LMFDB - Embedded newform 126.10.k.a.89.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,10,Mod(17,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("126.17");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	126.k (of order $6$, degree $2$, 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:	$64.8945153566$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.5
Character	$\chi$	$=$	126.89
Dual form			126.10.k.a.17.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.8564 - 8.00000i) q^{2} +(128.000 + 221.703i) q^{4} +(-356.977 + 618.302i) q^{5} +(3246.94 - 5459.94i) q^{7} -4096.00i q^{8} +O(q^{10})$	\(q+(-13.8564 - 8.00000i) q^{2} +(128.000 + 221.703i) q^{4} +(-356.977 + 618.302i) q^{5} +(3246.94 - 5459.94i) q^{7} -4096.00i q^{8} +(9892.83 - 5711.63i) q^{10} +(63845.5 - 36861.2i) q^{11} -55731.8i q^{13} +(-88670.5 + 49679.7i) q^{14} +(-32768.0 + 56755.8i) q^{16} +(169143. + 292964. i) q^{17} +(-383500. - 221414. i) q^{19} -182772. q^{20} -1.17956e6 q^{22} +(-3353.18 - 1935.96i) q^{23} +(721698. + 1.25002e6i) q^{25} +(-445854. + 772242. i) q^{26} +(1.62609e6 + 20981.5i) q^{28} -5.37860e6i q^{29} +(-5.16690e6 + 2.98311e6i) q^{31} +(908093. - 524288. i) q^{32} -5.41257e6i q^{34} +(2.21681e6 + 3.95666e6i) q^{35} +(-5.29472e6 + 9.17072e6i) q^{37} +(3.54262e6 + 6.13599e6i) q^{38} +(2.53256e6 + 1.46218e6i) q^{40} +2.43056e7 q^{41} +2.01744e7 q^{43} +(1.63445e7 + 9.43648e6i) q^{44} +(30975.4 + 53650.9i) q^{46} +(-728835. + 1.26238e6i) q^{47} +(-1.92684e7 - 3.54562e7i) q^{49} -2.30943e7i q^{50} +(1.23559e7 - 7.13367e6i) q^{52} +(1.32378e7 - 7.64283e6i) q^{53} +5.26344e7i q^{55} +(-2.23639e7 - 1.32995e7i) q^{56} +(-4.30288e7 + 7.45281e7i) q^{58} +(6.10144e7 + 1.05680e8i) q^{59} +(-1.46311e8 - 8.44725e7i) q^{61} +9.54596e7 q^{62} -1.67772e7 q^{64} +(3.44590e7 + 1.98949e7i) q^{65} +(-2.65696e7 - 4.60200e7i) q^{67} +(-4.33005e7 + 7.49987e7i) q^{68} +(936239. - 7.25596e7i) q^{70} -2.21676e8i q^{71} +(-1.41928e8 + 8.19423e7i) q^{73} +(1.46732e8 - 8.47155e7i) q^{74} -1.13364e8i q^{76} +(6.04222e6 - 4.68279e8i) q^{77} +(3.21535e8 - 5.56915e8i) q^{79} +(-2.33948e7 - 4.05210e7i) q^{80} +(-3.36788e8 - 1.94445e8i) q^{82} +5.56291e8 q^{83} -2.41520e8 q^{85} +(-2.79545e8 - 1.61395e8i) q^{86} +(-1.50984e8 - 2.61511e8i) q^{88} +(-8.45572e6 + 1.46457e7i) q^{89} +(-3.04292e8 - 1.80958e8i) q^{91} -991211. i q^{92} +(2.01981e7 - 1.16614e7i) q^{94} +(2.73801e8 - 1.58079e8i) q^{95} -1.52005e9i q^{97} +(-1.66591e7 + 6.45443e8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6144 q^{4} - 12720 q^{7}+O(q^{10}) $ 48 * q + 6144 * q^4 - 12720 * q^7	$ 48 q + 6144 q^{4} - 12720 q^{7} + 153792 q^{10} - 1572864 q^{16} - 2546532 q^{19} + 4853376 q^{22} - 6871164 q^{25} + 2380800 q^{28} - 6720912 q^{31} + 1881660 q^{37} + 39370752 q^{40} - 171303864 q^{43} + 54125568 q^{46} + 129836928 q^{49} - 58125312 q^{52} + 180566208 q^{58} - 632749248 q^{61} - 805306368 q^{64} + 721189428 q^{67} + 308075328 q^{70} - 853713108 q^{73} + 1452429384 q^{79} - 1355242752 q^{82} + 368938080 q^{85} + 621232128 q^{88} + 4577539644 q^{91} - 1279193472 q^{94}+O(q^{100}) $ 48 * q + 6144 * q^4 - 12720 * q^7 + 153792 * q^10 - 1572864 * q^16 - 2546532 * q^19 + 4853376 * q^22 - 6871164 * q^25 + 2380800 * q^28 - 6720912 * q^31 + 1881660 * q^37 + 39370752 * q^40 - 171303864 * q^43 + 54125568 * q^46 + 129836928 * q^49 - 58125312 * q^52 + 180566208 * q^58 - 632749248 * q^61 - 805306368 * q^64 + 721189428 * q^67 + 308075328 * q^70 - 853713108 * q^73 + 1452429384 * q^79 - 1355242752 * q^82 + 368938080 * q^85 + 621232128 * q^88 + 4577539644 * q^91 - 1279193472 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−13.8564	−	8.00000i	−0.612372	−	0.353553i
$2$	−13.8564	−	8.00000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	128.000	+	221.703i	0.250000	+	0.433013i
$5$	−356.977	+	618.302i	−0.255432	+	0.442421i	−0.965013	−	0.262203i	$-0.915551\pi$
$5$	−356.977	+	618.302i	−0.255432	+	0.442421i	0.709581	+	0.704624i	$0.248884\pi$
$6$		0			0
$7$	3246.94	−	5459.94i	0.511132	−	0.859502i
$7$	3246.94	−	5459.94i	0.511132	−	0.859502i
$8$		−	4096.00i		−	0.353553i
$9$		0			0
$10$	9892.83	−	5711.63i	0.312839	−	0.180617i
$11$	63845.5	−	36861.2i	1.31481	−	0.759107i	0.331922	−	0.943307i	$-0.392303\pi$
$11$	63845.5	−	36861.2i	1.31481	−	0.759107i	0.982889	+	0.184200i	$0.0589694\pi$
$12$		0			0
$13$		−	55731.8i		−	0.541200i	−0.962692	−	0.270600i	$-0.912778\pi$
$13$		−	55731.8i		−	0.541200i	0.962692	−	0.270600i	$-0.0872221\pi$
$14$	−88670.5	+	49679.7i	−0.616883	+	0.345623i
$15$		0			0
$16$	−32768.0	+	56755.8i	−0.125000	+	0.216506i
$17$	169143.	+	292964.i	0.491172	+	0.850734i	0.999948	−	0.0101643i	$-0.00323546\pi$
$17$	169143.	+	292964.i	0.491172	+	0.850734i	−0.508777	+	0.860899i	$0.669902\pi$
$18$		0			0
$19$	−383500.	−	221414.i	−0.675109	−	0.389774i	0.122901	−	0.992419i	$-0.460780\pi$
$19$	−383500.	−	221414.i	−0.675109	−	0.389774i	−0.798010	+	0.602645i	$0.794114\pi$
$20$	−182772.			−0.255432
$21$		0			0
$22$	−1.17956e6			−1.07354
$23$	−3353.18	−	1935.96i	−0.00249851	−	0.00144252i	0.498750	−	0.866746i	$-0.333793\pi$
$23$	−3353.18	−	1935.96i	−0.00249851	−	0.00144252i	−0.501249	+	0.865303i	$0.667126\pi$
$24$		0			0
$25$	721698.	+	1.25002e6i	0.369509	+	0.640009i
$26$	−445854.	+	772242.i	−0.191343	+	0.331416i
$27$		0			0
$28$	1.62609e6	+	20981.5i	0.499958	+	0.00645098i
$29$		−	5.37860e6i		−	1.41214i	−0.708141	−	0.706071i	$-0.750466\pi$
$29$		−	5.37860e6i		−	1.41214i	0.708141	−	0.706071i	$-0.249534\pi$
$30$		0			0
$31$	−5.16690e6	+	2.98311e6i	−1.00485	+	0.580152i	−0.909681	−	0.415308i	$-0.863674\pi$
$31$	−5.16690e6	+	2.98311e6i	−1.00485	+	0.580152i	−0.0951727	+	0.995461i	$0.530340\pi$
$32$	908093.	−	524288.i	0.153093	−	0.0883883i
$33$		0			0
$34$		−	5.41257e6i		−	0.694622i
$35$	2.21681e6	+	3.95666e6i	0.249702	+	0.445679i
$36$		0			0
$37$	−5.29472e6	+	9.17072e6i	−0.464446	+	0.804444i	−0.999176	−	0.0405790i	$-0.987080\pi$
$37$	−5.29472e6	+	9.17072e6i	−0.464446	+	0.804444i	0.534731	+	0.845023i	$0.320413\pi$
$38$	3.54262e6	+	6.13599e6i	0.275612	+	0.477374i
$39$		0			0
$40$	2.53256e6	+	1.46218e6i	0.156419	+	0.0903087i
$41$	2.43056e7			1.34332			0.671659	−	0.740860i	$-0.265582\pi$
$41$	2.43056e7			1.34332			0.671659	+	0.740860i	$0.265582\pi$
$42$		0			0
$43$	2.01744e7			0.899896			0.449948	−	0.893055i	$-0.351442\pi$
$43$	2.01744e7			0.899896			0.449948	+	0.893055i	$0.351442\pi$
$44$	1.63445e7	+	9.43648e6i	0.657406	+	0.379553i
$45$		0			0
$46$	30975.4	+	53650.9i	0.00102001	+	0.00176672i
$47$	−728835.	+	1.26238e6i	−0.0217866	+	0.0377355i	−0.876713	−	0.481014i	$-0.840269\pi$
$47$	−728835.	+	1.26238e6i	−0.0217866	+	0.0377355i	0.854927	+	0.518749i	$0.173602\pi$
$48$		0			0
$49$	−1.92684e7	−	3.54562e7i	−0.477489	−	0.878638i
$50$		−	2.30943e7i		−	0.522565i
$51$		0			0
$52$	1.23559e7	−	7.13367e6i	0.234346	−	0.135300i
$53$	1.32378e7	−	7.64283e6i	0.230448	−	0.133049i	−0.380331	−	0.924851i	$-0.624190\pi$
$53$	1.32378e7	−	7.64283e6i	0.230448	−	0.133049i	0.610779	+	0.791801i	$0.290856\pi$
$54$		0			0
$55$			5.26344e7i			0.775599i
$56$	−2.23639e7	−	1.32995e7i	−0.303880	−	0.180712i
$57$		0			0
$58$	−4.30288e7	+	7.45281e7i	−0.499268	+	0.864757i
$59$	6.10144e7	+	1.05680e8i	0.655538	+	1.13543i	0.981759	+	0.190132i	$0.0608916\pi$
$59$	6.10144e7	+	1.05680e8i	0.655538	+	1.13543i	−0.326220	+	0.945294i	$0.605775\pi$
$60$		0			0
$61$	−1.46311e8	−	8.44725e7i	−1.35298	−	0.781144i	−0.364315	−	0.931276i	$-0.618697\pi$
$61$	−1.46311e8	−	8.44725e7i	−1.35298	−	0.781144i	−0.988666	+	0.150132i	$0.952030\pi$
$62$	9.54596e7			0.820459
$63$		0			0
$64$	−1.67772e7			−0.125000
$65$	3.44590e7	+	1.98949e7i	0.239438	+	0.138240i
$66$		0			0
$67$	−2.65696e7	−	4.60200e7i	−0.161083	−	0.279003i	0.774175	−	0.632972i	$-0.218165\pi$
$67$	−2.65696e7	−	4.60200e7i	−0.161083	−	0.279003i	−0.935257	+	0.353969i	$0.884832\pi$
$68$	−4.33005e7	+	7.49987e7i	−0.245586	+	0.425367i
$69$		0			0
$70$	936239.	−	7.25596e7i	0.00466064	−	0.361205i
$71$		−	2.21676e8i		−	1.03528i	−0.855600	−	0.517638i	$-0.826811\pi$
$71$		−	2.21676e8i		−	1.03528i	0.855600	−	0.517638i	$-0.173189\pi$
$72$		0			0
$73$	−1.41928e8	+	8.19423e7i	−0.584946	+	0.337719i	−0.763097	−	0.646284i	$-0.776322\pi$
$73$	−1.41928e8	+	8.19423e7i	−0.584946	+	0.337719i	0.178150	+	0.984003i	$0.442989\pi$
$74$	1.46732e8	−	8.47155e7i	0.568828	−	0.328413i
$75$		0			0
$76$		−	1.13364e8i		−	0.389774i
$77$	6.04222e6	−	4.68279e8i	0.0195879	−	1.51809i
$78$		0			0
$79$	3.21535e8	−	5.56915e8i	0.928766	−	1.60867i	0.143376	−	0.989668i	$-0.454204\pi$
$79$	3.21535e8	−	5.56915e8i	0.928766	−	1.60867i	0.785390	−	0.619001i	$-0.212462\pi$
$80$	−2.33948e7	−	4.05210e7i	−0.0638579	−	0.110605i
$81$		0			0
$82$	−3.36788e8	−	1.94445e8i	−0.822611	−	0.474935i
$83$	5.56291e8			1.28662			0.643310	−	0.765606i	$-0.277561\pi$
$83$	5.56291e8			1.28662			0.643310	+	0.765606i	$0.277561\pi$
$84$		0			0
$85$	−2.41520e8			−0.501843
$86$	−2.79545e8	−	1.61395e8i	−0.551072	−	0.318161i
$87$		0			0
$88$	−1.50984e8	−	2.61511e8i	−0.268385	−	0.464856i
$89$	−8.45572e6	+	1.46457e7i	−0.0142855	+	0.0247432i	−0.873080	−	0.487577i	$-0.837881\pi$
$89$	−8.45572e6	+	1.46457e7i	−0.0142855	+	0.0247432i	0.858794	+	0.512321i	$0.171214\pi$
$90$		0			0
$91$	−3.04292e8	−	1.80958e8i	−0.465163	−	0.276624i
$92$		−	991211.i		−	0.00144252i
$93$		0			0
$94$	2.01981e7	−	1.16614e7i	0.0266830	−	0.0154054i
$95$	2.73801e8	−	1.58079e8i	0.344888	−	0.199121i
$96$		0			0
$97$		−	1.52005e9i		−	1.74335i	−0.490080	−	0.871677i	$-0.663033\pi$
$97$		−	1.52005e9i		−	1.74335i	0.490080	−	0.871677i	$-0.336967\pi$
$98$	−1.66591e7	+	6.45443e8i	−0.0182446	+	0.706871i
$99$		0			0
$100$	−1.84755e8	+	3.20004e8i	−0.184755	+	0.320004i
$101$	−6.84933e8	−	1.18634e9i	−0.654941	−	1.13439i	−0.981909	−	0.189355i	$-0.939360\pi$
$101$	−6.84933e8	−	1.18634e9i	−0.654941	−	1.13439i	0.326968	−	0.945035i	$-0.393973\pi$
$102$		0			0
$103$	−2.50556e8	−	1.44658e8i	−0.219350	−	0.126642i	0.386299	−	0.922373i	$-0.373753\pi$
$103$	−2.50556e8	−	1.44658e8i	−0.219350	−	0.126642i	−0.605649	+	0.795732i	$0.707086\pi$
$104$	−2.28277e8			−0.191343
$105$		0			0
$106$	−2.44570e8			−0.188160
$107$	−5.84468e7	−	3.37443e7i	−0.0431056	−	0.0248870i	0.478292	−	0.878201i	$-0.341256\pi$
$107$	−5.84468e7	−	3.37443e7i	−0.0431056	−	0.0248870i	−0.521398	+	0.853314i	$0.674589\pi$
$108$		0			0
$109$	−7.00714e8	−	1.21367e9i	−0.475468	−	0.823535i	0.524137	−	0.851634i	$-0.324388\pi$
$109$	−7.00714e8	−	1.21367e9i	−0.475468	−	0.823535i	−0.999605	+	0.0280987i	$0.991055\pi$
$110$	4.21075e8	−	7.29324e8i	0.274216	−	0.474956i
$111$		0			0
$112$	2.03488e8	+	3.63194e8i	0.122196	+	0.218101i
$113$		−	1.11691e9i		−	0.644412i	−0.946670	−	0.322206i	$-0.895576\pi$
$113$		−	1.11691e9i		−	0.644412i	0.946670	−	0.322206i	$-0.104424\pi$
$114$		0			0
$115$	2.39401e6	−	1.38218e6i	0.00127640	−	0.000736929i
$116$	1.19245e9	−	6.88461e8i	0.611475	−	0.353036i
$117$		0			0
$118$		−	1.95246e9i		−	0.927071i
$119$	2.14876e9	+	2.77256e7i	0.982261	+	0.0126742i
$120$		0			0
$121$	1.53853e9	−	2.66481e9i	0.652486	−	1.13014i
$122$	1.35156e9	+	2.34097e9i	0.552352	+	0.956702i
$123$		0			0
$124$	−1.32273e9	−	7.63677e8i	−0.502427	−	0.290076i
$125$	−2.42496e9			−0.888401
$126$		0			0
$127$	−3.47543e9			−1.18547			−0.592736	−	0.805397i	$-0.701952\pi$
$127$	−3.47543e9			−1.18547			−0.592736	+	0.805397i	$0.701952\pi$
$128$	2.32472e8	+	1.34218e8i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−3.18319e8	−	5.51345e8i	−0.0977502	−	0.169308i
$131$	−2.44780e7	+	4.23971e7i	−0.00726197	+	0.0125781i	−0.869634	−	0.493698i	$-0.835645\pi$
$131$	−2.44780e7	+	4.23971e7i	−0.00726197	+	0.0125781i	0.862372	+	0.506276i	$0.168978\pi$
$132$		0			0
$133$	−2.45411e9	+	1.37497e9i	−0.680081	+	0.381032i
$134$			8.50228e8i			0.227805i
$135$		0			0
$136$	1.19998e9	−	6.92809e8i	0.300780	−	0.173655i
$137$	6.62905e9	−	3.82729e9i	1.60771	−	0.928214i	0.617834	−	0.786308i	$-0.288010\pi$
$137$	6.62905e9	−	3.82729e9i	1.60771	−	0.928214i	0.989880	−	0.141906i	$-0.0453231\pi$
$138$		0			0
$139$			1.09251e9i			0.248233i	0.992268	+	0.124117i	$0.0396097\pi$
$139$			1.09251e9i			0.248233i	−0.992268	+	0.124117i	$0.960390\pi$
$140$	−5.93450e8	+	9.97925e8i	−0.130559	+	0.219544i
$141$		0			0
$142$	−1.77341e9	+	3.07163e9i	−0.366025	+	0.633975i
$143$	−2.05434e9	−	3.55822e9i	−0.410828	−	0.711576i
$144$		0			0
$145$	3.32560e9	+	1.92004e9i	0.624761	+	0.360706i
$146$	2.62215e9			0.477606
$147$		0			0
$148$	−2.71090e9			−0.464446
$149$	2.18908e8	+	1.26387e8i	0.0363851	+	0.0210069i	0.518082	−	0.855331i	$-0.326646\pi$
$149$	2.18908e8	+	1.26387e8i	0.0363851	+	0.0210069i	−0.481697	+	0.876338i	$0.659979\pi$
$150$		0			0
$151$	3.86750e9	+	6.69871e9i	0.605389	+	1.04856i	0.991990	+	0.126317i	$0.0403157\pi$
$151$	3.86750e9	+	6.69871e9i	0.605389	+	1.04856i	−0.386601	+	0.922247i	$0.626351\pi$
$152$	−9.06910e8	+	1.57081e9i	−0.137806	+	0.238687i
$153$		0			0
$154$	−3.82996e9	+	6.44033e9i	−0.548720	+	0.922709i
$155$		−	4.25961e9i		−	0.592757i
$156$		0			0
$157$	4.67596e9	−	2.69967e9i	0.614218	−	0.354619i	−0.160396	−	0.987053i	$-0.551277\pi$
$157$	4.67596e9	−	2.69967e9i	0.614218	−	0.354619i	0.774615	+	0.632434i	$0.217944\pi$
$158$	−8.91064e9	+	5.14456e9i	−1.13750	+	0.656737i
$159$		0			0
$160$			7.48634e8i			0.0903087i
$161$	−2.14578e7	+	1.20222e7i	−0.00251692	+	0.00141016i
$162$		0			0
$163$	1.25479e9	−	2.17336e9i	0.139228	−	0.241150i	−0.787976	−	0.615705i	$-0.788871\pi$
$163$	1.25479e9	−	2.17336e9i	0.139228	−	0.241150i	0.927205	+	0.374555i	$0.122204\pi$
$164$	3.11112e9	+	5.38861e9i	0.335830	+	0.581674i
$165$		0			0
$166$	−7.70819e9	−	4.45033e9i	−0.787891	−	0.454889i
$167$	1.41674e10			1.40950			0.704752	−	0.709454i	$-0.251058\pi$
$167$	1.41674e10			1.40950			0.704752	+	0.709454i	$0.251058\pi$
$168$		0			0
$169$	7.49847e9			0.707103
$170$	3.34660e9	+	1.93216e9i	0.307315	+	0.177428i
$171$		0			0
$172$	2.58232e9	+	4.47271e9i	0.224974	+	0.389667i
$173$	−7.41411e9	+	1.28416e10i	−0.629291	+	1.08996i	0.358403	+	0.933567i	$0.383321\pi$
$173$	−7.41411e9	+	1.28416e10i	−0.629291	+	1.08996i	−0.987694	+	0.156397i	$0.950012\pi$
$174$		0			0
$175$	9.16833e9	+	1.18299e8i	0.738957	+	0.00953479i
$176$			4.83148e9i			0.379553i
$177$		0			0
$178$	2.34332e8	−	1.35291e8i	0.0174961	−	0.0101014i
$179$	−1.99751e10	+	1.15326e10i	−1.45429	+	0.839635i	−0.998721	−	0.0505655i	$-0.983898\pi$
$179$	−1.99751e10	+	1.15326e10i	−1.45429	+	0.839635i	−0.455569	+	0.890200i	$0.650564\pi$
$180$		0			0
$181$			8.02907e9i			0.556047i	0.960574	+	0.278024i	$0.0896794\pi$
$181$			8.02907e9i			0.556047i	−0.960574	+	0.278024i	$0.910321\pi$
$182$	2.76874e9	+	4.94176e9i	0.187051	+	0.333857i
$183$		0			0
$184$	−7.92969e6	+	1.37346e7i	−0.000510007	+	0.000883358i
$185$	−3.78018e9	−	6.54746e9i	−0.237268	−	0.410961i
$186$		0			0
$187$	2.15980e10	+	1.24696e10i	1.29160	+	0.745703i
$188$	−3.73164e8			−0.0217866
$189$		0			0
$190$	−5.05853e9			−0.281600
$191$	−1.02685e10	−	5.92852e9i	−0.558286	−	0.322326i	0.194171	−	0.980968i	$-0.437798\pi$
$191$	−1.02685e10	−	5.92852e9i	−0.558286	−	0.322326i	−0.752457	+	0.658641i	$0.771132\pi$
$192$		0			0
$193$	9.56031e8	+	1.65589e9i	0.0495980	+	0.0859063i	0.889759	−	0.456431i	$-0.150873\pi$
$193$	9.56031e8	+	1.65589e9i	0.0495980	+	0.0859063i	−0.840161	+	0.542338i	$0.817539\pi$
$194$	−1.21604e10	+	2.10625e10i	−0.616369	+	1.06758i
$195$		0			0
$196$	5.39438e9	−	8.81024e9i	0.261089	−	0.426418i
$197$		−	3.30921e10i		−	1.56540i	−0.622396	−	0.782702i	$-0.713841\pi$
$197$		−	3.30921e10i		−	1.56540i	0.622396	−	0.782702i	$-0.286159\pi$
$198$		0			0
$199$	6.27531e9	−	3.62305e9i	0.283659	−	0.163771i	−0.351420	−	0.936218i	$-0.614301\pi$
$199$	6.27531e9	−	3.62305e9i	0.283659	−	0.163771i	0.635079	+	0.772447i	$0.280968\pi$
$200$	5.12007e9	−	2.95607e9i	0.226277	−	0.130641i
$201$		0			0
$202$			2.19179e10i			0.926226i
$203$	−2.93669e10	−	1.74640e10i	−1.21374	−	0.721791i
$204$		0			0
$205$	−8.67653e9	+	1.50282e10i	−0.343126	+	0.594312i
$206$	2.31453e9	+	4.00889e9i	0.0895491	+	0.155104i
$207$		0			0
$208$	3.16310e9	+	1.82622e9i	0.117173	+	0.0676500i
$209$	−3.26463e10			−1.18352
$210$		0			0
$211$	4.74583e10			1.64832			0.824159	−	0.566358i	$-0.191648\pi$
$211$	4.74583e10			1.64832			0.824159	+	0.566358i	$0.191648\pi$
$212$	3.38887e9	+	1.95656e9i	0.115224	+	0.0665246i
$213$		0			0
$214$	5.39908e8	+	9.35149e8i	0.0175978	+	0.0304803i
$215$	−7.20179e9	+	1.24739e10i	−0.229862	+	0.398133i
$216$		0			0
$217$	−4.88986e8	+	3.78970e10i	−0.0149702	+	1.16021i
$218$			2.24229e10i			0.672414i
$219$		0			0
$220$	−1.16692e10	+	6.73720e9i	−0.335844	+	0.193900i
$221$	1.63274e10	−	9.42662e9i	0.460417	−	0.265822i
$222$		0			0
$223$		−	4.60720e10i		−	1.24757i	−0.781596	−	0.623786i	$-0.785594\pi$
$223$		−	4.60720e10i		−	1.24757i	0.781596	−	0.623786i	$-0.214406\pi$
$224$	8.59403e7	−	6.66047e9i	0.00228077	−	0.176762i
$225$		0			0
$226$	−8.93525e9	+	1.54763e10i	−0.227834	+	0.394620i
$227$	−1.25589e10	−	2.17527e10i	−0.313932	−	0.543747i	0.665278	−	0.746596i	$-0.268313\pi$
$227$	−1.25589e10	−	2.17527e10i	−0.313932	−	0.543747i	−0.979210	+	0.202849i	$0.934980\pi$
$228$		0			0
$229$	−4.99859e9	−	2.88594e9i	−0.120112	−	0.0693470i	0.438740	−	0.898614i	$-0.355425\pi$
$229$	−4.99859e9	−	2.88594e9i	−0.120112	−	0.0693470i	−0.558853	+	0.829267i	$0.688758\pi$
$230$	−4.42299e7			−0.00104218
$231$		0			0
$232$	−2.20308e10			−0.499268
$233$	1.19208e10	+	6.88247e9i	0.264974	+	0.152983i	0.626601	−	0.779340i	$-0.284445\pi$
$233$	1.19208e10	+	6.88247e9i	0.264974	+	0.152983i	−0.361627	+	0.932323i	$0.617779\pi$
$234$		0			0
$235$	−5.20354e8	−	9.01280e8i	−0.0111300	−	0.0192777i
$236$	−1.56197e10	+	2.70541e10i	−0.327769	+	0.567713i
$237$		0			0
$238$	−2.95523e10	−	1.75743e10i	−0.597029	−	0.355043i
$239$			1.92429e9i			0.0381488i	0.999818	+	0.0190744i	$0.00607193\pi$
$239$			1.92429e9i			0.0381488i	−0.999818	+	0.0190744i	$0.993928\pi$
$240$		0			0
$241$	5.24502e10	−	3.02821e10i	1.00154	−	0.578242i	0.0928397	−	0.995681i	$-0.470406\pi$
$241$	5.24502e10	−	3.02821e10i	1.00154	−	0.578242i	0.908705	+	0.417439i	$0.137072\pi$
$242$	−4.26369e10	+	2.46164e10i	−0.799128	+	0.461377i
$243$		0			0
$244$		−	4.32499e10i		−	0.781144i
$245$	2.88010e10	+	7.43364e8i	0.510693	+	0.0131812i
$246$		0			0
$247$	−1.23398e10	+	2.13731e10i	−0.210946	+	0.365369i
$248$	1.22188e10	+	2.11636e10i	0.205115	+	0.355269i
$249$		0			0
$250$	3.36012e10	+	1.93997e10i	0.544032	+	0.314097i
$251$	−2.67413e10			−0.425257			−0.212628	−	0.977133i	$-0.568202\pi$
$251$	−2.67413e10			−0.425257			−0.212628	+	0.977133i	$0.568202\pi$
$252$		0			0
$253$	−2.85447e8			−0.00438010
$254$	4.81569e10	+	2.78034e10i	0.725950	+	0.419128i
$255$		0			0
$256$	−2.14748e9	−	3.71955e9i	−0.0312500	−	0.0541266i
$257$	4.78583e10	−	8.28931e10i	0.684319	−	1.18528i	−0.289331	−	0.957229i	$-0.593433\pi$
$257$	4.78583e10	−	8.28931e10i	0.684319	−	1.18528i	0.973650	−	0.228046i	$-0.0732338\pi$
$258$		0			0
$259$	3.28800e10	+	5.86856e10i	0.454028	+	0.810369i
$260$			1.01862e10i			0.138240i
$261$		0			0
$262$	6.78354e8	−	3.91648e8i	0.00889407	−	0.00513499i
$263$	3.09823e10	−	1.78876e10i	0.399313	−	0.230543i	−0.286875	−	0.957968i	$-0.592616\pi$
$263$	3.09823e10	−	1.78876e10i	0.399313	−	0.230543i	0.686187	+	0.727425i	$0.259283\pi$
$264$		0			0
$265$			1.09132e10i			0.135940i
$266$	4.50048e10	+	5.80699e8i	0.551178	+	0.00711187i
$267$		0			0
$268$	6.80183e9	−	1.17811e10i	0.0805414	−	0.139502i
$269$	−1.26079e10	−	2.18375e10i	−0.146811	−	0.254283i	0.783236	−	0.621724i	$-0.213567\pi$
$269$	−1.26079e10	−	2.18375e10i	−0.146811	−	0.254283i	−0.930047	+	0.367441i	$0.880234\pi$
$270$		0			0
$271$	−9.24325e10	−	5.33659e10i	−1.04103	−	0.601038i	−0.120904	−	0.992664i	$-0.538579\pi$
$271$	−9.24325e10	−	5.33659e10i	−1.04103	−	0.601038i	−0.920125	+	0.391626i	$0.871913\pi$
$272$	−2.21699e10			−0.245586
$273$		0			0
$274$	−1.22473e11			−1.31269
$275$	9.21544e10	+	5.32053e10i	0.971670	+	0.560994i
$276$		0			0
$277$	−2.84544e10	−	4.92844e10i	−0.290396	−	0.502980i	0.683508	−	0.729943i	$-0.260454\pi$
$277$	−2.84544e10	−	4.92844e10i	−0.290396	−	0.502980i	−0.973903	+	0.226963i	$0.927120\pi$
$278$	8.74009e9	−	1.51383e10i	0.0877636	−	0.152011i
$279$		0			0
$280$	1.62065e10	−	9.08006e9i	0.157571	−	0.0882831i
$281$			1.23979e11i			1.18623i	0.805116	+	0.593117i	$0.202103\pi$
$281$			1.23979e11i			1.18623i	−0.805116	+	0.593117i	$0.797897\pi$
$282$		0			0
$283$	−2.59643e10	+	1.49905e10i	−0.240623	+	0.138924i	−0.615463	−	0.788166i	$-0.711031\pi$
$283$	−2.59643e10	+	1.49905e10i	−0.240623	+	0.138924i	0.374840	+	0.927089i	$0.377698\pi$
$284$	4.91461e10	−	2.83745e10i	0.448288	−	0.258819i
$285$		0			0
$286$			6.57389e10i			0.580999i
$287$	7.89188e10	−	1.32707e11i	0.686613	−	1.15459i
$288$		0			0
$289$	2.07539e9	−	3.59469e9i	0.0175009	−	0.0303124i
$290$	−3.07206e10	−	5.32096e10i	−0.255058	−	0.441773i
$291$		0			0
$292$	−3.63336e10	−	2.09772e10i	−0.292473	−	0.168859i
$293$	−7.25083e9			−0.0574756			−0.0287378	−	0.999587i	$-0.509149\pi$
$293$	−7.25083e9			−0.0574756			−0.0287378	+	0.999587i	$0.509149\pi$
$294$		0			0
$295$	−8.71228e10			−0.669781
$296$	3.75633e10	+	2.16872e10i	0.284414	+	0.164206i
$297$		0			0
$298$	−2.02218e9	−	3.50253e9i	−0.0148541	−	0.0257281i
$299$	−1.07894e8	+	1.86879e8i	−0.000780690	+	0.00135220i
$300$		0			0
$301$	6.55050e10	−	1.10151e11i	0.459966	−	0.773463i
$302$		−	1.23760e11i		−	0.856149i
$303$		0			0
$304$	2.51330e10	−	1.45106e10i	0.168777	−	0.0974436i
$305$	1.04459e11	−	6.03094e10i	0.691189	−	0.399058i
$306$		0			0
$307$		−	1.32520e11i		−	0.851448i	−0.904853	−	0.425724i	$-0.860019\pi$
$307$		−	1.32520e11i		−	0.851448i	0.904853	−	0.425724i	$-0.139981\pi$
$308$	1.04592e11	−	5.86002e10i	0.662248	−	0.371040i
$309$		0			0
$310$	−3.40768e10	+	5.90228e10i	−0.209571	+	0.362988i
$311$	−9.99380e9	−	1.73098e10i	−0.0605772	−	0.104923i	0.834146	−	0.551543i	$-0.185961\pi$
$311$	−9.99380e9	−	1.73098e10i	−0.0605772	−	0.104923i	−0.894724	+	0.446620i	$0.852627\pi$
$312$		0			0
$313$	−1.15682e11	−	6.67890e10i	−0.681265	−	0.393328i	0.119067	−	0.992886i	$-0.462010\pi$
$313$	−1.15682e11	−	6.67890e10i	−0.681265	−	0.393328i	−0.800331	+	0.599558i	$0.795343\pi$
$314$	−8.63894e10			−0.501507
$315$		0			0
$316$	1.64626e11			0.928766
$317$	6.11457e10	+	3.53025e10i	0.340094	+	0.196353i	0.660314	−	0.750990i	$-0.270423\pi$
$317$	6.11457e10	+	3.53025e10i	0.340094	+	0.196353i	−0.320220	+	0.947343i	$0.603757\pi$
$318$		0			0
$319$	−1.98262e11	−	3.43400e11i	−1.07197	−	1.85670i
$320$	5.98907e9	−	1.03734e10i	0.0319290	−	0.0553026i
$321$		0			0
$322$	3.93506e8	+	5.07742e6i	0.00203986	+	2.63204e-5i
$323$		−	1.49802e11i		−	0.765784i
$324$		0			0
$325$	6.96657e10	−	4.02215e10i	0.346373	−	0.199978i
$326$	−3.47738e10	+	2.00767e10i	−0.170519	+	0.0984492i
$327$		0			0
$328$		−	9.95558e10i		−	0.474935i
$329$	4.52604e9	+	8.07827e9i	0.0212979	+	0.0380134i
$330$		0			0
$331$	−1.45414e11	+	2.51865e11i	−0.665858	+	1.15330i	0.313194	+	0.949689i	$0.398601\pi$
$331$	−1.45414e11	+	2.51865e11i	−0.665858	+	1.15330i	−0.979052	+	0.203611i	$0.934732\pi$
$332$	7.12052e10	+	1.23331e11i	0.321655	+	0.557123i
$333$		0			0
$334$	−1.96309e11	−	1.13339e11i	−0.863141	−	0.498335i
$335$	3.79390e10			0.164583
$336$		0			0
$337$	5.69469e10			0.240511			0.120256	−	0.992743i	$-0.461629\pi$
$337$	5.69469e10			0.240511			0.120256	+	0.992743i	$0.461629\pi$
$338$	−1.03902e11	−	5.99878e10i	−0.433010	−	0.249999i
$339$		0			0
$340$	−3.09146e10	−	5.35456e10i	−0.125461	−	0.217304i
$341$	−2.19922e11	+	3.80917e11i	−0.880795	+	1.52558i
$342$		0			0
$343$	−2.56152e11	−	9.91983e9i	−0.999251	−	0.0386973i
$344$		−	8.26343e10i		−	0.318161i
$345$		0			0
$346$	2.05466e11	−	1.18626e11i	0.770721	−	0.444976i
$347$	−1.50879e11	+	8.71101e10i	−0.558658	+	0.322542i	−0.752607	−	0.658470i	$-0.771204\pi$
$347$	−1.50879e11	+	8.71101e10i	−0.558658	+	0.322542i	0.193948	+	0.981012i	$0.437871\pi$
$348$		0			0
$349$			4.23796e11i			1.52912i	0.644551	+	0.764561i	$0.277044\pi$
$349$			4.23796e11i			1.52912i	−0.644551	+	0.764561i	$0.722956\pi$
$350$	−1.26094e11	−	7.49859e10i	−0.449146	−	0.267100i
$351$		0			0
$352$	3.86518e10	−	6.69469e10i	0.134192	−	0.232428i
$353$	−1.61862e11	−	2.80353e11i	−0.554829	−	0.960991i	−0.997917	−	0.0645132i	$-0.979451\pi$
$353$	−1.61862e11	−	2.80353e11i	−0.554829	−	0.960991i	0.443088	−	0.896478i	$-0.353883\pi$
$354$		0			0
$355$	1.37063e11	+	7.91332e10i	0.458028	+	0.264442i
$356$	−4.32933e9			−0.0142855
$357$		0			0
$358$	3.69045e11			1.18742
$359$	2.81556e11	+	1.62557e11i	0.894623	+	0.516511i	0.875452	−	0.483305i	$-0.160564\pi$
$359$	2.81556e11	+	1.62557e11i	0.894623	+	0.516511i	0.0191715	+	0.999816i	$0.493897\pi$
$360$		0			0
$361$	−6.32959e10	−	1.09632e11i	−0.196152	−	0.339745i
$362$	6.42326e10	−	1.11254e11i	0.196592	−	0.340508i
$363$		0			0
$364$	1.16934e9	−	9.06250e10i	0.00349127	−	0.270577i
$365$		−	1.17006e11i		−	0.345056i
$366$		0			0
$367$	5.61667e10	−	3.24279e10i	0.161615	−	0.0933084i	−0.417011	−	0.908901i	$-0.636922\pi$
$367$	5.61667e10	−	3.24279e10i	0.161615	−	0.0933084i	0.578626	+	0.815593i	$0.303589\pi$
$368$	2.19754e8	−	1.26875e8i	0.000624628	−	0.000360629i
$369$		0			0
$370$			1.20966e11i			0.335548i
$371$	1.25280e9	−	9.70932e10i	0.00343319	−	0.266076i
$372$		0			0
$373$	7.16305e10	−	1.24068e11i	0.191606	−	0.331871i	−0.754177	−	0.656671i	$-0.771964\pi$
$373$	7.16305e10	−	1.24068e11i	0.191606	−	0.331871i	0.945782	+	0.324801i	$0.105297\pi$
$374$	−1.99514e11	−	3.45568e11i	−0.527292	−	0.913296i
$375$		0			0
$376$	5.17071e9	+	2.98531e9i	0.0133415	+	0.00770272i
$377$	−2.99759e11			−0.764251
$378$		0			0
$379$	4.66316e11			1.16092			0.580462	−	0.814288i	$-0.302872\pi$
$379$	4.66316e11			1.16092			0.580462	+	0.814288i	$0.302872\pi$
$380$	7.00930e10	+	4.04682e10i	0.172444	+	0.0995607i
$381$		0			0
$382$	9.48563e10	+	1.64296e11i	0.227919	+	0.394768i
$383$	−3.91764e11	+	6.78554e11i	−0.930314	+	1.61135i	−0.147530	+	0.989058i	$0.547132\pi$
$383$	−3.91764e11	+	6.78554e11i	−0.930314	+	1.61135i	−0.782784	+	0.622294i	$0.786201\pi$
$384$		0			0
$385$	2.87381e11	+	1.70901e11i	0.666630	+	0.396434i
$386$		−	3.05930e10i		−	0.0701422i
$387$		0			0
$388$	3.36999e11	−	1.94567e11i	0.754895	−	0.435839i
$389$	1.02377e11	−	5.91073e10i	0.226688	−	0.130878i	−0.382355	−	0.924015i	$-0.624887\pi$
$389$	1.02377e11	−	5.91073e10i	0.226688	−	0.130878i	0.609043	+	0.793137i	$0.291554\pi$
$390$		0			0
$391$		−	1.30981e9i		−	0.00283409i
$392$	−1.45229e11	+	7.89233e10i	−0.310645	+	0.168818i
$393$		0			0
$394$	−2.64737e11	+	4.58538e11i	−0.553454	+	0.958611i
$395$	2.29561e11	+	3.97611e11i	0.474472	+	0.821810i
$396$		0			0
$397$	−5.92062e11	−	3.41827e11i	−1.19622	−	0.690636i	−0.236508	−	0.971630i	$-0.576003\pi$
$397$	−5.92062e11	−	3.41827e11i	−1.19622	−	0.690636i	−0.959710	+	0.280993i	$0.909336\pi$
$398$	−1.15938e11			−0.231607
$399$		0			0
$400$	−9.45944e10			−0.184755
$401$	2.33916e11	+	1.35051e11i	0.451762	+	0.260825i	0.708574	−	0.705636i	$-0.249339\pi$
$401$	2.33916e11	+	1.35051e11i	0.451762	+	0.260825i	−0.256812	+	0.966461i	$0.582672\pi$
$402$		0			0
$403$	1.66254e11	+	2.87961e11i	0.313978	+	0.543827i
$404$	1.75343e11	−	3.03703e11i	0.327470	−	0.567195i
$405$		0			0
$406$	2.67207e11	+	4.76923e11i	0.488069	+	0.871126i
$407$			7.80679e11i			1.41026i
$408$		0			0
$409$	−4.18323e11	+	2.41519e11i	−0.739191	+	0.426772i	−0.821775	−	0.569812i	$-0.807016\pi$
$409$	−4.18323e11	+	2.41519e11i	−0.739191	+	0.426772i	0.0825840	+	0.996584i	$0.473683\pi$
$410$	2.40451e11	−	1.38825e11i	0.420242	−	0.242627i
$411$		0			0
$412$		−	7.40651e10i		−	0.126642i
$413$	7.75117e11	+	1.00014e10i	1.31097	+	0.0169155i
$414$		0			0
$415$	−1.98583e11	+	3.43956e11i	−0.328644	+	0.569228i
$416$	−2.92195e10	−	5.06096e10i	−0.0478358	−	0.0828540i
$417$		0			0
$418$	4.52361e11	+	2.61170e11i	0.724755	+	0.418438i
$419$	−6.14901e11			−0.974635			−0.487317	−	0.873225i	$-0.662024\pi$
$419$	−6.14901e11			−0.974635			−0.487317	+	0.873225i	$0.662024\pi$
$420$		0			0
$421$	5.01910e11			0.778675			0.389337	−	0.921095i	$-0.372704\pi$
$421$	5.01910e11			0.778675			0.389337	+	0.921095i	$0.372704\pi$
$422$	−6.57602e11	−	3.79666e11i	−1.00938	−	0.582769i
$423$		0			0
$424$	−3.13050e10	−	5.42219e10i	−0.0470400	−	0.0814757i
$425$	−2.44140e11	+	4.22863e11i	−0.362985	+	0.628708i
$426$		0			0
$427$	−9.36277e11	+	5.24571e11i	−1.36295	+	0.763623i
$428$		−	1.72771e10i		−	0.0248870i
$429$		0			0
$430$	1.99582e11	−	1.15229e11i	0.281522	−	0.162537i
$431$	−3.96806e11	+	2.29096e11i	−0.553899	+	0.319794i	−0.750693	−	0.660651i	$-0.770280\pi$
$431$	−3.96806e11	+	2.29096e11i	−0.553899	+	0.319794i	0.196794	+	0.980445i	$0.436947\pi$
$432$		0			0
$433$			1.19537e12i			1.63421i	0.576490	+	0.817105i	$0.304422\pi$
$433$			1.19537e12i			1.63421i	−0.576490	+	0.817105i	$0.695578\pi$
$434$	3.09952e11	−	5.21204e11i	0.419363	−	0.705187i
$435$		0			0
$436$	1.79383e11	−	3.10700e11i	0.237734	−	0.411768i
$437$	8.57296e8	+	1.48488e9i	0.00112451	+	0.00194771i
$438$		0			0
$439$	1.00057e12	+	5.77682e11i	1.28576	+	0.742333i	0.977895	−	0.209098i	$-0.0670527\pi$
$439$	1.00057e12	+	5.77682e11i	1.28576	+	0.742333i	0.307863	+	0.951431i	$0.400386\pi$
$440$	2.15590e11			0.274216
$441$		0			0
$442$	−3.01652e11			−0.375929
$443$	−4.05805e11	−	2.34292e11i	−0.500612	−	0.289028i	0.228354	−	0.973578i	$-0.426665\pi$
$443$	−4.05805e11	−	2.34292e11i	−0.500612	−	0.289028i	−0.728966	+	0.684550i	$0.759999\pi$
$444$		0			0
$445$	−6.03699e9	−	1.04564e10i	−0.00729794	−	0.0126404i
$446$	−3.68576e11	+	6.38393e11i	−0.441083	+	0.763978i
$447$		0			0
$448$	−5.44746e10	+	9.16027e10i	−0.0638915	+	0.107438i
$449$			7.62318e11i			0.885172i	0.896726	+	0.442586i	$0.145939\pi$
$449$			7.62318e11i			0.885172i	−0.896726	+	0.442586i	$0.854061\pi$
$450$		0			0
$451$	1.55180e12	−	8.95935e11i	1.76621	−	1.01972i
$452$	2.47621e11	−	1.42964e11i	0.279039	−	0.161103i
$453$		0			0
$454$			4.01886e11i			0.443968i
$455$	2.20512e11	−	1.23547e11i	0.241202	−	0.135139i
$456$		0			0
$457$	−5.67997e11	+	9.83799e11i	−0.609148	+	1.05508i	0.382233	+	0.924066i	$0.375155\pi$
$457$	−5.67997e11	+	9.83799e11i	−0.609148	+	1.05508i	−0.991381	+	0.131009i	$0.958178\pi$
$458$	4.61750e10	+	7.99775e10i	0.0490357	+	0.0849324i
$459$		0			0
$460$	6.12868e8	+	3.53839e8i	0.000638199	+	0.000368465i
$461$	−5.03759e11			−0.519479			−0.259740	−	0.965679i	$-0.583637\pi$
$461$	−5.03759e11			−0.519479			−0.259740	+	0.965679i	$0.583637\pi$
$462$		0			0
$463$	−1.79584e12			−1.81616			−0.908078	−	0.418800i	$-0.862451\pi$
$463$	−1.79584e12			−1.81616			−0.908078	+	0.418800i	$0.862451\pi$
$464$	3.05267e11	+	1.76246e11i	0.305738	+	0.176518i
$465$		0			0
$466$	−1.10119e11	−	1.90732e11i	−0.108175	−	0.187365i
$467$	−3.38075e11	+	5.85562e11i	−0.328917	+	0.569701i	−0.982297	−	0.187329i	$-0.940017\pi$
$467$	−3.38075e11	+	5.85562e11i	−0.328917	+	0.569701i	0.653380	+	0.757030i	$0.273350\pi$
$468$		0			0
$469$	−3.37536e11	−	4.35524e9i	−0.322139	−	0.00415657i
$470$			1.66513e10i			0.0157401i
$471$		0			0
$472$	4.32865e11	−	2.49915e11i	0.401434	−	0.231768i
$473$	1.28805e12	−	7.43653e11i	1.18319	−	0.683117i
$474$		0			0
$475$		−	6.39175e11i		−	0.576101i
$476$	2.68895e11	+	4.79935e11i	0.240077	+	0.428500i
$477$		0			0
$478$	1.53943e10	−	2.66638e10i	0.0134876	−	0.0233613i
$479$	6.41006e11	+	1.11026e12i	0.556356	+	0.963636i	0.997797	+	0.0663460i	$0.0211341\pi$
$479$	6.41006e11	+	1.11026e12i	0.556356	+	0.963636i	−0.441441	+	0.897290i	$0.645533\pi$
$480$		0			0
$481$	5.11100e11	+	2.95084e11i	0.435365	+	0.251358i
$482$	−9.69028e11			−0.817758
$483$		0			0
$484$	7.87726e11			0.652486
$485$	9.39851e11	+	5.42623e11i	0.771296	+	0.445308i
$486$		0			0
$487$	−4.00769e11	−	6.94153e11i	−0.322860	−	0.559210i	0.658217	−	0.752828i	$-0.271311\pi$
$487$	−4.00769e11	−	6.94153e11i	−0.322860	−	0.559210i	−0.981077	+	0.193619i	$0.937978\pi$
$488$	−3.45999e11	+	5.99289e11i	−0.276176	+	0.478351i
$489$		0			0
$490$	−3.93131e11	−	2.40708e11i	−0.308074	−	0.188629i
$491$		−	2.17533e12i		−	1.68911i	−0.535468	−	0.844556i	$-0.679865\pi$
$491$		−	2.17533e12i		−	1.68911i	0.535468	−	0.844556i	$-0.320135\pi$
$492$		0			0
$493$	1.57574e12	−	9.09752e11i	1.20136	−	0.693604i
$494$	3.41970e11	−	1.97436e11i	0.258355	−	0.149161i
$495$		0			0
$496$		−	3.91003e11i		−	0.290076i
$497$	−1.21034e12	−	7.19769e11i	−0.889822	−	0.529163i
$498$		0			0
$499$	8.59529e11	−	1.48875e12i	0.620594	−	1.07490i	−0.368781	−	0.929516i	$-0.620225\pi$
$499$	8.59529e11	−	1.48875e12i	0.620594	−	1.07490i	0.989375	−	0.145385i	$-0.0464420\pi$
$500$	−3.10394e11	−	5.37619e11i	−0.222100	−	0.384689i
$501$		0			0
$502$	3.70539e11	+	2.13931e11i	0.260416	+	0.150351i
$503$	−5.70657e11			−0.397483			−0.198742	−	0.980052i	$-0.563685\pi$
$503$	−5.70657e11			−0.397483			−0.198742	+	0.980052i	$0.563685\pi$
$504$		0			0
$505$	9.78020e11			0.669170
$506$	3.95528e9	+	2.28358e9i	0.00268225	+	0.00154860i
$507$		0			0
$508$	−4.44854e11	−	7.70510e11i	−0.296368	−	0.513324i
$509$	1.09703e12	−	1.90012e12i	0.724420	−	1.25473i	−0.234793	−	0.972046i	$-0.575441\pi$
$509$	1.09703e12	−	1.90012e12i	0.724420	−	1.25473i	0.959212	−	0.282686i	$-0.0912256\pi$
$510$		0			0
$511$	−1.34318e10	+	1.04098e12i	−0.00871447	+	0.675381i
$512$			6.87195e10i			0.0441942i
$513$		0			0
$514$	−1.32629e12	+	7.65734e11i	−0.838116	+	0.483887i
$515$	1.78885e11	−	1.03279e11i	0.112058	−	0.0646965i
$516$		0			0
$517$			1.07463e11i			0.0661534i
$518$	1.38864e10	−	1.07621e12i	0.00847434	−	0.656771i
$519$		0			0
$520$	8.14897e10	−	1.41144e11i	0.0488751	−	0.0846541i
$521$	6.30922e11	+	1.09279e12i	0.375151	+	0.649781i	0.990350	−	0.138592i	$-0.0442575\pi$
$521$	6.30922e11	+	1.09279e12i	0.375151	+	0.649781i	−0.615199	+	0.788372i	$0.710924\pi$
$522$		0			0
$523$	−2.42561e12	−	1.40042e12i	−1.41763	−	0.818469i	−0.421540	−	0.906810i	$-0.638510\pi$
$523$	−2.42561e12	−	1.40042e12i	−1.41763	−	0.818469i	−0.996090	+	0.0883411i	$0.971843\pi$
$524$	−1.25327e10			−0.00726197
$525$		0			0
$526$	−5.72405e11			−0.326037
$527$	−1.74789e12	−	1.00914e12i	−0.987111	−	0.569909i
$528$		0			0
$529$	−9.00569e11	−	1.55983e12i	−0.499996	−	0.866018i
$530$	8.73059e10	−	1.51218e11i	0.0480621	−	0.0832459i
$531$		0			0
$532$	−6.18960e11	−	3.68085e11i	−0.335012	−	0.199226i
$533$		−	1.35459e12i		−	0.727004i
$534$		0			0
$535$	4.17283e10	−	2.40918e10i	0.0220211	−	0.0127139i
$536$	−1.88498e11	+	1.08829e11i	−0.0986426	+	0.0569513i
$537$		0			0
$538$			4.03453e11i			0.207622i
$539$	−2.53716e12	−	1.55346e12i	−1.29479	−	0.792778i
$540$		0			0
$541$	−1.46031e12	+	2.52933e12i	−0.732922	+	1.26946i	0.222707	+	0.974885i	$0.428511\pi$
$541$	−1.46031e12	+	2.52933e12i	−0.732922	+	1.26946i	−0.955629	+	0.294572i	$0.904823\pi$
$542$	8.53855e11	+	1.47892e12i	0.424998	+	0.736119i
$543$		0			0
$544$	3.07195e11	+	1.77359e11i	0.150390	+	0.0868277i
$545$	1.00055e12			0.485799
$546$		0			0
$547$	−5.02583e11			−0.240030			−0.120015	−	0.992772i	$-0.538294\pi$
$547$	−5.02583e11			−0.240030			−0.120015	+	0.992772i	$0.538294\pi$
$548$	1.69704e12	+	9.79785e11i	0.803857	+	0.464107i
$549$		0			0
$550$	−8.51286e11	−	1.47447e12i	−0.396683	−	0.687074i
$551$	−1.19090e12	+	2.06269e12i	−0.550417	+	0.953349i
$552$		0			0
$553$	−1.99672e12	−	3.56383e12i	−0.907933	−	1.62052i
$554$			9.10540e11i			0.410681i
$555$		0			0
$556$	−2.42213e11	+	1.39842e11i	−0.107488	+	0.0620583i
$557$	2.32962e12	−	1.34501e12i	1.02550	−	0.592074i	0.109810	−	0.993953i	$-0.464976\pi$
$557$	2.32962e12	−	1.34501e12i	1.02550	−	0.592074i	0.915693	+	0.401878i	$0.131643\pi$
$558$		0			0
$559$		−	1.12435e12i		−	0.487024i
$560$	−2.97204e11	−	3.83483e9i	−0.127705	−	0.00164778i
$561$		0			0
$562$	9.91834e11	−	1.71791e12i	0.419397	−	0.726417i
$563$	1.58266e11	+	2.74125e11i	0.0663896	+	0.114990i	0.897310	−	0.441402i	$-0.145519\pi$
$563$	1.58266e11	+	2.74125e11i	0.0663896	+	0.114990i	−0.830920	+	0.556392i	$0.812185\pi$
$564$		0			0
$565$	6.90585e11	+	3.98709e11i	0.285101	+	0.164603i
$566$	4.79695e11			0.196468
$567$		0			0
$568$	−9.07985e11			−0.366025
$569$	−1.69217e12	−	9.76974e11i	−0.676766	−	0.390731i	0.121870	−	0.992546i	$-0.461111\pi$
$569$	−1.69217e12	−	9.76974e11i	−0.676766	−	0.390731i	−0.798635	+	0.601815i	$0.794444\pi$
$570$		0			0
$571$	−2.16251e12	−	3.74558e12i	−0.851327	−	1.47454i	−0.880011	−	0.474953i	$-0.842465\pi$
$571$	−2.16251e12	−	3.74558e12i	−0.851327	−	1.47454i	0.0286844	−	0.999589i	$-0.490868\pi$
$572$	5.25911e11	−	9.10905e11i	0.205414	−	0.355788i
$573$		0			0
$574$	−2.15519e12	+	1.20750e12i	−0.828670	+	0.464282i
$575$		−	5.58871e9i		−	0.00213209i
$576$		0			0
$577$	3.77485e12	−	2.17941e12i	1.41778	−	0.818555i	0.421676	−	0.906747i	$-0.361442\pi$
$577$	3.77485e12	−	2.17941e12i	1.41778	−	0.818555i	0.996104	+	0.0881910i	$0.0281086\pi$
$578$	−5.75150e10	+	3.32063e10i	−0.0214341	+	0.0123750i
$579$		0			0
$580$			9.83058e11i			0.360706i
$581$	1.80624e12	−	3.03732e12i	0.657633	−	1.10585i
$582$		0			0
$583$	5.63448e11	−	9.75921e11i	0.201997	−	0.349869i
$584$	3.35636e11	+	5.81338e11i	0.119402	+	0.206810i
$585$		0			0
$586$	1.00470e11	+	5.80066e10i	0.0351965	+	0.0203207i
$587$	4.35153e12			1.51276			0.756380	−	0.654132i	$-0.226966\pi$
$587$	4.35153e12			1.51276			0.756380	+	0.654132i	$0.226966\pi$
$588$		0			0
$589$	2.64201e12			0.904514
$590$	1.20721e12	+	6.96983e11i	0.410156	+	0.236803i
$591$		0			0
$592$	−3.46995e11	−	6.01012e11i	−0.116111	−	0.201111i
$593$	1.62000e12	−	2.80592e12i	0.537982	−	0.931813i	−0.461030	−	0.887384i	$-0.652520\pi$
$593$	1.62000e12	−	2.80592e12i	0.537982	−	0.931813i	0.999013	−	0.0444284i	$-0.0141467\pi$
$594$		0			0
$595$	−7.84201e11	+	1.31869e12i	−0.256508	+	0.431335i
$596$			6.47099e10i			0.0210069i
$597$		0			0
$598$	2.99006e9	−	1.72631e9i	0.000956146	−	0.000552031i
$599$	5.77126e11	−	3.33204e11i	0.183168	−	0.105752i	−0.405612	−	0.914045i	$-0.632942\pi$
$599$	5.77126e11	−	3.33204e11i	0.183168	−	0.105752i	0.588780	+	0.808293i	$0.299608\pi$
$600$		0			0
$601$			6.04326e12i			1.88945i	0.327861	+	0.944726i	$0.393672\pi$
$601$			6.04326e12i			1.88945i	−0.327861	+	0.944726i	$0.606328\pi$
$602$	−1.78887e12	+	1.00226e12i	−0.555131	+	0.311025i
$603$		0			0
$604$	−9.90081e11	+	1.71487e12i	−0.302694	+	0.524282i
$605$	1.09844e12	+	1.90255e12i	0.333331	+	0.577346i
$606$		0			0
$607$	5.20573e12	+	3.00553e12i	1.55644	+	0.898612i	0.997593	+	0.0693424i	$0.0220901\pi$
$607$	5.20573e12	+	3.00553e12i	1.55644	+	0.898612i	0.558849	+	0.829270i	$0.311243\pi$
$608$	−4.64338e11			−0.137806
$609$		0			0
$610$	−1.92990e12			−0.564353
$611$	7.03547e10	+	4.06193e10i	0.0204224	+	0.0117909i
$612$		0			0
$613$	−2.25418e12	−	3.90435e12i	−0.644786	−	1.11680i	−0.984351	−	0.176220i	$-0.943613\pi$
$613$	−2.25418e12	−	3.90435e12i	−0.644786	−	1.11680i	0.339565	−	0.940583i	$-0.389720\pi$
$614$	−1.06016e12	+	1.83625e12i	−0.301032	+	0.521403i
$615$		0			0
$616$	−1.91807e12	−	2.47489e10i	−0.536725	−	0.00692538i
$617$		−	1.50317e11i		−	0.0417566i	−0.999782	−	0.0208783i	$-0.993354\pi$
$617$		−	1.50317e11i		−	0.0417566i	0.999782	−	0.0208783i	$-0.00664625\pi$
$618$		0			0
$619$	2.93736e12	−	1.69589e12i	0.804173	−	0.464290i	−0.0407550	−	0.999169i	$-0.512976\pi$
$619$	2.93736e12	−	1.69589e12i	0.804173	−	0.464290i	0.844928	+	0.534879i	$0.179643\pi$
$620$	9.44365e11	−	5.45230e11i	0.256671	−	0.148189i
$621$		0			0
$622$			3.19802e11i			0.0856691i
$623$	5.25097e10	+	9.37215e10i	0.0139651	+	0.0249255i
$624$		0			0
$625$	−5.43913e11	+	9.42085e11i	−0.142584	+	0.246962i
$626$	1.06862e12	+	1.85091e12i	0.278125	+	0.481727i
$627$		0			0
$628$	1.19705e12	+	6.91115e11i	0.307109	+	0.177310i
$629$	−3.58225e12			−0.912490
$630$		0			0
$631$	−2.64583e12			−0.664400			−0.332200	−	0.943209i	$-0.607791\pi$
$631$	−2.64583e12			−0.664400			−0.332200	+	0.943209i	$0.607791\pi$
$632$	−2.28112e12	−	1.31701e12i	−0.568751	−	0.328368i
$633$		0			0
$634$	−5.64839e11	−	9.78331e11i	−0.138843	−	0.240483i
$635$	1.24065e12	−	2.14886e12i	0.302807	−	0.524477i
$636$		0			0
$637$	−1.97604e12	+	1.07386e12i	−0.475519	+	0.258417i
$638$			6.34438e12i			1.51599i
$639$		0			0
$640$	−1.65974e11	+	9.58252e10i	−0.0391048	+	0.0225772i
$641$	3.31318e12	−	1.91286e12i	0.775146	−	0.447531i	−0.0595611	−	0.998225i	$-0.518970\pi$
$641$	3.31318e12	−	1.91286e12i	0.775146	−	0.447531i	0.834707	+	0.550694i	$0.185637\pi$
$642$		0			0
$643$			4.67863e12i			1.07937i	0.841868	+	0.539684i	$0.181456\pi$
$643$			4.67863e12i			1.07937i	−0.841868	+	0.539684i	$0.818544\pi$
$644$	−5.41196e9	−	3.21840e9i	−0.00123985	−	0.000737316i
$645$		0			0
$646$	−1.19842e12	+	2.07572e12i	−0.270746	+	0.468945i
$647$	3.11037e12	+	5.38731e12i	0.697818	+	1.20866i	0.969221	+	0.246191i	$0.0791790\pi$
$647$	3.11037e12	+	5.38731e12i	0.697818	+	1.20866i	−0.271403	+	0.962466i	$0.587488\pi$
$648$		0			0
$649$	7.79099e12	+	4.49813e12i	1.72382	+	0.995247i
$650$	−1.28709e12			−0.282812
$651$		0			0
$652$	6.42453e11			0.139228
$653$	−4.87677e12	−	2.81561e12i	−1.04960	−	0.605986i	−0.127061	−	0.991895i	$-0.540555\pi$
$653$	−4.87677e12	−	2.81561e12i	−1.04960	−	0.605986i	−0.922537	+	0.385909i	$0.873888\pi$
$654$		0			0
$655$	−1.74761e10	−	3.02695e10i	−0.00370988	−	0.00642569i
$656$	−7.96446e11	+	1.37949e12i	−0.167915	+	0.290837i
$657$		0			0
$658$	1.91151e9	−	1.48144e11i	0.000397521	−	0.0308083i
$659$			3.05368e12i			0.630725i	0.948971	+	0.315362i	$0.102126\pi$
$659$			3.05368e12i			0.630725i	−0.948971	+	0.315362i	$0.897874\pi$
$660$		0			0
$661$	−5.63702e11	+	3.25453e11i	−0.114853	+	0.0663105i	−0.556326	−	0.830964i	$-0.687789\pi$
$661$	−5.63702e11	+	3.25453e11i	−0.114853	+	0.0663105i	0.441473	+	0.897275i	$0.354456\pi$
$662$	4.02984e12	−	2.32663e12i	0.815506	−	0.470833i
$663$		0			0
$664$		−	2.27857e12i		−	0.454889i
$665$	2.59120e10	−	2.00821e12i	0.00513811	−	0.398210i
$666$		0			0
$667$	−1.04128e10	+	1.80354e10i	−0.00203704	+	0.00352826i
$668$	1.81343e12	+	3.14095e12i	0.352376	+	0.610333i
$669$		0			0
$670$	−5.25698e11	−	3.03512e11i	−0.100786	−	0.0581887i
$671$	−1.24550e13			−2.37189
$672$		0			0
$673$	3.39305e12			0.637563			0.318781	−	0.947828i	$-0.396726\pi$
$673$	3.39305e12			0.637563			0.318781	+	0.947828i	$0.396726\pi$
$674$	−7.89079e11	−	4.55575e11i	−0.147282	−	0.0850335i
$675$		0			0
$676$	9.59804e11	+	1.66243e12i	0.176776	+	0.306184i
$677$	1.95067e12	−	3.37866e12i	0.356890	−	0.618152i	−0.630549	−	0.776149i	$-0.717170\pi$
$677$	1.95067e12	−	3.37866e12i	0.356890	−	0.618152i	0.987440	+	0.157997i	$0.0505037\pi$
$678$		0			0
$679$	−8.29940e12	−	4.93552e12i	−1.49842	−	0.891084i
$680$			9.89266e11i			0.177428i
$681$		0			0
$682$	6.09467e12	−	3.51876e12i	1.07875	−	0.622816i
$683$	−3.02967e12	+	1.74918e12i	−0.532724	+	0.307568i	−0.742125	−	0.670261i	$-0.766182\pi$
$683$	−3.02967e12	+	1.74918e12i	−0.532724	+	0.307568i	0.209401	+	0.977830i	$0.432849\pi$
$684$		0			0
$685$			5.46501e12i			0.948381i
$686$	3.46999e12	+	2.18667e12i	0.598232	+	0.376986i
$687$		0			0
$688$	−6.61075e11	+	1.14501e12i	−0.112487	+	0.194833i
$689$	−4.25948e11	−	7.37764e11i	−0.0720063	−	0.124719i
$690$		0			0
$691$	−1.86937e12	−	1.07928e12i	−0.311921	−	0.180088i	0.335865	−	0.941910i	$-0.390972\pi$
$691$	−1.86937e12	−	1.07928e12i	−0.311921	−	0.180088i	−0.647786	+	0.761822i	$0.724305\pi$
$692$	−3.79602e12			−0.629291
$693$		0			0
$694$	2.78752e12			0.456143
$695$	−6.75502e11	−	3.90001e11i	−0.109823	−	0.0634066i
$696$		0			0
$697$	4.11112e12	+	7.12066e12i	0.659800	+	1.14281i
$698$	3.39037e12	−	5.87229e12i	0.540626	−	0.936392i
$699$		0			0
$700$	1.14732e12	+	2.04779e12i	0.180611	+	0.322362i
$701$			4.90220e12i			0.766761i	0.923590	+	0.383381i	$0.125240\pi$
$701$			4.90220e12i			0.766761i	−0.923590	+	0.383381i	$0.874760\pi$
$702$		0			0
$703$	4.06104e12	−	2.34464e12i	0.627103	−	0.362058i
$704$	−1.07115e12	+	6.18429e11i	−0.164351	+	0.0948883i
$705$		0			0
$706$			5.17958e12i			0.784646i
$707$	−8.70128e12	−	1.12273e11i	−1.30977	−	0.0169000i
$708$		0			0
$709$	2.72230e12	−	4.71517e12i	0.404602	−	0.700792i	−0.589673	−	0.807642i	$-0.700743\pi$
$709$	2.72230e12	−	4.71517e12i	0.404602	−	0.700792i	0.994275	+	0.106851i	$0.0340767\pi$
$710$	−1.26613e12	−	2.19300e12i	−0.186989	−	0.323874i
$711$		0			0
$712$	5.99889e10	+	3.46346e10i	0.00874805	+	0.00505069i
$713$	2.31007e10			0.00334752
$714$		0			0
$715$	2.93341e12			0.419754
$716$	−5.11363e12	−	2.95236e12i	−0.727145	−	0.419817i
$717$		0			0
$718$	−2.60091e12	−	4.50490e12i	−0.365229	−	0.632594i
$719$	−6.44498e12	+	1.11630e13i	−0.899377	+	1.55777i	−0.0710844	+	0.997470i	$0.522646\pi$
$719$	−6.44498e12	+	1.11630e13i	−0.899377	+	1.55777i	−0.828292	+	0.560296i	$0.810687\pi$
$720$		0			0
$721$	−1.60337e12	+	8.98323e11i	−0.220965	+	0.123801i
$722$			2.02547e12i			0.277401i
$723$		0			0
$724$	−1.78007e12	+	1.02772e12i	−0.240776	+	0.139012i
$725$	6.72335e12	−	3.88173e12i	0.903784	−	0.521800i
$726$		0			0
$727$			8.56007e12i			1.13651i	0.822853	+	0.568254i	$0.192381\pi$
$727$			8.56007e12i			1.13651i	−0.822853	+	0.568254i	$0.807619\pi$
$728$	−7.41202e11	+	1.24638e12i	−0.0978015	+	0.164460i
$729$		0			0
$730$	−9.36047e11	+	1.62128e12i	−0.121996	+	0.211303i
$731$	3.41235e12	+	5.91037e12i	0.442004	+	0.765573i
$732$		0			0
$733$	9.31054e12	+	5.37544e12i	1.19126	+	0.687775i	0.958592	−	0.284782i	$-0.0919211\pi$
$733$	9.31054e12	+	5.37544e12i	1.19126	+	0.687775i	0.232668	+	0.972556i	$0.425254\pi$
$734$	−1.03769e12			−0.131958
$735$		0			0
$736$	−4.06000e9			−0.000510007
$737$	−3.39270e12	−	1.95878e12i	−0.423587	−	0.244558i
$738$		0			0
$739$	−5.77050e12	−	9.99480e12i	−0.711727	−	1.23275i	−0.964208	−	0.265146i	$-0.914580\pi$
$739$	−5.77050e12	−	9.99480e12i	−0.711727	−	1.23275i	0.252481	−	0.967602i	$-0.418754\pi$
$740$	9.67726e11	−	1.67615e12i	0.118634	−	0.205480i
$741$		0			0
$742$	−7.94105e11	+	1.33534e12i	−0.0961746	+	0.161724i
$743$		−	8.63606e12i		−	1.03960i	−0.854288	−	0.519799i	$-0.826007\pi$
$743$		−	8.63606e12i		−	1.03960i	0.854288	−	0.519799i	$-0.173993\pi$
$744$		0			0
$745$	−1.56290e11	+	9.02341e10i	−0.0185878	+	0.0107317i
$746$	−1.98508e12	+	1.14609e12i	−0.234668	+	0.135486i
$747$		0			0
$748$			6.38445e12i			0.745703i
$749$	−3.74015e11	+	2.09551e11i	−0.0434231	+	0.0243288i
$750$		0			0
$751$	3.04625e12	−	5.27626e12i	0.349451	−	0.605267i	−0.636701	−	0.771111i	$-0.719701\pi$
$751$	3.04625e12	−	5.27626e12i	0.349451	−	0.605267i	0.986152	+	0.165844i	$0.0530348\pi$
$752$	−4.77650e10	−	8.27313e10i	−0.00544665	−	0.00943387i
$753$		0			0
$754$	4.15358e12	+	2.39807e12i	0.468006	+	0.270204i
$755$	−5.52243e12			−0.618542
$756$		0			0
$757$	1.51502e13			1.67682			0.838410	−	0.545039i	$-0.183485\pi$
$757$	1.51502e13			1.67682			0.838410	+	0.545039i	$0.183485\pi$
$758$	−6.46146e12	−	3.73052e12i	−0.710917	−	0.410448i
$759$		0			0
$760$	−6.47491e11	−	1.12149e12i	−0.0704000	−	0.121936i
$761$	−2.09653e12	+	3.63130e12i	−0.226605	+	0.392492i	−0.956800	−	0.290747i	$-0.906096\pi$
$761$	−2.09653e12	+	3.63130e12i	−0.226605	+	0.392492i	0.730194	+	0.683239i	$0.239429\pi$
$762$		0			0
$763$	−8.90176e12	−	1.14860e11i	−0.950858	−	0.0122689i
$764$		−	3.03540e12i		−	0.322326i
$765$		0			0
$766$	1.08569e13	−	6.26822e12i	1.13940	−	0.657831i
$767$	5.88973e12	−	3.40044e12i	0.614492	−	0.354777i
$768$		0			0
$769$			1.61914e13i			1.66961i	0.550544	+	0.834806i	$0.314420\pi$
$769$			1.61914e13i			1.66961i	−0.550544	+	0.834806i	$0.685580\pi$
$770$	−2.61486e12	−	4.66712e12i	−0.268065	−	0.478454i
$771$		0			0
$772$	−2.44744e11	+	4.23909e11i	−0.0247990	+	0.0429531i
$773$	9.08785e12	+	1.57406e13i	0.915490	+	1.58567i	0.806183	+	0.591667i	$0.201530\pi$
$773$	9.08785e12	+	1.57406e13i	0.915490	+	1.58567i	0.109307	+	0.994008i	$0.465137\pi$
$774$		0			0
$775$	−7.45789e12	−	4.30581e12i	−0.742605	−	0.428743i
$776$	−6.22613e12			−0.616369
$777$		0			0
$778$	−1.89143e12			−0.185090
$779$	−9.32119e12	−	5.38159e12i	−0.906886	−	0.523591i
$780$		0			0
$781$	−8.17125e12	−	1.41530e13i	−0.785885	−	1.36119i
$782$	−1.04785e10	+	1.81493e10i	−0.00100200	+	0.00173552i
$783$		0			0
$784$	2.64373e12	+	6.82357e10i	0.249917	+	0.00645044i
$785$			3.85488e12i			0.362324i
$786$		0			0
$787$	5.51229e12	−	3.18252e12i	0.512207	−	0.295723i	−0.221533	−	0.975153i	$-0.571106\pi$
$787$	5.51229e12	−	3.18252e12i	0.512207	−	0.295723i	0.733740	+	0.679430i	$0.237773\pi$
$788$	7.33661e12	−	4.23579e12i	0.677840	−	0.391351i
$789$		0			0
$790$		−	7.34595e12i		−	0.671005i
$791$	−6.09824e12	−	3.62652e12i	−0.553874	−	0.329379i
$792$		0			0
$793$	−4.70780e12	+	8.15415e12i	−0.422755	+	0.732233i
$794$	5.46924e12	+	9.47300e12i	0.488354	+	0.845853i
$795$		0			0
$796$	1.60648e12	+	9.27502e11i	0.141829	+	0.0818853i
$797$	2.00292e13			1.75833			0.879165	−	0.476517i	$-0.158101\pi$
$797$	2.00292e13			1.75833			0.879165	+	0.476517i	$0.158101\pi$
$798$		0			0
$799$	−4.93109e11			−0.0428038
$800$	1.31074e12	+	7.56755e11i	0.113139	+	0.0653206i
$801$		0			0
$802$	−2.16082e12	−	3.74265e12i	−0.184431	−	0.319444i
$803$	−6.04099e12	+	1.04633e13i	−0.512729	+	0.888073i
$804$		0			0
$805$	2.26565e8	−	1.75591e10i	1.90157e−5	−	0.00147374i
$806$		−	5.32013e12i		−	0.444033i
$807$		0			0
$808$	−4.85924e12	+	2.80549e12i	−0.401068	+	0.231556i
$809$	1.71579e13	−	9.90614e12i	1.40830	−	0.813085i	0.413080	−	0.910695i	$-0.364453\pi$
$809$	1.71579e13	−	9.90614e12i	1.40830	−	0.813085i	0.995225	+	0.0976099i	$0.0311198\pi$
$810$		0			0
$811$			1.20340e13i			0.976824i	0.872613	+	0.488412i	$0.162424\pi$
$811$			1.20340e13i			0.976824i	−0.872613	+	0.488412i	$0.837576\pi$
$812$	1.12851e11	−	8.74610e12i	0.00910970	−	0.706012i
$813$		0			0
$814$	6.24543e12	−	1.08174e13i	0.498601	−	0.863601i
$815$	8.95862e11	+	1.55168e12i	0.0711266	+	0.123195i
$816$		0			0
$817$	−7.73687e12	−	4.46689e12i	−0.607528	−	0.350756i
$818$	7.72860e12			0.603547
$819$		0			0
$820$	−4.44238e12			−0.343126
$821$	1.22672e13	+	7.08246e12i	0.942324	+	0.544051i	0.890688	−	0.454615i	$-0.150223\pi$
$821$	1.22672e13	+	7.08246e12i	0.942324	+	0.544051i	0.0516361	+	0.998666i	$0.483556\pi$
$822$		0			0
$823$	−8.23115e12	−	1.42568e13i	−0.625405	−	1.08323i	−0.988462	−	0.151466i	$-0.951601\pi$
$823$	−8.23115e12	−	1.42568e13i	−0.625405	−	1.08323i	0.363058	−	0.931767i	$-0.381733\pi$
$824$	−5.92521e11	+	1.02628e12i	−0.0447745	+	0.0775518i
$825$		0			0
$826$	−1.06603e13	−	6.33952e12i	−0.796820	−	0.473856i
$827$			2.52184e13i			1.87475i	0.348323	+	0.937375i	$0.386751\pi$
$827$			2.52184e13i			1.87475i	−0.348323	+	0.937375i	$0.613249\pi$
$828$		0			0
$829$	−8.36839e12	+	4.83149e12i	−0.615385	+	0.355293i	−0.775070	−	0.631875i	$-0.782285\pi$
$829$	−8.36839e12	+	4.83149e12i	−0.615385	+	0.355293i	0.159685	+	0.987168i	$0.448952\pi$
$830$	5.50329e12	−	3.17733e12i	0.402505	−	0.232386i
$831$		0			0
$832$			9.35024e11i			0.0676500i
$833$	7.12828e12	−	1.16421e13i	0.512959	−	0.837778i
$834$		0			0
$835$	−5.05743e12	+	8.75973e12i	−0.360032	+	0.623593i
$836$	−4.17873e12	−	7.23777e12i	−0.295880	−	0.512479i
$837$		0			0
$838$	8.52031e12	+	4.91920e12i	0.596839	+	0.344585i
$839$	−7.62750e12			−0.531439			−0.265719	−	0.964050i	$-0.585609\pi$
$839$	−7.62750e12			−0.531439			−0.265719	+	0.964050i	$0.585609\pi$
$840$		0			0
$841$	−1.44222e13			−0.994146
$842$	−6.95467e12	−	4.01528e12i	−0.476839	−	0.275303i
$843$		0			0
$844$	6.07466e12	+	1.05216e13i	0.412080	+	0.713743i
$845$	−2.67678e12	+	4.63632e12i	−0.180616	+	0.312837i
$846$		0			0
$847$	−9.55420e12	−	1.70527e13i	−0.637850	−	1.13846i
$848$			1.00176e12i			0.0665246i
$849$		0			0
$850$	6.76580e12	−	3.90624e12i	0.444564	−	0.256669i
$851$	3.55083e10	−	2.05007e10i	0.00232085	−	0.00133994i
$852$		0			0
$853$		−	9.07081e12i		−	0.586645i	−0.956014	−	0.293322i	$-0.905239\pi$
$853$		−	9.07081e12i		−	0.586645i	0.956014	−	0.293322i	$-0.0947610\pi$
$854$	1.71700e13	+	2.21545e11i	1.10461	+	0.0142529i
$855$		0			0
$856$	−1.38217e11	+	2.39398e11i	−0.00879889	+	0.0152401i
$857$	−1.49158e10	−	2.58350e10i	−0.000944569	−	0.00163604i	0.865553	−	0.500818i	$-0.166967\pi$
$857$	−1.49158e10	−	2.58350e10i	−0.000944569	−	0.00163604i	−0.866497	+	0.499182i	$0.833634\pi$
$858$		0			0
$859$	−1.06016e13	−	6.12085e12i	−0.664360	−	0.383568i	0.129576	−	0.991569i	$-0.458638\pi$
$859$	−1.06016e13	−	6.12085e12i	−0.664360	−	0.383568i	−0.793936	+	0.608001i	$0.791972\pi$
$860$	−3.68732e12			−0.229862
$861$		0			0
$862$	7.33108e12			0.452257
$863$	7.21623e12	+	4.16629e12i	0.442855	+	0.255682i	0.704808	−	0.709398i	$-0.251033\pi$
$863$	7.21623e12	+	4.16629e12i	0.442855	+	0.255682i	−0.261953	+	0.965081i	$0.584367\pi$
$864$		0			0
$865$	−5.29333e12	−	9.16831e12i	−0.321482	−	0.556823i
$866$	9.56298e12	−	1.65636e13i	0.577780	−	1.00074i
$867$		0			0
$868$	−8.46445e12	+	4.74241e12i	−0.506127	+	0.283570i
$869$		−	4.74087e13i		−	2.82013i
$870$		0			0
$871$	−2.56477e12	+	1.48077e12i	−0.150997	+	0.0871780i
$872$	−4.97120e12	+	2.87013e12i	−0.291164	+	0.168103i
$873$		0			0
$874$		−	2.74335e10i		−	0.00159030i
$875$	−7.87369e12	+	1.32401e13i	−0.454090	+	0.763583i
$876$		0			0
$877$	−1.10283e13	+	1.91017e13i	−0.629524	+	1.09037i	0.358123	+	0.933674i	$0.383417\pi$
$877$	−1.10283e13	+	1.91017e13i	−0.629524	+	1.09037i	−0.987647	+	0.156693i	$0.949917\pi$
$878$	−9.24291e12	−	1.60092e13i	−0.524909	−	0.909168i
$879$		0			0
$880$	−2.98731e12	−	1.72472e12i	−0.167922	−	0.0969499i
$881$	1.94614e13			1.08838			0.544192	−	0.838961i	$-0.316836\pi$
$881$	1.94614e13			1.08838			0.544192	+	0.838961i	$0.316836\pi$
$882$		0			0
$883$	8.75297e12			0.484543			0.242271	−	0.970209i	$-0.422108\pi$
$883$	8.75297e12			0.484543			0.242271	+	0.970209i	$0.422108\pi$
$884$	4.17981e12	+	2.41322e12i	0.230209	+	0.132911i
$885$		0			0
$886$	3.74867e12	+	6.49288e12i	0.204374	+	0.353986i
$887$	1.03934e13	−	1.80019e13i	0.563769	−	0.976476i	−0.433395	−	0.901204i	$-0.642684\pi$
$887$	1.03934e13	−	1.80019e13i	0.563769	−	0.976476i	0.997163	−	0.0752715i	$-0.0239823\pi$
$888$		0			0
$889$	−1.12845e13	+	1.89756e13i	−0.605932	+	1.01892i
$890$			1.93184e11i			0.0103208i
$891$		0			0
$892$	1.02143e13	−	5.89722e12i	0.540214	−	0.311893i
$893$	5.59016e11	−	3.22748e11i	0.0294166	−	0.0169837i
$894$		0			0
$895$		−	1.64675e13i		−	0.857877i
$896$	1.48764e12	−	8.33487e11i	0.0771104	−	0.0432029i
$897$		0			0
$898$	6.09854e12	−	1.05630e13i	0.312956	−	0.542055i
$899$	1.60450e13	+	2.77907e13i	0.819258	+	1.41900i
$900$		0			0
$901$	4.47814e12	+	2.58546e12i	0.226379	+	0.130700i
$902$	−2.86699e13			−1.44210
$903$		0			0
$904$	−4.57485e12			−0.227834
$905$	−4.96439e12	−	2.86619e12i	−0.246007	−	0.142032i
$906$		0			0
$907$	−1.68716e13	−	2.92225e13i	−0.827799	−	1.43379i	−0.899762	−	0.436382i	$-0.856260\pi$
$907$	−1.68716e13	−	2.92225e13i	−0.827799	−	1.43379i	0.0719631	−	0.997407i	$-0.477074\pi$
$908$	3.21509e12	−	5.56869e12i	0.156966	−	0.271874i
$909$		0			0
$910$	−4.04387e12	−	5.21782e10i	−0.195484	−	0.00252234i
$911$			3.25364e13i			1.56508i	0.622599	+	0.782541i	$0.286077\pi$
$911$			3.25364e13i			1.56508i	−0.622599	+	0.782541i	$0.713923\pi$
$912$		0			0
$913$	3.55167e13	−	2.05056e13i	1.69166	−	0.976682i
$914$	1.57408e13	−	9.08795e12i	0.746051	−	0.430733i
$915$		0			0
$916$		−	1.47760e12i		−	0.0693470i
$917$	1.52007e11	+	2.71309e11i	0.00709909	+	0.0126708i
$918$		0			0
$919$	4.78514e12	−	8.28810e12i	0.221297	−	0.383297i	−0.733905	−	0.679252i	$-0.762304\pi$
$919$	4.78514e12	−	8.28810e12i	0.221297	−	0.383297i	0.955202	+	0.295955i	$0.0956378\pi$
$920$	−5.66143e9	−	9.80588e9i	−0.000260544	−	0.000451275i
$921$		0			0
$922$	6.98028e12	+	4.03007e12i	0.318115	+	0.183664i
$923$	−1.23544e13			−0.560291
$924$		0			0
$925$	−1.52847e13			−0.686468
$926$	2.48839e13	+	1.43667e13i	1.11216	+	0.642108i
$927$		0			0
$928$	−2.81994e12	−	4.88427e12i	−0.124817	−	0.216189i
$929$	−3.93212e12	+	6.81062e12i	−0.173203	+	0.299996i	−0.939538	−	0.342445i	$-0.888745\pi$
$929$	−3.93212e12	+	6.81062e12i	−0.173203	+	0.299996i	0.766335	+	0.642441i	$0.222078\pi$
$930$		0			0
$931$	−4.61069e11	+	1.78637e13i	−0.0201137	+	0.779289i
$932$			3.52382e12i			0.152983i
$933$		0			0
$934$	9.36900e12	−	5.40919e12i	0.402840	−	0.232580i
$935$	−1.54200e13	+	8.90273e12i	−0.659829	+	0.380952i
$936$		0			0
$937$		−	2.95087e12i		−	0.125061i	−0.998043	−	0.0625304i	$-0.980083\pi$
$937$		−	2.95087e12i		−	0.125061i	0.998043	−	0.0625304i	$-0.0199170\pi$
$938$	4.64220e12	+	2.76064e12i	0.195799	+	0.116439i
$939$		0			0
$940$	1.33211e11	−	2.30728e11i	0.00556498	−	0.00963883i
$941$	−5.64395e12	−	9.77561e12i	−0.234655	−	0.406435i	0.724517	−	0.689257i	$-0.242063\pi$
$941$	−5.64395e12	−	9.77561e12i	−0.234655	−	0.406435i	−0.959172	+	0.282822i	$0.908729\pi$
$942$		0			0
$943$	−8.15011e10	−	4.70547e10i	−0.00335630	−	0.00193776i
$944$	−7.99728e12			−0.327769
$945$		0			0
$946$	−2.37969e13			−0.966074
$947$	−7.76317e11	−	4.48207e11i	−0.0313664	−	0.0181094i	0.484235	−	0.874938i	$-0.339098\pi$
$947$	−7.76317e11	−	4.48207e11i	−0.0313664	−	0.0181094i	−0.515601	+	0.856829i	$0.672431\pi$
$948$		0			0
$949$	4.56679e12	+	7.90991e12i	0.182773	+	0.316573i
$950$	−5.11340e12	+	8.85667e12i	−0.203682	+	0.352788i
$951$		0			0
$952$	1.13564e11	−	8.80133e12i	0.00448099	−	0.347282i
$953$		−	1.95854e13i		−	0.769155i	−0.923093	−	0.384577i	$-0.874347\pi$
$953$		−	1.95854e13i		−	0.769155i	0.923093	−	0.384577i	$-0.125653\pi$
$954$		0			0
$955$	7.33122e12	−	4.23268e12i	0.285208	−	0.164665i
$956$	−4.26620e11	+	2.46309e11i	−0.0165189	+	0.00953719i
$957$		0			0
$958$		−	2.05122e13i		−	0.786806i
$959$	6.27361e11	−	4.86212e13i	0.0239516	−	1.85627i
$960$		0			0
$961$	4.57811e12	−	7.92953e12i	0.173154	−	0.299911i
$962$	−4.72134e12	−	8.17761e12i	−0.177737	−	0.307849i
$963$		0			0
$964$	1.34272e13	+	7.75222e12i	0.500772	+	0.289121i
$965$	−1.36512e12			−0.0506756
$966$		0			0
$967$	1.10372e13			0.405918			0.202959	−	0.979187i	$-0.434944\pi$
$967$	1.10372e13			0.405918			0.202959	+	0.979187i	$0.434944\pi$
$968$	−1.09150e13	−	6.30181e12i	−0.399564	−	0.230689i
$969$		0			0
$970$	−8.68197e12	−	1.50376e13i	−0.314880	−	0.545389i
$971$	−1.80494e13	+	3.12624e13i	−0.651592	+	1.12859i	0.331145	+	0.943580i	$0.392565\pi$
$971$	−1.80494e13	+	3.12624e13i	−0.651592	+	1.12859i	−0.982737	+	0.185010i	$0.940768\pi$
$972$		0			0
$973$	5.96505e12	+	3.54732e12i	0.213357	+	0.126880i
$974$			1.28246e13i			0.456593i
$975$		0			0
$976$	9.58862e12	−	5.53599e12i	0.338245	−	0.195286i
$977$	6.07105e12	−	3.50512e12i	0.213176	−	0.123077i	−0.389611	−	0.920980i	$-0.627390\pi$
$977$	6.07105e12	−	3.50512e12i	0.213176	−	0.123077i	0.602787	+	0.797902i	$0.294057\pi$
$978$		0			0
$979$			1.24675e12i			0.0433769i
$980$	3.52172e12	+	6.48040e12i	0.121966	+	0.224432i
$981$		0			0
$982$	−1.74026e13	+	3.01422e13i	−0.597191	+	1.03437i
$983$	−1.01085e13	−	1.75084e13i	−0.345299	−	0.598076i	0.640109	−	0.768284i	$-0.278889\pi$
$983$	−1.01085e13	−	1.75084e13i	−0.345299	−	0.598076i	−0.985408	+	0.170208i	$0.945556\pi$
$984$		0			0
$985$	2.04609e13	+	1.18131e13i	0.692567	+	0.399854i
$986$	−2.91121e13			−0.980904
$987$		0			0
$988$	−6.31796e12			−0.210946
$989$	−6.76484e10	−	3.90568e10i	−0.00224840	−	0.00129812i
$990$		0			0
$991$	1.14125e13	+	1.97670e13i	0.375880	+	0.651043i	0.990458	−	0.137813i	$-0.0440073\pi$
$991$	1.14125e13	+	1.97670e13i	0.375880	+	0.651043i	−0.614579	+	0.788856i	$0.710674\pi$
$992$	−3.12802e12	+	5.41789e12i	−0.102557	+	0.177635i
$993$		0			0
$994$	1.10128e13	+	1.96561e13i	0.357815	+	0.638644i
$995$			5.17338e12i			0.167329i
$996$		0			0
$997$	6.79236e12	−	3.92157e12i	0.217717	−	0.125699i	−0.387176	−	0.922006i	$-0.626549\pi$
$997$	6.79236e12	−	3.92157e12i	0.217717	−	0.125699i	0.604893	+	0.796307i	$0.293216\pi$
$998$	−2.38200e13	+	1.37525e13i	−0.760070	+	0.438827i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.10.k.a.89.5	yes	48
3.2	odd	2	inner	126.10.k.a.89.20	yes	48
7.3	odd	6	inner	126.10.k.a.17.20	yes	48
21.17	even	6	inner	126.10.k.a.17.5	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.10.k.a.17.5	✓	48	21.17	even	6	inner
126.10.k.a.17.20	yes	48	7.3	odd	6	inner
126.10.k.a.89.5	yes	48	1.1	even	1	trivial
126.10.k.a.89.20	yes	48	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	126.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-13.8564 - 8.00000i) q^{2} +(128.000 + 221.703i) q^{4} +(-356.977 + 618.302i) q^{5} +(3246.94 - 5459.94i) q^{7} -4096.00i q^{8} +O(q^{10})\)	\(q+(-13.8564 - 8.00000i) q^{2} +(128.000 + 221.703i) q^{4} +(-356.977 + 618.302i) q^{5} +(3246.94 - 5459.94i) q^{7} -4096.00i q^{8} +(9892.83 - 5711.63i) q^{10} +(63845.5 - 36861.2i) q^{11} -55731.8i q^{13} +(-88670.5 + 49679.7i) q^{14} +(-32768.0 + 56755.8i) q^{16} +(169143. + 292964. i) q^{17} +(-383500. - 221414. i) q^{19} -182772. q^{20} -1.17956e6 q^{22} +(-3353.18 - 1935.96i) q^{23} +(721698. + 1.25002e6i) q^{25} +(-445854. + 772242. i) q^{26} +(1.62609e6 + 20981.5i) q^{28} -5.37860e6i q^{29} +(-5.16690e6 + 2.98311e6i) q^{31} +(908093. - 524288. i) q^{32} -5.41257e6i q^{34} +(2.21681e6 + 3.95666e6i) q^{35} +(-5.29472e6 + 9.17072e6i) q^{37} +(3.54262e6 + 6.13599e6i) q^{38} +(2.53256e6 + 1.46218e6i) q^{40} +2.43056e7 q^{41} +2.01744e7 q^{43} +(1.63445e7 + 9.43648e6i) q^{44} +(30975.4 + 53650.9i) q^{46} +(-728835. + 1.26238e6i) q^{47} +(-1.92684e7 - 3.54562e7i) q^{49} -2.30943e7i q^{50} +(1.23559e7 - 7.13367e6i) q^{52} +(1.32378e7 - 7.64283e6i) q^{53} +5.26344e7i q^{55} +(-2.23639e7 - 1.32995e7i) q^{56} +(-4.30288e7 + 7.45281e7i) q^{58} +(6.10144e7 + 1.05680e8i) q^{59} +(-1.46311e8 - 8.44725e7i) q^{61} +9.54596e7 q^{62} -1.67772e7 q^{64} +(3.44590e7 + 1.98949e7i) q^{65} +(-2.65696e7 - 4.60200e7i) q^{67} +(-4.33005e7 + 7.49987e7i) q^{68} +(936239. - 7.25596e7i) q^{70} -2.21676e8i q^{71} +(-1.41928e8 + 8.19423e7i) q^{73} +(1.46732e8 - 8.47155e7i) q^{74} -1.13364e8i q^{76} +(6.04222e6 - 4.68279e8i) q^{77} +(3.21535e8 - 5.56915e8i) q^{79} +(-2.33948e7 - 4.05210e7i) q^{80} +(-3.36788e8 - 1.94445e8i) q^{82} +5.56291e8 q^{83} -2.41520e8 q^{85} +(-2.79545e8 - 1.61395e8i) q^{86} +(-1.50984e8 - 2.61511e8i) q^{88} +(-8.45572e6 + 1.46457e7i) q^{89} +(-3.04292e8 - 1.80958e8i) q^{91} -991211. i q^{92} +(2.01981e7 - 1.16614e7i) q^{94} +(2.73801e8 - 1.58079e8i) q^{95} -1.52005e9i q^{97} +(-1.66591e7 + 6.45443e8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6144 q^{4} - 12720 q^{7}+O(q^{10}) \) 48 * q + 6144 * q^4 - 12720 * q^7	\( 48 q + 6144 q^{4} - 12720 q^{7} + 153792 q^{10} - 1572864 q^{16} - 2546532 q^{19} + 4853376 q^{22} - 6871164 q^{25} + 2380800 q^{28} - 6720912 q^{31} + 1881660 q^{37} + 39370752 q^{40} - 171303864 q^{43} + 54125568 q^{46} + 129836928 q^{49} - 58125312 q^{52} + 180566208 q^{58} - 632749248 q^{61} - 805306368 q^{64} + 721189428 q^{67} + 308075328 q^{70} - 853713108 q^{73} + 1452429384 q^{79} - 1355242752 q^{82} + 368938080 q^{85} + 621232128 q^{88} + 4577539644 q^{91} - 1279193472 q^{94}+O(q^{100}) \) 48 * q + 6144 * q^4 - 12720 * q^7 + 153792 * q^10 - 1572864 * q^16 - 2546532 * q^19 + 4853376 * q^22 - 6871164 * q^25 + 2380800 * q^28 - 6720912 * q^31 + 1881660 * q^37 + 39370752 * q^40 - 171303864 * q^43 + 54125568 * q^46 + 129836928 * q^49 - 58125312 * q^52 + 180566208 * q^58 - 632749248 * q^61 - 805306368 * q^64 + 721189428 * q^67 + 308075328 * q^70 - 853713108 * q^73 + 1452429384 * q^79 - 1355242752 * q^82 + 368938080 * q^85 + 621232128 * q^88 + 4577539644 * q^91 - 1279193472 * q^94

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