\pi$
$318$		0			0
$319$	−2.87124e7	+	4.97314e7i	−0.0495225	+	0.0857755i
$320$	1.23671e7	−	2.14204e7i	0.0210980	−	0.0365429i
$321$		0			0
$322$	−7.60478e7	−	1.31719e8i	−0.126938	−	0.219863i
$323$	−6.73149e8			−1.11148
$324$		0			0
$325$	−2.16071e8			−0.349145
$326$	3.49105e8	+	6.04668e8i	0.558077	+	0.966619i
$327$		0			0
$328$	−1.54208e8	+	2.67097e8i	−0.241296	+	0.417936i
$329$	−3.70378e7	+	6.41513e7i	−0.0573402	+	0.0993162i
$330$		0			0
$331$	2.31847e8	+	4.01571e8i	0.351402	+	0.608645i	0.986495	−	0.163790i	$-0.0523719\pi$
$331$	2.31847e8	+	4.01571e8i	0.351402	+	0.608645i	−0.635094	+	0.772435i	$0.719039\pi$
$332$	−2.19239e8			−0.328802
$333$		0			0
$334$	6.02168e8			0.884311
$335$	1.24651e8	+	2.15902e8i	0.181151	+	0.313762i
$336$		0			0
$337$	−5.27262e7	+	9.13245e7i	−0.0750450	+	0.129982i	−0.901106	−	0.433599i	$-0.857243\pi$
$337$	−5.27262e7	+	9.13245e7i	−0.0750450	+	0.129982i	0.826061	+	0.563581i	$0.190577\pi$
$338$	2.12021e8	−	3.67232e8i	0.298656	−	0.517287i
$339$		0			0
$340$	−1.03352e8	−	1.79011e8i	−0.142607	−	0.247003i
$341$	9.90794e8			1.35314
$342$		0			0
$343$	−3.25586e8			−0.435649
$344$	−1.75182e8	−	3.03424e8i	−0.232025	−	0.401879i
$345$		0			0
$346$	−1.06908e8	+	1.85170e8i	−0.138754	+	0.240328i
$347$	5.83453e7	−	1.01057e8i	0.0749640	−	0.129841i	−0.826107	−	0.563514i	$-0.809449\pi$
$347$	5.83453e7	−	1.01057e8i	0.0749640	−	0.129841i	0.901071	+	0.433672i	$0.142782\pi$
$348$		0			0
$349$	−4.91223e8	−	8.50823e8i	−0.618571	−	1.07140i	−0.989747	−	0.142834i	$-0.954378\pi$
$349$	−4.91223e8	−	8.50823e8i	−0.618571	−	1.07140i	0.371175	−	0.928563i	$-0.378955\pi$
$350$	−1.12269e8			−0.139966
$351$		0			0
$352$	1.02295e8			0.125013
$353$	1.69007e8	+	2.92728e8i	0.204499	+	0.354203i	0.949973	−	0.312332i	$-0.101110\pi$
$353$	1.69007e8	+	2.92728e8i	0.204499	+	0.354203i	−0.745474	+	0.666535i	$0.767777\pi$
$354$		0			0
$355$	1.00919e7	−	1.74796e7i	0.0119721	−	0.0207364i
$356$	3.25595e8	−	5.63948e8i	0.382475	−	0.662466i
$357$		0			0
$358$	5.54052e8	+	9.59645e8i	0.638204	+	1.10540i
$359$	3.59044e8			0.409559			0.204780	−	0.978808i	$-0.434352\pi$
$359$	3.59044e8			0.409559			0.204780	+	0.978808i	$0.434352\pi$
$360$		0			0
$361$	−5.07148e8			−0.567361
$362$	1.76535e8	+	3.05767e8i	0.195591	+	0.338774i
$363$		0			0
$364$	−2.02500e7	+	3.50740e7i	−0.0220074	+	0.0381180i
$365$	1.76042e8	−	3.04913e8i	0.189492	−	0.328210i
$366$		0			0
$367$	−2.56996e8	−	4.45131e8i	−0.271391	−	0.470064i	0.697827	−	0.716266i	$-0.254150\pi$
$367$	−2.56996e8	−	4.45131e8i	−0.271391	−	0.470064i	−0.969218	+	0.246203i	$0.920817\pi$
$368$	3.84116e8			0.401786
$369$		0			0
$370$	9.70914e7			0.0996494
$371$	8.37933e6	+	1.45134e7i	0.00851924	+	0.0147558i
$372$		0			0
$373$	−5.28875e8	+	9.16039e8i	−0.527682	+	0.913972i	0.471797	+	0.881707i	$0.343605\pi$
$373$	−5.28875e8	+	9.16039e8i	−0.527682	+	0.913972i	−0.999479	+	0.0322652i	$0.989728\pi$
$374$	4.27440e8	−	7.40348e8i	0.422498	−	0.731788i
$375$		0			0
$376$	−9.35386e7	−	1.62014e8i	−0.0907472	−	0.157179i
$377$	5.74176e7			0.0551888
$378$		0			0
$379$	−2.50117e8			−0.235997			−0.117999	−	0.993014i	$-0.537648\pi$
$379$	−2.50117e8			−0.235997			−0.117999	+	0.993014i	$0.537648\pi$
$380$	5.93755e7	+	1.02841e8i	0.0555091	+	0.0961446i
$381$		0			0
$382$	7.19868e8	−	1.24685e9i	0.660741	−	1.14444i
$383$	1.51148e8	−	2.61795e8i	0.137469	−	0.238104i	−0.789069	−	0.614305i	$-0.789436\pi$
$383$	1.51148e8	−	2.61795e8i	0.137469	−	0.238104i	0.926538	+	0.376201i	$0.122770\pi$
$384$		0			0
$385$	2.98576e7	+	5.17150e7i	0.0266651	+	0.0461853i
$386$	−1.68974e8			−0.149543
$387$		0			0
$388$	−1.38128e8			−0.120052
$389$	3.65061e7	+	6.32303e7i	0.0314443	+	0.0544631i	0.881319	−	0.472521i	$-0.156656\pi$
$389$	3.65061e7	+	6.32303e7i	0.0314443	+	0.0544631i	−0.849875	+	0.526984i	$0.823323\pi$
$390$		0			0
$391$	1.60503e9	−	2.78000e9i	1.35789	−	2.35194i
$392$	2.00305e8	−	3.46939e8i	0.167954	−	0.290905i
$393$		0			0
$394$	5.49494e8	+	9.51752e8i	0.452612	+	0.783948i
$395$	−3.37226e8			−0.275316
$396$		0			0
$397$	−9.92702e8			−0.796255			−0.398127	−	0.917330i	$-0.630340\pi$
$397$	−9.92702e8			−0.796255			−0.398127	+	0.917330i	$0.630340\pi$
$398$	3.87915e8	+	6.71889e8i	0.308423	+	0.534204i
$399$		0			0
$400$	1.41768e8	−	2.45549e8i	0.110756	−	0.191835i
$401$	−5.54239e8	+	9.59970e8i	−0.429232	+	0.743451i	−0.996805	−	0.0798719i	$-0.974549\pi$
$401$	−5.54239e8	+	9.59970e8i	−0.429232	+	0.743451i	0.567574	+	0.823323i	$0.307882\pi$
$402$		0			0
$403$	−4.95335e8	−	8.57945e8i	−0.376991	−	0.652968i
$404$	−2.61598e8			−0.197379
$405$		0			0
$406$	2.98339e7			0.0221242
$407$	2.00774e8	+	3.47752e8i	0.147614	+	0.255675i
$408$		0			0
$409$	7.15003e8	−	1.23842e9i	0.516745	−	0.895028i	−0.483066	−	0.875584i	$-0.660477\pi$
$409$	7.15003e8	−	1.23842e9i	0.516745	−	0.895028i	0.999811	−	0.0194442i	$-0.00618969\pi$
$410$	2.27345e8	−	3.93772e8i	0.162908	−	0.282164i
$411$		0			0
$412$	−5.00253e8	−	8.66464e8i	−0.352411	−	0.610394i
$413$	−1.78496e8			−0.124682
$414$		0			0
$415$	3.23217e8			0.221986
$416$	−5.11411e7	−	8.85790e7i	−0.0348292	−	0.0603259i
$417$		0			0
$418$	−2.45564e8	+	4.25329e8i	−0.164455	+	0.284845i
$419$	2.04771e8	−	3.54674e8i	0.135994	−	0.235548i	−0.789983	−	0.613129i	$-0.789911\pi$
$419$	2.04771e8	−	3.54674e8i	0.135994	−	0.235548i	0.925977	+	0.377581i	$0.123244\pi$
$420$		0			0
$421$	1.16626e9	+	2.02002e9i	0.761743	+	1.31938i	0.941952	+	0.335749i	$0.108989\pi$
$421$	1.16626e9	+	2.02002e9i	0.761743	+	1.31938i	−0.180209	+	0.983628i	$0.557677\pi$
$422$	1.26355e9			0.818465
$423$		0			0
$424$	−4.23238e7			−0.0269653
$425$	−1.18475e9	−	2.05205e9i	−0.748629	−	1.29666i
$426$		0			0
$427$	−2.93693e8	+	5.08692e8i	−0.182556	+	0.316197i
$428$	9.11818e6	−	1.57932e7i	0.00562154	−	0.00973679i
$429$		0			0
$430$	2.58266e8	+	4.47329e8i	0.156649	+	0.271324i
$431$	−1.45263e9			−0.873948			−0.436974	−	0.899474i	$-0.643950\pi$
$431$	−1.45263e9			−0.873948			−0.436974	+	0.899474i	$0.643950\pi$
$432$		0			0
$433$	−3.06024e9			−1.81154			−0.905770	−	0.423769i	$-0.860707\pi$
$433$	−3.06024e9			−1.81154			−0.905770	+	0.423769i	$0.860707\pi$
$434$	−2.57373e8	−	4.45783e8i	−0.151129	−	0.261764i
$435$		0			0
$436$	−3.79986e8	+	6.58156e8i	−0.219566	+	0.380300i
$437$	−9.22088e8	+	1.59710e9i	−0.528552	+	0.915479i
$438$		0			0
$439$	7.84435e8	+	1.35868e9i	0.442518	+	0.766464i	0.997876	−	0.0651480i	$-0.0207519\pi$
$439$	7.84435e8	+	1.35868e9i	0.442518	+	0.766464i	−0.555358	+	0.831612i	$0.687419\pi$
$440$	−1.50810e8			−0.0844009
$441$		0			0
$442$	−8.54774e8			−0.470840
$443$	−9.61980e8	−	1.66620e9i	−0.525718	−	0.910571i	−0.999551	−	0.0299561i	$-0.990463\pi$
$443$	−9.61980e8	−	1.66620e9i	−0.525718	−	0.910571i	0.473833	−	0.880615i	$-0.342870\pi$
$444$		0			0
$445$	−4.80015e8	+	8.31411e8i	−0.258223	+	0.447255i
$446$	−4.55263e8	+	7.88539e8i	−0.242991	+	0.420873i
$447$		0			0
$448$	−2.65726e7	−	4.60251e7i	−0.0139624	−	0.0241836i
$449$	1.96841e9			1.02625			0.513124	−	0.858315i	$-0.328488\pi$
$449$	1.96841e9			1.02625			0.513124	+	0.858315i	$0.328488\pi$
$450$		0			0
$451$	1.88050e9			0.965283
$452$	4.19691e8	+	7.26927e8i	0.213769	+	0.370259i
$453$		0			0
$454$	1.12515e8	−	1.94881e8i	0.0564304	−	0.0977403i
$455$	2.98539e7	−	5.17085e7i	0.0148580	−	0.0257349i
$456$		0			0
$457$	5.71536e8	+	9.89929e8i	0.280115	+	0.485174i	0.971413	−	0.237396i	$-0.0762939\pi$
$457$	5.71536e8	+	9.89929e8i	0.280115	+	0.485174i	−0.691298	+	0.722570i	$0.742961\pi$
$458$	−2.44891e9			−1.19109
$459$		0			0
$460$	−5.66290e8			−0.271261
$461$	1.76632e9	+	3.05936e9i	0.839687	+	1.45438i	0.890157	+	0.455655i	$0.150595\pi$
$461$	1.76632e9	+	3.05936e9i	0.839687	+	1.45438i	−0.0504698	+	0.998726i	$0.516072\pi$
$462$		0			0
$463$	−9.78759e8	+	1.69526e9i	−0.458292	+	0.793785i	−0.998871	−	0.0475084i	$-0.984872\pi$
$463$	−9.78759e8	+	1.69526e9i	−0.458292	+	0.793785i	0.540579	+	0.841293i	$0.318205\pi$
$464$	−3.76726e7	+	6.52508e7i	−0.0175070	+	0.0303231i
$465$		0			0
$466$	1.05031e8	+	1.81918e8i	0.0480801	+	0.0832771i
$467$	6.48657e8			0.294718			0.147359	−	0.989083i	$-0.452923\pi$
$467$	6.48657e8			0.294718			0.147359	+	0.989083i	$0.452923\pi$
$468$		0			0
$469$	5.35666e8			0.239767
$470$	1.37901e8	+	2.38852e8i	0.0612668	+	0.106117i
$471$		0			0
$472$	2.25395e8	−	3.90396e8i	0.0986616	−	0.170887i
$473$	−1.06813e9	+	1.85006e9i	−0.464099	+	0.803842i
$474$		0			0
$475$	6.80640e8	+	1.17890e9i	0.291400	+	0.504720i
$476$	−4.44135e8			−0.188752
$477$		0			0
$478$	1.32879e8			0.0556491
$479$	−1.95262e8	−	3.38203e8i	−0.0811788	−	0.140606i	0.822578	−	0.568653i	$-0.192535\pi$
$479$	−1.95262e8	−	3.38203e8i	−0.0811788	−	0.140606i	−0.903757	+	0.428047i	$0.859202\pi$
$480$		0			0
$481$	2.00749e8	−	3.47708e8i	0.0822520	−	0.142465i
$482$	−1.36721e9	+	2.36808e9i	−0.556123	+	0.963233i
$483$		0			0
$484$	3.11730e8	+	5.39932e8i	0.124974	+	0.216461i
$485$	2.03637e8			0.0810516
$486$		0			0
$487$	1.14248e9			0.448228			0.224114	−	0.974563i	$-0.428051\pi$
$487$	1.14248e9			0.448228			0.224114	+	0.974563i	$0.428051\pi$
$488$	−7.41720e8	−	1.28470e9i	−0.288915	−	0.500416i
$489$		0			0
$490$	−2.95304e8	+	5.11481e8i	−0.113392	+	0.196401i
$491$	1.68396e9	−	2.91671e9i	0.642018	−	1.11201i	−0.342964	−	0.939349i	$-0.611431\pi$
$491$	1.68396e9	−	2.91671e9i	0.642018	−	1.11201i	0.984982	−	0.172659i	$-0.0552358\pi$
$492$		0			0
$493$	3.14830e8	+	5.45302e8i	0.118335	+	0.204962i
$494$	4.91066e8			0.183272
$495$		0			0
$496$	1.29999e9			0.478358
$497$	−2.16840e7	−	3.75577e7i	−0.00792303	−	0.0137231i
$498$		0			0
$499$	9.99272e8	−	1.73079e9i	0.360024	−	0.623580i	−0.627940	−	0.778262i	$-0.716102\pi$
$499$	9.99272e8	−	1.73079e9i	0.360024	−	0.623580i	0.987964	+	0.154681i	$0.0494351\pi$
$500$	−4.44887e8	+	7.70566e8i	−0.159168	+	0.275686i
$501$		0			0
$502$	−1.42669e9	−	2.47110e9i	−0.503345	−	0.871820i
$503$	1.14200e9			0.400110			0.200055	−	0.979785i	$-0.435888\pi$
$503$	1.14200e9			0.400110			0.200055	+	0.979785i	$0.435888\pi$
$504$		0			0
$505$	3.85666e8			0.133258
$506$	−1.17103e9	−	2.02828e9i	−0.401828	−	0.695986i
$507$		0			0
$508$	−5.89551e8	+	1.02113e9i	−0.199526	+	0.345588i
$509$	−1.50303e9	+	2.60333e9i	−0.505192	+	0.875018i	0.494790	+	0.869012i	$0.335245\pi$
$509$	−1.50303e9	+	2.60333e9i	−0.505192	+	0.875018i	−0.999982	+	0.00600540i	$0.998088\pi$
$510$		0			0
$511$	−3.78254e8	−	6.55155e8i	−0.125404	−	0.217205i
$512$	1.34218e8			0.0441942
$513$		0			0
$514$	−2.37725e9			−0.772155
$515$	7.37508e8	+	1.27740e9i	0.237926	+	0.412099i
$516$		0			0
$517$	−5.70329e8	+	9.87838e8i	−0.181513	+	0.314390i
$518$	1.04308e8	−	1.80667e8i	0.0329734	−	0.0571117i
$519$		0			0
$520$	7.53957e7	+	1.30589e8i	0.0235145	+	0.0407282i
$521$	−1.82411e8			−0.0565091			−0.0282545	−	0.999601i	$-0.508995\pi$
$521$	−1.82411e8			−0.0565091			−0.0282545	+	0.999601i	$0.508995\pi$
$522$		0			0
$523$	−1.10431e9			−0.337547			−0.168774	−	0.985655i	$-0.553981\pi$
$523$	−1.10431e9			−0.337547			−0.168774	+	0.985655i	$0.553981\pi$
$524$	1.56447e8	+	2.70974e8i	0.0475015	+	0.0822751i
$525$		0			0
$526$	1.03226e9	−	1.78793e9i	0.309272	−	0.535674i
$527$	5.43200e9	−	9.40851e9i	1.61668	−	2.80016i
$528$		0			0
$529$	−2.69477e9	−	4.66748e9i	−0.791457	−	1.37084i
$530$	6.23967e7			0.0182052
$531$		0			0
$532$	2.55155e8			0.0734706
$533$	−9.40130e8	−	1.62835e9i	−0.268932	−	0.465804i
$534$		0			0
$535$	−1.34427e7	+	2.32834e7i	−0.00379531	+	0.00657366i
$536$	−6.76410e8	+	1.17158e9i	−0.189729	+	0.328620i
$537$		0			0
$538$	−1.22947e9	−	2.12951e9i	−0.340394	−	0.589579i
$539$	−2.44262e9			−0.671887
$540$		0			0
$541$	3.66157e9			0.994207			0.497104	−	0.867691i	$-0.334397\pi$
$541$	3.66157e9			0.994207			0.497104	+	0.867691i	$0.334397\pi$
$542$	1.17364e9	+	2.03280e9i	0.316618	+	0.548399i
$543$		0			0
$544$	5.60830e8	−	9.71386e8i	0.149360	−	0.258699i
$545$	5.60202e8	−	9.70299e8i	0.148237	−	0.256754i
$546$		0			0
$547$	−9.61269e8	−	1.66497e9i	−0.251125	−	0.434961i	0.712711	−	0.701458i	$-0.247467\pi$
$547$	−9.61269e8	−	1.66497e9i	−0.251125	−	0.434961i	−0.963836	+	0.266497i	$0.914134\pi$
$548$	8.77996e8			0.227908
$549$		0			0
$550$	−1.72879e9			−0.443070
$551$	−1.80870e8	−	3.13275e8i	−0.0460612	−	0.0797803i
$552$		0			0
$553$	−3.62292e8	+	6.27508e8i	−0.0911004	+	0.157791i
$554$	1.21423e9	−	2.10311e9i	0.303401	−	0.525506i
$555$		0			0
$556$	4.86802e8	+	8.43165e8i	0.120113	+	0.208042i
$557$	5.21647e9			1.27904			0.639519	−	0.768775i	$-0.279133\pi$
$557$	5.21647e9			1.27904			0.639519	+	0.768775i	$0.279133\pi$
$558$		0			0
$559$	2.13599e9			0.517200
$560$	3.91752e7	+	6.78534e7i	0.00942655	+	0.0163273i
$561$		0			0
$562$	−8.94045e8	+	1.54853e9i	−0.212462	+	0.367996i
$563$	−8.08033e8	+	1.39955e9i	−0.190831	+	0.330529i	−0.945526	−	0.325547i	$-0.894452\pi$
$563$	−8.08033e8	+	1.39955e9i	−0.190831	+	0.330529i	0.754695	+	0.656076i	$0.227785\pi$
$564$		0			0
$565$	−6.18738e8	−	1.07169e9i	−0.144324	−	0.249976i
$566$	4.44074e9			1.02943
$567$		0			0
$568$	1.09525e8			0.0250781
$569$	1.41802e9	+	2.45609e9i	0.322693	+	0.558922i	0.981043	−	0.193791i	$-0.0620784\pi$
$569$	1.41802e9	+	2.45609e9i	0.322693	+	0.558922i	−0.658349	+	0.752713i	$0.728745\pi$
$570$		0			0
$571$	2.29918e9	−	3.98230e9i	0.516829	−	0.895175i	−0.482980	−	0.875632i	$-0.660446\pi$
$571$	2.29918e9	−	3.98230e9i	0.516829	−	0.895175i	0.999809	−	0.0195431i	$-0.00622116\pi$
$572$	−3.11820e8	+	5.40089e8i	−0.0696656	+	0.120664i
$573$		0			0
$574$	−4.88486e8	−	8.46083e8i	−0.107810	−	0.186733i
$575$	−6.49156e9			−1.42401
$576$		0			0
$577$	2.74982e9			0.595921			0.297960	−	0.954578i	$-0.403694\pi$
$577$	2.74982e9			0.595921			0.297960	+	0.954578i	$0.403694\pi$
$578$	−3.04551e9	−	5.27497e9i	−0.656013	−	1.13625i
$579$		0			0
$580$	5.55395e7	−	9.61973e7i	0.0118196	−	0.0204722i
$581$	3.47242e8	−	6.01440e8i	0.0734540	−	0.127226i
$582$		0			0
$583$	1.29030e8	+	2.23486e8i	0.0269681	+	0.0467100i
$584$	1.91055e9			0.396930
$585$		0			0
$586$	4.16194e9			0.854385
$587$	3.91043e9	+	6.77306e9i	0.797978	+	1.38214i	0.920931	+	0.389726i	$0.127430\pi$
$587$	3.91043e9	+	6.77306e9i	0.797978	+	1.38214i	−0.122953	+	0.992412i	$0.539237\pi$
$588$		0			0
$589$	−3.12068e9	+	5.40518e9i	−0.629282	+	1.08995i
$590$	−3.32294e8	+	5.75549e8i	−0.0666101	+	0.115372i
$591$		0			0
$592$	2.63429e8	+	4.56273e8i	0.0521841	+	0.0903855i
$593$	−9.03436e9			−1.77912			−0.889562	−	0.456815i	$-0.848990\pi$
$593$	−9.03436e9			−1.77912			−0.889562	+	0.456815i	$0.848990\pi$
$594$		0			0
$595$	6.54775e8			0.127433
$596$	2.27015e9	+	3.93201e9i	0.439230	+	0.760769i
$597$		0			0
$598$	−1.17088e9	+	2.02802e9i	−0.223902	+	0.387810i
$599$	−5.09289e8	+	8.82115e8i	−0.0968212	+	0.167699i	−0.910367	−	0.413801i	$-0.864201\pi$
$599$	−5.09289e8	+	8.82115e8i	−0.0968212	+	0.167699i	0.813546	+	0.581501i	$0.197534\pi$
$600$		0			0
$601$	−4.75699e8	−	8.23935e8i	−0.0893864	−	0.154822i	0.817866	−	0.575409i	$-0.195157\pi$
$601$	−4.75699e8	−	8.23935e8i	−0.0893864	−	0.154822i	−0.907252	+	0.420588i	$0.861824\pi$
$602$	1.10985e9			0.207337
$603$		0			0
$604$	1.85583e9			0.342696
$605$	−4.59574e8	−	7.96006e8i	−0.0843746	−	0.146141i
$606$		0			0
$607$	−3.14424e9	+	5.44599e9i	−0.570631	+	0.988363i	0.425870	+	0.904784i	$0.359968\pi$
$607$	−3.14424e9	+	5.44599e9i	−0.570631	+	0.988363i	−0.996501	+	0.0835782i	$0.973365\pi$
$608$	−3.22196e8	+	5.58060e8i	−0.0581377	+	0.100697i
$609$		0			0
$610$	1.09349e9	+	1.89399e9i	0.195057	+	0.337849i
$611$	1.14051e9			0.202282
$612$		0			0
$613$	−7.77531e9			−1.36335			−0.681673	−	0.731657i	$-0.738747\pi$
$613$	−7.77531e9			−1.36335			−0.681673	+	0.731657i	$0.738747\pi$
$614$	−2.06409e9	−	3.57511e9i	−0.359865	−	0.623304i
$615$		0			0
$616$	−1.62020e8	+	2.80627e8i	−0.0279278	+	0.0483723i
$617$	−2.80552e9	+	4.85930e9i	−0.480856	+	0.832867i	−0.999759	−	0.0219663i	$-0.993007\pi$
$617$	−2.80552e9	+	4.85930e9i	−0.480856	+	0.832867i	0.518903	+	0.854833i	$0.326341\pi$
$618$		0			0
$619$	−1.76225e9	−	3.05231e9i	−0.298642	−	0.517263i	0.677184	−	0.735814i	$-0.263200\pi$
$619$	−1.76225e9	−	3.05231e9i	−0.298642	−	0.517263i	−0.975826	+	0.218551i	$0.929867\pi$
$620$	−1.91653e9			−0.322957
$621$		0			0
$622$	5.73771e9			0.956032
$623$	1.03139e9	+	1.78642e9i	0.170889	+	0.295989i
$624$		0			0
$625$	−2.04812e9	+	3.54745e9i	−0.335564	+	0.581214i
$626$	−9.43421e7	+	1.63405e8i	−0.0153708	+	0.0266229i
$627$		0			0
$628$	1.28773e9	+	2.23042e9i	0.207475	+	0.359358i
$629$	4.40296e9			0.705453
$630$		0			0
$631$	1.22930e9			0.194784			0.0973921	−	0.995246i	$-0.468950\pi$
$631$	1.22930e9			0.194784			0.0973921	+	0.995246i	$0.468950\pi$
$632$	−9.14964e8	−	1.58476e9i	−0.144176	−	0.249721i
$633$		0			0
$634$	−2.46662e9	+	4.27231e9i	−0.384405	+	0.665810i
$635$	8.69157e8	−	1.50542e9i	0.134707	−	0.233319i
$636$		0			0
$637$	1.22116e9	+	2.11511e9i	0.187191	+	0.324224i
$638$	4.59399e8			0.0700354
$639$		0			0
$640$	−1.97873e8			−0.0298371
$641$	−3.10360e9	−	5.37560e9i	−0.465439	−	0.806165i	0.533782	−	0.845622i	$-0.320770\pi$
$641$	−3.10360e9	−	5.37560e9i	−0.465439	−	0.806165i	−0.999221	+	0.0394574i	$0.987437\pi$
$642$		0			0
$643$	−9.15352e8	+	1.58544e9i	−0.135784	+	0.235186i	−0.925897	−	0.377776i	$-0.876689\pi$
$643$	−9.15352e8	+	1.58544e9i	−0.135784	+	0.235186i	0.790112	+	0.612962i	$0.210022\pi$
$644$	−6.08382e8	+	1.05375e9i	−0.0897586	+	0.155466i
$645$		0			0
$646$	2.69260e9	+	4.66371e9i	0.392968	+	0.680641i
$647$	−1.07212e10			−1.55624			−0.778121	−	0.628114i	$-0.783827\pi$
$647$	−1.07212e10			−1.55624			−0.778121	+	0.628114i	$0.783827\pi$
$648$		0			0
$649$	−2.74859e9			−0.394687
$650$	8.64285e8	+	1.49699e9i	0.123441	+	0.213807i
$651$		0			0
$652$	2.79284e9	−	4.83734e9i	0.394620	−	0.683503i
$653$	5.69305e8	−	9.86065e8i	0.0800108	−	0.138583i	−0.823244	−	0.567688i	$-0.807838\pi$
$653$	5.69305e8	−	9.86065e8i	0.0800108	−	0.138583i	0.903254	+	0.429106i	$0.141171\pi$
$654$		0			0
$655$	−2.30645e8	−	3.99489e8i	−0.0320700	−	0.0555469i
$656$	2.46733e9			0.341244
$657$		0			0
$658$	5.92605e8			0.0810913
$659$	2.46048e8	+	4.26168e8i	0.0334905	+	0.0580072i	0.882285	−	0.470716i	$-0.156004\pi$
$659$	2.46048e8	+	4.26168e8i	0.0334905	+	0.0580072i	−0.848794	+	0.528723i	$0.822671\pi$
$660$		0			0
$661$	1.49366e9	−	2.58710e9i	0.201162	−	0.348423i	−0.747741	−	0.663991i	$-0.768861\pi$
$661$	1.49366e9	−	2.58710e9i	0.201162	−	0.348423i	0.948903	+	0.315567i	$0.102195\pi$
$662$	1.85478e9	−	3.21257e9i	0.248478	−	0.430377i
$663$		0			0
$664$	8.76955e8	+	1.51893e9i	0.116249	+	0.201349i
$665$	−3.76168e8			−0.0496027
$666$		0			0
$667$	1.72503e9			0.225091
$668$	−2.40867e9	−	4.17194e9i	−0.312651	−	0.541527i
$669$		0			0
$670$	9.97210e8	−	1.72722e9i	0.128093	−	0.221863i
$671$	−4.52246e9	+	7.83313e9i	−0.577891	+	1.00094i
$672$		0			0
$673$	−4.16502e8	−	7.21403e8i	−0.0526701	−	0.0912273i	0.838488	−	0.544920i	$-0.183440\pi$
$673$	−4.16502e8	−	7.21403e8i	−0.0526701	−	0.0912273i	−0.891158	+	0.453692i	$0.850107\pi$
$674$	8.43620e8			0.106130
$675$		0			0
$676$	−3.39234e9			−0.422363
$677$	3.44143e9	+	5.96072e9i	0.426263	+	0.738310i	0.996537	−	0.0831446i	$-0.0264963\pi$
$677$	3.44143e9	+	5.96072e9i	0.426263	+	0.738310i	−0.570274	+	0.821454i	$0.693163\pi$
$678$		0			0
$679$	2.18774e8	−	3.78927e8i	0.0268195	−	0.0464528i
$680$	−8.26814e8	+	1.43208e9i	−0.100839	+	0.174658i
$681$		0			0
$682$	−3.96318e9	−	6.86442e9i	−0.478408	−	0.828626i
$683$	−8.85672e9			−1.06365			−0.531827	−	0.846853i	$-0.678494\pi$
$683$	−8.85672e9			−1.06365			−0.531827	+	0.846853i	$0.678494\pi$
$684$		0			0
$685$	−1.29440e9			−0.153869
$686$	1.30234e9	+	2.25573e9i	0.154025	+	0.266779i
$687$		0			0
$688$	−1.40146e9	+	2.42739e9i	−0.164067	+	0.284172i
$689$	1.29014e8	−	2.23458e8i	0.0150268	−	0.0260273i
$690$		0			0
$691$	−1.83277e9	−	3.17446e9i	−0.211318	−	0.366013i	0.740810	−	0.671715i	$-0.234442\pi$
$691$	−1.83277e9	−	3.17446e9i	−0.211318	−	0.366013i	−0.952127	+	0.305702i	$0.901109\pi$
$692$	1.71053e9			0.196227
$693$		0			0
$694$	−9.33525e8			−0.106015
$695$	−7.17677e8	−	1.24305e9i	−0.0810928	−	0.140457i
$696$		0			0
$697$	1.03098e10	−	1.78570e10i	1.15328	−	1.99754i
$698$	−3.92979e9	+	6.80659e9i	−0.437396	+	0.757592i
$699$		0			0
$700$	4.49078e8	+	7.77825e8i	0.0494855	+	0.0857115i
$701$	1.49934e10			1.64395			0.821974	−	0.569525i	$-0.192873\pi$
$701$	1.49934e10			1.64395			0.821974	+	0.569525i	$0.192873\pi$
$702$		0			0
$703$	−2.52950e9			−0.274594
$704$	−4.09180e8	−	7.08721e8i	−0.0441988	−	0.0765545i
$705$		0			0
$706$	1.35205e9	−	2.34182e9i	0.144603	−	0.250460i
$707$	4.14333e8	−	7.17646e8i	0.0440942	−	0.0763734i
$708$		0			0
$709$	6.34766e9	+	1.09945e10i	0.668886	+	1.15854i	0.978216	+	0.207589i	$0.0665618\pi$
$709$	6.34766e9	+	1.09945e10i	0.668886	+	1.15854i	−0.309330	+	0.950955i	$0.600105\pi$
$710$	−1.61470e8			−0.0169312
$711$		0			0
$712$	−5.20953e9			−0.540902
$713$	−1.48817e10	−	2.57758e10i	−1.53758	−	2.66317i
$714$		0			0
$715$	4.59707e8	−	7.96236e8i	0.0470338	−	0.0814649i
$716$	4.43241e9	−	7.67716e9i	0.451278	−	0.781637i
$717$		0			0
$718$	−1.43618e9	−	2.48753e9i	−0.144801	−	0.250803i
$719$	1.60779e10			1.61317			0.806583	−	0.591120i	$-0.201314\pi$
$719$	1.60779e10			1.61317			0.806583	+	0.591120i	$0.201314\pi$
$720$		0			0
$721$	3.16931e9			0.314913
$722$	2.02859e9	+	3.51363e9i	0.200593	+	0.347436i
$723$		0			0
$724$	1.41228e9	−	2.44613e9i	0.138304	−	0.239550i
$725$	6.36667e8	−	1.10274e9i	0.0620482	−	0.107471i
$726$		0			0
$727$	7.92634e9	+	1.37288e10i	0.765072	+	1.32514i	0.940209	+	0.340599i	$0.110630\pi$
$727$	7.92634e9	+	1.37288e10i	0.765072	+	1.32514i	−0.175137	+	0.984544i	$0.556037\pi$
$728$	3.23999e8			0.0311232
$729$		0			0
$730$	−2.81667e9			−0.267982
$731$	1.17120e10	+	2.02858e10i	1.10897	+	1.92079i
$732$		0			0
$733$	−4.13335e9	+	7.15918e9i	−0.387649	+	0.671428i	−0.992133	−	0.125190i	$-0.960046\pi$
$733$	−4.13335e9	+	7.15918e9i	−0.387649	+	0.671428i	0.604484	+	0.796617i	$0.293379\pi$
$734$	−2.05597e9	+	3.56105e9i	−0.191903	+	0.332385i
$735$		0			0
$736$	−1.53646e9	−	2.66123e9i	−0.142053	−	0.246043i
$737$	8.24849e9			0.758993
$738$		0			0
$739$	−1.46011e10			−1.33085			−0.665424	−	0.746465i	$-0.731749\pi$
$739$	−1.46011e10			−1.33085			−0.665424	+	0.746465i	$0.731749\pi$
$740$	−3.88366e8	−	6.72669e8i	−0.0352314	−	0.0610226i
$741$		0			0
$742$	6.70347e7	−	1.16107e8i	0.00602401	−	0.0104339i
$743$	9.86519e9	−	1.70870e10i	0.882358	−	1.52829i	0.0336456	−	0.999434i	$-0.489288\pi$
$743$	9.86519e9	−	1.70870e10i	0.882358	−	1.52829i	0.848712	−	0.528855i	$-0.177378\pi$
$744$		0			0
$745$	−3.34681e9	−	5.79685e9i	−0.296541	−	0.513623i
$746$	8.46201e9			0.746255
$747$		0			0
$748$	−6.83905e9			−0.597503
$749$	2.88837e7	+	5.00280e7i	0.00251169	+	0.00435038i
$750$		0			0
$751$	8.38564e9	−	1.45244e10i	0.722431	−	1.25129i	−0.237591	−	0.971365i	$-0.576358\pi$
$751$	8.38564e9	−	1.45244e10i	0.722431	−	1.25129i	0.960023	−	0.279922i	$-0.0903087\pi$
$752$	−7.48309e8	+	1.29611e9i	−0.0641680	+	0.111142i
$753$		0			0
$754$	−2.29671e8	−	3.97801e8i	−0.0195122	−	0.0337961i
$755$	−2.73599e9			−0.231367
$756$		0			0
$757$	1.74690e10			1.46363			0.731815	−	0.681503i	$-0.238673\pi$
$757$	1.74690e10			1.46363			0.731815	+	0.681503i	$0.238673\pi$
$758$	1.00047e9	+	1.73286e9i	0.0834376	+	0.144518i
$759$		0			0
$760$	4.75004e8	−	8.22731e8i	0.0392509	−	0.0679845i
$761$	5.28622e9	−	9.15600e9i	0.434810	−	0.753112i	−0.562471	−	0.826817i	$-0.690149\pi$
$761$	5.28622e9	−	9.15600e9i	0.434810	−	0.753112i	0.997280	+	0.0737051i	$0.0234824\pi$
$762$		0			0
$763$	−1.20368e9	−	2.08484e9i	−0.0981017	−	0.169917i
$764$	−1.15179e10			−0.934429
$765$		0			0
$766$	−2.41836e9			−0.194411
$767$	1.37412e9	+	2.38005e9i	0.109962	+	0.190459i
$768$		0			0
$769$	4.83332e9	−	8.37155e9i	0.383268	−	0.663840i	−0.608259	−	0.793739i	$-0.708132\pi$
$769$	4.83332e9	−	8.37155e9i	0.383268	−	0.663840i	0.991527	+	0.129898i	$0.0414651\pi$
$770$	2.38861e8	−	4.13720e8i	0.0188551	−	0.0326579i
$771$		0			0
$772$	6.75897e8	+	1.17069e9i	0.0528713	+	0.0915758i
$773$	8.80988e9			0.686028			0.343014	−	0.939330i	$-0.388552\pi$
$773$	8.80988e9			0.686028			0.343014	+	0.939330i	$0.388552\pi$
$774$		0			0
$775$	−2.19698e10			−1.69539
$776$	5.52511e8	+	9.56977e8i	0.0424448	+	0.0735166i
$777$		0			0
$778$	2.92048e8	−	5.05843e8i	0.0222344	−	0.0385112i
$779$	−5.92295e9	+	1.02589e10i	−0.448908	+	0.777531i
$780$		0			0
$781$	−3.33902e8	−	5.78335e8i	−0.0250807	−	0.0434411i
$782$	−2.56805e10			−1.92035
$783$		0			0
$784$	−3.20488e9			−0.237523
$785$	−1.89846e9	−	3.28824e9i	−0.140074	−	0.242616i
$786$		0			0
$787$	−6.40795e9	+	1.10989e10i	−0.468605	+	0.811648i	−0.999356	−	0.0358797i	$-0.988577\pi$
$787$	−6.40795e9	+	1.10989e10i	−0.468605	+	0.811648i	0.530751	+	0.847528i	$0.321910\pi$
$788$	4.39596e9	−	7.61402e9i	0.320045	−	0.554335i
$789$		0			0
$790$	1.34890e9	+	2.33637e9i	0.0973388	+	0.168596i
$791$	−2.65891e9			−0.191023
$792$		0			0
$793$	9.04378e9			0.644012
$794$	3.97081e9	+	6.87764e9i	0.281518	+	0.487604i
$795$		0			0
$796$	3.10332e9	−	5.37511e9i	0.218088	−	0.377739i
$797$	2.37858e7	−	4.11982e7i	0.00166423	−	0.00288253i	−0.865192	−	0.501441i	$-0.832804\pi$
$797$	2.37858e7	−	4.11982e7i	0.00166423	−	0.00288253i	0.866856	+	0.498558i	$0.166137\pi$
$798$		0			0
$799$	6.25363e9	+	1.08316e10i	0.433729	+	0.751240i
$800$	−2.26828e9			−0.156633
$801$		0			0
$802$	8.86782e9			0.607025
$803$	−5.82456e9	−	1.00884e10i	−0.396971	−	0.687574i
$804$		0			0
$805$	8.96919e8	−	1.55351e9i	0.0605993	−	0.104961i
$806$	−3.96268e9	+	6.86356e9i	−0.266573	+	0.461718i
$807$		0			0
$808$	1.04639e9	+	1.81241e9i	0.0697839	+	0.120869i
$809$	−2.20292e10			−1.46278			−0.731390	−	0.681959i	$-0.761128\pi$
$809$	−2.20292e10			−1.46278			−0.731390	+	0.681959i	$0.761128\pi$
$810$		0			0
$811$	1.42684e10			0.939298			0.469649	−	0.882853i	$-0.344380\pi$
$811$	1.42684e10			0.939298			0.469649	+	0.882853i	$0.344380\pi$
$812$	−1.19335e8	−	2.06695e8i	−0.00782210	−	0.0135483i
$813$		0			0
$814$	1.60620e9	−	2.78201e9i	0.104379	−	0.180790i
$815$	−4.11740e9	+	7.13154e9i	−0.266423	+	0.461458i
$816$		0			0
$817$	−6.72853e9	−	1.16542e10i	−0.431661	−	0.747659i
$818$	−1.14400e10			−0.730787
$819$		0			0
$820$	−3.63751e9			−0.230386
$821$	−9.70217e8	−	1.68047e9i	−0.0611882	−	0.105981i	0.833809	−	0.552054i	$-0.186156\pi$
$821$	−9.70217e8	−	1.68047e9i	−0.0611882	−	0.105981i	−0.894997	+	0.446073i	$0.852822\pi$
$822$		0			0
$823$	−1.18809e10	+	2.05782e10i	−0.742930	+	1.28679i	0.208225	+	0.978081i	$0.433231\pi$
$823$	−1.18809e10	+	2.05782e10i	−0.742930	+	1.28679i	−0.951155	+	0.308712i	$0.900102\pi$
$824$	−4.00203e9	+	6.93171e9i	−0.249192	+	0.431614i
$825$		0			0
$826$	7.13986e8	+	1.23666e9i	0.0440818	+	0.0763519i
$827$	6.55779e9			0.403170			0.201585	−	0.979471i	$-0.435391\pi$
$827$	6.55779e9			0.403170			0.201585	+	0.979471i	$0.435391\pi$
$828$		0			0
$829$	−1.56834e9			−0.0956091			−0.0478046	−	0.998857i	$-0.515222\pi$
$829$	−1.56834e9			−0.0956091			−0.0478046	+	0.998857i	$0.515222\pi$
$830$	−1.29287e9	−	2.23931e9i	−0.0784840	−	0.135938i
$831$		0			0
$832$	−4.09129e8	+	7.08632e8i	−0.0246280	+	0.0426569i
$833$	−1.33916e10	+	2.31950e10i	−0.802742	+	1.39039i
$834$		0			0
$835$	3.55103e9	+	6.15056e9i	0.211082	+	0.365605i
$836$	3.92902e9			0.232575
$837$		0			0
$838$	−3.27634e9			−0.192324
$839$	1.08962e10	+	1.88727e10i	0.636953	+	1.10324i	0.986098	+	0.166166i	$0.0531389\pi$
$839$	1.08962e10	+	1.88727e10i	0.636953	+	1.10324i	−0.349145	+	0.937069i	$0.613528\pi$
$840$		0			0
$841$	8.45575e9	−	1.46458e10i	0.490192	−	0.849038i
$842$	9.33008e9	−	1.61602e10i	0.538633	−	0.932940i
$843$		0			0
$844$	−5.05421e9	−	8.75415e9i	−0.289371	−	0.501205i
$845$	5.00123e9			0.285153
$846$		0			0
$847$	−1.97494e9			−0.111676
$848$	1.69295e8	+	2.93228e8i	0.00953366	+	0.0165128i
$849$		0			0
$850$	−9.47803e9	+	1.64164e10i	−0.529361	+	0.916880i
$851$	6.03124e9	−	1.04464e10i	0.335469	−	0.581050i
$852$		0			0
$853$	1.44291e10	+	2.49919e10i	0.796009	+	1.37873i	0.922197	+	0.386721i	$0.126392\pi$
$853$	1.44291e10	+	2.49919e10i	0.796009	+	1.37873i	−0.126188	+	0.992006i	$0.540274\pi$
$854$	4.69910e9			0.258174
$855$		0			0
$856$	−1.45891e8			−0.00795005
$857$	−8.05248e9	−	1.39473e10i	−0.437015	−	0.756933i	0.560442	−	0.828193i	$-0.310631\pi$
$857$	−8.05248e9	−	1.39473e10i	−0.437015	−	0.756933i	−0.997458	+	0.0712606i	$0.977298\pi$
$858$		0			0
$859$	−6.38497e9	+	1.10591e10i	−0.343702	+	0.595310i	−0.985117	−	0.171884i	$-0.945014\pi$
$859$	−6.38497e9	+	1.10591e10i	−0.343702	+	0.595310i	0.641415	+	0.767194i	$0.278348\pi$
$860$	2.06612e9	−	3.57863e9i	0.110767	−	0.191855i
$861$		0			0
$862$	5.81053e9	+	1.00641e10i	0.308987	+	0.535182i
$863$	−2.29006e10			−1.21285			−0.606427	−	0.795139i	$-0.707398\pi$
$863$	−2.29006e10			−1.21285			−0.606427	+	0.795139i	$0.707398\pi$
$864$		0			0
$865$	−2.52178e9			−0.132480
$866$	1.22410e10	+	2.12020e10i	0.640476	+	1.10934i
$867$		0			0
$868$	−2.05899e9	+	3.56627e9i	−0.106865	+	0.185095i
$869$	−5.57877e9	+	9.66271e9i	−0.288383	+	0.499494i
$870$		0			0
$871$	−4.12373e9	−	7.14250e9i	−0.211459	−	0.366258i
$872$	6.07978e9			0.310513
$873$		0			0
$874$	1.47534e10			0.747485
$875$	−1.40927e9	−	2.44092e9i	−0.0711157	−	0.123176i
$876$		0			0
$877$	−4.39522e9	+	7.61274e9i	−0.220030	+	0.381103i	−0.954817	−	0.297195i	$-0.903949\pi$
$877$	−4.39522e9	+	7.61274e9i	−0.220030	+	0.381103i	0.734787	+	0.678298i	$0.237282\pi$
$878$	6.27548e9	−	1.08694e10i	0.312907	−	0.541972i
$879$		0			0
$880$	6.03241e8	+	1.04484e9i	0.0298402	+	0.0516848i
$881$	2.01724e10			0.993898			0.496949	−	0.867780i	$-0.334454\pi$
$881$	2.01724e10			0.993898			0.496949	+	0.867780i	$0.334454\pi$
$882$		0			0
$883$	−1.47580e10			−0.721382			−0.360691	−	0.932685i	$-0.617459\pi$
$883$	−1.47580e10			−0.721382			−0.360691	+	0.932685i	$0.617459\pi$
$884$	3.41909e9	+	5.92205e9i	0.166467	+	0.288329i
$885$		0			0
$886$	−7.69584e9	+	1.33296e10i	−0.371739	+	0.643871i
$887$	−2.29636e9	+	3.97742e9i	−0.110486	+	0.191368i	−0.915966	−	0.401255i	$-0.868574\pi$
$887$	−2.29636e9	+	3.97742e9i	−0.110486	+	0.191368i	0.805480	+	0.592623i	$0.201907\pi$
$888$		0			0
$889$	−1.86752e9	−	3.23464e9i	−0.0891476	−	0.154408i
$890$	7.68024e9			0.365183
$891$		0			0
$892$	7.28421e9			0.343641
$893$	−3.59270e9	−	6.22274e9i	−0.168827	−	0.292416i
$894$		0			0
$895$	−6.53457e9	+	1.13182e10i	−0.304675	+	0.527712i
$896$	−2.12581e8	+	3.68201e8i	−0.00987293	+	0.0171004i
$897$		0			0
$898$	−7.87362e9	−	1.36375e10i	−0.362833	−	0.628446i
$899$	5.83814e9			0.267988
$900$		0			0
$901$	2.82961e9			0.128881
$902$	−7.52198e9	−	1.30285e10i	−0.341279	−	0.591112i
$903$		0			0
$904$	3.35753e9	−	5.81541e9i	0.151158	−	0.261813i
$905$	−2.08208e9	+	3.60626e9i	−0.0933741	+	0.161729i
$906$		0			0
$907$	−1.22663e10	−	2.12458e10i	−0.545868	−	0.945471i	−0.998552	−	0.0537998i	$-0.982867\pi$
$907$	−1.22663e10	−	2.12458e10i	−0.545868	−	0.945471i	0.452684	−	0.891671i	$-0.350467\pi$
$908$	−1.80023e9			−0.0798046
$909$		0			0
$910$	−4.77662e8			−0.0210124
$911$	−1.85075e9	−	3.20560e9i	−0.0811025	−	0.140474i	0.822621	−	0.568590i	$-0.192511\pi$
$911$	−1.85075e9	−	3.20560e9i	−0.0811025	−	0.140474i	−0.903724	+	0.428116i	$0.859177\pi$
$912$		0			0
$913$	5.34702e9	−	9.26131e9i	0.232522	−	0.402740i
$914$	4.57229e9	−	7.91944e9i	0.198071	−	0.343070i
$915$		0			0
$916$	9.79566e9	+	1.69666e10i	0.421114	+	0.729390i
$917$	−9.91155e8			−0.0424472
$918$		0			0
$919$	1.83943e10			0.781771			0.390885	−	0.920439i	$-0.372169\pi$
$919$	1.83943e10			0.781771			0.390885	+	0.920439i	$0.372169\pi$
$920$	2.26516e9	+	3.92337e9i	0.0959051	+	0.166113i
$921$		0			0
$922$	1.41306e10	−	2.44749e10i	0.593748	−	1.02840i
$923$	−3.33860e8	+	5.78263e8i	−0.0139752	+	0.0242058i
$924$		0			0
$925$	−4.45196e9	−	7.71102e9i	−0.184950	−	0.320343i
$926$	1.56601e10			0.648123
$927$		0			0
$928$	6.02761e8			0.0247587
$929$	−1.31887e10	−	2.28436e10i	−0.539695	−	0.934778i	−0.998920	−	0.0464587i	$-0.985206\pi$
$929$	−1.31887e10	−	2.28436e10i	−0.539695	−	0.934778i	0.459226	−	0.888320i	$-0.348127\pi$
$930$		0			0
$931$	7.69348e9	−	1.33255e10i	0.312463	−	0.541202i
$932$	8.40245e8	−	1.45535e9i	0.0339977	−	0.0588858i
$933$		0			0
$934$	−2.59463e9	−	4.49403e9i	−0.104198	−	0.180477i
$935$	1.00826e10			0.403396
$936$		0			0
$937$	1.51288e8			0.00600782			0.00300391	−	0.999995i	$-0.499044\pi$
$937$	1.51288e8			0.00600782			0.00300391	+	0.999995i	$0.499044\pi$
$938$	−2.14266e9	−	3.71120e9i	−0.0847704	−	0.146827i
$939$		0			0
$940$	1.10321e9	−	1.91081e9i	0.0433222	−	0.0750362i
$941$	−9.13477e9	+	1.58219e10i	−0.357383	+	0.619005i	−0.987523	−	0.157476i	$-0.949664\pi$
$941$	−9.13477e9	+	1.58219e10i	−0.357383	+	0.619005i	0.630140	+	0.776482i	$0.282998\pi$
$942$		0			0
$943$	−2.82449e10	−	4.89216e10i	−1.09686	−	1.89981i
$944$	−3.60633e9			−0.139529
$945$		0			0
$946$	1.70901e10			0.656334
$947$	1.00226e10	+	1.73596e10i	0.383490	+	0.664224i	0.991558	−	0.129660i	$-0.0413887\pi$
$947$	1.00226e10	+	1.73596e10i	0.383490	+	0.664224i	−0.608068	+	0.793885i	$0.708055\pi$
$948$		0			0
$949$	−5.82383e9	+	1.00872e10i	−0.221196	+	0.383123i
$950$	5.44512e9	−	9.43122e9i	0.206051	−	0.356891i
$951$		0			0
$952$	1.77654e9	+	3.07706e9i	0.0667338	+	0.115586i
$953$	−7.26479e9			−0.271893			−0.135946	−	0.990716i	$-0.543408\pi$
$953$	−7.26479e9			−0.271893			−0.135946	+	0.990716i	$0.543408\pi$
$954$		0			0
$955$	1.69805e10			0.630867
$956$	−5.31516e8	−	9.20612e8i	−0.0196749	−	0.0340780i
$957$		0			0
$958$	−1.56209e9	+	2.70562e9i	−0.0574021	+	0.0994233i
$959$	−1.39061e9	+	2.40861e9i	−0.0509145	+	0.0881865i
$960$		0			0
$961$	−3.66086e10	−	6.34079e10i	−1.33061	−	2.30469i
$962$	−3.21199e9			−0.116322
$963$		0			0
$964$	2.18754e10			0.786477
$965$	−9.96454e8	−	1.72591e9i	−0.0356954	−	0.0618262i
$966$		0			0
$967$	1.11784e10	−	1.93616e10i	0.397547	−	0.688572i	−0.595875	−	0.803077i	$-0.703195\pi$
$967$	1.11784e10	−	1.93616e10i	0.397547	−	0.688572i	0.993423	+	0.114505i	$0.0365281\pi$
$968$	2.49384e9	−	4.31946e9i	0.0883700	−	0.153061i
$969$		0			0
$970$	−8.14550e8	−	1.41084e9i	−0.0286561	−	0.0496337i
$971$	−4.85074e9			−0.170036			−0.0850180	−	0.996379i	$-0.527095\pi$
$971$	−4.85074e9			−0.170036			−0.0850180	+	0.996379i	$0.527095\pi$
$972$		0			0
$973$	−3.08409e9			−0.107333
$974$	−4.56994e9	−	7.91537e9i	−0.158473	−	0.274482i
$975$		0			0
$976$	−5.93376e9	+	1.02776e10i	−0.204294	+	0.353848i
$977$	1.60817e10	−	2.78544e10i	0.551699	−	0.955570i	−0.446454	−	0.894807i	$-0.647313\pi$
$977$	1.60817e10	−	2.78544e10i	0.551699	−	0.955570i	0.998152	−	0.0607632i	$-0.0193534\pi$
$978$		0			0
$979$	1.58819e10	+	2.75083e10i	0.540958	+	0.936966i
$980$	4.72486e9			0.160361
$981$		0			0
$982$	−2.69434e10			−0.907950
$983$	2.61035e9	+	4.52127e9i	0.0876521	+	0.151818i	0.906518	−	0.422167i	$-0.138730\pi$
$983$	2.61035e9	+	4.52127e9i	0.0876521	+	0.151818i	−0.818866	+	0.573984i	$0.805397\pi$
$984$		0			0
$985$	−6.48082e9	+	1.12251e10i	−0.216074	+	0.374252i
$986$	2.51864e9	−	4.36242e9i	0.0836753	−	0.144930i
$987$		0			0
$988$	−1.96427e9	−	3.40221e9i	−0.0647964	−	0.112231i
$989$	6.41730e10			2.10943
$990$		0			0
$991$	2.90352e9			0.0947691			0.0473845	−	0.998877i	$-0.484911\pi$
$991$	2.90352e9			0.0947691			0.0473845	+	0.998877i	$0.484911\pi$
$992$	−5.19995e9	−	9.00657e9i	−0.169125	−	0.292933i
$993$		0			0
$994$	−1.73472e8	+	3.00462e8i	−0.00560243	+	0.00970369i
$995$	−4.57513e9	+	7.92437e9i	−0.147239	+	0.255026i
$996$		0			0
$997$	1.66298e10	+	2.88036e10i	0.531439	+	0.920479i	0.999327	+	0.0366913i	$0.0116818\pi$
$997$	1.66298e10	+	2.88036e10i	0.531439	+	0.920479i	−0.467888	+	0.883788i	$0.654985\pi$
$998$	−1.59884e10			−0.509151
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.8.c.b.37.3		8
3.2	odd	2		18.8.c.b.13.3	yes	8
4.3	odd	2		432.8.i.b.145.3		8
9.2	odd	6		18.8.c.b.7.3	✓	8
9.4	even	3		162.8.a.i.1.2		4
9.5	odd	6		162.8.a.h.1.3		4
9.7	even	3	inner	54.8.c.b.19.3		8
12.11	even	2		144.8.i.b.49.2		8
36.7	odd	6		432.8.i.b.289.3		8
36.11	even	6		144.8.i.b.97.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.8.c.b.7.3	✓	8	9.2	odd	6
18.8.c.b.13.3	yes	8	3.2	odd	2
54.8.c.b.19.3		8	9.7	even	3	inner
54.8.c.b.37.3		8	1.1	even	1	trivial
144.8.i.b.49.2		8	12.11	even	2
144.8.i.b.97.2		8	36.11	even	6
162.8.a.h.1.3		4	9.5	odd	6
162.8.a.i.1.2		4	9.4	even	3
432.8.i.b.145.3		8	4.3	odd	2
432.8.i.b.289.3		8	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	54.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 - 6.92820i) q^{2} +(-32.0000 + 55.4256i) q^{4} +(47.1766 - 81.7123i) q^{5} +(-101.366 - 175.572i) q^{7} +512.000 q^{8} -754.826 q^{10} +(-1560.90 - 2703.55i) q^{11} +(-1560.70 + 2703.22i) q^{13} +(-810.932 + 1404.57i) q^{14} +(-2048.00 - 3547.24i) q^{16} -34230.3 q^{17} +19665.3 q^{19} +(3019.30 + 5229.59i) q^{20} +(-12487.2 + 21628.4i) q^{22} +(-46889.1 + 81214.4i) q^{23} +(34611.2 + 59948.4i) q^{25} +24971.2 q^{26} +12974.9 q^{28} +(-9197.41 - 15930.4i) q^{29} +(-158690. + 274859. i) q^{31} +(-16384.0 + 28377.9i) q^{32} +(136921. + 237155. i) q^{34} -19128.5 q^{35} -128628. q^{37} +(-78661.1 - 136245. i) q^{38} +(24154.4 - 41836.7i) q^{40} +(-301188. + 521673. i) q^{41} +(-342153. - 592626. i) q^{43} +199795. q^{44} +750226. q^{46} +(-182693. - 316433. i) q^{47} +(391221. - 677615. i) q^{49} +(276890. - 479587. i) q^{50} +(-99884.9 - 173006. i) q^{52} -82663.8 q^{53} -294552. q^{55} +(-51899.6 - 89892.8i) q^{56} +(-73579.2 + 127443. i) q^{58} +(440225. - 762493. i) q^{59} +(-1.44867e6 - 2.50917e6i) q^{61} +2.53904e6 q^{62} +262144. q^{64} +(147257. + 255057. i) q^{65} +(-1.32111e6 + 2.28823e6i) q^{67} +(1.09537e6 - 1.89724e6i) q^{68} +(76514.0 + 132526. i) q^{70} +213917. q^{71} +3.73155e6 q^{73} +(514510. + 891158. i) q^{74} +(-629289. + 1.08996e6i) q^{76} +(-316445. + 548099. i) q^{77} +(-1.78704e6 - 3.09524e6i) q^{79} -386471. q^{80} +4.81901e6 q^{82} +(1.71280e6 + 2.96666e6i) q^{83} +(-1.61487e6 + 2.79704e6i) q^{85} +(-2.73722e6 + 4.74100e6i) q^{86} +(-799180. - 1.38422e6i) q^{88} -1.01749e7 q^{89} +632811. q^{91} +(-3.00091e6 - 5.19772e6i) q^{92} +(-1.46154e6 + 2.53146e6i) q^{94} +(927742. - 1.60690e6i) q^{95} +(1.07912e6 + 1.86909e6i) q^{97} -6.25954e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{2} - 256 q^{4} - 54 q^{5} - 44 q^{7} + 4096 q^{8} + 864 q^{10} - 2172 q^{11} - 6398 q^{13} - 352 q^{14} - 16384 q^{16} + 51972 q^{17} + 90712 q^{19} - 3456 q^{20} - 17376 q^{22} + 2028 q^{23}+ \cdots + 20368608 q^{98}+O(q^{100}) \) 8 * q - 32 * q^2 - 256 * q^4 - 54 * q^5 - 44 * q^7 + 4096 * q^8 + 864 * q^10 - 2172 * q^11 - 6398 * q^13 - 352 * q^14 - 16384 * q^16 + 51972 * q^17 + 90712 * q^19 - 3456 * q^20 - 17376 * q^22 + 2028 * q^23 - 173446 * q^25 + 102368 * q^26 + 5632 * q^28 - 283098 * q^29 - 812 * q^31 - 131072 * q^32 - 207888 * q^34 + 1492992 * q^35 + 441688 * q^37 - 362848 * q^38 - 27648 * q^40 - 610704 * q^41 - 84380 * q^43 + 278016 * q^44 - 32448 * q^46 - 855708 * q^47 - 1273038 * q^49 - 1387568 * q^50 - 409472 * q^52 + 1842600 * q^53 + 7016760 * q^55 - 22528 * q^56 - 2264784 * q^58 - 380796 * q^59 - 3151130 * q^61 + 12992 * q^62 + 2097152 * q^64 + 326538 * q^65 - 9961580 * q^67 - 1663104 * q^68 - 5971968 * q^70 - 8970384 * q^71 + 29234932 * q^73 - 1766752 * q^74 - 2902784 * q^76 + 5954826 * q^77 - 17309396 * q^79 + 442368 * q^80 + 9771264 * q^82 + 11520192 * q^83 - 14675148 * q^85 - 675040 * q^86 - 1112064 * q^88 - 26066064 * q^89 + 26231936 * q^91 + 129792 * q^92 - 6845664 * q^94 + 31016952 * q^95 - 22003112 * q^97 + 20368608 * q^98

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