LMFDB - Embedded newform 42.12.f.a.5.2

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			5.2
Character	$\chi$	$=$	42.5
Dual form			42.12.f.a.17.2

$q$-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} +(-357.754 - 221.718i) q^{3} +(512.000 + 886.810i) q^{4} +(3644.72 - 6312.84i) q^{5} +(6366.89 + 11868.5i) q^{6} +(18530.2 - 40422.3i) q^{7} -32768.0i q^{8} +(78829.4 + 158641. i) q^{9} +(-202011. + 116631. i) q^{10} +(493282. - 284796. i) q^{11} +(13451.4 - 430780. i) q^{12} +1.29209e6i q^{13} +(-1.16028e6 + 823732. i) q^{14} +(-2.70358e6 + 1.45035e6i) q^{15} +(-524288. + 908093. i) q^{16} +(4.99824e6 + 8.65721e6i) q^{17} +(353673. - 5.65766e6i) q^{18} +(8.48276e6 + 4.89753e6i) q^{19} +7.46438e6 q^{20} +(-1.55916e7 + 1.03528e7i) q^{21} -1.82270e7 q^{22} +(1.68637e7 + 9.73628e6i) q^{23} +(-7.26525e6 + 1.17229e7i) q^{24} +(-2.15388e6 - 3.73063e6i) q^{25} +(2.06735e7 - 3.58075e7i) q^{26} +(6.97200e6 - 7.42324e7i) q^{27} +(4.53343e7 - 4.26345e6i) q^{28} +5.92065e7i q^{29} +(9.81294e7 + 3.06416e6i) q^{30} +(8.65515e7 - 4.99705e7i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(-2.39618e8 - 7.48223e6i) q^{33} -3.19888e8i q^{34} +(-1.87642e8 - 2.64306e8i) q^{35} +(-1.00324e8 + 1.51131e8i) q^{36} +(-1.95620e7 + 3.38823e7i) q^{37} +(-1.56721e8 - 2.71448e8i) q^{38} +(2.86480e8 - 4.62251e8i) q^{39} +(-2.06859e8 - 1.19430e8i) q^{40} +7.21720e8 q^{41} +(5.97731e8 - 3.74389e7i) q^{42} +4.17912e8 q^{43} +(5.05120e8 + 2.91631e8i) q^{44} +(1.28879e9 + 8.05650e7i) q^{45} +(-3.11561e8 - 5.39639e8i) q^{46} +(1.85279e8 - 3.20913e8i) q^{47} +(3.88907e8 - 2.08630e8i) q^{48} +(-1.29059e9 - 1.49806e9i) q^{49} +1.37848e8i q^{50} +(1.31315e8 - 4.20536e9i) q^{51} +(-1.14584e9 + 6.61551e8i) q^{52} +(2.83166e9 - 1.63486e9i) q^{53} +(-1.38093e9 + 1.94564e9i) q^{54} -4.15201e9i q^{55} +(-1.32456e9 - 6.07197e8i) q^{56} +(-1.94888e9 - 3.63289e9i) q^{57} +(9.47303e8 - 1.64078e9i) q^{58} +(3.11219e9 + 5.39046e9i) q^{59} +(-2.67042e9 - 1.65499e9i) q^{60} +(-4.99495e9 - 2.88383e9i) q^{61} -3.19812e9 q^{62} +(7.87335e9 - 2.46815e8i) q^{63} -1.07374e9 q^{64} +(8.15677e9 + 4.70931e9i) q^{65} +(6.52077e9 + 4.04124e9i) q^{66} +(1.00714e10 + 1.74442e10i) q^{67} +(-5.11820e9 + 8.86499e9i) q^{68} +(-3.87437e9 - 7.22219e9i) q^{69} +(9.71192e8 + 1.03269e10i) q^{70} -9.51546e9i q^{71} +(5.19835e9 - 2.58308e9i) q^{72} +(-8.51783e9 + 4.91777e9i) q^{73} +(1.08423e9 - 6.25983e8i) q^{74} +(-5.65873e7 + 1.81220e9i) q^{75} +1.00301e10i q^{76} +(-2.37151e9 - 2.52169e10i) q^{77} +(-1.53352e10 + 8.22661e9i) q^{78} +(-2.52441e10 + 4.37241e10i) q^{79} +(3.82176e9 + 6.61949e9i) q^{80} +(-1.89529e10 + 2.50112e10i) q^{81} +(-2.00009e10 - 1.15475e10i) q^{82} -3.99557e10 q^{83} +(-1.71638e10 - 8.52616e9i) q^{84} +7.28688e10 q^{85} +(-1.15815e10 - 6.68659e9i) q^{86} +(1.31271e10 - 2.11814e10i) q^{87} +(-9.33220e9 - 1.61638e10i) q^{88} +(2.26164e10 - 3.91728e10i) q^{89} +(-3.44269e10 - 2.28533e10i) q^{90} +(5.22293e10 + 2.39427e10i) q^{91} +1.99399e10i q^{92} +(-4.20436e10 - 1.31284e9i) q^{93} +(-1.02692e10 + 5.92894e9i) q^{94} +(6.18346e10 - 3.57002e10i) q^{95} +(-1.41158e10 - 4.40775e8i) q^{96} +1.01165e11i q^{97} +(1.17969e10 + 6.21650e10i) q^{98} +(8.40655e10 + 5.58044e10i) 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
$3$	−357.754	−	221.718i	−0.849998	−	0.526785i
$3$	−357.754	−	221.718i	−0.849998	−	0.526785i
$4$	512.000	+	886.810i	0.250000	+	0.433013i
$5$	3644.72	−	6312.84i	0.521590	−	0.903420i	−0.478095	−	0.878308i	$-0.658673\pi$
$5$	3644.72	−	6312.84i	0.521590	−	0.903420i	0.999685	−	0.0251116i	$-0.00799412\pi$
$6$	6366.89	+	11868.5i	0.334269	+	0.623109i
$7$	18530.2	−	40422.3i	0.416716	−	0.909037i
$7$	18530.2	−	40422.3i	0.416716	−	0.909037i
$8$		−	32768.0i		−	0.353553i
$9$	78829.4	+	158641.i	0.444994	+	0.895533i
$10$	−202011.	+	116631.i	−0.638814	+	0.368820i
$11$	493282.	−	284796.i	0.923496	−	0.533181i	0.0387474	−	0.999249i	$-0.487663\pi$
$11$	493282.	−	284796.i	0.923496	−	0.533181i	0.884749	+	0.466068i	$0.154330\pi$
$12$	13451.4	−	430780.i	0.0156052	−	0.499756i
$13$			1.29209e6i			0.965172i	0.875848	+	0.482586i	$0.160302\pi$
$13$			1.29209e6i			0.965172i	−0.875848	+	0.482586i	$0.839698\pi$
$14$	−1.16028e6	+	823732.i	−0.576578	+	0.409338i
$15$	−2.70358e6	+	1.45035e6i	−0.919259	+	0.493139i
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	4.99824e6	+	8.65721e6i	0.853785	+	1.47880i	0.877768	+	0.479086i	$0.159032\pi$
$17$	4.99824e6	+	8.65721e6i	0.853785	+	1.47880i	−0.0239831	+	0.999712i	$0.507635\pi$
$18$	353673.	−	5.65766e6i	0.0441167	−	0.705729i
$19$	8.48276e6	+	4.89753e6i	0.785946	+	0.453766i	0.838533	−	0.544850i	$-0.183414\pi$
$19$	8.48276e6	+	4.89753e6i	0.785946	+	0.453766i	−0.0525876	+	0.998616i	$0.516747\pi$
$20$	7.46438e6			0.521590
$21$	−1.55916e7	+	1.03528e7i	−0.833075	+	0.553160i
$22$	−1.82270e7			−0.754031
$23$	1.68637e7	+	9.73628e6i	0.546324	+	0.315421i	0.747638	−	0.664106i	$-0.231188\pi$
$23$	1.68637e7	+	9.73628e6i	0.546324	+	0.315421i	−0.201314	+	0.979527i	$0.564521\pi$
$24$	−7.26525e6	+	1.17229e7i	−0.186247	+	0.300520i
$25$	−2.15388e6	−	3.73063e6i	−0.0441115	−	0.0764033i
$26$	2.06735e7	−	3.58075e7i	0.341240	−	0.591045i
$27$	6.97200e6	−	7.42324e7i	0.0935097	−	0.995618i
$28$	4.53343e7	−	4.26345e6i	0.497803	−	0.0468158i
$29$			5.92065e7i			0.536019i	0.963416	+	0.268009i	$0.0863658\pi$
$29$			5.92065e7i			0.536019i	−0.963416	+	0.268009i	$0.913634\pi$
$30$	9.81294e7	+	3.06416e6i	0.737280	+	0.0230220i
$31$	8.65515e7	−	4.99705e7i	0.542982	−	0.313491i	−0.203305	−	0.979116i	$-0.565168\pi$
$31$	8.65515e7	−	4.99705e7i	0.542982	−	0.313491i	0.746287	+	0.665625i	$0.231835\pi$
$32$	2.90590e7	−	1.67772e7i	0.153093	−	0.0883883i
$33$	−2.39618e8	−	7.48223e6i	−1.06584	−	0.0332816i
$34$		−	3.19888e8i		−	1.20743i
$35$	−1.87642e8	−	2.64306e8i	−0.603887	−	0.850614i
$36$	−1.00324e8	+	1.51131e8i	−0.276529	+	0.416571i
$37$	−1.95620e7	+	3.38823e7i	−0.0463770	+	0.0803274i	−0.888282	−	0.459298i	$-0.848101\pi$
$37$	−1.95620e7	+	3.38823e7i	−0.0463770	+	0.0803274i	0.841905	+	0.539626i	$0.181434\pi$
$38$	−1.56721e8	−	2.71448e8i	−0.320861	−	0.555748i
$39$	2.86480e8	−	4.62251e8i	0.508439	−	0.820395i
$40$	−2.06859e8	−	1.19430e8i	−0.319407	−	0.184410i
$41$	7.21720e8			0.972876			0.486438	−	0.873715i	$-0.338296\pi$
$41$	7.21720e8			0.972876			0.486438	+	0.873715i	$0.338296\pi$
$42$	5.97731e8	−	3.74389e7i	0.705724	−	0.0442031i
$43$	4.17912e8			0.433519			0.216760	−	0.976225i	$-0.430451\pi$
$43$	4.17912e8			0.433519			0.216760	+	0.976225i	$0.430451\pi$
$44$	5.05120e8	+	2.91631e8i	0.461748	+	0.266590i
$45$	1.28879e9	+	8.05650e7i	1.04115	+	0.0650845i
$46$	−3.11561e8	−	5.39639e8i	−0.223036	−	0.386310i
$47$	1.85279e8	−	3.20913e8i	0.117839	−	0.204103i	−0.801072	−	0.598568i	$-0.795737\pi$
$47$	1.85279e8	−	3.20913e8i	0.117839	−	0.204103i	0.918911	+	0.394465i	$0.129070\pi$
$48$	3.88907e8	−	2.08630e8i	0.220302	−	0.118182i
$49$	−1.29059e9	−	1.49806e9i	−0.652695	−	0.757621i
$50$			1.37848e8i			0.0623831i
$51$	1.31315e8	−	4.20536e9i	0.0532940	−	1.70674i
$52$	−1.14584e9	+	6.61551e8i	−0.417932	+	0.241293i
$53$	2.83166e9	−	1.63486e9i	0.930087	−	0.536986i	0.0432481	−	0.999064i	$-0.486229\pi$
$53$	2.83166e9	−	1.63486e9i	0.930087	−	0.536986i	0.886839	+	0.462078i	$0.152896\pi$
$54$	−1.38093e9	+	1.94564e9i	−0.409267	+	0.576629i
$55$		−	4.15201e9i		−	1.11241i
$56$	−1.32456e9	−	6.07197e8i	−0.321393	−	0.147331i
$57$	−1.94888e9	−	3.63289e9i	−0.429015	−	0.799725i
$58$	9.47303e8	−	1.64078e9i	0.189511	−	0.328243i
$59$	3.11219e9	+	5.39046e9i	0.566734	+	0.981612i	0.996886	+	0.0788559i	$0.0251267\pi$
$59$	3.11219e9	+	5.39046e9i	0.566734	+	0.981612i	−0.430152	+	0.902757i	$0.641540\pi$
$60$	−2.67042e9	−	1.65499e9i	−0.443350	−	0.274766i
$61$	−4.99495e9	−	2.88383e9i	−0.757211	−	0.437176i	0.0710826	−	0.997470i	$-0.477355\pi$
$61$	−4.99495e9	−	2.88383e9i	−0.757211	−	0.437176i	−0.828293	+	0.560295i	$0.810688\pi$
$62$	−3.19812e9			−0.443343
$63$	7.87335e9	−	2.46815e8i	0.999509	−	0.0313327i
$64$	−1.07374e9			−0.125000
$65$	8.15677e9	+	4.70931e9i	0.871956	+	0.503424i
$66$	6.52077e9	+	4.04124e9i	0.640925	+	0.397213i
$67$	1.00714e10	+	1.74442e10i	0.911335	+	1.57848i	0.812181	+	0.583406i	$0.198280\pi$
$67$	1.00714e10	+	1.74442e10i	0.911335	+	1.57848i	0.0991542	+	0.995072i	$0.468386\pi$
$68$	−5.11820e9	+	8.86499e9i	−0.426892	+	0.739399i
$69$	−3.87437e9	−	7.22219e9i	−0.298216	−	0.555903i
$70$	9.71192e8	+	1.03269e10i	0.0690663	+	0.734399i
$71$		−	9.51546e9i		−	0.625906i	−0.949769	−	0.312953i	$-0.898682\pi$
$71$		−	9.51546e9i		−	0.625906i	0.949769	−	0.312953i	$-0.101318\pi$
$72$	5.19835e9	−	2.58308e9i	0.316619	−	0.157329i
$73$	−8.51783e9	+	4.91777e9i	−0.480898	+	0.277647i	−0.720791	−	0.693153i	$-0.756221\pi$
$73$	−8.51783e9	+	4.91777e9i	−0.480898	+	0.277647i	0.239893	+	0.970799i	$0.422888\pi$
$74$	1.08423e9	−	6.25983e8i	0.0568000	−	0.0327935i
$75$	−5.65873e7	+	1.81220e9i	−0.00275348	+	0.0881800i
$76$			1.00301e10i			0.453766i
$77$	−2.37151e9	−	2.52169e10i	−0.0998450	−	1.06168i
$78$	−1.53352e10	+	8.22661e9i	−0.601407	+	0.322627i
$79$	−2.52441e10	+	4.37241e10i	−0.923020	+	1.59872i	−0.128305	+	0.991735i	$0.540954\pi$
$79$	−2.52441e10	+	4.37241e10i	−0.923020	+	1.59872i	−0.794715	+	0.606983i	$0.792380\pi$
$80$	3.82176e9	+	6.61949e9i	0.130397	+	0.225855i
$81$	−1.89529e10	+	2.50112e10i	−0.603960	+	0.797014i
$82$	−2.00009e10	−	1.15475e10i	−0.595762	−	0.343964i
$83$	−3.99557e10			−1.11339			−0.556697	−	0.830715i	$-0.687932\pi$
$83$	−3.99557e10			−1.11339			−0.556697	+	0.830715i	$0.687932\pi$
$84$	−1.71638e10	−	8.52616e9i	−0.447794	−	0.222442i
$85$	7.28688e10			1.78130
$86$	−1.15815e10	−	6.68659e9i	−0.265475	−	0.153272i
$87$	1.31271e10	−	2.11814e10i	0.282367	−	0.455615i
$88$	−9.33220e9	−	1.61638e10i	−0.188508	−	0.326505i
$89$	2.26164e10	−	3.91728e10i	0.429318	−	0.743600i	−0.567495	−	0.823377i	$-0.692087\pi$
$89$	2.26164e10	−	3.91728e10i	0.429318	−	0.743600i	0.996813	+	0.0797768i	$0.0254208\pi$
$90$	−3.44269e10	−	2.28533e10i	−0.614559	−	0.407957i
$91$	5.22293e10	+	2.39427e10i	0.877377	+	0.402203i
$92$			1.99399e10i			0.315421i
$93$	−4.20436e10	−	1.31284e9i	−0.626676	−	0.0195684i
$94$	−1.02692e10	+	5.92894e9i	−0.144323	+	0.0833247i
$95$	6.18346e10	−	3.57002e10i	0.819882	−	0.473359i
$96$	−1.41158e10	−	4.40775e8i	−0.176691	−	0.00551728i
$97$			1.01165e11i			1.19615i	0.801440	+	0.598076i	$0.204068\pi$
$97$			1.01165e11i			1.19615i	−0.801440	+	0.598076i	$0.795932\pi$
$98$	1.17969e10	+	6.21650e10i	0.131833	+	0.694709i
$99$	8.40655e10	+	5.58044e10i	0.888432	+	0.589759i
$100$	2.20557e9	−	3.82017e9i	0.0220557	−	0.0382017i
$101$	−8.15863e10	−	1.41312e11i	−0.772413	−	1.33786i	−0.936237	−	0.351369i	$-0.885716\pi$
$101$	−8.15863e10	−	1.41312e11i	−0.772413	−	1.33786i	0.163824	−	0.986490i	$-0.447617\pi$
$102$	−7.09248e10	+	1.14441e11i	−0.636059	+	1.02632i
$103$	−1.37931e11	−	7.96343e10i	−1.17235	−	0.676855i	−0.218116	−	0.975923i	$-0.569991\pi$
$103$	−1.37931e11	−	7.96343e10i	−1.17235	−	0.676855i	−0.954232	+	0.299068i	$0.903324\pi$
$104$	4.23393e10			0.341240
$105$	8.52840e9	+	1.36160e11i	0.0652118	+	1.04114i
$106$	−1.04631e11			−0.759413
$107$	1.99458e11	+	1.15157e11i	1.37481	+	0.793745i	0.991529	−	0.129889i	$-0.0414620\pi$
$107$	1.99458e11	+	1.15157e11i	1.37481	+	0.793745i	0.383277	+	0.923633i	$0.374795\pi$
$108$	6.93997e10	−	3.18242e10i	0.454493	−	0.208414i
$109$	−6.99908e10	−	1.21228e11i	−0.435708	−	0.754668i	0.561645	−	0.827378i	$-0.310169\pi$
$109$	−6.99908e10	−	1.21228e11i	−0.435708	−	0.754668i	−0.997353	+	0.0727099i	$0.976835\pi$
$110$	−6.64321e10	+	1.15064e11i	−0.393295	+	0.681207i
$111$	1.45107e10	−	7.78431e9i	0.0817357	−	0.0438474i
$112$	2.69920e10	+	3.80200e10i	0.144723	+	0.203851i
$113$		−	2.42725e11i		−	1.23932i	−0.784871	−	0.619660i	$-0.787271\pi$
$113$		−	2.42725e11i		−	1.23932i	0.784871	−	0.619660i	$-0.212729\pi$
$114$	−4.11741e9	+	1.31860e11i	−0.0200284	+	0.641409i
$115$	1.22927e11	−	7.09720e10i	0.569914	−	0.329040i
$116$	−5.25049e10	+	3.03137e10i	−0.232103	+	0.134005i
$117$	−2.04979e11	+	1.01855e11i	−0.864344	+	0.429496i
$118$		−	1.99180e11i		−	0.801483i
$119$	4.42562e11	−	4.16206e10i	1.70007	−	0.159882i
$120$	4.75249e10	+	8.85910e10i	0.174351	+	0.325007i
$121$	1.95619e10	−	3.38823e10i	0.0685634	−	0.118755i
$122$	9.22827e10	+	1.59838e11i	0.309130	+	0.535429i
$123$	−2.58198e11	−	1.60018e11i	−0.826943	−	0.512497i
$124$	8.86288e10	+	5.11698e10i	0.271491	+	0.156745i
$125$	3.24528e11			0.951147
$126$	−2.22142e11	−	1.19134e11i	−0.623150	−	0.334193i
$127$	2.99579e11			0.804621			0.402310	−	0.915503i	$-0.368207\pi$
$127$	2.99579e11			0.804621			0.402310	+	0.915503i	$0.368207\pi$
$128$	2.97564e10	+	1.71799e10i	0.0765466	+	0.0441942i
$129$	−1.49510e11	−	9.26586e10i	−0.368491	−	0.228372i
$130$	−1.50698e11	−	2.61016e11i	−0.355974	−	0.616566i
$131$	3.53390e11	−	6.12090e11i	0.800318	−	1.38619i	−0.119089	−	0.992884i	$-0.537997\pi$
$131$	3.53390e11	−	6.12090e11i	0.800318	−	1.38619i	0.919407	−	0.393308i	$-0.128669\pi$
$132$	−1.16049e11	−	2.16327e11i	−0.252049	−	0.469844i
$133$	3.55156e11	−	2.52140e11i	0.740006	−	0.525362i
$134$		−	6.44569e11i		−	1.28882i
$135$	−4.43206e11	−	3.14569e11i	−0.850688	−	0.603783i
$136$	2.83680e11	−	1.63782e11i	0.522834	−	0.301859i
$137$	−7.73559e11	+	4.46615e11i	−1.36940	+	0.790624i	−0.990851	−	0.134957i	$-0.956910\pi$
$137$	−7.73559e11	+	4.46615e11i	−1.36940	+	0.790624i	−0.378549	+	0.925581i	$0.623577\pi$
$138$	−8.18540e9	+	2.62137e11i	−0.0139221	+	0.445855i
$139$		−	1.04407e12i		−	1.70667i	−0.521362	−	0.853336i	$-0.674576\pi$
$139$		−	1.04407e12i		−	1.70667i	0.521362	−	0.853336i	$-0.325424\pi$
$140$	1.38316e11	−	3.01727e11i	0.217355	−	0.474144i
$141$	−1.37437e11	+	7.37284e10i	−0.207681	+	0.111411i
$142$	−1.52247e11	+	2.63700e11i	−0.221291	+	0.383288i
$143$	3.67983e11	+	6.37365e11i	0.514611	+	0.891333i
$144$	−1.85390e11	−	1.15892e10i	−0.249513	−	0.0155976i
$145$	3.73761e11	+	2.15791e11i	0.484250	+	0.279582i
$146$	3.14737e11			0.392652
$147$	1.29567e11	+	8.22086e11i	0.155686	+	0.987807i
$148$	−4.00629e10			−0.0463770
$149$	2.66690e11	+	1.53974e11i	0.297497	+	0.171760i	0.641318	−	0.767275i	$-0.278388\pi$
$149$	2.66690e11	+	1.53974e11i	0.297497	+	0.171760i	−0.343821	+	0.939035i	$0.611721\pi$
$150$	3.05635e10	−	4.93159e10i	0.0328625	−	0.0530255i
$151$	−1.33779e11	−	2.31713e11i	−0.138681	−	0.240202i	0.788317	−	0.615269i	$-0.210953\pi$
$151$	−1.33779e11	−	2.31713e11i	−0.138681	−	0.240202i	−0.926997	+	0.375068i	$0.877619\pi$
$152$	1.60482e11	−	2.77963e11i	0.160431	−	0.277874i
$153$	−9.79381e11	+	1.47537e12i	−0.944384	+	1.42265i
$154$	−3.37749e11	+	7.36775e11i	−0.314217	+	0.685442i
$155$		−	7.28514e11i		−	0.654054i
$156$	5.56607e11	+	1.73804e10i	0.482351	+	0.0150617i
$157$	−1.21757e12	+	7.02966e11i	−1.01870	+	0.588148i	−0.913728	−	0.406327i	$-0.866809\pi$
$157$	−1.21757e12	+	7.02966e11i	−1.01870	+	0.588148i	−0.104974	+	0.994475i	$0.533476\pi$
$158$	1.39917e12	−	8.07812e11i	1.13046	−	0.652674i
$159$	−1.37552e12	−	4.29514e10i	−1.07345	−	0.0335192i
$160$		−	2.44593e11i		−	0.184410i
$161$	7.06050e11	−	5.01255e11i	0.514391	−	0.365188i
$162$	9.25417e11	−	3.89883e11i	0.651636	−	0.274537i
$163$	−1.32845e12	+	2.30094e12i	−0.904302	+	1.56630i	−0.0824510	+	0.996595i	$0.526275\pi$
$163$	−1.32845e12	+	2.30094e12i	−0.904302	+	1.56630i	−0.821851	+	0.569702i	$0.807059\pi$
$164$	3.69521e11	+	6.40028e11i	0.243219	+	0.421268i
$165$	−9.20574e11	+	1.48540e12i	−0.585999	+	0.945543i
$166$	1.10728e12	+	6.39291e11i	0.681812	+	0.393644i
$167$	6.28560e11			0.374461			0.187230	−	0.982316i	$-0.440049\pi$
$167$	6.28560e11			0.374461			0.187230	+	0.982316i	$0.440049\pi$
$168$	3.39240e11	+	5.10905e11i	0.195571	+	0.294537i
$169$	1.22659e11			0.0684421
$170$	−2.01940e12	−	1.16590e12i	−1.09082	−	0.629785i
$171$	−1.08258e11	+	1.73178e12i	−0.0566214	+	0.905764i
$172$	2.13971e11	+	3.70609e11i	0.108380	+	0.187719i
$173$	−1.03436e12	+	1.79157e12i	−0.507481	+	0.878982i	0.492482	+	0.870323i	$0.336090\pi$
$173$	−1.03436e12	+	1.79157e12i	−0.507481	+	0.878982i	−0.999963	+	0.00865953i	$0.997244\pi$
$174$	−7.02692e11	+	3.76961e11i	−0.333998	+	0.179174i
$175$	−1.90712e11	+	1.79355e10i	−0.0878354	+	0.00826045i
$176$			5.97261e11i			0.266590i
$177$	8.17641e10	−	2.61849e12i	0.0353761	−	1.13292i
$178$	−1.25353e12	+	7.23725e11i	−0.525805	+	0.303573i
$179$	1.89619e10	−	1.09477e10i	0.00771243	−	0.00445277i	−0.496139	−	0.868243i	$-0.665249\pi$
$179$	1.89619e10	−	1.09477e10i	0.00771243	−	0.00445277i	0.503851	+	0.863790i	$0.331916\pi$
$180$	5.88413e11	+	1.18416e12i	0.232104	+	0.467101i
$181$		−	1.55454e12i		−	0.594798i	−0.954753	−	0.297399i	$-0.903881\pi$
$181$		−	1.55454e12i		−	0.594798i	0.954753	−	0.297399i	$-0.0961191\pi$
$182$	−1.06434e12	−	1.49919e12i	−0.395081	−	0.556498i
$183$	1.14757e12	+	2.13917e12i	0.413330	+	0.770486i
$184$	3.19038e11	−	5.52591e11i	0.111518	−	0.193155i
$185$	1.42596e11	+	2.46983e11i	0.0483796	+	0.0837959i
$186$	1.14414e12	+	7.09079e11i	0.376841	+	0.233547i
$187$	4.93108e12	+	2.84696e12i	1.57693	+	0.910443i
$188$	3.79452e11			0.117839
$189$	−2.87145e12	−	1.65736e12i	−0.866087	−	0.499894i
$190$	−2.28481e12			−0.669431
$191$	−3.44195e12	−	1.98721e12i	−0.979762	−	0.565666i	−0.0775635	−	0.996987i	$-0.524714\pi$
$191$	−3.44195e12	−	1.98721e12i	−0.979762	−	0.565666i	−0.902198	+	0.431322i	$0.858047\pi$
$192$	3.84136e11	+	2.38068e11i	0.106250	+	0.0658482i
$193$	5.80150e11	+	1.00485e12i	0.155946	+	0.270107i	0.933403	−	0.358829i	$-0.116824\pi$
$193$	5.80150e11	+	1.00485e12i	0.155946	+	0.270107i	−0.777457	+	0.628936i	$0.783491\pi$
$194$	1.61864e12	−	2.80357e12i	0.422903	−	0.732490i
$195$	−1.87398e12	−	3.49328e12i	−0.475965	−	0.887243i
$196$	6.67715e11	−	1.91152e12i	0.164886	−	0.472030i
$197$			5.99527e11i			0.143961i	0.997406	+	0.0719804i	$0.0229319\pi$
$197$			5.99527e11i			0.143961i	−0.997406	+	0.0719804i	$0.977068\pi$
$198$	−1.43682e12	−	2.89154e12i	−0.335540	−	0.675260i
$199$	−6.20317e12	+	3.58140e12i	−1.40904	+	0.813507i	−0.995295	−	0.0968874i	$-0.969111\pi$
$199$	−6.20317e12	+	3.58140e12i	−1.40904	+	0.813507i	−0.413741	+	0.910395i	$0.635778\pi$
$200$	−1.22245e11	+	7.05784e10i	−0.0270127	+	0.0155958i
$201$	2.64598e11	−	8.47373e12i	0.0568863	−	1.82178i
$202$			5.22152e12i			1.09236i
$203$	2.39326e12	+	1.09711e12i	0.487261	+	0.223368i
$204$	3.79658e12	−	2.03669e12i	0.752363	−	0.403607i
$205$	2.63047e12	−	4.55610e12i	0.507442	−	0.878915i
$206$	2.54830e12	+	4.41378e12i	0.478609	+	0.828975i
$207$	−2.15216e11	+	3.44278e12i	−0.0393585	+	0.629612i
$208$	−1.17334e12	−	6.77428e11i	−0.208966	−	0.120647i
$209$	5.57919e12			0.967757
$210$	1.94222e12	−	3.90983e12i	0.328164	−	0.660621i
$211$	6.07874e12			1.00060			0.500300	−	0.865852i	$-0.333223\pi$
$211$	6.07874e12			1.00060			0.500300	+	0.865852i	$0.333223\pi$
$212$	2.89962e12	+	1.67410e12i	0.465044	+	0.268493i
$213$	−2.10975e12	+	3.40420e12i	−0.329718	+	0.532019i
$214$	−3.68503e12	−	6.38267e12i	−0.561262	−	0.972135i
$215$	1.52317e12	−	2.63821e12i	0.226119	−	0.391650i
$216$	−2.43245e12	−	2.28459e11i	−0.352004	−	0.0330607i
$217$	−4.16107e11	−	4.42457e12i	−0.0587052	−	0.624227i
$218$			4.47941e12i			0.616184i
$219$	4.13765e12	+	1.29201e11i	0.555023	+	0.0173310i
$220$	3.68204e12	−	2.12583e12i	0.481686	−	0.278102i
$221$	−1.11859e13	+	6.45819e12i	−1.42730	+	0.824050i
$222$	−5.26681e11	−	1.64460e10i	−0.0655551	−	0.00204700i
$223$		−	6.76371e12i		−	0.821312i	−0.911790	−	0.410656i	$-0.865300\pi$
$223$		−	6.76371e12i		−	0.821312i	0.911790	−	0.410656i	$-0.134700\pi$
$224$	−1.39705e11	−	1.48551e12i	−0.0165519	−	0.176000i
$225$	4.22042e11	−	6.35777e11i	0.0487924	−	0.0735024i
$226$	−3.88360e12	+	6.72659e12i	−0.438165	+	0.758925i
$227$	−2.55639e12	−	4.42780e12i	−0.281505	−	0.487580i	0.690251	−	0.723570i	$-0.257500\pi$
$227$	−2.55639e12	−	4.42780e12i	−0.281505	−	0.487580i	−0.971756	+	0.235990i	$0.924167\pi$
$228$	2.22386e12	−	3.58832e12i	0.239037	−	0.385700i
$229$	3.32820e11	+	1.92154e11i	0.0349233	+	0.0201630i	0.517360	−	0.855768i	$-0.326915\pi$
$229$	3.32820e11	+	1.92154e11i	0.0349233	+	0.0201630i	−0.482437	+	0.875931i	$0.660248\pi$
$230$	−4.54221e12			−0.465333
$231$	−4.74261e12	+	9.54726e12i	−0.474408	+	0.955020i
$232$	1.94008e12			0.189511
$233$	1.95515e12	+	1.12881e12i	0.186519	+	0.107687i	0.590352	−	0.807146i	$-0.298989\pi$
$233$	1.95515e12	+	1.12881e12i	0.186519	+	0.107687i	−0.403833	+	0.914833i	$0.632322\pi$
$234$	7.31022e12	+	4.56978e11i	0.681150	+	0.0425803i
$235$	−1.35058e12	−	2.33928e12i	−0.122927	−	0.212916i
$236$	−3.18688e12	+	5.51983e12i	−0.283367	+	0.490806i
$237$	1.87256e13	−	1.00454e13i	1.62675	−	0.872674i
$238$	−1.29306e13	−	5.92757e12i	−1.09760	−	0.503157i
$239$		−	5.84070e12i		−	0.484481i	−0.970216	−	0.242240i	$-0.922118\pi$
$239$		−	5.84070e12i		−	0.484481i	0.970216	−	0.242240i	$-0.0778823\pi$
$240$	1.00406e11	−	3.21550e12i	0.00813952	−	0.260668i
$241$	1.53029e13	−	8.83514e12i	1.21250	−	0.700035i	0.249194	−	0.968454i	$-0.419834\pi$
$241$	1.53029e13	−	8.83514e12i	1.21250	−	0.700035i	0.963302	+	0.268419i	$0.0865010\pi$
$242$	−1.08423e12	+	6.25982e11i	−0.0839727	+	0.0484816i
$243$	1.23259e13	−	4.74565e12i	0.933221	−	0.359303i
$244$		−	5.90609e12i		−	0.437176i
$245$	−1.41609e13	+	2.68728e12i	−1.02489	+	0.194491i
$246$	4.59511e12	+	8.56573e12i	0.325202	+	0.606207i
$247$	−6.32805e12	+	1.09605e13i	−0.437962	+	0.758573i
$248$	−1.63743e12	−	2.83612e12i	−0.110836	−	0.191973i
$249$	1.42943e13	+	8.85889e12i	0.946384	+	0.586520i
$250$	−8.99359e12	−	5.19245e12i	−0.582456	−	0.336281i
$251$	2.06121e13			1.30592			0.652960	−	0.757393i	$-0.273527\pi$
$251$	2.06121e13			1.30592			0.652960	+	0.757393i	$0.273527\pi$
$252$	4.25003e12	+	6.85580e12i	0.263445	+	0.424967i
$253$	1.10914e13			0.672705
$254$	−8.30218e12	−	4.79327e12i	−0.492728	−	0.284476i
$255$	−2.60691e13	−	1.61563e13i	−1.51410	−	0.938364i
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	−7.03638e12	+	1.21874e13i	−0.391487	+	0.678075i	−0.992646	−	0.121055i	$-0.961372\pi$
$257$	−7.03638e12	+	1.21874e13i	−0.391487	+	0.678075i	0.601159	+	0.799129i	$0.294706\pi$
$258$	2.66080e12	+	4.95999e12i	0.144912	+	0.270130i
$259$	1.00711e12	+	1.41858e12i	0.0536945	+	0.0756321i
$260$			9.64467e12i			0.503424i
$261$	−9.39258e12	+	4.66721e12i	−0.480023	+	0.238525i
$262$	−1.95869e13	+	1.13085e13i	−0.980185	+	0.565910i
$263$	−7.82553e12	+	4.51807e12i	−0.383493	+	0.221410i	−0.679337	−	0.733827i	$-0.737732\pi$
$263$	−7.82553e12	+	4.51807e12i	−0.383493	+	0.221410i	0.295844	+	0.955236i	$0.404399\pi$
$264$	−2.45178e11	+	7.85180e12i	−0.0117668	+	0.376832i
$265$		−	2.38344e13i		−	1.12035i
$266$	−1.38766e13	+	1.30502e12i	−0.638903	+	0.0600854i
$267$	−1.67764e13	+	8.99977e12i	−0.756637	+	0.405900i
$268$	−1.03131e13	+	1.78628e13i	−0.455667	+	0.789239i
$269$	−5.05278e12	−	8.75168e12i	−0.218722	−	0.378838i	0.735695	−	0.677313i	$-0.236856\pi$
$269$	−5.05278e12	−	8.75168e12i	−0.218722	−	0.378838i	−0.954418	+	0.298474i	$0.903522\pi$
$270$	7.24938e12	+	1.58089e13i	0.307468	+	0.670503i
$271$	2.58879e13	+	1.49464e13i	1.07589	+	0.621163i	0.929784	−	0.368106i	$-0.119994\pi$
$271$	2.58879e13	+	1.49464e13i	1.07589	+	0.621163i	0.146103	+	0.989269i	$0.453327\pi$
$272$	−1.04821e13			−0.426892
$273$	−1.33767e13	−	2.01458e13i	−0.533894	−	0.804061i
$274$	2.85833e13			1.11811
$275$	−2.12494e12	−	1.22683e12i	−0.0814736	−	0.0470388i
$276$	4.42103e12	−	7.13359e12i	0.166159	−	0.268107i
$277$	2.33871e13	+	4.05077e13i	0.861664	+	1.49245i	0.870322	+	0.492483i	$0.163911\pi$
$277$	2.33871e13	+	4.05077e13i	0.861664	+	1.49245i	−0.00865849	+	0.999963i	$0.502756\pi$
$278$	−1.67052e13	+	2.89342e13i	−0.603399	+	1.04512i
$279$	1.47502e13	+	9.79148e12i	0.522365	+	0.346757i
$280$	−8.66077e12	+	6.14865e12i	−0.300737	+	0.213506i
$281$			2.70903e12i			0.0922421i	0.998936	+	0.0461211i	$0.0146860\pi$
$281$			2.70903e12i			0.0922421i	−0.998936	+	0.0461211i	$0.985314\pi$
$282$	4.98841e12	+	1.55766e11i	0.166568	+	0.00520120i
$283$	1.43120e13	−	8.26305e12i	0.468679	−	0.270592i	−0.247007	−	0.969014i	$-0.579447\pi$
$283$	1.43120e13	−	8.26305e12i	0.468679	−	0.270592i	0.715687	+	0.698421i	$0.246114\pi$
$284$	8.43841e12	−	4.87192e12i	0.271025	−	0.156476i
$285$	−3.00370e13	−	9.37924e11i	−0.946257	−	0.0295475i
$286$		−	2.35509e13i		−	0.727770i
$287$	1.33736e13	−	2.91735e13i	0.405413	−	0.884380i
$288$	4.95226e12	+	3.28741e12i	0.147280	+	0.0977677i
$289$	−3.28289e13	+	5.68614e13i	−0.957897	+	1.65913i
$290$	−6.90531e12	−	1.19603e13i	−0.197694	−	0.342417i
$291$	2.24301e13	−	3.61922e13i	0.630115	−	1.01673i
$292$	−8.72225e12	−	5.03580e12i	−0.240449	−	0.138823i
$293$	−4.18076e13			−1.13105			−0.565527	−	0.824730i	$-0.691327\pi$
$293$	−4.18076e13			−1.13105			−0.565527	+	0.824730i	$0.691327\pi$
$294$	9.56270e12	−	2.48554e13i	0.253904	−	0.659949i
$295$	4.53722e13			1.18241
$296$	1.11026e12	+	6.41006e11i	0.0284000	+	0.0163968i
$297$	−1.77020e13	−	3.86031e13i	−0.444489	−	0.969307i
$298$	−4.92716e12	−	8.53410e12i	−0.121453	−	0.210362i
$299$	−1.25802e13	+	2.17895e13i	−0.304435	+	0.527297i
$300$	−1.63605e12	+	8.77666e11i	−0.0388714	+	0.0208527i
$301$	7.74399e12	−	1.68930e13i	0.180655	−	0.394085i
$302$			8.56187e12i			0.196124i
$303$	−2.14345e12	+	6.86440e13i	−0.0482147	+	1.54407i
$304$	−8.89482e12	+	5.13543e12i	−0.196486	+	0.113441i
$305$	−3.64104e13	+	2.10215e13i	−0.789907	+	0.456053i
$306$	5.07473e13	−	2.52165e13i	1.08130	−	0.537301i
$307$		−	5.05321e13i		−	1.05756i	−0.848758	−	0.528781i	$-0.822649\pi$
$307$		−	5.05321e13i		−	1.05756i	0.848758	−	0.528781i	$-0.177351\pi$
$308$	2.11484e13	−	1.50141e13i	0.434758	−	0.308653i
$309$	3.16890e13	+	5.90712e13i	0.639936	+	1.19290i
$310$	−1.16562e13	+	2.01892e13i	−0.231243	+	0.400525i
$311$	1.39170e13	+	2.41049e13i	0.271246	+	0.469811i	0.969181	−	0.246349i	$-0.0792311\pi$
$311$	1.39170e13	+	2.41049e13i	0.271246	+	0.469811i	−0.697935	+	0.716161i	$0.745898\pi$
$312$	−1.51471e13	−	9.38737e12i	−0.290053	−	0.179760i
$313$	−6.05869e13	−	3.49799e13i	−1.13995	−	0.658149i	−0.193530	−	0.981094i	$-0.561994\pi$
$313$	−6.05869e13	−	3.49799e13i	−1.13995	−	0.658149i	−0.946418	+	0.322945i	$0.895327\pi$
$314$	4.49898e13			0.831766
$315$	2.71381e13	−	5.06028e13i	0.493027	−	0.919319i
$316$	−5.16999e13			−0.923020
$317$	−2.60889e13	−	1.50624e13i	−0.457752	−	0.264283i	0.253347	−	0.967376i	$-0.418469\pi$
$317$	−2.60889e13	−	1.50624e13i	−0.457752	−	0.264283i	−0.711099	+	0.703092i	$0.751802\pi$
$318$	3.74322e13	+	2.31986e13i	0.645500	+	0.400048i
$319$	1.68618e13	+	2.92055e13i	0.285795	+	0.495011i
$320$	−3.91349e12	+	6.77836e12i	−0.0651987	+	0.112927i
$321$	−4.58247e13	−	8.54215e13i	−0.750450	−	1.39891i
$322$	−2.75867e13	+	2.59438e12i	−0.444112	+	0.0417664i
$323$			9.79161e13i			1.54967i
$324$	−3.18840e13	−	4.00193e12i	−0.496107	−	0.0622689i
$325$	4.82032e12	−	2.78301e12i	0.0737424	−	0.0425752i
$326$	7.36302e13	−	4.25104e13i	1.10754	−	0.639438i
$327$	−1.83882e12	+	5.88880e13i	−0.0271973	+	0.870991i
$328$		−	2.36493e13i		−	0.343964i
$329$	−9.53878e12	−	1.34360e13i	−0.136432	−	0.192173i
$330$	4.92781e13	−	2.64354e13i	0.693150	−	0.371843i
$331$	−7.39778e12	+	1.28133e13i	−0.102341	+	0.177259i	−0.912649	−	0.408745i	$-0.865966\pi$
$331$	−7.39778e12	+	1.28133e13i	−0.102341	+	0.177259i	0.810308	+	0.586004i	$0.199300\pi$
$332$	−2.04573e13	−	3.54331e13i	−0.278349	−	0.482114i
$333$	−6.91718e12	−	4.32409e11i	−0.0925734	−	0.00578697i
$334$	−1.74192e13	−	1.00570e13i	−0.229309	−	0.132392i
$335$	1.46830e14			1.90137
$336$	−1.22680e12	−	1.95865e13i	−0.0156281	−	0.249511i
$337$	7.01837e13			0.879573			0.439786	−	0.898102i	$-0.355054\pi$
$337$	7.01837e13			0.879573			0.439786	+	0.898102i	$0.355054\pi$
$338$	−3.39923e12	−	1.96255e12i	−0.0419121	−	0.0241979i
$339$	−5.38165e13	+	8.68359e13i	−0.652855	+	1.05342i
$340$	3.73088e13	+	6.46208e13i	0.445325	+	0.771326i
$341$	2.84628e13	−	4.92991e13i	0.334295	−	0.579015i
$342$	3.07087e13	−	4.62605e13i	0.354909	−	0.534646i
$343$	−8.44700e13	+	2.44093e13i	−0.960694	+	0.277611i
$344$		−	1.36941e13i		−	0.153272i
$345$	−5.97135e13	−	1.86459e12i	−0.657760	−	0.0205390i
$346$	5.73302e13	−	3.30996e13i	0.621534	−	0.358843i
$347$	9.31669e13	−	5.37899e13i	0.994145	−	0.573970i	0.0876342	−	0.996153i	$-0.472069\pi$
$347$	9.31669e13	−	5.37899e13i	0.994145	−	0.573970i	0.906511	+	0.422183i	$0.138736\pi$
$348$	2.55049e13	+	7.96409e11i	0.267879	+	0.00836470i
$349$		−	1.46584e14i		−	1.51547i	−0.652563	−	0.757734i	$-0.726306\pi$
$349$		−	1.46584e14i		−	1.51547i	0.652563	−	0.757734i	$-0.273694\pi$
$350$	5.57214e12	+	2.55436e12i	0.0567085	+	0.0259960i
$351$	9.59151e13	+	9.00847e12i	0.960943	+	0.0902530i
$352$	9.55618e12	−	1.65518e13i	0.0942539	−	0.163253i
$353$	−3.97517e13	−	6.88520e13i	−0.386007	−	0.668583i	0.605902	−	0.795540i	$-0.292812\pi$
$353$	−3.97517e13	−	6.88520e13i	−0.386007	−	0.668583i	−0.991908	+	0.126956i	$0.959479\pi$
$354$	−4.41617e13	+	7.12575e13i	−0.422210	+	0.681259i
$355$	−6.00696e13	−	3.46812e13i	−0.565456	−	0.326466i
$356$	4.63184e13			0.429318
$357$	−1.67557e14	−	8.32340e13i	−1.52928	−	0.759671i
$358$	−7.00651e11			−0.00629717
$359$	6.11968e12	+	3.53320e12i	0.0541638	+	0.0312715i	0.526837	−	0.849966i	$-0.323378\pi$
$359$	6.11968e12	+	3.53320e12i	0.0541638	+	0.0312715i	−0.472674	+	0.881238i	$0.656711\pi$
$360$	2.63995e12	−	4.22309e13i	0.0230108	−	0.368101i
$361$	−1.02736e13	−	1.77944e13i	−0.0881929	−	0.152755i
$362$	−2.48726e13	+	4.30806e13i	−0.210293	+	0.364238i
$363$	−1.45107e13	+	7.78430e12i	−0.120837	+	0.0648236i
$364$	5.50877e12	+	5.85761e13i	0.0451853	+	0.480466i
$365$			7.16955e13i			0.579270i
$366$	2.42447e12	−	7.76436e13i	0.0192962	−	0.617959i
$367$	8.14472e11	−	4.70236e11i	0.00638576	−	0.00368682i	−0.496804	−	0.867863i	$-0.665493\pi$
$367$	8.14472e11	−	4.70236e11i	0.00638576	−	0.00368682i	0.503189	+	0.864176i	$0.332160\pi$
$368$	−1.76829e13	+	1.02092e13i	−0.136581	+	0.0788551i
$369$	5.68927e13	+	1.14494e14i	0.432924	+	0.871243i
$370$		−	9.12613e12i		−	0.0684190i
$371$	−1.36136e13	−	1.44756e14i	−0.100558	−	1.06925i
$372$	−2.03621e13	−	3.79568e13i	−0.148196	−	0.276251i
$373$	−1.04359e13	+	1.80754e13i	−0.0748392	+	0.129625i	−0.901016	−	0.433785i	$-0.857178\pi$
$373$	−1.04359e13	+	1.80754e13i	−0.0748392	+	0.129625i	0.826177	+	0.563410i	$0.190511\pi$
$374$	−9.11028e13	−	1.57795e14i	−0.643781	−	1.11506i
$375$	−1.16101e14	−	7.19537e13i	−0.808473	−	0.501050i
$376$	−1.05157e13	−	6.07123e12i	−0.0721613	−	0.0416624i
$377$	−7.65002e13			−0.517351
$378$	5.30581e13	+	9.18734e13i	0.353628	+	0.612329i
$379$	2.87816e14			1.89060			0.945300	−	0.326203i	$-0.105769\pi$
$379$	2.87816e14			1.89060			0.945300	+	0.326203i	$0.105769\pi$
$380$	6.33186e13	+	3.65570e13i	0.409941	+	0.236680i
$381$	−1.07176e14	−	6.64221e13i	−0.683926	−	0.423862i
$382$	6.35907e13	+	1.10142e14i	0.399986	+	0.692796i
$383$	9.31323e13	−	1.61310e14i	0.577441	−	1.00016i	−0.418331	−	0.908295i	$-0.637385\pi$
$383$	9.31323e13	−	1.61310e14i	0.577441	−	1.00016i	0.995772	−	0.0918618i	$-0.0292818\pi$
$384$	−6.83640e12	−	1.27437e13i	−0.0417836	−	0.0778886i
$385$	−1.67834e14	−	7.69374e13i	−1.01122	−	0.463558i
$386$		−	3.71296e13i		−	0.220541i
$387$	3.29438e13	+	6.62980e13i	0.192914	+	0.388231i
$388$	−8.97142e13	+	5.17965e13i	−0.517949	+	0.299038i
$389$	−1.35119e14	+	7.80107e13i	−0.769117	+	0.444050i	−0.832559	−	0.553936i	$-0.813125\pi$
$389$	−1.35119e14	+	7.80107e13i	−0.769117	+	0.444050i	0.0634427	+	0.997985i	$0.479792\pi$
$390$	−3.95917e12	+	1.26792e14i	−0.0222202	+	0.711602i
$391$			1.94657e14i			1.07720i
$392$	−4.90885e13	+	4.22901e13i	−0.267859	+	0.230763i
$393$	−2.62138e14	+	1.40625e14i	−1.41049	+	0.756664i
$394$	9.59243e12	−	1.66146e13i	0.0508979	−	0.0881577i
$395$	1.84015e14	+	3.18724e14i	0.962875	+	1.66775i
$396$	−6.44639e12	+	1.03122e14i	−0.0332654	+	0.532142i
$397$	2.52966e14	+	1.46050e14i	1.28740	+	0.743283i	0.978190	−	0.207710i	$-0.0666010\pi$
$397$	2.52966e14	+	1.46050e14i	1.28740	+	0.743283i	0.309213	+	0.950993i	$0.399934\pi$
$398$	2.29210e14			1.15047
$399$	−1.82963e14	+	1.14599e13i	−0.905757	+	0.0567321i
$400$	4.51702e12			0.0220557
$401$	−1.21400e14	−	7.00902e13i	−0.584688	−	0.337570i	0.178306	−	0.983975i	$-0.442938\pi$
$401$	−1.21400e14	−	7.00902e13i	−0.584688	−	0.337570i	−0.762994	+	0.646405i	$0.776271\pi$
$402$	−1.42912e14	+	2.30597e14i	−0.678933	+	1.09550i
$403$	6.45665e13	+	1.11833e14i	0.302573	+	0.524071i
$404$	8.35444e13	−	1.44703e14i	0.386207	−	0.668929i
$405$	8.88133e13	+	2.10805e14i	0.405019	+	0.961344i
$406$	−4.87702e13	−	6.86960e13i	−0.219413	−	0.309057i
$407$			2.22847e13i			0.0989094i
$408$	−1.37801e14	−	4.30293e12i	−0.603423	−	0.0188423i
$409$	−1.02971e14	+	5.94505e13i	−0.444875	+	0.256849i	−0.705663	−	0.708547i	$-0.749351\pi$
$409$	−1.02971e14	+	5.94505e13i	−0.444875	+	0.256849i	0.260788	+	0.965396i	$0.416017\pi$
$410$	−1.45795e14	+	8.41749e13i	−0.621487	+	0.358816i
$411$	3.75767e14	+	1.17336e13i	1.58048	+	0.0493515i
$412$		−	1.63091e14i		−	0.676855i
$413$	2.75564e14	−	2.59153e13i	1.12849	−	0.106128i
$414$	6.10488e13	−	9.19658e13i	0.246704	−	0.371642i
$415$	−1.45627e14	+	2.52234e14i	−0.580735	+	1.00586i
$416$	2.16777e13	+	3.75469e13i	0.0853100	+	0.147761i
$417$	−2.31490e14	+	3.73522e14i	−0.899050	+	1.45067i
$418$	−1.54615e14	−	8.92670e13i	−0.592628	−	0.342154i
$419$	1.67020e14			0.631819			0.315909	−	0.948789i	$-0.397690\pi$
$419$	1.67020e14			0.631819			0.315909	+	0.948789i	$0.397690\pi$
$420$	−1.16382e14	+	7.72770e13i	−0.434523	+	0.288522i
$421$	2.20273e14			0.811725			0.405862	−	0.913934i	$-0.366971\pi$
$421$	2.20273e14			0.811725			0.405862	+	0.913934i	$0.366971\pi$
$422$	−1.68459e14	−	9.72599e13i	−0.612739	−	0.353765i
$423$	6.55155e13	+	4.09552e12i	0.235219	+	0.0147041i
$424$	−5.35711e13	−	9.27878e13i	−0.189853	−	0.328836i
$425$	2.15313e13	−	3.72932e13i	0.0753234	−	0.130464i
$426$	1.12934e14	−	6.05840e13i	0.390007	−	0.209221i
$427$	−2.09128e14	+	1.48469e14i	−0.712951	+	0.506154i
$428$			2.35842e14i			0.793745i
$429$	9.66773e12	−	3.09608e14i	0.0321225	−	1.02872i
$430$	−8.44228e13	+	4.87415e13i	−0.276938	+	0.159890i
$431$	−4.67591e13	+	2.69964e13i	−0.151440	+	0.0874340i	−0.573805	−	0.818992i	$-0.694533\pi$
$431$	−4.67591e13	+	2.69964e13i	−0.151440	+	0.0874340i	0.422365	+	0.906426i	$0.361200\pi$
$432$	6.37546e13	+	4.52504e13i	0.203869	+	0.144698i
$433$		−	4.11508e14i		−	1.29926i	−0.760252	−	0.649629i	$-0.774924\pi$
$433$		−	4.11508e14i		−	1.29926i	0.760252	−	0.649629i	$-0.225076\pi$
$434$	−5.92616e13	+	1.29275e14i	−0.184748	+	0.403015i
$435$	−8.58699e13	−	1.60070e14i	−0.264332	−	0.492740i
$436$	7.16706e13	−	1.24137e14i	0.217854	−	0.377334i
$437$	9.53674e13	+	1.65181e14i	0.286254	+	0.495807i
$438$	−1.12599e14	−	6.97829e13i	−0.333753	−	0.206843i
$439$	−3.53287e14	−	2.03971e14i	−1.03413	−	0.597053i	−0.115962	−	0.993254i	$-0.536995\pi$
$439$	−3.53287e14	−	2.03971e14i	−1.03413	−	0.597053i	−0.918164	+	0.396201i	$0.870328\pi$
$440$	−1.36053e14			−0.393295
$441$	1.35918e14	−	3.22832e14i	0.388029	−	0.921647i
$442$	4.13324e14			1.16538
$443$	−2.98636e14	−	1.72417e14i	−0.831612	−	0.480132i	0.0227920	−	0.999740i	$-0.492744\pi$
$443$	−2.98636e14	−	1.72417e14i	−0.831612	−	0.480132i	−0.854404	+	0.519609i	$0.826078\pi$
$444$	1.43327e13	+	8.88266e12i	0.0394204	+	0.0244307i
$445$	−1.64861e14	−	2.85547e14i	−0.447855	−	0.775708i
$446$	−1.08219e14	+	1.87441e14i	−0.290378	+	0.502949i
$447$	−6.12709e13	−	1.14215e14i	−0.162391	−	0.302713i
$448$	−1.98966e13	+	4.34031e13i	−0.0520895	+	0.113630i
$449$		−	6.74469e14i		−	1.74424i	−0.489290	−	0.872121i	$-0.662744\pi$
$449$		−	6.74469e14i		−	1.74424i	0.489290	−	0.872121i	$-0.337256\pi$
$450$	−2.18684e13	+	1.08665e13i	−0.0558661	+	0.0277601i
$451$	3.56011e14	−	2.05543e14i	0.898447	−	0.518719i
$452$	2.15251e14	−	1.24275e14i	0.536641	−	0.309830i
$453$	−3.51468e12	+	1.12557e14i	−0.00865657	+	0.277226i
$454$			1.63609e14i			0.398108i
$455$	3.41507e14	−	2.42451e14i	0.820989	−	0.582855i
$456$	−1.19043e14	+	6.38608e13i	−0.282746	+	0.151680i
$457$	4.07332e13	−	7.05520e13i	0.0955894	−	0.165566i	−0.814265	−	0.580493i	$-0.802860\pi$
$457$	4.07332e13	−	7.05520e13i	0.0955894	−	0.165566i	0.909854	+	0.414928i	$0.136193\pi$
$458$	−6.14893e12	−	1.06503e13i	−0.0142574	−	0.0246945i
$459$	6.77494e14	−	3.10674e14i	1.55216	−	0.711762i
$460$	1.25877e14	+	7.26753e13i	0.284957	+	0.164520i
$461$	−7.03207e14			−1.57300			−0.786499	−	0.617591i	$-0.788109\pi$
$461$	−7.03207e14			−1.57300			−0.786499	+	0.617591i	$0.788109\pi$
$462$	2.84187e14	−	1.88699e14i	0.628165	−	0.417100i
$463$	−2.84354e14			−0.621104			−0.310552	−	0.950556i	$-0.600514\pi$
$463$	−2.84354e14			−0.621104			−0.310552	+	0.950556i	$0.600514\pi$
$464$	−5.37650e13	−	3.10412e13i	−0.116051	−	0.0670024i
$465$	−1.61525e14	+	2.60629e14i	−0.344546	+	0.555945i
$466$	−3.61218e13	−	6.25648e13i	−0.0761460	−	0.131889i
$467$	1.05101e14	−	1.82040e14i	0.218959	−	0.379248i	−0.735531	−	0.677491i	$-0.763067\pi$
$467$	1.05101e14	−	1.82040e14i	0.218959	−	0.379248i	0.954490	+	0.298243i	$0.0964006\pi$
$468$	−1.95275e14	−	1.29628e14i	−0.402063	−	0.266898i
$469$	8.91757e14	−	8.38650e13i	1.81466	−	0.170659i
$470$			8.64373e13i			0.173845i
$471$	5.91452e14	+	1.84685e13i	1.17572	+	0.0367127i
$472$	1.76635e14	−	1.01980e14i	0.347052	−	0.200371i
$473$	2.06148e14	−	1.19020e14i	0.400353	−	0.231144i
$474$	−6.79666e14	−	2.12230e13i	−1.30471	−	0.0407405i
$475$		−	4.21948e13i		−	0.0800652i
$476$	2.63502e14	+	3.71159e14i	0.494248	+	0.696180i
$477$	4.82574e14	+	3.20343e14i	0.894772	+	0.593969i
$478$	−9.34512e13	+	1.61862e14i	−0.171290	+	0.296683i
$479$	1.50459e14	+	2.60603e14i	0.272630	+	0.472210i	0.969535	−	0.244955i	$-0.0787731\pi$
$479$	1.50459e14	+	2.60603e14i	0.272630	+	0.472210i	−0.696904	+	0.717164i	$0.745440\pi$
$480$	−5.42306e13	+	8.75042e13i	−0.0971444	+	0.156748i
$481$	−4.37791e13	−	2.52759e13i	−0.0775298	−	0.0447618i
$482$	−5.65449e14			−0.989999
$483$	−3.63730e14	+	2.27822e13i	−0.629607	+	0.0394355i
$484$	4.00628e13			0.0685634
$485$	6.38639e14	+	3.68718e14i	1.08063	+	0.623900i
$486$	−4.17516e14	−	6.56992e13i	−0.698512	−	0.109916i
$487$	−3.26405e14	−	5.65349e14i	−0.539942	−	0.935207i	−0.998907	−	0.0467522i	$-0.985113\pi$
$487$	−3.26405e14	−	5.65349e14i	−0.539942	−	0.935207i	0.458965	−	0.888455i	$-0.348220\pi$
$488$	−9.44975e13	+	1.63674e14i	−0.154565	+	0.267714i
$489$	9.85419e14	−	5.28632e14i	1.59376	−	0.854977i
$490$	4.35434e14	+	1.52102e14i	0.696376	+	0.243252i
$491$			3.92696e14i			0.621024i	0.950569	+	0.310512i	$0.100501\pi$
$491$			3.92696e14i			0.621024i	−0.950569	+	0.310512i	$0.899499\pi$
$492$	9.70813e12	−	3.10902e14i	0.0151819	−	0.486201i
$493$	−5.12563e14	+	2.95928e14i	−0.792664	+	0.457645i
$494$	3.50736e14	−	2.02498e14i	0.536392	−	0.309686i
$495$	6.58679e14	−	3.27300e14i	0.996197	−	0.495014i
$496$			1.04796e14i			0.156745i
$497$	−3.84637e14	−	1.76323e14i	−0.568971	−	0.260825i
$498$	−2.54394e14	−	4.74214e14i	−0.372173	−	0.693766i
$499$	−6.68974e14	+	1.15870e15i	−0.967958	+	1.67655i	−0.266508	+	0.963833i	$0.585870\pi$
$499$	−6.68974e14	+	1.15870e15i	−0.967958	+	1.67655i	−0.701449	+	0.712719i	$0.747463\pi$
$500$	1.66159e14	+	2.87795e14i	0.237787	+	0.411859i
$501$	−2.24870e14	−	1.39363e14i	−0.318291	−	0.197260i
$502$	−5.71219e14	−	3.29793e14i	−0.799709	−	0.461712i
$503$	−7.12689e14			−0.986907			−0.493454	−	0.869772i	$-0.664266\pi$
$503$	−7.12689e14			−0.986907			−0.493454	+	0.869772i	$0.664266\pi$
$504$	−8.08762e12	−	2.57994e14i	−0.0110778	−	0.353380i
$505$	−1.18944e15			−1.61153
$506$	−3.07374e14	−	1.77463e14i	−0.411946	−	0.237837i
$507$	−4.38819e13	−	2.71957e13i	−0.0581757	−	0.0360543i
$508$	1.53385e14	+	2.65670e14i	0.201155	+	0.348411i
$509$	−2.00169e14	+	3.46703e14i	−0.259686	+	0.449790i	−0.966158	−	0.257951i	$-0.916953\pi$
$509$	−2.00169e14	+	3.46703e14i	−0.259686	+	0.449790i	0.706471	+	0.707742i	$0.250286\pi$
$510$	4.63948e14	+	8.64843e14i	0.595433	+	1.10994i
$511$	4.09505e13	+	4.35437e14i	0.0519929	+	0.552854i
$512$			3.51844e13i			0.0441942i
$513$	4.22697e14	−	5.95550e14i	0.525271	−	0.740070i
$514$	3.89996e14	−	2.25164e14i	0.479471	−	0.276823i
$515$	−1.00544e15	+	5.80490e14i	−1.22297	+	0.706081i
$516$	5.62150e12	−	1.80028e14i	0.00676517	−	0.216654i
$517$		−	2.11067e14i		−	0.251318i
$518$	−5.21259e12	−	5.54268e13i	−0.00614101	−	0.0652989i
$519$	7.67271e14	−	4.11605e14i	0.894393	−	0.479800i
$520$	1.54315e14	−	2.67281e14i	0.177987	−	0.308283i
$521$	−1.61485e14	−	2.79701e14i	−0.184300	−	0.319217i	0.759040	−	0.651044i	$-0.225668\pi$
$521$	−1.61485e14	−	2.79701e14i	−0.184300	−	0.319217i	−0.943340	+	0.331827i	$0.892335\pi$
$522$	3.34970e14	+	2.09397e13i	0.378284	+	0.0236474i
$523$	5.48175e14	+	3.16489e14i	0.612576	+	0.353671i	0.773973	−	0.633219i	$-0.218267\pi$
$523$	5.48175e14	+	3.16489e14i	0.612576	+	0.353671i	−0.161397	+	0.986890i	$0.551600\pi$
$524$	7.23743e14			0.800318
$525$	7.22048e13	+	3.58678e13i	0.0790114	+	0.0392491i
$526$	2.89156e14			0.313120
$527$	8.65211e14	+	4.99530e14i	0.927180	+	0.535307i
$528$	1.32423e14	−	2.13673e14i	0.140436	−	0.226601i
$529$	−2.86815e14	−	4.96777e14i	−0.301020	−	0.521382i
$530$	−3.81350e14	+	6.60518e14i	−0.396102	+	0.686069i
$531$	−6.09817e14	+	9.18647e14i	−0.626873	+	0.944341i
$532$	4.05441e14	+	1.85860e14i	0.412490	+	0.189092i
$533$			9.32528e14i			0.938993i
$534$	6.08918e14	+	1.90139e13i	0.606851	+	0.0189493i
$535$	1.45394e15	−	8.39432e14i	1.43417	−	0.828018i
$536$	5.71610e14	−	3.30019e14i	0.558076	−	0.322206i
$537$	−9.21101e12	−	2.87620e11i	−0.00890120	−	0.000277946i
$538$			3.23378e14i			0.309320i
$539$	−1.06327e15	−	3.71411e14i	−1.00671	−	0.351655i
$540$	5.20417e13	−	5.54099e14i	0.0487737	−	0.519304i
$541$	−7.17849e14	+	1.24335e15i	−0.665960	+	1.15348i	0.313064	+	0.949732i	$0.398645\pi$
$541$	−7.17849e14	+	1.24335e15i	−0.665960	+	1.15348i	−0.979024	+	0.203745i	$0.934689\pi$
$542$	−4.78285e14	−	8.28414e14i	−0.439229	−	0.760767i
$543$	−3.44669e14	+	5.56143e14i	−0.313331	+	0.505577i
$544$	2.90488e14	+	1.67713e14i	0.261417	+	0.150929i
$545$	−1.02039e15			−0.909043
$546$	4.83745e13	+	7.72323e14i	0.0426636	+	0.681145i
$547$	−1.93149e15			−1.68641			−0.843204	−	0.537593i	$-0.819334\pi$
$547$	−1.93149e15			−1.68641			−0.843204	+	0.537593i	$0.819334\pi$
$548$	−7.92125e14	−	4.57334e14i	−0.684700	−	0.395312i
$549$	6.37459e13	−	1.01973e15i	0.0545512	−	0.872648i
$550$	3.92587e13	+	6.79981e13i	0.0332615	+	0.0576105i
$551$	−2.89965e14	+	5.02234e14i	−0.243227	+	0.421282i
$552$	−2.36657e14	+	1.26955e14i	−0.196541	+	0.105435i
$553$	1.29965e15	+	1.83064e15i	1.06866	+	1.50527i
$554$		−	1.49677e15i		−	1.21858i
$555$	3.74631e12	−	1.19975e14i	0.00301990	−	0.0967120i
$556$	9.25895e14	−	5.34566e14i	0.739010	−	0.426668i
$557$	−1.70727e15	+	9.85692e14i	−1.34927	+	0.779001i	−0.988146	−	0.153517i	$-0.950940\pi$
$557$	−1.70727e15	+	9.85692e14i	−1.34927	+	0.779001i	−0.361123	+	0.932518i	$0.617607\pi$
$558$	−2.52105e14	−	5.07352e14i	−0.197285	−	0.397028i
$559$			5.39981e14i			0.418421i
$560$	3.38393e14	−	3.18240e13i	0.259649	−	0.0244186i
$561$	−1.13289e15	−	2.11182e15i	−0.860783	−	1.60458i
$562$	4.33445e13	−	7.50749e13i	0.0326125	−	0.0564865i
$563$	−1.65664e14	−	2.86939e14i	−0.123433	−	0.213793i	0.797686	−	0.603073i	$-0.206057\pi$
$563$	−1.65664e14	−	2.86939e14i	−0.123433	−	0.213793i	−0.921119	+	0.389280i	$0.872724\pi$
$564$	−1.35751e14	−	8.41313e13i	−0.100163	−	0.0620758i
$565$	−1.53228e15	−	8.84664e14i	−1.11963	−	0.646416i
$566$	−5.28836e14			−0.382675
$567$	6.59806e14	+	1.22958e15i	0.472835	+	0.881151i
$568$	−3.11803e14			−0.221291
$569$	1.21968e15	+	7.04183e14i	0.857292	+	0.494958i	0.863105	−	0.505025i	$-0.168517\pi$
$569$	1.21968e15	+	7.04183e14i	0.857292	+	0.494958i	−0.00581253	+	0.999983i	$0.501850\pi$
$570$	8.17402e14	+	5.06584e14i	0.569015	+	0.352647i
$571$	−9.47106e13	−	1.64044e14i	−0.0652980	−	0.113100i	0.831528	−	0.555483i	$-0.187466\pi$
$571$	−9.47106e13	−	1.64044e14i	−0.0652980	−	0.113100i	−0.896826	+	0.442383i	$0.854133\pi$
$572$	−3.76814e14	+	6.52662e14i	−0.257306	+	0.445667i
$573$	7.90771e14	+	1.47407e15i	0.534811	+	0.996939i
$574$	−8.37397e14	+	5.94504e14i	−0.560939	+	0.398235i
$575$		−	8.38832e13i		−	0.0556547i
$576$	−8.46424e13	−	1.70340e14i	−0.0556243	−	0.111942i
$577$	−1.45574e15	+	8.40472e14i	−0.947582	+	0.547087i	−0.892329	−	0.451386i	$-0.850930\pi$
$577$	−1.45574e15	+	8.40472e14i	−0.947582	+	0.547087i	−0.0552528	+	0.998472i	$0.517596\pi$
$578$	1.81956e15	−	1.05053e15i	1.17318	−	0.677335i
$579$	1.52418e13	−	4.88119e14i	0.00973431	−	0.311741i
$580$			4.41940e14i			0.279582i
$581$	−7.40386e14	+	1.61510e15i	−0.463970	+	1.01212i
$582$	−1.20068e15	+	6.44107e14i	−0.745332	+	0.399836i
$583$	9.31203e14	−	1.61289e15i	0.572621	−	0.991809i
$584$	1.61145e14	+	2.79112e14i	0.0981629	+	0.170023i
$585$	−1.04097e14	+	1.66523e15i	−0.0628177	+	1.00489i
$586$	1.15861e15	+	6.68922e14i	0.692626	+	0.399888i
$587$	1.06585e15			0.631229			0.315615	−	0.948887i	$-0.397789\pi$
$587$	1.06585e15			0.631229			0.315615	+	0.948887i	$0.397789\pi$
$588$	−6.62696e14	+	5.35810e14i	−0.388811	+	0.314366i
$589$	9.78928e14			0.569006
$590$	−1.25739e15	−	7.25955e14i	−0.724076	−	0.418045i
$591$	1.32926e14	−	2.14483e14i	0.0758365	−	0.122367i
$592$	−2.05122e13	−	3.55282e13i	−0.0115943	−	0.0200818i
$593$	1.38859e15	−	2.40511e15i	0.777632	−	1.34690i	−0.155672	−	0.987809i	$-0.549754\pi$
$593$	1.38859e15	−	2.40511e15i	0.777632	−	1.34690i	0.933303	−	0.359089i	$-0.116912\pi$
$594$	−1.27078e14	+	1.35303e15i	−0.0705093	+	0.750728i
$595$	1.35027e15	−	2.94552e15i	0.742297	−	1.61927i
$596$			3.15338e14i			0.171760i
$597$	3.01327e15	+	9.40915e13i	1.62622	+	0.0507799i
$598$	6.97264e14	−	4.02565e14i	0.372855	−	0.215268i
$599$	2.01744e15	−	1.16477e15i	1.06894	−	0.617154i	0.141049	−	0.990003i	$-0.454952\pi$
$599$	2.01744e15	−	1.16477e15i	1.06894	−	0.617154i	0.927892	+	0.372849i	$0.121619\pi$
$600$	5.93823e13	+	1.85425e12i	0.0311763	+	0.000973502i
$601$			1.25190e15i			0.651271i	0.945495	+	0.325635i	$0.105578\pi$
$601$			1.25190e15i			0.651271i	−0.945495	+	0.325635i	$0.894422\pi$
$602$	−4.84895e14	+	3.44248e14i	−0.249958	+	0.177456i
$603$	−1.97344e15	+	2.97285e15i	−1.00804	+	1.51854i
$604$	1.36990e14	−	2.37274e14i	0.0693403	−	0.120101i
$605$	−1.42595e14	−	2.46983e14i	−0.0715239	−	0.123883i
$606$	1.15770e15	−	1.86802e15i	0.575438	−	0.928502i
$607$	−1.89754e15	−	1.09554e15i	−0.934656	−	0.539624i	−0.0463752	−	0.998924i	$-0.514767\pi$
$607$	−1.89754e15	−	1.09554e15i	−0.934656	−	0.539624i	−0.888281	+	0.459300i	$0.848100\pi$
$608$	3.28667e14			0.160431
$609$	−6.12951e14	−	9.23123e14i	−0.296504	−	0.446544i
$610$	1.34538e15			0.644956
$611$	4.14649e14	+	2.39398e14i	0.196995	+	0.113735i
$612$	−1.80982e15	−	1.13136e14i	−0.852121	−	0.0532681i
$613$	3.26696e13	+	5.65854e13i	0.0152444	+	0.0264041i	0.873547	−	0.486740i	$-0.161814\pi$
$613$	3.26696e13	+	5.65854e13i	0.0152444	+	0.0264041i	−0.858303	+	0.513144i	$0.828481\pi$
$614$	−8.08513e14	+	1.40039e15i	−0.373905	+	0.647622i
$615$	−1.95123e15	+	1.04674e15i	−0.894325	+	0.479763i
$616$	−8.26307e14	+	7.77097e13i	−0.375359	+	0.0353006i
$617$			7.42401e14i			0.334249i	0.985936	+	0.167124i	$0.0534482\pi$
$617$			7.42401e14i			0.334249i	−0.985936	+	0.167124i	$0.946552\pi$
$618$	6.69495e13	−	2.14405e15i	0.0298752	−	0.956751i
$619$	1.63738e15	−	9.45344e14i	0.724189	−	0.418111i	−0.0921037	−	0.995749i	$-0.529359\pi$
$619$	1.63738e15	−	9.45344e14i	0.724189	−	0.418111i	0.816292	+	0.577639i	$0.196026\pi$
$620$	6.46054e14	−	3.72999e14i	0.283214	−	0.163514i
$621$	8.40322e14	−	1.18395e15i	0.365125	−	0.514436i
$622$		−	8.90687e14i		−	0.383599i
$623$	−1.16437e15	−	1.64009e15i	−0.497056	−	0.700136i
$624$	2.69570e14	+	5.02503e14i	0.114066	+	0.212630i
$625$	1.28798e15	−	2.23085e15i	0.540220	−	0.935688i
$626$	1.11936e15	+	1.93878e15i	0.465382	+	0.806065i
$627$	−1.99598e15	−	1.23701e15i	−0.822592	−	0.509800i
$628$	−1.24679e15	−	7.19837e14i	−0.509351	−	0.294074i
$629$	−3.91102e14			−0.158384
$630$	−1.56172e15	+	9.68136e14i	−0.626944	+	0.388654i
$631$	−2.89883e15			−1.15362			−0.576808	−	0.816880i	$-0.695702\pi$
$631$	−2.89883e15			−1.15362			−0.576808	+	0.816880i	$0.695702\pi$
$632$	1.43275e15	+	8.27199e14i	0.565232	+	0.326337i
$633$	−2.17470e15	−	1.34777e15i	−0.850508	−	0.527101i
$634$	4.81998e14	+	8.34845e14i	0.186876	+	0.323679i
$635$	1.09188e15	−	1.89119e15i	0.419682	−	0.726910i
$636$	−6.66174e14	−	1.24181e15i	−0.253848	−	0.473197i
$637$	1.93564e15	−	1.66756e15i	0.731235	−	0.629963i
$638$		−	1.07915e15i		−	0.404175i
$639$	1.50954e15	−	7.50098e14i	0.560520	−	0.278524i
$640$	2.16907e14	−	1.25232e14i	0.0798518	−	0.0461024i
$641$	3.86372e15	−	2.23072e15i	1.41022	−	0.814191i	0.414811	−	0.909907i	$-0.363848\pi$
$641$	3.86372e15	−	2.23072e15i	1.41022	−	0.814191i	0.995409	+	0.0957166i	$0.0305143\pi$
$642$	−9.68141e13	+	3.10047e15i	−0.0350345	+	1.12198i
$643$			1.67564e15i			0.601204i	0.953750	+	0.300602i	$0.0971875\pi$
$643$			1.67564e15i			0.601204i	−0.953750	+	0.300602i	$0.902812\pi$
$644$	8.06016e14	+	3.69490e14i	0.286729	+	0.131441i
$645$	−1.12986e15	+	6.06117e14i	−0.398516	+	0.213785i
$646$	1.56666e15	−	2.71353e15i	0.547892	−	0.948978i
$647$	1.14322e15	+	1.98012e15i	0.396422	+	0.686623i	0.993282	−	0.115722i	$-0.0369183\pi$
$647$	1.14322e15	+	1.98012e15i	0.396422	+	0.686623i	−0.596859	+	0.802346i	$0.703585\pi$
$648$	8.19565e14	+	6.21049e14i	0.281787	+	0.213532i
$649$	3.07037e15	+	1.77268e15i	1.04675	+	0.604344i
$650$	−1.78113e14			−0.0602104
$651$	−8.32142e14	+	1.67517e15i	−0.278934	+	0.561517i
$652$	−2.72067e15			−0.904302
$653$	3.14312e15	+	1.81468e15i	1.03595	+	0.598105i	0.918683	−	0.394995i	$-0.129254\pi$
$653$	3.14312e15	+	1.81468e15i	1.03595	+	0.598105i	0.117266	+	0.993101i	$0.462587\pi$
$654$	9.93166e14	−	1.60253e15i	0.324597	−	0.523755i
$655$	−2.57602e15	−	4.46179e15i	−0.834875	−	1.44605i
$656$	−3.78389e14	+	6.55389e14i	−0.121609	+	0.210634i
$657$	−1.45162e15	−	9.63612e14i	−0.462639	−	0.307109i
$658$	4.93706e13	+	5.24970e14i	0.0156036	+	0.165917i
$659$		−	1.07821e15i		−	0.337936i	−0.985622	−	0.168968i	$-0.945957\pi$
$659$		−	1.07821e15i		−	0.337936i	0.985622	−	0.168968i	$-0.0540435\pi$
$660$	−1.78860e15	−	5.58502e13i	−0.555932	−	0.0173593i
$661$	−1.33173e15	+	7.68876e14i	−0.410496	+	0.237000i	−0.691003	−	0.722852i	$-0.742831\pi$
$661$	−1.33173e15	+	7.68876e14i	−0.410496	+	0.237000i	0.280507	+	0.959852i	$0.409497\pi$
$662$	4.10027e14	−	2.36729e14i	0.125341	−	0.0723657i
$663$	5.43371e15	+	1.69671e14i	1.64730	+	0.0514379i
$664$			1.30927e15i			0.393644i
$665$	−2.97277e14	−	3.16102e15i	−0.0886427	−	0.942560i
$666$	1.84776e14	+	1.22658e14i	0.0546434	+	0.0362734i
$667$	−5.76451e14	+	9.98442e14i	−0.169071	+	0.292840i
$668$	3.21823e14	+	5.57414e14i	0.0936152	+	0.162146i
$669$	−1.49964e15	+	2.41975e15i	−0.432655	+	0.698114i
$670$	−4.06906e15	−	2.34927e15i	−1.16435	−	0.672236i
$671$	−3.28522e15			−0.932375
$672$	−2.79385e14	+	5.62424e14i	−0.0786452	+	0.158319i
$673$	−1.05399e15			−0.294274			−0.147137	−	0.989116i	$-0.547006\pi$
$673$	−1.05399e15			−0.294274			−0.147137	+	0.989116i	$0.547006\pi$
$674$	−1.94499e15	−	1.12294e15i	−0.538626	−	0.310976i
$675$	−2.91951e14	+	1.33878e14i	−0.0801934	+	0.0367738i
$676$	6.28015e13	+	1.08775e14i	0.0171105	+	0.0296363i
$677$	1.88894e15	−	3.27174e15i	0.510482	−	0.884181i	−0.489444	−	0.872035i	$-0.662800\pi$
$677$	1.88894e15	−	3.27174e15i	0.510482	−	0.884181i	0.999926	−	0.0121460i	$-0.00386630\pi$
$678$	2.88078e15	−	1.54540e15i	0.772230	−	0.414266i
$679$	4.08932e15	+	1.87461e15i	1.08735	+	0.498456i
$680$		−	2.38776e15i		−	0.629785i
$681$	−6.71622e13	+	2.15086e15i	−0.0175718	+	0.562735i
$682$	−1.57757e15	+	9.10811e14i	−0.409425	+	0.236382i
$683$	3.05947e15	−	1.76639e15i	0.787650	−	0.454750i	−0.0514849	−	0.998674i	$-0.516395\pi$
$683$	3.05947e15	−	1.76639e15i	0.787650	−	0.454750i	0.839134	+	0.543924i	$0.183062\pi$
$684$	−1.59119e15	+	7.90669e14i	−0.406363	+	0.201923i
$685$			6.51114e15i			1.64952i
$686$	2.73145e15	+	6.75071e14i	0.686453	+	0.169655i
$687$	−7.64640e13	−	1.42536e14i	−0.0190632	−	0.0355355i
$688$	−2.19106e14	+	3.79503e14i	−0.0541899	+	0.0938597i
$689$	2.11239e15	+	3.65876e15i	0.518284	+	0.897695i
$690$	1.62499e15	+	1.00709e15i	0.395532	+	0.245131i
$691$	2.04672e14	+	1.18168e14i	0.0494231	+	0.0285344i	0.524508	−	0.851406i	$-0.324249\pi$
$691$	2.04672e14	+	1.18168e14i	0.0494231	+	0.0285344i	−0.475085	+	0.879940i	$0.657583\pi$
$692$	−2.11838e15			−0.507481
$693$	3.81349e15	−	2.36405e15i	0.906337	−	0.561855i
$694$	−3.44256e15			−0.811716
$695$	−6.59107e15	−	3.80536e15i	−1.54184	−	0.890182i
$696$	−6.94071e14	−	4.30150e14i	−0.161084	−	0.0998318i
$697$	3.60733e15	+	6.24808e15i	0.830627	+	1.43869i
$698$	−2.34535e15	+	4.06226e15i	−0.535799	+	0.928031i
$699$	−4.49187e14	−	8.37327e14i	−0.101813	−	0.189789i
$700$	−1.13550e14	−	1.59943e14i	−0.0255357	−	0.0359687i
$701$		−	2.03187e15i		−	0.453364i	−0.973969	−	0.226682i	$-0.927212\pi$
$701$		−	2.03187e15i		−	0.453364i	0.973969	−	0.226682i	$-0.0727878\pi$
$702$	−2.51394e15	−	1.78429e15i	−0.556546	−	0.395013i
$703$	−3.31879e14	+	1.91610e14i	−0.0728997	+	0.0420886i
$704$	−5.29657e14	+	3.05798e14i	−0.115437	+	0.0666476i
$705$	−3.54828e13	+	1.13633e15i	−0.00767322	+	0.245735i
$706$			2.54411e15i			0.545896i
$707$	−7.22394e15	+	6.79373e14i	−1.53804	+	0.144644i
$708$	2.36397e15	−	1.26816e15i	0.499411	−	0.267911i
$709$	1.50926e15	−	2.61411e15i	0.316380	−	0.547986i	−0.663350	−	0.748309i	$-0.730866\pi$
$709$	1.50926e15	−	2.61411e15i	0.316380	−	0.547986i	0.979730	+	0.200323i	$0.0641992\pi$
$710$	1.10980e15	+	1.92223e15i	0.230846	+	0.399838i
$711$	−8.92641e15	−	5.58010e14i	−1.84244	−	0.115175i
$712$	−1.28361e15	−	7.41095e14i	−0.262902	−	0.151787i
$713$	1.94611e15			0.395526
$714$	3.31172e15	+	4.98756e15i	0.667904	+	1.00588i
$715$	5.36478e15			1.07366
$716$	1.94170e13	+	1.12104e13i	0.00385621	+	0.00222639i
$717$	−1.29499e15	+	2.08954e15i	−0.255217	+	0.411808i
$718$	−1.13062e14	−	1.95830e14i	−0.0221123	−	0.0382996i
$719$	−4.83647e14	+	8.37700e14i	−0.0938683	+	0.162585i	−0.909136	−	0.416500i	$-0.863257\pi$
$719$	−4.83647e14	+	8.37700e14i	−0.0938683	+	0.162585i	0.815267	+	0.579085i	$0.196590\pi$
$720$	−7.48856e14	+	1.12810e15i	−0.144235	+	0.217279i
$721$	−5.77488e15	+	4.09983e15i	−1.10382	+	0.783650i
$722$			6.57511e14i			0.124724i
$723$	−7.43359e15	−	2.32119e14i	−1.39939	−	0.0436968i
$724$	1.37858e15	−	7.95924e14i	0.257555	−	0.148699i
$725$	2.20878e14	−	1.27524e14i	0.0409536	−	0.0236446i
$726$	5.26680e14	+	1.64459e13i	0.0969160	+	0.00302627i
$727$		−	4.83786e15i		−	0.883516i	−0.897134	−	0.441758i	$-0.854355\pi$
$727$		−	4.83786e15i		−	0.883516i	0.897134	−	0.441758i	$-0.145645\pi$
$728$	7.84554e14	−	1.71145e15i	0.142200	−	0.310200i
$729$	−5.46184e15	−	1.03510e15i	−0.982512	−	0.186200i
$730$	1.14713e15	−	1.98688e15i	0.204803	−	0.354729i
$731$	2.08883e15	+	3.61795e15i	0.370132	+	0.641088i
$732$	−1.30949e15	+	2.11293e15i	−0.230298	+	0.371599i
$733$	5.13379e15	+	2.96400e15i	0.896120	+	0.517375i	0.875939	−	0.482421i	$-0.160242\pi$
$733$	5.13379e15	+	2.96400e15i	0.896120	+	0.517375i	0.0201809	+	0.999796i	$0.493576\pi$
$734$	−3.00951e13			−0.00521395
$735$	5.66193e15	+	2.17833e15i	0.973608	+	0.374580i
$736$	6.53391e14			0.111518
$737$	9.93606e15	+	5.73659e15i	1.68323	+	0.971812i
$738$	2.55253e14	−	4.08325e15i	0.0429201	−	0.686587i
$739$	5.39988e14	+	9.35287e14i	0.0901239	+	0.156099i	0.907563	−	0.419916i	$-0.137940\pi$
$739$	5.39988e14	+	9.35287e14i	0.0901239	+	0.156099i	−0.817439	+	0.576015i	$0.804607\pi$
$740$	−1.46018e14	+	2.52911e14i	−0.0241898	+	0.0418979i
$741$	4.69403e15	−	2.51813e15i	0.771873	−	0.414074i
$742$	−1.93883e15	+	4.22942e15i	−0.316460	+	0.690334i
$743$		−	3.02442e15i		−	0.490008i	−0.969522	−	0.245004i	$-0.921211\pi$
$743$		−	3.02442e15i		−	0.490008i	0.969522	−	0.245004i	$-0.0787893\pi$
$744$	−4.30191e13	+	1.37768e15i	−0.00691847	+	0.221563i
$745$	1.94402e15	−	1.12238e15i	0.310343	−	0.179177i
$746$	5.78414e14	−	3.33947e14i	0.0916590	−	0.0529193i
$747$	−3.14968e15	−	6.33861e15i	−0.495454	−	0.997082i
$748$			5.83058e15i			0.910443i
$749$	8.35092e15	−	5.92867e15i	1.29445	−	0.918983i
$750$	2.06624e15	+	3.85166e15i	0.317939	+	0.592668i
$751$	−5.44854e15	+	9.43715e15i	−0.832263	+	1.44152i	0.0639768	+	0.997951i	$0.479622\pi$
$751$	−5.44854e15	+	9.43715e15i	−0.832263	+	1.44152i	−0.896240	+	0.443570i	$0.853712\pi$
$752$	1.94280e14	+	3.36502e14i	0.0294597	+	0.0510258i
$753$	−7.37406e15	−	4.57007e15i	−1.11003	−	0.687939i
$754$	2.12004e15	+	1.22400e15i	0.316811	+	0.182911i
$755$	−1.95035e15			−0.289337
$756$	−4.15246e11	−	3.39500e15i	−6.11555e−5	−	0.500000i
$757$	1.01384e15			0.148233			0.0741163	−	0.997250i	$-0.476386\pi$
$757$	1.01384e15			0.148233			0.0741163	+	0.997250i	$0.476386\pi$
$758$	−7.97619e15	−	4.60506e15i	−1.15775	−	0.668428i
$759$	−3.96800e15	−	2.45917e15i	−0.571798	−	0.354371i
$760$	−1.16982e15	−	2.02620e15i	−0.167358	−	0.289872i
$761$	−4.36398e15	+	7.55864e15i	−0.619823	+	1.07356i	0.369695	+	0.929153i	$0.379462\pi$
$761$	−4.36398e15	+	7.55864e15i	−0.619823	+	1.07356i	−0.989518	+	0.144411i	$0.953871\pi$
$762$	1.90739e15	+	3.55555e15i	0.268960	+	0.501366i
$763$	−6.19724e15	+	5.82817e14i	−0.867588	+	0.0815920i
$764$		−	4.06980e15i		−	0.565666i
$765$	5.74420e15	+	1.15600e16i	0.792669	+	1.59521i
$766$	−5.16192e15	+	2.98023e15i	−0.707217	+	0.408312i
$767$	−6.96497e15	+	4.02123e15i	−0.947425	+	0.546996i
$768$	−1.44433e13	+	4.62546e14i	−0.00195065	+	0.0624696i
$769$		−	9.54187e15i		−	1.27950i	−0.768585	−	0.639748i	$-0.779039\pi$
$769$		−	9.54187e15i		−	1.27950i	0.768585	−	0.639748i	$-0.220961\pi$
$770$	3.42014e15	+	4.81749e15i	0.455350	+	0.641389i
$771$	5.21945e15	−	2.79999e15i	0.689963	−	0.370133i
$772$	−5.94074e14	+	1.02897e15i	−0.0779732	+	0.135053i
$773$	−4.43476e15	−	7.68123e15i	−0.577940	−	1.00102i	−0.995715	−	0.0924714i	$-0.970523\pi$
$773$	−4.43476e15	−	7.68123e15i	−0.577940	−	1.00102i	0.417775	−	0.908550i	$-0.362810\pi$
$774$	1.47804e14	−	2.36441e15i	0.0191255	−	0.305947i
$775$	−3.72843e14	−	2.15261e14i	−0.0479035	−	0.0276571i
$776$	3.31498e15			0.422903
$777$	−4.57737e13	−	7.30800e14i	−0.00579829	−	0.0925727i
$778$	4.99269e15			0.627981
$779$	6.12218e15	+	3.53464e15i	0.764628	+	0.441458i
$780$	2.13840e15	−	3.45042e15i	0.265196	−	0.427909i
$781$	−2.70997e15	−	4.69380e15i	−0.333721	−	0.578022i
$782$	3.11452e15	−	5.39450e15i	0.380849	−	0.659651i
$783$	4.39504e15	+	4.12788e14i	0.533670	+	0.0501230i
$784$	2.03702e15	−	3.86561e14i	0.245617	−	0.0466101i
$785$			1.02485e16i			1.22709i
$786$	9.51459e15	+	2.97099e14i	1.13127	+	0.0353246i
$787$	7.27530e15	−	4.20040e15i	0.858994	−	0.495940i	−0.00468155	−	0.999989i	$-0.501490\pi$
$787$	7.27530e15	−	4.20040e15i	0.858994	−	0.495940i	0.863675	+	0.504049i	$0.168157\pi$
$788$	−5.31667e14	+	3.06958e14i	−0.0623369	+	0.0359902i
$789$	3.80135e15	+	1.18700e14i	0.442603	+	0.0138206i
$790$		−	1.17770e16i		−	1.36171i
$791$	−9.81149e15	−	4.49774e15i	−1.12659	−	0.516444i
$792$	1.82860e15	−	2.75466e15i	0.208511	−	0.314108i
$793$	3.72618e15	−	6.45393e15i	0.421950	−	0.730839i
$794$	−4.67360e15	−	8.09492e15i	−0.525580	−	0.910332i
$795$	−5.28451e15	+	8.52686e15i	−0.590182	+	0.952292i
$796$	−6.35205e15	−	3.66736e15i	−0.704518	−	0.406754i
$797$	−1.21429e16			−1.33753			−0.668765	−	0.743474i	$-0.733177\pi$
$797$	−1.21429e16			−1.33753			−0.668765	+	0.743474i	$0.733177\pi$
$798$	5.25377e15	+	2.60982e15i	0.574718	+	0.285492i
$799$	3.70429e15			0.402436
$800$	−1.25179e14	−	7.22723e13i	−0.0135063	−	0.00779788i
$801$	7.99725e15	+	4.99926e14i	0.856962	+	0.0535707i
$802$	2.24289e15	+	3.88479e15i	0.238698	+	0.413437i
$803$	−2.80112e15	+	4.85169e15i	−0.296072	+	0.512811i
$804$	7.65006e15	−	4.10390e15i	0.803076	−	0.430813i
$805$	−5.90987e14	−	6.28411e15i	−0.0616171	−	0.655189i
$806$		−	4.13226e15i		−	0.427902i
$807$	−1.32748e14	+	4.25124e15i	−0.0136528	+	0.437232i
$808$	−4.63050e15	+	2.67342e15i	−0.473005	+	0.273089i
$809$	2.02797e15	−	1.17085e15i	0.205753	−	0.118791i	−0.393583	−	0.919289i	$-0.628765\pi$
$809$	2.02797e15	−	1.17085e15i	0.205753	−	0.118791i	0.599336	+	0.800498i	$0.295431\pi$
$810$	9.11618e14	−	7.26302e15i	0.0918640	−	0.731897i
$811$		−	1.62586e16i		−	1.62730i	−0.581354	−	0.813651i	$-0.697477\pi$
$811$		−	1.62586e16i		−	1.62730i	0.581354	−	0.813651i	$-0.302523\pi$
$812$	2.52424e14	+	2.68408e15i	0.0250941	+	0.266832i
$813$	−5.94764e15	−	1.10870e16i	−0.587282	−	1.09475i
$814$	3.56555e14	−	6.17572e14i	0.0349697	−	0.0605694i
$815$	9.68366e15	+	1.67726e16i	0.943349	+	1.63393i
$816$	3.75001e15	+	2.32406e15i	0.362858	+	0.224881i
$817$	3.54505e15	+	2.04674e15i	0.340723	+	0.196716i
$818$	3.80483e15			0.363239
$819$	3.18907e14	+	1.01731e16i	0.0302415	+	0.964699i
$820$	5.38719e15			0.507442
$821$	−1.19155e16	−	6.87943e15i	−1.11487	−	0.643673i	−0.174786	−	0.984606i	$-0.555924\pi$
$821$	−1.19155e16	−	6.87943e15i	−1.11487	−	0.643673i	−0.940087	+	0.340934i	$0.889257\pi$
$822$	−1.02258e16	−	6.33744e15i	−0.950392	−	0.589005i
$823$	−5.09723e15	−	8.82866e15i	−0.470582	−	0.815072i	0.528852	−	0.848714i	$-0.322623\pi$
$823$	−5.09723e15	−	8.82866e15i	−0.470582	−	0.815072i	−0.999434	+	0.0336422i	$0.989289\pi$
$824$	−2.60946e15	+	4.51971e15i	−0.239304	+	0.414487i
$825$	4.88195e14	+	9.10043e14i	0.0444731	+	0.0829020i
$826$	−8.05130e15	−	3.69084e15i	−0.728578	−	0.333991i
$827$			1.48725e16i			1.33692i	0.743750	+	0.668458i	$0.233045\pi$
$827$			1.48725e16i			1.33692i	−0.743750	+	0.668458i	$0.766955\pi$
$828$	−3.16329e15	+	1.57185e15i	−0.282470	+	0.140360i
$829$	3.23519e15	−	1.86784e15i	0.286979	−	0.165687i	−0.349600	−	0.936899i	$-0.613682\pi$
$829$	3.23519e15	−	1.86784e15i	0.286979	−	0.165687i	0.636579	+	0.771212i	$0.280349\pi$
$830$	8.07148e15	−	4.66007e15i	0.711252	−	0.410642i
$831$	6.14431e14	−	1.96771e16i	0.0537858	−	1.72249i
$832$		−	1.38737e15i		−	0.120647i
$833$	6.51836e15	−	1.86606e16i	0.563107	−	1.61205i
$834$	1.23916e16	−	6.64751e15i	1.06344	−	0.570487i
$835$	2.29093e15	−	3.96800e15i	0.195315	−	0.338295i
$836$	2.85654e15	+	4.94768e15i	0.241939	+	0.419051i
$837$	−3.10600e15	−	6.77332e15i	−0.261343	−	0.569917i
$838$	−4.62861e15	−	2.67233e15i	−0.386908	−	0.223382i
$839$	−1.12128e16			−0.931160			−0.465580	−	0.885006i	$-0.654154\pi$
$839$	−1.12128e16			−0.931160			−0.465580	+	0.885006i	$0.654154\pi$
$840$	4.46169e15	−	2.79459e14i	0.368098	−	0.0230559i
$841$	8.69510e15			0.712684
$842$	−6.10437e15	−	3.52436e15i	−0.497078	−	0.286988i
$843$	6.00641e14	−	9.69168e14i	0.0485918	−	0.0784056i
$844$	3.11232e15	+	5.39069e15i	0.250150	+	0.433272i
$845$	4.47058e14	−	7.74328e14i	0.0356987	−	0.0618319i
$846$	−1.75009e15	−	1.16175e15i	−0.138843	−	0.0921668i
$847$	−1.00711e15	−	1.41858e15i	−0.0793814	−	0.111814i
$848$			3.42855e15i			0.268493i
$849$	−6.95226e15	−	2.17089e14i	−0.540921	−	0.0168906i
$850$	−1.19338e15	+	6.89000e14i	−0.0922520	+	0.0532617i
$851$	−6.59775e14	+	3.80922e14i	−0.0506738	+	0.0292565i
$852$	−4.09907e15	−	1.27996e14i	−0.312801	−	0.00976740i
$853$			1.88328e16i			1.42789i	0.700200	+	0.713947i	$0.253094\pi$
$853$			1.88328e16i			1.42789i	−0.700200	+	0.713947i	$0.746906\pi$
$854$	8.17104e15	−	7.68443e14i	0.615544	−	0.0578886i
$855$	1.05379e16	+	6.99528e15i	0.788752	+	0.523590i
$856$	3.77348e15	−	6.53585e15i	0.280631	−	0.486067i
$857$	7.73970e15	+	1.34056e16i	0.571912	+	0.990581i	0.996370	+	0.0851333i	$0.0271316\pi$
$857$	7.73970e15	+	1.34056e16i	0.571912	+	0.990581i	−0.424457	+	0.905448i	$0.639535\pi$
$858$	−5.22166e15	+	8.42544e15i	−0.383379	+	0.618604i
$859$	−4.14877e15	−	2.39529e15i	−0.302661	−	0.174742i	0.340977	−	0.940072i	$-0.389242\pi$
$859$	−4.14877e15	−	2.39529e15i	−0.302661	−	0.174742i	−0.643638	+	0.765330i	$0.722576\pi$
$860$	3.11946e15			0.226119
$861$	−1.12528e16	+	7.47180e15i	−0.810479	+	0.538156i
$862$	1.72777e15			0.123650
$863$	−8.87024e15	−	5.12124e15i	−0.630777	−	0.364179i	0.150276	−	0.988644i	$-0.451984\pi$
$863$	−8.87024e15	−	5.12124e15i	−0.630777	−	0.364179i	−0.781053	+	0.624465i	$0.785317\pi$
$864$	−1.04281e15	−	2.27409e15i	−0.0736854	−	0.160687i
$865$	7.53992e15	+	1.30595e16i	0.529393	+	0.916936i
$866$	−6.58413e15	+	1.14041e16i	−0.459357	+	0.795629i
$867$	2.43519e16	−	1.30637e16i	1.68821	−	0.905648i
$868$	3.71071e15	−	2.63439e15i	0.255622	−	0.181477i
$869$			2.87577e16i			1.96855i
$870$	−1.81418e14	+	5.80990e15i	−0.0123403	+	0.395196i
$871$	−2.25395e16	+	1.30132e16i	−1.52350	+	0.879595i
$872$	−3.97239e15	+	2.29346e15i	−0.266816	+	0.154046i
$873$	−1.60489e16	+	7.97478e15i	−1.07119	+	0.532280i
$874$		−	6.10351e15i		−	0.404825i
$875$	6.01357e15	−	1.31182e16i	0.396358	−	0.864627i
$876$	2.00390e15	+	3.73546e15i	0.131251	+	0.244665i
$877$	−1.41766e16	+	2.45546e16i	−0.922731	+	1.59822i	−0.127561	+	0.991831i	$0.540715\pi$
$877$	−1.41766e16	+	2.45546e16i	−0.922731	+	1.59822i	−0.795170	+	0.606387i	$0.792618\pi$
$878$	6.52706e15	+	1.13052e16i	0.422180	+	0.731237i
$879$	1.49569e16	+	9.26949e15i	0.961394	+	0.595823i
$880$	3.77041e15	+	2.17685e15i	0.240843	+	0.139051i
$881$	−1.57904e16			−1.00236			−0.501181	−	0.865342i	$-0.667101\pi$
$881$	−1.57904e16			−1.00236			−0.501181	+	0.865342i	$0.667101\pi$
$882$	−8.93198e15	+	6.77190e15i	−0.563470	+	0.427202i
$883$	4.78096e15			0.299730			0.149865	−	0.988706i	$-0.452116\pi$
$883$	4.78096e15			0.299730			0.149865	+	0.988706i	$0.452116\pi$
$884$	−1.14544e16	−	6.61319e15i	−0.713648	−	0.412025i
$885$	−1.62321e16	−	1.00598e16i	−1.00505	−	0.622877i
$886$	5.51735e15	+	9.55634e15i	0.339504	+	0.588039i
$887$	2.50326e15	−	4.33577e15i	0.153083	−	0.265147i	−0.779277	−	0.626680i	$-0.784413\pi$
$887$	2.50326e15	−	4.33577e15i	0.153083	−	0.265147i	0.932359	+	0.361533i	$0.117747\pi$
$888$	−2.55076e14	−	4.75486e14i	−0.0155024	−	0.0288979i
$889$	5.55126e15	−	1.21097e16i	0.335298	−	0.731430i
$890$			1.05511e16i			0.633363i
$891$	−2.22604e15	+	1.77353e16i	−0.132802	+	1.05806i
$892$	5.99812e15	−	3.46302e15i	0.355639	−	0.205328i
$893$	3.14336e15	−	1.81482e15i	0.185230	−	0.106943i
$894$	−1.29448e14	+	4.14555e15i	−0.00758119	+	0.242787i
$895$		−	1.59605e14i		−	0.00929008i
$896$	1.24584e15	−	8.84475e14i	0.0720723	−	0.0511672i
$897$	9.33173e15	−	5.00604e15i	0.536542	−	0.287830i
$898$	−1.07915e16	+	1.86914e16i	−0.616683	+	1.06813i
$899$	2.95858e15	+	5.12441e15i	0.168037	+	0.291049i
$900$	7.79900e14	+	4.87533e13i	0.0440256	+	0.00275214i
$901$	2.83066e16	+	1.63429e16i	1.58819	+	0.916941i
$902$	−1.31548e16			−0.733579
$903$	−6.51592e15	+	4.32655e15i	−0.361154	+	0.239805i
$904$	−7.95361e15			−0.438165
$905$	−9.81355e15	−	5.66586e15i	−0.537352	−	0.310240i
$906$	1.89832e15	−	3.06305e15i	0.103315	−	0.166705i
$907$	4.27257e15	+	7.40031e15i	0.231126	+	0.400322i	0.958140	−	0.286301i	$-0.0924256\pi$
$907$	4.27257e15	+	7.40031e15i	0.231126	+	0.400322i	−0.727014	+	0.686623i	$0.759092\pi$
$908$	2.61775e15	−	4.53407e15i	0.140752	−	0.243790i
$909$	1.59864e16	−	2.40824e16i	0.854378	−	1.28706i
$910$	−1.33433e16	+	1.25487e15i	−0.708821	+	0.0666609i
$911$		−	2.59382e16i		−	1.36958i	−0.728738	−	0.684792i	$-0.759893\pi$
$911$		−	2.59382e16i		−	1.36958i	0.728738	−	0.684792i	$-0.240107\pi$
$912$	4.32078e15	+	1.34919e14i	0.226772	+	0.00708112i
$913$	−1.97094e16	+	1.13792e16i	−1.02822	+	0.593641i
$914$	−2.25767e15	+	1.30346e15i	−0.117073	+	0.0675919i
$915$	1.76868e16	+	5.52282e14i	0.911661	+	0.0284672i
$916$			3.93531e14i			0.0201630i
$917$	−1.81937e16	−	2.56270e16i	−0.926593	−	1.30517i
$918$	−2.37460e16	−	2.23026e15i	−1.20214	−	0.112907i
$919$	1.57041e16	−	2.72003e16i	0.790273	−	1.36879i	−0.135525	−	0.990774i	$-0.543272\pi$
$919$	1.57041e16	−	2.72003e16i	0.790273	−	1.36879i	0.925798	−	0.378019i	$-0.123394\pi$
$920$	−2.32561e15	−	4.02807e15i	−0.116333	−	0.201495i
$921$	−1.12039e16	+	1.80781e16i	−0.557109	+	0.898926i
$922$	1.94879e16	+	1.12513e16i	0.963261	+	0.556139i
$923$	1.22949e16			0.604107
$924$	−1.08948e16	+	6.82398e14i	−0.532138	+	0.0333305i
$925$	1.68537e14			0.00818304
$926$	7.88025e15	+	4.54967e15i	0.380347	+	0.219593i
$927$	1.76028e15	−	2.81590e16i	0.0844586	−	1.35107i
$928$	9.93320e14	+	1.72048e15i	0.0473778	+	0.0820608i
$929$	−7.76290e15	+	1.34457e16i	−0.368076	+	0.637526i	−0.989265	−	0.146135i	$-0.953317\pi$
$929$	−7.76290e15	+	1.34457e16i	−0.368076	+	0.637526i	0.621189	+	0.783661i	$0.286650\pi$
$930$	8.64637e15	−	4.63837e15i	0.407547	−	0.218630i
$931$	−3.61098e15	−	1.90284e16i	−0.169201	−	0.891620i
$932$			2.31180e15i			0.107687i
$933$	3.65630e14	−	1.17093e16i	0.0169314	−	0.542227i
$934$	−5.82527e15	+	3.36322e15i	−0.268169	+	0.154827i
$935$	3.59448e16	−	2.07528e16i	1.64502	−	0.949755i
$936$	3.33758e15	+	6.71675e15i	0.151850	+	0.305592i
$937$			1.12774e16i			0.510085i	0.966930	+	0.255043i	$0.0820895\pi$
$937$			1.12774e16i			0.510085i	−0.966930	+	0.255043i	$0.917910\pi$
$938$	−2.60549e16	−	1.19440e16i	−1.17159	−	0.537073i
$939$	1.39196e16	+	2.59474e16i	0.622250	+	1.15993i
$940$	1.38300e15	−	2.39542e15i	0.0614636	−	0.106458i
$941$	−9.51339e15	−	1.64777e16i	−0.420332	−	0.728037i	0.575640	−	0.817703i	$-0.304753\pi$
$941$	−9.51339e15	−	1.64777e16i	−0.420332	−	0.728037i	−0.995972	+	0.0896668i	$0.971420\pi$
$942$	−1.60953e16	−	9.97505e15i	−0.707000	−	0.438162i
$943$	1.21709e16	+	7.02687e15i	0.531506	+	0.306865i
$944$	−6.52673e15			−0.283367
$945$	−2.09283e16	+	1.20864e16i	−0.903356	+	0.521700i
$946$	−7.61727e15			−0.326887
$947$	−9.10221e14	−	5.25516e14i	−0.0388349	−	0.0224213i	0.480457	−	0.877018i	$-0.340471\pi$
$947$	−9.10221e14	−	5.25516e14i	−0.0388349	−	0.0224213i	−0.519292	+	0.854597i	$0.673804\pi$
$948$	1.84959e16	+	1.14628e16i	0.784565	+	0.486233i
$949$	−6.35421e15	−	1.10058e16i	−0.267977	−	0.464150i
$950$	−6.75116e14	+	1.16934e15i	−0.0283073	+	0.0490297i
$951$	5.99381e15	+	1.11730e16i	0.249868	+	0.465777i
$952$	−1.36383e15	−	1.45019e16i	−0.0565269	−	0.601065i
$953$		−	3.68656e15i		−	0.151919i	−0.997111	−	0.0759593i	$-0.975798\pi$
$953$		−	3.68656e15i		−	0.151919i	0.997111	−	0.0759593i	$-0.0242019\pi$
$954$	−8.24800e15	−	1.65988e16i	−0.337934	−	0.680080i
$955$	−2.50898e16	+	1.44856e16i	−1.02207	+	0.590091i
$956$	5.17959e15	−	2.99044e15i	0.209786	−	0.121120i
$957$	4.42996e14	−	1.41869e16i	0.0178396	−	0.571311i
$958$		−	9.62941e15i		−	0.385558i
$959$	3.71898e15	+	3.95449e16i	0.148055	+	1.57430i
$960$	2.90295e15	−	1.55730e15i	0.114907	−	0.0616424i
$961$	−7.71013e15	+	1.33543e16i	−0.303447	+	0.525586i
$962$	8.08827e14	+	1.40093e15i	0.0316514	+	0.0548218i
$963$	−2.54550e15	+	4.07201e16i	−0.0990442	+	1.58440i
$964$	1.56702e16	+	9.04718e15i	0.606248	+	0.350018i
$965$	8.45793e15			0.325360
$966$	1.04445e16	+	5.18832e15i	0.399497	+	0.198451i
$967$	−6.06449e15			−0.230647			−0.115324	−	0.993328i	$-0.536791\pi$
$967$	−6.06449e15			−0.230647			−0.115324	+	0.993328i	$0.536791\pi$
$968$	−1.11025e15	−	6.41005e14i	−0.0419863	−	0.0242408i
$969$	2.17098e16	−	3.50299e16i	0.816346	−	1.31722i
$970$	−1.17990e16	−	2.04364e16i	−0.441164	−	0.764118i
$971$	1.66405e16	−	2.88222e16i	0.618672	−	1.07157i	−0.371056	−	0.928611i	$-0.621004\pi$
$971$	1.66405e16	−	2.88222e16i	0.618672	−	1.07157i	0.989728	−	0.142962i	$-0.0456625\pi$
$972$	1.05194e16	+	8.50097e15i	0.388888	+	0.314271i
$973$	−4.22038e16	−	1.93469e16i	−1.55143	−	0.711197i
$974$			2.08899e16i			0.763593i
$975$	−2.34153e15	−	7.31159e13i	−0.0851089	−	0.00265758i
$976$	5.23758e15	−	3.02392e15i	0.189303	−	0.109294i
$977$	2.62296e16	−	1.51437e16i	0.942695	−	0.544265i	0.0518907	−	0.998653i	$-0.483475\pi$
$977$	2.62296e16	−	1.51437e16i	0.942695	−	0.544265i	0.890804	+	0.454388i	$0.150142\pi$
$978$	−3.57668e16	−	1.11684e15i	−1.27825	−	0.0399143i
$979$		−	2.57643e16i		−	0.915616i
$980$	−9.63347e15	−	1.11821e16i	−0.340439	−	0.395167i
$981$	1.37144e16	−	2.06597e16i	0.481943	−	0.726014i
$982$	6.28314e15	−	1.08827e16i	0.219565	−	0.380298i
$983$	2.38556e15	+	4.13191e15i	0.0828984	+	0.143584i	0.904494	−	0.426487i	$-0.140249\pi$
$983$	2.38556e15	+	4.13191e15i	0.0828984	+	0.143584i	−0.821595	+	0.570071i	$0.806916\pi$
$984$	−5.24348e15	+	8.46065e15i	−0.181195	+	0.292368i
$985$	3.78472e15	+	2.18511e15i	0.130057	+	0.0750885i
$986$	1.89394e16			0.647207
$987$	4.33541e14	+	6.92170e15i	0.0147328	+	0.235217i
$988$	−1.29599e16			−0.437962
$989$	7.04756e15	+	4.06891e15i	0.236842	+	0.136741i
$990$	−2.34907e16	−	1.46845e15i	−0.785058	−	0.0490757i
$991$	9.57648e15	+	1.65869e16i	0.318274	+	0.551266i	0.980128	−	0.198366i	$-0.0635636\pi$
$991$	9.57648e15	+	1.65869e16i	0.318274	+	0.551266i	−0.661854	+	0.749633i	$0.730230\pi$
$992$	1.67673e15	−	2.90419e15i	0.0554179	−	0.0959866i
$993$	5.48754e15	−	2.94381e15i	0.180367	−	0.0967584i
$994$	7.83819e15	+	1.10406e16i	0.256207	+	0.360884i
$995$			5.22128e16i			1.69727i
$996$	−5.37459e14	+	1.72121e16i	−0.0173748	+	0.556426i
$997$	4.13372e15	−	2.38660e15i	0.132898	−	0.0767286i	−0.432077	−	0.901837i	$-0.642219\pi$
$997$	4.13372e15	−	2.38660e15i	0.132898	−	0.0767286i	0.564975	+	0.825108i	$0.308886\pi$
$998$	3.70783e16	−	2.14072e16i	1.18550	−	0.684449i
$999$	2.37878e15	+	1.68836e15i	0.0756387	+	0.0536852i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.12.f.a.5.2	✓	60
3.2	odd	2	inner	42.12.f.a.5.23	yes	60
7.3	odd	6	inner	42.12.f.a.17.23	yes	60
21.17	even	6	inner	42.12.f.a.17.2	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.12.f.a.5.2	✓	60	1.1	even	1	trivial
42.12.f.a.5.23	yes	60	3.2	odd	2	inner
42.12.f.a.17.2	yes	60	21.17	even	6	inner
42.12.f.a.17.23	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} +(-357.754 - 221.718i) q^{3} +(512.000 + 886.810i) q^{4} +(3644.72 - 6312.84i) q^{5} +(6366.89 + 11868.5i) q^{6} +(18530.2 - 40422.3i) q^{7} -32768.0i q^{8} +(78829.4 + 158641. i) q^{9} +(-202011. + 116631. i) q^{10} +(493282. - 284796. i) q^{11} +(13451.4 - 430780. i) q^{12} +1.29209e6i q^{13} +(-1.16028e6 + 823732. i) q^{14} +(-2.70358e6 + 1.45035e6i) q^{15} +(-524288. + 908093. i) q^{16} +(4.99824e6 + 8.65721e6i) q^{17} +(353673. - 5.65766e6i) q^{18} +(8.48276e6 + 4.89753e6i) q^{19} +7.46438e6 q^{20} +(-1.55916e7 + 1.03528e7i) q^{21} -1.82270e7 q^{22} +(1.68637e7 + 9.73628e6i) q^{23} +(-7.26525e6 + 1.17229e7i) q^{24} +(-2.15388e6 - 3.73063e6i) q^{25} +(2.06735e7 - 3.58075e7i) q^{26} +(6.97200e6 - 7.42324e7i) q^{27} +(4.53343e7 - 4.26345e6i) q^{28} +5.92065e7i q^{29} +(9.81294e7 + 3.06416e6i) q^{30} +(8.65515e7 - 4.99705e7i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(-2.39618e8 - 7.48223e6i) q^{33} -3.19888e8i q^{34} +(-1.87642e8 - 2.64306e8i) q^{35} +(-1.00324e8 + 1.51131e8i) q^{36} +(-1.95620e7 + 3.38823e7i) q^{37} +(-1.56721e8 - 2.71448e8i) q^{38} +(2.86480e8 - 4.62251e8i) q^{39} +(-2.06859e8 - 1.19430e8i) q^{40} +7.21720e8 q^{41} +(5.97731e8 - 3.74389e7i) q^{42} +4.17912e8 q^{43} +(5.05120e8 + 2.91631e8i) q^{44} +(1.28879e9 + 8.05650e7i) q^{45} +(-3.11561e8 - 5.39639e8i) q^{46} +(1.85279e8 - 3.20913e8i) q^{47} +(3.88907e8 - 2.08630e8i) q^{48} +(-1.29059e9 - 1.49806e9i) q^{49} +1.37848e8i q^{50} +(1.31315e8 - 4.20536e9i) q^{51} +(-1.14584e9 + 6.61551e8i) q^{52} +(2.83166e9 - 1.63486e9i) q^{53} +(-1.38093e9 + 1.94564e9i) q^{54} -4.15201e9i q^{55} +(-1.32456e9 - 6.07197e8i) q^{56} +(-1.94888e9 - 3.63289e9i) q^{57} +(9.47303e8 - 1.64078e9i) q^{58} +(3.11219e9 + 5.39046e9i) q^{59} +(-2.67042e9 - 1.65499e9i) q^{60} +(-4.99495e9 - 2.88383e9i) q^{61} -3.19812e9 q^{62} +(7.87335e9 - 2.46815e8i) q^{63} -1.07374e9 q^{64} +(8.15677e9 + 4.70931e9i) q^{65} +(6.52077e9 + 4.04124e9i) q^{66} +(1.00714e10 + 1.74442e10i) q^{67} +(-5.11820e9 + 8.86499e9i) q^{68} +(-3.87437e9 - 7.22219e9i) q^{69} +(9.71192e8 + 1.03269e10i) q^{70} -9.51546e9i q^{71} +(5.19835e9 - 2.58308e9i) q^{72} +(-8.51783e9 + 4.91777e9i) q^{73} +(1.08423e9 - 6.25983e8i) q^{74} +(-5.65873e7 + 1.81220e9i) q^{75} +1.00301e10i q^{76} +(-2.37151e9 - 2.52169e10i) q^{77} +(-1.53352e10 + 8.22661e9i) q^{78} +(-2.52441e10 + 4.37241e10i) q^{79} +(3.82176e9 + 6.61949e9i) q^{80} +(-1.89529e10 + 2.50112e10i) q^{81} +(-2.00009e10 - 1.15475e10i) q^{82} -3.99557e10 q^{83} +(-1.71638e10 - 8.52616e9i) q^{84} +7.28688e10 q^{85} +(-1.15815e10 - 6.68659e9i) q^{86} +(1.31271e10 - 2.11814e10i) q^{87} +(-9.33220e9 - 1.61638e10i) q^{88} +(2.26164e10 - 3.91728e10i) q^{89} +(-3.44269e10 - 2.28533e10i) q^{90} +(5.22293e10 + 2.39427e10i) q^{91} +1.99399e10i q^{92} +(-4.20436e10 - 1.31284e9i) q^{93} +(-1.02692e10 + 5.92894e9i) q^{94} +(6.18346e10 - 3.57002e10i) q^{95} +(-1.41158e10 - 4.40775e8i) q^{96} +1.01165e11i q^{97} +(1.17969e10 + 6.21650e10i) q^{98} +(8.40655e10 + 5.58044e10i) 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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