LMFDB - Embedded newform 42.12.f.a.5.10

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			5.10
Character	$\chi$	$=$	42.5
Dual form			42.12.f.a.17.10

$q$-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} +(142.282 + 396.110i) q^{3} +(512.000 + 886.810i) q^{4} +(-497.386 + 861.497i) q^{5} +(2394.71 - 13253.8i) q^{6} +(43875.4 + 7230.30i) q^{7} -32768.0i q^{8} +(-136659. + 112719. i) q^{9} +(27567.9 - 15916.3i) q^{10} +(679278. - 392181. i) q^{11} +(-278425. + 328985. i) q^{12} -2.21641e6i q^{13} +(-1.10023e6 - 902378. i) q^{14} +(-412016. - 74443.5i) q^{15} +(-524288. + 908093. i) q^{16} +(-1.27277e6 - 2.20450e6i) q^{17} +(5.59069e6 - 937214. i) q^{18} +(8.92235e6 + 5.15132e6i) q^{19} -1.01865e6 q^{20} +(3.37870e6 + 1.84082e7i) q^{21} -2.50996e7 q^{22} +(-4.12803e7 - 2.38332e7i) q^{23} +(1.29797e7 - 4.66230e6i) q^{24} +(2.39193e7 + 4.14294e7i) q^{25} +(-3.54625e7 + 6.14229e7i) q^{26} +(-6.40930e7 - 3.80939e7i) q^{27} +(1.60523e7 + 4.26110e7i) q^{28} +7.25633e6i q^{29} +(1.02270e7 + 8.65530e6i) q^{30} +(2.47090e8 - 1.42657e8i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(2.51996e8 + 2.13268e8i) q^{33} +8.14574e7i q^{34} +(-2.80519e7 + 3.42023e7i) q^{35} +(-1.69929e8 - 6.34782e7i) q^{36} +(-2.56198e7 + 4.43749e7i) q^{37} +(-1.64842e8 - 2.85515e8i) q^{38} +(8.77940e8 - 3.15355e8i) q^{39} +(2.82295e7 + 1.62983e7i) q^{40} +3.75363e8 q^{41} +(2.00898e8 - 5.64202e8i) q^{42} +1.20437e9 q^{43} +(6.95580e8 + 4.01593e8i) q^{44} +(-2.91348e7 - 1.73796e8i) q^{45} +(7.62662e8 + 1.32097e9i) q^{46} +(9.56863e8 - 1.65734e9i) q^{47} +(-4.34301e8 - 7.84700e7i) q^{48} +(1.87277e9 + 6.34464e8i) q^{49} -1.53083e9i q^{50} +(6.92133e8 - 8.17819e8i) q^{51} +(1.96553e9 - 1.13480e9i) q^{52} +(-3.04240e9 + 1.75653e9i) q^{53} +(1.16670e9 + 2.08118e9i) q^{54} +7.80261e8i q^{55} +(2.36922e8 - 1.43771e9i) q^{56} +(-7.70996e8 + 4.26717e9i) q^{57} +(1.16101e8 - 2.01093e8i) q^{58} +(1.92744e9 + 3.33842e9i) q^{59} +(-1.44935e8 - 4.03495e8i) q^{60} +(1.02075e10 + 5.89329e9i) q^{61} -9.13006e9 q^{62} +(-6.81094e9 + 3.95749e9i) q^{63} -1.07374e9 q^{64} +(1.90943e9 + 1.10241e9i) q^{65} +(-3.57122e9 - 9.94219e9i) q^{66} +(-2.75067e9 - 4.76430e9i) q^{67} +(1.30332e9 - 2.25741e9i) q^{68} +(3.56710e9 - 1.97425e10i) q^{69} +(1.32463e9 - 4.99011e8i) q^{70} +2.05647e8i q^{71} +(3.69357e9 + 4.47803e9i) q^{72} +(-1.89380e10 + 1.09339e10i) q^{73} +(1.42000e9 - 8.19835e8i) q^{74} +(-1.30073e10 + 1.53693e10i) q^{75} +1.05499e10i q^{76} +(3.26392e10 - 1.22957e10i) q^{77} +(-2.93759e10 - 5.30766e9i) q^{78} +(-2.85550e9 + 4.94587e9i) q^{79} +(-5.21547e8 - 9.03345e8i) q^{80} +(5.97006e9 - 3.08079e10i) q^{81} +(-1.04024e10 - 6.00581e9i) q^{82} +1.40877e10 q^{83} +(-1.45947e10 + 1.24213e10i) q^{84} +2.53223e9 q^{85} +(-3.33766e10 - 1.92700e10i) q^{86} +(-2.87430e9 + 1.03245e9i) q^{87} +(-1.28510e10 - 2.22586e10i) q^{88} +(-3.72572e10 + 6.45313e10i) q^{89} +(-1.97332e9 + 5.28252e9i) q^{90} +(1.60253e10 - 9.72457e10i) q^{91} -4.88104e10i q^{92} +(9.16644e10 + 7.75770e10i) q^{93} +(-5.30347e10 + 3.06196e10i) q^{94} +(-8.87569e9 + 5.12438e9i) q^{95} +(1.07802e10 + 9.12344e9i) q^{96} +8.84815e10i q^{97} +(-4.17484e10 - 4.75471e10i) q^{98} +(-4.86230e10 + 1.30162e11i) 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
$3$	142.282	+	396.110i	0.338052	+	0.941127i
$3$	142.282	+	396.110i	0.338052	+	0.941127i
$4$	512.000	+	886.810i	0.250000	+	0.433013i
$5$	−497.386	+	861.497i	−0.0711800	+	0.123287i	−0.899419	−	0.437088i	$-0.856010\pi$
$5$	−497.386	+	861.497i	−0.0711800	+	0.123287i	0.828239	+	0.560375i	$0.189343\pi$
$6$	2394.71	−	13253.8i	0.125725	−	0.695840i
$7$	43875.4	+	7230.30i	0.986692	+	0.162599i
$7$	43875.4	+	7230.30i	0.986692	+	0.162599i
$8$		−	32768.0i		−	0.353553i
$9$	−136659.	+	112719.i	−0.771442	+	0.636300i
$10$	27567.9	−	15916.3i	0.0871774	−	0.0503319i
$11$	679278.	−	392181.i	1.27171	−	0.734221i	0.296399	−	0.955064i	$-0.404214\pi$
$11$	679278.	−	392181.i	1.27171	−	0.734221i	0.975309	+	0.220843i	$0.0708808\pi$
$12$	−278425.	+	328985.i	−0.323007	+	0.381663i
$13$		−	2.21641e6i		−	1.65562i	−0.561008	−	0.827811i	$-0.689586\pi$
$13$		−	2.21641e6i		−	1.65562i	0.561008	−	0.827811i	$-0.310414\pi$
$14$	−1.10023e6	−	902378.i	−0.546736	−	0.448419i
$15$	−412016.	−	74443.5i	−0.140092	−	0.0253119i
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	−1.27277e6	−	2.20450e6i	−0.217411	−	0.376567i	0.736605	−	0.676323i	$-0.236428\pi$
$17$	−1.27277e6	−	2.20450e6i	−0.217411	−	0.376567i	−0.954016	+	0.299757i	$0.903094\pi$
$18$	5.59069e6	−	937214.i	0.697376	−	0.116907i
$19$	8.92235e6	+	5.15132e6i	0.826674	+	0.477280i	0.852712	−	0.522381i	$-0.174956\pi$
$19$	8.92235e6	+	5.15132e6i	0.826674	+	0.477280i	−0.0260386	+	0.999661i	$0.508289\pi$
$20$	−1.01865e6			−0.0711800
$21$	3.37870e6	+	1.84082e7i	0.180527	+	0.983570i
$22$	−2.50996e7			−1.03835
$23$	−4.12803e7	−	2.38332e7i	−1.33733	−	0.772109i	−0.350922	−	0.936405i	$-0.614132\pi$
$23$	−4.12803e7	−	2.38332e7i	−1.33733	−	0.772109i	−0.986411	+	0.164295i	$0.947465\pi$
$24$	1.29797e7	−	4.66230e6i	0.332739	−	0.119519i
$25$	2.39193e7	+	4.14294e7i	0.489867	+	0.848474i
$26$	−3.54625e7	+	6.14229e7i	−0.585350	+	1.01386i
$27$	−6.40930e7	−	3.80939e7i	−0.859627	−	0.510922i
$28$	1.60523e7	+	4.26110e7i	0.176266	+	0.467900i
$29$			7.25633e6i			0.0656944i	0.999460	+	0.0328472i	$0.0104575\pi$
$29$			7.25633e6i			0.0656944i	−0.999460	+	0.0328472i	$0.989543\pi$
$30$	1.02270e7	+	8.65530e6i	0.0768392	+	0.0650302i
$31$	2.47090e8	−	1.42657e8i	1.55012	−	0.894962i	0.551989	−	0.833852i	$-0.313869\pi$
$31$	2.47090e8	−	1.42657e8i	1.55012	−	0.894962i	0.998131	−	0.0611103i	$-0.0194641\pi$
$32$	2.90590e7	−	1.67772e7i	0.153093	−	0.0883883i
$33$	2.51996e8	+	2.13268e8i	1.12090	+	0.948635i
$34$			8.14574e7i			0.307465i
$35$	−2.80519e7	+	3.42023e7i	−0.0902792	+	0.110073i
$36$	−1.69929e8	−	6.34782e7i	−0.468386	−	0.174969i
$37$	−2.56198e7	+	4.43749e7i	−0.0607389	+	0.105203i	−0.894796	−	0.446475i	$-0.852679\pi$
$37$	−2.56198e7	+	4.43749e7i	−0.0607389	+	0.105203i	0.834057	+	0.551678i	$0.186012\pi$
$38$	−1.64842e8	−	2.85515e8i	−0.337488	−	0.584547i
$39$	8.77940e8	−	3.15355e8i	1.55815	−	0.559686i
$40$	2.82295e7	+	1.62983e7i	0.0435887	+	0.0251659i
$41$	3.75363e8			0.505988			0.252994	−	0.967468i	$-0.418585\pi$
$41$	3.75363e8			0.505988			0.252994	+	0.967468i	$0.418585\pi$
$42$	2.00898e8	−	5.64202e8i	0.237195	−	0.666137i
$43$	1.20437e9			1.24935			0.624676	−	0.780884i	$-0.285231\pi$
$43$	1.20437e9			1.24935			0.624676	+	0.780884i	$0.285231\pi$
$44$	6.95580e8	+	4.01593e8i	0.635854	+	0.367111i
$45$	−2.91348e7	−	1.73796e8i	−0.0235366	−	0.140401i
$46$	7.62662e8	+	1.32097e9i	0.545964	+	0.945637i
$47$	9.56863e8	−	1.65734e9i	0.608571	−	1.05408i	−0.382905	−	0.923788i	$-0.625076\pi$
$47$	9.56863e8	−	1.65734e9i	0.608571	−	1.05408i	0.991476	−	0.130289i	$-0.0415905\pi$
$48$	−4.34301e8	−	7.84700e7i	−0.246017	−	0.0444505i
$49$	1.87277e9	+	6.34464e8i	0.947123	+	0.320870i
$50$		−	1.53083e9i		−	0.692776i
$51$	6.92133e8	−	8.17819e8i	0.280901	−	0.331911i
$52$	1.96553e9	−	1.13480e9i	0.716905	−	0.413905i
$53$	−3.04240e9	+	1.75653e9i	−0.999308	+	0.576950i	−0.908043	−	0.418876i	$-0.862424\pi$
$53$	−3.04240e9	+	1.75653e9i	−0.999308	+	0.576950i	−0.0912642	+	0.995827i	$0.529091\pi$
$54$	1.16670e9	+	2.08118e9i	0.345774	+	0.616799i
$55$			7.80261e8i			0.209048i
$56$	2.36922e8	−	1.43771e9i	0.0574873	−	0.348848i
$57$	−7.70996e8	+	4.26717e9i	−0.169723	+	0.939351i
$58$	1.16101e8	−	2.01093e8i	0.0232265	−	0.0402294i
$59$	1.92744e9	+	3.33842e9i	0.350989	+	0.607932i	0.986423	−	0.164224i	$-0.0525120\pi$
$59$	1.92744e9	+	3.33842e9i	0.350989	+	0.607932i	−0.635434	+	0.772156i	$0.719179\pi$
$60$	−1.44935e8	−	4.03495e8i	−0.0240626	−	0.0669895i
$61$	1.02075e10	+	5.89329e9i	1.54741	+	0.893395i	0.998339	+	0.0576173i	$0.0183503\pi$
$61$	1.02075e10	+	5.89329e9i	1.54741	+	0.893395i	0.549067	+	0.835778i	$0.314983\pi$
$62$	−9.13006e9			−1.26567
$63$	−6.81094e9	+	3.95749e9i	−0.864637	+	0.502397i
$64$	−1.07374e9			−0.125000
$65$	1.90943e9	+	1.10241e9i	0.204117	+	0.117847i
$66$	−3.57122e9	−	9.94219e9i	−0.351015	−	0.977215i
$67$	−2.75067e9	−	4.76430e9i	−0.248901	−	0.431110i	0.714320	−	0.699819i	$-0.246736\pi$
$67$	−2.75067e9	−	4.76430e9i	−0.248901	−	0.431110i	−0.963221	+	0.268710i	$0.913403\pi$
$68$	1.30332e9	−	2.25741e9i	0.108705	−	0.188283i
$69$	3.56710e9	−	1.97425e10i	0.274565	−	1.51961i
$70$	1.32463e9	−	4.99011e8i	0.0942011	−	0.0354872i
$71$			2.05647e8i			0.0135270i	0.999977	+	0.00676351i	$0.00215291\pi$
$71$			2.05647e8i			0.0135270i	−0.999977	+	0.00676351i	$0.997847\pi$
$72$	3.69357e9	+	4.47803e9i	0.224966	+	0.272746i
$73$	−1.89380e10	+	1.09339e10i	−1.06920	+	0.617303i	−0.927963	−	0.372673i	$-0.878441\pi$
$73$	−1.89380e10	+	1.09339e10i	−1.06920	+	0.617303i	−0.141237	+	0.989976i	$0.545108\pi$
$74$	1.42000e9	−	8.19835e8i	0.0743896	−	0.0429489i
$75$	−1.30073e10	+	1.53693e10i	−0.632922	+	0.747856i
$76$			1.05499e10i			0.477280i
$77$	3.26392e10	−	1.22957e10i	1.37417	−	0.517672i
$78$	−2.93759e10	−	5.30766e9i	−1.15205	−	0.208153i
$79$	−2.85550e9	+	4.94587e9i	−0.104408	+	0.180840i	−0.913496	−	0.406847i	$-0.866628\pi$
$79$	−2.85550e9	+	4.94587e9i	−0.104408	+	0.180840i	0.809088	+	0.587687i	$0.199961\pi$
$80$	−5.21547e8	−	9.03345e8i	−0.0177950	−	0.0308219i
$81$	5.97006e9	−	3.08079e10i	0.190244	−	0.981737i
$82$	−1.04024e10	−	6.00581e9i	−0.309853	−	0.178894i
$83$	1.40877e10			0.392564			0.196282	−	0.980547i	$-0.437113\pi$
$83$	1.40877e10			0.392564			0.196282	+	0.980547i	$0.437113\pi$
$84$	−1.45947e10	+	1.24213e10i	−0.380766	+	0.324063i
$85$	2.53223e9			0.0619013
$86$	−3.33766e10	−	1.92700e10i	−0.765069	−	0.441713i
$87$	−2.87430e9	+	1.03245e9i	−0.0618268	+	0.0222081i
$88$	−1.28510e10	−	2.22586e10i	−0.259586	−	0.449617i
$89$	−3.72572e10	+	6.45313e10i	−0.707236	+	1.22497i	0.258642	+	0.965973i	$0.416725\pi$
$89$	−3.72572e10	+	6.45313e10i	−0.707236	+	1.22497i	−0.965878	+	0.258996i	$0.916608\pi$
$90$	−1.97332e9	+	5.28252e9i	−0.0352261	+	0.0942991i
$91$	1.60253e10	−	9.72457e10i	0.269202	−	1.63359i
$92$		−	4.88104e10i		−	0.772109i
$93$	9.16644e10	+	7.75770e10i	1.36629	+	1.15632i
$94$	−5.30347e10	+	3.06196e10i	−0.745345	+	0.430325i
$95$	−8.87569e9	+	5.12438e9i	−0.117685	+	0.0679457i
$96$	1.07802e10	+	9.12344e9i	0.134938	+	0.114200i
$97$			8.84815e10i			1.04618i	0.852276	+	0.523092i	$0.175221\pi$
$97$			8.84815e10i			1.04618i	−0.852276	+	0.523092i	$0.824779\pi$
$98$	−4.17484e10	−	4.75471e10i	−0.466548	−	0.531350i
$99$	−4.86230e10	+	1.30162e11i	−0.513864	+	1.37560i
$100$	−2.44933e10	+	4.24237e10i	−0.244933	+	0.424237i
$101$	−8.38869e10	−	1.45296e11i	−0.794194	−	1.37558i	−0.923350	−	0.383960i	$-0.874560\pi$
$101$	−8.38869e10	−	1.45296e11i	−0.794194	−	1.37558i	0.129156	−	0.991624i	$-0.458773\pi$
$102$	−3.22660e10	+	1.15899e10i	−0.289364	+	0.103939i
$103$	−1.01053e11	−	5.83431e10i	−0.858906	−	0.495889i	0.00474007	−	0.999989i	$-0.498491\pi$
$103$	−1.01053e11	−	5.83431e10i	−0.858906	−	0.495889i	−0.863646	+	0.504099i	$0.831825\pi$
$104$	−7.26272e10			−0.585350
$105$	−1.75391e10	−	6.24524e9i	−0.134112	−	0.0477538i
$106$	1.12418e11			0.815931
$107$	2.23779e11	+	1.29199e11i	1.54244	+	0.890530i	0.998684	+	0.0512898i	$0.0163332\pi$
$107$	2.23779e11	+	1.29199e11i	1.54244	+	0.890530i	0.543760	+	0.839241i	$0.317000\pi$
$108$	9.66430e8	−	7.63424e10i	0.00632907	−	0.499960i
$109$	3.74818e10	+	6.49204e10i	0.233332	+	0.404144i	0.958787	−	0.284127i	$-0.0917036\pi$
$109$	3.74818e10	+	6.49204e10i	0.233332	+	0.404144i	−0.725454	+	0.688270i	$0.758370\pi$
$110$	1.24842e10	−	2.16232e10i	0.0739095	−	0.128015i
$111$	−2.12226e10	−	3.83451e9i	−0.119542	−	0.0215990i
$112$	−2.95691e10	+	3.60522e10i	−0.158540	+	0.193300i
$113$		−	1.60780e11i		−	0.820922i	−0.911878	−	0.410461i	$-0.865368\pi$
$113$		−	1.60780e11i		−	0.820922i	0.911878	−	0.410461i	$-0.134632\pi$
$114$	8.96411e10	−	1.05919e11i	0.436044	−	0.515227i
$115$	4.10644e10	−	2.37086e10i	0.190383	−	0.109918i
$116$	−6.43499e9	+	3.71524e9i	−0.0284465	+	0.0164236i
$117$	2.49830e11	+	3.02891e11i	1.05347	+	1.27722i
$118$		−	1.23356e11i		−	0.496374i
$119$	−3.99041e10	−	1.05926e11i	−0.153288	−	0.406906i
$120$	−2.43936e9	+	1.35010e10i	−0.00894911	+	0.0495299i
$121$	1.64956e11	−	2.85713e11i	0.578161	−	1.00141i
$122$	−1.88585e11	−	3.26639e11i	−0.631726	−	1.09418i
$123$	5.34075e10	+	1.48685e11i	0.171050	+	0.476200i
$124$	2.53020e11	+	1.46081e11i	0.775060	+	0.447481i
$125$	−9.61612e10			−0.281835
$126$	2.52070e11	−	6.98271e8i	0.707104	−	0.00195878i
$127$	−9.60879e10			−0.258076			−0.129038	−	0.991640i	$-0.541189\pi$
$127$	−9.60879e10			−0.258076			−0.129038	+	0.991640i	$0.541189\pi$
$128$	2.97564e10	+	1.71799e10i	0.0765466	+	0.0441942i
$129$	1.71361e11	+	4.77064e11i	0.422346	+	1.17580i
$130$	−3.52771e10	−	6.11017e10i	−0.0833305	−	0.144333i
$131$	−9.26764e10	+	1.60520e11i	−0.209883	+	0.363528i	−0.951677	−	0.307099i	$-0.900642\pi$
$131$	−9.26764e10	+	1.60520e11i	−0.209883	+	0.363528i	0.741795	+	0.670627i	$0.233975\pi$
$132$	−6.01063e10	+	3.32666e11i	−0.130546	+	0.722522i
$133$	3.54226e11	+	2.90527e11i	0.738068	+	0.605345i
$134$			1.76043e11i			0.352000i
$135$	6.46967e10	−	3.62686e10i	0.124179	−	0.0696137i
$136$	−7.22372e10	+	4.17062e10i	−0.133136	+	0.0768664i
$137$	8.28352e11	−	4.78249e11i	1.46640	−	0.846625i	0.467104	−	0.884202i	$-0.345297\pi$
$137$	8.28352e11	−	4.78249e11i	1.46640	−	0.846625i	0.999294	+	0.0375772i	$0.0119640\pi$
$138$	−4.14735e11	+	4.90048e11i	−0.705401	+	0.833496i
$139$		−	1.16705e11i		−	0.190770i	−0.995440	−	0.0953848i	$-0.969592\pi$
$139$		−	1.16705e11i		−	0.190770i	0.995440	−	0.0953848i	$-0.0304082\pi$
$140$	−4.46935e10	−	7.36511e9i	−0.0702328	−	0.0115738i
$141$	7.92631e11	+	1.43213e11i	1.19775	+	0.216410i
$142$	3.29036e9	−	5.69906e9i	0.00478252	−	0.00828357i
$143$	−8.69233e11	−	1.50556e12i	−1.21559	−	2.10547i
$144$	−3.07106e10	−	1.83196e11i	−0.0413328	−	0.246560i
$145$	−6.25131e9	−	3.60920e9i	−0.00809929	−	0.00467613i
$146$	6.99767e11			0.872998
$147$	1.51448e10	+	8.32096e11i	0.0181977	+	0.999834i
$148$	−5.24694e10			−0.0607389
$149$	−3.62606e11	−	2.09350e11i	−0.404492	−	0.233534i	0.283928	−	0.958846i	$-0.408362\pi$
$149$	−3.62606e11	−	2.09350e11i	−0.404492	−	0.233534i	−0.688420	+	0.725312i	$0.741696\pi$
$150$	6.06378e11	−	2.17810e11i	0.651991	−	0.234194i
$151$	−5.97081e10	−	1.03418e11i	−0.0618957	−	0.107206i	0.833417	−	0.552645i	$-0.186381\pi$
$151$	−5.97081e10	−	1.03418e11i	−0.0618957	−	0.107206i	−0.895313	+	0.445438i	$0.853048\pi$
$152$	1.68798e11	−	2.92367e11i	0.168744	−	0.292273i
$153$	4.22424e11	+	1.57799e11i	0.407329	+	0.152161i
$154$	−1.10125e12	−	1.81478e11i	−1.02453	−	0.168834i
$155$			2.83823e11i			0.254814i
$156$	7.29165e11	+	6.17104e11i	0.631889	+	0.534777i
$157$	−5.33133e11	+	3.07804e11i	−0.446054	+	0.257529i	−0.706162	−	0.708050i	$-0.749575\pi$
$157$	−5.33133e11	+	3.07804e11i	−0.446054	+	0.257529i	0.260108	+	0.965579i	$0.416242\pi$
$158$	1.58268e11	−	9.13759e10i	0.127873	−	0.0738275i
$159$	−1.12866e12	−	9.55201e11i	−0.880802	−	0.745436i
$160$			3.33790e10i			0.0251659i
$161$	−1.63887e12	−	1.34416e12i	−1.19399	−	0.979283i
$162$	−6.58374e11	+	7.58254e11i	−0.463597	+	0.533927i
$163$	8.86763e11	−	1.53592e12i	0.603637	−	1.04553i	−0.388629	−	0.921395i	$-0.627051\pi$
$163$	8.86763e11	−	1.53592e12i	0.603637	−	1.04553i	0.992265	−	0.124135i	$-0.0396156\pi$
$164$	1.92186e11	+	3.32876e11i	0.126497	+	0.219099i
$165$	−3.09069e11	+	1.11017e11i	−0.196740	+	0.0706690i
$166$	−3.90410e11	−	2.25403e11i	−0.240395	−	0.138792i
$167$	−1.46576e12			−0.873217			−0.436608	−	0.899652i	$-0.643820\pi$
$167$	−1.46576e12			−0.873217			−0.436608	+	0.899652i	$0.643820\pi$
$168$	6.03200e11	−	1.10713e11i	0.347744	−	0.0638260i
$169$	−3.12030e12			−1.74108
$170$	−7.01753e10	−	4.05157e10i	−0.0379066	−	0.0218854i
$171$	−1.79996e12	+	3.01743e11i	−0.941424	+	0.157819i
$172$	6.16640e11	+	1.06805e12i	0.312338	+	0.540986i
$173$	−2.89299e11	+	5.01081e11i	−0.141936	+	0.245841i	−0.928226	−	0.372017i	$-0.878666\pi$
$173$	−2.89299e11	+	5.01081e11i	−0.141936	+	0.245841i	0.786289	+	0.617858i	$0.212000\pi$
$174$	9.61742e10	+	1.73768e10i	0.0457128	+	0.00825943i
$175$	7.49921e11	+	1.99067e12i	0.345387	+	0.916835i
$176$			8.22463e11i			0.367111i
$177$	−1.04814e12	+	1.23847e12i	−0.453488	+	0.535838i
$178$	2.06500e12	−	1.19223e12i	0.866184	−	0.500092i
$179$	1.24062e12	−	7.16274e11i	0.504601	−	0.291332i	−0.226010	−	0.974125i	$-0.572568\pi$
$179$	1.24062e12	−	7.16274e11i	0.504601	−	0.291332i	0.730612	+	0.682793i	$0.239235\pi$
$180$	1.39207e11	−	1.14820e11i	0.0549112	−	0.0452919i
$181$		−	5.95958e11i		−	0.228025i	−0.993479	−	0.114013i	$-0.963630\pi$
$181$		−	5.95958e11i		−	0.228025i	0.993479	−	0.114013i	$-0.0363705\pi$
$182$	−2.00004e12	+	2.43855e12i	−0.742413	+	0.905187i
$183$	−8.82046e11	+	4.88179e12i	−0.317695	+	1.75832i
$184$	−7.80966e11	+	1.35267e12i	−0.272982	+	0.472819i
$185$	−2.54859e10	−	4.41428e10i	−0.00864679	−	0.0149767i
$186$	−1.29905e12	−	3.61651e12i	−0.427861	−	1.19115i
$187$	−1.72913e12	−	9.98314e11i	−0.552967	−	0.319255i
$188$	1.95966e12			0.608571
$189$	−2.53668e12	−	2.13480e12i	−0.765112	−	0.643897i
$190$	3.27960e11			0.0960897
$191$	−1.46653e12	−	8.46701e11i	−0.417453	−	0.241016i	0.276534	−	0.961004i	$-0.410814\pi$
$191$	−1.46653e12	−	8.46701e11i	−0.417453	−	0.241016i	−0.693987	+	0.719988i	$0.744147\pi$
$192$	−1.52774e11	−	4.25319e11i	−0.0422565	−	0.117641i
$193$	−5.18618e11	−	8.98272e11i	−0.139406	−	0.241459i	0.787866	−	0.615847i	$-0.211186\pi$
$193$	−5.18618e11	−	8.98272e11i	−0.139406	−	0.241459i	−0.927272	+	0.374388i	$0.877853\pi$
$194$	1.41570e12	−	2.45207e12i	0.369882	−	0.640654i
$195$	−1.64997e11	+	9.13196e11i	−0.0419069	+	0.231939i
$196$	3.96210e11	+	1.98564e12i	0.0978402	+	0.490334i
$197$		−	3.72659e12i		−	0.894844i	−0.894323	−	0.447422i	$-0.852342\pi$
$197$		−	3.72659e12i		−	0.894844i	0.894323	−	0.447422i	$-0.147658\pi$
$198$	3.43007e12	−	2.82919e12i	0.801023	−	0.660699i
$199$	5.15083e11	−	2.97384e11i	0.117000	−	0.0675499i	−0.440358	−	0.897822i	$-0.645148\pi$
$199$	5.15083e11	−	2.97384e11i	0.117000	−	0.0675499i	0.557358	+	0.830272i	$0.311815\pi$
$200$	1.35756e12	−	7.83787e11i	0.299981	−	0.173194i
$201$	1.49581e12	−	1.76744e12i	0.321588	−	0.379985i
$202$			5.36876e12i			1.12316i
$203$	−5.24655e10	+	3.18374e11i	−0.0106818	+	0.0648201i
$204$	1.07962e12	+	1.95067e11i	0.213947	+	0.0386561i
$205$	−1.86700e11	+	3.23374e11i	−0.0360163	+	0.0623820i
$206$	1.86698e12	+	3.23370e12i	0.350647	+	0.607338i
$207$	8.32775e12	−	1.39605e12i	1.52297	−	0.255308i
$208$	2.01270e12	+	1.16204e12i	0.358452	+	0.206953i
$209$	8.08100e12			1.40172
$210$	3.86135e11	+	4.53699e11i	0.0652428	+	0.0766588i
$211$	8.56765e12			1.41029			0.705145	−	0.709064i	$-0.250882\pi$
$211$	8.56765e12			1.41029			0.705145	+	0.709064i	$0.250882\pi$
$212$	−3.11542e12	−	1.79869e12i	−0.499654	−	0.288475i
$213$	−8.14589e10	+	2.92599e10i	−0.0127306	+	0.00457284i
$214$	−4.13437e12	−	7.16094e12i	−0.629700	−	1.09067i
$215$	−5.99038e11	+	1.03757e12i	−0.0889290	+	0.154029i
$216$	−1.24826e12	+	2.10020e12i	−0.180638	+	0.303924i
$217$	1.18726e13	−	4.47261e12i	1.67501	−	0.631005i
$218$		−	2.39884e12i		−	0.329982i
$219$	−7.02555e12	−	5.94583e12i	−0.942405	−	0.797572i
$220$	−6.91943e11	+	3.99494e11i	−0.0905202	+	0.0522619i
$221$	−4.88608e12	+	2.82098e12i	−0.623452	+	0.359950i
$222$	5.26784e11	+	4.45826e11i	0.0655679	+	0.0554912i
$223$			4.00699e12i			0.486566i	0.969955	+	0.243283i	$0.0782243\pi$
$223$			4.00699e12i			0.486566i	−0.969955	+	0.243283i	$0.921776\pi$
$224$	1.39628e12	−	5.26002e11i	0.165428	−	0.0623194i
$225$	−7.93864e12	−	2.96553e12i	−0.917788	−	0.342846i
$226$	−2.57249e12	+	4.45568e12i	−0.290240	+	0.502710i
$227$	3.53516e12	+	6.12308e12i	0.389284	+	0.674260i	0.992353	−	0.123429i	$-0.0393891\pi$
$227$	3.53516e12	+	6.12308e12i	0.389284	+	0.674260i	−0.603069	+	0.797689i	$0.706056\pi$
$228$	−4.17892e12	+	1.50106e12i	−0.449182	+	0.161346i
$229$	−8.55962e11	−	4.94190e11i	−0.0898172	−	0.0518560i	0.454419	−	0.890788i	$-0.349847\pi$
$229$	−8.55962e11	−	4.94190e11i	−0.0898172	−	0.0518560i	−0.544236	+	0.838932i	$0.683180\pi$
$230$	−1.51735e12			−0.155447
$231$	9.51442e12	+	1.11792e13i	0.951736	+	1.11827i
$232$	2.37776e11			0.0232265
$233$	2.78107e12	+	1.60565e12i	0.265311	+	0.153177i	0.626755	−	0.779217i	$-0.284383\pi$
$233$	2.78107e12	+	1.60565e12i	0.265311	+	0.153177i	−0.361444	+	0.932394i	$0.617716\pi$
$234$	−2.07725e12	−	1.23912e13i	−0.193554	−	1.15459i
$235$	9.51860e11	+	1.64867e12i	0.0866363	+	0.150058i
$236$	−1.97370e12	+	3.41854e12i	−0.175495	+	0.303966i
$237$	−2.36539e12	−	4.27381e11i	−0.205488	−	0.0371278i
$238$	−5.88961e11	+	3.57397e12i	−0.0499935	+	0.303374i
$239$			2.22770e13i			1.84785i	0.382568	+	0.923927i	$0.375040\pi$
$239$			2.22770e13i			1.84785i	−0.382568	+	0.923927i	$0.624960\pi$
$240$	2.83617e11	−	3.35120e11i	0.0229917	−	0.0271668i
$241$	6.07664e12	−	3.50835e12i	0.481470	−	0.277977i	−0.239559	−	0.970882i	$-0.577003\pi$
$241$	6.07664e12	−	3.50835e12i	0.481470	−	0.277977i	0.721029	+	0.692905i	$0.243669\pi$
$242$	−9.14280e12	+	5.27860e12i	−0.708100	+	0.408822i
$243$	1.30528e13	−	2.01862e12i	0.988252	−	0.152834i
$244$			1.20695e13i			0.893395i
$245$	−1.47808e12	+	1.29781e12i	−0.106975	+	0.0939289i
$246$	8.98888e11	−	4.97500e12i	0.0636154	−	0.352087i
$247$	1.14174e13	−	1.97755e13i	0.790196	−	1.36866i
$248$	−4.67459e12	−	8.09663e12i	−0.316417	−	0.548050i
$249$	2.00443e12	+	5.58027e12i	0.132707	+	0.369453i
$250$	2.66490e12	+	1.53858e12i	0.172588	+	0.0996437i
$251$	1.66970e12			0.105787			0.0528937	−	0.998600i	$-0.483156\pi$
$251$	1.66970e12			0.105787			0.0528937	+	0.998600i	$0.483156\pi$
$252$	−6.99674e12	−	4.01377e12i	−0.433704	−	0.248800i
$253$	−3.73877e13			−2.26760
$254$	2.66287e12	+	1.53741e12i	0.158039	+	0.0912438i
$255$	3.60292e11	+	1.00304e12i	0.0209258	+	0.0582570i
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	−1.59535e12	+	2.76322e12i	−0.0887612	+	0.153739i	−0.906988	−	0.421157i	$-0.861624\pi$
$257$	−1.59535e12	+	2.76322e12i	−0.0887612	+	0.153739i	0.818227	+	0.574896i	$0.194957\pi$
$258$	2.88413e12	−	1.59626e13i	0.157075	−	0.869349i
$259$	−1.44492e12	+	1.76172e12i	−0.0770364	+	0.0939268i
$260$			2.25773e12i			0.117847i
$261$	−8.17924e11	−	9.91640e11i	−0.0418013	−	0.0506794i
$262$	5.13664e12	−	2.96564e12i	0.257053	−	0.148410i
$263$	5.09999e12	−	2.94448e12i	0.249927	−	0.144295i	−0.369804	−	0.929110i	$-0.620575\pi$
$263$	5.09999e12	−	2.94448e12i	0.249927	−	0.144295i	0.619731	+	0.784815i	$0.287242\pi$
$264$	6.98836e12	−	8.25740e12i	0.335393	−	0.396298i
$265$		−	3.49469e12i		−	0.164269i
$266$	−5.16816e12	−	1.37189e13i	−0.237950	−	0.631643i
$267$	−3.08625e13	−	5.57626e12i	−1.39194	−	0.251496i
$268$	2.81669e12	−	4.87865e12i	0.124451	−	0.215555i
$269$	1.29113e13	+	2.23630e13i	0.558898	+	0.968040i	0.997589	+	0.0694020i	$0.0221091\pi$
$269$	1.29113e13	+	2.23630e13i	0.558898	+	0.968040i	−0.438690	+	0.898638i	$0.644558\pi$
$270$	−2.37323e12	−	3.00430e10i	−0.100656	−	0.00127422i
$271$	−3.31230e13	−	1.91236e13i	−1.37657	−	0.794763i	−0.384826	−	0.922989i	$-0.625738\pi$
$271$	−3.31230e13	−	1.91236e13i	−1.37657	−	0.794763i	−0.991745	+	0.128226i	$0.959072\pi$
$272$	2.66919e12			0.108705
$273$	4.08001e13	−	7.48856e12i	1.62842	−	0.298885i
$274$	−3.06080e13			−1.19731
$275$	3.24957e13	+	1.87614e13i	1.24594	+	0.719341i
$276$	1.93342e13	−	6.94484e12i	0.726653	−	0.261013i
$277$	−1.63187e13	−	2.82649e13i	−0.601240	−	1.04138i	−0.992634	−	0.121154i	$-0.961340\pi$
$277$	−1.63187e13	−	2.82649e13i	−0.601240	−	1.04138i	0.391394	−	0.920223i	$-0.371993\pi$
$278$	−1.86728e12	+	3.23423e12i	−0.0674472	+	0.116822i
$279$	−1.76868e13	+	4.73469e13i	−0.626362	+	1.67675i
$280$	1.12074e12	+	9.19204e11i	0.0389167	+	0.0319185i
$281$		−	2.74313e13i		−	0.934033i	−0.884249	−	0.467017i	$-0.845329\pi$
$281$		−	2.74313e13i		−	0.934033i	0.884249	−	0.467017i	$-0.154671\pi$
$282$	−1.96746e13	−	1.66509e13i	−0.656956	−	0.555992i
$283$	−3.68169e12	+	2.12562e12i	−0.120565	+	0.0696082i	−0.559070	−	0.829121i	$-0.688842\pi$
$283$	−3.68169e12	+	2.12562e12i	−0.120565	+	0.0696082i	0.438505	+	0.898729i	$0.355508\pi$
$284$	−1.82370e11	+	1.05291e11i	−0.00585737	+	0.00338175i
$285$	−3.29267e12	−	2.78664e12i	−0.103729	−	0.0877877i
$286$			5.56309e13i			1.71911i
$287$	1.64692e13	+	2.71399e12i	0.499255	+	0.0822731i
$288$	−2.08005e12	+	5.56824e12i	−0.0618609	+	0.165600i
$289$	1.38961e13	−	2.40687e13i	0.405465	−	0.702286i
$290$	1.15494e11	+	2.00042e11i	0.00330652	+	0.00572706i
$291$	−3.50484e13	+	1.25893e13i	−0.984592	+	0.353664i
$292$	−1.93925e13	−	1.11963e13i	−0.534600	−	0.308651i
$293$	8.56053e12			0.231595			0.115797	−	0.993273i	$-0.463058\pi$
$293$	8.56053e12			0.231595			0.115797	+	0.993273i	$0.463058\pi$
$294$	1.28938e13	−	2.33020e13i	0.342351	−	0.618705i
$295$	−3.83472e12			−0.0999338
$296$	1.45408e12	+	8.39511e11i	0.0371948	+	0.0214744i
$297$	−5.84767e13	−	7.40265e11i	−1.46832	−	0.0185877i
$298$	6.69922e12	+	1.16034e13i	0.165133	+	0.286019i
$299$	−5.28240e13	+	9.14939e13i	−1.27832	+	2.21412i
$300$	−2.02894e13	−	3.66591e12i	−0.482061	−	0.0870993i
$301$	5.28424e13	+	8.70799e12i	1.23273	+	0.203143i
$302$			3.82132e12i			0.0875337i
$303$	4.56177e13	−	5.39015e13i	1.02612	−	1.21246i
$304$	−9.35576e12	+	5.40155e12i	−0.206668	+	0.119320i
$305$	−1.01541e13	+	5.86247e12i	−0.220289	+	0.127184i
$306$	−9.18177e12	−	1.11318e13i	−0.195640	−	0.237192i
$307$			2.15529e13i			0.451070i	0.974235	+	0.225535i	$0.0724130\pi$
$307$			2.15529e13i			0.451070i	−0.974235	+	0.225535i	$0.927587\pi$
$308$	2.76152e13	+	2.26493e13i	0.567701	+	0.465614i
$309$	8.73219e12	−	4.83293e13i	0.176340	−	0.975976i
$310$	4.54116e12	−	7.86552e12i	0.0900902	−	0.156041i
$311$	−3.90118e12	−	6.75704e12i	−0.0760350	−	0.131697i	0.825501	−	0.564401i	$-0.190893\pi$
$311$	−3.90118e12	−	6.75704e12i	−0.0760350	−	0.131697i	−0.901536	+	0.432704i	$0.857559\pi$
$312$	−1.03336e13	−	2.87683e13i	−0.197879	−	0.550889i
$313$	2.40590e13	+	1.38904e13i	0.452671	+	0.261350i	0.708958	−	0.705251i	$-0.249166\pi$
$313$	2.40590e13	+	1.38904e13i	0.452671	+	0.261350i	−0.256286	+	0.966601i	$0.582499\pi$
$314$	1.96995e13			0.364201
$315$	−2.17069e10	−	7.83600e12i	−0.000394357	−	0.142360i
$316$	−5.84806e12			−0.104408
$317$	−9.41455e13	−	5.43549e13i	−1.65186	−	0.953703i	−0.976306	−	0.216393i	$-0.930571\pi$
$317$	−9.41455e13	−	5.43549e13i	−1.65186	−	0.953703i	−0.675555	−	0.737309i	$-0.736096\pi$
$318$	1.59951e13	+	4.45298e13i	0.275827	+	0.767895i
$319$	2.84580e12	+	4.92907e12i	0.0482342	+	0.0835441i
$320$	5.34064e11	−	9.25025e11i	0.00889750	−	0.0154109i
$321$	−1.93372e13	+	1.07024e14i	−0.316676	+	1.75268i
$322$	2.39111e13	+	6.34723e13i	0.384939	+	1.02183i
$323$		−	2.62258e13i		−	0.415064i
$324$	3.03775e13	−	1.04794e13i	0.472666	−	0.163056i
$325$	9.18244e13	−	5.30148e13i	1.40475	−	0.811034i
$326$	−4.91494e13	+	2.83764e13i	−0.739301	+	0.426836i
$327$	−2.03826e13	+	2.40839e13i	−0.301472	+	0.356217i
$328$		−	1.22999e13i		−	0.178894i
$329$	5.39658e13	−	6.57978e13i	0.771864	−	0.941096i
$330$	1.03414e13	+	1.86850e12i	0.145464	+	0.0262825i
$331$	2.21921e13	−	3.84378e13i	0.307004	−	0.531746i	−0.670702	−	0.741727i	$-0.734007\pi$
$331$	2.21921e13	−	3.84378e13i	0.307004	−	0.531746i	0.977705	+	0.209981i	$0.0673402\pi$
$332$	7.21290e12	+	1.24931e13i	0.0981410	+	0.169985i
$333$	−1.50070e12	−	8.95204e12i	−0.0200841	−	0.119806i
$334$	4.06203e13	+	2.34521e13i	0.534734	+	0.308729i
$335$	5.47258e12			0.0708672
$336$	−1.84878e13	−	6.58303e12i	−0.235515	−	0.0838609i
$337$	−7.97174e13			−0.999054			−0.499527	−	0.866298i	$-0.666493\pi$
$337$	−7.97174e13			−0.999054			−0.499527	+	0.866298i	$0.666493\pi$
$338$	8.64722e13	+	4.99248e13i	1.06619	+	0.615565i
$339$	6.36867e13	−	2.28762e13i	0.772592	−	0.277514i
$340$	1.29650e12	+	2.24561e12i	0.0154753	+	0.0268040i
$341$	1.11895e14	−	1.93808e14i	1.31420	−	2.27626i
$342$	5.47100e13	+	2.04373e13i	0.632300	+	0.236200i
$343$	7.75812e13	+	4.13781e13i	0.882346	+	0.470601i
$344$		−	3.94649e13i		−	0.441713i
$345$	1.52339e13	+	1.28927e13i	0.167806	+	0.142017i
$346$	1.60346e13	−	9.25757e12i	0.173836	−	0.100364i
$347$	−7.24585e13	+	4.18339e13i	−0.773174	+	0.446392i	−0.834006	−	0.551756i	$-0.813958\pi$
$347$	−7.24585e13	+	4.18339e13i	−0.773174	+	0.446392i	0.0608315	+	0.998148i	$0.480625\pi$
$348$	−2.38723e12	−	2.02035e12i	−0.0250731	−	0.0212198i
$349$			1.13754e14i			1.17606i	0.808841	+	0.588028i	$0.200096\pi$
$349$			1.13754e14i			1.17606i	−0.808841	+	0.588028i	$0.799904\pi$
$350$	1.10684e13	−	6.71659e13i	0.112645	−	0.683557i
$351$	−8.44316e13	+	1.42056e14i	−0.845894	+	1.42322i
$352$	1.31594e13	−	2.27928e13i	0.129793	−	0.224808i
$353$	−1.69464e13	−	2.93519e13i	−0.164557	−	0.285020i	0.771941	−	0.635694i	$-0.219286\pi$
$353$	−1.69464e13	−	2.93519e13i	−0.164557	−	0.285020i	−0.936498	+	0.350674i	$0.885953\pi$
$354$	4.88625e13	−	1.75514e13i	0.467151	−	0.167800i
$355$	−1.77165e11	−	1.02286e11i	−0.00166771	−	0.000962853i
$356$	−7.63027e13			−0.707236
$357$	3.62807e13	−	3.08778e13i	0.331131	−	0.281819i
$358$	−4.58416e13			−0.412005
$359$	−9.96930e13	−	5.75578e13i	−0.882359	−	0.509430i	−0.0109235	−	0.999940i	$-0.503477\pi$
$359$	−9.96930e13	−	5.75578e13i	−0.882359	−	0.509430i	−0.871435	+	0.490510i	$0.836810\pi$
$360$	−5.69493e12	+	9.54689e11i	−0.0496392	+	0.00832144i
$361$	−5.17297e12	−	8.95984e12i	−0.0444069	−	0.0769150i
$362$	−9.53532e12	+	1.65157e13i	−0.0806191	+	0.139636i
$363$	1.36644e14	+	2.46889e13i	1.13790	+	0.205597i
$364$	9.44434e13	−	3.55784e13i	0.774665	−	0.291829i
$365$		−	2.17534e13i		−	0.175758i
$366$	1.02553e14	−	1.21175e14i	0.816208	−	0.964425i
$367$	6.67947e13	−	3.85639e13i	0.523695	−	0.302355i	−0.214750	−	0.976669i	$-0.568894\pi$
$367$	6.67947e13	−	3.85639e13i	0.523695	−	0.302355i	0.738445	+	0.674314i	$0.235560\pi$
$368$	4.32855e13	−	2.49909e13i	0.334333	−	0.193027i
$369$	−5.12966e13	+	4.23105e13i	−0.390341	+	0.321961i
$370$			1.63110e12i			0.0122284i
$371$	−1.46187e14	+	5.50710e13i	−1.07982	+	0.406787i
$372$	−2.18639e13	+	1.21008e14i	−0.159126	+	0.880702i
$373$	1.52358e13	−	2.63891e13i	0.109261	−	0.189246i	−0.806210	−	0.591630i	$-0.798485\pi$
$373$	1.52358e13	−	2.63891e13i	0.109261	−	0.189246i	0.915471	+	0.402384i	$0.131818\pi$
$374$	3.19460e13	+	5.53322e13i	0.225748	+	0.391006i
$375$	−1.36820e13	−	3.80904e13i	−0.0952749	−	0.265243i
$376$	−5.43076e13	−	3.13545e13i	−0.372672	−	0.215163i
$377$	1.60830e13			0.108765
$378$	3.61417e13	+	9.97480e13i	0.240881	+	0.664813i
$379$	−1.50049e14			−0.985641			−0.492821	−	0.870131i	$-0.664034\pi$
$379$	−1.50049e14			−0.985641			−0.492821	+	0.870131i	$0.664034\pi$
$380$	−9.08871e12	−	5.24737e12i	−0.0588427	−	0.0339728i
$381$	−1.36716e13	−	3.80613e13i	−0.0872433	−	0.242883i
$382$	2.70944e13	+	4.69289e13i	0.170424	+	0.295184i
$383$	−3.65697e13	+	6.33406e13i	−0.226740	+	0.392725i	−0.956840	−	0.290615i	$-0.906140\pi$
$383$	−3.65697e13	+	6.33406e13i	−0.226740	+	0.392725i	0.730100	+	0.683340i	$0.239473\pi$
$384$	−2.57130e12	+	1.42312e13i	−0.0157156	+	0.0869800i
$385$	−5.64152e12	+	3.42342e13i	−0.0339909	+	0.206266i
$386$			3.31915e13i			0.197150i
$387$	−1.64588e14	+	1.35755e14i	−0.963803	+	0.794963i
$388$	−7.84663e13	+	4.53025e13i	−0.453011	+	0.261546i
$389$	1.87309e14	−	1.08143e14i	1.06619	−	0.615568i	0.139055	−	0.990285i	$-0.455593\pi$
$389$	1.87309e14	−	1.08143e14i	1.06619	−	0.615568i	0.927139	+	0.374717i	$0.122260\pi$
$390$	1.91837e13	−	2.26673e13i	0.107665	−	0.127217i
$391$			1.21337e14i			0.671460i
$392$	2.07901e13	−	6.13670e13i	0.113445	−	0.334859i
$393$	−7.67698e13	−	1.38708e13i	−0.413077	−	0.0746352i
$394$	−5.96254e13	+	1.03274e14i	−0.316375	+	0.547978i
$395$	−2.84057e12	−	4.92001e12i	−0.0148635	−	0.0257443i
$396$	−1.40324e14	+	2.35237e13i	−0.724117	+	0.121390i
$397$	−2.09761e14	−	1.21105e14i	−1.06752	−	0.616334i	−0.140018	−	0.990149i	$-0.544716\pi$
$397$	−2.09761e14	−	1.21105e14i	−1.06752	−	0.616334i	−0.927503	+	0.373815i	$0.878049\pi$
$398$	−1.90325e13			−0.0955300
$399$	−6.46806e13	+	1.81649e14i	−0.320201	+	0.899254i
$400$	−5.01624e13			−0.244933
$401$	−1.99482e14	−	1.15171e14i	−0.960749	−	0.554689i	−0.0643454	−	0.997928i	$-0.520496\pi$
$401$	−1.99482e14	−	1.15171e14i	−0.960749	−	0.554689i	−0.896403	+	0.443239i	$0.853829\pi$
$402$	−6.97323e13	+	2.50478e13i	−0.331277	+	0.118994i
$403$	−3.16186e14	−	5.47651e14i	−1.48172	−	2.56641i
$404$	8.59002e13	−	1.48783e14i	0.397097	−	0.687792i
$405$	2.35715e13	+	2.04666e13i	0.107494	+	0.0933348i
$406$	6.54796e12	−	7.98360e12i	0.0294586	−	0.0359175i
$407$			4.01905e13i			0.178383i
$408$	−2.67983e13	−	2.26798e13i	−0.117348	−	0.0993135i
$409$	5.70363e13	−	3.29299e13i	0.246418	−	0.142270i	−0.371705	−	0.928351i	$-0.621227\pi$
$409$	5.70363e13	−	3.29299e13i	0.246418	−	0.142270i	0.618123	+	0.786081i	$0.287893\pi$
$410$	1.03480e13	−	5.97441e12i	0.0441107	−	0.0254674i
$411$	3.07299e14	+	2.60072e14i	1.29250	+	1.09386i
$412$		−	1.19487e14i		−	0.495889i
$413$	6.04293e13	+	1.60410e14i	0.247470	+	0.656912i
$414$	−2.53122e14	−	9.45555e13i	−1.02289	−	0.382107i
$415$	−7.00702e12	+	1.21365e13i	−0.0279427	+	0.0483982i
$416$	−3.71851e13	−	6.44065e13i	−0.146338	−	0.253464i
$417$	4.62281e13	−	1.66051e13i	0.179538	−	0.0644901i
$418$	−2.23947e14	−	1.29296e14i	−0.858373	−	0.495582i
$419$	1.41185e14			0.534087			0.267044	−	0.963684i	$-0.413953\pi$
$419$	1.41185e14			0.534087			0.267044	+	0.963684i	$0.413953\pi$
$420$	−3.44169e12	−	1.87514e13i	−0.0128499	−	0.0700105i
$421$	−1.89460e14			−0.698177			−0.349088	−	0.937090i	$-0.613509\pi$
$421$	−1.89460e14			−0.698177			−0.349088	+	0.937090i	$0.613509\pi$
$422$	−2.37434e14	−	1.37082e14i	−0.863622	−	0.498613i
$423$	5.60491e13	+	3.34345e14i	0.201232	+	1.20039i
$424$	5.75580e13	+	9.96934e13i	0.203983	+	0.353309i
$425$	6.08875e13	−	1.05460e14i	0.213005	−	0.368935i
$426$	2.72561e12	+	4.92466e11i	0.00941264	+	0.00170068i
$427$	4.05247e14	+	3.32373e14i	1.38155	+	1.13311i
$428$			2.64600e14i			0.890530i
$429$	4.72689e14	−	5.58525e14i	1.57058	−	1.85578i
$430$	3.32021e13	−	1.91692e13i	0.108915	−	0.0628823i
$431$	4.85686e13	−	2.80411e13i	0.157301	−	0.0908176i	−0.419283	−	0.907855i	$-0.637719\pi$
$431$	4.85686e13	−	2.80411e13i	0.157301	−	0.0908176i	0.576584	+	0.817038i	$0.304385\pi$
$432$	6.81960e13	−	3.82303e13i	0.218071	−	0.122249i
$433$			1.92194e14i			0.606814i	0.952861	+	0.303407i	$0.0981242\pi$
$433$			1.92194e14i			0.606814i	−0.952861	+	0.303407i	$0.901876\pi$
$434$	−4.00585e14	−	6.60131e13i	−1.24882	−	0.205796i
$435$	5.40187e11	−	2.98973e12i	0.00166285	−	0.00920324i
$436$	−3.83814e13	+	6.64785e13i	−0.116666	+	0.202072i
$437$	−2.45545e14	−	4.25296e14i	−0.737025	−	1.27657i
$438$	9.95644e13	+	2.77185e14i	0.295119	+	0.821602i
$439$	−7.32536e13	−	4.22930e13i	−0.214424	−	0.123798i	0.388941	−	0.921262i	$-0.372841\pi$
$439$	−7.32536e13	−	4.22930e13i	−0.214424	−	0.123798i	−0.603366	+	0.797464i	$0.706174\pi$
$440$	2.55676e13			0.0739095
$441$	−3.27446e14	+	1.24391e14i	−0.934820	+	0.355123i
$442$	1.80543e14			0.509046
$443$	5.11958e14	+	2.95579e14i	1.42565	+	0.823101i	0.996774	−	0.0802611i	$-0.0255754\pi$
$443$	5.11958e14	+	2.95579e14i	1.42565	+	0.823101i	0.428879	+	0.903362i	$0.358909\pi$
$444$	−7.46546e12	−	2.07836e13i	−0.0205329	−	0.0571630i
$445$	−3.70623e13	−	6.41939e13i	−0.100682	−	0.174387i
$446$	6.41118e13	−	1.11045e14i	0.172027	−	0.297959i
$447$	3.13334e13	−	1.73418e14i	0.0830455	−	0.459625i
$448$	−4.71108e13	−	7.76347e12i	−0.123337	−	0.0203248i
$449$			3.82324e14i			0.988727i	0.869255	+	0.494364i	$0.164599\pi$
$449$			3.82324e14i			0.988727i	−0.869255	+	0.494364i	$0.835401\pi$
$450$	1.72554e14	+	2.09202e14i	0.440814	+	0.534436i
$451$	2.54976e14	−	1.47210e14i	0.643470	−	0.371507i
$452$	1.42582e14	−	8.23196e13i	0.355470	−	0.205231i
$453$	3.24693e13	−	3.83654e13i	0.0799710	−	0.0944931i
$454$		−	2.26250e14i		−	0.550531i
$455$	7.58061e13	+	6.21743e13i	0.182239	+	0.149468i
$456$	1.39827e14	+	2.52640e13i	0.332111	+	0.0600061i
$457$	−2.03815e14	+	3.53018e14i	−0.478296	+	0.828433i	−0.999690	−	0.0248831i	$-0.992079\pi$
$457$	−2.03815e14	+	3.53018e14i	−0.478296	+	0.828433i	0.521395	+	0.853316i	$0.325412\pi$
$458$	1.58141e13	+	2.73908e13i	0.0366677	+	0.0635103i
$459$	−2.40243e12	+	1.89778e14i	−0.00550403	+	0.434787i
$460$	4.20500e13	+	2.42776e13i	0.0951914	+	0.0549588i
$461$	−3.53947e13			−0.0791741			−0.0395870	−	0.999216i	$-0.512604\pi$
$461$	−3.53947e13			−0.0791741			−0.0395870	+	0.999216i	$0.512604\pi$
$462$	−8.48039e13	−	4.62038e14i	−0.187450	−	1.02129i
$463$	7.12754e14			1.55684			0.778420	−	0.627744i	$-0.216021\pi$
$463$	7.12754e14			1.55684			0.778420	+	0.627744i	$0.216021\pi$
$464$	−6.58943e12	−	3.80441e12i	−0.0142233	−	0.00821180i
$465$	−1.12425e14	+	4.03829e13i	−0.239812	+	0.0861403i
$466$	−5.13809e13	−	8.89944e13i	−0.108313	−	0.187603i
$467$	−3.65831e14	+	6.33638e14i	−0.762145	+	1.32007i	0.179597	+	0.983740i	$0.442521\pi$
$467$	−3.65831e14	+	6.33638e14i	−0.762145	+	1.32007i	−0.941743	+	0.336334i	$0.890813\pi$
$468$	−1.40694e14	+	3.76632e14i	−0.289682	+	0.775471i
$469$	−8.62394e13	−	2.28924e14i	−0.175491	−	0.465844i
$470$		−	6.09190e13i		−	0.122522i
$471$	−1.97780e14	−	1.67384e14i	−0.393157	−	0.332735i
$472$	1.09393e14	−	6.31583e13i	0.214936	−	0.124094i
$473$	8.18105e14	−	4.72333e14i	1.58881	−	0.917301i
$474$	5.87136e13	+	4.96902e13i	0.112709	+	0.0953872i
$475$			4.92863e14i			0.935215i
$476$	7.35053e13	−	8.96215e13i	0.137873	−	0.168102i
$477$	2.17776e14	−	5.82980e14i	0.403794	−	1.08094i
$478$	3.56432e14	−	6.17358e14i	0.653315	−	1.13158i
$479$	6.55762e13	+	1.13581e14i	0.118823	+	0.205808i	0.919302	−	0.393554i	$-0.128755\pi$
$479$	6.55762e13	+	1.13581e14i	0.118823	+	0.205808i	−0.800478	+	0.599362i	$0.795421\pi$
$480$	−1.32217e13	+	4.74923e12i	−0.0236844	+	0.00850740i
$481$	9.83527e13	+	5.67840e13i	0.174176	+	0.100561i
$482$	−2.24534e14			−0.393119
$483$	2.99253e14	−	8.40421e14i	0.517999	−	1.45475i
$484$	3.37830e14			0.578161
$485$	−7.62265e13	−	4.40094e13i	−0.128981	−	0.0744674i
$486$	−3.94026e14	−	1.52902e14i	−0.659213	−	0.255808i
$487$	4.74189e14	+	8.21319e14i	0.784408	+	1.35863i	0.929352	+	0.369195i	$0.120366\pi$
$487$	4.74189e14	+	8.21319e14i	0.784408	+	1.35863i	−0.144944	+	0.989440i	$0.546300\pi$
$488$	1.93111e14	−	3.34479e14i	0.315863	−	0.547091i
$489$	7.34563e14	+	1.32721e14i	1.18804	+	0.214656i
$490$	6.17268e13	−	1.23168e13i	0.0987177	−	0.0196979i
$491$			4.20384e14i			0.664810i	0.943137	+	0.332405i	$0.107860\pi$
$491$			4.20384e14i			0.664810i	−0.943137	+	0.332405i	$0.892140\pi$
$492$	−1.04511e14	+	1.23489e14i	−0.163438	+	0.193117i
$493$	1.59966e13	−	9.23565e12i	0.0247383	−	0.0142827i
$494$	−6.32817e14	+	3.65357e14i	−0.967788	+	0.558753i
$495$	−8.79500e13	−	1.06629e14i	−0.133017	−	0.161268i
$496$			2.99174e14i			0.447481i
$497$	−1.48689e12	+	9.02285e12i	−0.00219947	+	0.0133470i
$498$	3.37360e13	−	1.86716e14i	0.0493551	−	0.273162i
$499$	−3.41241e14	+	5.91047e14i	−0.493751	+	0.855202i	−0.999974	−	0.00720059i	$-0.997708\pi$
$499$	−3.41241e14	+	5.91047e14i	−0.493751	+	0.855202i	0.506223	+	0.862403i	$0.331041\pi$
$500$	−4.92345e13	−	8.52767e13i	−0.0704587	−	0.122038i
$501$	−2.08551e14	−	5.80601e14i	−0.295193	−	0.821808i
$502$	−4.62722e13	−	2.67152e13i	−0.0647813	−	0.0374015i
$503$	−4.44929e14			−0.616122			−0.308061	−	0.951367i	$-0.599680\pi$
$503$	−4.44929e14			−0.616122			−0.308061	+	0.951367i	$0.599680\pi$
$504$	1.29679e14	+	2.23181e14i	0.177624	+	0.305695i
$505$	1.66897e14			0.226123
$506$	1.03612e15	+	5.98203e14i	1.38861	+	0.801716i
$507$	−4.43963e14	−	1.23598e15i	−0.588576	−	1.63858i
$508$	−4.91970e13	−	8.52117e13i	−0.0645191	−	0.111750i
$509$	−6.86325e14	+	1.18875e15i	−0.890394	+	1.54221i	−0.0509905	+	0.998699i	$0.516238\pi$
$509$	−6.86325e14	+	1.18875e15i	−0.890394	+	1.54221i	−0.839404	+	0.543509i	$0.817095\pi$
$510$	6.06397e12	−	3.35618e13i	0.00778254	−	0.0430734i
$511$	−9.09968e14	+	3.42800e14i	−1.15534	+	0.435237i
$512$			3.51844e13i			0.0441942i
$513$	−3.75626e14	−	6.70050e14i	−0.466778	−	0.832649i
$514$	8.84231e13	−	5.10511e13i	0.108710	−	0.0627636i
$515$	1.00525e14	−	5.80380e13i	0.122274	−	0.0705948i
$516$	−3.35328e14	+	3.96222e14i	−0.403550	+	0.476831i
$517$		−	1.50105e15i		−	1.78730i
$518$	6.82305e13	−	2.57036e13i	0.0803831	−	0.0302817i
$519$	−2.39645e14	−	4.32993e13i	−0.279350	−	0.0504731i
$520$	3.61237e13	−	6.25681e13i	0.0416653	−	0.0721664i
$521$	1.28033e14	+	2.21759e14i	0.146121	+	0.253089i	0.929791	−	0.368089i	$-0.119988\pi$
$521$	1.28033e14	+	2.21759e14i	0.146121	+	0.253089i	−0.783670	+	0.621178i	$0.786654\pi$
$522$	6.80074e12	+	4.05679e13i	0.00768013	+	0.0458137i
$523$	9.28292e13	+	5.35950e13i	0.103735	+	0.0598914i	0.550970	−	0.834525i	$-0.314258\pi$
$523$	9.28292e13	+	5.35950e13i	0.103735	+	0.0598914i	−0.447235	+	0.894417i	$0.647591\pi$
$524$	−1.89801e14			−0.209883
$525$	−6.81825e14	+	5.80288e14i	−0.746099	+	0.634991i
$526$	−1.88447e14			−0.204064
$527$	−6.28977e14	−	3.63140e14i	−0.674026	−	0.389149i
$528$	−3.25786e14	+	1.17022e14i	−0.345498	+	0.124103i
$529$	6.59636e14	+	1.14252e15i	0.692306	+	1.19911i
$530$	−5.59151e13	+	9.68478e13i	−0.0580780	+	0.100594i
$531$	−6.39703e14	−	2.38965e14i	−0.657595	−	0.245649i
$532$	−7.62789e13	+	4.62881e14i	−0.0776052	+	0.470929i
$533$		−	8.31958e14i		−	0.837725i
$534$	7.66066e14	+	6.48334e14i	0.763465	+	0.646133i
$535$	−2.22609e14	+	1.28524e14i	−0.219582	+	0.126776i
$536$	−1.56117e14	+	9.01340e13i	−0.152420	+	0.0879999i
$537$	4.60242e14	+	3.89510e14i	0.444762	+	0.376409i
$538$		−	8.26324e14i		−	0.790402i
$539$	1.52096e15	−	3.03489e14i	1.44005	−	0.287345i
$540$	6.52881e13	+	3.88042e13i	0.0611883	+	0.0363675i
$541$	−3.36470e14	+	5.82783e14i	−0.312148	+	0.540657i	−0.978827	−	0.204688i	$-0.934382\pi$
$541$	−3.36470e14	+	5.82783e14i	−0.312148	+	0.540657i	0.666679	+	0.745345i	$0.267715\pi$
$542$	6.11954e14	+	1.05994e15i	0.561983	+	0.973382i
$543$	2.36064e14	−	8.47941e13i	0.214601	−	0.0770845i
$544$	−7.39709e13	−	4.27071e13i	−0.0665682	−	0.0384332i
$545$	−7.45717e13			−0.0664344
$546$	−1.25050e15	−	4.45272e14i	−1.10287	−	0.392704i
$547$	−9.93325e14			−0.867284			−0.433642	−	0.901085i	$-0.642772\pi$
$547$	−9.93325e14			−0.867284			−0.433642	+	0.901085i	$0.642772\pi$
$548$	8.48232e14	+	4.89727e14i	0.733199	+	0.423313i
$549$	−2.05922e15	+	3.45205e14i	−1.76220	+	0.295412i
$550$	−6.00364e14	−	1.03986e15i	−0.508651	−	0.881009i
$551$	−3.73797e13	+	6.47435e13i	−0.0313546	+	0.0543078i
$552$	−6.46924e14	−	1.16887e14i	−0.537265	−	0.0970735i
$553$	−1.61046e14	+	1.96356e14i	−0.132423	+	0.161456i
$554$			1.04440e15i			0.850281i
$555$	1.38592e13	−	1.63759e13i	0.0111719	−	0.0132006i
$556$	1.03495e14	−	5.97531e13i	0.0826057	−	0.0476924i
$557$	−9.78521e14	+	5.64950e14i	−0.773333	+	0.446484i	−0.834062	−	0.551670i	$-0.813991\pi$
$557$	−9.78521e14	+	5.64950e14i	−0.773333	+	0.446484i	0.0607291	+	0.998154i	$0.480657\pi$
$558$	1.24770e15	−	1.02913e15i	0.976388	−	0.805344i
$559$		−	2.66938e15i		−	2.06845i
$560$	−1.63516e13	−	4.34056e13i	−0.0125466	−	0.0333051i
$561$	1.49417e14	−	8.26967e14i	0.113528	−	0.628337i
$562$	−4.38902e14	+	7.60200e14i	−0.330231	+	0.571976i
$563$	7.00006e14	+	1.21245e15i	0.521562	+	0.903371i	0.999685	+	0.0250789i	$0.00798369\pi$
$563$	7.00006e14	+	1.21245e15i	0.521562	+	0.903371i	−0.478124	+	0.878292i	$0.658683\pi$
$564$	2.78824e14	+	7.76238e14i	0.205729	+	0.572743i
$565$	1.38512e14	+	7.99699e13i	0.101209	+	0.0584333i
$566$	1.36040e14			0.0984409
$567$	4.84690e14	−	1.30854e15i	0.347342	−	0.937739i
$568$	6.73865e12			0.00478252
$569$	2.79177e14	+	1.61183e14i	0.196229	+	0.113293i	0.594895	−	0.803803i	$-0.297194\pi$
$569$	2.79177e14	+	1.61183e14i	0.196229	+	0.113293i	−0.398666	+	0.917096i	$0.630527\pi$
$570$	4.66629e13	+	1.29908e14i	0.0324833	+	0.0904326i
$571$	−4.74464e14	−	8.21796e14i	−0.327118	−	0.566586i	0.654820	−	0.755785i	$-0.272744\pi$
$571$	−4.74464e14	−	8.21796e14i	−0.327118	−	0.566586i	−0.981939	+	0.189199i	$0.939411\pi$
$572$	8.90094e14	−	1.54169e15i	0.607796	−	1.05273i
$573$	1.26725e14	−	7.01377e14i	0.0857064	−	0.474352i
$574$	−4.12984e14	−	3.38720e14i	−0.276642	−	0.226895i
$575$		−	2.28029e15i		−	1.51292i
$576$	1.46736e14	−	1.21031e14i	0.0964302	−	0.0795375i
$577$	−1.43035e15	+	8.25812e14i	−0.931054	+	0.537544i	−0.887145	−	0.461491i	$-0.847315\pi$
$577$	−1.43035e15	+	8.25812e14i	−0.931054	+	0.537544i	−0.0439092	+	0.999036i	$0.513981\pi$
$578$	−7.70198e14	+	4.44674e14i	−0.496591	+	0.286707i
$579$	2.82024e14	−	3.33238e14i	0.180117	−	0.212825i
$580$		−	7.39163e12i		−	0.00467613i
$581$	6.18103e14	+	1.01858e14i	0.387340	+	0.0638304i
$582$	1.17272e15	+	2.11888e14i	0.727976	+	0.131531i
$583$	−1.37776e15	+	2.38634e15i	−0.847219	+	1.46743i
$584$	3.58281e14	+	6.20561e14i	0.218249	+	0.378019i
$585$	−3.85202e14	+	6.45746e13i	−0.232451	+	0.0389677i
$586$	−2.37236e14	−	1.36969e14i	−0.141822	−	0.0818812i
$587$	−1.80536e15			−1.06919			−0.534595	−	0.845108i	$-0.679536\pi$
$587$	−1.80536e15			−1.06919			−0.534595	+	0.845108i	$0.679536\pi$
$588$	−7.30157e14	+	4.39464e14i	−0.428392	+	0.257838i
$589$	2.93949e15			1.70859
$590$	1.06271e14	+	6.13555e13i	0.0611967	+	0.0353319i
$591$	1.47614e15	−	5.30227e14i	0.842162	−	0.302504i
$592$	−2.68643e13	−	4.65304e13i	−0.0151847	−	0.0263007i
$593$	−3.64725e14	+	6.31723e14i	−0.204252	+	0.353774i	−0.949894	−	0.312572i	$-0.898809\pi$
$593$	−3.64725e14	+	6.31723e14i	−0.204252	+	0.353774i	0.745642	+	0.666346i	$0.232143\pi$
$594$	1.60871e15	+	9.56141e14i	0.892590	+	0.530514i
$595$	1.11103e14	+	1.83088e13i	0.0610775	+	0.0100651i
$596$		−	4.28750e14i		−	0.233534i
$597$	1.91084e14	+	1.61717e14i	0.103125	+	0.0872764i
$598$	2.92780e15	−	1.69037e15i	1.56562	−	0.903909i
$599$	1.40013e15	−	8.08368e14i	0.741860	−	0.428313i	−0.0808849	−	0.996723i	$-0.525775\pi$
$599$	1.40013e15	−	8.08368e14i	0.741860	−	0.428313i	0.822745	+	0.568410i	$0.192441\pi$
$600$	5.03622e14	+	4.26223e14i	0.264407	+	0.223772i
$601$			3.78655e13i			0.0196986i	0.999951	+	0.00984928i	$0.00313517\pi$
$601$			3.78655e13i			0.0196986i	−0.999951	+	0.00984928i	$0.996865\pi$
$602$	−1.32508e15	−	1.08680e15i	−0.683066	−	0.560234i
$603$	9.12929e14	+	3.41031e14i	0.466328	+	0.174200i
$604$	6.11411e13	−	1.05900e14i	0.0309478	−	0.0536032i
$605$	1.64094e14	+	2.84219e14i	0.0823071	+	0.142560i
$606$	−2.12662e15	+	7.63879e14i	−1.05704	+	0.379687i
$607$	−1.84619e15	−	1.06590e15i	−0.909366	−	0.525023i	−0.0291391	−	0.999575i	$-0.509277\pi$
$607$	−1.84619e15	−	1.06590e15i	−0.909366	−	0.525023i	−0.880227	+	0.474553i	$0.842610\pi$
$608$	3.45699e14			0.168744
$609$	−1.33576e14	+	2.45169e13i	−0.0646150	+	0.0118596i
$610$	3.75198e14			0.179865
$611$	−3.67333e15	−	2.12080e15i	−1.74515	−	1.00756i
$612$	7.63430e13	+	4.55403e14i	0.0359448	+	0.214419i
$613$	8.18246e14	+	1.41724e15i	0.381813	+	0.661320i	0.991322	−	0.131460i	$-0.0419664\pi$
$613$	8.18246e14	+	1.41724e15i	0.381813	+	0.661320i	−0.609508	+	0.792780i	$0.708633\pi$
$614$	3.44846e14	−	5.97291e14i	0.159477	−	0.276223i
$615$	−1.54656e14	−	2.79434e13i	−0.0708848	−	0.0128075i
$616$	−4.02906e14	−	1.06952e15i	−0.183025	−	0.485842i
$617$			7.85723e14i			0.353754i	0.984233	+	0.176877i	$0.0565995\pi$
$617$			7.85723e14i			0.353754i	−0.984233	+	0.176877i	$0.943401\pi$
$618$	−1.01526e15	+	1.19963e15i	−0.453046	+	0.535315i
$619$	−2.44813e15	+	1.41343e15i	−1.08277	+	0.625138i	−0.931642	−	0.363376i	$-0.881624\pi$
$619$	−2.44813e15	+	1.41343e15i	−1.08277	+	0.625138i	−0.151128	+	0.988514i	$0.548291\pi$
$620$	−2.51697e14	+	1.45317e14i	−0.110338	+	0.0637034i
$621$	1.73788e15	+	3.10007e15i	0.755119	+	1.34700i
$622$			2.49675e14i			0.107530i
$623$	−2.10125e15	+	2.56195e15i	−0.897003	+	1.09367i
$624$	−1.73921e14	+	9.62588e14i	−0.0735932	+	0.407310i
$625$	−1.12010e15	+	1.94008e15i	−0.469806	+	0.813727i
$626$	−4.44494e14	−	7.69887e14i	−0.184802	−	0.320087i
$627$	1.14978e15	+	3.20096e15i	0.473854	+	1.31919i
$628$	−5.45928e14	−	3.15192e14i	−0.223027	−	0.128765i
$629$	1.30433e14			0.0528212
$630$	−1.24774e14	+	2.17505e14i	−0.0500902	+	0.0873165i
$631$	4.81674e15			1.91687			0.958434	−	0.285315i	$-0.0920982\pi$
$631$	4.81674e15			1.91687			0.958434	+	0.285315i	$0.0920982\pi$
$632$	1.62066e14	+	9.35690e13i	0.0639365	+	0.0369137i
$633$	1.21902e15	+	3.39373e15i	0.476751	+	1.32726i
$634$	1.73936e15	+	3.01266e15i	0.674370	+	1.16804i
$635$	4.77927e13	−	8.27795e13i	0.0183699	−	0.0318176i
$636$	2.69209e14	−	1.48997e15i	0.102583	−	0.567758i
$637$	1.40623e15	−	4.15082e15i	0.531239	−	1.56808i
$638$		−	1.82131e14i		−	0.0682135i
$639$	−2.31803e13	−	2.81035e13i	−0.00860724	−	0.0104353i
$640$	−2.96008e13	+	1.70900e13i	−0.0108972	+	0.00629149i
$641$	4.16978e15	−	2.40742e15i	1.52193	−	0.878684i	0.522261	−	0.852785i	$-0.325089\pi$
$641$	4.16978e15	−	2.40742e15i	1.52193	−	0.878684i	0.999665	−	0.0258989i	$-0.00824481\pi$
$642$	2.24827e15	−	2.65654e15i	0.813590	−	0.961332i
$643$		−	2.48025e15i		−	0.889887i	−0.895559	−	0.444943i	$-0.853224\pi$
$643$		−	2.48025e15i		−	0.889887i	0.895559	−	0.444943i	$-0.146776\pi$
$644$	3.52913e14	−	2.14157e15i	0.125544	−	0.761834i
$645$	−4.96222e14	−	8.96578e13i	−0.175024	−	0.0316235i
$646$	−4.19613e14	+	7.26791e14i	−0.146747	+	0.254174i
$647$	3.50641e14	+	6.07328e14i	0.121588	+	0.210596i	0.920394	−	0.390992i	$-0.127868\pi$
$647$	3.50641e14	+	6.07328e14i	0.121588	+	0.210596i	−0.798806	+	0.601588i	$0.794535\pi$
$648$	−1.00951e15	−	1.95627e14i	−0.347096	−	0.0672615i
$649$	2.61853e15	+	1.51181e15i	0.892713	+	0.515408i
$650$	−3.39295e15			−1.14698
$651$	3.46090e15	+	4.06648e15i	1.16010	+	1.36309i
$652$	1.81609e15			0.603637
$653$	−3.26014e15	−	1.88225e15i	−1.07452	−	0.620374i	−0.145107	−	0.989416i	$-0.546353\pi$
$653$	−3.26014e15	−	1.88225e15i	−1.07452	−	0.620374i	−0.929413	+	0.369042i	$0.879686\pi$
$654$	9.50202e14	−	3.41312e14i	0.310555	−	0.111551i
$655$	−9.21918e13	−	1.59681e14i	−0.0298789	−	0.0517518i
$656$	−1.96798e14	+	3.40865e14i	−0.0632486	+	0.109550i
$657$	1.35559e15	−	3.62887e15i	0.432035	−	1.15654i
$658$	−2.54831e15	+	9.59991e14i	−0.805396	+	0.303406i
$659$		−	5.76613e15i		−	1.80723i	−0.428341	−	0.903617i	$-0.640902\pi$
$659$		−	5.76613e15i		−	1.80723i	0.428341	−	0.903617i	$-0.359098\pi$
$660$	−2.56694e14	−	2.17244e14i	−0.0797856	−	0.0675238i
$661$	4.76808e15	−	2.75285e15i	1.46972	−	0.848545i	0.470301	−	0.882506i	$-0.344146\pi$
$661$	4.76808e15	−	2.75285e15i	1.46972	−	0.848545i	0.999423	+	0.0339609i	$0.0108122\pi$
$662$	−1.23001e15	+	7.10146e14i	−0.376001	+	0.217085i
$663$	−1.81262e15	−	1.53405e15i	−0.549518	−	0.465066i
$664$		−	4.61626e14i		−	0.138792i
$665$	−4.26475e14	+	1.60660e14i	−0.127167	+	0.0479060i
$666$	−1.01644e14	+	2.72097e14i	−0.0300589	+	0.0804667i
$667$	1.72942e14	−	2.99543e14i	0.0507233	−	0.0878553i
$668$	−7.50469e14	−	1.29985e15i	−0.218304	−	0.378114i
$669$	−1.58721e15	+	5.70123e14i	−0.457920	+	0.164484i
$670$	−1.51660e14	−	8.75612e13i	−0.0433971	−	0.0250553i
$671$	9.24495e15			2.62380
$672$	4.07020e14	+	4.78239e14i	0.114574	+	0.134621i
$673$	−2.50963e15			−0.700691			−0.350346	−	0.936620i	$-0.613936\pi$
$673$	−2.50963e15			−0.700691			−0.350346	+	0.936620i	$0.613936\pi$
$674$	2.20919e15	+	1.27548e15i	0.611793	+	0.353219i
$675$	4.51490e13	−	3.56651e15i	0.0124016	−	0.979655i
$676$	−1.59759e15	−	2.76711e15i	−0.435270	−	0.753910i
$677$	4.71508e14	−	8.16676e14i	0.127424	−	0.220705i	−0.795254	−	0.606277i	$-0.792662\pi$
$677$	4.71508e14	−	8.16676e14i	0.127424	−	0.220705i	0.922678	+	0.385572i	$0.125996\pi$
$678$	−2.13096e15	−	3.85023e14i	−0.571230	−	0.103210i
$679$	−6.39747e14	+	3.88216e15i	−0.170108	+	1.03226i
$680$		−	8.29762e13i		−	0.0218854i
$681$	−1.92242e15	+	2.27152e15i	−0.502966	+	0.594301i
$682$	−6.20185e15	+	3.58064e15i	−1.60956	+	0.929280i
$683$	3.66848e15	−	2.11800e15i	0.944436	−	0.545270i	0.0530877	−	0.998590i	$-0.483094\pi$
$683$	3.66848e15	−	2.11800e15i	0.944436	−	0.545270i	0.891348	+	0.453320i	$0.149760\pi$
$684$	−1.18917e15	−	1.44173e15i	−0.303694	−	0.368194i
$685$			9.51497e14i			0.241051i
$686$	−1.48795e15	−	2.38800e15i	−0.373942	−	0.600139i
$687$	7.39652e13	−	4.09369e14i	0.0184402	−	0.102059i
$688$	−6.31439e14	+	1.09368e15i	−0.156169	+	0.270493i
$689$	3.89319e15	+	6.74320e15i	0.955211	+	1.65447i
$690$	−2.15892e14	−	6.01036e14i	−0.0525491	−	0.146295i
$691$	−3.95325e15	−	2.28241e15i	−0.954607	−	0.551143i	−0.0600982	−	0.998192i	$-0.519141\pi$
$691$	−3.95325e15	−	2.28241e15i	−0.954607	−	0.551143i	−0.894509	+	0.447050i	$0.852475\pi$
$692$	−5.92485e14			−0.141936
$693$	−3.07446e15	+	5.35936e15i	−0.730696	+	1.27374i
$694$	2.67737e15			0.631294
$695$	1.00541e14	+	5.80475e13i	0.0235195	+	0.0135790i
$696$	3.38312e13	+	9.41852e13i	0.00785176	+	0.0218591i
$697$	−4.77752e14	−	8.27490e14i	−0.110007	−	0.190538i
$698$	1.82007e15	−	3.15245e15i	0.415799	−	0.720184i
$699$	−2.40318e14	+	1.33007e15i	−0.0544705	+	0.301473i
$700$	−1.38139e15	+	1.68426e15i	−0.310654	+	0.378766i
$701$			7.20467e15i			1.60755i	0.594932	+	0.803776i	$0.297179\pi$
$701$			7.20467e15i			1.60755i	−0.594932	+	0.803776i	$0.702821\pi$
$702$	4.61274e15	−	2.58587e15i	1.02118	−	0.572470i
$703$	−4.57178e14	+	2.63952e14i	−0.100423	+	0.0579790i
$704$	−7.29369e14	+	4.21101e14i	−0.158964	+	0.0917776i
$705$	−5.17621e14	+	6.11617e14i	−0.111937	+	0.132263i
$706$			1.08457e15i			0.232718i
$707$	−2.63003e15	−	6.98146e15i	−0.559957	−	1.48641i
$708$	−1.63494e15	−	2.95402e14i	−0.345397	−	0.0624066i
$709$	1.27853e15	−	2.21447e15i	0.268013	−	0.464212i	−0.700336	−	0.713814i	$-0.746966\pi$
$709$	1.27853e15	−	2.21447e15i	0.268013	−	0.464212i	0.968349	+	0.249602i	$0.0802997\pi$
$710$	3.27315e12	+	5.66926e12i	0.000680840	+	0.00117925i
$711$	−1.67263e14	−	9.97763e14i	−0.0345238	−	0.205942i
$712$	2.11456e15	+	1.22084e15i	0.433092	+	0.250046i
$713$	−1.35999e16			−2.76403
$714$	−1.49948e15	+	2.75220e14i	−0.302414	+	0.0555059i
$715$	1.72938e15			0.346104
$716$	1.27040e15	+	7.33465e14i	0.252301	+	0.145666i
$717$	−8.82413e15	+	3.16962e15i	−1.73907	+	0.624671i
$718$	1.84185e15	+	3.19018e15i	0.360222	+	0.623922i
$719$	−2.75951e15	+	4.77962e15i	−0.535579	+	0.927650i	0.463556	+	0.886068i	$0.346573\pi$
$719$	−2.75951e15	+	4.77962e15i	−0.535579	+	0.927650i	−0.999135	+	0.0415827i	$0.986760\pi$
$720$	1.73098e14	+	6.46618e13i	0.0333398	+	0.0124543i
$721$	−4.01191e15	−	3.29047e15i	−0.766845	−	0.628947i
$722$			3.31070e14i			0.0628008i
$723$	2.25429e15	+	1.90784e15i	0.424374	+	0.359154i
$724$	5.28501e14	−	3.05130e14i	0.0987379	−	0.0570063i
$725$	−3.00626e14	+	1.73566e14i	−0.0557400	+	0.0321815i
$726$	−3.39176e15	−	2.87050e15i	−0.624128	−	0.528210i
$727$		−	2.93675e15i		−	0.536325i	−0.963374	−	0.268163i	$-0.913584\pi$
$727$		−	2.93675e15i		−	0.536325i	0.963374	−	0.268163i	$-0.0864165\pi$
$728$	−3.18655e15	−	5.25116e14i	−0.577561	−	0.0951772i
$729$	2.65677e15	+	4.88311e15i	0.477917	+	0.878405i
$730$	−3.48054e14	+	6.02848e14i	−0.0621400	+	0.107630i
$731$	−1.53289e15	−	2.65505e15i	−0.271623	−	0.470465i
$732$	−4.78083e15	+	1.71727e15i	−0.840799	+	0.302014i
$733$	−2.07885e14	−	1.20023e14i	−0.0362871	−	0.0209503i	0.481747	−	0.876310i	$-0.340003\pi$
$733$	−2.07885e14	−	1.20023e14i	−0.0362871	−	0.0209503i	−0.518034	+	0.855360i	$0.673336\pi$
$734$	−2.46809e15			−0.427595
$735$	−7.24381e14	−	4.00825e14i	−0.124562	−	0.0689247i
$736$	−1.59942e15			−0.272982
$737$	−3.73694e15	−	2.15752e15i	−0.633060	−	0.365497i
$738$	2.09854e15	−	3.51796e14i	0.352864	−	0.0591535i
$739$	−1.51899e15	−	2.63097e15i	−0.253519	−	0.439108i	0.710973	−	0.703219i	$-0.248255\pi$
$739$	−1.51899e15	−	2.63097e15i	−0.253519	−	0.439108i	−0.964492	+	0.264111i	$0.914921\pi$
$740$	2.60975e13	−	4.52023e13i	0.00432340	−	0.00748834i
$741$	9.45778e15	+	1.70884e15i	1.55521	+	0.280997i
$742$	4.93238e15	+	8.12816e14i	0.805073	+	0.132669i
$743$		−	5.04901e15i		−	0.818028i	−0.912528	−	0.409014i	$-0.865873\pi$
$743$		−	5.04901e15i		−	0.818028i	0.912528	−	0.409014i	$-0.134127\pi$
$744$	2.54204e15	−	3.00366e15i	0.408820	−	0.483058i
$745$	3.60710e14	−	2.08256e14i	0.0575835	−	0.0332459i
$746$	−8.44453e14	+	4.87545e14i	−0.133817	+	0.0772594i
$747$	−1.92520e15	+	1.58795e15i	−0.302840	+	0.249788i
$748$		−	2.04455e15i		−	0.319255i
$749$	8.88426e15	+	7.28665e15i	1.37712	+	1.12948i
$750$	−2.30279e14	+	1.27450e15i	−0.0354337	+	0.196112i
$751$	−2.74205e15	+	4.74938e15i	−0.418848	+	0.725466i	−0.995824	−	0.0912952i	$-0.970899\pi$
$751$	−2.74205e15	+	4.74938e15i	−0.418848	+	0.725466i	0.576976	+	0.816761i	$0.304233\pi$
$752$	1.00334e15	+	1.73784e15i	0.152143	+	0.263519i
$753$	2.37569e14	+	6.61385e14i	0.0357616	+	0.0995594i
$754$	−4.45705e14	−	2.57328e14i	−0.0666047	−	0.0384542i
$755$	1.18792e14			0.0176229
$756$	5.94381e14	−	3.34257e15i	0.0875377	−	0.492278i
$757$	−1.05069e16			−1.53619			−0.768096	−	0.640334i	$-0.778796\pi$
$757$	−1.05069e16			−1.53619			−0.768096	+	0.640334i	$0.778796\pi$
$758$	4.15829e15	+	2.40079e15i	0.603580	+	0.348477i
$759$	−5.31960e15	−	1.48096e16i	−0.766566	−	2.13410i
$760$	1.67916e14	+	2.90839e14i	0.0240224	+	0.0416081i
$761$	−4.74452e15	+	8.21774e15i	−0.673870	+	1.16718i	0.302927	+	0.953014i	$0.402036\pi$
$761$	−4.74452e15	+	8.21774e15i	−0.673870	+	1.16718i	−0.976798	+	0.214164i	$0.931297\pi$
$762$	−2.30103e14	+	1.27353e15i	−0.0324467	+	0.179580i
$763$	1.17514e15	+	3.11941e15i	0.164514	+	0.436705i
$764$		−	1.73404e15i		−	0.241016i
$765$	−3.46051e14	+	2.85430e14i	−0.0477532	+	0.0393878i
$766$	2.02690e15	−	1.17023e15i	0.277699	−	0.160329i
$767$	7.39929e15	−	4.27198e15i	1.00650	−	0.581106i
$768$	2.98957e14	−	3.53245e14i	0.0403759	−	0.0477078i
$769$			3.01829e15i			0.404731i	0.979310	+	0.202365i	$0.0648629\pi$
$769$			3.01829e15i			0.404731i	−0.979310	+	0.202365i	$0.935137\pi$
$770$	7.04090e14	−	8.58463e14i	0.0937410	−	0.114294i
$771$	−1.32153e15	−	2.38775e14i	−0.174694	−	0.0315638i
$772$	5.31065e14	−	9.19831e14i	0.0697031	−	0.120729i
$773$	−5.46147e15	−	9.45954e15i	−0.711742	−	1.23277i	−0.964203	−	0.265165i	$-0.914573\pi$
$773$	−5.46147e15	−	9.45954e15i	−0.711742	−	1.23277i	0.252461	−	0.967607i	$-0.418760\pi$
$774$	6.73329e15	−	1.12876e15i	0.871268	−	0.146058i
$775$	1.18204e16	+	6.82452e15i	1.51870	+	0.876824i
$776$	2.89936e15			0.369882
$777$	−9.03423e14	−	3.21686e14i	−0.114439	−	0.0407490i
$778$	−6.92115e15			−0.870544
$779$	3.34912e15	+	1.93362e15i	0.418287	+	0.241498i
$780$	−8.94310e14	+	3.21235e14i	−0.110909	+	0.0398385i
$781$	8.06510e13	+	1.39692e14i	0.00993182	+	0.0172024i
$782$	1.94139e15	−	3.36258e15i	0.237397	−	0.411184i
$783$	2.76422e14	−	4.65080e14i	0.0335647	−	0.0564727i
$784$	−1.55802e15	+	1.36801e15i	−0.187861	+	0.164950i
$785$		−	6.12390e14i		−	0.0733238i
$786$	1.90557e15	+	1.61272e15i	0.226570	+	0.191749i
$787$	6.78581e15	−	3.91779e15i	0.801199	−	0.462573i	−0.0426909	−	0.999088i	$-0.513593\pi$
$787$	6.78581e15	−	3.91779e15i	0.801199	−	0.462573i	0.843890	+	0.536516i	$0.180260\pi$
$788$	3.30478e15	−	1.90801e15i	0.387479	−	0.223711i
$789$	1.89198e15	+	1.60121e15i	0.220289	+	0.186434i
$790$			1.81796e14i			0.0210202i
$791$	1.16249e15	−	7.05431e15i	0.133481	−	0.809997i
$792$	4.26515e15	+	1.59328e15i	0.486347	+	0.181678i
$793$	1.30619e16	−	2.26239e16i	1.47912	−	2.56192i
$794$	3.87537e15	+	6.71234e15i	0.435814	+	0.754851i
$795$	1.38428e15	−	4.97232e14i	0.154598	−	0.0555316i
$796$	5.27445e14	+	3.04521e14i	0.0585000	+	0.0337750i
$797$	7.87452e15			0.867367			0.433684	−	0.901065i	$-0.357214\pi$
$797$	7.87452e15			0.867367			0.433684	+	0.901065i	$0.357214\pi$
$798$	4.69887e15	−	3.99912e15i	0.514017	−	0.437470i
$799$	−4.87147e15			−0.529240
$800$	1.39014e15	+	8.02598e14i	0.149990	+	0.0865970i
$801$	−2.18237e15	−	1.30183e16i	−0.233857	−	1.39501i
$802$	3.68547e15	+	6.38343e15i	0.392224	+	0.679352i
$803$	−8.57611e15	+	1.48543e16i	−0.906473	+	1.57006i
$804$	2.33324e15	+	4.21572e14i	0.244935	+	0.0442552i
$805$	1.97314e15	−	7.43314e14i	0.205722	−	0.0774988i
$806$			2.02359e16i			2.09547i
$807$	−7.02117e15	+	8.29616e15i	−0.722112	+	0.853242i
$808$	−4.76107e15	+	2.74881e15i	−0.486343	+	0.280790i
$809$	5.13780e15	−	2.96631e15i	0.521267	−	0.300954i	−0.216186	−	0.976352i	$-0.569362\pi$
$809$	5.13780e15	−	2.96631e15i	0.521267	−	0.300954i	0.737453	+	0.675398i	$0.236028\pi$
$810$	−3.25767e14	−	9.44332e14i	−0.0328277	−	0.0951606i
$811$			1.06832e16i			1.06927i	0.845082	+	0.534636i	$0.179551\pi$
$811$			1.06832e16i			1.06927i	−0.845082	+	0.534636i	$0.820449\pi$
$812$	−3.09200e14	+	1.16481e14i	−0.0307384	+	0.0115797i
$813$	2.86222e15	−	1.58413e16i	0.282621	−	1.56420i
$814$	6.43047e14	−	1.11379e15i	0.0630680	−	0.109237i
$815$	8.82126e14	+	1.52789e15i	0.0859338	+	0.148842i
$816$	3.79779e14	+	1.05729e15i	0.0367481	+	0.102306i
$817$	1.07458e16	+	6.20412e15i	1.03281	+	0.596291i
$818$	−2.10751e15			−0.201200
$819$	8.77141e15	+	1.50958e16i	0.831779	+	1.43151i
$820$	−3.82362e14			−0.0360163
$821$	−3.57061e15	−	2.06149e15i	−0.334083	−	0.192883i	0.323569	−	0.946204i	$-0.395117\pi$
$821$	−3.57061e15	−	2.06149e15i	−0.334083	−	0.192883i	−0.657652	+	0.753321i	$0.728450\pi$
$822$	−4.35497e15	−	1.21241e16i	−0.404753	−	1.12682i
$823$	−9.65855e15	−	1.67291e16i	−0.891688	−	1.54445i	−0.837851	−	0.545899i	$-0.816188\pi$
$823$	−9.65855e15	−	1.67291e16i	−0.891688	−	1.54445i	−0.0538372	−	0.998550i	$-0.517145\pi$
$824$	−1.91179e15	+	3.31131e15i	−0.175323	+	0.303669i
$825$	−2.80801e15	+	1.55413e16i	−0.255801	+	1.41576i
$826$	8.91900e14	−	5.41229e15i	0.0807098	−	0.489768i
$827$			7.80124e15i			0.701267i	0.936513	+	0.350634i	$0.114034\pi$
$827$			7.80124e15i			0.701267i	−0.936513	+	0.350634i	$0.885966\pi$
$828$	5.50184e15	+	6.67035e15i	0.491293	+	0.595637i
$829$	−5.83622e15	+	3.36954e15i	−0.517704	+	0.298896i	−0.735995	−	0.676987i	$-0.763285\pi$
$829$	−5.83622e15	+	3.36954e15i	−0.517704	+	0.298896i	0.218291	+	0.975884i	$0.429952\pi$
$830$	3.88368e14	−	2.24224e14i	0.0342227	−	0.0197585i
$831$	8.87412e15	−	1.04856e16i	0.776819	−	0.917883i
$832$			2.37985e15i			0.206953i
$833$	−9.84932e14	−	4.93606e15i	−0.0850861	−	0.426416i
$834$	−1.54679e15	−	2.79476e14i	−0.132745	−	0.0239845i
$835$	7.29048e14	−	1.26275e15i	0.0621556	−	0.107657i
$836$	4.13747e15	+	7.16631e15i	0.350429	+	0.606961i
$837$	−2.12711e16	−	2.69274e14i	−1.78978	−	0.0226571i
$838$	−3.91264e15	−	2.25896e15i	−0.327060	−	0.188828i
$839$	−1.36784e16			−1.13591			−0.567956	−	0.823059i	$-0.692266\pi$
$839$	−1.36784e16			−1.13591			−0.567956	+	0.823059i	$0.692266\pi$
$840$	−2.04644e14	+	5.74722e14i	−0.0168835	+	0.0474157i
$841$	1.21479e16			0.995684
$842$	5.25046e15	+	3.03136e15i	0.427544	+	0.246843i
$843$	1.08658e16	−	3.90299e15i	0.879044	−	0.315752i
$844$	4.38664e15	+	7.59788e15i	0.352572	+	0.610673i
$845$	1.55199e15	−	2.68813e15i	0.123930	−	0.214653i
$846$	3.79625e15	−	1.01624e16i	0.301174	−	0.806234i
$847$	9.30330e15	−	1.13431e16i	0.733295	−	0.894070i
$848$		−	3.68371e15i		−	0.288475i
$849$	−1.36582e15	−	1.15591e15i	−0.106267	−	0.0899358i
$850$	−3.37473e15	+	1.94840e15i	−0.260876	+	0.150617i
$851$	2.11519e15	−	1.22120e15i	0.162456	−	0.0937941i
$852$	−6.76549e13	−	5.72574e13i	−0.00516276	−	0.00436932i
$853$			1.59642e16i			1.21040i	0.796074	+	0.605199i	$0.206907\pi$
$853$			1.59642e16i			1.21040i	−0.796074	+	0.605199i	$0.793093\pi$
$854$	−5.91255e15	−	1.56950e16i	−0.445407	−	1.18234i
$855$	6.35326e14	−	1.70075e15i	0.0475535	−	0.127299i
$856$	4.23360e15	−	7.33280e15i	0.314850	−	0.545336i
$857$	1.07140e16	+	1.85572e16i	0.791696	+	1.37126i	0.924916	+	0.380171i	$0.124135\pi$
$857$	1.07140e16	+	1.85572e16i	0.791696	+	1.37126i	−0.133220	+	0.991086i	$0.542532\pi$
$858$	−2.20359e16	+	7.91529e15i	−1.61790	+	0.581148i
$859$	−2.06836e16	−	1.19417e16i	−1.50891	−	0.871171i	−0.999946	−	0.0103837i	$-0.996695\pi$
$859$	−2.06836e16	−	1.19417e16i	−1.50891	−	0.871171i	−0.508966	−	0.860787i	$-0.669972\pi$
$860$	−1.22683e15			−0.0889290
$861$	1.26824e15	+	6.90976e15i	0.0913447	+	0.497675i
$862$	−1.79463e15			−0.128436
$863$	2.21904e15	+	1.28116e15i	0.157800	+	0.0911056i	0.576820	−	0.816871i	$-0.304293\pi$
$863$	2.21904e15	+	1.28116e15i	0.157800	+	0.0911056i	−0.419021	+	0.907977i	$0.637627\pi$
$864$	−2.50159e15	−	3.16680e13i	−0.176763	−	0.00223766i
$865$	−2.87786e14	−	4.98461e14i	−0.0202061	−	0.0349979i
$866$	3.07510e15	−	5.32623e15i	0.214541	−	0.371596i
$867$	1.15110e16	+	2.07982e15i	0.798009	+	0.144185i
$868$	1.00451e16	+	8.23877e15i	0.691986	+	0.567550i
$869$			4.47949e15i			0.306634i
$870$	−6.28057e13	+	7.42108e13i	−0.00427212	+	0.00504790i
$871$	−1.05596e16	+	6.09661e15i	−0.713755	+	0.412086i
$872$	2.12731e15	−	1.22820e15i	0.142886	−	0.0824955i
$873$	−9.97351e15	−	1.20918e16i	−0.665687	−	0.807069i
$874$			1.57149e16i			1.04231i
$875$	−4.21911e15	−	6.95274e14i	−0.278084	−	0.0458260i
$876$	1.67574e15	−	9.27460e15i	0.109758	−	0.607467i
$877$	8.97030e14	−	1.55370e15i	0.0583861	−	0.101128i	−0.835355	−	0.549711i	$-0.814738\pi$
$877$	8.97030e14	−	1.55370e15i	0.0583861	−	0.101128i	0.893741	+	0.448583i	$0.148071\pi$
$878$	1.35338e15	+	2.34412e15i	0.0875384	+	0.151621i
$879$	1.21801e15	+	3.39091e15i	0.0782911	+	0.217960i
$880$	−7.08550e14	−	4.09081e14i	−0.0452601	−	0.0261309i
$881$	−1.02815e16			−0.652660			−0.326330	−	0.945256i	$-0.605812\pi$
$881$	−1.02815e16			−0.652660			−0.326330	+	0.945256i	$0.605812\pi$
$882$	1.10647e16	+	1.79191e15i	0.698013	+	0.113041i
$883$	−2.80151e16			−1.75634			−0.878168	−	0.478352i	$-0.841234\pi$
$883$	−2.80151e16			−1.75634			−0.878168	+	0.478352i	$0.841234\pi$
$884$	−5.00334e15	−	2.88868e15i	−0.311726	−	0.179975i
$885$	−5.45612e14	−	1.51897e15i	−0.0337828	−	0.0940504i
$886$	−9.45853e15	−	1.63827e16i	−0.582020	−	1.00809i
$887$	−2.70759e15	+	4.68969e15i	−0.165578	+	0.286790i	−0.936861	−	0.349703i	$-0.886282\pi$
$887$	−2.70759e15	+	4.68969e15i	−0.165578	+	0.286790i	0.771282	+	0.636493i	$0.219616\pi$
$888$	−1.25649e14	+	6.95421e14i	−0.00763640	+	0.0422645i
$889$	−4.21589e15	−	6.94744e14i	−0.254642	−	0.0419629i
$890$			2.37199e15i			0.142386i
$891$	−8.02696e15	−	2.32685e16i	−0.478877	−	1.38816i
$892$	−3.55344e15	+	2.05158e15i	−0.210689	+	0.121641i
$893$	1.70749e16	−	9.85821e15i	1.00618	−	0.580918i
$894$	−3.64303e15	+	4.30458e15i	−0.213357	+	0.252101i
$895$			1.42506e15i			0.0829480i
$896$	1.18136e15	+	9.68921e14i	0.0683420	+	0.0560524i
$897$	−4.37575e16	−	7.90615e15i	−2.51590	−	0.454576i
$898$	6.11718e15	−	1.05953e16i	0.349568	−	0.605469i
$899$	1.03517e15	+	1.79296e15i	0.0587940	+	0.101834i
$900$	−1.43472e15	−	8.55842e15i	−0.0809903	−	0.483125i
$901$	7.74456e15	+	4.47132e15i	0.434521	+	0.250871i
$902$	−9.42147e15			−0.525391
$903$	4.06921e15	+	2.21704e16i	0.225542	+	1.22883i
$904$	−5.26846e15			−0.290240
$905$	5.13416e14	+	2.96421e14i	0.0281127	+	0.0162309i
$906$	−1.51366e15	+	5.43706e14i	−0.0823804	+	0.0295910i
$907$	−8.40682e15	−	1.45610e16i	−0.454770	−	0.787685i	0.543905	−	0.839147i	$-0.316945\pi$
$907$	−8.40682e15	−	1.45610e16i	−0.454770	−	0.787685i	−0.998675	+	0.0514622i	$0.983612\pi$
$908$	−3.62000e15	+	6.27003e15i	−0.194642	+	0.337130i
$909$	2.78415e16	+	1.04004e16i	1.48796	+	0.555837i
$910$	−1.10601e15	−	2.93592e15i	−0.0587533	−	0.155961i
$911$			2.09532e16i			1.10637i	0.833059	+	0.553185i	$0.186588\pi$
$911$			2.09532e16i			1.10637i	−0.833059	+	0.553185i	$0.813412\pi$
$912$	−3.47076e15	−	2.93736e15i	−0.182160	−	0.154165i
$913$	9.56945e15	−	5.52493e15i	0.499227	−	0.288229i
$914$	1.12966e16	−	6.52207e15i	0.585790	−	0.338206i
$915$	−3.76693e15	−	3.18801e15i	−0.194165	−	0.164325i
$916$		−	1.01210e15i		−	0.0518560i
$917$	−5.22682e15	+	6.37281e15i	−0.266199	+	0.324563i
$918$	3.10303e15	−	5.22085e15i	0.157091	−	0.264306i
$919$	−1.08039e16	+	1.87129e16i	−0.543683	+	0.941687i	0.455005	+	0.890489i	$0.349637\pi$
$919$	−1.08039e16	+	1.87129e16i	−0.543683	+	0.941687i	−0.998689	+	0.0511980i	$0.983696\pi$
$920$	−7.76882e14	−	1.34560e15i	−0.0388617	−	0.0673105i
$921$	−8.53730e15	+	3.06659e15i	−0.424514	+	0.152485i
$922$	9.80886e14	+	5.66315e14i	0.0484840	+	0.0279923i
$923$	4.55798e14			0.0223956
$924$	−5.04246e15	+	1.41612e16i	−0.246290	+	0.691681i
$925$	−2.45123e15			−0.119016
$926$	−1.97524e16	−	1.14041e16i	−0.953366	−	0.550426i
$927$	2.03861e16	−	3.41750e15i	0.978130	−	0.163972i
$928$	1.21741e14	+	2.10862e14i	0.00580662	+	0.0100574i
$929$	8.98996e15	−	1.55711e16i	0.426257	−	0.738298i	−0.570280	−	0.821450i	$-0.693165\pi$
$929$	8.98996e15	−	1.55711e16i	0.426257	−	0.738298i	0.996537	+	0.0831520i	$0.0264987\pi$
$930$	3.76174e15	+	6.79674e14i	0.177310	+	0.0320364i
$931$	1.34412e16	+	1.53082e16i	0.629817	+	0.717298i
$932$			3.28838e15i			0.153177i
$933$	2.12146e15	−	2.50670e15i	0.0982394	−	0.116079i
$934$	2.02764e16	−	1.17066e16i	0.933434	−	0.538918i
$935$	1.72009e15	−	9.93094e14i	0.0787203	−	0.0454492i
$936$	9.92513e15	−	8.18644e15i	0.451564	−	0.372459i
$937$		−	8.51933e14i		−	0.0385334i	−0.999814	−	0.0192667i	$-0.993867\pi$
$937$		−	8.51933e14i		−	0.0385334i	0.999814	−	0.0192667i	$-0.00613316\pi$
$938$	−1.27284e15	+	7.72395e15i	−0.0572347	+	0.347315i
$939$	−2.07898e15	+	1.15063e16i	−0.0929371	+	0.514371i
$940$	−9.74704e14	+	1.68824e15i	−0.0433181	+	0.0750292i
$941$	1.24176e16	+	2.15080e16i	0.548650	+	0.950290i	0.998367	+	0.0571192i	$0.0181915\pi$
$941$	1.24176e16	+	2.15080e16i	0.548650	+	0.950290i	−0.449717	+	0.893171i	$0.648475\pi$
$942$	2.80288e15	+	7.80315e15i	0.123119	+	0.342760i
$943$	−1.54951e16	−	8.94610e15i	−0.676675	−	0.390679i
$944$	−4.04213e15			−0.175495
$945$	3.10083e15	−	1.12352e15i	0.133845	−	0.0484961i
$946$	−3.02293e16			−1.29726
$947$	−1.84805e16	−	1.06697e16i	−0.788479	−	0.455228i	0.0509480	−	0.998701i	$-0.483776\pi$
$947$	−1.84805e16	−	1.06697e16i	−0.788479	−	0.455228i	−0.839427	+	0.543473i	$0.817109\pi$
$948$	−8.32075e14	−	2.31647e15i	−0.0352953	−	0.0982610i
$949$	2.42339e16	+	4.19743e16i	1.02202	+	1.77019i
$950$	7.88581e15	−	1.36586e16i	0.330649	−	0.572700i
$951$	8.13528e15	−	4.50257e16i	0.339140	−	1.87701i
$952$	−3.47098e15	+	1.30758e15i	−0.143863	+	0.0541956i
$953$		−	6.95504e15i		−	0.286608i	−0.989679	−	0.143304i	$-0.954227\pi$
$953$		−	6.95504e15i		−	0.286608i	0.989679	−	0.143304i	$-0.0457727\pi$
$954$	−1.53629e16	+	1.26716e16i	−0.629443	+	0.519177i
$955$	1.45886e15	−	8.42274e14i	0.0594286	−	0.0343111i
$956$	−1.97555e16	+	1.14058e16i	−0.800145	+	0.461964i
$957$	−1.54754e15	+	1.82857e15i	−0.0623200	+	0.0736368i
$958$		−	4.19688e15i		−	0.168041i
$959$	3.98021e16	−	1.49941e16i	1.58454	−	0.596924i
$960$	4.42399e14	+	7.99331e13i	0.0175115	+	0.00316399i
$961$	2.79980e16	−	4.84939e16i	1.10191	−	1.90857i
$962$	−1.81709e15	−	3.14729e15i	−0.0711071	−	0.123161i
$963$	−4.51445e16	+	7.56795e15i	−1.75655	+	0.294465i
$964$	6.22248e15	+	3.59255e15i	0.240735	+	0.138989i
$965$	1.03181e15			0.0396918
$966$	−2.17399e16	+	1.85024e16i	−0.831539	+	0.707707i
$967$	1.76632e15			0.0671773			0.0335887	−	0.999436i	$-0.489306\pi$
$967$	1.76632e15			0.0671773			0.0335887	+	0.999436i	$0.489306\pi$
$968$	−9.36223e15	−	5.40529e15i	−0.354050	−	0.204411i
$969$	1.03883e16	−	3.73146e15i	0.390628	−	0.140313i
$970$	1.40830e15	+	2.43925e15i	0.0526564	+	0.0912035i
$971$	−4.42280e15	+	7.66051e15i	−0.164434	+	0.284808i	−0.936454	−	0.350790i	$-0.885913\pi$
$971$	−4.42280e15	+	7.66051e15i	−0.164434	+	0.284808i	0.772020	+	0.635598i	$0.219246\pi$
$972$	8.47314e15	+	1.05418e16i	0.313242	+	0.389717i
$973$	8.43814e14	−	5.12049e15i	0.0310189	−	0.188231i
$974$		−	3.03481e16i		−	1.10932i
$975$	3.40647e16	+	2.88295e16i	1.23817	+	1.04788i
$976$	−1.07033e16	+	6.17956e15i	−0.386852	+	0.223349i
$977$	2.45277e16	−	1.41611e16i	0.881531	−	0.508952i	0.0103681	−	0.999946i	$-0.496700\pi$
$977$	2.45277e16	−	1.41611e16i	0.881531	−	0.508952i	0.871163	+	0.490994i	$0.163366\pi$
$978$	−1.82333e16	−	1.54311e16i	−0.651629	−	0.551484i
$979$			5.84462e16i			2.07707i
$980$	−1.90769e15	−	6.46294e14i	−0.0674163	−	0.0228395i
$981$	−1.24400e16	−	4.64703e15i	−0.437159	−	0.163304i
$982$	6.72614e15	−	1.16500e16i	0.235046	−	0.407111i
$983$	1.64213e16	+	2.84425e16i	0.570641	+	0.988380i	0.996500	+	0.0835903i	$0.0266387\pi$
$983$	1.64213e16	+	2.84425e16i	0.570641	+	0.988380i	−0.425859	+	0.904790i	$0.640028\pi$
$984$	4.87211e15	−	1.75006e15i	0.168362	−	0.0604755i
$985$	3.21044e15	+	1.85355e15i	0.110323	+	0.0636950i
$986$	−5.91082e14			−0.0201988
$987$	3.37415e16	+	1.20145e16i	1.14662	+	0.408283i
$988$	2.33829e16			0.790196
$989$	−4.97169e16	−	2.87041e16i	−1.67080	−	0.964637i
$990$	7.31272e14	+	4.36220e15i	0.0244391	+	0.145785i
$991$	2.11332e16	+	3.66039e16i	0.702362	+	1.21653i	0.967635	+	0.252354i	$0.0812047\pi$
$991$	2.11332e16	+	3.66039e16i	0.702362	+	1.21653i	−0.265273	+	0.964173i	$0.585462\pi$
$992$	4.78678e15	−	8.29095e15i	0.158208	−	0.274025i
$993$	1.83831e16	+	3.32148e15i	0.604224	+	0.109172i
$994$	1.85572e14	−	2.26258e14i	0.00606578	−	0.00739571i
$995$			5.91657e14i			0.0192328i
$996$	−3.92237e15	+	4.63464e15i	−0.126801	+	0.149827i
$997$	−3.25674e15	+	1.88028e15i	−0.104703	+	0.0604505i	−0.551437	−	0.834216i	$-0.685920\pi$
$997$	−3.25674e15	+	1.88028e15i	−0.104703	+	0.0604505i	0.446734	+	0.894667i	$0.352587\pi$
$998$	1.89135e16	−	1.09197e16i	0.604719	−	0.349135i
$999$	3.33246e15	−	1.86816e15i	0.105963	−	0.0594024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.12.f.a.5.10	✓	60
3.2	odd	2	inner	42.12.f.a.5.20	yes	60
7.3	odd	6	inner	42.12.f.a.17.20	yes	60
21.17	even	6	inner	42.12.f.a.17.10	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.12.f.a.5.10	✓	60	1.1	even	1	trivial
42.12.f.a.5.20	yes	60	3.2	odd	2	inner
42.12.f.a.17.10	yes	60	21.17	even	6	inner
42.12.f.a.17.20	yes	60	7.3	odd	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} +(142.282 + 396.110i) q^{3} +(512.000 + 886.810i) q^{4} +(-497.386 + 861.497i) q^{5} +(2394.71 - 13253.8i) q^{6} +(43875.4 + 7230.30i) q^{7} -32768.0i q^{8} +(-136659. + 112719. i) q^{9} +(27567.9 - 15916.3i) q^{10} +(679278. - 392181. i) q^{11} +(-278425. + 328985. i) q^{12} -2.21641e6i q^{13} +(-1.10023e6 - 902378. i) q^{14} +(-412016. - 74443.5i) q^{15} +(-524288. + 908093. i) q^{16} +(-1.27277e6 - 2.20450e6i) q^{17} +(5.59069e6 - 937214. i) q^{18} +(8.92235e6 + 5.15132e6i) q^{19} -1.01865e6 q^{20} +(3.37870e6 + 1.84082e7i) q^{21} -2.50996e7 q^{22} +(-4.12803e7 - 2.38332e7i) q^{23} +(1.29797e7 - 4.66230e6i) q^{24} +(2.39193e7 + 4.14294e7i) q^{25} +(-3.54625e7 + 6.14229e7i) q^{26} +(-6.40930e7 - 3.80939e7i) q^{27} +(1.60523e7 + 4.26110e7i) q^{28} +7.25633e6i q^{29} +(1.02270e7 + 8.65530e6i) q^{30} +(2.47090e8 - 1.42657e8i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(2.51996e8 + 2.13268e8i) q^{33} +8.14574e7i q^{34} +(-2.80519e7 + 3.42023e7i) q^{35} +(-1.69929e8 - 6.34782e7i) q^{36} +(-2.56198e7 + 4.43749e7i) q^{37} +(-1.64842e8 - 2.85515e8i) q^{38} +(8.77940e8 - 3.15355e8i) q^{39} +(2.82295e7 + 1.62983e7i) q^{40} +3.75363e8 q^{41} +(2.00898e8 - 5.64202e8i) q^{42} +1.20437e9 q^{43} +(6.95580e8 + 4.01593e8i) q^{44} +(-2.91348e7 - 1.73796e8i) q^{45} +(7.62662e8 + 1.32097e9i) q^{46} +(9.56863e8 - 1.65734e9i) q^{47} +(-4.34301e8 - 7.84700e7i) q^{48} +(1.87277e9 + 6.34464e8i) q^{49} -1.53083e9i q^{50} +(6.92133e8 - 8.17819e8i) q^{51} +(1.96553e9 - 1.13480e9i) q^{52} +(-3.04240e9 + 1.75653e9i) q^{53} +(1.16670e9 + 2.08118e9i) q^{54} +7.80261e8i q^{55} +(2.36922e8 - 1.43771e9i) q^{56} +(-7.70996e8 + 4.26717e9i) q^{57} +(1.16101e8 - 2.01093e8i) q^{58} +(1.92744e9 + 3.33842e9i) q^{59} +(-1.44935e8 - 4.03495e8i) q^{60} +(1.02075e10 + 5.89329e9i) q^{61} -9.13006e9 q^{62} +(-6.81094e9 + 3.95749e9i) q^{63} -1.07374e9 q^{64} +(1.90943e9 + 1.10241e9i) q^{65} +(-3.57122e9 - 9.94219e9i) q^{66} +(-2.75067e9 - 4.76430e9i) q^{67} +(1.30332e9 - 2.25741e9i) q^{68} +(3.56710e9 - 1.97425e10i) q^{69} +(1.32463e9 - 4.99011e8i) q^{70} +2.05647e8i q^{71} +(3.69357e9 + 4.47803e9i) q^{72} +(-1.89380e10 + 1.09339e10i) q^{73} +(1.42000e9 - 8.19835e8i) q^{74} +(-1.30073e10 + 1.53693e10i) q^{75} +1.05499e10i q^{76} +(3.26392e10 - 1.22957e10i) q^{77} +(-2.93759e10 - 5.30766e9i) q^{78} +(-2.85550e9 + 4.94587e9i) q^{79} +(-5.21547e8 - 9.03345e8i) q^{80} +(5.97006e9 - 3.08079e10i) q^{81} +(-1.04024e10 - 6.00581e9i) q^{82} +1.40877e10 q^{83} +(-1.45947e10 + 1.24213e10i) q^{84} +2.53223e9 q^{85} +(-3.33766e10 - 1.92700e10i) q^{86} +(-2.87430e9 + 1.03245e9i) q^{87} +(-1.28510e10 - 2.22586e10i) q^{88} +(-3.72572e10 + 6.45313e10i) q^{89} +(-1.97332e9 + 5.28252e9i) q^{90} +(1.60253e10 - 9.72457e10i) q^{91} -4.88104e10i q^{92} +(9.16644e10 + 7.75770e10i) q^{93} +(-5.30347e10 + 3.06196e10i) q^{94} +(-8.87569e9 + 5.12438e9i) q^{95} +(1.07802e10 + 9.12344e9i) q^{96} +8.84815e10i q^{97} +(-4.17484e10 - 4.75471e10i) q^{98} +(-4.86230e10 + 1.30162e11i) 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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