LMFDB - Embedded newform 21.18.g.b.17.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,18,Mod(5,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("21.5");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	21.g (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:	$38.4766383424$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.19
Character	$\chi$	$=$	21.17
Dual form			21.18.g.b.5.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-79.9248 + 46.1446i) q^{2} +(-11319.8 - 1000.90i) q^{3} +(-61277.4 + 106135. i) q^{4} +(-734013. - 1.27135e6i) q^{5} +(950921. - 442352. i) q^{6} +(2.42839e6 + 1.50577e7i) q^{7} -2.34070e7i q^{8} +(1.27137e8 + 2.26601e7i) q^{9} +O(q^{10})$	\(q+(-79.9248 + 46.1446i) q^{2} +(-11319.8 - 1000.90i) q^{3} +(-61277.4 + 106135. i) q^{4} +(-734013. - 1.27135e6i) q^{5} +(950921. - 442352. i) q^{6} +(2.42839e6 + 1.50577e7i) q^{7} -2.34070e7i q^{8} +(1.27137e8 + 2.26601e7i) q^{9} +(1.17332e8 + 6.77415e7i) q^{10} +(4.06141e8 + 2.34486e8i) q^{11} +(7.99880e8 - 1.14010e9i) q^{12} +4.52505e9i q^{13} +(-8.88919e8 - 1.09142e9i) q^{14} +(7.03640e9 + 1.51261e10i) q^{15} +(-6.95164e9 - 1.20406e10i) q^{16} +(-1.96624e10 + 3.40563e10i) q^{17} +(-1.12070e10 + 4.05556e9i) q^{18} +(3.69461e10 - 2.13308e10i) q^{19} +1.79913e11 q^{20} +(-1.24177e10 - 1.72881e11i) q^{21} -4.32810e10 q^{22} +(4.10597e11 - 2.37058e11i) q^{23} +(-2.34281e10 + 2.64963e11i) q^{24} +(-6.96080e11 + 1.20565e12i) q^{25} +(-2.08806e11 - 3.61663e11i) q^{26} +(-1.41648e12 - 3.83759e11i) q^{27} +(-1.74696e12 - 6.64956e11i) q^{28} +2.92508e11i q^{29} +(-1.26037e12 - 8.84259e11i) q^{30} +(2.09285e12 + 1.20831e12i) q^{31} +(3.76819e12 + 2.17556e12i) q^{32} +(-4.36275e12 - 3.06084e12i) q^{33} -3.62926e12i q^{34} +(1.73611e13 - 1.41399e13i) q^{35} +(-1.01956e13 + 1.21051e13i) q^{36} +(-1.91679e11 - 3.31998e11i) q^{37} +(-1.96861e12 + 3.40973e12i) q^{38} +(4.52913e12 - 5.12227e13i) q^{39} +(-2.97584e13 + 1.71810e13i) q^{40} -9.25534e12 q^{41} +(8.96999e12 + 1.32444e13i) q^{42} -8.75471e13 q^{43} +(-4.97745e13 + 2.87373e13i) q^{44} +(-6.45110e13 - 1.78268e14i) q^{45} +(-2.18779e13 + 3.78937e13i) q^{46} +(-1.21116e14 - 2.09780e14i) q^{47} +(6.66398e13 + 1.43255e14i) q^{48} +(-2.20836e14 + 7.31318e13i) q^{49} -1.28481e14i q^{50} +(2.56662e14 - 3.65831e14i) q^{51} +(-4.80268e14 - 2.77283e14i) q^{52} +(1.66581e14 + 9.61754e13i) q^{53} +(1.30921e14 - 3.46911e13i) q^{54} -6.88462e14i q^{55} +(3.52455e14 - 5.68414e13i) q^{56} +(-4.39573e14 + 2.04482e14i) q^{57} +(-1.34976e13 - 2.33786e13i) q^{58} +(-8.77544e14 + 1.51995e15i) q^{59} +(-2.03659e15 - 1.80076e14i) q^{60} +(-6.24413e14 + 3.60505e14i) q^{61} -2.23028e14 q^{62} +(-3.24708e13 + 1.96941e15i) q^{63} +1.42077e15 q^{64} +(5.75291e15 - 3.32144e15i) q^{65} +(4.89933e14 + 4.33201e13i) q^{66} +(1.76829e15 - 3.06277e15i) q^{67} +(-2.40972e15 - 4.17376e15i) q^{68} +(-4.88516e15 + 2.27249e15i) q^{69} +(-7.35102e14 + 1.93124e15i) q^{70} +6.31583e15i q^{71} +(5.30405e14 - 2.97589e15i) q^{72} +(-5.25992e15 - 3.03682e15i) q^{73} +(3.06398e13 + 1.76899e13i) q^{74} +(9.08624e15 - 1.29510e16i) q^{75} +5.22839e15i q^{76} +(-2.54454e15 + 6.68496e15i) q^{77} +(2.00166e15 + 4.30296e15i) q^{78} +(9.53144e15 + 1.65089e16i) q^{79} +(-1.02052e16 + 1.76759e16i) q^{80} +(1.56502e16 + 5.76185e15i) q^{81} +(7.39731e14 - 4.27084e14i) q^{82} -4.73849e15 q^{83} +(1.91097e16 + 9.27572e15i) q^{84} +5.77299e16 q^{85} +(6.99718e15 - 4.03982e15i) q^{86} +(2.92772e14 - 3.31113e15i) q^{87} +(5.48861e15 - 9.50655e15i) q^{88} +(-6.90732e14 - 1.19638e15i) q^{89} +(1.33821e16 + 1.12712e16i) q^{90} +(-6.81366e16 + 1.09886e16i) q^{91} +5.81052e16i q^{92} +(-2.24813e16 - 1.57726e16i) q^{93} +(1.93604e16 + 1.11777e16i) q^{94} +(-5.42378e16 - 3.13142e16i) q^{95} +(-4.04777e16 - 2.83986e16i) q^{96} -3.04698e16i q^{97} +(1.42757e16 - 1.60355e16i) q^{98} +(4.63219e16 + 3.90149e16i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 19686 q^{3} + 2752510 q^{4} - 4340518 q^{7} - 98670996 q^{9}+O(q^{10}) $ 84 * q - 19686 * q^3 + 2752510 * q^4 - 4340518 * q^7 - 98670996 * q^9	$ 84 q - 19686 q^{3} + 2752510 q^{4} - 4340518 q^{7} - 98670996 q^{9} + 465470970 q^{10} - 2491764528 q^{12} - 7104382296 q^{15} - 110459605130 q^{16} - 14553542550 q^{18} + 404032278750 q^{19} + 228767508522 q^{21} - 832496305460 q^{22} - 1354439880378 q^{24} - 7199868598470 q^{25} - 7749926510914 q^{28} + 284772818082 q^{30} + 20192079903726 q^{31} - 18426553023870 q^{33} - 6006594191052 q^{36} + 46546034438938 q^{37} + 156966454169838 q^{39} + 52009146351690 q^{40} + 273411312457290 q^{42} + 262809922393900 q^{43} - 463828715581158 q^{45} - 691873824309656 q^{46} + 158652002613594 q^{49} + 123926983295328 q^{51} + 180256725379488 q^{52} + 528953393499678 q^{54} - 13\!\cdots\!84 q^{57}+ \cdots + 30\!\cdots\!80 q^{99}+O(q^{100}) $ 84 * q - 19686 * q^3 + 2752510 * q^4 - 4340518 * q^7 - 98670996 * q^9 + 465470970 * q^10 - 2491764528 * q^12 - 7104382296 * q^15 - 110459605130 * q^16 - 14553542550 * q^18 + 404032278750 * q^19 + 228767508522 * q^21 - 832496305460 * q^22 - 1354439880378 * q^24 - 7199868598470 * q^25 - 7749926510914 * q^28 + 284772818082 * q^30 + 20192079903726 * q^31 - 18426553023870 * q^33 - 6006594191052 * q^36 + 46546034438938 * q^37 + 156966454169838 * q^39 + 52009146351690 * q^40 + 273411312457290 * q^42 + 262809922393900 * q^43 - 463828715581158 * q^45 - 691873824309656 * q^46 + 158652002613594 * q^49 + 123926983295328 * q^51 + 180256725379488 * q^52 + 528953393499678 * q^54 - 1311284732111784 * q^57 + 521920547533210 * q^58 - 416477060451846 * q^60 - 6052836877037172 * q^61 - 13769533594398750 * q^63 + 1053936792659996 * q^64 + 21705058495057878 * q^66 + 3639355527884298 * q^67 + 44463964567209810 * q^70 + 7798479140884800 * q^72 - 31719690947775954 * q^73 + 17256341731591290 * q^75 - 67997864561346840 * q^78 - 31267401781398294 * q^79 + 44133415784265492 * q^81 + 4877409168868320 * q^82 + 25637268676337472 * q^84 + 2464288230356616 * q^85 - 61426317616508880 * q^87 - 112618869011616970 * q^88 - 223816788036276750 * q^91 + 104033604109825260 * q^93 + 248077621213302516 * q^94 - 363875964512101146 * q^96 + 303894121197814080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−79.9248	+	46.1446i	−0.220763	+	0.127458i	−0.606304	−	0.795233i	$-0.707348\pi$
$2$	−79.9248	+	46.1446i	−0.220763	+	0.127458i	0.385540	+	0.922691i	$0.374015\pi$
$3$	−11319.8	−	1000.90i	−0.996114	−	0.0880767i
$3$	−11319.8	−	1000.90i	−0.996114	−	0.0880767i
$4$	−61277.4	+	106135.i	−0.467509	+	0.809749i
$5$	−734013.	−	1.27135e6i	−0.840347	−	1.45552i	−0.889601	−	0.456738i	$-0.849018\pi$
$5$	−734013.	−	1.27135e6i	−0.840347	−	1.45552i	0.0492543	−	0.998786i	$-0.484316\pi$
$6$	950921.	−	442352.i	0.231131	−	0.107518i
$7$	2.42839e6	+	1.50577e7i	0.159215	+	0.987244i
$7$	2.42839e6	+	1.50577e7i	0.159215	+	0.987244i
$8$		−	2.34070e7i		−	0.493266i
$9$	1.27137e8	+	2.26601e7i	0.984485	+	0.175469i
$10$	1.17332e8	+	6.77415e7i	0.371035	+	0.214217i
$11$	4.06141e8	+	2.34486e8i	0.571267	+	0.329821i	0.757655	−	0.652655i	$-0.226345\pi$
$11$	4.06141e8	+	2.34486e8i	0.571267	+	0.329821i	−0.186388	+	0.982476i	$0.559678\pi$
$12$	7.99880e8	−	1.14010e9i	0.537012	−	0.765426i
$13$			4.52505e9i			1.53852i	0.638933	+	0.769262i	$0.279376\pi$
$13$			4.52505e9i			1.53852i	−0.638933	+	0.769262i	$0.720624\pi$
$14$	−8.88919e8	−	1.09142e9i	−0.160981	−	0.197654i
$15$	7.03640e9	+	1.51261e10i	0.708884	+	1.52388i
$16$	−6.95164e9	−	1.20406e10i	−0.404639	−	0.700855i
$17$	−1.96624e10	+	3.40563e10i	−0.683630	+	1.18408i	0.290236	+	0.956955i	$0.406266\pi$
$17$	−1.96624e10	+	3.40563e10i	−0.683630	+	1.18408i	−0.973865	+	0.227126i	$0.927067\pi$
$18$	−1.12070e10	+	4.05556e9i	−0.239703	+	0.0867431i
$19$	3.69461e10	−	2.13308e10i	0.499072	−	0.288139i	−0.229258	−	0.973366i	$-0.573630\pi$
$19$	3.69461e10	−	2.13308e10i	0.499072	−	0.288139i	0.728330	+	0.685226i	$0.240297\pi$
$20$	1.79913e11			1.57148
$21$	−1.24177e10	−	1.72881e11i	−0.0716435	−	0.997430i
$22$	−4.32810e10			−0.168153
$23$	4.10597e11	−	2.37058e11i	1.09327	−	0.631202i	0.158828	−	0.987306i	$-0.449229\pi$
$23$	4.10597e11	−	2.37058e11i	1.09327	−	0.631202i	0.934446	+	0.356104i	$0.115895\pi$
$24$	−2.34281e10	+	2.64963e11i	−0.0434452	+	0.491349i
$25$	−6.96080e11	+	1.20565e12i	−0.912367	+	1.58027i
$26$	−2.08806e11	−	3.61663e11i	−0.196097	−	0.339650i
$27$	−1.41648e12	−	3.83759e11i	−0.965204	−	0.261497i
$28$	−1.74696e12	−	6.64956e11i	−0.873855	−	0.332621i
$29$			2.92508e11i			0.108581i	0.998525	+	0.0542905i	$0.0172897\pi$
$29$			2.92508e11i			0.108581i	−0.998525	+	0.0542905i	$0.982710\pi$
$30$	−1.26037e12	−	8.84259e11i	−0.350726	−	0.246064i
$31$	2.09285e12	+	1.20831e12i	0.440721	+	0.254450i	0.703903	−	0.710296i	$-0.251439\pi$
$31$	2.09285e12	+	1.20831e12i	0.440721	+	0.254450i	−0.263182	+	0.964746i	$0.584772\pi$
$32$	3.76819e12	+	2.17556e12i	0.605839	+	0.349781i
$33$	−4.36275e12	−	3.06084e12i	−0.539997	−	0.378855i
$34$		−	3.62926e12i		−	0.348535i
$35$	1.73611e13	−	1.41399e13i	1.30316	−	1.06137i
$36$	−1.01956e13	+	1.21051e13i	−0.602342	+	0.715153i
$37$	−1.91679e11	−	3.31998e11i	−0.00897139	−	0.0155389i	0.861505	−	0.507749i	$-0.169522\pi$
$37$	−1.91679e11	−	3.31998e11i	−0.00897139	−	0.0155389i	−0.870476	+	0.492210i	$0.836189\pi$
$38$	−1.96861e12	+	3.40973e12i	−0.0734511	+	0.127221i
$39$	4.52913e12	−	5.12227e13i	0.135508	−	1.53255i
$40$	−2.97584e13	+	1.71810e13i	−0.717960	+	0.414515i
$41$	−9.25534e12			−0.181021			−0.0905106	−	0.995895i	$-0.528850\pi$
$41$	−9.25534e12			−0.181021			−0.0905106	+	0.995895i	$0.528850\pi$
$42$	8.96999e12	+	1.32444e13i	0.142946	+	0.211064i
$43$	−8.75471e13			−1.14225			−0.571123	−	0.820864i	$-0.693492\pi$
$43$	−8.75471e13			−1.14225			−0.571123	+	0.820864i	$0.693492\pi$
$44$	−4.97745e13	+	2.87373e13i	−0.534145	+	0.308389i
$45$	−6.45110e13	−	1.78268e14i	−0.571910	−	1.58040i
$46$	−2.18779e13	+	3.78937e13i	−0.160903	+	0.278692i
$47$	−1.21116e14	−	2.09780e14i	−0.741944	−	1.28508i	−0.951609	−	0.307311i	$-0.900571\pi$
$47$	−1.21116e14	−	2.09780e14i	−0.741944	−	1.28508i	0.209665	−	0.977773i	$-0.432763\pi$
$48$	6.66398e13	+	1.43255e14i	0.341337	+	0.733770i
$49$	−2.20836e14	+	7.31318e13i	−0.949301	+	0.314369i
$50$		−	1.28481e14i		−	0.465152i
$51$	2.56662e14	−	3.65831e14i	0.785263	−	1.11927i
$52$	−4.80268e14	−	2.77283e14i	−1.24582	−	0.719274i
$53$	1.66581e14	+	9.61754e13i	0.367519	+	0.212187i	0.672374	−	0.740212i	$-0.265275\pi$
$53$	1.66581e14	+	9.61754e13i	0.367519	+	0.212187i	−0.304855	+	0.952399i	$0.598608\pi$
$54$	1.30921e14	−	3.46911e13i	0.246411	−	0.0652937i
$55$		−	6.88462e14i		−	1.10866i
$56$	3.52455e14	−	5.68414e13i	0.486974	−	0.0785355i
$57$	−4.39573e14	+	2.04482e14i	−0.522511	+	0.243063i
$58$	−1.34976e13	−	2.33786e13i	−0.0138395	−	0.0239707i
$59$	−8.77544e14	+	1.51995e15i	−0.778084	+	1.34768i	0.154960	+	0.987921i	$0.450475\pi$
$59$	−8.77544e14	+	1.51995e15i	−0.778084	+	1.34768i	−0.933045	+	0.359761i	$0.882858\pi$
$60$	−2.03659e15	−	1.80076e14i	−1.56537	−	0.138411i
$61$	−6.24413e14	+	3.60505e14i	−0.417031	+	0.240773i	−0.693806	−	0.720162i	$-0.744068\pi$
$61$	−6.24413e14	+	3.60505e14i	−0.417031	+	0.240773i	0.276775	+	0.960935i	$0.410734\pi$
$62$	−2.23028e14			−0.129727
$63$	−3.24708e13	+	1.96941e15i	−0.0164854	+	0.999864i
$64$	1.42077e15			0.630948
$65$	5.75291e15	−	3.32144e15i	2.23936	−	1.29289i
$66$	4.89933e14	+	4.33201e13i	0.167499	+	0.0148104i
$67$	1.76829e15	−	3.06277e15i	0.532007	−	0.921463i	−0.467295	−	0.884101i	$-0.654771\pi$
$67$	1.76829e15	−	3.06277e15i	0.532007	−	0.921463i	0.999302	−	0.0373615i	$-0.0118953\pi$
$68$	−2.40972e15	−	4.17376e15i	−0.639206	−	1.10714i
$69$	−4.88516e15	+	2.27249e15i	−1.14462	+	0.532457i
$70$	−7.35102e14	+	1.93124e15i	−0.152410	+	0.400409i
$71$			6.31583e15i			1.16074i	0.814353	+	0.580370i	$0.197092\pi$
$71$			6.31583e15i			1.16074i	−0.814353	+	0.580370i	$0.802908\pi$
$72$	5.30405e14	−	2.97589e15i	0.0865528	−	0.485613i
$73$	−5.25992e15	−	3.03682e15i	−0.763370	−	0.440732i	0.0671346	−	0.997744i	$-0.478614\pi$
$73$	−5.25992e15	−	3.03682e15i	−0.763370	−	0.440732i	−0.830504	+	0.557012i	$0.811948\pi$
$74$	3.06398e13	+	1.76899e13i	0.00396110	+	0.00228694i
$75$	9.08624e15	−	1.29510e16i	1.04801	−	1.49377i
$76$			5.22839e15i			0.538831i
$77$	−2.54454e15	+	6.68496e15i	−0.234659	+	0.616493i
$78$	2.00166e15	+	4.30296e15i	0.165419	+	0.355601i
$79$	9.53144e15	+	1.65089e16i	0.706852	+	1.22430i	0.966019	+	0.258471i	$0.0832186\pi$
$79$	9.53144e15	+	1.65089e16i	0.706852	+	1.22430i	−0.259167	+	0.965832i	$0.583448\pi$
$80$	−1.02052e16	+	1.76759e16i	−0.680074	+	1.17792i
$81$	1.56502e16	+	5.76185e15i	0.938421	+	0.345493i
$82$	7.39731e14	−	4.27084e14i	0.0399628	−	0.0230725i
$83$	−4.73849e15			−0.230928			−0.115464	−	0.993312i	$-0.536835\pi$
$83$	−4.73849e15			−0.230928			−0.115464	+	0.993312i	$0.536835\pi$
$84$	1.91097e16	+	9.27572e15i	0.841163	+	0.408294i
$85$	5.77299e16			2.29794
$86$	6.99718e15	−	4.03982e15i	0.252166	−	0.145588i
$87$	2.92772e14	−	3.31113e15i	0.00956346	−	0.108159i
$88$	5.48861e15	−	9.50655e15i	0.162690	−	0.281787i
$89$	−6.90732e14	−	1.19638e15i	−0.0185992	−	0.0322148i	0.856576	−	0.516021i	$-0.172587\pi$
$89$	−6.90732e14	−	1.19638e15i	−0.0185992	−	0.0322148i	−0.875175	+	0.483806i	$0.839254\pi$
$90$	1.33821e16	+	1.12712e16i	0.327690	+	0.275999i
$91$	−6.81366e16	+	1.09886e16i	−1.51890	+	0.244957i
$92$			5.81052e16i			1.18037i
$93$	−2.24813e16	−	1.57726e16i	−0.416597	−	0.292279i
$94$	1.93604e16	+	1.11777e16i	0.327588	+	0.189133i
$95$	−5.42378e16	−	3.13142e16i	−0.838787	−	0.484274i
$96$	−4.04777e16	−	2.83986e16i	−0.572677	−	0.401782i
$97$		−	3.04698e16i		−	0.394739i	−0.980329	−	0.197370i	$-0.936760\pi$
$97$		−	3.04698e16i		−	0.394739i	0.980329	−	0.197370i	$-0.0632399\pi$
$98$	1.42757e16	−	1.60355e16i	0.169502	−	0.190397i
$99$	4.63219e16	+	3.90149e16i	0.504531	+	0.424944i
$100$	−8.53079e16	−	1.47758e17i	−0.853079	−	1.47758i
$101$	8.06796e16	−	1.39741e17i	0.741365	−	1.28408i	−0.210508	−	0.977592i	$-0.567512\pi$
$101$	8.06796e16	−	1.39741e17i	0.741365	−	1.28408i	0.951874	−	0.306490i	$-0.0991547\pi$
$102$	−3.63253e15	+	4.10825e16i	−0.0306979	+	0.347181i
$103$	−1.04789e17	+	6.05001e16i	−0.815080	+	0.470587i	−0.848717	−	0.528847i	$-0.822624\pi$
$103$	−1.04789e17	+	6.05001e16i	−0.815080	+	0.470587i	0.0336368	+	0.999434i	$0.489291\pi$
$104$	1.05918e17			0.758902
$105$	−2.10677e17	+	1.42684e17i	−1.39158	+	0.942466i
$106$	−1.77519e16			−0.108180
$107$	1.92472e16	−	1.11124e16i	0.108295	−	0.0625239i	−0.444874	−	0.895593i	$-0.646752\pi$
$107$	1.92472e16	−	1.11124e16i	0.108295	−	0.0625239i	0.553169	+	0.833069i	$0.313418\pi$
$108$	1.27529e17	−	1.26823e17i	0.662989	−	0.659321i
$109$	−1.85362e16	+	3.21056e16i	−0.0891034	+	0.154332i	−0.907132	−	0.420845i	$-0.861734\pi$
$109$	−1.85362e16	+	3.21056e16i	−0.0891034	+	0.154332i	0.818029	+	0.575177i	$0.195067\pi$
$110$	3.17688e16	+	5.50252e16i	0.141307	+	0.244751i
$111$	1.83747e15	+	3.95001e15i	0.00756791	+	0.0162687i
$112$	1.64422e17	−	1.33915e17i	0.627490	−	0.511064i
$113$			3.77172e15i			0.0133466i	0.999978	+	0.00667332i	$0.00212420\pi$
$113$			3.77172e15i			0.0133466i	−0.999978	+	0.00667332i	$0.997876\pi$
$114$	2.56971e16	−	3.66271e16i	0.0843709	−	0.120257i
$115$	−6.02767e17	−	3.48008e17i	−1.83746	−	1.06086i
$116$	−3.10454e16	−	1.79241e16i	−0.0879235	−	0.0507626i
$117$	−1.02538e17	+	5.75299e17i	−0.269963	+	1.51465i
$118$		−	1.61976e17i		−	0.396691i
$119$	−5.60556e17	−	2.13368e17i	−1.27782	−	0.486385i
$120$	3.54057e17	−	1.64701e17i	0.751679	−	0.349668i
$121$	−1.42756e17	−	2.47261e17i	−0.282436	−	0.489193i
$122$	3.32707e16	−	5.76266e16i	0.0613768	−	0.106308i
$123$	1.04769e17	+	9.26369e15i	0.180318	+	0.0159438i
$124$	−2.56489e17	+	1.48084e17i	−0.412082	+	0.237916i
$125$	9.23714e17			1.38612
$126$	−8.82823e16	−	1.58903e17i	−0.123801	−	0.222834i
$127$	−2.25801e17			−0.296070			−0.148035	−	0.988982i	$-0.547295\pi$
$127$	−2.25801e17			−0.296070			−0.148035	+	0.988982i	$0.547295\pi$
$128$	−6.07458e17	+	3.50716e17i	−0.745129	+	0.430201i
$129$	9.91017e17	+	8.76261e16i	1.13781	+	0.100605i
$130$	−3.06533e17	+	5.30931e17i	−0.329579	+	0.570847i
$131$	−6.01018e17	−	1.04099e18i	−0.605454	−	1.04868i	−0.991980	−	0.126399i	$-0.959658\pi$
$131$	−6.01018e17	−	1.04099e18i	−0.605454	−	1.04868i	0.386525	−	0.922279i	$-0.373675\pi$
$132$	5.92202e17	−	2.75482e17i	0.559231	−	0.260145i
$133$	4.10912e17	+	5.04523e17i	0.363924	+	0.446829i
$134$			3.26388e17i			0.271233i
$135$	5.51825e17	+	2.08253e18i	0.430491	+	1.62463i
$136$	7.97156e17	+	4.60238e17i	0.584067	+	0.337211i
$137$	−4.54264e17	−	2.62270e17i	−0.312740	−	0.180561i	0.335412	−	0.942072i	$-0.391125\pi$
$137$	−4.54264e17	−	2.62270e17i	−0.312740	−	0.180561i	−0.648152	+	0.761511i	$0.724458\pi$
$138$	2.85582e17	−	4.07052e17i	0.184824	−	0.263437i
$139$		−	2.60384e18i		−	1.58485i	−0.609968	−	0.792426i	$-0.708818\pi$
$139$		−	2.60384e18i		−	1.58485i	0.609968	−	0.792426i	$-0.291182\pi$
$140$	4.36900e17	+	2.70908e18i	0.250204	+	1.55143i
$141$	1.16105e18	+	2.49590e18i	0.625875	+	1.34544i
$142$	−2.91442e17	−	5.04792e17i	−0.147945	−	0.256249i
$143$	−1.06106e18	+	1.83781e18i	−0.507438	+	0.878909i
$144$	−6.10967e17	−	1.68832e18i	−0.275382	−	0.760982i
$145$	3.71879e17	−	2.14704e17i	0.158042	−	0.0912458i
$146$	5.60531e17			0.224699
$147$	2.57303e18	−	6.06803e17i	0.973300	−	0.229536i
$148$	4.69823e16			0.0167768
$149$	3.92857e18	−	2.26816e18i	1.32480	−	0.764876i	0.340313	−	0.940312i	$-0.389467\pi$
$149$	3.92857e18	−	2.26816e18i	1.32480	−	0.764876i	0.984491	+	0.175437i	$0.0561337\pi$
$150$	−1.28597e17	+	1.45439e18i	−0.0409691	+	0.463345i
$151$	−1.49341e17	+	2.58666e17i	−0.0449650	+	0.0778817i	−0.887632	−	0.460553i	$-0.847651\pi$
$151$	−1.49341e17	+	2.58666e17i	−0.0449650	+	0.0778817i	0.842667	+	0.538435i	$0.180984\pi$
$152$	−4.99291e17	−	8.64798e17i	−0.142129	−	0.246175i
$153$	−3.27153e18	+	3.88425e18i	−0.880793	+	1.04575i
$154$	−1.05103e17	−	6.51711e17i	−0.0267726	−	0.166008i
$155$		−	3.54765e18i		−	0.855307i
$156$	5.15901e18	+	3.61949e18i	1.17763	+	0.826207i
$157$	−5.22708e18	−	3.01785e18i	−1.13009	−	0.652456i	−0.186130	−	0.982525i	$-0.559595\pi$
$157$	−5.22708e18	−	3.01785e18i	−1.13009	−	0.652456i	−0.943957	+	0.330069i	$0.892928\pi$
$158$	−1.52360e18	−	8.79649e17i	−0.312094	−	0.180187i
$159$	−1.78940e18	−	1.25542e18i	−0.347402	−	0.243732i
$160$		−	6.38757e18i		−	1.17575i
$161$	4.56663e18	+	5.60696e18i	0.797217	+	0.978831i
$162$	−1.51672e18	+	2.61659e17i	−0.251205	+	0.0433369i
$163$	−1.29873e17	−	2.24947e17i	−0.0204138	−	0.0353578i	0.855638	−	0.517575i	$-0.173165\pi$
$163$	−1.29873e17	−	2.24947e17i	−0.0204138	−	0.0353578i	−0.876052	+	0.482217i	$0.839832\pi$
$164$	5.67142e17	−	9.82319e17i	0.0846290	−	0.146582i
$165$	−6.89084e17	+	7.79327e18i	−0.0976469	+	1.10435i
$166$	3.78723e17	−	2.18656e17i	0.0509803	−	0.0294335i
$167$	−7.08073e18			−0.905707			−0.452854	−	0.891585i	$-0.649594\pi$
$167$	−7.08073e18			−0.905707			−0.452854	+	0.891585i	$0.649594\pi$
$168$	−4.04662e18	+	2.90661e17i	−0.491998	+	0.0353393i
$169$	−1.18256e19			−1.36706
$170$	−4.61405e18	+	2.66392e18i	−0.507302	+	0.292891i
$171$	5.18056e18	−	1.87473e18i	0.541888	−	0.196097i
$172$	5.36465e18	−	9.29185e18i	0.534010	−	0.924933i
$173$	3.23872e18	+	5.60963e18i	0.306889	+	0.531548i	0.977680	−	0.210099i	$-0.0673786\pi$
$173$	3.23872e18	+	5.60963e18i	0.306889	+	0.531548i	−0.670791	+	0.741646i	$0.734045\pi$
$174$	1.29391e17	+	2.78151e17i	0.0116744	+	0.0250965i
$175$	−1.98446e19	−	7.55357e18i	−1.70537	−	0.649126i
$176$		−	6.52024e18i		−	0.533834i
$177$	1.14550e19	−	1.63272e19i	0.893760	−	1.27391i
$178$	1.10413e17	+	6.37471e16i	0.00821204	+	0.00474123i
$179$	−9.08454e18	−	5.24496e18i	−0.644247	−	0.371956i	0.142002	−	0.989866i	$-0.454646\pi$
$179$	−9.08454e18	−	5.24496e18i	−0.644247	−	0.371956i	−0.786248	+	0.617910i	$0.787979\pi$
$180$	2.28736e19	+	4.07685e18i	1.54710	+	0.275746i
$181$			1.64267e19i			1.05994i	0.848016	+	0.529970i	$0.177797\pi$
$181$			1.64267e19i			1.05994i	−0.848016	+	0.529970i	$0.822203\pi$
$182$	4.93874e18	−	4.02240e18i	0.304095	−	0.247673i
$183$	7.42908e18	−	3.45588e18i	0.436617	−	0.203107i
$184$	−5.54882e18	−	9.61085e18i	−0.311350	−	0.539275i
$185$	−2.81390e17	+	4.87381e17i	−0.0150782	+	0.0261161i
$186$	2.52463e18	+	2.23229e17i	0.129222	+	0.0114259i
$187$	−1.59714e19	+	9.22111e18i	−0.781070	+	0.450951i
$188$	2.96868e19			1.38746
$189$	2.33875e18	−	2.22608e19i	0.104486	−	0.994526i
$190$	5.77993e18			0.246898
$191$	−3.25161e19	+	1.87732e19i	−1.32836	+	0.766928i	−0.985046	−	0.172294i	$-0.944882\pi$
$191$	−3.25161e19	+	1.87732e19i	−1.32836	+	0.766928i	−0.343312	+	0.939221i	$0.611549\pi$
$192$	−1.60828e19	−	1.42205e18i	−0.628496	−	0.0555718i
$193$	−7.11027e18	+	1.23153e19i	−0.265858	+	0.460479i	−0.967788	−	0.251767i	$-0.918988\pi$
$193$	−7.11027e18	+	1.23153e19i	−0.265858	+	0.460479i	0.701930	+	0.712246i	$0.252322\pi$
$194$	1.40602e18	+	2.43530e18i	0.0503126	+	0.0871439i
$195$	−6.84463e19	+	3.18400e19i	−2.34453	+	1.09063i
$196$	5.77039e18	−	2.79199e19i	0.189247	−	0.915666i
$197$		−	5.33128e19i		−	1.67443i	−0.546870	−	0.837217i	$-0.684181\pi$
$197$		−	5.33128e19i		−	1.67443i	0.546870	−	0.837217i	$-0.315819\pi$
$198$	−5.50260e18	−	9.80751e17i	−0.165544	−	0.0295056i
$199$	1.82587e19	+	1.05417e19i	0.526282	+	0.303849i	0.739501	−	0.673156i	$-0.235062\pi$
$199$	1.82587e19	+	1.05417e19i	0.526282	+	0.303849i	−0.213219	+	0.977004i	$0.568395\pi$
$200$	2.82206e19	+	1.62932e19i	0.779491	+	0.450039i
$201$	−2.30822e19	+	3.29001e19i	−0.611099	+	0.871024i
$202$			1.48917e19i			0.377971i
$203$	−4.40448e18	+	7.10322e17i	−0.107196	+	0.0172878i
$204$	2.31001e19	+	4.96581e19i	0.539209	+	1.15913i
$205$	6.79354e18	+	1.17668e19i	0.152121	+	0.263481i
$206$	5.58351e18	−	9.67092e18i	0.119960	−	0.207776i
$207$	5.75736e19	−	2.08346e19i	1.18707	−	0.429573i
$208$	5.44842e19	−	3.14565e19i	1.07828	−	0.622546i
$209$	2.00071e19			0.380138
$210$	1.02542e19	−	2.11256e19i	0.187085	−	0.385429i
$211$	6.88003e19			1.20556			0.602781	−	0.797907i	$-0.294059\pi$
$211$	6.88003e19			1.20556			0.602781	+	0.797907i	$0.294059\pi$
$212$	−2.04152e19	+	1.17867e19i	−0.343637	+	0.198399i
$213$	6.32154e18	−	7.14941e19i	0.102234	−	1.15623i
$214$	−1.02555e18	+	1.77631e18i	−0.0159383	+	0.0276059i
$215$	6.42607e19	+	1.11303e20i	0.959883	+	1.66257i
$216$	−8.98266e18	+	3.31556e19i	−0.128988	+	0.476102i
$217$	−1.31120e19	+	3.44477e19i	−0.181035	+	0.475612i
$218$		−	3.42137e18i		−	0.0454277i
$219$	5.65018e19	+	3.96409e19i	0.721585	+	0.506254i
$220$	7.30703e19	+	4.21871e19i	0.897735	+	0.518307i
$221$	−1.54106e20	−	8.89733e19i	−1.82174	−	1.05178i
$222$	−3.29131e17	−	2.30914e17i	−0.00374428	−	0.00262694i
$223$		−	2.12738e19i		−	0.232945i	−0.993194	−	0.116472i	$-0.962841\pi$
$223$		−	2.12738e19i		−	0.232945i	0.993194	−	0.116472i	$-0.0371587\pi$
$224$	−2.36083e19	+	6.20232e19i	−0.248861	+	0.653802i
$225$	−1.15817e20	+	1.37509e20i	−1.17550	+	1.39566i
$226$	−1.74044e17	−	3.01454e17i	−0.00170113	−	0.00294645i
$227$	−4.52204e19	+	7.83241e19i	−0.425711	+	0.737353i	−0.996487	−	0.0837531i	$-0.973309\pi$
$227$	−4.52204e19	+	7.83241e19i	−0.425711	+	0.737353i	0.570776	+	0.821106i	$0.306643\pi$
$228$	5.23311e18	−	5.91844e19i	0.0474585	−	0.536737i
$229$	7.62278e19	−	4.40102e19i	0.666058	−	0.384549i	−0.128523	−	0.991706i	$-0.541024\pi$
$229$	7.62278e19	−	4.40102e19i	0.666058	−	0.384549i	0.794581	+	0.607158i	$0.207690\pi$
$230$	6.42347e19			0.540858
$231$	3.54947e19	−	7.31258e19i	0.288046	−	0.593429i
$232$	6.84673e18			0.0535593
$233$	−2.04518e19	+	1.18078e19i	−0.154243	+	0.0890523i	−0.575135	−	0.818058i	$-0.695050\pi$
$233$	−2.04518e19	+	1.18078e19i	−0.154243	+	0.0890523i	0.420892	+	0.907111i	$0.361717\pi$
$234$	−1.83516e19	−	5.07122e19i	−0.133456	−	0.368789i
$235$	−1.77802e20	+	3.07962e20i	−1.24698	+	2.15983i
$236$	−1.07547e20	−	1.86277e20i	−0.727523	−	1.26011i
$237$	−9.13704e19	−	1.96418e20i	−0.596272	−	1.28180i
$238$	5.46481e19	−	8.81325e18i	0.344089	−	0.0554922i
$239$		−	2.76259e20i		−	1.67855i	−0.543707	−	0.839275i	$-0.682980\pi$
$239$		−	2.76259e20i		−	1.67855i	0.543707	−	0.839275i	$-0.317020\pi$
$240$	1.33213e20	−	1.89874e20i	0.781178	−	1.11345i
$241$	−1.78690e20	−	1.03167e20i	−1.01148	−	0.583977i	−0.0998537	−	0.995002i	$-0.531837\pi$
$241$	−1.78690e20	−	1.03167e20i	−1.01148	−	0.583977i	−0.911624	+	0.411025i	$0.865171\pi$
$242$	2.28196e19	+	1.31749e19i	0.124703	+	0.0719972i
$243$	−1.71391e20	−	8.08874e19i	−0.904344	−	0.426803i
$244$		−	8.83632e19i		−	0.450254i
$245$	2.55073e20	+	2.27080e20i	1.25531	+	1.11755i
$246$	−8.80109e18	+	4.09411e18i	−0.0418397	+	0.0194631i
$247$	9.65230e19	+	1.67183e20i	0.443309	+	0.767834i
$248$	2.82829e19	−	4.89874e19i	0.125512	−	0.217393i
$249$	5.36389e19	+	4.74277e18i	0.230030	+	0.0203394i
$250$	−7.38276e19	+	4.26244e19i	−0.306005	+	0.176672i
$251$	2.18494e20			0.875412			0.437706	−	0.899118i	$-0.355791\pi$
$251$	2.18494e20			0.875412			0.437706	+	0.899118i	$0.355791\pi$
$252$	−2.07034e20	−	1.24126e20i	−0.801932	−	0.480795i
$253$	2.22347e20			0.832735
$254$	1.80471e19	−	1.04195e19i	0.0653614	−	0.0377364i
$255$	−6.53492e20	−	5.77820e19i	−2.28901	−	0.202395i
$256$	−6.07442e19	+	1.05212e20i	−0.205809	+	0.356472i
$257$	−2.66878e20	−	4.62246e20i	−0.874744	−	1.51510i	−0.857036	−	0.515257i	$-0.827696\pi$
$257$	−2.66878e20	−	4.62246e20i	−0.874744	−	1.51510i	−0.0177080	−	0.999843i	$-0.505637\pi$
$258$	−8.32503e19	+	3.87266e19i	−0.264009	+	0.122812i
$259$	4.53364e18	−	3.69246e18i	0.0139123	−	0.0113310i
$260$			8.14117e20i			2.41776i
$261$	−6.62824e18	+	3.71884e19i	−0.0190526	+	0.106896i
$262$	9.60724e19	+	5.54674e19i	0.267324	+	0.154340i
$263$	6.11771e19	+	3.53206e19i	0.164803	+	0.0951490i	0.580133	−	0.814522i	$-0.303001\pi$
$263$	6.11771e19	+	3.53206e19i	0.164803	+	0.0951490i	−0.415330	+	0.909671i	$0.636334\pi$
$264$	−7.16452e19	+	1.02119e20i	−0.186876	+	0.266362i
$265$		−	2.82376e20i		−	0.713243i
$266$	−5.61231e19	−	2.13625e19i	−0.137293	−	0.0522586i
$267$	6.62150e18	+	1.42342e19i	0.0156896	+	0.0337278i
$268$	2.16712e20	+	3.75356e20i	0.497436	+	0.861585i
$269$	2.18185e20	−	3.77907e20i	0.485210	−	0.840409i	−0.514645	−	0.857403i	$-0.672076\pi$
$269$	2.18185e20	−	3.77907e20i	0.485210	−	0.840409i	0.999856	+	0.0169942i	$0.00540969\pi$
$270$	−1.40202e20	−	1.40982e20i	−0.302108	−	0.303788i
$271$	5.07989e19	−	2.93287e19i	0.106075	−	0.0612427i	−0.446024	−	0.895021i	$-0.647160\pi$
$271$	5.07989e19	−	2.93287e19i	0.106075	−	0.0612427i	0.552099	+	0.833778i	$0.313827\pi$
$272$	5.46744e20			1.10649
$273$	7.82293e20	−	5.61906e19i	1.53457	−	0.110225i
$274$	4.84093e19			0.0920554
$275$	−5.65414e20	+	3.26442e20i	−1.04241	+	0.601836i
$276$	5.81577e19	−	6.57741e20i	0.103963	−	1.17578i
$277$	−3.88374e20	+	6.72683e20i	−0.673243	+	1.16609i	0.303736	+	0.952756i	$0.401766\pi$
$277$	−3.88374e20	+	6.72683e20i	−0.673243	+	1.16609i	−0.976979	+	0.213335i	$0.931567\pi$
$278$	1.20153e20	+	2.08112e20i	0.202002	+	0.349877i
$279$	2.38697e20	+	2.01044e20i	0.389235	+	0.327835i
$280$	−3.30972e20	−	4.06371e20i	−0.523537	−	0.642805i
$281$		−	5.64431e19i		−	0.0866179i	−0.999062	−	0.0433089i	$-0.986210\pi$
$281$		−	5.64431e19i		−	0.0866179i	0.999062	−	0.0433089i	$-0.0137900\pi$
$282$	−2.07969e20	−	1.45908e20i	−0.309656	−	0.217251i
$283$	4.84809e20	+	2.79905e20i	0.700465	+	0.404414i	0.807521	−	0.589839i	$-0.200809\pi$
$283$	4.84809e20	+	2.79905e20i	0.700465	+	0.404414i	−0.107056	+	0.994253i	$0.534142\pi$
$284$	−6.70334e20	−	3.87018e20i	−0.939908	−	0.542656i
$285$	5.82620e20	+	4.08758e20i	0.792874	+	0.556270i
$286$		−	1.95849e20i		−	0.258707i
$287$	−2.24756e19	−	1.39364e20i	−0.0288214	−	0.178712i
$288$	4.29776e20	+	3.61981e20i	0.535064	+	0.450661i
$289$	−3.59601e20	−	6.22846e20i	−0.434699	−	0.752921i
$290$	−1.98149e19	+	3.43204e19i	−0.0232599	+	0.0402874i
$291$	−3.04973e19	+	3.44913e20i	−0.0347673	+	0.393205i
$292$	6.44628e20	−	3.72176e20i	0.713764	−	0.412092i
$293$	−1.78486e21			−1.91968			−0.959842	−	0.280542i	$-0.909486\pi$
$293$	−1.78486e21			−1.91968			−0.959842	+	0.280542i	$0.909486\pi$
$294$	−1.77648e20	+	1.67230e20i	−0.185613	+	0.174728i
$295$	2.57651e21			2.61544
$296$	−7.77107e18	+	4.48663e18i	−0.00766481	+	0.00442528i
$297$	−4.85306e20	−	4.88005e20i	−0.465142	−	0.467730i
$298$	−2.09327e20	+	3.62565e20i	−0.194979	+	0.337713i
$299$	1.07270e21	+	1.85797e21i	0.971120	+	1.68203i
$300$	8.17780e20	+	1.75798e21i	0.719624	+	1.54697i
$301$	−2.12598e20	−	1.31825e21i	−0.181863	−	1.12768i
$302$		−	2.75651e19i		−	0.0229246i
$303$	−1.05315e21	+	1.50109e21i	−0.851582	+	1.21380i
$304$	−5.13672e20	−	2.96569e20i	−0.403887	−	0.233185i
$305$	9.16655e20	+	5.29231e20i	0.700902	+	0.404666i
$306$	8.22392e19	−	4.61411e20i	0.0611571	−	0.343128i
$307$			1.62566e21i			1.17585i	0.808914	+	0.587927i	$0.200056\pi$
$307$			1.62566e21i			1.17585i	−0.808914	+	0.587927i	$0.799944\pi$
$308$	−5.53589e20	−	6.79703e20i	−0.389499	−	0.478231i
$309$	1.24675e21	−	5.79967e20i	0.853360	−	0.396968i
$310$	1.63705e20	+	2.83546e20i	0.109015	+	0.188820i
$311$	5.50141e20	−	9.52873e20i	0.356460	−	0.617407i	−0.630907	−	0.775859i	$-0.717317\pi$
$311$	5.50141e20	−	9.52873e20i	0.356460	−	0.617407i	0.987367	+	0.158452i	$0.0506502\pi$
$312$	−1.19897e21	−	1.06013e20i	−0.755952	−	0.0668416i
$313$	−2.40581e20	+	1.38900e20i	−0.147616	+	0.0852264i	−0.571989	−	0.820261i	$-0.693828\pi$
$313$	−2.40581e20	+	1.38900e20i	−0.147616	+	0.0852264i	0.424373	+	0.905488i	$0.360495\pi$
$314$	5.57031e20			0.332642
$315$	2.52764e21	−	1.40429e21i	1.46918	−	0.816238i
$316$	−2.33625e21			−1.32184
$317$	1.55579e21	−	8.98235e20i	0.856933	−	0.494750i	−0.00605110	−	0.999982i	$-0.501926\pi$
$317$	1.55579e21	−	8.98235e20i	0.856933	−	0.494750i	0.862984	+	0.505231i	$0.168593\pi$
$318$	2.00948e20	+	1.77679e19i	0.107759	+	0.00952810i
$319$	−6.85888e19	+	1.18799e20i	−0.0358123	+	0.0620288i
$320$	−1.04286e21	−	1.80629e21i	−0.530215	−	0.918360i
$321$	−2.28998e20	+	1.06526e20i	−0.113381	+	0.0527427i
$322$	−6.23718e20	−	2.37410e20i	−0.300756	−	0.114478i
$323$			1.67766e21i			0.787922i
$324$	−1.57054e21	+	1.30797e21i	−0.718483	+	0.598365i
$325$	−5.45561e21	−	3.14980e21i	−2.43128	−	1.40370i
$326$	2.07602e19	+	1.19859e19i	0.00901324	+	0.00520380i
$327$	2.41961e20	−	3.44876e20i	0.102350	−	0.145884i
$328$			2.16640e20i			0.0892916i
$329$	2.86468e21	−	2.33316e21i	1.15056	−	0.937085i
$330$	−3.04542e20	−	6.54673e20i	−0.119201	−	0.256245i
$331$	−1.36027e21	−	2.35605e21i	−0.518903	−	0.898766i	−0.999759	−	0.0219663i	$-0.993007\pi$
$331$	−1.36027e21	−	2.35605e21i	−0.518903	−	0.898766i	0.480856	−	0.876800i	$-0.340326\pi$
$332$	2.90362e20	−	5.02922e20i	0.107961	−	0.186994i
$333$	−1.68463e19	−	4.65525e19i	−0.00610560	−	0.0168720i
$334$	5.65926e20	−	3.26737e20i	0.199947	−	0.115439i
$335$	−5.19179e21			−1.78828
$336$	−1.99526e21	+	1.35132e21i	−0.670064	+	0.453810i
$337$	1.00709e21			0.329771			0.164885	−	0.986313i	$-0.447275\pi$
$337$	1.00709e21			0.329771			0.164885	+	0.986313i	$0.447275\pi$
$338$	9.45160e20	−	5.45689e20i	0.301796	−	0.174242i
$339$	3.77512e18	−	4.26951e19i	0.00117553	−	0.0132948i
$340$	−3.53753e21	+	6.12719e21i	−1.07431	+	1.86076i
$341$	5.66662e20	+	9.81487e20i	0.167846	+	0.290718i
$342$	−3.27547e20	+	3.88892e20i	−0.0946349	+	0.112359i
$343$	−1.63747e21	−	3.14769e21i	−0.461502	−	0.887139i
$344$			2.04921e21i			0.563431i
$345$	6.47489e21	+	4.54270e21i	1.73688	+	1.21857i
$346$	−5.17708e20	−	2.98899e20i	−0.135500	−	0.0782308i
$347$	−1.97993e21	−	1.14311e21i	−0.505648	−	0.291936i	0.225395	−	0.974267i	$-0.427633\pi$
$347$	−1.97993e21	−	1.14311e21i	−0.505648	−	0.291936i	−0.731043	+	0.682331i	$0.760966\pi$
$348$	3.33488e20	+	2.33971e20i	0.0831107	+	0.0583094i
$349$		−	4.73852e21i		−	1.15246i	−0.817286	−	0.576232i	$-0.804523\pi$
$349$		−	4.73852e21i		−	1.15246i	0.817286	−	0.576232i	$-0.195477\pi$
$350$	1.93463e21	−	3.12003e20i	0.459219	−	0.0740595i
$351$	1.73653e21	−	6.40965e21i	0.402320	−	1.48499i
$352$	1.02028e21	+	1.76717e21i	0.230731	+	0.399637i
$353$	1.18938e20	−	2.06007e20i	0.0262564	−	0.0454774i	−0.852599	−	0.522566i	$-0.824975\pi$
$353$	1.18938e20	−	2.06007e20i	0.0262564	−	0.0454774i	0.878855	+	0.477089i	$0.158308\pi$
$354$	−1.62122e20	+	1.83354e21i	−0.0349393	+	0.395150i
$355$	8.02962e21	−	4.63590e21i	1.68948	−	0.975424i
$356$	1.69305e20			0.0347812
$357$	6.13184e21	+	2.97635e21i	1.23002	+	0.597041i
$358$	9.68106e20			0.189635
$359$	−2.04928e21	+	1.18315e21i	−0.392011	+	0.226328i	−0.683031	−	0.730389i	$-0.739339\pi$
$359$	−2.04928e21	+	1.18315e21i	−0.392011	+	0.226328i	0.291020	+	0.956717i	$0.406005\pi$
$360$	−4.17271e21	+	1.51001e21i	−0.779555	+	0.282104i
$361$	−1.83018e21	+	3.16997e21i	−0.333952	+	0.578421i
$362$	−7.58001e20	−	1.31290e21i	−0.135097	−	0.233996i
$363$	1.36849e21	+	2.94184e21i	0.238252	+	0.512168i
$364$	3.00896e21	−	7.90507e21i	0.511745	−	1.34445i
$365$			8.91625e21i			1.48147i
$366$	−4.34297e20	+	6.19022e20i	−0.0705015	+	0.100489i
$367$	−7.69193e21	−	4.44094e21i	−1.22004	−	0.704390i	−0.255113	−	0.966911i	$-0.582113\pi$
$367$	−7.69193e21	−	4.44094e21i	−1.22004	−	0.704390i	−0.964926	+	0.262521i	$0.915446\pi$
$368$	−5.70864e21	−	3.29589e21i	−0.884762	−	0.510817i
$369$	−1.17669e21	−	2.09727e20i	−0.178213	−	0.0317636i
$370$		−	5.19384e19i		−	0.00768731i
$371$	−1.04365e21	+	2.74187e21i	−0.150966	+	0.396614i
$372$	3.05162e21	−	1.41956e21i	0.431436	−	0.200696i
$373$	6.19096e21	+	1.07231e22i	0.855526	+	1.48181i	0.876156	+	0.482027i	$0.160099\pi$
$373$	6.19096e21	+	1.07231e22i	0.855526	+	1.48181i	−0.0206301	+	0.999787i	$0.506567\pi$
$374$	8.51009e20	−	1.47399e21i	0.114954	−	0.199107i
$375$	−1.04563e22	−	9.24547e20i	−1.38074	−	0.122085i
$376$	−4.91032e21	+	2.83497e21i	−0.633888	+	0.365976i
$377$	−1.32361e21			−0.167055
$378$	8.40294e20	+	1.88711e21i	0.103693	+	0.232872i
$379$	3.49719e21			0.421974			0.210987	−	0.977489i	$-0.432332\pi$
$379$	3.49719e21			0.421974			0.210987	+	0.977489i	$0.432332\pi$
$380$	6.64710e21	−	3.83771e21i	0.784281	−	0.452805i
$381$	2.55603e21	+	2.26005e20i	0.294919	+	0.0260769i
$382$	1.73256e21	−	3.00089e21i	0.195502	−	0.338619i
$383$	4.82828e21	+	8.36282e21i	0.532847	+	0.922918i	0.999264	+	0.0383535i	$0.0122113\pi$
$383$	4.82828e21	+	8.36282e21i	0.532847	+	0.922918i	−0.466417	+	0.884565i	$0.654455\pi$
$384$	7.22735e21	−	3.36204e21i	0.780124	−	0.362900i
$385$	1.03666e22	−	1.67186e21i	1.09452	−	0.176515i
$386$		−	1.31240e21i		−	0.135542i
$387$	−1.11304e22	−	1.98382e21i	−1.12452	−	0.200429i
$388$	3.23393e21	+	1.86711e21i	0.319640	+	0.184544i
$389$	2.98514e21	+	1.72347e21i	0.288665	+	0.166661i	0.637339	−	0.770583i	$-0.280035\pi$
$389$	2.98514e21	+	1.72347e21i	0.288665	+	0.166661i	−0.348675	+	0.937244i	$0.613368\pi$
$390$	4.00131e21	−	5.70324e21i	0.378576	−	0.539600i
$391$			1.86445e22i			1.72603i
$392$	1.71180e21	+	5.16912e21i	0.155067	+	0.468258i
$393$	5.76148e21	+	1.23854e22i	0.510737	+	1.09793i
$394$	2.46010e21	+	4.26101e21i	0.213420	+	0.369654i
$395$	1.39924e22	−	2.42356e22i	1.18800	−	2.05768i
$396$	−6.97935e21	+	2.52567e21i	−0.579971	+	0.209878i
$397$	−1.06240e22	+	6.13374e21i	−0.864106	+	0.498892i	−0.865385	−	0.501107i	$-0.832926\pi$
$397$	−1.06240e22	+	6.13374e21i	−0.864106	+	0.498892i	0.00127913	+	0.999999i	$0.499593\pi$
$398$	−1.94576e21			−0.154911
$399$	−4.14648e21	−	6.12239e21i	−0.323154	−	0.477146i
$400$	1.93556e22			1.47671
$401$	−1.35553e22	+	7.82618e21i	−1.01247	+	0.584551i	−0.911915	−	0.410380i	$-0.865396\pi$
$401$	−1.35553e22	+	7.82618e21i	−1.01247	+	0.584551i	−0.100558	+	0.994931i	$0.532063\pi$
$402$	3.26682e20	−	3.69465e21i	0.0238894	−	0.270179i
$403$	−5.46765e21	+	9.47024e21i	−0.391478	+	0.678060i
$404$	9.88767e21	+	1.71259e22i	0.693190	+	1.20064i
$405$	−4.16215e21	−	2.41261e22i	−0.285726	−	1.65623i
$406$	3.19250e20	−	2.60015e20i	0.0214615	−	0.0174795i
$407$		−	1.79784e20i		−	0.0118358i
$408$	−8.56301e21	−	6.00769e21i	−0.552096	−	0.387343i
$409$	−1.88845e22	−	1.09030e22i	−1.19250	−	0.688488i	−0.233624	−	0.972327i	$-0.575058\pi$
$409$	−1.88845e22	−	1.09030e22i	−1.19250	−	0.688488i	−0.958872	+	0.283839i	$0.908392\pi$
$410$	−1.08594e21	−	6.26970e20i	−0.0671653	−	0.0387779i
$411$	4.87968e21	+	3.42352e21i	0.295622	+	0.207404i
$412$		−	1.48291e22i		−	0.880014i
$413$	−2.50179e22	−	9.52273e21i	−1.45437	−	0.553587i
$414$	−3.64016e21	+	4.32191e21i	−0.207309	+	0.246135i
$415$	3.47811e21	+	6.02427e21i	0.194060	+	0.336121i
$416$	−9.84452e21	+	1.70512e22i	−0.538147	+	0.932099i
$417$	−2.60619e21	+	2.94750e22i	−0.139589	+	1.57869i
$418$	−1.59906e21	+	9.23220e20i	−0.0839204	+	0.0484515i
$419$	3.68900e22			1.89710			0.948549	−	0.316631i	$-0.102552\pi$
$419$	3.68900e22			1.89710			0.948549	+	0.316631i	$0.102552\pi$
$420$	−2.23411e21	−	3.11036e22i	−0.112586	−	1.56744i
$421$	2.26825e22			1.12019			0.560096	−	0.828428i	$-0.310764\pi$
$421$	2.26825e22			1.12019			0.560096	+	0.828428i	$0.310764\pi$
$422$	−5.49885e21	+	3.17476e21i	−0.266144	+	0.153658i
$423$	−1.06447e22	−	2.94152e22i	−0.504940	−	1.39533i
$424$	2.25118e21	−	3.89915e21i	0.104665	−	0.181285i
$425$	−2.73732e22	−	4.74118e22i	−1.24744	−	2.16063i
$426$	2.79382e21	+	6.00586e21i	0.124801	+	0.268283i
$427$	−6.94469e21	−	8.52676e21i	−0.304100	−	0.373377i
$428$			2.72375e21i			0.116922i
$429$	1.38505e22	−	1.97416e22i	0.582877	−	0.830799i
$430$	−1.02720e22	−	5.93057e21i	−0.423814	−	0.244689i
$431$	−1.45287e22	−	8.38816e21i	−0.587720	−	0.339320i	0.176475	−	0.984305i	$-0.443530\pi$
$431$	−1.45287e22	−	8.38816e21i	−0.587720	−	0.339320i	−0.764195	+	0.644985i	$0.776864\pi$
$432$	5.22618e21	+	1.97230e22i	0.207287	+	0.782280i
$433$			3.39961e22i			1.32215i	0.750319	+	0.661076i	$0.229900\pi$
$433$			3.39961e22i			1.32215i	−0.750319	+	0.661076i	$0.770100\pi$
$434$	−5.41598e20	−	3.35827e21i	−0.0206545	−	0.128072i
$435$	−4.42450e21	+	2.05820e21i	−0.165465	+	0.0769713i
$436$	−2.27169e21	−	3.93469e21i	−0.0833133	−	0.144303i
$437$	1.01133e22	−	1.75168e22i	0.363748	−	0.630030i
$438$	−6.34511e21	−	5.61037e20i	−0.223825	−	0.0197907i
$439$	−1.94889e22	+	1.12519e22i	−0.674277	+	0.389294i	−0.797695	−	0.603061i	$-0.793948\pi$
$439$	−1.94889e22	+	1.12519e22i	−0.674277	+	0.389294i	0.123418	+	0.992355i	$0.460614\pi$
$440$	−1.61148e22			−0.546863
$441$	−2.97335e22	+	4.29356e21i	−0.989734	+	0.142919i
$442$	1.64226e22			0.536230
$443$	1.25951e22	−	7.27180e21i	0.403432	−	0.232922i	−0.284532	−	0.958667i	$-0.591838\pi$
$443$	1.25951e22	−	7.27180e21i	0.403432	−	0.232922i	0.687964	+	0.725745i	$0.258505\pi$
$444$	−5.31831e20	−	4.70247e19i	−0.0167116	−	0.00147765i
$445$	−1.01401e21	+	1.75632e21i	−0.0312596	+	0.0541432i
$446$	9.81670e20	+	1.70030e21i	0.0296906	+	0.0514256i
$447$	−4.67409e22	+	2.17431e22i	−1.38702	+	0.645219i
$448$	3.45018e21	+	2.13935e22i	0.100457	+	0.622899i
$449$			1.12196e22i			0.320542i	0.987073	+	0.160271i	$0.0512368\pi$
$449$			1.12196e22i			0.320542i	−0.987073	+	0.160271i	$0.948763\pi$
$450$	2.91140e21	−	1.63347e22i	0.0816198	−	0.457936i
$451$	−3.75897e21	−	2.17024e21i	−0.103411	−	0.0597046i
$452$	−4.00313e20	−	2.31121e20i	−0.0108074	−	0.00623968i
$453$	1.94941e21	−	2.77858e21i	0.0516499	−	0.0736187i
$454$		−	8.34671e21i		−	0.217040i
$455$	6.39835e22	+	7.85596e22i	1.63294	+	2.00495i
$456$	4.78631e21	+	1.02891e22i	0.119895	+	0.257737i
$457$	−7.04344e21	−	1.21996e22i	−0.173180	−	0.299956i	0.766350	−	0.642423i	$-0.222071\pi$
$457$	−7.04344e21	−	1.21996e22i	−0.173180	−	0.299956i	−0.939530	+	0.342467i	$0.888737\pi$
$458$	−4.06166e21	+	7.03501e21i	−0.0980274	+	0.169788i
$459$	4.09209e22	−	4.06945e22i	0.969476	−	0.964113i
$460$	7.38719e22	−	4.26500e22i	1.71806	−	0.991921i
$461$	1.68000e22			0.383575			0.191788	−	0.981436i	$-0.438572\pi$
$461$	1.68000e22			0.383575			0.191788	+	0.981436i	$0.438572\pi$
$462$	5.37450e20	+	7.48245e21i	0.0120471	+	0.167721i
$463$	−5.93090e22			−1.30522			−0.652608	−	0.757696i	$-0.726325\pi$
$463$	−5.93090e22			−1.30522			−0.652608	+	0.757696i	$0.726325\pi$
$464$	3.52196e21	−	2.03341e21i	0.0760995	−	0.0439361i
$465$	−3.55086e21	+	4.01588e22i	−0.0753326	+	0.851983i
$466$	1.08974e21	−	1.88748e21i	0.0227008	−	0.0393189i
$467$	−5.38706e21	−	9.33066e21i	−0.110194	−	0.190862i	0.805654	−	0.592386i	$-0.201814\pi$
$467$	−5.38706e21	−	9.33066e21i	−0.110194	−	0.190862i	−0.915848	+	0.401524i	$0.868481\pi$
$468$	−5.47764e22	−	4.61357e22i	−1.10028	−	0.926717i
$469$	5.04122e22	+	1.91887e22i	0.994412	+	0.378509i
$470$		−	3.28184e22i		−	0.635749i
$471$	5.61490e22	+	3.93934e22i	1.06823	+	0.749455i
$472$	3.55775e22	+	2.05407e22i	0.664765	+	0.383802i
$473$	−3.55565e22	−	2.05285e22i	−0.652528	−	0.376737i
$474$	1.63664e22	+	1.14824e22i	0.295010	+	0.206975i
$475$			5.93919e22i			1.05155i
$476$	5.69953e22	−	4.64203e22i	0.991243	−	0.807326i
$477$	1.89991e22	+	1.60021e22i	0.324585	+	0.273383i
$478$	1.27479e22	+	2.20800e22i	0.213944	+	0.370562i
$479$	−3.64521e22	+	6.31369e22i	−0.600995	+	1.04095i	0.391676	+	0.920103i	$0.371896\pi$
$479$	−3.64521e22	+	6.31369e22i	−0.600995	+	1.04095i	−0.992671	+	0.120851i	$0.961438\pi$
$480$	−6.39333e21	+	7.23061e22i	−0.103556	+	1.17118i
$481$	1.50230e21	−	8.67356e20i	0.0239070	−	0.0138027i
$482$	1.90424e22			0.297729
$483$	−4.60815e22	−	6.80406e22i	−0.707906	−	1.04524i
$484$	3.49909e22			0.528165
$485$	−3.87378e22	+	2.23653e22i	−0.574553	+	0.331718i
$486$	1.74309e22	−	1.44384e21i	0.254045	−	0.0210432i
$487$	1.81327e22	−	3.14067e22i	0.259696	−	0.449807i	−0.706464	−	0.707749i	$-0.749711\pi$
$487$	1.81327e22	−	3.14067e22i	0.259696	−	0.449807i	0.966161	+	0.257942i	$0.0830442\pi$
$488$	8.43835e21	+	1.46156e22i	0.118765	+	0.205707i
$489$	1.24499e21	+	2.67635e21i	0.0172203	+	0.0370184i
$490$	−3.08652e22	−	6.37910e21i	−0.419567	−	0.0867147i
$491$		−	1.82539e22i		−	0.243872i	−0.992538	−	0.121936i	$-0.961090\pi$
$491$		−	1.82539e22i		−	0.243872i	0.992538	−	0.121936i	$-0.0389103\pi$
$492$	−7.40316e21	+	1.05520e22i	−0.0972106	+	0.138558i
$493$	−9.96172e21	−	5.75140e21i	−0.128569	−	0.0742292i
$494$	−1.54292e22	−	8.90804e21i	−0.195733	−	0.113006i
$495$	1.56006e22	−	8.75287e22i	0.194535	−	1.09146i
$496$		−	3.35989e22i		−	0.411842i
$497$	−9.51017e22	+	1.53373e22i	−1.14593	+	0.184808i
$498$	−4.50593e21	+	2.09608e21i	−0.0533746	+	0.0248289i
$499$	2.74377e22	+	4.75234e22i	0.319516	+	0.553418i	0.980387	−	0.197081i	$-0.0631463\pi$
$499$	2.74377e22	+	4.75234e22i	0.319516	+	0.553418i	−0.660871	+	0.750499i	$0.729813\pi$
$500$	−5.66027e22	+	9.80388e22i	−0.648026	+	1.12241i
$501$	8.01526e22	+	7.08712e21i	0.902188	+	0.0797717i
$502$	−1.74631e22	+	1.00823e22i	−0.193259	+	0.111578i
$503$	−1.61889e22			−0.176152			−0.0880761	−	0.996114i	$-0.528072\pi$
$503$	−1.61889e22			−0.176152			−0.0880761	+	0.996114i	$0.528072\pi$
$504$	4.60979e22	+	7.60044e20i	0.493199	+	0.00813166i
$505$	−2.36880e23			−2.49202
$506$	−1.77710e22	+	1.02601e22i	−0.183837	+	0.106139i
$507$	1.33864e23	+	1.18363e22i	1.36175	+	0.120406i
$508$	1.38365e22	−	2.39655e22i	0.138415	−	0.239743i
$509$	−6.32676e21	−	1.09583e22i	−0.0622415	−	0.107805i	0.833226	−	0.552933i	$-0.186492\pi$
$509$	−6.32676e21	−	1.09583e22i	−0.0622415	−	0.107805i	−0.895467	+	0.445128i	$0.853158\pi$
$510$	5.48965e22	−	2.55369e22i	0.531127	−	0.247071i
$511$	3.29542e22	−	8.65767e22i	0.313569	−	0.823803i
$512$		−	1.03150e23i		−	0.965329i
$513$	−6.05194e22	+	1.60364e22i	−0.557054	+	0.147607i
$514$	4.26603e22	+	2.46299e22i	0.386222	+	0.222986i
$515$	1.53833e23	+	8.88157e22i	1.36990	+	0.790912i
$516$	−7.00271e22	+	9.98126e22i	−0.613400	+	0.874305i
$517$		−	1.13600e23i		−	0.978836i
$518$	−1.91963e20	+	5.04322e20i	−0.00162710	+	0.00427469i
$519$	−3.10470e22	−	6.67416e22i	−0.258880	−	0.556512i
$520$	−7.77450e22	−	1.34658e23i	−0.637741	−	1.10460i
$521$	7.55220e22	−	1.30808e23i	0.609471	−	1.05563i	−0.381857	−	0.924221i	$-0.624715\pi$
$521$	7.55220e22	−	1.30808e23i	0.609471	−	1.05563i	0.991328	−	0.131413i	$-0.0419513\pi$
$522$	−1.18628e21	−	3.27813e21i	−0.00941866	−	0.0260272i
$523$	−9.71089e22	+	5.60658e22i	−0.758568	+	0.437959i	−0.828781	−	0.559573i	$-0.810965\pi$
$523$	−9.71089e22	+	5.60658e22i	−0.758568	+	0.437959i	0.0702134	+	0.997532i	$0.477632\pi$
$524$	1.47315e23			1.13222
$525$	2.17077e23	+	1.05368e23i	1.64157	+	0.796806i
$526$	−6.51942e21			−0.0485099
$527$	−8.23010e22	+	4.75165e22i	−0.602580	+	0.347900i
$528$	−6.52613e21	+	7.38079e22i	−0.0470183	+	0.531759i
$529$	4.18682e22	−	7.25179e22i	0.296832	−	0.514129i
$530$	1.30301e22	+	2.25688e22i	0.0909083	+	0.157458i
$531$	−1.46010e23	+	1.73356e23i	−1.00249	+	1.19024i
$532$	−7.87274e22	+	1.26966e22i	−0.531957	+	0.0857902i
$533$		−	4.18808e22i		−	0.278506i
$534$	−1.18605e21	−	8.32119e20i	−0.00776254	−	0.00544609i
$535$	−2.82555e22	−	1.63133e22i	−0.182010	−	0.105084i
$536$	−7.16902e22	−	4.13903e22i	−0.454526	−	0.262421i
$537$	9.75857e22	+	6.84648e22i	0.608982	+	0.427253i
$538$			4.02722e22i			0.247375i
$539$	−1.06839e23	−	2.20811e22i	−0.645990	−	0.133511i
$540$	−2.54844e23	−	6.90435e22i	−1.51680	−	0.410937i
$541$	−1.51356e23	−	2.62157e23i	−0.886797	−	1.53598i	−0.843640	−	0.536909i	$-0.819592\pi$
$541$	−1.51356e23	−	2.62157e23i	−0.886797	−	1.53598i	−0.0431567	−	0.999068i	$-0.513741\pi$
$542$	−2.70673e21	+	4.68819e21i	−0.0156117	+	0.0270403i
$543$	1.64415e22	−	1.85947e23i	0.0933560	−	1.05582i
$544$	−1.48183e23	+	8.55536e22i	−0.828339	+	0.478242i
$545$	5.44231e22			0.299511
$546$	−5.99317e22	+	4.05896e22i	−0.324728	+	0.219927i
$547$	−5.19641e22			−0.277211			−0.138606	−	0.990348i	$-0.544262\pi$
$547$	−5.19641e22			−0.277211			−0.138606	+	0.990348i	$0.544262\pi$
$548$	5.56722e22	−	3.21424e22i	0.292418	−	0.168827i
$549$	−8.75548e22	+	3.16841e22i	−0.452809	+	0.163861i
$550$	3.01271e22	−	5.21816e22i	0.153417	−	0.265726i
$551$	6.23943e21	+	1.08070e22i	0.0312865	+	0.0541897i
$552$	5.31922e22	+	1.14347e23i	0.262643	+	0.564602i
$553$	−2.25440e23	+	1.83611e23i	−1.09614	+	0.892763i
$554$		−	7.16854e22i		−	0.343240i
$555$	3.67310e21	−	5.23542e21i	0.0173198	−	0.0246866i
$556$	2.76360e23	+	1.59557e23i	1.28333	+	0.740933i
$557$	2.49681e23	+	1.44153e23i	1.14187	+	0.659258i	0.946893	−	0.321549i	$-0.104204\pi$
$557$	2.49681e23	+	1.44153e23i	1.14187	+	0.659258i	0.194976	+	0.980808i	$0.437537\pi$
$558$	−2.83550e22	−	5.05382e21i	−0.127714	−	0.0227630i
$559$		−	3.96154e23i		−	1.75737i
$560$	−2.90940e23	−	1.10742e23i	−1.27117	−	0.483855i
$561$	1.90023e23	−	8.83955e22i	0.817753	−	0.380404i
$562$	2.60455e21	+	4.51121e21i	0.0110401	+	0.0191220i
$563$	1.03727e23	−	1.79660e23i	0.433082	−	0.750120i	−0.564055	−	0.825737i	$-0.690759\pi$
$563$	1.03727e23	−	1.79660e23i	0.433082	−	0.750120i	0.997137	+	0.0756172i	$0.0240927\pi$
$564$	−3.36049e23	−	2.97136e22i	−1.38207	−	0.122203i
$565$	4.79516e21	−	2.76849e21i	0.0194264	−	0.0112158i
$566$	−5.16644e22			−0.206182
$567$	−4.87552e22	+	2.49648e23i	−0.191675	+	0.981459i
$568$	1.47835e23			0.572553
$569$	3.12856e23	−	1.80628e23i	1.19369	−	0.689176i	0.234546	−	0.972105i	$-0.424640\pi$
$569$	3.12856e23	−	1.80628e23i	1.19369	−	0.689176i	0.959141	+	0.282929i	$0.0913062\pi$
$570$	−6.54278e22	−	5.78515e21i	−0.245938	−	0.0217459i
$571$	9.08261e21	−	1.57315e22i	0.0336360	−	0.0582592i	−0.848717	−	0.528847i	$-0.822625\pi$
$571$	9.08261e21	−	1.57315e22i	0.0336360	−	0.0582592i	0.882353	+	0.470587i	$0.155958\pi$
$572$	−1.30038e23	−	2.25232e23i	−0.474464	−	0.821795i
$573$	3.86867e23	−	1.79964e23i	1.39074	−	0.646950i
$574$	8.22724e21	+	1.01015e22i	0.0291409	+	0.0357795i
$575$			6.60046e23i			2.30355i
$576$	1.80632e23	+	3.21947e22i	0.621159	+	0.110712i
$577$	4.07229e23	+	2.35114e23i	1.37989	+	0.796680i	0.992146	−	0.125087i	$-0.0399211\pi$
$577$	4.07229e23	+	2.35114e23i	1.37989	+	0.796680i	0.387744	+	0.921767i	$0.373254\pi$
$578$	5.74820e22	+	3.31872e22i	0.191931	+	0.110811i
$579$	9.28134e22	−	1.32291e23i	0.305382	−	0.435273i
$580$			5.26260e22i			0.170633i
$581$	−1.15069e22	−	7.13506e22i	−0.0367673	−	0.227982i
$582$	−1.34784e22	−	2.89744e22i	−0.0424417	−	0.0912366i
$583$	4.51035e22	+	7.81216e22i	0.139968	+	0.242431i
$584$	−7.10828e22	+	1.23119e23i	−0.217398	+	0.376544i
$585$	8.06669e23	−	2.91915e23i	2.43148	−	0.879898i
$586$	1.42655e23	−	8.23617e22i	0.423795	−	0.244678i
$587$	−5.96296e23			−1.74598			−0.872988	−	0.487742i	$-0.837821\pi$
$587$	−5.96296e23			−1.74598			−0.872988	+	0.487742i	$0.837821\pi$
$588$	−9.32648e22	+	3.10273e23i	−0.269160	+	0.895439i
$589$	1.03097e23			0.293269
$590$	−2.05927e23	+	1.18892e23i	−0.577394	+	0.333358i
$591$	−5.33609e22	+	6.03491e23i	−0.147479	+	1.66793i
$592$	−2.66496e21	+	4.61585e21i	−0.00726034	+	0.0125753i
$593$	−1.70224e22	−	2.94837e22i	−0.0457148	−	0.0791803i	0.842263	−	0.539067i	$-0.181223\pi$
$593$	−1.70224e22	−	2.94837e22i	−0.0457148	−	0.0791803i	−0.887977	+	0.459887i	$0.847890\pi$
$594$	6.13068e22	+	1.66095e22i	0.162302	+	0.0439715i
$595$	1.40191e23	+	8.69277e23i	0.365868	+	2.26863i
$596$			5.55948e23i			1.43035i
$597$	−1.96134e23	−	1.37605e23i	−0.497474	−	0.349021i
$598$	−1.71471e23	−	9.89986e22i	−0.428775	−	0.247553i
$599$	−3.67911e23	−	2.12413e23i	−0.907015	−	0.523665i	−0.0275455	−	0.999621i	$-0.508769\pi$
$599$	−3.67911e23	−	2.12413e23i	−0.907015	−	0.523665i	−0.879470	+	0.475955i	$0.842102\pi$
$600$	−3.03144e23	−	2.12682e23i	−0.736824	−	0.516945i
$601$			2.57078e23i			0.616073i	0.951375	+	0.308036i	$0.0996719\pi$
$601$			2.57078e23i			0.616073i	−0.951375	+	0.308036i	$0.900328\pi$
$602$	7.78222e22	+	9.55510e22i	0.183880	+	0.225769i
$603$	2.94217e23	−	3.49320e23i	0.685441	−	0.813816i
$604$	−1.83024e22	−	3.17008e22i	−0.0420431	−	0.0728208i
$605$	−2.09570e23	+	3.62986e23i	−0.474688	+	0.822184i
$606$	1.49052e22	−	1.68572e23i	0.0332904	−	0.376502i
$607$	−2.73804e23	+	1.58081e23i	−0.603026	+	0.348157i	−0.770231	−	0.637765i	$-0.779859\pi$
$607$	−2.73804e23	+	1.58081e23i	−0.603026	+	0.348157i	0.167205	+	0.985922i	$0.446526\pi$
$608$	1.85626e23			0.403143
$609$	5.05689e22	−	3.63227e21i	0.108302	−	0.00777912i
$610$	−9.76846e22			−0.206311
$611$	9.49263e23	−	5.48057e23i	1.97713	−	1.14150i
$612$	−2.11786e23	−	5.85242e23i	−0.435021	−	1.20212i
$613$	3.44564e23	−	5.96802e23i	0.698000	−	1.20897i	−0.271158	−	0.962535i	$-0.587407\pi$
$613$	3.44564e23	−	5.96802e23i	0.698000	−	1.20897i	0.969159	−	0.246437i	$-0.0792600\pi$
$614$	−7.50154e22	−	1.29931e23i	−0.149872	−	0.259585i
$615$	−6.51242e22	−	1.39997e23i	−0.128323	−	0.275855i
$616$	1.56475e23	+	5.95601e22i	0.304095	+	0.115749i
$617$		−	7.01388e23i		−	1.34442i	−0.740361	−	0.672209i	$-0.765346\pi$
$617$		−	7.01388e23i		−	1.34442i	0.740361	−	0.672209i	$-0.234654\pi$
$618$	−7.28839e22	+	1.03885e23i	−0.137794	+	0.196403i
$619$	4.80691e23	+	2.77527e23i	0.896388	+	0.517530i	0.876026	−	0.482263i	$-0.160185\pi$
$619$	4.80691e23	+	2.77527e23i	0.896388	+	0.517530i	0.0203612	+	0.999793i	$0.493518\pi$
$620$	3.76532e23	+	2.17391e23i	0.692584	+	0.399864i
$621$	−6.72577e23	+	1.78218e23i	−1.22029	+	0.323351i
$622$			1.01544e23i			0.181734i
$623$	1.63374e22	−	1.33061e22i	0.0288426	−	0.0234911i
$624$	−6.48237e23	+	3.01548e23i	−1.12892	+	0.525155i
$625$	−1.46951e23	−	2.54526e23i	−0.252459	−	0.437272i
$626$	1.28189e22	−	2.22030e22i	0.0217255	−	0.0376297i
$627$	−2.26477e23	−	2.00252e22i	−0.378660	−	0.0334813i
$628$	6.40603e23	−	3.69852e23i	1.05665	−	0.610058i
$629$	1.50755e22			0.0245324
$630$	−1.37220e23	+	2.28874e23i	−0.220305	+	0.367453i
$631$	−4.53837e23			−0.718870			−0.359435	−	0.933170i	$-0.617030\pi$
$631$	−4.53837e23			−0.718870			−0.359435	+	0.933170i	$0.617030\pi$
$632$	3.86425e23	−	2.23103e23i	0.603907	−	0.348666i
$633$	−7.78807e23	−	6.88624e22i	−1.20088	−	0.106182i
$634$	−8.28974e22	+	1.43582e23i	−0.126119	+	0.218445i
$635$	1.65741e23	+	2.87072e23i	0.248802	+	0.430937i
$636$	2.42894e23	−	1.12990e23i	0.359776	−	0.167361i
$637$	−3.30925e23	−	9.99295e23i	−0.483664	−	1.46052i
$638$		−	1.26600e22i		−	0.0182582i
$639$	−1.43117e23	+	8.02973e23i	−0.203674	+	1.14273i
$640$	8.91764e23	+	5.14860e23i	1.25233	+	0.723036i
$641$	−4.95195e22	−	2.85901e22i	−0.0686251	−	0.0396207i	0.465295	−	0.885156i	$-0.345948\pi$
$641$	−4.95195e22	−	2.85901e22i	−0.0686251	−	0.0396207i	−0.533920	+	0.845535i	$0.679282\pi$
$642$	1.33870e22	−	1.90811e22i	0.0183078	−	0.0260949i
$643$		−	2.34939e23i		−	0.317074i	−0.987353	−	0.158537i	$-0.949322\pi$
$643$		−	2.34939e23i		−	0.317074i	0.987353	−	0.158537i	$-0.0506778\pi$
$644$	−8.74929e23	+	1.41102e23i	−1.16531	+	0.187933i
$645$	−6.16016e23	−	1.32425e24i	−0.809719	−	1.74065i
$646$	−7.74151e22	−	1.34087e23i	−0.100427	−	0.173944i
$647$	−7.13276e22	+	1.23543e23i	−0.0913211	+	0.158173i	−0.908067	−	0.418824i	$-0.862442\pi$
$647$	−7.13276e22	+	1.23543e23i	−0.0913211	+	0.158173i	0.816746	+	0.576997i	$0.195776\pi$
$648$	1.34868e23	−	3.66325e23i	0.170420	−	0.462891i
$649$	−7.12813e23	+	4.11543e23i	−0.888988	+	0.513257i
$650$	5.81384e23			0.715649
$651$	1.82905e23	−	3.76818e23i	0.222222	−	0.457818i
$652$	3.18331e22			0.0381746
$653$	−6.68514e23	+	3.85967e23i	−0.791313	+	0.456865i	−0.840425	−	0.541928i	$-0.817694\pi$
$653$	−6.68514e23	+	3.85967e23i	−0.791313	+	0.456865i	0.0491114	+	0.998793i	$0.484361\pi$
$654$	−3.42446e21	+	3.87294e22i	−0.00400112	+	0.0452511i
$655$	−8.82310e23	+	1.52821e24i	−1.01758	+	1.76251i
$656$	6.43397e22	+	1.11440e23i	0.0732481	+	0.126870i
$657$	−5.99914e23	−	5.05281e23i	−0.674191	−	0.567841i
$658$	−1.21296e23	+	3.18667e23i	−0.134563	+	0.353522i
$659$		−	4.13308e21i		−	0.00452635i	−0.999997	−	0.00226317i	$-0.999280\pi$
$659$		−	4.13308e21i		−	0.00452635i	0.999997	−	0.00226317i	$-0.000720391\pi$
$660$	−7.84917e23	−	5.50687e23i	−0.848595	−	0.595363i
$661$	−3.49346e22	−	2.01695e22i	−0.0372858	−	0.0215270i	0.481241	−	0.876588i	$-0.340186\pi$
$661$	−3.49346e22	−	2.01695e22i	−0.0372858	−	0.0215270i	−0.518527	+	0.855061i	$0.673519\pi$
$662$	2.17438e23	+	1.25538e23i	0.229109	+	0.132276i
$663$	1.65540e24	+	1.16141e24i	1.72202	+	1.20815i
$664$			1.10914e23i			0.113909i
$665$	3.39809e23	−	8.92739e23i	0.344549	−	0.905191i
$666$	3.49458e21	+	2.94333e21i	0.00349836	+	0.00294651i
$667$	6.93413e22	+	1.20103e23i	0.0685366	+	0.118709i
$668$	4.33888e23	−	7.51517e23i	0.423426	−	0.733396i
$669$	−2.12930e22	+	2.40815e23i	−0.0205170	+	0.232040i
$670$	4.14952e23	−	2.39573e23i	0.394787	−	0.227930i
$671$	−3.38133e23			−0.317648
$672$	3.29321e23	−	6.78462e23i	0.305478	−	0.629342i
$673$	−7.28098e23			−0.666902			−0.333451	−	0.942767i	$-0.608213\pi$
$673$	−7.28098e23			−0.666902			−0.333451	+	0.942767i	$0.608213\pi$
$674$	−8.04911e22	+	4.64715e22i	−0.0728012	+	0.0420318i
$675$	1.44866e24	−	1.44065e24i	1.29386	−	1.28670i
$676$	7.24643e23	−	1.25512e24i	0.639112	−	1.10697i
$677$	4.02350e23	+	6.96890e23i	0.350429	+	0.606961i	0.986325	−	0.164814i	$-0.0527025\pi$
$677$	4.02350e23	+	6.96890e23i	0.350429	+	0.606961i	−0.635896	+	0.771775i	$0.719369\pi$
$678$	1.66842e21	+	3.58660e21i	0.00143501	+	0.00308483i
$679$	4.58805e23	−	7.39927e22i	0.389704	−	0.0628486i
$680$		−	1.35128e24i		−	1.13350i
$681$	5.90282e23	−	8.41353e23i	0.489000	−	0.696992i
$682$	−9.05807e22	−	5.22968e22i	−0.0741086	−	0.0427866i
$683$	−4.59873e23	−	2.65508e23i	−0.371588	−	0.214536i	0.302564	−	0.953129i	$-0.402157\pi$
$683$	−4.59873e23	−	2.65508e23i	−0.371588	−	0.214536i	−0.674152	+	0.738593i	$0.735491\pi$
$684$	−1.18476e23	+	6.64720e23i	−0.0945480	+	0.530471i
$685$			7.70037e23i			0.606934i
$686$	2.76123e23	+	1.76018e23i	0.214955	+	0.137026i
$687$	−9.06935e23	+	4.21890e23i	−0.697339	+	0.324390i
$688$	6.08595e23	+	1.05412e24i	0.462197	+	0.800548i
$689$	−4.35198e23	+	7.53785e23i	−0.326455	+	0.565437i
$690$	−7.27125e23	−	6.42927e22i	−0.538756	−	0.0476370i
$691$	−2.08587e24	+	1.20428e24i	−1.52659	+	0.881380i	−0.527093	+	0.849808i	$0.676718\pi$
$691$	−2.08587e24	+	1.20428e24i	−1.52659	+	0.881380i	−0.999501	+	0.0315722i	$0.989949\pi$
$692$	−7.93841e23			−0.573894
$693$	−4.74986e23	+	7.92244e23i	−0.339194	+	0.565752i
$694$	2.10994e23			0.148838
$695$	−3.31039e24	+	1.91125e24i	−2.30679	+	1.33183i
$696$	−7.75037e22	−	6.85291e21i	−0.0533512	−	0.00471733i
$697$	1.81982e23	−	3.15202e23i	0.123751	−	0.214344i
$698$	2.18657e23	+	3.78726e23i	0.146890	+	0.254421i
$699$	2.43329e23	−	1.13192e23i	0.161487	−	0.0751210i
$700$	2.01773e24	−	1.64335e24i	1.32291	−	1.07745i
$701$			1.47007e23i			0.0952212i	0.998866	+	0.0476106i	$0.0151607\pi$
$701$			1.47007e23i			0.0952212i	−0.998866	+	0.0476106i	$0.984839\pi$
$702$	1.56979e23	+	5.92421e23i	0.100456	+	0.379110i
$703$	−1.41636e22	−	8.17735e21i	−0.00895473	−	0.00517002i
$704$	5.77033e23	+	3.33150e23i	0.360440	+	0.208100i
$705$	2.32093e24	−	3.30811e24i	1.43237	−	2.04161i
$706$			2.19534e22i			0.0133863i
$707$	2.30010e24	+	8.75501e23i	1.38574	+	0.527463i
$708$	1.03097e24	+	2.21627e24i	0.613710	+	1.31929i
$709$	5.74867e22	+	9.95700e22i	0.0338123	+	0.0585646i	0.882436	−	0.470432i	$-0.155902\pi$
$709$	5.74867e22	+	9.95700e22i	0.0338123	+	0.0585646i	−0.848624	+	0.528996i	$0.822568\pi$
$710$	−4.27844e23	+	7.41047e23i	−0.248651	+	0.430675i
$711$	8.37701e23	+	2.31487e24i	0.481058	+	1.32934i
$712$	−2.80038e22	+	1.61680e22i	−0.0158905	+	0.00917436i
$713$	1.14576e24			0.642439
$714$	−6.27428e23	+	4.50670e22i	−0.347640	+	0.0249703i
$715$	3.11532e24			1.70570
$716$	1.11335e24	−	6.42795e23i	0.602382	−	0.347786i
$717$	−2.76508e23	+	3.12720e24i	−0.147841	+	1.67203i
$718$	1.09192e23	−	1.89126e23i	0.0576944	−	0.0999296i
$719$	−1.43019e24	−	2.47716e24i	−0.746789	−	1.29348i	−0.949354	−	0.314207i	$-0.898261\pi$
$719$	−1.43019e24	−	2.47716e24i	−0.746789	−	1.29348i	0.202566	−	0.979269i	$-0.435072\pi$
$720$	−1.69799e24	+	2.01600e24i	−0.876211	+	1.04032i
$721$	−1.16546e24	−	1.43096e24i	−0.594357	−	0.729758i
$722$		−	3.37812e23i		−	0.170259i
$723$	1.91948e24	+	1.34668e24i	0.956112	+	0.670795i
$724$	−1.74345e24	−	1.00658e24i	−0.858286	−	0.495531i
$725$	−3.52661e23	−	2.03609e23i	−0.171587	−	0.0990657i
$726$	−2.45126e23	−	1.71977e23i	−0.117877	−	0.0827009i
$727$			2.32662e24i			1.10582i	0.833242	+	0.552908i	$0.186482\pi$
$727$			2.32662e24i			1.10582i	−0.833242	+	0.552908i	$0.813518\pi$
$728$	2.57210e23	+	1.59487e24i	0.120829	+	0.749221i
$729$	1.85915e24	+	1.08718e24i	0.863238	+	0.504796i
$730$	−4.11437e23	−	7.12630e23i	−0.188825	−	0.327054i
$731$	1.72139e24	−	2.98153e24i	0.780873	−	1.35251i
$732$	−8.84430e22	+	1.00026e24i	−0.0396569	+	0.448505i
$733$	2.70443e24	−	1.56140e24i	1.19865	−	0.692039i	0.238394	−	0.971169i	$-0.423379\pi$
$733$	2.70443e24	−	1.56140e24i	1.19865	−	0.692039i	0.960254	+	0.279129i	$0.0900458\pi$
$734$	8.19701e23			0.359120
$735$	−2.66009e24	−	2.82581e24i	−1.15201	−	1.22377i
$736$	2.06294e24			0.883131
$737$	1.43635e24	−	8.29277e23i	0.607836	−	0.350934i
$738$	1.03725e23	−	3.75356e22i	0.0433913	−	0.0157023i
$739$	−9.17980e23	+	1.58999e24i	−0.379625	+	0.657530i	−0.991008	−	0.133805i	$-0.957280\pi$
$739$	−9.17980e23	+	1.58999e24i	−0.379625	+	0.657530i	0.611382	+	0.791335i	$0.290614\pi$
$740$	−3.44856e22	−	5.97308e22i	−0.0140984	−	0.0244191i
$741$	−9.25290e23	−	1.98909e24i	−0.373958	−	0.803896i
$742$	−4.31085e22	−	2.67302e23i	−0.0172238	−	0.106800i
$743$			2.04356e24i			0.807202i	0.914935	+	0.403601i	$0.132242\pi$
$743$			2.04356e24i			0.807202i	−0.914935	+	0.403601i	$0.867758\pi$
$744$	−3.69189e23	+	5.26220e23i	−0.144171	+	0.205493i
$745$	−5.76725e24	−	3.32972e24i	−2.22659	−	1.28552i
$746$	−9.89623e23	−	5.71359e23i	−0.377737	−	0.218087i
$747$	−6.02435e23	−	1.07375e23i	−0.227345	−	0.0405206i
$748$		−	2.26018e24i		−	0.843295i
$749$	2.14067e23	+	2.62833e23i	0.0789685	+	0.0969583i
$750$	8.78378e23	−	4.08606e23i	0.320377	−	0.149034i
$751$	−1.56853e24	−	2.71677e24i	−0.565656	−	0.979746i	−0.996988	−	0.0775522i	$-0.975290\pi$
$751$	−1.56853e24	−	2.71677e24i	−0.565656	−	0.979746i	0.431332	−	0.902193i	$-0.358044\pi$
$752$	−1.68391e24	+	2.91663e24i	−0.600438	+	1.03999i
$753$	−2.47331e24	−	2.18691e23i	−0.872010	−	0.0771034i
$754$	1.05789e23	−	6.10775e22i	0.0368795	−	0.0212924i
$755$	4.38473e23			0.151145
$756$	2.21935e24	+	1.61231e24i	0.756469	+	0.549558i
$757$	−4.04026e24			−1.36174			−0.680870	−	0.732404i	$-0.738398\pi$
$757$	−4.04026e24			−1.36174			−0.680870	+	0.732404i	$0.738398\pi$
$758$	−2.79512e23	+	1.61376e23i	−0.0931562	+	0.0537838i
$759$	−2.51693e24	−	2.22548e23i	−0.829499	−	0.0733446i
$760$	−7.32973e23	+	1.26955e24i	−0.238876	+	0.413745i
$761$	9.87715e23	+	1.71077e24i	0.318318	+	0.551344i	0.980137	−	0.198320i	$-0.0635485\pi$
$761$	9.87715e23	+	1.71077e24i	0.318318	+	0.551344i	−0.661819	+	0.749664i	$0.730215\pi$
$762$	−2.14719e23	+	9.98835e22i	−0.0684310	+	0.0318329i
$763$	−5.28448e23	−	2.01146e23i	−0.166550	−	0.0633948i
$764$		−	4.60148e24i		−	1.43418i
$765$	7.33957e24	+	1.30816e24i	2.26229	+	0.403218i
$766$	−7.71798e23	−	4.45598e23i	−0.235266	−	0.135831i
$767$	−6.87784e24	−	3.97093e24i	−2.07344	−	1.19710i
$768$	7.92920e23	−	1.13018e24i	0.236406	−	0.336960i
$769$			1.05584e24i			0.311333i	0.987810	+	0.155667i	$0.0497525\pi$
$769$			1.05584e24i			0.311333i	−0.987810	+	0.155667i	$0.950247\pi$
$770$	−7.51404e23	+	6.11987e23i	−0.219130	+	0.178472i
$771$	2.55835e24	+	5.49966e24i	0.737899	+	1.58626i
$772$	−8.71397e23	−	1.50930e24i	−0.248582	−	0.430556i
$773$	2.02003e24	−	3.49880e24i	0.569944	−	0.987172i	−0.426627	−	0.904428i	$-0.640298\pi$
$773$	2.02003e24	−	3.49880e24i	0.569944	−	0.987172i	0.996571	−	0.0827442i	$-0.0263684\pi$
$774$	9.81140e23	−	3.55053e23i	0.273800	−	0.0990820i
$775$	−2.91358e24	+	1.68216e24i	−0.804198	+	0.464304i
$776$	−7.13208e23			−0.194711
$777$	−5.50158e22	+	3.72602e22i	−0.0148562	+	0.0100616i
$778$	−3.18116e23			−0.0849687
$779$	−3.41949e23	+	1.97424e23i	−0.0903426	+	0.0521593i
$780$	8.14852e23	−	9.21566e24i	0.212948	−	2.40836i
$781$	−1.48097e24	+	2.56512e24i	−0.382837	+	0.663092i
$782$	−8.60345e23	−	1.49016e24i	−0.219996	−	0.381045i
$783$	1.12252e23	−	4.14332e23i	0.0283936	−	0.104803i
$784$	2.41572e24	+	2.15061e24i	0.604451	+	0.538116i
$785$			8.86058e24i			2.19316i
$786$	−1.03201e24	−	7.24041e23i	−0.252691	−	0.177285i
$787$	−5.16303e23	−	2.98088e23i	−0.125060	−	0.0722036i	0.436165	−	0.899867i	$-0.356336\pi$
$787$	−5.16303e23	−	2.98088e23i	−0.125060	−	0.0722036i	−0.561225	+	0.827663i	$0.689670\pi$
$788$	5.65838e24	+	3.26686e24i	1.35587	+	0.782814i
$789$	−6.57161e23	−	4.61055e23i	−0.155782	−	0.109295i
$790$			2.58270e24i			0.605680i
$791$	−5.67932e22	+	9.15920e21i	−0.0131764	+	0.00212499i
$792$	9.13222e23	−	1.08426e24i	0.209610	−	0.248868i
$793$	−1.63130e24	−	2.82550e24i	−0.370435	−	0.641613i
$794$	5.66078e23	−	9.80477e23i	0.127175	−	0.220274i
$795$	−2.82631e23	+	3.19645e24i	−0.0628202	+	0.710472i
$796$	−2.23769e24	+	1.29193e24i	−0.492083	+	0.284104i
$797$	4.51882e24			0.983172			0.491586	−	0.870829i	$-0.336417\pi$
$797$	4.51882e24			0.983172			0.491586	+	0.870829i	$0.336417\pi$
$798$	6.13922e23	+	2.97993e23i	0.132156	+	0.0641478i
$799$	9.52576e24			2.02886
$800$	−5.24592e24	+	3.02873e24i	−1.10550	+	0.638258i
$801$	−6.07072e22	−	1.67756e23i	−0.0126580	−	0.0349786i
$802$	7.22272e23	−	1.25101e24i	0.149011	−	0.258095i
$803$	−1.42418e24	−	2.46675e24i	−0.290725	−	0.503551i
$804$	−2.07745e24	−	4.46587e24i	−0.419617	−	0.902049i
$805$	3.77643e24	−	9.92136e24i	0.754773	−	1.98293i
$806$		−	1.00921e24i		−	0.199588i
$807$	−2.84806e24	+	4.05946e24i	−0.557345	+	0.794407i
$808$	−3.27092e24	−	1.88847e24i	−0.633394	−	0.365690i
$809$	5.39691e23	+	3.11591e23i	0.103415	+	0.0597065i	0.550815	−	0.834627i	$-0.314317\pi$
$809$	5.39691e23	+	3.11591e23i	0.103415	+	0.0597065i	−0.447401	+	0.894334i	$0.647650\pi$
$810$	1.44595e24	+	1.73622e24i	0.274177	+	0.329216i
$811$			7.87106e22i			0.0147692i	0.999973	+	0.00738458i	$0.00235061\pi$
$811$			7.87106e22i			0.0147692i	−0.999973	+	0.00738458i	$0.997649\pi$
$812$	1.94505e23	−	5.10998e23i	0.0361163	−	0.0948841i
$813$	−6.04389e23	+	2.81151e23i	−0.111057	+	0.0516619i
$814$	8.29606e21	+	1.43692e22i	0.00150857	+	0.00261291i
$815$	−1.90657e23	+	3.30228e23i	−0.0343094	+	0.0594256i
$816$	−6.18904e24	−	5.47237e23i	−1.10219	−	0.0974562i
$817$	−3.23452e24	+	1.86745e24i	−0.570063	+	0.329126i
$818$	2.01245e24			0.351012
$819$	−8.91166e24	−	1.46932e23i	−1.53832	−	0.0253631i
$820$	−1.66516e24			−0.284471
$821$	4.60199e23	−	2.65696e23i	0.0778089	−	0.0449230i	−0.460591	−	0.887613i	$-0.652362\pi$
$821$	4.60199e23	−	2.65696e23i	0.0778089	−	0.0449230i	0.538400	+	0.842690i	$0.319029\pi$
$822$	−5.47985e23	−	4.84530e22i	−0.0916976	−	0.00810793i
$823$	−2.20782e24	+	3.82406e24i	−0.365650	+	0.633324i	−0.988880	−	0.148714i	$-0.952487\pi$
$823$	−2.20782e24	+	3.82406e24i	−0.365650	+	0.633324i	0.623230	+	0.782038i	$0.285820\pi$
$824$	1.41613e24	+	2.45280e24i	0.232124	+	0.402051i
$825$	6.72712e24	−	3.12934e24i	1.09137	−	0.507685i
$826$	2.43898e24	−	3.93340e23i	0.391631	−	0.0631594i
$827$		−	5.44925e24i		−	0.866043i	−0.901383	−	0.433022i	$-0.857447\pi$
$827$		−	5.44925e24i		−	0.866043i	0.901383	−	0.433022i	$-0.142553\pi$
$828$	−1.31667e24	+	7.38730e24i	−0.207118	+	1.16206i
$829$	8.18529e24	+	4.72578e24i	1.27444	+	0.735800i	0.975821	−	0.218572i	$-0.0701397\pi$
$829$	8.18529e24	+	4.72578e24i	1.27444	+	0.735800i	0.298622	+	0.954371i	$0.403473\pi$
$830$	−5.55975e23	−	3.20992e23i	−0.0856824	−	0.0494687i
$831$	5.06961e24	−	7.22593e24i	0.773332	−	1.10226i
$832$			6.42904e24i			0.970729i
$833$	1.85158e24	−	8.95881e24i	0.276732	−	1.33896i
$834$	−1.15181e24	−	2.47605e24i	−0.170401	−	0.366309i
$835$	5.19735e24	+	9.00207e24i	0.761109	+	1.31828i
$836$	−1.22598e24	+	2.12346e24i	−0.177718	+	0.307816i
$837$	−2.50079e24	−	2.51470e24i	−0.358848	−	0.360844i
$838$	−2.94843e24	+	1.70228e24i	−0.418809	+	0.241800i
$839$	−1.41664e24			−0.199197			−0.0995987	−	0.995028i	$-0.531756\pi$
$839$	−1.41664e24			−0.199197			−0.0995987	+	0.995028i	$0.531756\pi$
$840$	3.33980e24	+	4.93131e24i	0.464886	+	0.686418i
$841$	7.17159e24			0.988210
$842$	−1.81289e24	+	1.04667e24i	−0.247297	+	0.142777i
$843$	−5.64941e22	+	6.38926e23i	−0.00762902	+	0.0862812i
$844$	−4.21590e24	+	7.30216e24i	−0.563611	+	0.976203i
$845$	8.68016e24	+	1.50345e25i	1.14880	+	1.98979i
$846$	2.20813e24	+	1.85981e24i	0.289318	+	0.243680i
$847$	3.37651e24	−	2.75003e24i	0.437985	−	0.356720i
$848$		−	2.67431e24i		−	0.343436i
$849$	−5.20780e24	−	3.65372e24i	−0.662123	−	0.464537i
$850$	4.37560e24	+	2.52625e24i	0.550778	+	0.317992i
$851$	−1.57406e23	−	9.08781e22i	−0.0196164	−	0.0113255i
$852$	7.20070e24	+	5.05191e24i	0.888460	+	0.623331i
$853$		−	1.17381e25i		−	1.43394i	−0.697103	−	0.716971i	$-0.745528\pi$
$853$		−	1.17381e25i		−	1.43394i	0.697103	−	0.716971i	$-0.254472\pi$
$854$	9.48517e23	+	3.61040e23i	0.114724	+	0.0436680i
$855$	−6.18603e24	−	5.21022e24i	−0.740798	−	0.623942i
$856$	−2.60108e23	−	4.50520e23i	−0.0308409	−	0.0534180i
$857$	2.03039e24	−	3.51674e24i	0.238365	−	0.412861i	−0.721880	−	0.692018i	$-0.756722\pi$
$857$	2.03039e24	−	3.51674e24i	0.238365	−	0.412861i	0.960245	+	0.279157i	$0.0900551\pi$
$858$	−1.96025e23	+	2.21697e24i	−0.0227861	+	0.257702i
$859$	8.23747e24	−	4.75591e24i	0.948095	−	0.547383i	0.0556066	−	0.998453i	$-0.482291\pi$
$859$	8.23747e24	−	4.75591e24i	0.948095	−	0.547383i	0.892489	+	0.451070i	$0.148957\pi$
$860$	−1.57509e25			−1.79502
$861$	1.14930e23	+	1.60007e24i	0.0129690	+	0.180556i
$862$	1.54827e24			0.172996
$863$	−2.58889e24	+	1.49470e24i	−0.286432	+	0.165372i	−0.636332	−	0.771415i	$-0.719549\pi$
$863$	−2.58889e24	+	1.49470e24i	−0.286432	+	0.165372i	0.349899	+	0.936787i	$0.386216\pi$
$864$	−4.50268e24	−	4.52772e24i	−0.493292	−	0.496036i
$865$	4.75453e24	−	8.23508e24i	0.515787	−	0.893369i
$866$	−1.56874e24	−	2.71713e24i	−0.168519	−	0.291883i
$867$	3.44721e24	+	7.41043e24i	0.366695	+	0.788282i
$868$	−2.85265e24	−	3.50252e24i	−0.300491	−	0.368946i
$869$			8.93995e24i			0.932539i
$870$	2.58652e23	−	3.68668e23i	0.0267179	−	0.0380822i
$871$	1.38592e25	+	8.00159e24i	1.41769	+	0.818506i
$872$	7.51495e23	+	4.33876e23i	0.0761265	+	0.0439517i
$873$	6.90449e23	−	3.87383e24i	0.0692645	−	0.388615i
$874$			1.86670e24i			0.185450i
$875$	2.24314e24	+	1.39090e25i	0.220692	+	1.36844i
$876$	−7.66959e24	+	3.56776e24i	−0.747286	+	0.347625i
$877$	−2.90914e23	−	5.03877e23i	−0.0280716	−	0.0486215i	0.851648	−	0.524114i	$-0.175603\pi$
$877$	−2.90914e23	−	5.03877e23i	−0.0280716	−	0.0486215i	−0.879720	+	0.475492i	$0.842270\pi$
$878$	1.03843e24	−	1.79861e24i	0.0992370	−	0.171884i
$879$	2.02043e25	+	1.78647e24i	1.91222	+	0.169079i
$880$	−8.28949e24	+	4.78594e24i	−0.777008	+	0.448606i
$881$	−1.26793e25			−1.17707			−0.588534	−	0.808472i	$-0.700295\pi$
$881$	−1.26793e25			−1.17707			−0.588534	+	0.808472i	$0.700295\pi$
$882$	2.17832e24	−	1.71520e24i	0.200281	−	0.157700i
$883$	−6.14656e24			−0.559714			−0.279857	−	0.960042i	$-0.590287\pi$
$883$	−6.14656e24			−0.559714			−0.279857	+	0.960042i	$0.590287\pi$
$884$	1.88864e25	−	1.09041e25i	1.70336	−	0.983434i
$885$	−2.91657e25	−	2.57884e24i	−2.60528	−	0.230360i
$886$	−6.71108e23	+	1.16239e24i	−0.0593753	+	0.102841i
$887$	−8.06992e23	−	1.39775e24i	−0.0707161	−	0.122484i	0.828499	−	0.559990i	$-0.189195\pi$
$887$	−8.06992e23	−	1.39775e24i	−0.0707161	−	0.122484i	−0.899215	+	0.437506i	$0.855862\pi$
$888$	9.24578e22	−	4.30098e22i	0.00802478	−	0.00373299i
$889$	−5.48333e23	−	3.40004e24i	−0.0471389	−	0.292293i
$890$		−	1.87165e23i		−	0.0159371i
$891$	5.00513e24	+	6.00988e24i	0.422138	+	0.506880i
$892$	2.25790e24	+	1.30360e24i	0.188627	+	0.108904i
$893$	−8.94956e24	−	5.16703e24i	−0.740567	−	0.427566i
$894$	2.73244e24	−	3.89465e24i	0.223965	−	0.319227i
$895$			1.53995e25i			1.25029i
$896$	−6.75611e24	−	8.29523e24i	−0.543349	−	0.667130i
$897$	−1.02831e25	−	2.21056e25i	−0.819198	−	1.76103i
$898$	−5.17726e23	−	8.96728e23i	−0.0408555	−	0.0707639i
$899$	−3.53439e23	+	6.12174e23i	−0.0276285	+	0.0478540i
$900$	−7.49756e24	−	2.07185e25i	−0.580575	−	1.60434i
$901$	−6.55075e24	+	3.78208e24i	−0.502494	+	0.290115i
$902$	4.00580e23			0.0304392
$903$	1.08713e24	+	1.51352e25i	0.0818345	+	1.13931i
$904$	8.82846e22			0.00658344
$905$	2.08840e25	−	1.20574e25i	1.54277	−	0.890717i
$906$	−2.75900e22	+	3.12032e23i	−0.00201912	+	0.0228355i
$907$	−7.43801e24	+	1.28830e25i	−0.539256	+	0.934018i	0.459689	+	0.888080i	$0.347961\pi$
$907$	−7.43801e24	+	1.28830e25i	−0.539256	+	0.934018i	−0.998944	+	0.0459379i	$0.985372\pi$
$908$	−5.54198e24	−	9.59898e24i	−0.398047	−	0.689438i
$909$	1.34239e25	−	1.59380e25i	0.955179	−	1.13407i
$910$	−8.73897e24	−	3.32637e24i	−0.616039	−	0.234487i
$911$			7.28224e23i			0.0508580i	0.999677	+	0.0254290i	$0.00809517\pi$
$911$			7.28224e23i			0.0508580i	−0.999677	+	0.0254290i	$0.991905\pi$
$912$	5.51784e24	+	3.87124e24i	0.381780	+	0.267851i
$913$	−1.92450e24	−	1.11111e24i	−0.131921	−	0.0761649i
$914$	1.12589e24	+	6.50033e23i	0.0764634	+	0.0441462i
$915$	−9.84666e24	−	6.90828e24i	−0.662536	−	0.464826i
$916$			1.07873e25i			0.719120i
$917$	1.42154e25	−	1.15779e25i	0.938903	−	0.764697i
$918$	−1.39276e24	+	5.14078e24i	−0.0911410	+	0.336408i
$919$	−7.58918e24	−	1.31448e25i	−0.492054	−	0.852263i	0.507904	−	0.861414i	$-0.330420\pi$
$919$	−7.58918e24	−	1.31448e25i	−0.492054	−	0.852263i	−0.999958	+	0.00915082i	$0.997087\pi$
$920$	−8.14582e24	+	1.41090e25i	−0.523285	+	0.906356i
$921$	1.62713e24	−	1.84022e25i	0.103565	−	1.17128i
$922$	−1.34273e24	+	7.75227e23i	−0.0846792	+	0.0488896i
$923$	−2.85794e25			−1.78583
$924$	5.58621e24	+	8.24820e24i	0.345864	+	0.510678i
$925$	5.33696e23			0.0327408
$926$	4.74026e24	−	2.73679e24i	0.288143	−	0.166360i
$927$	−1.46935e25	+	5.31724e24i	−0.885008	+	0.320264i
$928$	−6.36368e23	+	1.10222e24i	−0.0379796	+	0.0657827i
$929$	−3.53715e23	−	6.12653e23i	−0.0209180	−	0.0362310i	0.855377	−	0.518006i	$-0.173326\pi$
$929$	−3.53715e23	−	6.12653e23i	−0.0209180	−	0.0362310i	−0.876295	+	0.481775i	$0.839992\pi$
$930$	−1.56931e24	−	3.37354e24i	−0.0919611	−	0.197688i
$931$	−6.59908e24	+	7.41256e24i	−0.383187	+	0.430424i
$932$		−	2.89421e24i		−	0.166531i
$933$	−7.18123e24	+	1.02357e25i	−0.409454	+	0.583612i
$934$	8.61119e23	+	4.97167e23i	0.0486536	+	0.0280902i
$935$	2.34465e25	+	1.35368e25i	1.31274	+	0.757911i
$936$	1.34660e25	+	2.40011e24i	0.747127	+	0.133164i
$937$		−	2.88373e24i		−	0.158550i	−0.996853	−	0.0792752i	$-0.974739\pi$
$937$		−	2.88373e24i		−	0.158550i	0.996853	−	0.0792752i	$-0.0252606\pi$
$938$	−4.91464e24	+	7.92597e23i	−0.267774	+	0.0431845i
$939$	2.86236e24	−	1.33152e24i	0.154549	−	0.0718936i
$940$	−2.17905e25	−	3.77422e25i	−1.16595	−	2.01948i
$941$	2.01508e24	−	3.49022e24i	0.106852	−	0.185072i	−0.807642	−	0.589674i	$-0.799256\pi$
$941$	2.01508e24	−	3.49022e24i	0.106852	−	0.185072i	0.914493	+	0.404601i	$0.132590\pi$
$942$	−6.30549e24	−	5.57534e23i	−0.331349	−	0.0292980i
$943$	−3.80021e24	+	2.19405e24i	−0.197906	+	0.114261i
$944$	2.44015e25			1.25937
$945$	−3.00179e25	+	1.33664e25i	−1.53536	+	0.683665i
$946$	3.78912e24			0.192072
$947$	−2.49232e25	+	1.43894e25i	−1.25207	+	0.722883i	−0.971520	−	0.236956i	$-0.923850\pi$
$947$	−2.49232e25	+	1.43894e25i	−1.25207	+	0.722883i	−0.280550	+	0.959839i	$0.590517\pi$
$948$	2.64459e25	+	2.33835e24i	1.31670	+	0.116423i
$949$	1.37417e25	−	2.38014e25i	0.678077	−	1.17446i
$950$	−2.74062e24	−	4.74689e24i	−0.134029	−	0.232145i
$951$	−1.85103e25	+	8.61067e24i	−0.897179	+	0.417352i
$952$	−4.99431e24	+	1.31209e25i	−0.239917	+	0.630306i
$953$			1.38085e24i			0.0657443i	0.999460	+	0.0328722i	$0.0104654\pi$
$953$			1.38085e24i			0.0657443i	−0.999460	+	0.0328722i	$0.989535\pi$
$954$	−2.25692e24	−	4.02259e23i	−0.106501	−	0.0189821i
$955$	4.77345e25	+	2.75595e25i	2.23256	+	1.28897i
$956$	2.93209e25	+	1.69284e25i	1.35921	+	0.784738i
$957$	8.95320e23	−	1.27614e24i	0.0411364	−	0.0586335i
$958$		−	6.72827e24i		−	0.306406i
$959$	2.84604e24	−	7.47705e24i	0.128464	−	0.337499i
$960$	9.99709e24	+	2.14907e25i	0.447269	+	0.961490i
$961$	−8.35504e24	−	1.44714e25i	−0.370510	−	0.641742i
$962$	−8.00476e22	+	1.38646e23i	−0.00351852	+	0.00609426i
$963$	2.69884e24	−	9.76648e23i	0.117585	−	0.0425515i
$964$	2.18993e25	−	1.26436e25i	0.945750	−	0.546029i
$965$	2.08761e25			0.893650
$966$	6.82276e24	+	3.31172e24i	0.289504	+	0.140523i
$967$	−1.20876e25			−0.508410			−0.254205	−	0.967150i	$-0.581814\pi$
$967$	−1.20876e25			−0.508410			−0.254205	+	0.967150i	$0.581814\pi$
$968$	−5.78765e24	+	3.34150e24i	−0.241302	+	0.139316i
$969$	1.67918e24	−	1.89908e25i	0.0693976	−	0.784860i
$970$	2.06407e24	−	3.57508e24i	0.0845600	−	0.146462i
$971$	4.58714e24	+	7.94515e24i	0.186285	+	0.322655i	0.944009	−	0.329920i	$-0.107022\pi$
$971$	4.58714e24	+	7.94515e24i	0.186285	+	0.322655i	−0.757724	+	0.652575i	$0.773689\pi$
$972$	1.90874e25	−	1.32341e25i	0.768393	−	0.532758i
$973$	3.92078e25	−	6.32315e24i	1.56464	−	0.252333i
$974$			3.34690e24i			0.132401i
$975$	5.86039e25	+	4.11157e25i	2.29820	+	1.61238i
$976$	8.68139e24	+	5.01220e24i	0.337494	+	0.194852i
$977$	−2.01698e25	−	1.16450e25i	−0.777316	−	0.448784i	0.0581622	−	0.998307i	$-0.481476\pi$
$977$	−2.01698e25	−	1.16450e25i	−0.777316	−	0.448784i	−0.835478	+	0.549524i	$0.814809\pi$
$978$	−2.23005e23	−	1.56457e23i	−0.00851988	−	0.00597743i
$979$		−	6.47867e23i		−	0.0245377i
$980$	−3.97314e25	+	1.31574e25i	−1.49181	+	0.494024i
$981$	−3.08414e24	+	3.66176e24i	−0.114801	+	0.136302i
$982$	8.42317e23	+	1.45894e24i	0.0310834	+	0.0538380i
$983$	−3.36911e23	+	5.83548e23i	−0.0123257	+	0.0213487i	−0.872122	−	0.489288i	$-0.837257\pi$
$983$	−3.36911e23	+	5.83548e23i	−0.0123257	+	0.0213487i	0.859797	+	0.510636i	$0.170590\pi$
$984$	2.16835e23	−	2.45232e24i	0.00786451	−	0.0889445i
$985$	−6.77791e25	+	3.91323e25i	−2.43718	+	1.40711i
$986$	1.06158e24			0.0378443
$987$	−3.47629e25	+	2.35437e25i	−1.22863	+	0.832105i
$988$	−2.36587e25			−0.829005
$989$	−3.59466e25	+	2.07538e25i	−1.24879	+	0.720988i
$990$	2.79210e24	+	7.71560e24i	0.0961684	+	0.265748i
$991$	8.49374e24	−	1.47116e25i	0.290050	−	0.502381i	−0.683771	−	0.729696i	$-0.739661\pi$
$991$	8.49374e24	−	1.47116e25i	0.290050	−	0.502381i	0.973821	+	0.227315i	$0.0729948\pi$
$992$	5.25750e24	+	9.10625e24i	0.178004	+	0.308312i
$993$	1.30398e25	+	2.80316e25i	0.437726	+	0.940976i
$994$	6.89325e24	−	5.61426e24i	0.229425	−	0.186857i
$995$		−	3.09508e25i		−	1.02135i
$996$	−3.79022e24	+	5.40236e24i	−0.124011	+	0.176758i
$997$	1.49532e25	+	8.63323e24i	0.485093	+	0.280069i	0.722536	−	0.691333i	$-0.242976\pi$
$997$	1.49532e25	+	8.63323e24i	0.485093	+	0.280069i	−0.237444	+	0.971401i	$0.576309\pi$
$998$	−4.38590e24	−	2.53220e24i	−0.141075	−	0.0814495i
$999$	1.44103e23	+	5.43827e23i	0.00459584	+	0.0173442i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.18.g.b.17.19	yes	84
3.2	odd	2	inner	21.18.g.b.17.24	yes	84
7.5	odd	6	inner	21.18.g.b.5.24	yes	84
21.5	even	6	inner	21.18.g.b.5.19	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.18.g.b.5.19	✓	84	21.5	even	6	inner
21.18.g.b.5.24	yes	84	7.5	odd	6	inner
21.18.g.b.17.19	yes	84	1.1	even	1	trivial
21.18.g.b.17.24	yes	84	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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	21.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-79.9248 + 46.1446i) q^{2} +(-11319.8 - 1000.90i) q^{3} +(-61277.4 + 106135. i) q^{4} +(-734013. - 1.27135e6i) q^{5} +(950921. - 442352. i) q^{6} +(2.42839e6 + 1.50577e7i) q^{7} -2.34070e7i q^{8} +(1.27137e8 + 2.26601e7i) q^{9} +O(q^{10})\)	\(q+(-79.9248 + 46.1446i) q^{2} +(-11319.8 - 1000.90i) q^{3} +(-61277.4 + 106135. i) q^{4} +(-734013. - 1.27135e6i) q^{5} +(950921. - 442352. i) q^{6} +(2.42839e6 + 1.50577e7i) q^{7} -2.34070e7i q^{8} +(1.27137e8 + 2.26601e7i) q^{9} +(1.17332e8 + 6.77415e7i) q^{10} +(4.06141e8 + 2.34486e8i) q^{11} +(7.99880e8 - 1.14010e9i) q^{12} +4.52505e9i q^{13} +(-8.88919e8 - 1.09142e9i) q^{14} +(7.03640e9 + 1.51261e10i) q^{15} +(-6.95164e9 - 1.20406e10i) q^{16} +(-1.96624e10 + 3.40563e10i) q^{17} +(-1.12070e10 + 4.05556e9i) q^{18} +(3.69461e10 - 2.13308e10i) q^{19} +1.79913e11 q^{20} +(-1.24177e10 - 1.72881e11i) q^{21} -4.32810e10 q^{22} +(4.10597e11 - 2.37058e11i) q^{23} +(-2.34281e10 + 2.64963e11i) q^{24} +(-6.96080e11 + 1.20565e12i) q^{25} +(-2.08806e11 - 3.61663e11i) q^{26} +(-1.41648e12 - 3.83759e11i) q^{27} +(-1.74696e12 - 6.64956e11i) q^{28} +2.92508e11i q^{29} +(-1.26037e12 - 8.84259e11i) q^{30} +(2.09285e12 + 1.20831e12i) q^{31} +(3.76819e12 + 2.17556e12i) q^{32} +(-4.36275e12 - 3.06084e12i) q^{33} -3.62926e12i q^{34} +(1.73611e13 - 1.41399e13i) q^{35} +(-1.01956e13 + 1.21051e13i) q^{36} +(-1.91679e11 - 3.31998e11i) q^{37} +(-1.96861e12 + 3.40973e12i) q^{38} +(4.52913e12 - 5.12227e13i) q^{39} +(-2.97584e13 + 1.71810e13i) q^{40} -9.25534e12 q^{41} +(8.96999e12 + 1.32444e13i) q^{42} -8.75471e13 q^{43} +(-4.97745e13 + 2.87373e13i) q^{44} +(-6.45110e13 - 1.78268e14i) q^{45} +(-2.18779e13 + 3.78937e13i) q^{46} +(-1.21116e14 - 2.09780e14i) q^{47} +(6.66398e13 + 1.43255e14i) q^{48} +(-2.20836e14 + 7.31318e13i) q^{49} -1.28481e14i q^{50} +(2.56662e14 - 3.65831e14i) q^{51} +(-4.80268e14 - 2.77283e14i) q^{52} +(1.66581e14 + 9.61754e13i) q^{53} +(1.30921e14 - 3.46911e13i) q^{54} -6.88462e14i q^{55} +(3.52455e14 - 5.68414e13i) q^{56} +(-4.39573e14 + 2.04482e14i) q^{57} +(-1.34976e13 - 2.33786e13i) q^{58} +(-8.77544e14 + 1.51995e15i) q^{59} +(-2.03659e15 - 1.80076e14i) q^{60} +(-6.24413e14 + 3.60505e14i) q^{61} -2.23028e14 q^{62} +(-3.24708e13 + 1.96941e15i) q^{63} +1.42077e15 q^{64} +(5.75291e15 - 3.32144e15i) q^{65} +(4.89933e14 + 4.33201e13i) q^{66} +(1.76829e15 - 3.06277e15i) q^{67} +(-2.40972e15 - 4.17376e15i) q^{68} +(-4.88516e15 + 2.27249e15i) q^{69} +(-7.35102e14 + 1.93124e15i) q^{70} +6.31583e15i q^{71} +(5.30405e14 - 2.97589e15i) q^{72} +(-5.25992e15 - 3.03682e15i) q^{73} +(3.06398e13 + 1.76899e13i) q^{74} +(9.08624e15 - 1.29510e16i) q^{75} +5.22839e15i q^{76} +(-2.54454e15 + 6.68496e15i) q^{77} +(2.00166e15 + 4.30296e15i) q^{78} +(9.53144e15 + 1.65089e16i) q^{79} +(-1.02052e16 + 1.76759e16i) q^{80} +(1.56502e16 + 5.76185e15i) q^{81} +(7.39731e14 - 4.27084e14i) q^{82} -4.73849e15 q^{83} +(1.91097e16 + 9.27572e15i) q^{84} +5.77299e16 q^{85} +(6.99718e15 - 4.03982e15i) q^{86} +(2.92772e14 - 3.31113e15i) q^{87} +(5.48861e15 - 9.50655e15i) q^{88} +(-6.90732e14 - 1.19638e15i) q^{89} +(1.33821e16 + 1.12712e16i) q^{90} +(-6.81366e16 + 1.09886e16i) q^{91} +5.81052e16i q^{92} +(-2.24813e16 - 1.57726e16i) q^{93} +(1.93604e16 + 1.11777e16i) q^{94} +(-5.42378e16 - 3.13142e16i) q^{95} +(-4.04777e16 - 2.83986e16i) q^{96} -3.04698e16i q^{97} +(1.42757e16 - 1.60355e16i) q^{98} +(4.63219e16 + 3.90149e16i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 19686 q^{3} + 2752510 q^{4} - 4340518 q^{7} - 98670996 q^{9}+O(q^{10}) \) 84 * q - 19686 * q^3 + 2752510 * q^4 - 4340518 * q^7 - 98670996 * q^9	\( 84 q - 19686 q^{3} + 2752510 q^{4} - 4340518 q^{7} - 98670996 q^{9} + 465470970 q^{10} - 2491764528 q^{12} - 7104382296 q^{15} - 110459605130 q^{16} - 14553542550 q^{18} + 404032278750 q^{19} + 228767508522 q^{21} - 832496305460 q^{22} - 1354439880378 q^{24} - 7199868598470 q^{25} - 7749926510914 q^{28} + 284772818082 q^{30} + 20192079903726 q^{31} - 18426553023870 q^{33} - 6006594191052 q^{36} + 46546034438938 q^{37} + 156966454169838 q^{39} + 52009146351690 q^{40} + 273411312457290 q^{42} + 262809922393900 q^{43} - 463828715581158 q^{45} - 691873824309656 q^{46} + 158652002613594 q^{49} + 123926983295328 q^{51} + 180256725379488 q^{52} + 528953393499678 q^{54} - 13\!\cdots\!84 q^{57}+ \cdots + 30\!\cdots\!80 q^{99}+O(q^{100}) \) 84 * q - 19686 * q^3 + 2752510 * q^4 - 4340518 * q^7 - 98670996 * q^9 + 465470970 * q^10 - 2491764528 * q^12 - 7104382296 * q^15 - 110459605130 * q^16 - 14553542550 * q^18 + 404032278750 * q^19 + 228767508522 * q^21 - 832496305460 * q^22 - 1354439880378 * q^24 - 7199868598470 * q^25 - 7749926510914 * q^28 + 284772818082 * q^30 + 20192079903726 * q^31 - 18426553023870 * q^33 - 6006594191052 * q^36 + 46546034438938 * q^37 + 156966454169838 * q^39 + 52009146351690 * q^40 + 273411312457290 * q^42 + 262809922393900 * q^43 - 463828715581158 * q^45 - 691873824309656 * q^46 + 158652002613594 * q^49 + 123926983295328 * q^51 + 180256725379488 * q^52 + 528953393499678 * q^54 - 1311284732111784 * q^57 + 521920547533210 * q^58 - 416477060451846 * q^60 - 6052836877037172 * q^61 - 13769533594398750 * q^63 + 1053936792659996 * q^64 + 21705058495057878 * q^66 + 3639355527884298 * q^67 + 44463964567209810 * q^70 + 7798479140884800 * q^72 - 31719690947775954 * q^73 + 17256341731591290 * q^75 - 67997864561346840 * q^78 - 31267401781398294 * q^79 + 44133415784265492 * q^81 + 4877409168868320 * q^82 + 25637268676337472 * q^84 + 2464288230356616 * q^85 - 61426317616508880 * q^87 - 112618869011616970 * q^88 - 223816788036276750 * q^91 + 104033604109825260 * q^93 + 248077621213302516 * q^94 - 363875964512101146 * q^96 + 303894121197814080 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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