LMFDB - Embedded newform 42.12.f.a.5.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [42,12,Mod(5,42)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("42.5"); S:= CuspForms(chi, 12); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 12, names="a")

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	42.f (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$32.2704135835$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.18
Character	$\chi$	$=$	42.5
Dual form			42.12.f.a.17.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(27.7128 + 16.0000i) q^{2} +(-398.196 + 136.334i) q^{3} +(512.000 + 886.810i) q^{4} +(-1584.15 + 2743.83i) q^{5} +(-13216.5 - 2592.95i) q^{6} +(44235.4 - 4533.49i) q^{7} +32768.0i q^{8} +(139973. - 108575. i) q^{9} +(-87802.6 + 50692.9i) q^{10} +(583405. - 336829. i) q^{11} +(-324778. - 283321. i) q^{12} +816776. i q^{13} +(1.29842e6 + 582131. i) q^{14} +(256726. - 1.30856e6i) q^{15} +(-524288. + 908093. i) q^{16} +(1.34064e6 + 2.32205e6i) q^{17} +(5.61625e6 - 769349. i) q^{18} +(-4.52671e6 - 2.61350e6i) q^{19} -3.24434e6 q^{20} +(-1.69963e7 + 7.83600e6i) q^{21} +2.15571e7 q^{22} +(1.54699e6 + 893152. i) q^{23} +(-4.46738e6 - 1.30481e7i) q^{24} +(1.93950e7 + 3.35931e7i) q^{25} +(-1.30684e7 + 2.26352e7i) q^{26} +(-4.09344e7 + 6.23172e7i) q^{27} +(2.66689e7 + 3.69073e7i) q^{28} +1.55447e8i q^{29} +(2.80515e7 - 3.21562e7i) q^{30} +(-7.14627e7 + 4.12590e7i) q^{31} +(-2.90590e7 + 1.67772e7i) q^{32} +(-1.86388e8 + 2.13662e8i) q^{33} +8.58007e7i q^{34} +(-5.76365e7 + 1.28556e8i) q^{35} +(1.67952e8 + 6.85392e7i) q^{36} +(2.05663e8 - 3.56220e8i) q^{37} +(-8.36319e7 - 1.44855e8i) q^{38} +(-1.11354e8 - 3.25237e8i) q^{39} +(-8.99099e7 - 5.19095e7i) q^{40} -1.21386e7 q^{41} +(-5.96392e8 - 5.47834e7i) q^{42} +6.33739e7 q^{43} +(5.97407e8 + 3.44913e8i) q^{44} +(7.61729e7 + 5.56063e8i) q^{45} +(2.85809e7 + 4.95035e7i) q^{46} +(-1.13844e9 + 1.97184e9i) q^{47} +(8.49657e7 - 4.33077e8i) q^{48} +(1.93622e9 - 4.01082e8i) q^{49} +1.24128e9i q^{50} +(-8.50410e8 - 7.41857e8i) q^{51} +(-7.24325e8 + 4.18189e8i) q^{52} +(-4.01627e9 + 2.31879e9i) q^{53} +(-2.13148e9 + 1.07204e9i) q^{54} +2.13435e9i q^{55} +(1.48554e8 + 1.44951e9i) q^{56} +(2.15883e9 + 4.23541e8i) q^{57} +(-2.48715e9 + 4.30787e9i) q^{58} +(1.66576e9 + 2.88518e9i) q^{59} +(1.29189e9 - 4.42313e8i) q^{60} +(5.04102e9 + 2.91043e9i) q^{61} -2.64058e9 q^{62} +(5.69955e9 - 5.43743e9i) q^{63} -1.07374e9 q^{64} +(-2.24110e9 - 1.29390e9i) q^{65} +(-8.58394e9 + 2.93895e9i) q^{66} +(4.92922e9 + 8.53766e9i) q^{67} +(-1.37281e9 + 2.37778e9i) q^{68} +(-7.37770e8 - 1.44744e8i) q^{69} +(-3.65417e9 + 2.64047e9i) q^{70} -1.71476e10i q^{71} +(3.55779e9 + 4.58664e9i) q^{72} +(3.55971e8 - 2.05520e8i) q^{73} +(1.13990e10 - 6.58123e9i) q^{74} +(-1.23029e10 - 1.07325e10i) q^{75} -5.35244e9i q^{76} +(2.42802e10 - 1.75446e10i) q^{77} +(2.11786e9 - 1.07949e10i) q^{78} +(1.80530e10 - 3.12687e10i) q^{79} +(-1.66110e9 - 2.87712e9i) q^{80} +(7.80396e9 - 3.03952e10i) q^{81} +(-3.36396e8 - 1.94218e8i) q^{82} +1.10999e10 q^{83} +(-1.56512e10 - 1.10605e10i) q^{84} -8.49509e9 q^{85} +(1.75627e9 + 1.01398e9i) q^{86} +(-2.11927e10 - 6.18984e10i) q^{87} +(1.10372e10 + 1.91170e10i) q^{88} +(-3.61396e10 + 6.25957e10i) q^{89} +(-6.78604e9 + 1.66288e10i) q^{90} +(3.70285e9 + 3.61305e10i) q^{91} +1.82918e9i q^{92} +(2.28312e10 - 2.61720e10i) q^{93} +(-6.30990e10 + 3.64302e10i) q^{94} +(1.43420e10 - 8.28036e9i) q^{95} +(9.28388e9 - 1.06423e10i) q^{96} -1.16139e11i q^{97} +(6.00755e10 + 1.98644e10i) q^{98} +(4.50899e10 - 1.10490e11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 30720 q^{4} - 95298 q^{7} - 91434 q^{9} + 245184 q^{10} - 8480820 q^{15} - 31457280 q^{16} + 12170496 q^{18} + 1649724 q^{19} + 43254216 q^{21} + 20705664 q^{22} + 4521984 q^{24} - 336132444 q^{25}+ \cdots + 288758042496 q^{99}+O(q^{100}) $ 60 * q + 30720 * q^4 - 95298 * q^7 - 91434 * q^9 + 245184 * q^10 - 8480820 * q^15 - 31457280 * q^16 + 12170496 * q^18 + 1649724 * q^19 + 43254216 * q^21 + 20705664 * q^22 + 4521984 * q^24 - 336132444 * q^25 + 28121088 * q^28 - 77109120 * q^30 - 275992974 * q^31 + 1056712914 * q^33 - 187256832 * q^36 + 555437556 * q^37 - 563926680 * q^39 + 251068416 * q^40 + 1167043776 * q^42 + 2546594304 * q^43 + 544480776 * q^45 - 452472192 * q^46 - 1309143414 * q^49 + 2007979044 * q^51 + 3219419136 * q^52 - 9840998592 * q^54 + 17053196256 * q^57 + 12235419456 * q^58 - 4342179840 * q^60 - 3056592000 * q^61 - 42499692960 * q^63 - 64424509440 * q^64 + 48796070400 * q^66 + 27979853436 * q^67 - 4966503360 * q^70 - 12462587904 * q^72 - 105678747168 * q^73 + 173211633504 * q^75 - 16600538880 * q^78 - 27787555926 * q^79 - 71399556486 * q^81 + 31231064832 * q^82 - 25272410112 * q^84 + 12868048152 * q^85 + 137017459998 * q^87 + 10601299968 * q^88 + 333571182180 * q^91 - 14607989424 * q^93 - 430917051648 * q^94 + 4630511616 * q^96 + 288758042496 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	27.7128	+	16.0000i	0.612372	+	0.353553i
$2$	27.7128	+	16.0000i	0.612372	+	0.353553i
$3$	−398.196	+	136.334i	−0.946085	+	0.323919i
$3$	−398.196	+	136.334i	−0.946085	+	0.323919i
$4$	512.000	+	886.810i	0.250000	+	0.433013i
$5$	−1584.15	+	2743.83i	−0.226705	+	0.392665i	−0.956830	−	0.290649i	$-0.906129\pi$
$5$	−1584.15	+	2743.83i	−0.226705	+	0.392665i	0.730124	+	0.683314i	$0.239462\pi$
$6$	−13216.5	−	2592.95i	−0.693879	−	0.136132i
$7$	44235.4	−	4533.49i	0.994789	−	0.101952i
$7$	44235.4	−	4533.49i	0.994789	−	0.101952i
$8$			32768.0i			0.353553i
$9$	139973.	−	108575.i	0.790153	−	0.612910i
$10$	−87802.6	+	50692.9i	−0.277656	+	0.160305i
$11$	583405.	−	336829.i	1.09222	−	0.630594i	0.158054	−	0.987430i	$-0.449478\pi$
$11$	583405.	−	336829.i	1.09222	−	0.630594i	0.934167	+	0.356836i	$0.116145\pi$
$12$	−324778.	−	283321.i	−0.376782	−	0.328687i
$13$			816776.i			0.610119i	0.952333	+	0.305060i	$0.0986764\pi$
$13$			816776.i			0.610119i	−0.952333	+	0.305060i	$0.901324\pi$
$14$	1.29842e6	+	582131.i	0.645227	+	0.289279i
$15$	256726.	−	1.30856e6i	0.0872909	−	0.444929i
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	1.34064e6	+	2.32205e6i	0.229003	+	0.396646i	0.957513	−	0.288390i	$-0.0931200\pi$
$17$	1.34064e6	+	2.32205e6i	0.229003	+	0.396646i	−0.728510	+	0.685036i	$0.759787\pi$
$18$	5.61625e6	−	769349.i	0.700564	−	0.0959676i
$19$	−4.52671e6	−	2.61350e6i	−0.419409	−	0.242146i	0.275415	−	0.961325i	$-0.411185\pi$
$19$	−4.52671e6	−	2.61350e6i	−0.419409	−	0.242146i	−0.694825	+	0.719179i	$0.744518\pi$
$20$	−3.24434e6			−0.226705
$21$	−1.69963e7	+	7.83600e6i	−0.908131	+	0.418686i
$22$	2.15571e7			0.891795
$23$	1.54699e6	+	893152.i	0.0501168	+	0.0289349i	0.524849	−	0.851195i	$-0.324122\pi$
$23$	1.54699e6	+	893152.i	0.0501168	+	0.0289349i	−0.474732	+	0.880130i	$0.657455\pi$
$24$	−4.46738e6	−	1.30481e7i	−0.114523	−	0.334492i
$25$	1.93950e7	+	3.35931e7i	0.397209	+	0.687987i
$26$	−1.30684e7	+	2.26352e7i	−0.215710	+	0.373620i
$27$	−4.09344e7	+	6.23172e7i	−0.549019	+	0.835810i
$28$	2.66689e7	+	3.69073e7i	0.292844	+	0.405269i
$29$			1.55447e8i			1.40732i	0.710536	+	0.703660i	$0.248452\pi$
$29$			1.55447e8i			1.40732i	−0.710536	+	0.703660i	$0.751548\pi$
$30$	2.80515e7	−	3.21562e7i	0.210761	−	0.241600i
$31$	−7.14627e7	+	4.12590e7i	−0.448322	+	0.258839i	−0.707121	−	0.707092i	$-0.750007\pi$
$31$	−7.14627e7	+	4.12590e7i	−0.448322	+	0.258839i	0.258799	+	0.965931i	$0.416673\pi$
$32$	−2.90590e7	+	1.67772e7i	−0.153093	+	0.0883883i
$33$	−1.86388e8	+	2.13662e8i	−0.829072	+	0.950386i
$34$			8.58007e7i			0.323860i
$35$	−5.76365e7	+	1.28556e8i	−0.185491	+	0.413732i
$36$	1.67952e8	+	6.85392e7i	0.462936	+	0.188919i
$37$	2.05663e8	−	3.56220e8i	0.487582	−	0.844517i	−0.512316	−	0.858797i	$-0.671212\pi$
$37$	2.05663e8	−	3.56220e8i	0.487582	−	0.844517i	0.999898	+	0.0142802i	$0.00454569\pi$
$38$	−8.36319e7	−	1.44855e8i	−0.171223	−	0.296567i
$39$	−1.11354e8	−	3.25237e8i	−0.197629	−	0.577225i
$40$	−8.99099e7	−	5.19095e7i	−0.138828	−	0.0801525i
$41$	−1.21386e7			−0.0163629			−0.00818143	−	0.999967i	$-0.502604\pi$
$41$	−1.21386e7			−0.0163629			−0.00818143	+	0.999967i	$0.502604\pi$
$42$	−5.96392e8	−	5.47834e7i	−0.704142	−	0.0646811i
$43$	6.33739e7			0.0657406			0.0328703	−	0.999460i	$-0.489535\pi$
$43$	6.33739e7			0.0657406			0.0328703	+	0.999460i	$0.489535\pi$
$44$	5.97407e8	+	3.44913e8i	0.546110	+	0.315297i
$45$	7.61729e7	+	5.56063e8i	0.0615363	+	0.449216i
$46$	2.85809e7	+	4.95035e7i	0.0204601	+	0.0354379i
$47$	−1.13844e9	+	1.97184e9i	−0.724059	+	1.25411i	0.235302	+	0.971922i	$0.424392\pi$
$47$	−1.13844e9	+	1.97184e9i	−0.724059	+	1.25411i	−0.959360	+	0.282184i	$0.908941\pi$
$48$	8.49657e7	−	4.33077e8i	0.0481301	−	0.245323i
$49$	1.93622e9	−	4.01082e8i	0.979212	−	0.202841i
$50$			1.24128e9i			0.561739i
$51$	−8.50410e8	−	7.41857e8i	−0.345138	−	0.301082i
$52$	−7.24325e8	+	4.18189e8i	−0.264189	+	0.152530i
$53$	−4.01627e9	+	2.31879e9i	−1.31918	+	0.761631i	−0.983597	−	0.180379i	$-0.942268\pi$
$53$	−4.01627e9	+	2.31879e9i	−1.31918	+	0.761631i	−0.335586	+	0.942010i	$0.608934\pi$
$54$	−2.13148e9	+	1.07204e9i	−0.631707	+	0.317720i
$55$			2.13435e9i			0.571836i
$56$	1.48554e8	+	1.44951e9i	0.0360453	+	0.351711i
$57$	2.15883e9	+	4.23541e8i	0.475232	+	0.0932361i
$58$	−2.48715e9	+	4.30787e9i	−0.497563	+	0.861804i
$59$	1.66576e9	+	2.88518e9i	0.303337	+	0.525396i	0.976890	−	0.213744i	$-0.0685658\pi$
$59$	1.66576e9	+	2.88518e9i	0.303337	+	0.525396i	−0.673552	+	0.739139i	$0.735232\pi$
$60$	1.29189e9	−	4.42313e8i	0.214483	−	0.0734342i
$61$	5.04102e9	+	2.91043e9i	0.764195	+	0.441208i	0.830800	−	0.556571i	$-0.187883\pi$
$61$	5.04102e9	+	2.91043e9i	0.764195	+	0.441208i	−0.0666049	+	0.997779i	$0.521217\pi$
$62$	−2.64058e9			−0.366054
$63$	5.69955e9	−	5.43743e9i	0.723549	−	0.690273i
$64$	−1.07374e9			−0.125000
$65$	−2.24110e9	−	1.29390e9i	−0.239573	−	0.138317i
$66$	−8.58394e9	+	2.93895e9i	−0.843713	+	0.288869i
$67$	4.92922e9	+	8.53766e9i	0.446033	+	0.772552i	0.998124	−	0.0612325i	$-0.0195031\pi$
$67$	4.92922e9	+	8.53766e9i	0.446033	+	0.772552i	−0.552091	+	0.833784i	$0.686170\pi$
$68$	−1.37281e9	+	2.37778e9i	−0.114502	+	0.198323i
$69$	−7.37770e8	−	1.44744e8i	−0.0567873	−	0.0111411i
$70$	−3.65417e9	+	2.64047e9i	−0.259866	+	0.187777i
$71$		−	1.71476e10i		−	1.12793i	−0.825797	−	0.563967i	$-0.809275\pi$
$71$		−	1.71476e10i		−	1.12793i	0.825797	−	0.563967i	$-0.190725\pi$
$72$	3.55779e9	+	4.58664e9i	0.216696	+	0.279361i
$73$	3.55971e8	−	2.05520e8i	0.0200974	−	0.0116032i	−0.489918	−	0.871769i	$-0.662973\pi$
$73$	3.55971e8	−	2.05520e8i	0.0200974	−	0.0116032i	0.510015	+	0.860165i	$0.329640\pi$
$74$	1.13990e10	−	6.58123e9i	0.597164	−	0.344773i
$75$	−1.23029e10	−	1.07325e10i	−0.598646	−	0.522230i
$76$		−	5.35244e9i		−	0.242146i
$77$	2.42802e10	−	1.75446e10i	1.02224	−	0.738662i
$78$	2.11786e9	−	1.07949e10i	0.0830570	−	0.423349i
$79$	1.80530e10	−	3.12687e10i	0.660086	−	1.14330i	−0.320507	−	0.947246i	$-0.603853\pi$
$79$	1.80530e10	−	3.12687e10i	0.660086	−	1.14330i	0.980593	−	0.196056i	$-0.0628133\pi$
$80$	−1.66110e9	−	2.87712e9i	−0.0566764	−	0.0981663i
$81$	7.80396e9	−	3.03952e10i	0.248684	−	0.968585i
$82$	−3.36396e8	−	1.94218e8i	−0.0100202	−	0.00578514i
$83$	1.10999e10			0.309307			0.154654	−	0.987969i	$-0.450574\pi$
$83$	1.10999e10			0.309307			0.154654	+	0.987969i	$0.450574\pi$
$84$	−1.56512e10	−	1.10605e10i	−0.408329	−	0.288561i
$85$	−8.49509e9			−0.207665
$86$	1.75627e9	+	1.01398e9i	0.0402578	+	0.0232428i
$87$	−2.11927e10	−	6.18984e10i	−0.455858	−	1.33144i
$88$	1.10372e10	+	1.91170e10i	0.222949	+	0.386158i
$89$	−3.61396e10	+	6.25957e10i	−0.686023	+	1.18823i	0.287091	+	0.957903i	$0.407312\pi$
$89$	−3.61396e10	+	6.25957e10i	−0.686023	+	1.18823i	−0.973114	+	0.230324i	$0.926022\pi$
$90$	−6.78604e9	+	1.66288e10i	−0.121139	+	0.296844i
$91$	3.70285e9	+	3.61305e10i	0.0622026	+	0.606940i
$92$			1.82918e9i			0.0289349i
$93$	2.28312e10	−	2.61720e10i	0.340308	−	0.390104i
$94$	−6.30990e10	+	3.64302e10i	−0.886787	+	0.511987i
$95$	1.43420e10	−	8.28036e9i	0.190165	−	0.109792i
$96$	9.28388e9	−	1.06423e10i	0.116208	−	0.133213i
$97$		−	1.16139e11i		−	1.37320i	−0.727035	−	0.686600i	$-0.759102\pi$
$97$		−	1.16139e11i		−	1.37320i	0.727035	−	0.686600i	$-0.240898\pi$
$98$	6.00755e10	+	1.98644e10i	0.671357	+	0.221990i
$99$	4.50899e10	−	1.10490e11i	0.476525	−	1.16770i
$100$	−1.98605e10	+	3.43993e10i	−0.198605	+	0.343993i
$101$	−4.71067e10	−	8.15913e10i	−0.445980	−	0.772460i	0.552140	−	0.833752i	$-0.313811\pi$
$101$	−4.71067e10	−	8.15913e10i	−0.445980	−	0.772460i	−0.998120	+	0.0612912i	$0.980478\pi$
$102$	−1.16975e10	−	3.41655e10i	−0.104904	−	0.306399i
$103$	1.90646e11	+	1.10069e11i	1.62040	+	0.935540i	0.986812	+	0.161870i	$0.0517527\pi$
$103$	1.90646e11	+	1.10069e11i	1.62040	+	0.935540i	0.633590	+	0.773669i	$0.281581\pi$
$104$	−2.67641e10			−0.215710
$105$	5.42408e9	−	5.90485e10i	0.0414748	−	0.451510i
$106$	−1.48403e11			−1.07711
$107$	1.75334e11	+	1.01229e11i	1.20852	+	0.697740i	0.962436	−	0.271508i	$-0.0875225\pi$
$107$	1.75334e11	+	1.01229e11i	1.20852	+	0.697740i	0.246085	+	0.969248i	$0.420856\pi$
$108$	−7.62219e10	−	4.39456e9i	−0.499171	−	0.0287796i
$109$	−8.26750e10	−	1.43197e11i	−0.514669	−	0.891434i	−0.999855	−	0.0170225i	$-0.994581\pi$
$109$	−8.26750e10	−	1.43197e11i	−0.514669	−	0.891434i	0.485186	−	0.874411i	$-0.338752\pi$
$110$	−3.41497e10	+	5.91490e10i	−0.202175	+	0.350177i
$111$	−3.33297e10	+	1.69884e11i	−0.187739	+	0.956922i
$112$	−1.90753e10	+	4.25468e10i	−0.102276	+	0.228122i
$113$			1.89673e11i			0.968445i	0.874945	+	0.484222i	$0.160897\pi$
$113$			1.89673e11i			0.968445i	−0.874945	+	0.484222i	$0.839103\pi$
$114$	5.30505e10	+	4.62787e10i	0.258055	+	0.225115i
$115$	−4.90132e9	+	2.82978e9i	−0.0227235	+	0.0131194i
$116$	−1.37852e11	+	7.95888e10i	−0.609388	+	0.351830i
$117$	8.86816e10	+	1.14327e11i	0.373948	+	0.482088i
$118$			1.06608e11i			0.428984i
$119$	6.98306e10	+	9.66392e10i	0.268249	+	0.371231i
$120$	4.28788e10	+	8.41241e9i	0.157306	+	0.0308620i
$121$	8.42519e10	−	1.45928e11i	0.295298	−	0.511470i
$122$	9.31339e10	+	1.61313e11i	0.311981	+	0.540367i
$123$	4.83356e9	−	1.65491e9i	0.0154807	−	0.00530024i
$124$	−7.31778e10	−	4.22492e10i	−0.224161	−	0.129419i
$125$	−2.77601e11			−0.813609
$126$	2.44950e11	−	5.94938e10i	0.687130	−	0.166891i
$127$	3.58494e11			0.962856			0.481428	−	0.876486i	$-0.340118\pi$
$127$	3.58494e11			0.962856			0.481428	+	0.876486i	$0.340118\pi$
$128$	−2.97564e10	−	1.71799e10i	−0.0765466	−	0.0441942i
$129$	−2.52352e10	+	8.64000e9i	−0.0621962	+	0.0212946i
$130$	−4.14047e10	−	7.17151e10i	−0.0978051	−	0.169403i
$131$	−3.50316e11	+	6.06765e11i	−0.793355	+	1.37413i	0.130523	+	0.991445i	$0.458334\pi$
$131$	−3.50316e11	+	6.06765e11i	−0.793355	+	1.37413i	−0.923878	+	0.382686i	$0.874999\pi$
$132$	−2.84908e11	−	5.58963e10i	−0.618797	−	0.121402i
$133$	−2.12089e11	−	9.50874e10i	−0.441911	−	0.198125i
$134$			3.15470e11i			0.630786i
$135$	−1.06142e11	−	2.11037e11i	−0.203728	−	0.405063i
$136$	−7.60889e10	+	4.39300e10i	−0.140235	+	0.0809649i
$137$	−8.23730e11	+	4.75581e11i	−1.45822	+	0.841901i	−0.998924	−	0.0463838i	$-0.985230\pi$
$137$	−8.23730e11	+	4.75581e11i	−1.45822	+	0.841901i	−0.459292	+	0.888285i	$0.651897\pi$
$138$	−1.81298e10	−	1.58156e10i	−0.0308360	−	0.0268999i
$139$			4.61993e10i			0.0755186i	0.999287	+	0.0377593i	$0.0120220\pi$
$139$			4.61993e10i			0.0755186i	−0.999287	+	0.0377593i	$0.987978\pi$
$140$	−1.43515e11	+	1.47082e10i	−0.225524	+	0.0231130i
$141$	1.84495e11	−	9.40389e11i	0.278792	−	1.42103i
$142$	2.74362e11	−	4.75209e11i	0.398785	−	0.690716i
$143$	2.75114e11	+	4.76511e11i	0.384738	+	0.666385i
$144$	2.52100e10	+	1.84033e11i	0.0339297	+	0.247687i
$145$	−4.26520e11	−	2.46252e11i	−0.552606	−	0.319047i
$146$	1.31533e10			0.0164094
$147$	−7.16315e11	+	4.23682e11i	−0.860714	+	0.509090i
$148$	4.21199e11			0.487582
$149$	1.37637e12	+	7.94648e11i	1.53536	+	0.886442i	0.999101	+	0.0423893i	$0.0134970\pi$
$149$	1.37637e12	+	7.94648e11i	1.53536	+	0.886442i	0.536261	+	0.844052i	$0.319836\pi$
$150$	−1.69228e11	−	4.94272e11i	−0.181958	−	0.531453i
$151$	−4.52665e11	−	7.84039e11i	−0.469249	−	0.812764i	0.530133	−	0.847915i	$-0.322142\pi$
$151$	−4.52665e11	−	7.84039e11i	−0.469249	−	0.812764i	−0.999382	+	0.0351510i	$0.988809\pi$
$152$	8.56391e10	−	1.48331e11i	0.0856115	−	0.148284i
$153$	4.39770e11	+	1.79465e11i	0.424056	+	0.173052i
$154$	9.53586e11	−	9.77288e10i	0.887148	−	0.0909198i
$155$		−	2.61442e11i		−	0.234721i
$156$	2.31410e11	−	2.65271e11i	0.200538	−	0.229882i
$157$	−1.67038e12	+	9.64395e11i	−1.39755	+	0.806876i	−0.994136	−	0.108140i	$-0.965510\pi$
$157$	−1.67038e12	+	9.64395e11i	−1.39755	+	0.806876i	−0.403415	+	0.915017i	$0.632177\pi$
$158$	1.00060e12	−	5.77696e11i	0.808436	−	0.466751i
$159$	1.28313e12	−	1.47089e12i	1.00135	−	1.14788i
$160$		−	1.06311e11i		−	0.0801525i
$161$	7.24807e10	+	3.24957e10i	0.0528056	+	0.0236747i
$162$	7.02593e11	−	7.17474e11i	0.494733	−	0.505212i
$163$	−5.36340e11	+	9.28969e11i	−0.365097	+	0.632367i	−0.988792	−	0.149301i	$-0.952298\pi$
$163$	−5.36340e11	+	9.28969e11i	−0.365097	+	0.632367i	0.623694	+	0.781668i	$0.285631\pi$
$164$	−6.21499e9	−	1.07647e10i	−0.00409071	−	0.00708533i
$165$	−2.90984e11	−	8.49892e11i	−0.185229	−	0.541006i
$166$	3.07610e11	+	1.77599e11i	0.189411	+	0.109357i
$167$	−1.71101e11			−0.101932			−0.0509661	−	0.998700i	$-0.516230\pi$
$167$	−1.71101e11			−0.101932			−0.0509661	+	0.998700i	$0.516230\pi$
$168$	−2.56770e11	−	5.56935e11i	−0.148028	−	0.321073i
$169$	1.12504e12			0.627755
$170$	−2.35423e11	−	1.35921e11i	−0.127168	−	0.0734208i
$171$	−9.17379e11	+	1.25668e11i	−0.479811	+	0.0657275i
$172$	3.24474e10	+	5.62006e10i	0.0164352	+	0.0284665i
$173$	8.21970e11	−	1.42369e12i	0.403276	−	0.698494i	−0.590843	−	0.806786i	$-0.701205\pi$
$173$	8.21970e11	−	1.42369e12i	0.403276	−	0.698494i	0.994119	+	0.108292i	$0.0345382\pi$
$174$	4.03066e11	−	2.05446e12i	0.191582	−	0.976510i
$175$	1.01024e12	+	1.39808e12i	0.465281	+	0.643906i
$176$			7.06382e11i			0.315297i
$177$	−1.05665e12	−	9.21767e11i	−0.457168	−	0.398812i
$178$	−2.00306e12	+	1.15647e12i	−0.840203	+	0.485092i
$179$	1.57185e12	−	9.07506e11i	0.639321	−	0.369112i	−0.145032	−	0.989427i	$-0.546329\pi$
$179$	1.57185e12	−	9.07506e11i	0.639321	−	0.369112i	0.784353	+	0.620315i	$0.212995\pi$
$180$	−4.54121e11	+	3.52255e11i	−0.179132	+	0.138950i
$181$			1.08738e12i			0.416053i	0.978123	+	0.208026i	$0.0667040\pi$
$181$			1.08738e12i			0.416053i	−0.978123	+	0.208026i	$0.933296\pi$
$182$	−4.75471e11	+	1.06052e12i	−0.176495	+	0.393665i
$183$	−2.40410e12	−	4.71662e11i	−0.865909	−	0.169883i
$184$	−2.92668e10	+	5.06916e10i	−0.0102300	+	0.0177190i
$185$	6.51605e11	+	1.12861e12i	0.221075	+	0.382913i
$186$	1.05147e12	−	3.60000e11i	0.346318	−	0.118572i
$187$	1.56427e12	+	9.03131e11i	0.500245	+	0.288816i
$188$	−2.33153e12			−0.724059
$189$	−1.52823e12	+	2.94221e12i	−0.460946	+	0.887428i
$190$	5.29943e11			0.155269
$191$	−2.08047e12	−	1.20116e12i	−0.592213	−	0.341914i	0.173759	−	0.984788i	$-0.444409\pi$
$191$	−2.08047e12	−	1.20116e12i	−0.592213	−	0.341914i	−0.765972	+	0.642874i	$0.777742\pi$
$192$	4.27560e11	−	1.46387e11i	0.118261	−	0.0404899i
$193$	−2.82117e12	−	4.88640e12i	−0.758339	−	1.31348i	−0.943697	−	0.330810i	$-0.892678\pi$
$193$	−2.82117e12	−	4.88640e12i	−0.758339	−	1.31348i	0.185358	−	0.982671i	$-0.440655\pi$
$194$	1.85823e12	−	3.21854e12i	0.485500	−	0.840910i
$195$	1.06880e12	+	2.09688e11i	0.271460	+	0.0532578i
$196$	1.34703e12	+	1.51171e12i	0.332635	+	0.373301i
$197$		−	5.41266e11i		−	0.129971i	−0.997886	−	0.0649855i	$-0.979300\pi$
$197$		−	5.41266e11i		−	0.129971i	0.997886	−	0.0649855i	$-0.0207001\pi$
$198$	3.01741e12	−	2.34056e12i	0.704654	−	0.546589i
$199$	4.96571e12	−	2.86695e12i	1.12795	−	0.651222i	0.184531	−	0.982827i	$-0.440924\pi$
$199$	4.96571e12	−	2.86695e12i	1.12795	−	0.651222i	0.943418	+	0.331605i	$0.107590\pi$
$200$	−1.10078e12	+	6.35535e11i	−0.243240	+	0.140435i
$201$	−3.12677e12	−	2.72764e12i	−0.672229	−	0.586421i
$202$		−	3.01483e12i		−	0.630711i
$203$	7.04718e11	+	6.87626e12i	0.143479	+	1.39999i
$204$	2.22477e11	−	1.13398e12i	0.0440878	−	0.224719i
$205$	1.92295e10	−	3.33064e10i	0.00370955	−	0.00642513i
$206$	3.52222e12	+	6.10067e12i	0.661526	+	1.14580i
$207$	3.13511e11	−	4.29466e10i	0.0573344	−	0.00785402i
$208$	−7.41709e11	−	4.28226e11i	−0.132095	−	0.0762649i
$209$	−3.52121e12			−0.610783
$210$	1.09509e12	−	1.54961e12i	0.185031	−	0.261829i
$211$	−5.98222e11			−0.0984711			−0.0492356	−	0.998787i	$-0.515679\pi$
$211$	−5.98222e11			−0.0984711			−0.0492356	+	0.998787i	$0.515679\pi$
$212$	−4.11266e12	−	2.37444e12i	−0.659592	−	0.380815i
$213$	2.33780e12	+	6.82813e12i	0.365359	+	1.06712i
$214$	3.23932e12	+	5.61067e12i	0.493377	+	0.854553i
$215$	−1.00394e11	+	1.73887e11i	−0.0149038	+	0.0258141i
$216$	−2.04201e12	−	1.34134e12i	−0.295503	−	0.194107i
$217$	−2.97414e12	+	2.14909e12i	−0.419597	+	0.303197i
$218$		−	5.29120e12i		−	0.727853i
$219$	−1.13727e11	+	1.30368e11i	−0.0152553	+	0.0174875i
$220$	−1.89277e12	+	1.09279e12i	−0.247612	+	0.142959i
$221$	−1.89660e12	+	1.09500e12i	−0.242001	+	0.139719i
$222$	−3.64180e12	+	4.17469e12i	−0.453289	+	0.519617i
$223$		−	5.04672e11i		−	0.0612820i	−0.999530	−	0.0306410i	$-0.990245\pi$
$223$		−	5.04672e11i		−	0.0612820i	0.999530	−	0.0306410i	$-0.00975485\pi$
$224$	−1.20938e12	+	8.73886e11i	−0.143284	+	0.103536i
$225$	6.36215e12	+	2.59632e12i	0.735530	+	0.300161i
$226$	−3.03477e12	+	5.25638e12i	−0.342397	+	0.593049i
$227$	−2.97432e12	−	5.15167e12i	−0.327525	−	0.567291i	0.654495	−	0.756067i	$-0.272881\pi$
$227$	−2.97432e12	−	5.15167e12i	−0.327525	−	0.567291i	−0.982020	+	0.188776i	$0.939548\pi$
$228$	7.29718e11	+	2.13132e12i	0.0784357	+	0.229091i
$229$	6.09129e12	+	3.51681e12i	0.639167	+	0.369023i	0.784294	−	0.620390i	$-0.213026\pi$
$229$	6.09129e12	+	3.51681e12i	0.639167	+	0.369023i	−0.145127	+	0.989413i	$0.546359\pi$
$230$	−1.81106e11			−0.0185537
$231$	−7.27634e12	+	1.02964e13i	−0.727859	+	1.02996i
$232$	−5.09368e12			−0.497563
$233$	3.06773e12	+	1.77115e12i	0.292657	+	0.168966i	0.639140	−	0.769091i	$-0.279291\pi$
$233$	3.06773e12	+	1.77115e12i	0.292657	+	0.168966i	−0.346482	+	0.938057i	$0.612624\pi$
$234$	6.28386e11	+	4.58722e12i	0.0585517	+	0.427428i
$235$	−3.60694e12	−	6.24740e12i	−0.328296	−	0.568625i
$236$	−1.70574e12	+	2.95442e12i	−0.151669	+	0.262698i
$237$	−2.92565e12	+	1.49123e13i	−0.254160	+	1.29547i
$238$	3.88977e11	+	3.79543e12i	0.0330180	+	0.322172i
$239$		−	8.35576e12i		−	0.693103i	−0.938031	−	0.346551i	$-0.887353\pi$
$239$		−	8.35576e12i		−	0.693103i	0.938031	−	0.346551i	$-0.112647\pi$
$240$	1.05369e12	+	9.19192e11i	0.0854186	+	0.0745151i
$241$	1.10896e13	−	6.40261e12i	0.878666	−	0.507298i	0.00844764	−	0.999964i	$-0.497311\pi$
$241$	1.10896e13	−	6.40261e12i	0.878666	−	0.507298i	0.870218	+	0.492666i	$0.163978\pi$
$242$	4.66971e12	−	2.69606e12i	0.361664	−	0.208807i
$243$	1.03639e12	+	1.31672e13i	0.0784670	+	0.996917i
$244$			5.96057e12i			0.441208i
$245$	−1.96677e12	+	5.94804e12i	−0.142344	+	0.430488i
$246$	1.60430e11	+	3.14749e10i	0.0113538	+	0.00222752i
$247$	2.13464e12	−	3.69731e12i	0.147738	−	0.255890i
$248$	−1.35198e12	−	2.34169e12i	−0.0915134	−	0.158506i
$249$	−4.41994e12	+	1.51329e12i	−0.292631	+	0.100190i
$250$	−7.69310e12	−	4.44161e12i	−0.498232	−	0.287654i
$251$	−2.19061e13			−1.38791			−0.693954	−	0.720020i	$-0.744133\pi$
$251$	−2.19061e13			−1.38791			−0.693954	+	0.720020i	$0.744133\pi$
$252$	7.74014e12	+	2.27045e12i	0.479784	+	0.140738i
$253$	1.20336e12			0.0729848
$254$	9.93488e12	+	5.73590e12i	0.589627	+	0.340421i
$255$	3.38271e12	−	1.15817e12i	0.196469	−	0.0672667i
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	1.53336e13	−	2.65586e13i	0.853126	−	1.47766i	−0.0252472	−	0.999681i	$-0.508037\pi$
$257$	1.53336e13	−	2.65586e13i	0.853126	−	1.47766i	0.878373	−	0.477976i	$-0.158629\pi$
$258$	−8.37579e11	−	1.64325e11i	−0.0456160	−	0.00894944i
$259$	7.48269e12	−	1.66899e13i	0.398942	−	0.889826i
$260$		−	2.64990e12i		−	0.138317i
$261$	1.68777e13	+	2.17584e13i	0.862560	+	1.11200i
$262$	−1.94165e13	+	1.12101e13i	−0.971658	+	0.560987i
$263$	3.24401e13	−	1.87293e13i	1.58974	−	0.917835i	0.596388	−	0.802697i	$-0.296602\pi$
$263$	3.24401e13	−	1.87293e13i	1.58974	−	0.917835i	0.993349	−	0.115139i	$-0.0367312\pi$
$264$	−7.00127e12	−	6.10758e12i	−0.336012	−	0.293121i
$265$		−	1.46933e13i		−	0.690663i
$266$	−4.35619e12	−	6.02857e12i	−0.200566	−	0.277565i
$267$	5.85676e12	−	2.98524e13i	0.264147	−	1.34638i
$268$	−5.04752e12	+	8.74256e12i	−0.223016	+	0.386276i
$269$	−1.10829e13	−	1.91962e13i	−0.479752	−	0.830956i	0.519978	−	0.854180i	$-0.325940\pi$
$269$	−1.10829e13	−	1.91962e13i	−0.479752	−	0.830956i	−0.999730	+	0.0232241i	$0.992607\pi$
$270$	4.35104e11	−	7.54670e12i	0.0184541	−	0.320078i
$271$	−6.66739e11	−	3.84942e11i	−0.0277093	−	0.0159979i	0.486081	−	0.873914i	$-0.338426\pi$
$271$	−6.66739e11	−	3.84942e11i	−0.0277093	−	0.0159979i	−0.513791	+	0.857916i	$0.671759\pi$
$272$	−2.81152e12			−0.114502
$273$	−6.40026e12	−	1.38822e13i	−0.255448	−	0.554068i
$274$	−3.04372e13			−1.19063
$275$	2.26303e13	+	1.30656e13i	0.867681	+	0.500956i
$276$	−2.49378e11	−	7.28371e11i	−0.00937257	−	0.0273749i
$277$	−1.30530e13	−	2.26085e13i	−0.480919	−	0.832977i	0.518841	−	0.854871i	$-0.326364\pi$
$277$	−1.30530e13	−	2.26085e13i	−0.480919	−	0.832977i	−0.999760	+	0.0218940i	$0.993030\pi$
$278$	−7.39188e11	+	1.28031e12i	−0.0266998	+	0.0462455i
$279$	−5.52317e12	+	1.35342e13i	−0.195598	+	0.479303i
$280$	−4.21254e12	−	1.88863e12i	−0.146276	−	0.0655811i
$281$		−	4.98590e13i		−	1.69769i	−0.528642	−	0.848845i	$-0.677299\pi$
$281$		−	4.98590e13i		−	1.69769i	0.528642	−	0.848845i	$-0.322701\pi$
$282$	2.01591e13	−	2.31089e13i	0.673134	−	0.771630i
$283$	4.46655e13	−	2.57876e13i	1.46267	−	0.844474i	0.463537	−	0.886078i	$-0.346580\pi$
$283$	4.46655e13	−	2.57876e13i	1.46267	−	0.844474i	0.999134	+	0.0416040i	$0.0132468\pi$
$284$	1.52067e13	−	8.77959e12i	0.488410	−	0.281983i
$285$	−4.58204e12	+	5.25250e12i	−0.144348	+	0.165470i
$286$			1.76073e13i			0.544101i
$287$	−5.36959e11	+	5.50305e10i	−0.0162776	+	0.00166822i
$288$	−2.24589e12	+	5.50344e12i	−0.0667929	+	0.163673i
$289$	1.35413e13	−	2.34543e13i	0.395115	−	0.684359i
$290$	−7.88005e12	−	1.36486e13i	−0.225601	−	0.390752i
$291$	1.58337e13	+	4.62461e13i	0.444806	+	1.29916i
$292$	3.64515e11	+	2.10453e11i	0.0100487	+	0.00580161i
$293$	−5.71399e13			−1.54585			−0.772925	−	0.634497i	$-0.781207\pi$
$293$	−5.71399e13			−1.54585			−0.772925	+	0.634497i	$0.781207\pi$
$294$	−2.66300e13	+	2.80371e11i	−0.707068	+	0.00744428i
$295$	−1.05553e13			−0.275073
$296$	1.16726e13	+	6.73918e12i	0.298582	+	0.172386i
$297$	−2.89105e12	+	5.01441e13i	−0.0725931	+	1.25910i
$298$	2.54287e13	+	4.40438e13i	0.626809	+	1.08566i
$299$	−7.29506e11	+	1.26354e12i	−0.0176538	+	0.0305772i
$300$	3.21857e12	−	1.64053e13i	0.0764709	−	0.389779i
$301$	2.80337e12	−	2.87305e11i	0.0653981	−	0.00670236i
$302$		−	2.89706e13i		−	0.663619i
$303$	2.98814e13	+	2.60671e13i	0.672150	+	0.586352i
$304$	4.74660e12	−	2.74045e12i	0.104852	−	0.0605365i
$305$	−1.59715e13	+	9.22114e12i	−0.346494	+	0.200049i
$306$	9.31582e12	+	1.20098e13i	0.198497	+	0.255899i
$307$			4.90002e13i			1.02550i	0.858537	+	0.512751i	$0.171374\pi$
$307$			4.90002e13i			1.02550i	−0.858537	+	0.512751i	$0.828626\pi$
$308$	2.79902e13	+	1.25490e13i	0.575410	+	0.257977i
$309$	−9.09206e13	−	1.78378e13i	−1.83608	−	0.360221i
$310$	4.18308e12	−	7.24530e12i	0.0829863	−	0.143737i
$311$	−1.40492e12	−	2.43340e12i	−0.0273824	−	0.0474276i	0.852009	−	0.523526i	$-0.175384\pi$
$311$	−1.40492e12	−	2.43340e12i	−0.0273824	−	0.0474276i	−0.879392	+	0.476099i	$0.842050\pi$
$312$	1.06574e13	−	3.64885e12i	0.204080	−	0.0698725i
$313$	−5.71628e13	−	3.30029e13i	−1.07552	−	0.620953i	−0.145837	−	0.989309i	$-0.546588\pi$
$313$	−5.71628e13	−	3.30029e13i	−1.07552	−	0.620953i	−0.929685	+	0.368355i	$0.879921\pi$
$314$	−6.17213e13			−1.14110
$315$	5.89045e12	+	2.42523e13i	0.107014	+	0.440601i
$316$	3.69725e13			0.660086
$317$	8.10113e13	+	4.67719e13i	1.42141	+	0.820652i	0.996420	−	0.0845450i	$-0.0269437\pi$
$317$	8.10113e13	+	4.67719e13i	1.42141	+	0.820652i	0.424992	+	0.905197i	$0.360277\pi$
$318$	5.90934e13	−	2.02323e13i	1.01904	−	0.348896i
$319$	5.23590e13	+	9.06885e13i	0.887448	+	1.53711i
$320$	1.70097e12	−	2.94617e12i	0.0283382	−	0.0490832i
$321$	−8.36180e13	−	1.64051e13i	−1.36937	−	0.268658i
$322$	1.48871e12	+	2.06024e12i	0.0239664	+	0.0331673i
$323$		−	1.40150e13i		−	0.221809i
$324$	3.09504e13	−	8.64172e12i	0.481580	−	0.134463i
$325$	−2.74380e13	+	1.58414e13i	−0.419754	+	0.242345i
$326$	−2.97270e13	+	1.71629e13i	−0.447151	+	0.258163i
$327$	5.24435e13	+	4.57492e13i	0.775673	+	0.676661i
$328$		−	3.97759e11i		−	0.00578514i
$329$	−4.14203e13	+	9.23865e13i	−0.592428	+	1.32139i
$330$	5.53427e12	−	2.82086e13i	0.0778455	−	0.396785i
$331$	−2.32633e13	+	4.02932e13i	−0.321823	+	0.557413i	−0.980864	−	0.194693i	$-0.937629\pi$
$331$	−2.32633e13	+	4.02932e13i	−0.321823	+	0.557413i	0.659041	+	0.752107i	$0.270962\pi$
$332$	5.68316e12	+	9.84351e12i	0.0773268	+	0.133934i
$333$	−9.88919e12	−	7.21911e13i	−0.132348	−	0.966141i
$334$	−4.74168e12	−	2.73761e12i	−0.0624204	−	0.0360384i
$335$	−3.12345e13			−0.404472
$336$	1.79514e12	−	1.95426e13i	0.0228682	−	0.248952i
$337$	−7.77884e13			−0.974878			−0.487439	−	0.873157i	$-0.662069\pi$
$337$	−7.77884e13			−0.974878			−0.487439	+	0.873157i	$0.662069\pi$
$338$	3.11779e13	+	1.80006e13i	0.384420	+	0.221945i
$339$	−2.58589e13	−	7.55272e13i	−0.313698	−	0.916231i
$340$	−4.34949e12	−	7.53353e12i	−0.0519163	−	0.0899217i
$341$	−2.77945e13	+	4.81414e13i	−0.326445	+	0.565419i
$342$	−2.74338e13	−	1.11954e13i	−0.317061	−	0.129389i
$343$	8.38313e13	−	2.65199e13i	0.953430	−	0.301616i
$344$			2.07664e12i			0.0232428i
$345$	1.56589e12	−	1.79502e12i	0.0172487	−	0.0197726i
$346$	4.55582e13	−	2.63030e13i	0.493910	−	0.285159i
$347$	2.99487e13	−	1.72909e13i	0.319570	−	0.184504i	−0.331631	−	0.943409i	$-0.607599\pi$
$347$	2.99487e13	−	1.72909e13i	0.319570	−	0.184504i	0.651201	+	0.758905i	$0.274265\pi$
$348$	4.40414e13	−	5.04858e13i	0.462568	−	0.530253i
$349$		−	5.90882e13i		−	0.610887i	−0.952210	−	0.305443i	$-0.901195\pi$
$349$		−	5.90882e13i		−	0.610887i	0.952210	−	0.305443i	$-0.0988047\pi$
$350$	5.62733e12	+	5.49085e13i	0.0572701	+	0.558812i
$351$	−5.08992e13	−	3.34342e13i	−0.509944	−	0.334967i
$352$	−1.13021e13	+	1.95758e13i	−0.111474	+	0.193079i
$353$	8.70342e13	+	1.50748e14i	0.845141	+	1.46383i	0.885499	+	0.464641i	$0.153817\pi$
$353$	8.70342e13	+	1.50748e14i	0.845141	+	1.46383i	−0.0403583	+	0.999185i	$0.512850\pi$
$354$	−1.45343e13	−	4.24511e13i	−0.138956	−	0.405855i
$355$	4.70503e13	+	2.71645e13i	0.442900	+	0.255709i
$356$	−7.40140e13			−0.686023
$357$	−4.09815e13	−	2.89611e13i	−0.374035	−	0.264326i
$358$	5.80804e13			0.522003
$359$	5.17202e13	+	2.98607e13i	0.457763	+	0.264289i	0.711103	−	0.703088i	$-0.248196\pi$
$359$	5.17202e13	+	2.98607e13i	0.457763	+	0.264289i	−0.253340	+	0.967377i	$0.581529\pi$
$360$	−1.82211e13	+	2.49603e12i	−0.158822	+	0.0217564i
$361$	−4.45844e13	−	7.72224e13i	−0.382731	−	0.662909i
$362$	−1.73980e13	+	3.01343e13i	−0.147097	+	0.254779i
$363$	−1.36538e13	+	6.95945e13i	−0.113702	+	0.579547i
$364$	−3.01450e13	+	2.17825e13i	−0.247262	+	0.178670i
$365$			1.30230e12i			0.0105221i
$366$	−5.90779e13	−	5.15368e13i	−0.470196	−	0.410177i
$367$	5.80547e12	−	3.35179e12i	0.0455170	−	0.0262793i	−0.477069	−	0.878866i	$-0.658301\pi$
$367$	5.80547e12	−	3.35179e12i	0.0455170	−	0.0262793i	0.522586	+	0.852587i	$0.324967\pi$
$368$	−1.62213e12	+	9.36538e11i	−0.0125292	+	0.00723373i
$369$	−1.69909e12	+	1.31796e12i	−0.0129292	+	0.0100290i
$370$			4.17027e13i			0.312647i
$371$	−1.67149e14	+	1.20780e14i	−1.23466	+	0.892155i
$372$	3.48991e13	+	6.84688e12i	0.253997	+	0.0498318i
$373$	−8.89764e12	+	1.54112e13i	−0.0638081	+	0.110519i	−0.896165	−	0.443722i	$-0.853658\pi$
$373$	−8.89764e12	+	1.54112e13i	−0.0638081	+	0.110519i	0.832357	+	0.554241i	$0.186991\pi$
$374$	2.89002e13	+	5.00566e13i	0.204224	+	0.353726i
$375$	1.10540e14	−	3.78463e13i	0.769743	−	0.263543i
$376$	−6.46134e13	−	3.73046e13i	−0.443394	−	0.255993i
$377$	−1.26965e14			−0.858633
$378$	−8.94270e13	+	5.70851e13i	−0.596024	+	0.380468i
$379$	1.35456e14			0.889780			0.444890	−	0.895585i	$-0.353243\pi$
$379$	1.35456e14			0.889780			0.444890	+	0.895585i	$0.353243\pi$
$380$	1.46862e13	+	8.47909e12i	0.0950823	+	0.0548958i
$381$	−1.42751e14	+	4.88748e13i	−0.910944	+	0.311887i
$382$	−3.84371e13	−	6.65750e13i	−0.241770	−	0.418758i
$383$	7.03880e13	−	1.21916e14i	0.436421	−	0.755903i	−0.560990	−	0.827823i	$-0.689579\pi$
$383$	7.03880e13	−	1.21916e14i	0.436421	−	0.755903i	0.997410	+	0.0719199i	$0.0229126\pi$
$384$	1.41911e13	+	2.78416e12i	0.0867349	+	0.0170166i
$385$	9.67608e12	+	9.44141e13i	0.0582996	+	0.568857i
$386$		−	1.80555e14i		−	1.07245i
$387$	8.87065e12	−	6.88083e12i	0.0519452	−	0.0402931i
$388$	1.02993e14	−	5.94632e13i	0.594613	−	0.343300i
$389$	2.00252e14	−	1.15616e14i	1.13987	−	0.658104i	0.193471	−	0.981106i	$-0.438025\pi$
$389$	2.00252e14	−	1.15616e14i	1.13987	−	0.658104i	0.946398	+	0.323002i	$0.104692\pi$
$390$	2.62644e13	+	2.29118e13i	0.147405	+	0.128589i
$391$			4.78957e12i			0.0265048i
$392$	1.31427e13	+	6.34461e13i	0.0717150	+	0.346204i
$393$	5.67719e13	−	2.89371e14i	0.305474	−	1.55703i
$394$	8.66026e12	−	1.50000e13i	0.0459517	−	0.0795907i
$395$	5.71974e13	+	9.90688e13i	0.299290	+	0.518385i
$396$	1.21070e14	−	1.65849e13i	0.624759	−	0.0855834i
$397$	−2.48329e14	−	1.43373e14i	−1.26380	−	0.729657i	−0.289994	−	0.957028i	$-0.593653\pi$
$397$	−2.48329e14	−	1.43373e14i	−1.26380	−	0.729657i	−0.973808	+	0.227372i	$0.926987\pi$
$398$	1.83485e14			0.920966
$399$	9.74168e13	+	8.94851e12i	0.482262	+	0.0442996i
$400$	−4.06742e13			−0.198605
$401$	−8.76278e13	−	5.05919e13i	−0.422034	−	0.243662i	0.273913	−	0.961754i	$-0.411682\pi$
$401$	−8.76278e13	−	5.05919e13i	−0.422034	−	0.243662i	−0.695947	+	0.718093i	$0.745015\pi$
$402$	−4.30092e13	−	1.25619e14i	−0.204323	−	0.596777i
$403$	−3.36994e13	−	5.83691e13i	−0.157923	−	0.273530i
$404$	4.82373e13	−	8.35495e13i	0.222990	−	0.386230i
$405$	7.10367e13	+	6.95634e13i	0.323952	+	0.317233i
$406$	−9.04905e13	+	2.01836e14i	−0.407108	+	0.908041i
$407$		−	2.77094e14i		−	1.22987i
$408$	2.43092e13	−	2.78662e13i	0.106448	−	0.122025i
$409$	2.61255e13	−	1.50836e13i	0.112872	−	0.0651668i	−0.442501	−	0.896768i	$-0.645909\pi$
$409$	2.61255e13	−	1.50836e13i	0.112872	−	0.0651668i	0.555373	+	0.831601i	$0.312575\pi$
$410$	1.06581e12	−	6.15343e11i	0.00454325	−	0.00262305i
$411$	2.63168e14	−	3.01677e14i	1.10689	−	1.26885i
$412$			2.25422e14i			0.935540i
$413$	8.67655e13	+	1.20075e14i	0.355322	+	0.491732i
$414$	9.37541e12	+	3.82600e12i	0.0378868	+	0.0154612i
$415$	−1.75840e13	+	3.04563e13i	−0.0701216	+	0.121454i
$416$	−1.37032e13	−	2.37347e13i	−0.0539274	−	0.0934050i
$417$	−6.29852e12	−	1.83964e13i	−0.0244619	−	0.0714470i
$418$	−9.75826e13	−	5.63393e13i	−0.374027	−	0.215944i
$419$	7.20731e13			0.272644			0.136322	−	0.990665i	$-0.456472\pi$
$419$	7.20731e13			0.272644			0.136322	+	0.990665i	$0.456472\pi$
$420$	5.51419e13	−	2.54227e13i	0.205878	−	0.0949184i
$421$	−1.66505e14			−0.613585			−0.306793	−	0.951776i	$-0.599256\pi$
$421$	−1.66505e14			−0.613585			−0.306793	+	0.951776i	$0.599256\pi$
$422$	−1.65784e13	−	9.57155e12i	−0.0603010	−	0.0348148i
$423$	5.47413e13	+	3.99612e14i	0.196537	+	1.43472i
$424$	−7.59822e13	−	1.31605e14i	−0.269277	−	0.466402i
$425$	−5.20032e13	+	9.00723e13i	−0.181925	+	0.315103i
$426$	−4.44629e13	+	2.26631e14i	−0.153548	+	0.782649i
$427$	2.36186e14	+	1.05891e14i	0.805195	+	0.360998i
$428$			2.07317e14i			0.697740i
$429$	−1.74514e14	−	1.52238e14i	−0.579849	−	0.505833i
$430$	−5.56440e12	+	3.21261e12i	−0.0182533	+	0.0105386i
$431$	−2.32771e14	+	1.34390e14i	−0.753882	+	0.435254i	−0.827095	−	0.562062i	$-0.810008\pi$
$431$	−2.32771e14	+	1.34390e14i	−0.753882	+	0.435254i	0.0732128	+	0.997316i	$0.476675\pi$
$432$	−3.51285e13	−	6.98444e13i	−0.112331	−	0.223342i
$433$		−	5.42597e14i		−	1.71314i	−0.516028	−	0.856572i	$-0.672590\pi$
$433$		−	5.42597e14i		−	1.71314i	0.516028	−	0.856572i	$-0.327410\pi$
$434$	−1.16807e14	+	1.19710e13i	−0.364146	+	0.0373197i
$435$	2.03411e14	+	3.99073e13i	0.626158	+	0.122846i
$436$	8.46592e13	−	1.46634e14i	0.257335	−	0.445717i
$437$	−4.66850e12	−	8.08608e12i	−0.0140130	−	0.0242712i
$438$	−5.23759e12	+	1.79324e12i	−0.0155247	+	0.00531533i
$439$	2.41862e14	+	1.39639e14i	0.707968	+	0.408745i	0.810308	−	0.586004i	$-0.199300\pi$
$439$	2.41862e14	+	1.39639e14i	0.707968	+	0.408745i	−0.102340	+	0.994749i	$0.532633\pi$
$440$	−6.99385e13			−0.202175
$441$	2.27472e14	−	2.66366e14i	0.649404	−	0.760443i
$442$	−7.00800e13			−0.197593
$443$	2.04283e14	+	1.17943e14i	0.568869	+	0.328437i	0.756697	−	0.653765i	$-0.226812\pi$
$443$	2.04283e14	+	1.17943e14i	0.568869	+	0.328437i	−0.187829	+	0.982202i	$0.560145\pi$
$444$	−1.67720e14	+	5.74236e13i	−0.461294	+	0.157937i
$445$	−1.14501e14	−	1.98322e14i	−0.311050	−	0.538755i
$446$	8.07475e12	−	1.39859e13i	0.0216664	−	0.0375274i
$447$	−6.56402e14	−	1.28780e14i	−1.73972	−	0.341316i
$448$	−4.74974e13	+	4.86780e12i	−0.124349	+	0.0127439i
$449$			5.78864e13i			0.149700i	0.997195	+	0.0748500i	$0.0238478\pi$
$449$			5.78864e13i			0.149700i	−0.997195	+	0.0748500i	$0.976152\pi$
$450$	1.34772e14	+	1.73746e14i	0.344295	+	0.443860i
$451$	−7.08175e12	+	4.08865e12i	−0.0178719	+	0.0103183i
$452$	−1.68204e14	+	9.71128e13i	−0.419349	+	0.242111i
$453$	2.87140e14	+	2.50488e14i	0.707219	+	0.616945i
$454$		−	1.90356e14i		−	0.463191i
$455$	−1.05002e14	−	4.70762e13i	−0.252426	−	0.113172i
$456$	−1.38786e13	+	7.07404e13i	−0.0329639	+	0.168020i
$457$	−2.60403e14	+	4.51031e14i	−0.611092	+	1.05844i	0.379964	+	0.925001i	$0.375936\pi$
$457$	−2.60403e14	+	4.51031e14i	−0.611092	+	1.05844i	−0.991057	+	0.133442i	$0.957397\pi$
$458$	1.12538e14	+	1.94921e14i	0.260939	+	0.451959i
$459$	−1.99582e14	−	1.15069e13i	−0.457247	−	0.0263625i
$460$	−5.01895e12	−	2.89769e12i	−0.0113617	−	0.00655971i
$461$	−2.61836e14			−0.585700			−0.292850	−	0.956158i	$-0.594604\pi$
$461$	−2.61836e14			−0.585700			−0.292850	+	0.956158i	$0.594604\pi$
$462$	−3.66391e14	+	1.68921e14i	−0.809866	+	0.373382i
$463$	3.59394e14			0.785010			0.392505	−	0.919750i	$-0.371609\pi$
$463$	3.59394e14			0.785010			0.392505	+	0.919750i	$0.371609\pi$
$464$	−1.41160e14	−	8.14990e13i	−0.304694	−	0.175915i
$465$	3.56434e13	+	1.04105e14i	0.0760305	+	0.222066i
$466$	5.66769e13	+	9.81673e13i	0.119477	+	0.206940i
$467$	−5.61820e13	+	9.73102e13i	−0.117045	+	0.202729i	−0.918596	−	0.395199i	$-0.870676\pi$
$467$	−5.61820e13	+	9.73102e13i	−0.117045	+	0.202729i	0.801550	+	0.597928i	$0.204009\pi$
$468$	−5.59812e13	+	1.37179e14i	−0.115263	+	0.282446i
$469$	2.56752e14	+	3.55321e14i	0.522472	+	0.723052i
$470$		−	2.30844e14i		−	0.464281i
$471$	5.33660e14	−	6.11748e14i	1.06084	−	1.21607i
$472$	−9.45415e13	+	5.45836e13i	−0.185755	+	0.107246i
$473$	3.69727e13	−	2.13462e13i	0.0718033	−	0.0414557i
$474$	−3.19675e14	+	3.66451e14i	−0.613660	+	0.703454i
$475$		−	2.02755e14i		−	0.384731i
$476$	−4.99473e13	+	1.11406e14i	−0.0936858	+	0.208963i
$477$	−3.10407e14	+	7.60635e14i	−0.575546	+	1.41034i
$478$	1.33692e14	−	2.31562e14i	0.245049	−	0.424437i
$479$	−2.55321e14	−	4.42228e14i	−0.462637	−	0.801311i	0.536454	−	0.843929i	$-0.319763\pi$
$479$	−2.55321e14	−	4.42228e14i	−0.462637	−	0.801311i	−0.999091	+	0.0426185i	$0.986430\pi$
$480$	1.44937e13	+	4.23325e13i	0.0259629	+	0.0758310i
$481$	2.90952e14	+	1.67981e14i	0.515256	+	0.297483i
$482$	4.09767e14			0.717428
$483$	−3.32918e13	−	3.05812e12i	−0.0576272	−	0.00529353i
$484$	1.72548e14			0.295298
$485$	3.18666e14	+	1.83982e14i	0.539208	+	0.311312i
$486$	−1.81954e14	+	3.81482e14i	−0.304412	+	0.638227i
$487$	5.00826e13	+	8.67456e13i	0.0828472	+	0.143495i	0.904472	−	0.426533i	$-0.140265\pi$
$487$	5.00826e13	+	8.67456e13i	0.0828472	+	0.143495i	−0.821625	+	0.570029i	$0.806932\pi$
$488$	−9.53691e13	+	1.65184e14i	−0.155991	+	0.270184i
$489$	8.69189e13	−	4.43033e14i	0.140577	−	0.716535i
$490$	−1.49673e14	+	1.33369e14i	−0.239368	+	0.213292i
$491$			1.53858e14i			0.243317i	0.992572	+	0.121658i	$0.0388212\pi$
$491$			1.53858e14i			0.243317i	−0.992572	+	0.121658i	$0.961179\pi$
$492$	3.94237e12	+	3.43914e12i	0.00616523	+	0.00537826i
$493$	−3.60956e14	+	2.08398e14i	−0.558207	+	0.322281i
$494$	1.18314e14	−	6.83086e13i	0.180941	−	0.104466i
$495$	2.31738e14	+	2.98753e14i	0.350484	+	0.451838i
$496$		−	8.65264e13i		−	0.129419i
$497$	−7.77387e13	−	7.58534e14i	−0.114995	−	1.12206i
$498$	−1.46702e14	−	2.87815e13i	−0.214622	−	0.0421068i
$499$	−2.10071e14	+	3.63853e14i	−0.303957	+	0.526469i	−0.977029	−	0.213108i	$-0.931641\pi$
$499$	−2.10071e14	+	3.63853e14i	−0.303957	+	0.526469i	0.673072	+	0.739577i	$0.264975\pi$
$500$	−1.42132e14	−	2.46179e14i	−0.203402	−	0.352303i
$501$	6.81316e13	−	2.33268e13i	0.0964364	−	0.0330177i
$502$	−6.07081e14	−	3.50498e14i	−0.849916	−	0.490699i
$503$	7.54896e14			1.04535			0.522677	−	0.852531i	$-0.324933\pi$
$503$	7.54896e14			1.04535			0.522677	+	0.852531i	$0.324933\pi$
$504$	1.78174e14	+	1.86763e14i	0.244048	+	0.255813i
$505$	2.98497e14			0.404425
$506$	3.33485e13	+	1.92537e13i	0.0446939	+	0.0258040i
$507$	−4.47985e14	+	1.53380e14i	−0.593909	+	0.203342i
$508$	1.83549e14	+	3.17916e14i	0.240714	+	0.416929i
$509$	−2.32748e13	+	4.03131e13i	−0.0301952	+	0.0522996i	−0.880728	−	0.473622i	$-0.842946\pi$
$509$	−2.32748e13	+	4.03131e13i	−0.0301952	+	0.0522996i	0.850533	+	0.525922i	$0.176280\pi$
$510$	1.12275e14	+	2.20273e13i	0.144095	+	0.0282700i
$511$	1.48148e13	−	1.07051e13i	0.0188097	−	0.0135917i
$512$		−	3.51844e13i		−	0.0441942i
$513$	3.48164e14	−	1.75110e14i	0.432652	−	0.217604i
$514$	8.49877e14	−	4.90676e14i	1.04486	−	0.603251i
$515$	−6.04024e14	+	3.48734e14i	−0.734708	+	0.424184i
$516$	−2.05825e13	−	1.79552e13i	−0.0247699	−	0.0216081i
$517$			1.53385e15i			1.82635i
$518$	4.74405e14	−	3.42801e14i	0.558902	−	0.403858i
$519$	−1.33208e14	+	6.78971e14i	−0.155278	+	0.791464i
$520$	4.23985e13	−	7.34363e13i	0.0489026	−	0.0847017i
$521$	−5.41937e14	−	9.38662e14i	−0.618502	−	1.07128i	−0.989759	−	0.142747i	$-0.954407\pi$
$521$	−5.41937e14	−	9.38662e14i	−0.618502	−	1.07128i	0.371257	−	0.928530i	$-0.378927\pi$
$522$	1.19593e14	+	8.73029e14i	0.135057	+	0.985919i
$523$	9.46968e13	+	5.46732e13i	0.105822	+	0.0610964i	0.551977	−	0.833859i	$-0.313874\pi$
$523$	9.46968e13	+	5.46732e13i	0.105822	+	0.0610964i	−0.446155	+	0.894956i	$0.647207\pi$
$524$	−7.17447e14			−0.793355
$525$	−5.92879e14	−	4.18980e14i	−0.648768	−	0.458476i
$526$	1.19867e15			1.29801
$527$	−1.91611e14	−	1.10627e14i	−0.205335	−	0.118550i
$528$	−9.63036e13	−	2.81278e14i	−0.102131	−	0.298298i
$529$	−4.74809e14	−	8.22394e14i	−0.498326	−	0.863125i
$530$	2.35092e14	−	4.07192e14i	0.244186	−	0.422943i
$531$	5.46420e14	+	2.22988e14i	0.561703	+	0.229225i
$532$	−2.42653e13	−	2.36768e14i	−0.0246872	−	0.240884i
$533$		−	9.91456e12i		−	0.00998329i
$534$	6.39946e14	−	7.33586e14i	0.637773	−	0.731096i
$535$	−5.55510e14	+	3.20724e14i	−0.547957	+	0.316363i
$536$	−2.79762e14	+	1.61521e14i	−0.273138	+	0.157696i
$537$	−5.02180e14	+	5.75661e14i	−0.485289	+	0.556299i
$538$		−	7.09308e14i		−	0.678472i
$539$	9.94505e14	−	8.86169e14i	0.941605	−	0.839032i
$540$	1.32805e14	−	2.02179e14i	0.124466	−	0.189483i
$541$	−9.14224e14	+	1.58348e15i	−0.848141	+	1.46902i	0.0347251	+	0.999397i	$0.488944\pi$
$541$	−9.14224e14	+	1.58348e15i	−0.848141	+	1.46902i	−0.882866	+	0.469626i	$0.844389\pi$
$542$	−1.23181e13	−	2.13357e13i	−0.0113123	−	0.0195934i
$543$	−1.48246e14	−	4.32990e14i	−0.134767	−	0.393621i
$544$	−7.79151e13	−	4.49843e13i	−0.0701177	−	0.0404825i
$545$	5.23879e14			0.466714
$546$	4.47458e13	−	4.87119e14i	0.0394632	−	0.429611i
$547$	−1.94763e15			−1.70050			−0.850250	−	0.526378i	$-0.823550\pi$
$547$	−1.94763e15			−1.70050			−0.850250	+	0.526378i	$0.823550\pi$
$548$	−8.43500e14	−	4.86995e14i	−0.729108	−	0.420951i
$549$	1.02161e15	−	1.39946e14i	0.874252	−	0.119760i
$550$	4.18099e14	+	7.24169e14i	0.354229	+	0.613543i
$551$	4.06260e14	−	7.03663e14i	0.340777	−	0.590243i
$552$	4.74296e12	−	2.41753e13i	0.00393898	−	0.0200773i
$553$	6.56826e14	−	1.46503e15i	0.540085	−	1.20464i
$554$		−	8.35393e14i		−	0.680123i
$555$	−4.13334e14	−	3.60573e14i	−0.333188	−	0.290658i
$556$	−4.09700e13	+	2.36540e13i	−0.0327005	+	0.0188796i
$557$	5.85688e13	−	3.38147e13i	0.0462874	−	0.0267240i	−0.476678	−	0.879078i	$-0.658159\pi$
$557$	5.85688e13	−	3.38147e13i	0.0462874	−	0.0267240i	0.522965	+	0.852354i	$0.324826\pi$
$558$	−3.69610e14	+	2.86701e14i	−0.289238	+	0.224358i
$559$			5.17623e13i			0.0401096i
$560$	−8.65231e13	−	1.19740e14i	−0.0663893	−	0.0918766i
$561$	−7.46013e14	−	1.46361e14i	−0.566827	−	0.111206i
$562$	7.97743e14	−	1.38173e15i	0.600224	−	1.03962i
$563$	−6.70237e14	−	1.16088e15i	−0.499381	−	0.864953i	0.500619	−	0.865668i	$-0.333106\pi$
$563$	−6.70237e14	−	1.16088e15i	−0.499381	−	0.864953i	−1.00000		0.000714549i	$0.999773\pi$
$564$	9.28408e14	−	3.17867e14i	0.685021	−	0.234536i
$565$	−5.20432e14	−	3.00472e14i	−0.380275	−	0.219552i
$566$	1.65041e15			1.19427
$567$	2.07415e14	−	1.37992e15i	0.148639	−	0.988891i
$568$	5.61894e14			0.398785
$569$	−6.04781e14	−	3.49171e14i	−0.425090	−	0.245426i	0.272163	−	0.962251i	$-0.412261\pi$
$569$	−6.04781e14	−	3.49171e14i	−0.425090	−	0.245426i	−0.697253	+	0.716825i	$0.745594\pi$
$570$	−2.11021e14	+	7.22491e13i	−0.146897	+	0.0502945i
$571$	−5.38227e14	−	9.32237e14i	−0.371080	−	0.642729i	0.618652	−	0.785665i	$-0.287679\pi$
$571$	−5.38227e14	−	9.32237e14i	−0.371080	−	0.642729i	−0.989732	+	0.142936i	$0.954346\pi$
$572$	−2.81717e14	+	4.87948e14i	−0.192369	+	0.333192i
$573$	9.92193e14	+	1.94659e14i	0.671036	+	0.131651i
$574$	−1.57611e13	−	7.06629e12i	−0.0105578	−	0.00473343i
$575$			6.92907e13i			0.0459729i
$576$	−1.50295e14	+	1.16582e14i	−0.0987691	+	0.0766137i
$577$	1.80151e15	−	1.04010e15i	1.17266	−	0.677033i	0.218352	−	0.975870i	$-0.429932\pi$
$577$	1.80151e15	−	1.04010e15i	1.17266	−	0.677033i	0.954304	+	0.298837i	$0.0965987\pi$
$578$	7.50537e14	−	4.33323e14i	0.483915	−	0.279388i
$579$	1.78956e15	+	1.56113e15i	1.14291	+	0.997025i
$580$		−	5.04323e14i		−	0.319047i
$581$	4.91010e14	−	5.03214e13i	0.307696	−	0.0315343i
$582$	−3.01143e14	+	1.53495e15i	−0.186937	+	0.952835i
$583$	−1.56207e15	+	2.70559e15i	−0.960560	+	1.66374i
$584$	6.73448e12	+	1.16645e13i	0.00410236	+	0.00710549i
$585$	−4.54179e14	+	6.22162e13i	−0.274075	+	0.0375445i
$586$	−1.58351e15	−	9.14238e14i	−0.946636	−	0.546541i
$587$	2.73901e15			1.62212			0.811061	−	0.584961i	$-0.198890\pi$
$587$	2.73901e15			1.62212			0.811061	+	0.584961i	$0.198890\pi$
$588$	−7.42478e14	−	4.18310e14i	−0.435621	−	0.245427i
$589$	4.31321e14			0.250707
$590$	−2.92516e14	−	1.68884e14i	−0.168447	−	0.0972529i
$591$	7.37928e13	+	2.15530e14i	0.0421001	+	0.122964i
$592$	2.15654e14	+	3.73523e14i	0.121895	+	0.211129i
$593$	−8.09448e13	+	1.40201e14i	−0.0453303	+	0.0785143i	−0.887800	−	0.460229i	$-0.847767\pi$
$593$	−8.09448e13	+	1.40201e14i	−0.0453303	+	0.0785143i	0.842470	+	0.538743i	$0.181101\pi$
$594$	−8.82424e14	+	1.34338e15i	−0.489612	+	0.745371i
$595$	−3.75784e14	+	3.85124e13i	−0.206583	+	0.0211718i
$596$			1.62744e15i			0.886442i
$597$	−1.58646e15	+	1.81860e15i	−0.856192	+	0.981475i
$598$	−4.04333e13	+	2.33442e13i	−0.0216213	+	0.0124831i
$599$	−2.42182e15	+	1.39824e15i	−1.28320	+	0.740855i	−0.977432	−	0.211251i	$-0.932246\pi$
$599$	−2.42182e15	+	1.39824e15i	−1.28320	+	0.740855i	−0.305767	+	0.952106i	$0.598913\pi$
$600$	3.51681e14	−	4.03141e14i	0.184636	−	0.211653i
$601$		−	1.50448e15i		−	0.782669i	−0.920248	−	0.391335i	$-0.872014\pi$
$601$		−	1.50448e15i		−	0.782669i	0.920248	−	0.391335i	$-0.127986\pi$
$602$	8.22862e13	+	3.68919e13i	0.0424176	+	0.0190174i
$603$	1.61694e15	+	6.59853e14i	0.825938	+	0.337056i
$604$	4.63529e14	−	8.02856e14i	0.234625	−	0.406382i
$605$	2.66936e14	+	4.62346e14i	0.133891	+	0.231906i
$606$	4.11023e14	+	1.20049e15i	0.204299	+	0.596706i
$607$	1.57170e15	+	9.07420e14i	0.774160	+	0.446962i	0.834357	−	0.551225i	$-0.185839\pi$
$607$	1.57170e15	+	9.07420e14i	0.774160	+	0.446962i	−0.0601964	+	0.998187i	$0.519173\pi$
$608$	1.75389e14			0.0856115
$609$	−1.21808e15	−	2.64202e15i	−0.589225	−	1.27803i
$610$	−5.90153e14			−0.282911
$611$	−1.61056e15	−	9.29855e14i	−0.765154	−	0.441762i
$612$	6.60107e13	+	4.81879e14i	0.0310800	+	0.226885i
$613$	7.13243e14	+	1.23537e15i	0.332816	+	0.576455i	0.983063	−	0.183268i	$-0.0586678\pi$
$613$	7.13243e14	+	1.23537e15i	0.332816	+	0.576455i	−0.650247	+	0.759723i	$0.725334\pi$
$614$	−7.84003e14	+	1.35793e15i	−0.362570	+	0.627989i
$615$	−3.11631e12	+	1.58841e13i	−0.00142833	+	0.00728031i
$616$	5.74903e14	+	7.95613e14i	0.261156	+	0.361416i
$617$			4.26804e15i			1.92158i	0.277269	+	0.960792i	$0.410571\pi$
$617$			4.26804e15i			1.92158i	−0.277269	+	0.960792i	$0.589429\pi$
$618$	−2.23426e15	−	1.94906e15i	−0.997005	−	0.869740i
$619$	5.16844e14	−	2.98400e14i	0.228592	−	0.131978i	−0.381330	−	0.924439i	$-0.624534\pi$
$619$	5.16844e14	−	2.98400e14i	0.228592	−	0.131978i	0.609922	+	0.792461i	$0.291201\pi$
$620$	2.31850e14	−	1.33858e14i	0.101637	−	0.0586802i
$621$	−1.18984e14	+	5.98432e13i	−0.0516992	+	0.0260023i
$622$		−	8.99152e13i		−	0.0387245i
$623$	−1.31488e15	+	2.93279e15i	−0.561307	+	1.25198i
$624$	3.53727e14	+	6.93980e13i	0.149676	+	0.0293651i
$625$	−5.07259e14	+	8.78598e14i	−0.212760	+	0.368511i
$626$	−1.05609e15	−	1.82921e15i	−0.439080	−	0.760509i
$627$	1.40213e15	−	4.80059e14i	0.577853	−	0.197844i
$628$	−1.71047e15	−	9.87541e14i	−0.698776	−	0.403438i
$629$	1.10288e15			0.446632
$630$	−2.24797e14	+	7.66348e14i	−0.0902437	+	0.307647i
$631$	−2.11081e15			−0.840014			−0.420007	−	0.907521i	$-0.637972\pi$
$631$	−2.11081e15			−0.840014			−0.420007	+	0.907521i	$0.637972\pi$
$632$	1.02461e15	+	5.91560e14i	0.404218	+	0.233375i
$633$	2.38210e14	−	8.15578e13i	0.0931620	−	0.0318967i
$634$	1.49670e15	+	2.59236e15i	0.580289	+	1.00509i
$635$	−5.67909e14	+	9.83647e14i	−0.218285	+	0.378080i
$636$	1.96136e15	+	3.84800e14i	0.747383	+	0.146629i
$637$	3.27594e14	+	1.58146e15i	0.123757	+	0.597436i
$638$			3.35098e15i			1.25504i
$639$	−1.86181e15	−	2.40021e15i	−0.691321	−	0.891240i
$640$	9.42774e13	−	5.44311e13i	0.0347070	−	0.0200381i
$641$	−1.51064e15	+	8.72167e14i	−0.551368	+	0.318332i	−0.749673	−	0.661808i	$-0.769789\pi$
$641$	−1.51064e15	+	8.72167e14i	−0.551368	+	0.318332i	0.198306	+	0.980140i	$0.436456\pi$
$642$	−2.05481e15	−	1.79252e15i	−0.743582	−	0.648666i
$643$		−	2.90640e15i		−	1.04278i	−0.853317	−	0.521392i	$-0.825413\pi$
$643$		−	2.90640e15i		−	1.04278i	0.853317	−	0.521392i	$-0.174587\pi$
$644$	8.29256e12	+	8.09144e13i	0.00294996	+	0.0287842i
$645$	1.62698e13	−	8.29283e13i	0.00573856	−	0.0292499i
$646$	2.24240e14	−	3.88395e14i	0.0784213	−	0.135830i
$647$	1.19564e15	+	2.07091e15i	0.414597	+	0.718104i	0.995386	−	0.0959505i	$-0.0305891\pi$
$647$	1.19564e15	+	2.07091e15i	0.414597	+	0.718104i	−0.580789	+	0.814054i	$0.697256\pi$
$648$	9.95990e14	+	2.55720e14i	0.342446	+	0.0879230i
$649$	1.94362e15	+	1.12215e15i	0.662623	+	0.382565i
$650$	−1.01385e15			−0.342728
$651$	8.91297e14	−	1.26123e15i	0.298763	−	0.422766i
$652$	−1.09843e15			−0.365097
$653$	−1.60365e15	−	9.25869e14i	−0.528552	−	0.305160i	0.211875	−	0.977297i	$-0.432043\pi$
$653$	−1.60365e15	−	9.25869e14i	−0.528552	−	0.305160i	−0.740427	+	0.672137i	$0.765376\pi$
$654$	7.21369e14	+	2.10693e15i	0.235765	+	0.688610i
$655$	−1.10991e15	−	1.92242e15i	−0.359716	−	0.623046i
$656$	6.36415e12	−	1.10230e13i	0.00204536	−	0.00354266i
$657$	2.75121e13	−	6.74169e13i	0.00876827	−	0.0214862i
$658$	−2.62606e15	+	1.89757e15i	−0.829968	+	0.599728i
$659$			3.93497e15i			1.23331i	0.787234	+	0.616655i	$0.211513\pi$
$659$			3.93497e15i			1.23331i	−0.787234	+	0.616655i	$0.788487\pi$
$660$	6.04708e14	−	6.93192e14i	0.187955	−	0.215458i
$661$	3.45487e15	−	1.99467e15i	1.06494	−	0.614841i	0.138142	−	0.990412i	$-0.455887\pi$
$661$	3.45487e15	−	1.99467e15i	1.06494	−	0.614841i	0.926793	+	0.375572i	$0.122554\pi$
$662$	−1.28938e15	+	7.44425e14i	−0.394151	+	0.227563i
$663$	6.05932e14	−	6.94595e14i	0.183696	−	0.210575i
$664$			3.63722e14i			0.109357i
$665$	5.96886e14	−	4.31305e14i	0.177980	−	0.128607i
$666$	8.81001e14	−	2.15885e15i	0.260536	−	0.638430i
$667$	−1.38838e14	+	2.40474e14i	−0.0407207	+	0.0705304i
$668$	−8.76035e13	−	1.51734e14i	−0.0254830	−	0.0441379i
$669$	6.88038e13	+	2.00958e14i	0.0198504	+	0.0579779i
$670$	−8.65597e14	−	4.99753e14i	−0.247688	−	0.143003i
$671$	3.92127e15			1.11289
$672$	3.62429e14	−	5.12857e14i	0.102022	−	0.144366i
$673$	3.79236e15			1.05883			0.529415	−	0.848363i	$-0.322411\pi$
$673$	3.79236e15			1.05883			0.529415	+	0.848363i	$0.322411\pi$
$674$	−2.15573e15	−	1.24461e15i	−0.596988	−	0.344671i
$675$	−2.88735e15	−	1.66470e14i	−0.793101	−	0.0457261i
$676$	5.76019e14	+	9.97694e14i	0.156939	+	0.271826i
$677$	3.26857e15	−	5.66133e15i	0.883324	−	1.52996i	0.0357008	−	0.999363i	$-0.488634\pi$
$677$	3.26857e15	−	5.66133e15i	0.883324	−	1.52996i	0.847623	−	0.530599i	$-0.178033\pi$
$678$	4.91813e14	−	2.50681e15i	0.131837	−	0.671984i
$679$	−5.26516e14	−	5.13747e15i	−0.140000	−	1.36605i
$680$		−	2.78367e14i		−	0.0734208i
$681$	1.88671e15	+	1.64587e15i	0.493623	+	0.430614i
$682$	−1.54053e15	+	8.89423e14i	−0.399811	+	0.230831i
$683$	−3.74115e14	+	2.15995e14i	−0.0963144	+	0.0556072i	−0.547384	−	0.836882i	$-0.684376\pi$
$683$	−3.74115e14	+	2.15995e14i	−0.0963144	+	0.0556072i	0.451069	+	0.892489i	$0.351043\pi$
$684$	−5.81142e14	−	7.49199e14i	−0.148414	−	0.191332i
$685$		−	3.01357e15i		−	0.763455i
$686$	2.74752e15	+	6.06360e14i	0.690491	+	0.152387i
$687$	−2.90499e15	−	5.69931e14i	−0.724240	−	0.142089i
$688$	−3.32262e13	+	5.75494e13i	−0.00821758	+	0.0142333i
$689$	−1.89393e15	−	3.28039e15i	−0.464686	−	0.804859i
$690$	7.21156e13	−	2.46908e13i	0.0175533	−	0.00600988i
$691$	−1.78510e15	−	1.03063e15i	−0.431055	−	0.248870i	0.268741	−	0.963212i	$-0.413392\pi$
$691$	−1.78510e15	−	1.03063e15i	−0.431055	−	0.248870i	−0.699796	+	0.714343i	$0.746726\pi$
$692$	1.68339e15			0.403276
$693$	1.49366e15	−	5.09200e15i	0.354993	−	1.21020i
$694$	1.10662e15			0.260928
$695$	−1.26763e14	−	7.31867e13i	−0.0296535	−	0.0171205i
$696$	2.02829e15	−	6.94441e14i	0.470737	−	0.161170i
$697$	−1.62735e13	−	2.81866e13i	−0.00374715	−	0.00649025i
$698$	9.45411e14	−	1.63750e15i	0.215981	−	0.374090i
$699$	−1.46303e15	−	2.87032e14i	−0.331610	−	0.0650587i
$700$	−7.22587e14	+	1.61171e15i	−0.162499	+	0.362449i
$701$			1.84483e15i			0.411630i	0.978591	+	0.205815i	$0.0659845\pi$
$701$			1.84483e15i			0.411630i	−0.978591	+	0.205815i	$0.934015\pi$
$702$	−8.75614e14	−	1.74094e15i	−0.193847	−	0.385417i
$703$	−1.86196e15	+	1.07500e15i	−0.408993	+	0.236132i
$704$	−6.26426e14	+	3.61667e14i	−0.136528	+	0.0788243i
$705$	2.28800e15	+	1.99594e15i	0.494784	+	0.431627i
$706$			5.57019e15i			1.19521i
$707$	−2.45368e15	−	3.39567e15i	−0.522410	−	0.722967i
$708$	2.76430e14	−	1.40899e15i	0.0583986	−	0.297663i
$709$	−1.53495e15	+	2.65862e15i	−0.321766	+	0.557316i	−0.980853	−	0.194752i	$-0.937610\pi$
$709$	−1.53495e15	+	2.65862e15i	−0.321766	+	0.557316i	0.659086	+	0.752067i	$0.270943\pi$
$710$	8.69264e14	+	1.50561e15i	0.180813	+	0.313178i
$711$	−8.68066e14	−	6.33689e15i	−0.179172	−	1.30796i
$712$	−2.05114e15	−	1.18422e15i	−0.420102	−	0.242546i
$713$	−1.47402e14			−0.0299579
$714$	−6.72335e14	−	1.45830e15i	−0.135595	−	0.294107i
$715$	−1.74329e15			−0.348888
$716$	1.60957e15	+	9.29287e14i	0.319660	+	0.184556i
$717$	1.13917e15	+	3.32723e15i	0.224509	+	0.655734i
$718$	9.55541e14	+	1.65505e15i	0.186881	+	0.323687i
$719$	−4.14263e14	+	7.17525e14i	−0.0804022	+	0.139261i	−0.903423	−	0.428751i	$-0.858954\pi$
$719$	−4.14263e14	+	7.17525e14i	−0.0804022	+	0.139261i	0.823021	+	0.568012i	$0.192287\pi$
$720$	−5.44893e14	−	2.22365e14i	−0.104950	−	0.0428289i
$721$	8.93231e15	+	4.00468e15i	1.70734	+	0.765462i
$722$		−	2.85340e15i		−	0.541263i
$723$	−3.54296e15	+	4.06139e15i	−0.666969	+	0.764564i
$724$	−9.64298e14	+	5.56738e14i	−0.180156	+	0.104013i
$725$	−5.22194e15	+	3.01489e15i	−0.968218	+	0.559001i
$726$	−1.49190e15	+	1.71020e15i	−0.274529	+	0.314699i
$727$			3.83160e15i			0.699747i	0.936797	+	0.349873i	$0.113775\pi$
$727$			3.83160e15i			0.699747i	−0.936797	+	0.349873i	$0.886225\pi$
$728$	−1.18392e15	+	1.21335e14i	−0.214586	+	0.0219919i
$729$	−2.20782e15	−	5.10183e15i	−0.397157	−	0.917751i
$730$	−2.08368e13	+	3.60904e13i	−0.00372011	+	0.00644342i
$731$	8.49614e13	+	1.47157e14i	0.0150548	+	0.0260757i
$732$	−8.12626e14	−	2.37347e15i	−0.142916	−	0.417420i
$733$	7.83714e15	+	4.52477e15i	1.36800	+	0.789814i	0.990672	−	0.136267i	$-0.0435103\pi$
$733$	7.83714e15	+	4.52477e15i	1.36800	+	0.789814i	0.377326	+	0.926081i	$0.376844\pi$
$734$	2.14514e14			0.0371645
$735$	−2.77594e13	−	2.63662e15i	−0.00477342	−	0.453386i
$736$	−5.99384e13			−0.0102300
$737$	5.75146e15	+	3.32061e15i	0.974333	+	0.562531i
$738$	−6.81737e13	+	9.33886e12i	−0.0114632	+	0.00157030i
$739$	−1.94003e15	−	3.36023e15i	−0.323791	−	0.560822i	0.657476	−	0.753475i	$-0.271624\pi$
$739$	−1.94003e15	−	3.36023e15i	−0.323791	−	0.560822i	−0.981267	+	0.192653i	$0.938291\pi$
$740$	−6.67243e14	+	1.15570e15i	−0.110537	+	0.191457i
$741$	−3.45939e14	+	1.76328e15i	−0.0568851	+	0.289948i
$742$	−6.56466e15	+	6.72783e14i	−1.07150	+	0.109813i
$743$		−	6.76994e15i		−	1.09685i	−0.836200	−	0.548424i	$-0.815228\pi$
$743$		−	6.76994e15i		−	1.09685i	0.836200	−	0.548424i	$-0.184772\pi$
$744$	8.57603e14	+	7.48132e14i	0.137922	+	0.120317i
$745$	−4.36076e15	+	2.51769e15i	−0.696150	+	0.401922i
$746$	−4.93157e14	+	2.84724e14i	−0.0781487	+	0.0451192i
$747$	1.55369e15	−	1.20517e15i	0.244400	−	0.189577i
$748$			1.84961e15i			0.288816i
$749$	8.21488e15	+	3.68303e15i	1.27336	+	0.570894i
$750$	3.66890e15	+	7.19804e14i	0.564546	+	0.110759i
$751$	5.59963e15	−	9.69885e15i	0.855342	−	1.48150i	−0.0209854	−	0.999780i	$-0.506680\pi$
$751$	5.59963e15	−	9.69885e15i	0.855342	−	1.48150i	0.876327	−	0.481716i	$-0.159986\pi$
$752$	−1.19375e15	−	2.06763e15i	−0.181015	−	0.313527i
$753$	8.72294e15	−	2.98655e15i	1.31308	−	0.449569i
$754$	−3.51857e15	−	2.03145e15i	−0.525803	−	0.303573i
$755$	2.86836e15			0.425526
$756$	−3.39163e15	+	1.51156e14i	−0.499504	+	0.0222616i
$757$	8.91438e15			1.30336			0.651679	−	0.758495i	$-0.274065\pi$
$757$	8.91438e15			1.30336			0.651679	+	0.758495i	$0.274065\pi$
$758$	3.75387e15	+	2.16730e15i	0.544877	+	0.314585i
$759$	−4.79173e14	+	1.64058e14i	−0.0690498	+	0.0236411i
$760$	2.71331e14	+	4.69959e14i	0.0388172	+	0.0672334i
$761$	3.69763e14	−	6.40448e14i	0.0525179	−	0.0909637i	−0.838571	−	0.544792i	$-0.816609\pi$
$761$	3.69763e14	−	6.40448e14i	0.0525179	−	0.0909637i	0.891089	+	0.453828i	$0.149942\pi$
$762$	−4.73803e15	−	9.29556e14i	−0.668106	−	0.131076i
$763$	−4.30635e15	−	5.95959e15i	−0.602871	−	0.834317i
$764$		−	2.45997e15i		−	0.341914i
$765$	−1.18909e15	+	9.22355e14i	−0.164087	+	0.127280i
$766$	3.90130e15	−	2.25242e15i	0.534504	−	0.308596i
$767$	−2.35654e15	+	1.36055e15i	−0.320554	+	0.185072i
$768$	3.48728e14	+	3.04214e14i	0.0470978	+	0.0410859i
$769$			1.69537e15i			0.227337i	0.993519	+	0.113668i	$0.0362601\pi$
$769$			1.69537e15i			0.227337i	−0.993519	+	0.113668i	$0.963740\pi$
$770$	−1.24247e15	+	2.77130e15i	−0.165420	+	0.368964i
$771$	−2.48496e15	+	1.26660e16i	−0.328488	+	1.67433i
$772$	2.88887e15	−	5.00367e15i	0.379169	−	0.656741i
$773$	−4.38701e15	−	7.59853e15i	−0.571718	−	0.990244i	−0.996390	−	0.0848971i	$-0.972944\pi$
$773$	−4.38701e15	−	7.59853e15i	−0.571718	−	0.990244i	0.424672	−	0.905347i	$-0.360389\pi$
$774$	3.55924e14	−	4.87567e13i	0.0460555	−	0.00630897i
$775$	−2.77204e15	−	1.60044e15i	−0.356155	−	0.205626i
$776$	3.80565e15			0.485500
$777$	−7.04184e14	+	7.66600e15i	−0.0892011	+	0.971076i
$778$	7.39941e15			0.930699
$779$	5.49482e13	+	3.17243e13i	0.00686273	+	0.00396220i
$780$	3.61271e14	+	1.05518e15i	0.0448036	+	0.130860i
$781$	−5.77583e15	−	1.00040e16i	−0.711268	−	1.23195i
$782$	−7.66331e13	+	1.32732e14i	−0.00937086	+	0.0162308i
$783$	−9.68702e15	−	6.36312e15i	−1.17625	−	0.772646i
$784$	−6.50918e14	+	1.96855e15i	−0.0784852	+	0.237361i
$785$		−	6.11100e15i		−	0.731693i
$786$	6.20325e15	−	7.11094e15i	0.737556	−	0.845480i
$787$	−1.35434e16	+	7.81931e15i	−1.59907	+	0.923225i	−0.607407	+	0.794391i	$0.707790\pi$
$787$	−1.35434e16	+	7.81931e15i	−1.59907	+	0.923225i	−0.991666	+	0.128834i	$0.958877\pi$
$788$	4.80000e14	−	2.77128e14i	0.0562791	−	0.0324928i
$789$	−1.03641e16	+	1.18806e16i	−1.20672	+	1.38330i
$790$			3.66063e15i			0.423260i
$791$	8.59883e14	+	8.39029e15i	0.0987344	+	0.963399i
$792$	3.62055e15	+	1.47750e15i	0.412844	+	0.168477i
$793$	−2.37717e15	+	4.11738e15i	−0.269190	+	0.466250i
$794$	−4.58793e15	−	7.94652e15i	−0.515945	−	0.893643i
$795$	2.00319e15	+	5.85081e15i	0.223719	+	0.653426i
$796$	5.08489e15	+	2.93576e15i	0.563974	+	0.325611i
$797$	−1.04077e16			−1.14639			−0.573196	−	0.819418i	$-0.694297\pi$
$797$	−1.04077e16			−1.14639			−0.573196	+	0.819418i	$0.694297\pi$
$798$	2.55652e15	+	1.80666e15i	0.279661	+	0.197633i
$799$	−6.10496e15			−0.663247
$800$	−1.12720e15	−	6.50788e14i	−0.121620	−	0.0702173i
$801$	1.73775e15	+	1.26856e16i	0.186212	+	1.35935i
$802$	−1.61894e15	−	2.80409e15i	−0.172295	−	0.298423i
$803$	1.38450e14	−	2.39803e14i	0.0146338	−	0.0253466i
$804$	8.17997e14	−	4.16940e15i	0.0858704	−	0.437689i
$805$	−2.03983e14	+	1.47397e14i	−0.0212675	+	0.0153677i
$806$		−	2.15676e15i		−	0.223336i
$807$	7.03027e15	+	6.13288e15i	0.723049	+	0.630754i
$808$	2.67358e15	−	1.54359e15i	0.273106	−	0.157678i
$809$	−4.93140e15	+	2.84715e15i	−0.500327	+	0.288864i	−0.728849	−	0.684675i	$-0.759944\pi$
$809$	−4.93140e15	+	2.84715e15i	−0.500327	+	0.288864i	0.228522	+	0.973539i	$0.426611\pi$
$810$	8.55613e14	+	3.06439e15i	0.0862203	+	0.308799i
$811$		−	9.45803e14i		−	0.0946643i	−0.998879	−	0.0473321i	$-0.984928\pi$
$811$		−	9.45803e14i		−	0.0946643i	0.998879	−	0.0473321i	$-0.0150719\pi$
$812$	−5.73712e15	+	4.14560e15i	−0.570343	+	0.412125i
$813$	3.17974e14	+	6.23834e13i	0.0313973	+	0.00615986i
$814$	4.43350e15	−	7.67905e15i	0.434823	−	0.753135i
$815$	−1.69929e15	−	2.94326e15i	−0.165539	−	0.286722i
$816$	1.11954e15	−	3.83305e14i	0.108328	−	0.0370893i
$817$	−2.86875e14	−	1.65628e14i	−0.0275722	−	0.0159188i
$818$	9.65350e14			0.0921598
$819$	4.44117e15	+	4.65526e15i	0.421149	+	0.441451i
$820$	3.93820e13			0.00370955
$821$	7.74329e15	+	4.47059e15i	0.724500	+	0.418290i	0.816407	−	0.577477i	$-0.195963\pi$
$821$	7.74329e15	+	4.47059e15i	0.724500	+	0.418290i	−0.0919069	+	0.995768i	$0.529296\pi$
$822$	1.21200e16	−	4.14961e15i	1.12644	−	0.385667i
$823$	1.41041e15	+	2.44290e15i	0.130211	+	0.225532i	0.923758	−	0.382977i	$-0.125101\pi$
$823$	1.41041e15	+	2.44290e15i	0.130211	+	0.225532i	−0.793547	+	0.608509i	$0.791768\pi$
$824$	−3.60676e15	+	6.24709e15i	−0.330763	+	0.572899i
$825$	−1.07926e16	−	2.11740e15i	−0.983168	−	0.192888i
$826$	4.83309e14	+	4.71587e15i	0.0437355	+	0.426748i
$827$		−	1.02778e16i		−	0.923892i	−0.886908	−	0.461946i	$-0.847151\pi$
$827$		−	1.02778e16i		−	0.923892i	0.886908	−	0.461946i	$-0.152849\pi$
$828$	1.98603e14	+	2.56036e14i	0.0177345	+	0.0228630i
$829$	3.47305e15	−	2.00517e15i	0.308079	−	0.177869i	−0.337988	−	0.941151i	$-0.609746\pi$
$829$	3.47305e15	−	2.00517e15i	0.308079	−	0.177869i	0.646066	+	0.763281i	$0.276413\pi$
$830$	−9.74602e14	+	5.62687e14i	−0.0858811	+	0.0495835i
$831$	8.27996e15	+	7.22305e15i	0.724808	+	0.632288i
$832$		−	8.77007e14i		−	0.0762649i
$833$	3.52710e15	+	3.95830e15i	0.304699	+	0.341949i
$834$	1.19792e14	−	6.10591e14i	0.0102805	−	0.0524007i
$835$	2.71050e14	−	4.69472e14i	0.0231086	−	0.0400252i
$836$	−1.80286e15	−	3.12264e15i	−0.152696	−	0.264477i
$837$	3.54132e14	−	6.14227e15i	0.0297972	−	0.516820i
$838$	1.99735e15	+	1.15317e15i	0.166960	+	0.0963942i
$839$	−1.72783e16			−1.43487			−0.717433	−	0.696628i	$-0.754683\pi$
$839$	−1.72783e16			−1.43487			−0.717433	+	0.696628i	$0.754683\pi$
$840$	1.93490e15	+	1.77736e14i	0.159633	+	0.0146636i
$841$	−1.19632e16			−0.980552
$842$	−4.61431e15	−	2.66407e15i	−0.375743	−	0.216935i
$843$	6.79746e15	+	1.98536e16i	0.549914	+	1.60616i
$844$	−3.06290e14	−	5.30509e14i	−0.0246178	−	0.0426393i
$845$	−1.78223e15	+	3.08691e15i	−0.142315	+	0.246497i
$846$	−4.87676e15	+	1.19502e16i	−0.386896	+	0.948068i
$847$	3.06535e15	−	6.83717e15i	0.241614	−	0.538911i
$848$		−	4.86286e15i		−	0.380815i
$849$	−1.42699e16	+	1.63579e16i	−1.11027	+	1.27273i
$850$	−2.88231e15	+	1.66410e15i	−0.222811	+	0.128640i
$851$	6.36317e14	−	3.67378e14i	0.0488721	−	0.0282163i
$852$	−4.85830e15	+	5.56919e15i	−0.370737	+	0.424985i
$853$		−	1.34570e16i		−	1.02030i	−0.860086	−	0.510149i	$-0.829590\pi$
$853$		−	1.34570e16i		−	1.02030i	0.860086	−	0.510149i	$-0.170410\pi$
$854$	4.85113e15	+	6.71351e15i	0.365447	+	0.505745i
$855$	1.10846e15	−	2.71621e15i	0.0829669	−	0.203306i
$856$	−3.31707e15	+	5.74533e15i	−0.246688	+	0.427277i
$857$	−5.92315e13	−	1.02592e14i	−0.00437682	−	0.00758087i	0.863829	−	0.503786i	$-0.168060\pi$
$857$	−5.92315e13	−	1.02592e14i	−0.00437682	−	0.00758087i	−0.868206	+	0.496205i	$0.834727\pi$
$858$	−2.40047e15	−	7.01116e15i	−0.176245	−	0.514766i
$859$	2.15298e16	+	1.24303e16i	1.57065	+	0.906813i	0.996090	+	0.0883473i	$0.0281585\pi$
$859$	2.15298e16	+	1.24303e16i	1.57065	+	0.906813i	0.574556	+	0.818465i	$0.305175\pi$
$860$	−2.05607e14			−0.0149038
$861$	2.06312e14	−	9.51185e13i	0.0148596	−	0.00685090i
$862$	−8.60098e15			−0.615542
$863$	1.80612e16	+	1.04276e16i	1.28436	+	0.741525i	0.977642	−	0.210276i	$-0.0674363\pi$
$863$	1.80612e16	+	1.04276e16i	1.28436	+	0.741525i	0.306716	+	0.951801i	$0.400770\pi$
$864$	1.44001e14	−	2.49764e15i	0.0101751	−	0.176484i
$865$	2.60425e15	+	4.51070e15i	0.182850	+	0.316705i
$866$	8.68155e15	−	1.50369e16i	0.605688	−	1.04908i
$867$	−2.19450e15	+	1.11855e16i	−0.152135	+	0.775447i
$868$	−3.42859e15	−	1.53716e15i	−0.236188	−	0.105892i
$869$		−	2.43231e16i		−	1.66498i
$870$	4.99858e15	+	4.36052e15i	0.340009	+	0.296608i
$871$	−6.97336e15	+	4.02607e15i	−0.471349	+	0.272133i
$872$	4.69229e15	−	2.70909e15i	0.315169	−	0.181963i
$873$	−1.26098e16	−	1.62564e16i	−0.841648	−	1.08504i
$874$		−	2.98784e14i		−	0.0198173i
$875$	−1.22798e16	+	1.25850e15i	−0.809370	+	0.0829487i
$876$	−1.73840e14	−	3.41058e13i	−0.0113862	−	0.00223386i
$877$	7.42261e15	−	1.28563e16i	0.483124	−	0.836795i	−0.516688	−	0.856174i	$-0.672835\pi$
$877$	7.42261e15	−	1.28563e16i	0.483124	−	0.836795i	0.999812	+	0.0193782i	$0.00616867\pi$
$878$	4.46846e15	+	7.73959e15i	0.289027	+	0.500609i
$879$	2.27529e16	−	7.79009e15i	1.46251	−	0.500730i
$880$	−1.93819e15	−	1.11902e15i	−0.123806	−	0.0714795i
$881$	1.67500e16			1.06328			0.531638	−	0.846971i	$-0.321577\pi$
$881$	1.67500e16			1.06328			0.531638	+	0.846971i	$0.321577\pi$
$882$	1.05657e16	−	3.74221e15i	0.666535	−	0.236075i
$883$	−1.50678e16			−0.944639			−0.472320	−	0.881427i	$-0.656583\pi$
$883$	−1.50678e16			−0.944639			−0.472320	+	0.881427i	$0.656583\pi$
$884$	−1.94211e15	−	1.12128e15i	−0.121001	−	0.0698597i
$885$	4.20306e15	−	1.43904e15i	0.260242	−	0.0891013i
$886$	3.77417e15	+	6.53706e15i	0.232240	+	0.402251i
$887$	1.42113e16	−	2.46148e16i	0.869071	−	1.50528i	0.00612358	−	0.999981i	$-0.498051\pi$
$887$	1.42113e16	−	2.46148e16i	0.869071	−	1.50528i	0.862947	−	0.505294i	$-0.168616\pi$
$888$	−5.56676e15	−	1.09215e15i	−0.338323	−	0.0663757i
$889$	1.58581e16	−	1.62523e15i	0.957839	−	0.0981647i
$890$		−	7.32809e15i		−	0.439892i
$891$	−5.68512e15	−	2.03613e16i	−0.339166	−	1.21473i
$892$	4.47548e14	−	2.58392e14i	0.0265359	−	0.0153205i
$893$	1.03068e16	−	5.95064e15i	0.607354	−	0.350656i
$894$	−1.61303e16	−	1.40713e16i	−0.944682	−	0.824096i
$895$			5.75051e15i			0.334719i
$896$	−1.39417e15	−	6.25059e14i	−0.0806534	−	0.0361599i
$897$	1.18223e14	−	6.02593e14i	0.00679742	−	0.0346470i
$898$	−9.26183e14	+	1.60420e15i	−0.0529269	+	0.0916722i
$899$	−6.41359e15	−	1.11087e16i	−0.364269	−	0.630933i
$900$	9.54977e14	+	6.97134e15i	0.0539087	+	0.393534i
$901$	−1.07687e16	−	6.21731e15i	−0.604195	−	0.348832i
$902$	−2.61674e14			−0.0145923
$903$	−1.07712e15	+	4.96598e14i	−0.0597011	+	0.0275247i
$904$	−6.21522e15			−0.342397
$905$	−2.98358e15	−	1.72257e15i	−0.163370	−	0.0943214i
$906$	3.94966e15	+	1.15360e16i	0.214959	+	0.627840i
$907$	7.98610e15	+	1.38323e16i	0.432011	+	0.748265i	0.997046	−	0.0768015i	$-0.0244708\pi$
$907$	7.98610e15	+	1.38323e16i	0.432011	+	0.748265i	−0.565035	+	0.825067i	$0.691137\pi$
$908$	3.04570e15	−	5.27531e15i	0.163763	−	0.283645i
$909$	−1.54525e16	−	6.30598e15i	−0.825841	−	0.337016i
$910$	−2.15668e15	−	2.98464e15i	−0.114566	−	0.158549i
$911$		−	2.26807e16i		−	1.19758i	−0.800905	−	0.598791i	$-0.795648\pi$
$911$		−	2.26807e16i		−	1.19758i	0.800905	−	0.598791i	$-0.204352\pi$
$912$	−1.51646e15	+	1.73836e15i	−0.0795902	+	0.0912363i
$913$	6.47575e15	−	3.73877e15i	0.337832	−	0.195047i
$914$	−1.44330e16	+	8.33290e15i	−0.748432	+	0.432108i
$915$	5.10263e15	−	5.84927e15i	0.263014	−	0.301499i
$916$			7.20243e15i			0.369023i
$917$	−1.27456e16	+	2.84287e16i	−0.649127	+	1.44786i
$918$	−5.34687e15	−	3.51220e15i	−0.270685	−	0.177805i
$919$	7.66590e14	−	1.32777e15i	0.0385769	−	0.0668172i	−0.846092	−	0.533036i	$-0.821051\pi$
$919$	7.66590e14	−	1.32777e15i	0.0385769	−	0.0668172i	0.884669	+	0.466219i	$0.154384\pi$
$920$	−9.27262e13	−	1.60606e14i	−0.00463841	−	0.00803397i
$921$	−6.68037e15	−	1.95117e16i	−0.332179	−	0.970212i
$922$	−7.25623e15	−	4.18938e15i	−0.358666	−	0.207076i
$923$	1.40058e16			0.688174
$924$	−1.28565e16	−	1.18097e15i	−0.627950	−	0.0576823i
$925$	1.59554e16			0.774688
$926$	9.95982e15	+	5.75030e15i	0.480719	+	0.277543i
$927$	3.86361e16	−	5.29262e15i	1.85377	−	0.253940i
$928$	−2.60797e15	−	4.51713e15i	−0.124391	−	0.215451i
$929$	−2.70623e14	+	4.68732e14i	−0.0128315	+	0.0222248i	−0.872370	−	0.488846i	$-0.837418\pi$
$929$	−2.70623e14	+	4.68732e14i	−0.0128315	+	0.0222248i	0.859538	+	0.511071i	$0.170751\pi$
$930$	−6.77906e14	+	3.45535e15i	−0.0319531	+	0.162868i
$931$	−9.81294e15	−	3.24473e15i	−0.459807	−	0.152039i
$932$			3.62732e15i			0.168966i
$933$	8.91190e14	+	7.77432e14i	0.0412687	+	0.0360009i
$934$	−3.11392e15	+	1.79783e15i	−0.143351	+	0.0827637i
$935$	−4.95608e15	+	2.86139e15i	−0.226816	+	0.130952i
$936$	−3.74626e15	+	2.90592e15i	−0.170444	+	0.132211i
$937$			1.56066e15i			0.0705897i	0.999377	+	0.0352949i	$0.0112370\pi$
$937$			1.56066e15i			0.0705897i	−0.999377	+	0.0352949i	$0.988763\pi$
$938$	1.43018e15	+	1.39550e16i	0.0643096	+	0.627499i
$939$	2.72614e16	+	5.34843e15i	1.21867	+	0.239092i
$940$	3.69351e15	−	6.39734e15i	0.164148	−	0.284313i
$941$	−1.26365e16	−	2.18871e16i	−0.558323	−	0.967043i	−0.997637	−	0.0687095i	$-0.978112\pi$
$941$	−1.26365e16	−	2.18871e16i	−0.558323	−	0.967043i	0.439314	−	0.898333i	$-0.355221\pi$
$942$	2.45772e16	−	8.41469e15i	1.07957	−	0.369622i
$943$	−1.87783e13	−	1.08417e13i	−0.000820054	−	0.000473458i
$944$	−3.49335e15			−0.151669
$945$	−5.65197e15	−	8.85412e15i	−0.243963	−	0.382182i
$946$	1.36616e15			0.0586272
$947$	1.78413e16	+	1.03007e16i	0.761205	+	0.439482i	0.829728	−	0.558168i	$-0.188495\pi$
$947$	1.78413e16	+	1.03007e16i	0.761205	+	0.439482i	−0.0685235	+	0.997649i	$0.521829\pi$
$948$	−1.47223e16	+	5.04060e15i	−0.624497	+	0.213814i
$949$	1.67864e14	+	2.90749e14i	0.00707935	+	0.0122618i
$950$	3.24408e15	−	5.61891e15i	0.136023	−	0.235598i
$951$	−3.86350e16	−	7.57982e15i	−1.61060	−	0.315985i
$952$	−3.16667e15	+	2.28821e15i	−0.131250	+	0.0948403i
$953$			1.35601e16i			0.558794i	0.960176	+	0.279397i	$0.0901346\pi$
$953$			1.35601e16i			0.558794i	−0.960176	+	0.279397i	$0.909865\pi$
$954$	−2.07724e16	+	1.61128e16i	−0.851081	+	0.660170i
$955$	6.59156e15	−	3.80564e15i	0.268516	−	0.155028i
$956$	7.40997e15	−	4.27815e15i	0.300122	−	0.173276i
$957$	−3.32131e16	−	2.89735e16i	−1.33750	−	1.16677i
$958$		−	1.63405e16i		−	0.654268i
$959$	−3.42820e16	+	2.47719e16i	−1.36478	+	0.986182i
$960$	−2.75658e14	+	1.40505e15i	−0.0109114	+	0.0556161i
$961$	−9.29963e15	+	1.61074e16i	−0.366005	+	0.633939i
$962$	5.37539e15	+	9.31045e15i	0.210352	+	0.364341i
$963$	3.55329e16	−	4.86752e15i	1.38257	−	0.189393i
$964$	1.13558e16	+	6.55627e15i	0.439333	+	0.253649i
$965$	1.78766e16			0.687678
$966$	−8.73679e14	−	6.17418e14i	−0.0334178	−	0.0236159i
$967$	−2.67580e15			−0.101767			−0.0508836	−	0.998705i	$-0.516204\pi$
$967$	−2.67580e15			−0.101767			−0.0508836	+	0.998705i	$0.516204\pi$
$968$	4.78178e15	+	2.76076e15i	0.180832	+	0.104403i
$969$	1.91072e15	+	5.58072e15i	0.0718481	+	0.209850i
$970$	5.88743e15	+	1.01973e16i	0.220131	+	0.381278i
$971$	3.04352e15	−	5.27153e15i	0.113154	−	0.195989i	−0.803886	−	0.594783i	$-0.797238\pi$
$971$	3.04352e15	−	5.27153e15i	0.113154	−	0.195989i	0.917040	+	0.398794i	$0.130571\pi$
$972$	−1.11462e16	+	7.66068e15i	−0.412061	+	0.283206i
$973$	2.09444e14	+	2.04365e15i	0.00769923	+	0.0751251i
$974$			3.20529e15i			0.117164i
$975$	8.76601e15	−	1.00487e16i	0.318623	−	0.365245i
$976$	−5.28589e15	+	3.05181e15i	−0.191049	+	0.110302i
$977$	−3.67631e16	+	2.12252e16i	−1.32127	+	0.762837i	−0.983932	−	0.178545i	$-0.942861\pi$
$977$	−3.67631e16	+	2.12252e16i	−1.32127	+	0.762837i	−0.337341	+	0.941383i	$0.609528\pi$
$978$	9.49730e15	−	1.08870e16i	0.339419	−	0.389085i
$979$			4.86915e16i			1.73041i
$980$	−6.28177e15	+	1.30125e15i	−0.221993	+	0.0459851i
$981$	−2.71199e16	−	1.10673e16i	−0.953036	−	0.388923i
$982$	−2.46173e15	+	4.26384e15i	−0.0860254	+	0.149000i
$983$	1.96688e16	+	3.40673e16i	0.683491	+	1.18384i	0.973909	+	0.226941i	$0.0728724\pi$
$983$	1.96688e16	+	3.40673e16i	0.683491	+	1.18384i	−0.290418	+	0.956900i	$0.593794\pi$
$984$	5.42280e13	+	1.58386e14i	0.00187392	+	0.00547324i
$985$	1.48514e15	+	8.57448e14i	0.0510351	+	0.0294652i
$986$	−1.33375e16			−0.455775
$987$	3.89799e15	−	4.24349e16i	0.132464	−	1.44205i
$988$	4.37175e15			0.147738
$989$	9.80385e13	+	5.66025e13i	0.00329471	+	0.00190220i
$990$	1.64206e15	+	1.19871e16i	0.0548778	+	0.400608i
$991$	−1.02458e16	−	1.77462e16i	−0.340518	−	0.589795i	0.644011	−	0.765016i	$-0.277269\pi$
$991$	−1.02458e16	−	1.77462e16i	−0.340518	−	0.589795i	−0.984529	+	0.175221i	$0.943936\pi$
$992$	1.38442e15	−	2.39789e15i	0.0457567	−	0.0792529i
$993$	3.77003e15	−	1.92161e16i	0.123915	−	0.631605i
$994$	9.98218e15	−	2.22649e16i	0.326287	−	0.727773i
$995$			1.81668e16i			0.590542i
$996$	−3.60501e15	−	3.14484e15i	−0.116541	−	0.101665i
$997$	4.13523e16	−	2.38748e16i	1.32946	−	0.767567i	0.344247	−	0.938879i	$-0.388134\pi$
$997$	4.13523e16	−	2.38748e16i	1.32946	−	0.767567i	0.985217	+	0.171312i	$0.0548007\pi$
$998$	−1.16433e16	+	6.72226e15i	−0.372270	+	0.214930i
$999$	1.37799e16	+	2.73980e16i	0.438164	+	0.871181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.12.f.a.5.18	yes	60
3.2	odd	2	inner	42.12.f.a.5.3	✓	60
7.3	odd	6	inner	42.12.f.a.17.3	yes	60
21.17	even	6	inner	42.12.f.a.17.18	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.12.f.a.5.3	✓	60	3.2	odd	2	inner
42.12.f.a.5.18	yes	60	1.1	even	1	trivial
42.12.f.a.17.3	yes	60	7.3	odd	6	inner
42.12.f.a.17.18	yes	60	21.17	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	42.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(27.7128 + 16.0000i) q^{2} +(-398.196 + 136.334i) q^{3} +(512.000 + 886.810i) q^{4} +(-1584.15 + 2743.83i) q^{5} +(-13216.5 - 2592.95i) q^{6} +(44235.4 - 4533.49i) q^{7} +32768.0i q^{8} +(139973. - 108575. i) q^{9} +(-87802.6 + 50692.9i) q^{10} +(583405. - 336829. i) q^{11} +(-324778. - 283321. i) q^{12} +816776. i q^{13} +(1.29842e6 + 582131. i) q^{14} +(256726. - 1.30856e6i) q^{15} +(-524288. + 908093. i) q^{16} +(1.34064e6 + 2.32205e6i) q^{17} +(5.61625e6 - 769349. i) q^{18} +(-4.52671e6 - 2.61350e6i) q^{19} -3.24434e6 q^{20} +(-1.69963e7 + 7.83600e6i) q^{21} +2.15571e7 q^{22} +(1.54699e6 + 893152. i) q^{23} +(-4.46738e6 - 1.30481e7i) q^{24} +(1.93950e7 + 3.35931e7i) q^{25} +(-1.30684e7 + 2.26352e7i) q^{26} +(-4.09344e7 + 6.23172e7i) q^{27} +(2.66689e7 + 3.69073e7i) q^{28} +1.55447e8i q^{29} +(2.80515e7 - 3.21562e7i) q^{30} +(-7.14627e7 + 4.12590e7i) q^{31} +(-2.90590e7 + 1.67772e7i) q^{32} +(-1.86388e8 + 2.13662e8i) q^{33} +8.58007e7i q^{34} +(-5.76365e7 + 1.28556e8i) q^{35} +(1.67952e8 + 6.85392e7i) q^{36} +(2.05663e8 - 3.56220e8i) q^{37} +(-8.36319e7 - 1.44855e8i) q^{38} +(-1.11354e8 - 3.25237e8i) q^{39} +(-8.99099e7 - 5.19095e7i) q^{40} -1.21386e7 q^{41} +(-5.96392e8 - 5.47834e7i) q^{42} +6.33739e7 q^{43} +(5.97407e8 + 3.44913e8i) q^{44} +(7.61729e7 + 5.56063e8i) q^{45} +(2.85809e7 + 4.95035e7i) q^{46} +(-1.13844e9 + 1.97184e9i) q^{47} +(8.49657e7 - 4.33077e8i) q^{48} +(1.93622e9 - 4.01082e8i) q^{49} +1.24128e9i q^{50} +(-8.50410e8 - 7.41857e8i) q^{51} +(-7.24325e8 + 4.18189e8i) q^{52} +(-4.01627e9 + 2.31879e9i) q^{53} +(-2.13148e9 + 1.07204e9i) q^{54} +2.13435e9i q^{55} +(1.48554e8 + 1.44951e9i) q^{56} +(2.15883e9 + 4.23541e8i) q^{57} +(-2.48715e9 + 4.30787e9i) q^{58} +(1.66576e9 + 2.88518e9i) q^{59} +(1.29189e9 - 4.42313e8i) q^{60} +(5.04102e9 + 2.91043e9i) q^{61} -2.64058e9 q^{62} +(5.69955e9 - 5.43743e9i) q^{63} -1.07374e9 q^{64} +(-2.24110e9 - 1.29390e9i) q^{65} +(-8.58394e9 + 2.93895e9i) q^{66} +(4.92922e9 + 8.53766e9i) q^{67} +(-1.37281e9 + 2.37778e9i) q^{68} +(-7.37770e8 - 1.44744e8i) q^{69} +(-3.65417e9 + 2.64047e9i) q^{70} -1.71476e10i q^{71} +(3.55779e9 + 4.58664e9i) q^{72} +(3.55971e8 - 2.05520e8i) q^{73} +(1.13990e10 - 6.58123e9i) q^{74} +(-1.23029e10 - 1.07325e10i) q^{75} -5.35244e9i q^{76} +(2.42802e10 - 1.75446e10i) q^{77} +(2.11786e9 - 1.07949e10i) q^{78} +(1.80530e10 - 3.12687e10i) q^{79} +(-1.66110e9 - 2.87712e9i) q^{80} +(7.80396e9 - 3.03952e10i) q^{81} +(-3.36396e8 - 1.94218e8i) q^{82} +1.10999e10 q^{83} +(-1.56512e10 - 1.10605e10i) q^{84} -8.49509e9 q^{85} +(1.75627e9 + 1.01398e9i) q^{86} +(-2.11927e10 - 6.18984e10i) q^{87} +(1.10372e10 + 1.91170e10i) q^{88} +(-3.61396e10 + 6.25957e10i) q^{89} +(-6.78604e9 + 1.66288e10i) q^{90} +(3.70285e9 + 3.61305e10i) q^{91} +1.82918e9i q^{92} +(2.28312e10 - 2.61720e10i) q^{93} +(-6.30990e10 + 3.64302e10i) q^{94} +(1.43420e10 - 8.28036e9i) q^{95} +(9.28388e9 - 1.06423e10i) q^{96} -1.16139e11i q^{97} +(6.00755e10 + 1.98644e10i) q^{98} +(4.50899e10 - 1.10490e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30720 q^{4} - 95298 q^{7} - 91434 q^{9} + 245184 q^{10} - 8480820 q^{15} - 31457280 q^{16} + 12170496 q^{18} + 1649724 q^{19} + 43254216 q^{21} + 20705664 q^{22} + 4521984 q^{24} - 336132444 q^{25}+ \cdots + 288758042496 q^{99}+O(q^{100}) \) 60 * q + 30720 * q^4 - 95298 * q^7 - 91434 * q^9 + 245184 * q^10 - 8480820 * q^15 - 31457280 * q^16 + 12170496 * q^18 + 1649724 * q^19 + 43254216 * q^21 + 20705664 * q^22 + 4521984 * q^24 - 336132444 * q^25 + 28121088 * q^28 - 77109120 * q^30 - 275992974 * q^31 + 1056712914 * q^33 - 187256832 * q^36 + 555437556 * q^37 - 563926680 * q^39 + 251068416 * q^40 + 1167043776 * q^42 + 2546594304 * q^43 + 544480776 * q^45 - 452472192 * q^46 - 1309143414 * q^49 + 2007979044 * q^51 + 3219419136 * q^52 - 9840998592 * q^54 + 17053196256 * q^57 + 12235419456 * q^58 - 4342179840 * q^60 - 3056592000 * q^61 - 42499692960 * q^63 - 64424509440 * q^64 + 48796070400 * q^66 + 27979853436 * q^67 - 4966503360 * q^70 - 12462587904 * q^72 - 105678747168 * q^73 + 173211633504 * q^75 - 16600538880 * q^78 - 27787555926 * q^79 - 71399556486 * q^81 + 31231064832 * q^82 - 25272410112 * q^84 + 12868048152 * q^85 + 137017459998 * q^87 + 10601299968 * q^88 + 333571182180 * q^91 - 14607989424 * q^93 - 430917051648 * q^94 + 4630511616 * q^96 + 288758042496 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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