LMFDB - Embedded newform 42.12.f.a.5.20

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			5.20
Character	$\chi$	$=$	42.5
Dual form			42.12.f.a.17.20

$q$-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} +(-271.900 - 321.275i) 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} +(-29287.9 + 174709. i) q^{9} +(27567.9 - 15916.3i) q^{10} +(-679278. + 392181. i) q^{11} +(145697. - 405616. 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} +(-3.60700e6 + 4.37307e6i) q^{18} +(8.92235e6 + 5.15132e6i) q^{19} +1.01865e6 q^{20} +(-9.60680e6 - 1.60620e7i) q^{21} -2.50996e7 q^{22} +(4.12803e7 + 2.38332e7i) q^{23} +(1.05275e7 - 8.90961e6i) 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} +(-1.26092e7 - 4.52922e6i) q^{30} +(2.47090e8 - 1.42657e8i) q^{31} +(-2.90590e7 + 1.67772e7i) q^{32} +(3.10693e8 + 1.11601e8i) 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} +(-7.12075e8 + 6.02641e8i) q^{39} +(2.82295e7 + 1.62983e7i) q^{40} -3.75363e8 q^{41} +(-9.23987e6 - 5.98831e8i) q^{42} +1.20437e9 q^{43} +(-6.95580e8 - 4.01593e8i) q^{44} +(1.35944e8 + 1.12129e8i) 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} +(3.62185e8 - 1.00831e9i) q^{51} +(1.96553e9 - 1.13480e9i) q^{52} +(3.04240e9 - 1.75653e9i) q^{53} +(2.38570e9 - 3.02009e7i) 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} +(-2.76970e8 - 3.27265e8i) q^{60} +(1.02075e10 + 5.89329e9i) q^{61} +9.13006e9 q^{62} +(-2.54822e9 + 7.45367e9i) q^{63} -1.07374e9 q^{64} +(-1.90943e9 - 1.10241e9i) q^{65} +(6.82458e9 + 8.06387e9i) 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} +(-5.72487e9 - 9.59707e8i) q^{72} +(-1.89380e10 + 1.09339e10i) q^{73} +(-1.42000e9 + 8.19835e8i) q^{74} +(6.80657e9 - 1.89493e10i) 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} +(-2.96655e10 - 1.02337e10i) q^{81} +(-1.04024e10 - 6.00581e9i) q^{82} -1.40877e10 q^{83} +(9.32524e9 - 1.67431e10i) q^{84} +2.53223e9 q^{85} +(3.33766e10 + 1.92700e10i) q^{86} +(-2.33128e9 + 1.97300e9i) 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} +(-1.13016e11 - 4.05952e10i) q^{93} +(-5.30347e10 + 3.06196e10i) q^{94} +(8.87569e9 - 5.12438e9i) q^{95} +(1.32912e10 + 4.77420e9i) 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
$3$	−271.900	−	321.275i	−0.646014	−	0.763325i
$3$	−271.900	−	321.275i	−0.646014	−	0.763325i
$4$	512.000	+	886.810i	0.250000	+	0.433013i
$5$	497.386	−	861.497i	0.0711800	−	0.123287i	−0.828239	−	0.560375i	$-0.810657\pi$
$5$	497.386	−	861.497i	0.0711800	−	0.123287i	0.899419	+	0.437088i	$0.143990\pi$
$6$	−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
$9$	−29287.9	+	174709.i	−0.165331	+	0.986238i
$10$	27567.9	−	15916.3i	0.0871774	−	0.0503319i
$11$	−679278.	+	392181.i	−1.27171	+	0.734221i	−0.975309	−	0.220843i	$-0.929119\pi$
$11$	−679278.	+	392181.i	−1.27171	+	0.734221i	−0.296399	+	0.955064i	$0.595786\pi$
$12$	145697.	−	405616.i	0.169026	−	0.470564i
$13$		−	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	0.954016	−	0.299757i	$-0.0969055\pi$
$17$	1.27277e6	+	2.20450e6i	0.217411	+	0.376567i	−0.736605	+	0.676323i	$0.763572\pi$
$18$	−3.60700e6	+	4.37307e6i	−0.449932	+	0.545492i
$19$	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
$21$	−9.60680e6	−	1.60620e7i	−0.513302	−	0.858208i
$22$	−2.50996e7			−1.03835
$23$	4.12803e7	+	2.38332e7i	1.33733	+	0.772109i	0.986411	−	0.164295i	$-0.0525350\pi$
$23$	4.12803e7	+	2.38332e7i	1.33733	+	0.772109i	0.350922	+	0.936405i	$0.385868\pi$
$24$	1.05275e7	−	8.90961e6i	0.269876	−	0.228401i
$25$	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	$-0.989543\pi$
$29$		−	7.25633e6i		−	0.0656944i	0.999460	−	0.0328472i	$-0.0104575\pi$
$30$	−1.26092e7	−	4.52922e6i	−0.0947374	−	0.0340296i
$31$	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
$33$	3.10693e8	+	1.11601e8i	1.38199	+	0.496410i
$34$			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
$39$	−7.12075e8	+	6.02641e8i	−1.26378	+	1.06955i
$40$	2.82295e7	+	1.62983e7i	0.0435887	+	0.0251659i
$41$	−3.75363e8			−0.505988			−0.252994	−	0.967468i	$-0.581415\pi$
$41$	−3.75363e8			−0.505988			−0.252994	+	0.967468i	$0.581415\pi$
$42$	−9.23987e6	−	5.98831e8i	−0.0109092	−	0.707023i
$43$	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
$45$	1.35944e8	+	1.12129e8i	0.109822	+	0.0905837i
$46$	7.62662e8	+	1.32097e9i	0.545964	+	0.945637i
$47$	−9.56863e8	+	1.65734e9i	−0.608571	+	1.05408i	0.382905	+	0.923788i	$0.374924\pi$
$47$	−9.56863e8	+	1.65734e9i	−0.608571	+	1.05408i	−0.991476	+	0.130289i	$0.958410\pi$
$48$	4.34301e8	−	7.84700e7i	0.246017	−	0.0444505i
$49$	1.87277e9	+	6.34464e8i	0.947123	+	0.320870i
$50$			1.53083e9i			0.692776i
$51$	3.62185e8	−	1.00831e9i	0.146992	−	0.409223i
$52$	1.96553e9	−	1.13480e9i	0.716905	−	0.413905i
$53$	3.04240e9	−	1.75653e9i	0.999308	−	0.576950i	0.0912642	−	0.995827i	$-0.470909\pi$
$53$	3.04240e9	−	1.75653e9i	0.999308	−	0.576950i	0.908043	+	0.418876i	$0.137576\pi$
$54$	2.38570e9	−	3.02009e7i	0.707050	−	0.00895065i
$55$			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	0.635434	−	0.772156i	$-0.280821\pi$
$59$	−1.92744e9	−	3.33842e9i	−0.350989	−	0.607932i	−0.986423	+	0.164224i	$0.947488\pi$
$60$	−2.76970e8	−	3.27265e8i	−0.0459833	−	0.0543335i
$61$	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
$63$	−2.54822e9	+	7.45367e9i	−0.323492	+	0.946231i
$64$	−1.07374e9			−0.125000
$65$	−1.90943e9	−	1.10241e9i	−0.204117	−	0.117847i
$66$	6.82458e9	+	8.06387e9i	0.670786	+	0.792596i
$67$	−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	$-0.997847\pi$
$71$		−	2.05647e8i		−	0.0135270i	0.999977	−	0.00676351i	$-0.00215291\pi$
$72$	−5.72487e9	−	9.59707e8i	−0.348688	−	0.0584534i
$73$	−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
$75$	6.80657e9	−	1.89493e10i	0.331201	−	0.922054i
$76$			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
$81$	−2.96655e10	−	1.02337e10i	−0.945331	−	0.326112i
$82$	−1.04024e10	−	6.00581e9i	−0.309853	−	0.178894i
$83$	−1.40877e10			−0.392564			−0.196282	−	0.980547i	$-0.562887\pi$
$83$	−1.40877e10			−0.392564			−0.196282	+	0.980547i	$0.562887\pi$
$84$	9.32524e9	−	1.67431e10i	0.243290	−	0.436818i
$85$	2.53223e9			0.0619013
$86$	3.33766e10	+	1.92700e10i	0.765069	+	0.441713i
$87$	−2.33128e9	+	1.97300e9i	−0.0501462	+	0.0424395i
$88$	−1.28510e10	−	2.22586e10i	−0.259586	−	0.449617i
$89$	3.72572e10	−	6.45313e10i	0.707236	−	1.22497i	−0.258642	−	0.965973i	$-0.583275\pi$
$89$	3.72572e10	−	6.45313e10i	0.707236	−	1.22497i	0.965878	−	0.258996i	$-0.0833917\pi$
$90$	1.97332e9	+	5.28252e9i	0.0352261	+	0.0942991i
$91$	1.60253e10	−	9.72457e10i	0.269202	−	1.63359i
$92$			4.88104e10i			0.772109i
$93$	−1.13016e11	−	4.05952e10i	−1.68455	−	0.605088i
$94$	−5.30347e10	+	3.06196e10i	−0.745345	+	0.430325i
$95$	8.87569e9	−	5.12438e9i	0.117685	−	0.0679457i
$96$	1.32912e10	+	4.77420e9i	0.166369	+	0.0597597i
$97$			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	$0.125440\pi$
$101$	8.38869e10	+	1.45296e11i	0.794194	+	1.37558i	−0.129156	+	0.991624i	$0.541227\pi$
$102$	2.61702e10	−	2.21482e10i	0.234696	−	0.198627i
$103$	−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
$105$	−1.86156e10	+	2.87236e8i	−0.142343	+	0.00219633i
$106$	1.12418e11			0.815931
$107$	−2.23779e11	−	1.29199e11i	−1.54244	−	0.890530i	−0.998684	−	0.0512898i	$-0.983667\pi$
$107$	−2.23779e11	−	1.29199e11i	−1.54244	−	0.890530i	−0.543760	−	0.839241i	$-0.683000\pi$
$108$	6.65977e10	+	3.73343e10i	0.436143	+	0.244499i
$109$	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	$0.134632\pi$
$113$			1.60780e11i			0.820922i	−0.911878	+	0.410461i	$0.865368\pi$
$114$	4.69082e10	−	1.30591e11i	0.228177	−	0.635239i
$115$	4.10644e10	−	2.37086e10i	0.190383	−	0.109918i
$116$	6.43499e9	−	3.71524e9i	0.0284465	−	0.0164236i
$117$	3.87226e11	+	6.49140e10i	1.63284	+	0.273726i
$118$		−	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
$123$	1.02061e11	+	1.20595e11i	0.326876	+	0.386234i
$124$	2.53020e11	+	1.46081e11i	0.775060	+	0.447481i
$125$	9.61612e10			0.281835
$126$	−1.89877e11	+	1.65791e11i	−0.532641	+	0.465074i
$127$	−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
$129$	−3.27469e11	−	3.86935e11i	−0.807100	−	0.953663i
$130$	−3.52771e10	−	6.11017e10i	−0.0833305	−	0.144333i
$131$	9.26764e10	−	1.60520e11i	0.209883	−	0.363528i	−0.741795	−	0.670627i	$-0.766025\pi$
$131$	9.26764e10	−	1.60520e11i	0.209883	−	0.363528i	0.951677	+	0.307099i	$0.0993584\pi$
$132$	6.01063e10	+	3.32666e11i	0.130546	+	0.722522i
$133$	3.54226e11	+	2.90527e11i	0.738068	+	0.605345i
$134$		−	1.76043e11i		−	0.352000i
$135$	−9.38844e8	−	7.41633e10i	−0.00180201	−	0.142349i
$136$	−7.22372e10	+	4.17062e10i	−0.133136	+	0.0768664i
$137$	−8.28352e11	+	4.78249e11i	−1.46640	+	0.846625i	−0.999294	−	0.0375772i	$-0.988036\pi$
$137$	−8.28352e11	+	4.78249e11i	−1.46640	+	0.846625i	−0.467104	+	0.884202i	$0.654703\pi$
$138$	2.17026e11	−	6.04195e11i	0.369128	−	1.02764i
$139$		−	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
$144$	−1.43297e11	−	1.18194e11i	−0.192860	−	0.159075i
$145$	−6.25131e9	−	3.60920e9i	−0.00809929	−	0.00467613i
$146$	−6.99767e11			−0.872998
$147$	−3.05369e11	−	7.74185e11i	−0.366927	−	0.930250i
$148$	−5.24694e10			−0.0607389
$149$	3.62606e11	+	2.09350e11i	0.404492	+	0.233534i	0.688420	−	0.725312i	$-0.258304\pi$
$149$	3.62606e11	+	2.09350e11i	0.404492	+	0.233534i	−0.283928	+	0.958846i	$0.591638\pi$
$150$	4.91818e11	−	4.16233e11i	0.528814	−	0.447543i
$151$	−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
$156$	−8.99010e11	−	3.22924e11i	−0.779075	−	0.279843i
$157$	−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
$159$	−1.39156e12	−	4.99846e11i	−1.08597	−	0.390079i
$160$			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
$165$	2.50678e11	−	2.12153e11i	0.159571	−	0.135048i
$166$	−3.90410e11	−	2.25403e11i	−0.240395	−	0.138792i
$167$	1.46576e12			0.873217			0.436608	−	0.899652i	$-0.356180\pi$
$167$	1.46576e12			0.873217			0.436608	+	0.899652i	$0.356180\pi$
$168$	5.26319e11	−	3.14796e11i	0.303422	−	0.181479i
$169$	−3.12030e12			−1.74108
$170$	7.01753e10	+	4.05157e10i	0.0379066	+	0.0218854i
$171$	−1.16130e12	+	1.40794e12i	−0.607387	+	0.736388i
$172$	6.16640e11	+	1.06805e12i	0.312338	+	0.540986i
$173$	2.89299e11	−	5.01081e11i	0.141936	−	0.245841i	−0.786289	−	0.617858i	$-0.788000\pi$
$173$	2.89299e11	−	5.01081e11i	0.141936	−	0.245841i	0.928226	+	0.372017i	$0.121334\pi$
$174$	−9.61742e10	+	1.73768e10i	−0.0457128	+	0.00825943i
$175$	7.49921e11	+	1.99067e12i	0.345387	+	0.916835i
$176$		−	8.22463e11i		−	0.367111i
$177$	−5.48480e11	+	1.52695e12i	−0.237305	+	0.660652i
$178$	2.06500e12	−	1.19223e12i	0.866184	−	0.500092i
$179$	−1.24062e12	+	7.16274e11i	−0.504601	+	0.291332i	−0.730612	−	0.682793i	$-0.760765\pi$
$179$	−1.24062e12	+	7.16274e11i	−0.504601	+	0.291332i	0.226010	+	0.974125i	$0.427432\pi$
$180$	−2.98340e10	+	1.77967e11i	−0.0117683	+	0.0702005i
$181$		−	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
$186$	−2.48246e12	−	2.93326e12i	−0.817639	−	0.966116i
$187$	−1.72913e12	−	9.98314e11i	−0.552967	−	0.319255i
$188$	−1.95966e12			−0.608571
$189$	3.08754e12	−	1.20797e12i	0.931263	−	0.364349i
$190$	3.27960e11			0.0960897
$191$	1.46653e12	+	8.46701e11i	0.417453	+	0.241016i	0.693987	−	0.719988i	$-0.255853\pi$
$191$	1.46653e12	+	8.46701e11i	0.417453	+	0.241016i	−0.276534	+	0.961004i	$0.589186\pi$
$192$	2.91950e11	+	3.44966e11i	0.0807518	+	0.0954157i
$193$	−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	$0.147658\pi$
$197$			3.72659e12i			0.894844i	−0.894323	+	0.447422i	$0.852342\pi$
$198$	7.35115e11	−	4.38513e12i	0.171671	−	1.02406i
$199$	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
$201$	−7.82743e11	+	2.17913e12i	−0.168283	+	0.468496i
$202$			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
$207$	−5.37289e12	+	6.51402e12i	−0.982587	+	1.19127i
$208$	2.01270e12	+	1.16204e12i	0.358452	+	0.206953i
$209$	−8.08100e12			−1.40172
$210$	−5.20487e11	−	2.89890e11i	−0.0879435	−	0.0489809i
$211$	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
$213$	−6.60693e10	+	5.59155e10i	−0.0103255	+	0.00873865i
$214$	−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
$219$	8.66202e12	+	3.11139e12i	1.16192	+	0.417361i
$220$	−6.91943e11	+	3.99494e11i	−0.0905202	+	0.0522619i
$221$	4.88608e12	−	2.82098e12i	0.623452	−	0.359950i
$222$	6.49489e11	+	2.33296e11i	0.0808407	+	0.0290379i
$223$			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	0.603069	−	0.797689i	$-0.293944\pi$
$227$	−3.53516e12	−	6.12308e12i	−0.389284	−	0.674260i	−0.992353	+	0.123429i	$0.960611\pi$
$228$	3.38942e12	−	2.86852e12i	0.364320	−	0.308330i
$229$	−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
$231$	1.28249e13	+	7.14293e12i	1.28288	+	0.714514i
$232$	2.37776e11			0.0232265
$233$	−2.78107e12	−	1.60565e12i	−0.265311	−	0.153177i	0.361444	−	0.932394i	$-0.382284\pi$
$233$	−2.78107e12	−	1.60565e12i	−0.265311	−	0.153177i	−0.626755	+	0.779217i	$0.715617\pi$
$234$	9.69251e12	+	7.99457e12i	0.903127	+	0.744917i
$235$	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	$-0.624960\pi$
$239$		−	2.22770e13i		−	1.84785i	0.382568	−	0.923927i	$-0.375040\pi$
$240$	1.48414e11	−	4.13179e11i	0.0120313	−	0.0334947i
$241$	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
$243$	4.77820e12	+	1.23133e13i	0.361768	+	0.932268i
$244$			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
$249$	3.83044e12	+	4.52602e12i	0.253602	+	0.299654i
$250$	2.66490e12	+	1.53858e12i	0.172588	+	0.0996437i
$251$	−1.66970e12			−0.105787			−0.0528937	−	0.998600i	$-0.516844\pi$
$251$	−1.66970e12			−0.105787			−0.0528937	+	0.998600i	$0.516844\pi$
$252$	−7.91468e12	+	1.55649e12i	−0.490603	+	0.0964815i
$253$	−3.73877e13			−2.26760
$254$	−2.66287e12	−	1.53741e12i	−0.158039	−	0.0912438i
$255$	−6.88514e11	−	8.13542e11i	−0.0399891	−	0.0472508i
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	1.59535e12	−	2.76322e12i	0.0887612	−	0.153739i	−0.818227	−	0.574896i	$-0.805043\pi$
$257$	1.59535e12	−	2.76322e12i	0.0887612	−	0.153739i	0.906988	+	0.421157i	$0.138376\pi$
$258$	−2.88413e12	−	1.59626e13i	−0.157075	−	0.869349i
$259$	−1.44492e12	+	1.76172e12i	−0.0770364	+	0.0939268i
$260$		−	2.25773e12i		−	0.117847i
$261$	1.26775e12	+	2.12523e11i	0.0647903	+	0.0108613i
$262$	5.13664e12	−	2.96564e12i	0.257053	−	0.148410i
$263$	−5.09999e12	+	2.94448e12i	−0.249927	+	0.144295i	−0.619731	−	0.784815i	$-0.712758\pi$
$263$	−5.09999e12	+	2.94448e12i	−0.249927	+	0.144295i	0.369804	+	0.929110i	$0.379425\pi$
$264$	−3.65693e12	+	1.01808e13i	−0.175507	+	0.488608i
$265$		−	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	$-0.977891\pi$
$269$	−1.29113e13	−	2.23630e13i	−0.558898	−	0.968040i	0.438690	−	0.898638i	$-0.355442\pi$
$270$	1.16059e12	−	2.07030e12i	0.0492243	−	0.0878075i
$271$	−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
$273$	−3.55999e13	+	2.12926e13i	−1.42087	+	0.849833i
$274$	−3.06080e13			−1.19731
$275$	−3.24957e13	−	1.87614e13i	−1.24594	−	0.719341i
$276$	1.56815e13	−	1.32715e13i	0.589371	−	0.498794i
$277$	−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	$0.154671\pi$
$281$			2.74313e13i			0.934033i	−0.884249	+	0.467017i	$0.845329\pi$
$282$	2.42574e13	+	8.71325e12i	0.809981	+	0.290945i
$283$	−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
$285$	−4.05963e12	−	1.45822e12i	−0.127891	−	0.0459383i
$286$			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
$291$	2.84269e13	−	2.40581e13i	0.798578	−	0.675849i
$292$	−1.93925e13	−	1.11963e13i	−0.534600	−	0.308651i
$293$	−8.56053e12			−0.231595			−0.115797	−	0.993273i	$-0.536942\pi$
$293$	−8.56053e12			−0.231595			−0.115797	+	0.993273i	$0.536942\pi$
$294$	3.92433e12	−	2.63408e13i	0.104197	−	0.699388i
$295$	−3.83472e12			−0.0999338
$296$	−1.45408e12	−	8.39511e11i	−0.0371948	−	0.0214744i
$297$	−2.85972e13	+	5.10124e13i	−0.718065	+	1.28090i
$298$	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
$303$	2.38712e13	−	6.64568e13i	0.536958	−	1.49488i
$304$	−9.35576e12	+	5.40155e12i	−0.206668	+	0.119320i
$305$	1.01541e13	−	5.86247e12i	0.220289	−	0.127184i
$306$	−1.42313e13	−	2.38572e12i	−0.303234	−	0.0508337i
$307$			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	0.901536	−	0.432704i	$-0.142441\pi$
$311$	3.90118e12	+	6.75704e12i	0.0760350	+	0.131697i	−0.825501	+	0.564401i	$0.809107\pi$
$312$	−1.97473e13	−	2.33333e13i	−0.378145	−	0.446813i
$313$	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
$315$	5.15387e12	+	5.90263e12i	0.0936322	+	0.107235i
$316$	−5.84806e12			−0.104408
$317$	9.41455e13	+	5.43549e13i	1.65186	+	0.953703i	0.976306	+	0.216393i	$0.0694293\pi$
$317$	9.41455e13	+	5.43549e13i	1.65186	+	0.953703i	0.675555	+	0.737309i	$0.263904\pi$
$318$	−3.05664e13	−	3.61171e13i	−0.527103	−	0.622821i
$319$	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
$324$	−6.11335e12	−	3.15473e13i	−0.0951221	−	0.490868i
$325$	9.18244e13	−	5.30148e13i	1.40475	−	0.811034i
$326$	4.91494e13	−	2.83764e13i	0.739301	−	0.426836i
$327$	1.06660e13	−	2.96938e13i	0.157757	−	0.439191i
$328$		−	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
$333$	−7.00234e12	−	5.77567e12i	−0.0937130	−	0.0772963i
$334$	4.06203e13	+	2.34521e13i	0.534734	+	0.308729i
$335$	−5.47258e12			−0.0708672
$336$	1.96225e13	−	3.02772e11i	0.249970	−	0.00385700i
$337$	−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
$339$	5.16547e13	−	4.37162e13i	0.626631	−	0.530327i
$340$	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
$345$	−1.87824e13	−	6.74661e12i	−0.206893	−	0.0743157i
$346$	1.60346e13	−	9.25757e12i	0.173836	−	0.100364i
$347$	7.24585e13	−	4.18339e13i	0.773174	−	0.446392i	−0.0608315	−	0.998148i	$-0.519375\pi$
$347$	7.24585e13	−	4.18339e13i	0.773174	−	0.446392i	0.834006	+	0.551756i	$0.186042\pi$
$348$	−2.94329e12	−	1.05723e12i	−0.0309134	−	0.0111041i
$349$			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	0.936498	−	0.350674i	$-0.114047\pi$
$353$	1.69464e13	+	2.93519e13i	0.164557	+	0.285020i	−0.771941	+	0.635694i	$0.780714\pi$
$354$	−3.96312e13	+	3.35405e13i	−0.378895	+	0.320665i
$355$	−1.77165e11	−	1.02286e11i	−0.00166771	−	0.000962853i
$356$	7.63027e13			0.707236
$357$	2.31814e13	−	4.16214e13i	0.211575	−	0.379876i
$358$	−4.58416e13			−0.412005
$359$	9.96930e13	+	5.75578e13i	0.882359	+	0.509430i	0.871435	−	0.490510i	$-0.163190\pi$
$359$	9.96930e13	+	5.75578e13i	0.882359	+	0.509430i	0.0109235	+	0.999940i	$0.496523\pi$
$360$	−3.67425e12	+	4.45461e12i	−0.0320262	+	0.0388281i
$361$	−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
$366$	5.36646e13	−	1.49401e14i	0.427113	−	1.18907i
$367$	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
$369$	1.09936e13	−	6.55794e13i	0.0836557	−	0.499025i
$370$			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
$375$	−2.61462e13	−	3.08942e13i	−0.182069	−	0.215132i
$376$	−5.43076e13	−	3.13545e13i	−0.372672	−	0.215163i
$377$	−1.60830e13			−0.108765
$378$	1.04892e14	+	1.59242e13i	0.699096	+	0.106134i
$379$	−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
$381$	2.61263e13	+	3.08706e13i	0.166721	+	0.196996i
$382$	2.70944e13	+	4.69289e13i	0.170424	+	0.295184i
$383$	3.65697e13	−	6.33406e13i	0.226740	−	0.392725i	−0.730100	−	0.683340i	$-0.760527\pi$
$383$	3.65697e13	−	6.33406e13i	0.226740	−	0.392725i	0.956840	+	0.290615i	$0.0938599\pi$
$384$	2.57130e12	+	1.42312e13i	0.0157156	+	0.0869800i
$385$	−5.64152e12	+	3.42342e13i	−0.0339909	+	0.206266i
$386$		−	3.31915e13i		−	0.197150i
$387$	−3.52737e13	+	2.10415e14i	−0.206557	+	1.23216i
$388$	−7.84663e13	+	4.53025e13i	−0.453011	+	0.261546i
$389$	−1.87309e14	+	1.08143e14i	−1.06619	+	0.615568i	−0.927139	−	0.374717i	$-0.877740\pi$
$389$	−1.87309e14	+	1.08143e14i	−1.06619	+	0.615568i	−0.139055	+	0.990285i	$0.544407\pi$
$390$	−1.00386e13	+	2.79472e13i	−0.0563401	+	0.156849i
$391$			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
$396$	9.05342e13	−	1.09762e14i	0.467185	−	0.566409i
$397$	−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
$399$	−2.97484e12	−	1.92798e14i	−0.0147270	−	0.954447i
$400$	−5.01624e13			−0.244933
$401$	1.99482e14	+	1.15171e14i	0.960749	+	0.554689i	0.896403	−	0.443239i	$-0.146171\pi$
$401$	1.99482e14	+	1.15171e14i	0.960749	+	0.554689i	0.0643454	+	0.997928i	$0.479504\pi$
$402$	−5.65582e13	+	4.78661e13i	−0.268690	+	0.227397i
$403$	−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
$408$	3.30404e13	+	1.18681e13i	0.144682	+	0.0519697i
$409$	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
$411$	3.78878e14	+	1.36093e14i	1.59356	+	0.572407i
$412$		−	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
$417$	−3.74945e13	+	3.17322e13i	−0.145619	+	0.123240i
$418$	−2.23947e14	−	1.29296e14i	−0.858373	−	0.495582i
$419$	−1.41185e14			−0.534087			−0.267044	−	0.963684i	$-0.586047\pi$
$419$	−1.41185e14			−0.534087			−0.267044	+	0.963684i	$0.586047\pi$
$420$	−9.78592e12	−	1.63615e13i	−0.0365368	−	0.0610873i
$421$	−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
$423$	−2.61527e14	−	2.15713e14i	−0.938955	−	0.774468i
$424$	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
$429$	2.47353e14	−	6.88623e14i	0.821867	−	2.28805i
$430$	3.32021e13	−	1.91692e13i	0.108915	−	0.0628823i
$431$	−4.85686e13	+	2.80411e13i	−0.157301	+	0.0908176i	−0.576584	−	0.817038i	$-0.695615\pi$
$431$	−4.85686e13	+	2.80411e13i	−0.157301	+	0.0908176i	0.419283	+	0.907855i	$0.362281\pi$
$432$	9.89624e11	+	7.81746e13i	0.00316453	+	0.249980i
$433$			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
$438$	1.90267e14	+	2.24818e14i	0.563969	+	0.666381i
$439$	−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
$441$	−1.65696e14	+	3.08608e14i	−0.473043	+	0.881039i
$442$	1.80543e14			0.509046
$443$	−5.11958e14	−	2.95579e14i	−1.42565	−	0.823101i	−0.428879	−	0.903362i	$-0.641091\pi$
$443$	−5.11958e14	−	2.95579e14i	−1.42565	−	0.823101i	−0.996774	+	0.0802611i	$0.974425\pi$
$444$	1.42664e13	+	1.68571e13i	0.0392382	+	0.0463635i
$445$	−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	$-0.835401\pi$
$449$		−	3.82324e14i		−	0.988727i	0.869255	−	0.494364i	$-0.164599\pi$
$450$	−2.67451e14	−	4.48350e13i	−0.683242	−	0.114538i
$451$	2.54976e14	−	1.47210e14i	0.643470	−	0.371507i
$452$	−1.42582e14	+	8.23196e13i	−0.355470	+	0.205231i
$453$	−1.69908e13	+	4.73019e13i	−0.0418479	+	0.116503i
$454$		−	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
$459$	1.65554e14	+	9.28085e13i	0.379289	+	0.212627i
$460$	4.20500e13	+	2.42776e13i	0.0951914	+	0.0549588i
$461$	3.53947e13			0.0791741			0.0395870	−	0.999216i	$-0.487396\pi$
$461$	3.53947e13			0.0791741			0.0395870	+	0.999216i	$0.487396\pi$
$462$	2.41127e14	+	4.03149e14i	0.532984	+	0.891117i
$463$	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
$465$	−9.11851e13	+	7.71713e13i	−0.194506	+	0.164613i
$466$	−5.13809e13	−	8.89944e13i	−0.108313	−	0.187603i
$467$	3.65831e14	−	6.33638e14i	0.762145	−	1.32007i	−0.179597	−	0.983740i	$-0.557479\pi$
$467$	3.65831e14	−	6.33638e14i	0.762145	−	1.32007i	0.941743	−	0.336334i	$-0.109187\pi$
$468$	1.40694e14	+	3.76632e14i	0.289682	+	0.775471i
$469$	−8.62394e13	−	2.28924e14i	−0.175491	−	0.465844i
$470$			6.09190e13i			0.122522i
$471$	2.43848e14	+	8.75901e13i	0.484736	+	0.174117i
$472$	1.09393e14	−	6.31583e13i	0.214936	−	0.124094i
$473$	−8.18105e14	+	4.72333e14i	−1.58881	+	0.917301i
$474$	7.23898e13	+	2.60023e13i	0.138962	+	0.0499151i
$475$			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	0.800478	−	0.599362i	$-0.204579\pi$
$479$	−6.55762e13	−	1.13581e14i	−0.118823	−	0.205808i	−0.919302	+	0.393554i	$0.871245\pi$
$480$	1.07238e13	−	9.07574e12i	0.0192098	−	0.0162576i
$481$	9.83527e13	+	5.67840e13i	0.174176	+	0.100561i
$482$	2.24534e14			0.393119
$483$	−1.37635e13	−	8.92003e14i	−0.0238242	−	1.54404i
$484$	3.37830e14			0.578161
$485$	7.62265e13	+	4.40094e13i	0.128981	+	0.0744674i
$486$	−6.45959e13	+	4.17688e14i	−0.108070	+	0.698800i
$487$	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	$-0.892140\pi$
$491$		−	4.20384e14i		−	0.664810i	0.943137	−	0.332405i	$-0.107860\pi$
$492$	−5.46893e13	+	1.52253e14i	−0.0855252	+	0.238100i
$493$	1.59966e13	−	9.23565e12i	0.0247383	−	0.0142827i
$494$	6.32817e14	−	3.65357e14i	0.967788	−	0.558753i
$495$	−1.36319e14	−	2.28522e13i	−0.206171	−	0.0345621i
$496$			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
$501$	−3.98540e14	−	4.70911e14i	−0.564110	−	0.666549i
$502$	−4.62722e13	−	2.67152e13i	−0.0647813	−	0.0374015i
$503$	4.44929e14			0.616122			0.308061	−	0.951367i	$-0.400320\pi$
$503$	4.44929e14			0.616122			0.308061	+	0.951367i	$0.400320\pi$
$504$	−2.44242e14	−	8.35000e13i	−0.334543	−	0.114372i
$505$	1.66897e14			0.226123
$506$	−1.03612e15	−	5.98203e14i	−1.38861	−	0.801716i
$507$	8.48408e14	+	1.00247e15i	1.12476	+	1.32901i
$508$	−4.91970e13	−	8.52117e13i	−0.0645191	−	0.111750i
$509$	6.86325e14	−	1.18875e15i	0.890394	−	1.54221i	0.0509905	−	0.998699i	$-0.483762\pi$
$509$	6.86325e14	−	1.18875e15i	0.890394	−	1.54221i	0.839404	−	0.543509i	$-0.182905\pi$
$510$	−6.06397e12	−	3.35618e13i	−0.00778254	−	0.0430734i
$511$	−9.09968e14	+	3.42800e14i	−1.15534	+	0.435237i
$512$		−	3.51844e13i		−	0.0441942i
$513$	7.68094e14	−	9.72342e12i	0.954484	−	0.0120830i
$514$	8.84231e13	−	5.10511e13i	0.108710	−	0.0627636i
$515$	−1.00525e14	+	5.80380e13i	−0.122274	+	0.0705948i
$516$	1.75474e14	−	4.88514e14i	0.211173	−	0.587900i
$517$		−	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	0.783670	−	0.621178i	$-0.213346\pi$
$521$	−1.28033e14	−	2.21759e14i	−0.146121	−	0.253089i	−0.929791	+	0.368089i	$0.880012\pi$
$522$	3.17325e13	+	2.61736e13i	0.0358357	+	0.0295580i
$523$	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
$525$	4.35650e14	−	7.82195e14i	0.476718	−	0.855931i
$526$	−1.88447e14			−0.204064
$527$	6.28977e14	+	3.63140e14i	0.674026	+	0.389149i
$528$	−2.64237e14	+	2.23628e14i	−0.280225	+	0.237159i
$529$	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
$534$	−9.44507e14	−	3.39266e14i	−0.941300	−	0.338114i
$535$	−2.22609e14	+	1.28524e14i	−0.219582	+	0.126776i
$536$	1.56117e14	−	9.01340e13i	0.152420	−	0.0879999i
$537$	5.67446e14	+	2.03826e14i	0.548360	+	0.196971i
$538$		−	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
$543$	−1.91466e14	+	1.62041e14i	−0.174058	+	0.147308i
$544$	−7.39709e13	−	4.27071e13i	−0.0665682	−	0.0384332i
$545$	7.45717e13			0.0664344
$546$	−1.32725e15	+	2.04793e13i	−1.17056	+	0.0180616i
$547$	−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
$549$	−1.32857e15	+	1.61074e15i	−1.13694	+	1.37840i
$550$	−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
$555$	7.25237e12	−	2.01904e13i	0.00584613	−	0.0162755i
$556$	1.03495e14	−	5.97531e13i	0.0826057	−	0.0476924i
$557$	9.78521e14	−	5.64950e14i	0.773333	−	0.446484i	−0.0607291	−	0.998154i	$-0.519343\pi$
$557$	9.78521e14	−	5.64950e14i	0.773333	−	0.446484i	0.834062	+	0.551670i	$0.186009\pi$
$558$	−2.67401e14	+	1.59511e15i	−0.209254	+	1.24825i
$559$		−	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	$-0.992016\pi$
$563$	−7.00006e14	−	1.21245e15i	−0.521562	−	0.903371i	0.478124	−	0.878292i	$-0.341317\pi$
$564$	5.32830e14	+	6.29588e14i	0.393146	+	0.464538i
$565$	1.38512e14	+	7.99699e13i	0.101209	+	0.0584333i
$566$	−1.36040e14			−0.0984409
$567$	−1.22759e15	−	6.63500e14i	−0.879726	−	0.475482i
$568$	6.73865e12			0.00478252
$569$	−2.79177e14	−	1.61183e14i	−0.196229	−	0.113293i	0.398666	−	0.917096i	$-0.369473\pi$
$569$	−2.79177e14	−	1.61183e14i	−0.196229	−	0.113293i	−0.594895	+	0.803803i	$0.702806\pi$
$570$	−8.91724e13	−	1.05365e14i	−0.0620753	−	0.0733477i
$571$	−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
$576$	3.14477e13	−	1.87592e14i	0.0206664	−	0.123280i
$577$	−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
$579$	−1.47580e14	+	4.10859e14i	−0.0942531	+	0.262398i
$580$		−	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
$585$	2.48524e14	−	3.01307e14i	0.149972	−	0.181824i
$586$	−2.37236e14	−	1.36969e14i	−0.141822	−	0.0818812i
$587$	1.80536e15			1.06919			0.534595	−	0.845108i	$-0.320464\pi$
$587$	1.80536e15			1.06919			0.534595	+	0.845108i	$0.320464\pi$
$588$	5.30206e14	−	6.67187e14i	0.311078	−	0.391447i
$589$	2.93949e15			1.70859
$590$	−1.06271e14	−	6.13555e13i	−0.0611967	−	0.0353319i
$591$	1.19726e15	−	1.01326e15i	0.683057	−	0.578082i
$592$	−2.68643e13	−	4.65304e13i	−0.0151847	−	0.0263007i
$593$	3.64725e14	−	6.31723e14i	0.204252	−	0.353774i	−0.745642	−	0.666346i	$-0.767857\pi$
$593$	3.64725e14	−	6.31723e14i	0.204252	−	0.353774i	0.949894	+	0.312572i	$0.101191\pi$
$594$	−1.60871e15	+	9.56141e14i	−0.892590	+	0.530514i
$595$	1.11103e14	+	1.83088e13i	0.0610775	+	0.0100651i
$596$			4.28750e14i			0.233534i
$597$	−2.35593e14	−	8.46248e13i	−0.127146	−	0.0456708i
$598$	2.92780e15	−	1.69037e15i	1.56562	−	0.903909i
$599$	−1.40013e15	+	8.08368e14i	−0.741860	+	0.428313i	−0.822745	−	0.568410i	$-0.807559\pi$
$599$	−1.40013e15	+	8.08368e14i	−0.741860	+	0.428313i	0.0808849	+	0.996723i	$0.474225\pi$
$600$	6.20931e14	+	2.23038e14i	0.325995	+	0.117097i
$601$			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
$606$	1.72485e15	−	1.45977e15i	0.857336	−	0.725577i
$607$	−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
$609$	−1.16551e14	+	6.97101e13i	−0.0563795	+	0.0337210i
$610$	3.75198e14			0.179865
$611$	3.67333e15	+	2.12080e15i	1.74515	+	1.00756i
$612$	−3.56219e14	−	2.93816e14i	−0.167720	−	0.138339i
$613$	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	$-0.943401\pi$
$617$		−	7.85723e14i		−	0.353754i	0.984233	−	0.176877i	$-0.0565995\pi$
$618$	−5.31276e14	+	1.47906e15i	−0.237074	+	0.660006i
$619$	−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
$621$	3.55368e15	−	4.49865e13i	1.54410	−	0.0195469i
$622$			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
$627$	2.19722e15	+	2.59622e15i	0.905529	+	1.06997i
$628$	−5.45928e14	−	3.15192e14i	−0.223027	−	0.128765i
$629$	−1.30433e14			−0.0528212
$630$	4.83861e13	+	2.46040e14i	0.0194244	+	0.0987719i
$631$	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
$633$	−2.32954e15	−	2.75257e15i	−0.911067	−	1.07651i
$634$	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
$639$	3.59285e13	+	6.02299e12i	0.0133409	+	0.00223644i
$640$	−2.96008e13	+	1.70900e13i	−0.0108972	+	0.00629149i
$641$	−4.16978e15	+	2.40742e15i	−1.52193	+	0.878684i	−0.522261	+	0.852785i	$0.674911\pi$
$641$	−4.16978e15	+	2.40742e15i	−1.52193	+	0.878684i	−0.999665	+	0.0258989i	$0.991755\pi$
$642$	−1.17649e15	+	3.27533e15i	−0.425743	+	1.18526i
$643$		−	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	0.798806	−	0.601588i	$-0.205465\pi$
$647$	−3.50641e14	−	6.07328e14i	−0.121588	−	0.210596i	−0.920394	+	0.390992i	$0.872132\pi$
$648$	3.35339e14	−	9.72079e14i	0.115298	−	0.334225i
$649$	2.61853e15	+	1.51181e15i	0.892713	+	0.515408i
$650$	3.39295e15			1.14698
$651$	−4.66510e15	−	2.59827e15i	−1.56374	−	0.870940i
$652$	1.81609e15			0.603637
$653$	3.26014e15	+	1.88225e15i	1.07452	+	0.620374i	0.929413	−	0.369042i	$-0.120314\pi$
$653$	3.26014e15	+	1.88225e15i	1.07452	+	0.620374i	0.145107	+	0.989416i	$0.453647\pi$
$654$	7.70686e14	−	6.52243e14i	0.251884	−	0.213173i
$655$	−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	$0.359098\pi$
$659$			5.76613e15i			1.80723i	−0.428341	+	0.903617i	$0.640902\pi$
$660$	3.16486e14	+	1.13682e14i	0.0983702	+	0.0353345i
$661$	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
$663$	−2.23483e15	−	8.02750e14i	−0.677518	−	0.243364i
$664$		−	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
$669$	1.28734e15	−	1.08950e15i	0.371408	−	0.314328i
$670$	−1.51660e14	−	8.75612e13i	−0.0433971	−	0.0250553i
$671$	−9.24495e15			−2.62380
$672$	5.48639e14	+	3.05569e14i	0.154439	+	0.0860159i
$673$	−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
$675$	3.11127e15	+	1.74416e15i	0.854607	+	0.479087i
$676$	−1.59759e15	−	2.76711e15i	−0.435270	−	0.753910i
$677$	−4.71508e14	+	8.16676e14i	−0.127424	+	0.220705i	−0.922678	−	0.385572i	$-0.874004\pi$
$677$	−4.71508e14	+	8.16676e14i	−0.127424	+	0.220705i	0.795254	+	0.606277i	$0.207338\pi$
$678$	2.13096e15	−	3.85023e14i	0.571230	−	0.103210i
$679$	−6.39747e14	+	3.88216e15i	−0.170108	+	1.03226i
$680$			8.29762e13i			0.0218854i
$681$	−1.00598e15	+	2.80062e15i	−0.263197	+	0.732732i
$682$	−6.20185e15	+	3.58064e15i	−1.60956	+	0.929280i
$683$	−3.66848e15	+	2.11800e15i	−0.944436	+	0.545270i	−0.891348	−	0.453320i	$-0.850240\pi$
$683$	−3.66848e15	+	2.11800e15i	−0.944436	+	0.545270i	−0.0530877	+	0.998590i	$0.516906\pi$
$684$	−1.84316e15	−	3.08985e14i	−0.470712	−	0.0789094i
$685$			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
$690$	−4.12567e14	−	4.87486e14i	−0.100421	−	0.118657i
$691$	−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
$693$	−1.19224e15	−	6.06247e15i	−0.283355	−	1.44084i
$694$	2.67737e15			0.631294
$695$	−1.00541e14	−	5.80475e13i	−0.0235195	−	0.0135790i
$696$	−6.46511e13	−	7.63913e13i	−0.0150046	−	0.0177294i
$697$	−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	$-0.702821\pi$
$701$		−	7.20467e15i		−	1.60755i	0.594932	−	0.803776i	$-0.297179\pi$
$702$	−6.69376e13	−	5.28768e15i	−0.0148189	−	1.17061i
$703$	−4.57178e14	+	2.63952e14i	−0.100423	+	0.0579790i
$704$	7.29369e14	−	4.21101e14i	0.158964	−	0.0917776i
$705$	2.70865e14	−	7.54082e14i	0.0585751	−	0.163072i
$706$			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
$711$	−7.80457e14	−	6.43736e14i	−0.161089	−	0.132869i
$712$	2.11456e15	+	1.22084e15i	0.433092	+	0.250046i
$713$	1.35999e16			2.76403
$714$	1.30837e15	−	7.82544e14i	0.263869	−	0.157822i
$715$	1.72938e15			0.346104
$716$	−1.27040e15	−	7.33465e14i	−0.252301	−	0.145666i
$717$	−7.15703e15	+	6.05711e15i	−1.41051	+	1.19374i
$718$	1.84185e15	+	3.19018e15i	0.360222	+	0.623922i
$719$	2.75951e15	−	4.77962e15i	0.535579	−	0.927650i	−0.463556	−	0.886068i	$-0.653427\pi$
$719$	2.75951e15	−	4.77962e15i	0.535579	−	0.927650i	0.999135	−	0.0415827i	$-0.0132400\pi$
$720$	−1.73098e14	+	6.46618e13i	−0.0333398	+	0.0124543i
$721$	−4.01191e15	−	3.29047e15i	−0.766845	−	0.628947i
$722$		−	3.31070e14i		−	0.0628008i
$723$	−2.77938e15	−	9.98351e14i	−0.523224	−	0.187941i
$724$	5.28501e14	−	3.05130e14i	0.0987379	−	0.0570063i
$725$	3.00626e14	−	1.73566e14i	0.0557400	−	0.0321815i
$726$	−4.18181e15	−	1.50210e15i	−0.769507	−	0.276406i
$727$		−	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
$732$	3.87761e15	−	3.28168e15i	0.681951	−	0.577146i
$733$	−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
$735$	−8.18845e14	−	1.21994e14i	−0.140806	−	0.0209777i
$736$	−1.59942e15			−0.272982
$737$	3.73694e15	+	2.15752e15i	0.633060	+	0.365497i
$738$	1.35393e15	−	1.64149e15i	0.227660	−	0.276012i
$739$	−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	$0.134127\pi$
$743$			5.04901e15i			0.818028i	−0.912528	+	0.409014i	$0.865873\pi$
$744$	1.33022e15	−	3.70330e15i	0.213931	−	0.595577i
$745$	3.60710e14	−	2.08256e14i	0.0575835	−	0.0332459i
$746$	8.44453e14	−	4.87545e14i	0.133817	−	0.0772594i
$747$	4.12600e14	−	2.46125e15i	0.0649031	−	0.387161i
$748$		−	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
$753$	4.53992e14	+	5.36433e14i	0.0683401	+	0.0807502i
$754$	−4.45705e14	−	2.57328e14i	−0.0666047	−	0.0384542i
$755$	−1.18792e14			−0.0176229
$756$	2.65206e15	+	2.11958e15i	0.390583	+	0.312161i
$757$	−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
$759$	1.01657e16	+	1.20117e16i	1.46490	+	1.73091i
$760$	1.67916e14	+	2.90839e14i	0.0240224	+	0.0416081i
$761$	4.74452e15	−	8.21774e15i	0.673870	−	1.16718i	−0.302927	−	0.953014i	$-0.597964\pi$
$761$	4.74452e15	−	8.21774e15i	0.673870	−	1.16718i	0.976798	−	0.214164i	$-0.0687027\pi$
$762$	2.30103e14	+	1.27353e15i	0.0324467	+	0.179580i
$763$	1.17514e15	+	3.11941e15i	0.164514	+	0.436705i
$764$			1.73404e15i			0.241016i
$765$	−7.41639e13	+	4.42404e14i	−0.0102342	+	0.0610494i
$766$	2.02690e15	−	1.17023e15i	0.277699	−	0.160329i
$767$	−7.39929e15	+	4.27198e15i	−1.00650	+	0.581106i
$768$	−1.56441e14	+	4.35527e14i	−0.0211283	+	0.0588205i
$769$			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	$0.0854266\pi$
$773$	5.46147e15	+	9.45954e15i	0.711742	+	1.23277i	−0.252461	+	0.967607i	$0.581240\pi$
$774$	−4.34418e15	+	5.26682e15i	−0.562124	+	0.681511i
$775$	1.18204e16	+	6.82452e15i	1.51870	+	0.876824i
$776$	−2.89936e15			−0.369882
$777$	9.58872e14	−	1.47952e13i	0.121463	−	0.00187416i
$778$	−6.92115e15			−0.870544
$779$	−3.34912e15	−	1.93362e15i	−0.418287	−	0.241498i
$780$	−7.25353e14	+	6.13877e14i	−0.0899557	+	0.0761309i
$781$	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
$786$	−2.34944e15	−	8.43916e14i	−0.279345	−	0.100340i
$787$	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
$789$	2.33267e15	+	8.37895e14i	0.271601	+	0.0975587i
$790$			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
$795$	−1.12276e15	+	9.50206e14i	−0.125391	+	0.106120i
$796$	5.27445e14	+	3.04521e14i	0.0585000	+	0.0337750i
$797$	−7.87452e15			−0.867367			−0.433684	−	0.901065i	$-0.642786\pi$
$797$	−7.87452e15			−0.867367			−0.433684	+	0.901065i	$0.642786\pi$
$798$	3.00233e15	−	5.39058e15i	0.328430	−	0.589684i
$799$	−4.87147e15			−0.529240
$800$	−1.39014e15	−	8.02598e14i	−0.149990	−	0.0865970i
$801$	1.01830e16	+	8.39915e15i	1.09118	+	0.900029i
$802$	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
$807$	−3.67410e15	+	1.02286e16i	−0.377873	+	1.05199i
$808$	−4.76107e15	+	2.74881e15i	−0.486343	+	0.280790i
$809$	−5.13780e15	+	2.96631e15i	−0.521267	+	0.300954i	−0.737453	−	0.675398i	$-0.763972\pi$
$809$	−5.13780e15	+	2.96631e15i	−0.521267	+	0.300954i	0.216186	+	0.976352i	$0.430638\pi$
$810$	−9.80699e14	+	1.90043e14i	−0.0988253	+	0.0191507i
$811$			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
$816$	7.25754e14	+	8.57545e14i	0.0702253	+	0.0829776i
$817$	1.07458e16	+	6.20412e15i	1.03281	+	0.596291i
$818$	2.10751e15			0.201200
$819$	1.65204e16	+	5.64789e15i	1.56660	+	0.535580i
$820$	−3.82362e14			−0.0360163
$821$	3.57061e15	+	2.06149e15i	0.334083	+	0.192883i	0.657652	−	0.753321i	$-0.271550\pi$
$821$	3.57061e15	+	2.06149e15i	0.334083	+	0.192883i	−0.323569	+	0.946204i	$0.604883\pi$
$822$	8.32230e15	+	9.83356e15i	0.773478	+	0.913936i
$823$	−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	$-0.885966\pi$
$827$		−	7.80124e15i		−	0.701267i	0.936513	−	0.350634i	$-0.114034\pi$
$828$	−8.52761e15	−	1.42955e15i	−0.761484	−	0.127654i
$829$	−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
$831$	−4.64373e15	+	1.29280e16i	−0.406501	+	1.13169i
$832$			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
$837$	1.04023e16	−	1.85559e16i	0.875269	−	1.56132i
$838$	−3.91264e15	−	2.25896e15i	−0.327060	−	0.188828i
$839$	1.36784e16			1.13591			0.567956	−	0.823059i	$-0.307734\pi$
$839$	1.36784e16			1.13591			0.567956	+	0.823059i	$0.307734\pi$
$840$	−9.41215e12	−	6.09997e14i	−0.000776520	−	0.0503259i
$841$	1.21479e16			0.995684
$842$	−5.25046e15	−	3.03136e15i	−0.427544	−	0.246843i
$843$	8.81300e15	−	7.45858e15i	0.712971	−	0.603399i
$844$	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
$849$	1.68396e15	+	6.04876e14i	0.131020	+	0.0470624i
$850$	−3.37473e15	+	1.94840e15i	−0.260876	+	0.150617i
$851$	−2.11519e15	+	1.22120e15i	−0.162456	+	0.0937941i
$852$	−8.34139e13	−	2.99622e13i	−0.00636532	−	0.00228642i
$853$			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	$-0.875865\pi$
$857$	−1.07140e16	−	1.85572e16i	−0.791696	−	1.37126i	0.133220	−	0.991086i	$-0.457468\pi$
$858$	1.78728e16	−	1.51260e16i	1.31224	−	1.11057i
$859$	−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
$861$	3.60604e15	+	6.02907e15i	0.259725	+	0.434244i
$862$	−1.79463e15			−0.128436
$863$	−2.21904e15	−	1.28116e15i	−0.157800	−	0.0911056i	0.419021	−	0.907977i	$-0.362373\pi$
$863$	−2.21904e15	−	1.28116e15i	−0.157800	−	0.0911056i	−0.576820	+	0.816871i	$0.695707\pi$
$864$	−1.22337e15	+	2.18227e15i	−0.0864434	+	0.154200i
$865$	−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
$870$	−3.28656e13	+	9.14968e13i	−0.00223555	+	0.00622372i
$871$	−1.05596e16	+	6.09661e15i	−0.713755	+	0.412086i
$872$	−2.12731e15	+	1.22820e15i	−0.142886	+	0.0824955i
$873$	−1.54585e16	−	2.59144e15i	−1.03179	−	0.172967i
$874$			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
$879$	2.32761e15	+	2.75028e15i	0.149614	+	0.176782i
$880$	−7.08550e14	−	4.09081e14i	−0.0452601	−	0.0261309i
$881$	1.02815e16			0.652660			0.326330	−	0.945256i	$-0.394188\pi$
$881$	1.02815e16			0.652660			0.326330	+	0.945256i	$0.394188\pi$
$882$	−9.52964e15	+	5.90126e15i	−0.601173	+	0.372278i
$883$	−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
$885$	1.04266e15	+	1.23200e15i	0.0645586	+	0.0762820i
$886$	−9.45853e15	−	1.63827e16i	−0.582020	−	1.00809i
$887$	2.70759e15	−	4.68969e15i	0.165578	−	0.286790i	−0.771282	−	0.636493i	$-0.780384\pi$
$887$	2.70759e15	−	4.68969e15i	0.165578	−	0.286790i	0.936861	+	0.349703i	$0.113718\pi$
$888$	1.25649e14	+	6.95421e14i	0.00763640	+	0.0422645i
$889$	−4.21589e15	−	6.94744e14i	−0.254642	−	0.0419629i
$890$		−	2.37199e15i		−	0.142386i
$891$	2.41646e16	−	4.68269e15i	1.44162	−	0.279363i
$892$	−3.55344e15	+	2.05158e15i	−0.210689	+	0.121641i
$893$	−1.70749e16	+	9.85821e15i	−1.00618	+	0.580918i
$894$	1.90636e15	−	5.30725e15i	0.111647	−	0.310823i
$895$			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
$900$	−6.69445e15	−	5.52171e15i	−0.377904	−	0.311702i
$901$	7.74456e15	+	4.47132e15i	0.434521	+	0.250871i
$902$	9.42147e15			0.525391
$903$	−1.15702e16	−	1.93446e16i	−0.641295	−	1.07220i
$904$	−5.26846e15			−0.290240
$905$	−5.13416e14	−	2.96421e14i	−0.0281127	−	0.0162309i
$906$	−1.22769e15	+	1.03902e15i	−0.0668167	+	0.0565480i
$907$	−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	$-0.813412\pi$
$911$		−	2.09532e16i		−	1.10637i	0.833059	−	0.553185i	$-0.186588\pi$
$912$	4.27921e15	+	1.53709e15i	0.224591	+	0.0806728i
$913$	9.56945e15	−	5.52493e15i	0.499227	−	0.288229i
$914$	−1.12966e16	+	6.52207e15i	−0.585790	+	0.338206i
$915$	−4.64436e15	−	1.66825e15i	−0.239392	−	0.0859895i
$916$		−	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
$921$	6.92439e15	−	5.86022e15i	0.344313	−	0.291398i
$922$	9.80886e14	+	5.66315e14i	0.0484840	+	0.0279923i
$923$	−4.55798e14			−0.0223956
$924$	2.31917e14	+	1.50304e16i	0.0113276	+	0.734134i
$925$	−2.45123e15			−0.119016
$926$	1.97524e16	+	1.14041e16i	0.953366	+	0.550426i
$927$	1.31527e16	−	1.59462e16i	0.631069	−	0.765099i
$928$	1.21741e14	+	2.10862e14i	0.00580662	+	0.0100574i
$929$	−8.98996e15	+	1.55711e16i	−0.426257	+	0.738298i	−0.996537	−	0.0831520i	$-0.973501\pi$
$929$	−8.98996e15	+	1.55711e16i	−0.426257	+	0.738298i	0.570280	+	0.821450i	$0.306835\pi$
$930$	−3.76174e15	+	6.79674e14i	−0.177310	+	0.0320364i
$931$	1.34412e16	+	1.53082e16i	0.629817	+	0.717298i
$932$		−	3.28838e15i		−	0.153177i
$933$	1.11014e15	−	3.09059e15i	0.0514076	−	0.143117i
$934$	2.02764e16	−	1.17066e16i	0.933434	−	0.538918i
$935$	−1.72009e15	+	9.93094e14i	−0.0787203	+	0.0454492i
$936$	−2.12710e15	+	1.26886e16i	−0.0967768	+	0.577295i
$937$		−	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	$-0.981808\pi$
$941$	−1.24176e16	−	2.15080e16i	−0.548650	−	0.950290i	0.449717	−	0.893171i	$-0.351525\pi$
$942$	5.35628e15	+	6.32895e15i	0.235279	+	0.278004i
$943$	−1.54951e16	−	8.94610e15i	−0.676675	−	0.390679i
$944$	4.04213e15			0.175495
$945$	4.95031e14	−	3.26073e15i	0.0213677	−	0.140747i
$946$	−3.02293e16			−1.29726
$947$	1.84805e16	+	1.06697e16i	0.788479	+	0.455228i	0.839427	−	0.543473i	$-0.182891\pi$
$947$	1.84805e16	+	1.06697e16i	0.788479	+	0.455228i	−0.0509480	+	0.998701i	$0.516224\pi$
$948$	1.59009e15	+	1.87883e15i	0.0674489	+	0.0796971i
$949$	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	$0.0457727\pi$
$953$			6.95504e15i			0.286608i	−0.989679	+	0.143304i	$0.954227\pi$
$954$	−3.29249e15	+	1.96404e16i	−0.134899	+	0.804702i
$955$	1.45886e15	−	8.42274e14i	0.0594286	−	0.0343111i
$956$	1.97555e16	−	1.14058e16i	0.800145	−	0.461964i
$957$	8.09812e14	−	2.25449e15i	0.0326114	−	0.0907891i
$958$		−	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
$963$	2.91263e16	−	3.53123e16i	1.13329	−	1.37398i
$964$	6.22248e15	+	3.59255e15i	0.240735	+	0.138989i
$965$	−1.03181e15			−0.0396918
$966$	1.38906e16	−	2.49401e16i	0.531310	−	0.953948i
$967$	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
$969$	8.42569e15	−	7.13079e15i	0.316829	−	0.268137i
$970$	1.40830e15	+	2.43925e15i	0.0526564	+	0.0912035i
$971$	4.42280e15	−	7.66051e15i	0.164434	−	0.284808i	−0.772020	−	0.635598i	$-0.780754\pi$
$971$	4.42280e15	−	7.66051e15i	0.164434	−	0.284808i	0.936454	+	0.350790i	$0.114087\pi$
$972$	−8.47314e15	+	1.05418e16i	−0.313242	+	0.389717i
$973$	8.43814e14	−	5.12049e15i	0.0310189	−	0.188231i
$974$			3.03481e16i			1.10932i
$975$	−4.19994e16	−	1.50861e16i	−1.52657	−	0.548343i
$976$	−1.07033e16	+	6.17956e15i	−0.386852	+	0.223349i
$977$	−2.45277e16	+	1.41611e16i	−0.881531	+	0.508952i	−0.871163	−	0.490994i	$-0.836634\pi$
$977$	−2.45277e16	+	1.41611e16i	−0.881531	+	0.508952i	−0.0103681	+	0.999946i	$0.503300\pi$
$978$	−2.24803e16	−	8.07492e15i	−0.803414	−	0.288585i
$979$			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	$-0.973361\pi$
$983$	−1.64213e16	−	2.84425e16i	−0.570641	−	0.988380i	0.425859	−	0.904790i	$-0.359972\pi$
$984$	−3.95165e15	+	3.34434e15i	−0.136554	+	0.115568i
$985$	3.21044e15	+	1.85355e15i	0.110323	+	0.0636950i
$986$	5.91082e14			0.0201988
$987$	3.58125e16	−	5.52581e14i	1.21700	−	0.0187781i
$988$	2.33829e16			0.790196
$989$	4.97169e16	+	2.87041e16i	1.67080	+	0.964637i
$990$	−3.41214e15	−	2.81440e15i	−0.114034	−	0.0940572i
$991$	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
$996$	−2.05253e15	+	5.71420e15i	−0.0663535	+	0.184726i
$997$	−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
$999$	4.83589e13	+	3.82008e15i	0.00153768	+	0.121468i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.12.f.a.5.10	✓	60	3.2	odd	2	inner
42.12.f.a.5.20	yes	60	1.1	even	1	trivial
42.12.f.a.17.10	yes	60	7.3	odd	6	inner
42.12.f.a.17.20	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} +(-271.900 - 321.275i) 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} +(-29287.9 + 174709. i) q^{9} +(27567.9 - 15916.3i) q^{10} +(-679278. + 392181. i) q^{11} +(145697. - 405616. 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} +(-3.60700e6 + 4.37307e6i) q^{18} +(8.92235e6 + 5.15132e6i) q^{19} +1.01865e6 q^{20} +(-9.60680e6 - 1.60620e7i) q^{21} -2.50996e7 q^{22} +(4.12803e7 + 2.38332e7i) q^{23} +(1.05275e7 - 8.90961e6i) 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} +(-1.26092e7 - 4.52922e6i) q^{30} +(2.47090e8 - 1.42657e8i) q^{31} +(-2.90590e7 + 1.67772e7i) q^{32} +(3.10693e8 + 1.11601e8i) 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} +(-7.12075e8 + 6.02641e8i) q^{39} +(2.82295e7 + 1.62983e7i) q^{40} -3.75363e8 q^{41} +(-9.23987e6 - 5.98831e8i) q^{42} +1.20437e9 q^{43} +(-6.95580e8 - 4.01593e8i) q^{44} +(1.35944e8 + 1.12129e8i) 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} +(3.62185e8 - 1.00831e9i) q^{51} +(1.96553e9 - 1.13480e9i) q^{52} +(3.04240e9 - 1.75653e9i) q^{53} +(2.38570e9 - 3.02009e7i) 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} +(-2.76970e8 - 3.27265e8i) q^{60} +(1.02075e10 + 5.89329e9i) q^{61} +9.13006e9 q^{62} +(-2.54822e9 + 7.45367e9i) q^{63} -1.07374e9 q^{64} +(-1.90943e9 - 1.10241e9i) q^{65} +(6.82458e9 + 8.06387e9i) 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} +(-5.72487e9 - 9.59707e8i) q^{72} +(-1.89380e10 + 1.09339e10i) q^{73} +(-1.42000e9 + 8.19835e8i) q^{74} +(6.80657e9 - 1.89493e10i) 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} +(-2.96655e10 - 1.02337e10i) q^{81} +(-1.04024e10 - 6.00581e9i) q^{82} -1.40877e10 q^{83} +(9.32524e9 - 1.67431e10i) q^{84} +2.53223e9 q^{85} +(3.33766e10 + 1.92700e10i) q^{86} +(-2.33128e9 + 1.97300e9i) 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} +(-1.13016e11 - 4.05952e10i) q^{93} +(-5.30347e10 + 3.06196e10i) q^{94} +(8.87569e9 - 5.12438e9i) q^{95} +(1.32912e10 + 4.77420e9i) 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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