LMFDB - Embedded newform 42.12.f.a.5.24

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			5.24
Character	$\chi$	$=$	42.5
Dual form			42.12.f.a.17.24

$q$-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} +(110.742 + 406.058i) q^{3} +(512.000 + 886.810i) q^{4} +(3221.21 - 5579.29i) q^{5} +(-3427.95 + 13024.9i) q^{6} +(25344.2 + 36537.6i) q^{7} +32768.0i q^{8} +(-152619. + 89935.6i) q^{9} +(178537. - 103079. i) q^{10} +(-104738. + 60470.5i) q^{11} +(-303396. + 306109. i) q^{12} -50908.1i q^{13} +(117756. + 1.41807e6i) q^{14} +(2.62224e6 + 690133. i) q^{15} +(-524288. + 908093. i) q^{16} +(4.53557e6 + 7.85584e6i) q^{17} +(-5.66848e6 + 50458.2i) q^{18} +(8.06088e6 + 4.65395e6i) q^{19} +6.59703e6 q^{20} +(-1.20297e7 + 1.43375e7i) q^{21} -3.87011e6 q^{22} +(-2.27133e7 - 1.31135e7i) q^{23} +(-1.33057e7 + 3.62880e6i) q^{24} +(3.66173e6 + 6.34231e6i) q^{25} +(814529. - 1.41081e6i) q^{26} +(-5.34205e7 - 5.20126e7i) q^{27} +(-1.94257e7 + 4.11827e7i) q^{28} -6.87194e6i q^{29} +(6.16275e7 + 6.10814e7i) q^{30} +(-2.29050e8 + 1.32242e8i) q^{31} +(-2.90590e7 + 1.67772e7i) q^{32} +(-3.61534e7 - 3.58330e7i) q^{33} +2.90277e8i q^{34} +(2.85493e8 - 2.37072e7i) q^{35} +(-1.57897e8 - 8.92973e7i) q^{36} +(1.04519e8 - 1.81032e8i) q^{37} +(1.48927e8 + 2.57948e8i) q^{38} +(2.06716e7 - 5.63767e6i) q^{39} +(1.82822e8 + 1.05552e8i) q^{40} -1.44633e8 q^{41} +(-5.62777e8 + 2.04856e8i) q^{42} -1.24766e9 q^{43} +(-1.07252e8 - 6.19217e7i) q^{44} +(1.01585e7 + 1.14121e9i) q^{45} +(-4.19632e8 - 7.26824e8i) q^{46} +(-7.02288e7 + 1.21640e8i) q^{47} +(-4.26800e8 - 1.12327e8i) q^{48} +(-6.92673e8 + 1.85203e9i) q^{49} +2.34351e8i q^{50} +(-2.68765e9 + 2.71168e9i) q^{51} +(4.51458e7 - 2.60649e7i) q^{52} +(4.50048e9 - 2.59835e9i) q^{53} +(-6.48229e8 - 2.29614e9i) q^{54} +7.79151e8i q^{55} +(-1.19727e9 + 8.30478e8i) q^{56} +(-9.97095e8 + 3.78858e9i) q^{57} +(1.09951e8 - 1.90441e8i) q^{58} +(2.19074e9 + 3.79447e9i) q^{59} +(7.30570e8 + 2.67878e9i) q^{60} +(-2.62835e9 - 1.51748e9i) q^{61} -8.46349e9 q^{62} +(-7.15404e9 - 3.29701e9i) q^{63} -1.07374e9 q^{64} +(-2.84031e8 - 1.63985e8i) q^{65} +(-4.28585e8 - 1.57149e9i) q^{66} +(4.30716e9 + 7.46022e9i) q^{67} +(-4.64443e9 + 8.04439e9i) q^{68} +(2.80953e9 - 1.06751e10i) q^{69} +(8.29113e9 + 3.91089e9i) q^{70} +1.02508e10i q^{71} +(-2.94701e9 - 5.00103e9i) q^{72} +(2.57319e10 - 1.48563e10i) q^{73} +(5.79304e9 - 3.34461e9i) q^{74} +(-2.16984e9 + 2.18924e9i) q^{75} +9.53130e9i q^{76} +(-4.86394e9 - 2.29430e9i) q^{77} +(6.63072e8 + 1.74510e8i) q^{78} +(1.06233e10 - 1.84001e10i) q^{79} +(3.37768e9 + 5.85031e9i) q^{80} +(1.52043e10 - 2.74518e10i) q^{81} +(-4.00818e9 - 2.31412e9i) q^{82} +3.90065e10 q^{83} +(-1.88738e10 - 3.32731e9i) q^{84} +5.84401e10 q^{85} +(-3.45761e10 - 1.99625e10i) q^{86} +(2.79041e9 - 7.61014e8i) q^{87} +(-1.98150e9 - 3.43205e9i) q^{88} +(4.37364e10 - 7.57537e10i) q^{89} +(-1.79778e10 + 3.17886e10i) q^{90} +(1.86006e9 - 1.29022e9i) q^{91} -2.68565e10i q^{92} +(-7.90635e10 - 7.83628e10i) q^{93} +(-3.89247e9 + 2.24732e9i) q^{94} +(5.19315e10 - 2.99827e10i) q^{95} +(-1.00306e10 - 9.94169e9i) q^{96} -9.26196e10i q^{97} +(-4.88284e10 + 4.02423e10i) q^{98} +(1.05466e10 - 1.86486e10i) 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
$3$	110.742	+	406.058i	0.263115	+	0.964764i
$3$	110.742	+	406.058i	0.263115	+	0.964764i
$4$	512.000	+	886.810i	0.250000	+	0.433013i
$5$	3221.21	−	5579.29i	0.460981	−	0.798443i	−0.538029	−	0.842926i	$-0.680831\pi$
$5$	3221.21	−	5579.29i	0.460981	−	0.798443i	0.999010	+	0.0444833i	$0.0141641\pi$
$6$	−3427.95	+	13024.9i	−0.179971	+	0.683820i
$7$	25344.2	+	36537.6i	0.569953	+	0.821677i
$7$	25344.2	+	36537.6i	0.569953	+	0.821677i
$8$			32768.0i			0.353553i
$9$	−152619.	+	89935.6i	−0.861540	+	0.507689i
$10$	178537.	−	103079.i	0.564585	−	0.325963i
$11$	−104738.	+	60470.5i	−0.196085	+	0.113210i	−0.594828	−	0.803853i	$-0.702780\pi$
$11$	−104738.	+	60470.5i	−0.196085	+	0.113210i	0.398743	+	0.917063i	$0.369447\pi$
$12$	−303396.	+	306109.i	−0.351976	+	0.355123i
$13$		−	50908.1i		−	0.0380275i	−0.999819	−	0.0190138i	$-0.993947\pi$
$13$		−	50908.1i		−	0.0380275i	0.999819	−	0.0190138i	$-0.00605264\pi$
$14$	117756.	+	1.41807e6i	0.0585165	+	0.704681i
$15$	2.62224e6	+	690133.i	0.891601	+	0.234656i
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	4.53557e6	+	7.85584e6i	0.774753	+	1.34191i	0.934933	+	0.354824i	$0.115459\pi$
$17$	4.53557e6	+	7.85584e6i	0.774753	+	1.34191i	−0.160180	+	0.987088i	$0.551208\pi$
$18$	−5.66848e6	+	50458.2i	−0.707079	+	0.00629409i
$19$	8.06088e6	+	4.65395e6i	0.746858	+	0.431198i	0.824557	−	0.565778i	$-0.191424\pi$
$19$	8.06088e6	+	4.65395e6i	0.746858	+	0.431198i	−0.0776997	+	0.996977i	$0.524758\pi$
$20$	6.59703e6			0.460981
$21$	−1.20297e7	+	1.43375e7i	−0.642762	+	0.766066i
$22$	−3.87011e6			−0.160103
$23$	−2.27133e7	−	1.31135e7i	−0.735828	−	0.424831i	0.0847223	−	0.996405i	$-0.473000\pi$
$23$	−2.27133e7	−	1.31135e7i	−0.735828	−	0.424831i	−0.820551	+	0.571574i	$0.806333\pi$
$24$	−1.33057e7	+	3.62880e6i	−0.341096	+	0.0930254i
$25$	3.66173e6	+	6.34231e6i	0.0749923	+	0.129890i
$26$	814529.	−	1.41081e6i	0.0134448	−	0.0232870i
$27$	−5.34205e7	−	5.20126e7i	−0.716485	−	0.697603i
$28$	−1.94257e7	+	4.11827e7i	−0.213309	+	0.452216i
$29$		−	6.87194e6i		−	0.0622143i	−0.999516	−	0.0311071i	$-0.990097\pi$
$29$		−	6.87194e6i		−	0.0622143i	0.999516	−	0.0311071i	$-0.00990331\pi$
$30$	6.16275e7	+	6.10814e7i	0.463028	+	0.458925i
$31$	−2.29050e8	+	1.32242e8i	−1.43695	+	0.829622i	−0.997636	−	0.0687127i	$-0.978111\pi$
$31$	−2.29050e8	+	1.32242e8i	−1.43695	+	0.829622i	−0.439311	+	0.898335i	$0.644777\pi$
$32$	−2.90590e7	+	1.67772e7i	−0.153093	+	0.0883883i
$33$	−3.61534e7	−	3.58330e7i	−0.160814	−	0.159388i
$34$			2.90277e8i			1.09567i
$35$	2.85493e8	−	2.37072e7i	0.918800	−	0.0762968i
$36$	−1.57897e8	−	8.92973e7i	−0.435221	−	0.246136i
$37$	1.04519e8	−	1.81032e8i	0.247791	−	0.429187i	−0.715121	−	0.699000i	$-0.753629\pi$
$37$	1.04519e8	−	1.81032e8i	0.247791	−	0.429187i	0.962913	+	0.269813i	$0.0869619\pi$
$38$	1.48927e8	+	2.57948e8i	0.304903	+	0.528108i
$39$	2.06716e7	−	5.63767e6i	0.0366876	−	0.0100056i
$40$	1.82822e8	+	1.05552e8i	0.282292	+	0.162982i
$41$	−1.44633e8			−0.194965			−0.0974823	−	0.995237i	$-0.531079\pi$
$41$	−1.44633e8			−0.194965			−0.0974823	+	0.995237i	$0.531079\pi$
$42$	−5.62777e8	+	2.04856e8i	−0.664455	+	0.241867i
$43$	−1.24766e9			−1.29425			−0.647126	−	0.762383i	$-0.724029\pi$
$43$	−1.24766e9			−1.29425			−0.647126	+	0.762383i	$0.724029\pi$
$44$	−1.07252e8	−	6.19217e7i	−0.0980424	−	0.0566048i
$45$	1.01585e7	+	1.14121e9i	0.00820657	+	0.921926i
$46$	−4.19632e8	−	7.26824e8i	−0.300401	−	0.520309i
$47$	−7.02288e7	+	1.21640e8i	−0.0446660	+	0.0773637i	−0.887494	−	0.460819i	$-0.847556\pi$
$47$	−7.02288e7	+	1.21640e8i	−0.0446660	+	0.0773637i	0.842828	+	0.538183i	$0.180889\pi$
$48$	−4.26800e8	−	1.12327e8i	−0.241767	−	0.0636294i
$49$	−6.92673e8	+	1.85203e9i	−0.350308	+	0.936635i
$50$			2.34351e8i			0.106055i
$51$	−2.68765e9	+	2.71168e9i	−1.09078	+	1.10053i
$52$	4.51458e7	−	2.60649e7i	0.0164664	−	0.00950689i
$53$	4.50048e9	−	2.59835e9i	1.47823	−	0.853455i	0.478531	−	0.878071i	$-0.341169\pi$
$53$	4.50048e9	−	2.59835e9i	1.47823	−	0.853455i	0.999697	+	0.0246152i	$0.00783605\pi$
$54$	−6.48229e8	−	2.29614e9i	−0.192116	−	0.680508i
$55$			7.79151e8i			0.208750i
$56$	−1.19727e9	+	8.30478e8i	−0.290507	+	0.201509i
$57$	−9.97095e8	+	3.78858e9i	−0.219495	+	0.833997i
$58$	1.09951e8	−	1.90441e8i	0.0219961	−	0.0380983i
$59$	2.19074e9	+	3.79447e9i	0.398937	+	0.690978i	0.993595	−	0.113000i	$-0.0360460\pi$
$59$	2.19074e9	+	3.79447e9i	0.398937	+	0.690978i	−0.594658	+	0.803978i	$0.702713\pi$
$60$	7.30570e8	+	2.67878e9i	0.121291	+	0.444738i
$61$	−2.62835e9	−	1.51748e9i	−0.398446	−	0.230043i	0.287367	−	0.957821i	$-0.407220\pi$
$61$	−2.62835e9	−	1.51748e9i	−0.398446	−	0.230043i	−0.685813	+	0.727777i	$0.740553\pi$
$62$	−8.46349e9			−1.17326
$63$	−7.15404e9	−	3.29701e9i	−0.908194	−	0.418550i
$64$	−1.07374e9			−0.125000
$65$	−2.84031e8	−	1.63985e8i	−0.0303628	−	0.0175300i
$66$	−4.28585e8	−	1.57149e9i	−0.0421255	−	0.154461i
$67$	4.30716e9	+	7.46022e9i	0.389744	+	0.675056i	0.992415	−	0.122933i	$-0.0392302\pi$
$67$	4.30716e9	+	7.46022e9i	0.389744	+	0.675056i	−0.602671	+	0.797990i	$0.705897\pi$
$68$	−4.64443e9	+	8.04439e9i	−0.387376	+	0.670956i
$69$	2.80953e9	−	1.06751e10i	0.216254	−	0.821680i
$70$	8.29113e9	+	3.91089e9i	0.589623	+	0.278123i
$71$			1.02508e10i			0.674274i	0.941456	+	0.337137i	$0.109459\pi$
$71$			1.02508e10i			0.674274i	−0.941456	+	0.337137i	$0.890541\pi$
$72$	−2.94701e9	−	5.00103e9i	−0.179495	−	0.304601i
$73$	2.57319e10	−	1.48563e10i	1.45276	−	0.838754i	0.454127	−	0.890937i	$-0.349951\pi$
$73$	2.57319e10	−	1.48563e10i	1.45276	−	0.838754i	0.998638	+	0.0521826i	$0.0166178\pi$
$74$	5.79304e9	−	3.34461e9i	0.303481	−	0.175215i
$75$	−2.16984e9	+	2.18924e9i	−0.105582	+	0.106526i
$76$			9.53130e9i			0.431198i
$77$	−4.86394e9	−	2.29430e9i	−0.204781	−	0.0965944i
$78$	6.63072e8	+	1.74510e8i	0.0260040	+	0.00684386i
$79$	1.06233e10	−	1.84001e10i	0.388427	−	0.672776i	−0.603811	−	0.797128i	$-0.706352\pi$
$79$	1.06233e10	−	1.84001e10i	0.388427	−	0.672776i	0.992238	+	0.124352i	$0.0396852\pi$
$80$	3.37768e9	+	5.85031e9i	0.115245	+	0.199611i
$81$	1.52043e10	−	2.74518e10i	0.484504	−	0.874789i
$82$	−4.00818e9	−	2.31412e9i	−0.119391	−	0.0689304i
$83$	3.90065e10			1.08695			0.543473	−	0.839427i	$-0.317109\pi$
$83$	3.90065e10			1.08695			0.543473	+	0.839427i	$0.317109\pi$
$84$	−1.88738e10	−	3.32731e9i	−0.492407	−	0.0868075i
$85$	5.84401e10			1.42859
$86$	−3.45761e10	−	1.99625e10i	−0.792564	−	0.457587i
$87$	2.79041e9	−	7.61014e8i	0.0600221	−	0.0163695i
$88$	−1.98150e9	−	3.43205e9i	−0.0400257	−	0.0693265i
$89$	4.37364e10	−	7.57537e10i	0.830229	−	1.43800i	−0.0676269	−	0.997711i	$-0.521543\pi$
$89$	4.37364e10	−	7.57537e10i	0.830229	−	1.43800i	0.897856	−	0.440289i	$-0.145124\pi$
$90$	−1.79778e10	+	3.17886e10i	−0.320925	+	0.567464i
$91$	1.86006e9	−	1.29022e9i	0.0312464	−	0.0216739i
$92$		−	2.68565e10i		−	0.424831i
$93$	−7.90635e10	−	7.83628e10i	−1.17847	−	1.16803i
$94$	−3.89247e9	+	2.24732e9i	−0.0547044	+	0.0315836i
$95$	5.19315e10	−	2.99827e10i	0.688575	−	0.397549i
$96$	−1.00306e10	−	9.94169e9i	−0.125555	−	0.124442i
$97$		−	9.26196e10i		−	1.09511i	−0.836769	−	0.547556i	$-0.815558\pi$
$97$		−	9.26196e10i		−	1.09511i	0.836769	−	0.547556i	$-0.184442\pi$
$98$	−4.88284e10	+	4.02423e10i	−0.545669	+	0.449717i
$99$	1.05466e10	−	1.86486e10i	0.111460	−	0.197085i
$100$	−3.74962e9	+	6.49452e9i	−0.0374962	+	0.0649452i
$101$	6.35841e10	+	1.10131e11i	0.601978	+	1.04266i	0.992521	+	0.122072i	$0.0389540\pi$
$101$	6.35841e10	+	1.10131e11i	0.601978	+	1.04266i	−0.390543	+	0.920585i	$0.627713\pi$
$102$	−1.17869e11	+	3.21459e10i	−1.05706	+	0.288287i
$103$	−9.96928e10	−	5.75577e10i	−0.847343	−	0.489214i	0.0124105	−	0.999923i	$-0.496050\pi$
$103$	−9.96928e10	−	5.75577e10i	−0.847343	−	0.489214i	−0.859753	+	0.510709i	$0.829383\pi$
$104$	1.66816e9			0.0134448
$105$	4.12426e10	+	1.13301e11i	0.315359	+	0.866351i
$106$	1.66295e11			1.20697
$107$	1.62755e11	+	9.39667e10i	1.12182	+	0.647684i	0.941865	−	0.335991i	$-0.109071\pi$
$107$	1.62755e11	+	9.39667e10i	1.12182	+	0.647684i	0.179956	+	0.983675i	$0.442404\pi$
$108$	1.87741e10	−	7.40043e10i	0.122950	−	0.484648i
$109$	3.16943e10	+	5.48961e10i	0.197303	+	0.341740i	0.947653	−	0.319301i	$-0.103448\pi$
$109$	3.16943e10	+	5.48961e10i	0.197303	+	0.341740i	−0.750350	+	0.661041i	$0.770115\pi$
$110$	−1.24664e10	+	2.15925e10i	−0.0738043	+	0.127833i
$111$	8.50844e10	+	2.23929e10i	0.479262	+	0.126135i
$112$	−4.64672e10	+	3.85862e9i	−0.249142	+	0.0206887i
$113$			1.53892e11i			0.785752i	0.919591	+	0.392876i	$0.128520\pi$
$113$			1.53892e11i			0.785752i	−0.919591	+	0.392876i	$0.871480\pi$
$114$	−8.82495e10	+	8.90386e10i	−0.429275	+	0.433113i
$115$	−1.46328e11	+	8.44826e10i	−0.678406	+	0.391678i
$116$	6.09410e9	−	3.51843e9i	0.0269396	−	0.0155536i
$117$	4.57845e9	+	7.76956e9i	0.0193062	+	0.0327623i
$118$			1.40207e11i			0.564182i
$119$	−1.72084e11	+	3.64819e11i	−0.661046	+	1.40142i
$120$	−2.26143e10	+	8.59256e10i	−0.0829633	+	0.315229i
$121$	−1.35342e11	+	2.34420e11i	−0.474367	+	0.821628i
$122$	−4.85594e10	−	8.41073e10i	−0.162665	−	0.281744i
$123$	−1.60170e10	−	5.87293e10i	−0.0512982	−	0.188095i
$124$	−2.34547e11	−	1.35416e11i	−0.718474	−	0.414811i
$125$	3.61752e11			1.06024
$126$	−1.45507e11	−	2.05834e11i	−0.408173	−	0.577403i
$127$	−5.94681e11			−1.59722			−0.798608	−	0.601851i	$-0.794430\pi$
$127$	−5.94681e11			−1.59722			−0.798608	+	0.601851i	$0.794430\pi$
$128$	−2.97564e10	−	1.71799e10i	−0.0765466	−	0.0441942i
$129$	−1.38168e11	−	5.06621e11i	−0.340538	−	1.24865i
$130$	−5.24753e9	−	9.08899e9i	−0.0123956	−	0.0214698i
$131$	2.19837e11	−	3.80768e11i	0.497861	−	0.862321i	−0.502136	−	0.864789i	$-0.667452\pi$
$131$	2.19837e11	−	3.80768e11i	0.497861	−	0.862321i	0.999997	+	0.00246806i	$0.000785609\pi$
$132$	1.32665e10	−	5.04077e10i	0.0288138	−	0.109481i
$133$	3.42519e10	+	4.12476e11i	0.0713675	+	0.859439i
$134$			2.75658e11i			0.551181i
$135$	−4.62272e11	+	1.30505e11i	−0.887282	+	0.250490i
$136$	−2.57420e11	+	1.48622e11i	−0.474437	+	0.273917i
$137$	6.10753e11	−	3.52618e11i	1.08119	−	0.624226i	0.149974	−	0.988690i	$-0.452081\pi$
$137$	6.10753e11	−	3.52618e11i	1.08119	−	0.624226i	0.931217	+	0.364464i	$0.118748\pi$
$138$	2.48662e11	−	2.50885e11i	0.422936	−	0.426717i
$139$		−	5.03076e11i		−	0.822342i	−0.911558	−	0.411171i	$-0.865120\pi$
$139$		−	5.03076e11i		−	0.822342i	0.911558	−	0.411171i	$-0.134880\pi$
$140$	1.67196e11	+	2.41040e11i	0.262738	+	0.378778i
$141$	−5.71701e10	−	1.50463e10i	−0.0863901	−	0.0227365i
$142$	−1.64013e11	+	2.84078e11i	−0.238392	+	0.412907i
$143$	3.07843e9	+	5.33201e9i	0.00430509	+	0.00745663i
$144$	−1.65342e9	−	1.85745e11i	−0.00222530	−	0.249990i
$145$	−3.83405e10	−	2.21359e10i	−0.0496746	−	0.0286796i
$146$	9.50803e11			1.18618
$147$	−8.28741e11	−	7.61672e10i	−0.995803	−	0.0915214i
$148$	2.14055e11			0.247791
$149$	3.38203e11	+	1.95261e11i	0.377270	+	0.217817i	0.676630	−	0.736323i	$-0.263440\pi$
$149$	3.38203e11	+	1.95261e11i	0.377270	+	0.217817i	−0.299360	+	0.954140i	$0.596773\pi$
$150$	−9.51601e10	+	2.59526e10i	−0.102318	+	0.0279047i
$151$	1.13993e11	+	1.97442e11i	0.118170	+	0.204676i	0.919042	−	0.394159i	$-0.128964\pi$
$151$	1.13993e11	+	1.97442e11i	0.118170	+	0.204676i	−0.800873	+	0.598835i	$0.795631\pi$
$152$	−1.52501e11	+	2.64139e11i	−0.152452	+	0.264054i
$153$	−1.39874e12	−	7.91044e11i	−1.34875	−	0.762778i
$154$	−9.80847e10	−	1.41405e11i	−0.0912509	−	0.131553i
$155$			1.70392e12i			1.52976i
$156$	1.55834e10	+	1.54453e10i	0.0135045	+	0.0133848i
$157$	2.21949e11	−	1.28142e11i	0.185697	−	0.107212i	−0.404270	−	0.914640i	$-0.632474\pi$
$157$	2.21949e11	−	1.28142e11i	0.185697	−	0.107212i	0.589967	+	0.807428i	$0.299141\pi$
$158$	5.88802e11	−	3.39945e11i	0.475724	−	0.274660i
$159$	1.55348e12	+	1.53971e12i	1.21233	+	1.20158i
$160$			2.16171e11i			0.162982i
$161$	−9.65120e10	−	1.16224e12i	−0.0703135	−	0.846747i
$162$	8.60581e11	−	5.17499e11i	0.605982	−	0.364399i
$163$	1.14815e12	−	1.98865e12i	0.781568	−	1.35371i	−0.149461	−	0.988768i	$-0.547754\pi$
$163$	1.14815e12	−	1.98865e12i	0.781568	−	1.35371i	0.931028	−	0.364947i	$-0.118913\pi$
$164$	−7.40520e10	−	1.28262e11i	−0.0487411	−	0.0844221i
$165$	−3.16381e11	+	8.62849e10i	−0.201395	+	0.0549254i
$166$	1.08098e12	+	6.24104e11i	0.665615	+	0.384293i
$167$	−1.67604e12			−0.998491			−0.499246	−	0.866461i	$-0.666389\pi$
$167$	−1.67604e12			−0.998491			−0.499246	+	0.866461i	$0.666389\pi$
$168$	−4.69810e11	−	3.94190e11i	−0.270845	−	0.227251i
$169$	1.78957e12			0.998554
$170$	1.61954e12	+	9.35041e11i	0.874827	+	0.505082i
$171$	−1.64880e12	+	1.46769e10i	−0.862363	+	0.00767636i
$172$	−6.38800e11	−	1.10643e12i	−0.323563	−	0.560427i
$173$	−1.01491e12	+	1.75788e12i	−0.497937	+	0.862452i	−0.999997	−	0.00238076i	$-0.999242\pi$
$173$	−1.01491e12	+	1.75788e12i	−0.497937	+	0.862452i	0.502060	+	0.864833i	$0.332576\pi$
$174$	8.95062e10	+	2.35567e10i	0.0425434	+	0.0111968i
$175$	−1.38929e11	+	2.94532e11i	−0.0639860	+	0.135651i
$176$		−	1.26816e11i		−	0.0566048i
$177$	−1.29817e12	+	1.30977e12i	−0.561665	+	0.566687i
$178$	2.42412e12	−	1.39957e12i	1.01682	−	0.587061i
$179$	2.05515e12	−	1.18654e12i	0.835894	−	0.482603i	−0.0199727	−	0.999801i	$-0.506358\pi$
$179$	2.05515e12	−	1.18654e12i	0.835894	−	0.482603i	0.855866	+	0.517197i	$0.173025\pi$
$180$	−1.00683e12	+	5.93307e11i	−0.397154	+	0.234035i
$181$		−	1.80880e12i		−	0.692085i	−0.938219	−	0.346042i	$-0.887525\pi$
$181$		−	1.80880e12i		−	0.692085i	0.938219	−	0.346042i	$-0.112475\pi$
$182$	7.21911e10	−	5.99472e9i	0.0267973	−	0.00222524i
$183$	3.25116e11	−	1.23531e12i	0.117100	−	0.444935i
$184$	4.29703e11	−	7.44268e11i	0.150200	−	0.260155i
$185$	−6.73355e11	−	1.16629e12i	−0.228455	−	0.395695i
$186$	−9.37266e11	−	3.43667e12i	−0.308704	−	1.13192i
$187$	−9.50093e11	−	5.48536e11i	−0.303835	−	0.175419i
$188$	−1.43828e11			−0.0446660
$189$	5.46522e11	−	3.27008e12i	0.164842	−	0.986320i
$190$	1.91889e12			0.562219
$191$	9.20403e11	+	5.31395e11i	0.261996	+	0.151263i	0.625245	−	0.780429i	$-0.284999\pi$
$191$	9.20403e11	+	5.31395e11i	0.261996	+	0.151263i	−0.363249	+	0.931692i	$0.618333\pi$
$192$	−1.18909e11	−	4.36002e11i	−0.0328894	−	0.120596i
$193$	1.99091e12	+	3.44835e12i	0.535163	+	0.926929i	0.999155	+	0.0410900i	$0.0130830\pi$
$193$	1.99091e12	+	3.44835e12i	0.535163	+	0.926929i	−0.463993	+	0.885839i	$0.653584\pi$
$194$	1.48191e12	−	2.56675e12i	0.387180	−	0.670616i
$195$	3.51334e10	−	1.33493e11i	0.00892338	−	0.0339054i
$196$	−1.99705e12	+	3.33971e11i	−0.493152	+	0.0824709i
$197$			4.44591e11i			0.106757i	0.998574	+	0.0533785i	$0.0169990\pi$
$197$			4.44591e11i			0.106757i	−0.998574	+	0.0533785i	$0.983001\pi$
$198$	5.90653e11	−	3.48060e11i	0.137935	−	0.0812823i
$199$	−5.19502e12	+	2.99934e12i	−1.18004	+	0.681294i	−0.956023	−	0.293292i	$-0.905249\pi$
$199$	−5.19502e12	+	2.99934e12i	−1.18004	+	0.681294i	−0.224013	+	0.974586i	$0.571916\pi$
$200$	−2.07825e11	+	1.19988e11i	−0.0459232	+	0.0265138i
$201$	−2.55230e12	+	2.57512e12i	−0.548723	+	0.553629i
$202$			4.06938e12i			0.851326i
$203$	2.51084e11	−	1.74164e11i	0.0511201	−	0.0354592i
$204$	−3.78082e12	−	9.95054e11i	−0.749239	−	0.197188i
$205$	−4.65892e11	+	8.06948e11i	−0.0898750	+	0.155668i
$206$	−1.84185e12	−	3.19017e12i	−0.345926	−	0.599162i
$207$	4.64585e12	−	4.13553e10i	0.849628	−	0.00756300i
$208$	4.62293e10	+	2.66905e10i	0.00823320	+	0.00475344i
$209$	−1.12571e12			−0.195263
$210$	−6.69872e11	+	3.79978e12i	−0.113184	+	0.642026i
$211$	7.80379e12			1.28455			0.642277	−	0.766473i	$-0.277990\pi$
$211$	7.80379e12			1.28455			0.642277	+	0.766473i	$0.277990\pi$
$212$	4.60849e12	+	2.66071e12i	0.739114	+	0.426728i
$213$	−4.16241e12	+	1.13519e12i	−0.650515	+	0.177412i
$214$	3.00693e12	+	5.20816e12i	0.457982	+	0.793247i
$215$	−4.01896e12	+	6.96104e12i	−0.596626	+	1.03339i
$216$	1.70435e12	−	1.75048e12i	0.246640	−	0.253316i
$217$	−1.06369e13	−	5.01738e12i	−1.50067	−	0.707862i
$218$			2.02843e12i			0.279029i
$219$	8.88212e12	+	8.80341e12i	1.19145	+	1.18089i
$220$	−6.90959e11	+	3.98925e11i	−0.0903915	+	0.0521875i
$221$	3.99926e11	−	2.30897e11i	0.0510296	−	0.0294619i
$222$	1.99964e12	+	1.98192e12i	0.248892	+	0.246686i
$223$		−	6.64946e12i		−	0.807439i	−0.914883	−	0.403719i	$-0.867717\pi$
$223$		−	6.64946e12i		−	0.807439i	0.914883	−	0.403719i	$-0.132283\pi$
$224$	−1.34948e12	−	6.36543e11i	−0.159883	−	0.0754160i
$225$	−1.12925e12	−	6.38639e11i	−0.130553	−	0.0738332i
$226$	−2.46228e12	+	4.26479e12i	−0.277805	+	0.481173i
$227$	−3.32433e12	−	5.75790e12i	−0.366068	−	0.634048i	0.622879	−	0.782318i	$-0.285963\pi$
$227$	−3.32433e12	−	5.75790e12i	−0.366068	−	0.634048i	−0.988947	+	0.148270i	$0.952629\pi$
$228$	−3.87026e12	+	1.05552e12i	−0.416005	+	0.113455i
$229$	−8.88140e12	−	5.12768e12i	−0.931937	−	0.538054i	−0.0445130	−	0.999009i	$-0.514174\pi$
$229$	−8.88140e12	−	5.12768e12i	−0.931937	−	0.538054i	−0.887424	+	0.460955i	$0.847507\pi$
$230$	−5.40689e12			−0.553916
$231$	3.92976e11	−	2.22912e12i	0.0393098	−	0.222981i
$232$	2.25180e11			0.0219961
$233$	−4.97741e12	−	2.87371e12i	−0.474838	−	0.274148i	0.243425	−	0.969920i	$-0.421729\pi$
$233$	−4.97741e12	−	2.87371e12i	−0.474838	−	0.274148i	−0.718263	+	0.695772i	$0.755062\pi$
$234$	2.56873e9	+	2.88571e11i	0.000239349	+	0.0268885i
$235$	4.52442e11	+	7.83653e11i	0.0411804	+	0.0713265i
$236$	−2.24331e12	+	3.88553e12i	−0.199468	+	0.345489i
$237$	8.64794e12	+	2.27600e12i	0.751271	+	0.197723i
$238$	−1.06060e13	+	7.35682e12i	−0.900284	+	0.624478i
$239$		−	4.62568e12i		−	0.383695i	−0.981425	−	0.191848i	$-0.938552\pi$
$239$		−	4.62568e12i		−	0.383695i	0.981425	−	0.191848i	$-0.0614480\pi$
$240$	−2.00151e12	+	2.01941e12i	−0.162255	+	0.163705i
$241$	−7.15594e12	+	4.13149e12i	−0.566987	+	0.327350i	−0.755945	−	0.654635i	$-0.772822\pi$
$241$	−7.15594e12	+	4.13149e12i	−0.566987	+	0.327350i	0.188958	+	0.981985i	$0.439489\pi$
$242$	−7.50144e12	+	4.33096e12i	−0.580979	+	0.335428i
$243$	1.28308e13	+	3.13373e12i	0.971446	+	0.237262i
$244$		−	3.10780e12i		−	0.230043i
$245$	8.10179e12	+	9.83040e12i	0.586364	+	0.711472i
$246$	4.95794e11	−	1.88383e12i	0.0350880	−	0.133321i
$247$	2.36924e11	−	4.10364e11i	0.0163974	−	0.0284012i
$248$	−4.33331e12	−	7.50551e12i	−0.293316	−	0.508038i
$249$	4.31967e12	+	1.58389e13i	0.285992	+	1.04865i
$250$	1.00252e13	+	5.78803e12i	0.649264	+	0.374853i
$251$	−9.21617e12			−0.583909			−0.291954	−	0.956432i	$-0.594306\pi$
$251$	−9.21617e12			−0.583909			−0.291954	+	0.956432i	$0.594306\pi$
$252$	−7.39050e11	−	8.03235e12i	−0.0458111	−	0.497897i
$253$	3.17192e12			0.192380
$254$	−1.64803e13	−	9.51490e12i	−0.978091	−	0.564701i
$255$	6.47178e12	+	2.37301e13i	0.375883	+	1.37825i
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	1.75644e13	−	3.04224e13i	0.977238	−	1.69263i	0.304895	−	0.952386i	$-0.401379\pi$
$257$	1.75644e13	−	3.04224e13i	0.977238	−	1.69263i	0.672343	−	0.740240i	$-0.265288\pi$
$258$	4.27691e12	−	1.62506e13i	0.232928	−	0.885035i
$259$	9.26345e12	−	7.69233e11i	0.493883	−	0.0410119i
$260$		−	3.35842e11i		−	0.0175300i
$261$	6.18031e11	+	1.04879e12i	0.0315855	+	0.0536001i
$262$	1.21846e13	−	7.03478e12i	0.609753	−	0.352041i
$263$	−3.22586e11	+	1.86245e11i	−0.0158085	+	0.00912702i	−0.507883	−	0.861426i	$-0.669572\pi$
$263$	−3.22586e11	+	1.86245e11i	−0.0158085	+	0.00912702i	0.492075	+	0.870553i	$0.336239\pi$
$264$	1.17418e12	−	1.18468e12i	0.0563523	−	0.0568562i
$265$		−	3.34793e13i		−	1.57371i
$266$	−5.65041e12	+	1.19789e13i	−0.260154	+	0.551529i
$267$	3.56039e13	+	9.37039e12i	1.60578	+	0.422616i
$268$	−4.41053e12	+	7.63926e12i	−0.194872	+	0.337528i
$269$	9.79631e12	+	1.69677e13i	0.424058	+	0.734490i	0.996332	−	0.0855726i	$-0.0272720\pi$
$269$	9.79631e12	+	1.69677e13i	0.424058	+	0.734490i	−0.572274	+	0.820062i	$0.693939\pi$
$270$	−1.48989e13	−	3.77969e12i	−0.631909	−	0.160308i
$271$	−2.52272e13	−	1.45649e13i	−1.04843	−	0.605308i	−0.126217	−	0.992003i	$-0.540284\pi$
$271$	−2.52272e13	−	1.45649e13i	−1.04843	−	0.605308i	−0.922208	+	0.386694i	$0.873617\pi$
$272$	−9.51179e12			−0.387376
$273$	7.29893e11	+	6.12411e11i	0.0291316	+	0.0244427i
$274$	2.25676e13			0.882789
$275$	−7.67045e11	−	4.42853e11i	−0.0294097	−	0.0169797i
$276$	1.09053e13	−	2.97415e12i	0.409861	−	0.111780i
$277$	3.83146e12	+	6.63629e12i	0.141165	+	0.244504i	0.927935	−	0.372741i	$-0.121582\pi$
$277$	3.83146e12	+	6.63629e12i	0.141165	+	0.244504i	−0.786771	+	0.617245i	$0.788249\pi$
$278$	8.04922e12	−	1.39417e13i	0.290742	−	0.503579i
$279$	2.30642e13	−	4.07824e13i	0.816799	−	1.44428i
$280$	7.76838e11	+	9.35503e12i	0.0269750	+	0.324845i
$281$		−	5.40056e13i		−	1.83888i	−0.393226	−	0.919442i	$-0.628641\pi$
$281$		−	5.40056e13i		−	1.83888i	0.393226	−	0.919442i	$-0.371359\pi$
$282$	−1.34360e12	−	1.33170e12i	−0.0448643	−	0.0444667i
$283$	1.66859e13	−	9.63361e12i	0.546417	−	0.315474i	−0.201259	−	0.979538i	$-0.564503\pi$
$283$	1.66859e13	−	9.63361e12i	0.546417	−	0.315474i	0.747676	+	0.664064i	$0.231170\pi$
$284$	−9.09050e12	+	5.24840e12i	−0.291969	+	0.168568i
$285$	1.79257e13	+	1.77669e13i	0.564716	+	0.559711i
$286$			1.97020e11i			0.00608831i
$287$	−3.66560e12	−	5.28454e12i	−0.111121	−	0.160198i
$288$	2.92609e12	−	5.17396e12i	0.0870221	−	0.153874i
$289$	−2.40069e13	+	4.15812e13i	−0.700484	+	1.21327i
$290$	−7.08349e11	−	1.22690e12i	−0.0202796	−	0.0351252i
$291$	3.76089e13	−	1.02569e13i	1.05652	−	0.288141i
$292$	2.63494e13	+	1.52128e13i	0.726382	+	0.419377i
$293$	−6.76028e13			−1.82891			−0.914457	−	0.404684i	$-0.867382\pi$
$293$	−6.76028e13			−1.82891			−0.914457	+	0.404684i	$0.867382\pi$
$294$	−2.17481e13	−	1.53707e13i	−0.577445	−	0.408115i
$295$	2.82272e13			0.735609
$296$	5.93207e12	+	3.42488e12i	0.151741	+	0.0876075i
$297$	8.74038e12	+	2.21734e12i	0.219467	+	0.0556764i
$298$	6.24836e12	+	1.08225e13i	0.154020	+	0.266770i
$299$	−6.67584e11	+	1.15629e12i	−0.0161553	+	0.0279817i
$300$	−3.05240e12	−	8.03344e11i	−0.0725227	−	0.0190869i
$301$	−3.16208e13	−	4.55864e13i	−0.737662	−	1.06346i
$302$			7.29558e12i			0.167117i
$303$	−3.76781e13	+	3.80150e13i	−0.847529	+	0.855107i
$304$	−8.45245e12	+	4.88002e12i	−0.186714	+	0.107800i
$305$	−1.69329e13	+	9.77623e12i	−0.367353	+	0.212091i
$306$	−2.61062e13	−	4.43018e13i	−0.556257	−	0.943961i
$307$		−	7.52333e13i		−	1.57452i	−0.616619	−	0.787261i	$-0.711498\pi$
$307$		−	7.52333e13i		−	1.57452i	0.616619	−	0.787261i	$-0.288502\pi$
$308$	−4.55728e11	−	5.48808e12i	−0.00936864	−	0.112821i
$309$	1.23316e13	−	4.68551e13i	0.249027	−	0.946206i
$310$	−2.72626e13	+	4.72203e13i	−0.540852	+	0.936784i
$311$	4.22459e13	+	7.31720e13i	0.823384	+	1.42614i	0.903148	+	0.429329i	$0.141250\pi$
$311$	4.22459e13	+	7.31720e13i	0.823384	+	1.42614i	−0.0797640	+	0.996814i	$0.525417\pi$
$312$	1.84735e11	+	6.77368e11i	0.00353753	+	0.0129710i
$313$	2.62298e13	+	1.51438e13i	0.493516	+	0.284932i	0.726032	−	0.687661i	$-0.241362\pi$
$313$	2.62298e13	+	1.51438e13i	0.493516	+	0.284932i	−0.232516	+	0.972593i	$0.574696\pi$
$314$	8.20110e12			0.151621
$315$	−4.14396e13	+	2.92941e13i	−0.752849	+	0.532198i
$316$	2.17565e13			0.388427
$317$	−6.61046e13	−	3.81655e13i	−1.15986	−	0.669645i	−0.208589	−	0.978003i	$-0.566887\pi$
$317$	−6.61046e13	−	3.81655e13i	−1.15986	−	0.669645i	−0.951270	+	0.308358i	$0.900221\pi$
$318$	1.84158e13	+	6.75253e13i	0.317572	+	1.16444i
$319$	4.15549e11	+	7.19752e11i	0.00704326	+	0.0121993i
$320$	−3.45874e12	+	5.99072e12i	−0.0576227	+	0.0998054i
$321$	−2.01321e13	+	7.64941e13i	−0.329694	+	1.25271i
$322$	1.59212e13	−	3.37531e13i	0.256312	−	0.543384i
$323$			8.44334e13i			1.33629i
$324$	3.21291e13	−	5.72043e11i	0.499921	−	0.00890084i
$325$	3.22875e11	−	1.86412e11i	0.00493942	−	0.00285177i
$326$	6.36369e13	−	3.67408e13i	0.957221	−	0.552652i
$327$	−1.87811e13	+	1.89490e13i	−0.277785	+	0.280268i
$328$		−	4.73933e12i		−	0.0689304i
$329$	−6.22432e12	+	5.16865e11i	−0.0890255	+	0.00739265i
$330$	−1.01484e13	−	2.67089e12i	−0.142748	−	0.0375690i
$331$	−6.65071e13	+	1.15194e14i	−0.920055	+	1.59358i	−0.120729	+	0.992685i	$0.538523\pi$
$331$	−6.65071e13	+	1.15194e14i	−0.920055	+	1.59358i	−0.799326	+	0.600897i	$0.794810\pi$
$332$	1.99713e13	+	3.45914e13i	0.271736	+	0.470661i
$333$	3.29616e11	+	3.70290e13i	0.00441128	+	0.495563i
$334$	−4.64478e13	−	2.68167e13i	−0.611448	−	0.353020i
$335$	5.54970e13			0.718659
$336$	−6.71271e12	−	1.84411e13i	−0.0855130	−	0.234920i
$337$	6.59253e13			0.826205			0.413102	−	0.910685i	$-0.364445\pi$
$337$	6.59253e13			0.826205			0.413102	+	0.910685i	$0.364445\pi$
$338$	4.95940e13	+	2.86331e13i	0.611487	+	0.353042i
$339$	−6.24892e13	+	1.70424e13i	−0.758065	+	0.206743i
$340$	2.99213e13	+	5.18252e13i	0.357147	+	0.618596i
$341$	1.59935e13	−	2.77015e13i	0.187842	−	0.325353i
$342$	−4.59278e13	−	2.59741e13i	−0.530801	−	0.300191i
$343$	−8.52241e13	+	2.16296e13i	−0.969270	+	0.245997i
$344$		−	4.08832e13i		−	0.457587i
$345$	−5.05096e13	−	5.00619e13i	−0.556376	−	0.551446i
$346$	−5.62521e13	+	3.24771e13i	−0.609846	+	0.352094i
$347$	−5.88757e13	+	3.39919e13i	−0.628238	+	0.362713i	−0.780069	−	0.625693i	$-0.784816\pi$
$347$	−5.88757e13	+	3.39919e13i	−0.628238	+	0.362713i	0.151831	+	0.988406i	$0.451483\pi$
$348$	2.10356e12	+	2.08492e12i	0.0220938	+	0.0218980i
$349$		−	1.54262e14i		−	1.59484i	−0.603423	−	0.797422i	$-0.706197\pi$
$349$		−	1.54262e14i		−	1.59484i	0.603423	−	0.797422i	$-0.293803\pi$
$350$	−8.56263e12	+	5.93943e12i	−0.0871431	+	0.0604464i
$351$	−2.64786e12	+	2.71953e12i	−0.0265281	+	0.0272462i
$352$	2.02905e12	−	3.51442e12i	0.0200128	−	0.0346632i
$353$	−1.30253e13	−	2.25604e13i	−0.126481	−	0.219071i	0.795830	−	0.605520i	$-0.207035\pi$
$353$	−1.30253e13	−	2.25604e13i	−0.126481	−	0.219071i	−0.922311	+	0.386449i	$0.873702\pi$
$354$	−5.69322e13	+	1.55268e13i	−0.544302	+	0.148445i
$355$	5.71921e13	+	3.30199e13i	0.538369	+	0.310828i
$356$	8.95722e13			0.830229
$357$	−1.67195e14	−	2.94751e13i	−1.52597	−	0.269017i
$358$	7.59385e13			0.682504
$359$	1.09426e14	+	6.31769e13i	0.968499	+	0.559163i	0.898778	−	0.438403i	$-0.144456\pi$
$359$	1.09426e14	+	6.31769e13i	0.968499	+	0.559163i	0.0697208	+	0.997567i	$0.477789\pi$
$360$	−3.73951e13	+	3.32874e11i	−0.325950	+	0.00290146i
$361$	−1.49266e13	−	2.58536e13i	−0.128136	−	0.221938i
$362$	2.89409e13	−	5.01270e13i	0.244689	−	0.423814i
$363$	−1.10176e14	−	2.89967e13i	−0.917491	−	0.241469i
$364$	2.09653e12	+	9.88927e11i	0.0171967	+	0.00811160i
$365$		−	1.91421e14i		−	1.54660i
$366$	2.87749e13	−	2.90322e13i	0.229017	−	0.231065i
$367$	−9.09957e13	+	5.25364e13i	−0.713440	+	0.411905i	−0.812333	−	0.583193i	$-0.801803\pi$
$367$	−9.09957e13	+	5.25364e13i	−0.713440	+	0.411905i	0.0988935	+	0.995098i	$0.468470\pi$
$368$	2.38166e13	−	1.37505e13i	0.183957	−	0.106208i
$369$	2.20738e13	−	1.30076e13i	0.167970	−	0.0989813i
$370$		−	4.30947e13i		−	0.323083i
$371$	2.08999e14	+	9.85838e13i	1.54379	+	0.728198i
$372$	2.90124e13	−	1.10236e14i	0.211153	−	0.802301i
$373$	−9.92170e13	+	1.71849e14i	−0.711521	+	1.23239i	0.252765	+	0.967528i	$0.418660\pi$
$373$	−9.92170e13	+	1.71849e14i	−0.711521	+	1.23239i	−0.964286	+	0.264863i	$0.914673\pi$
$374$	−1.75532e13	−	3.04030e13i	−0.124040	−	0.214844i
$375$	4.00612e13	+	1.46892e14i	0.278966	+	1.02288i
$376$	−3.98589e12	−	2.30126e12i	−0.0273522	−	0.0157918i
$377$	−3.49837e11			−0.00236586
$378$	6.74669e13	−	8.18786e13i	0.449662	−	0.545715i
$379$	1.57834e14			1.03677			0.518387	−	0.855146i	$-0.326533\pi$
$379$	1.57834e14			1.03677			0.518387	+	0.855146i	$0.326533\pi$
$380$	5.31779e13	+	3.07023e13i	0.344288	+	0.198774i
$381$	−6.58563e13	−	2.41475e14i	−0.420252	−	1.54094i
$382$	1.70046e13	+	2.94529e13i	0.106959	+	0.185259i
$383$	−8.52988e13	+	1.47742e14i	−0.528871	+	0.916032i	0.470562	+	0.882367i	$0.344051\pi$
$383$	−8.52988e13	+	1.47742e14i	−0.528871	+	0.916032i	−0.999433	+	0.0336648i	$0.989282\pi$
$384$	3.68073e12	−	1.39854e13i	0.0224964	−	0.0854776i
$385$	−2.84683e13	+	1.97469e13i	−0.171525	+	0.118978i
$386$			1.27418e14i			0.756834i
$387$	1.90417e14	−	1.12209e14i	1.11505	−	0.657077i
$388$	8.21360e13	−	4.74212e13i	0.474197	−	0.273778i
$389$	−1.97095e13	+	1.13793e13i	−0.112190	+	0.0647729i	−0.555045	−	0.831820i	$-0.687299\pi$
$389$	−1.97095e13	+	1.13793e13i	−0.112190	+	0.0647729i	0.442855	+	0.896593i	$0.353966\pi$
$390$	3.10954e12	−	3.13734e12i	0.0174518	−	0.0176078i
$391$		−	2.37909e14i		−	1.31656i
$392$	−6.06874e13	−	2.26975e13i	−0.331150	−	0.123853i
$393$	1.78959e14	+	4.70993e13i	0.962931	+	0.253429i
$394$	−7.11345e12	+	1.23209e13i	−0.0377443	+	0.0653750i
$395$	−6.84395e13	−	1.18541e14i	−0.358115	−	0.620274i
$396$	2.19376e13	−	1.95279e11i	0.113205	−	0.00100770i
$397$	6.36468e13	+	3.67465e13i	0.323913	+	0.187011i	0.653135	−	0.757241i	$-0.273453\pi$
$397$	6.36468e13	+	3.67465e13i	0.323913	+	0.187011i	−0.329222	+	0.944252i	$0.606787\pi$
$398$	−1.91958e14			−0.963495
$399$	−1.63696e14	+	5.95868e13i	−0.810378	+	0.294984i
$400$	−7.67921e12			−0.0374962
$401$	5.70677e13	+	3.29480e13i	0.274850	+	0.158685i	0.631090	−	0.775710i	$-0.282608\pi$
$401$	5.70677e13	+	3.29480e13i	0.274850	+	0.158685i	−0.356240	+	0.934395i	$0.615941\pi$
$402$	−1.11933e14	+	3.05270e13i	−0.531760	+	0.145024i
$403$	6.73219e12	+	1.16605e13i	0.0315485	+	0.0546436i
$404$	−6.51101e13	+	1.12774e14i	−0.300989	+	0.521329i
$405$	−1.04186e14	−	1.73257e14i	−0.475122	−	0.790110i
$406$	9.74487e12	−	8.09210e11i	0.0438412	−	0.00364056i
$407$			2.52813e13i			0.112210i
$408$	−8.88563e13	−	8.80689e13i	−0.389097	−	0.385649i
$409$	2.28700e14	−	1.32040e14i	0.988071	−	0.570463i	0.0833742	−	0.996518i	$-0.473430\pi$
$409$	2.28700e14	−	1.32040e14i	0.988071	−	0.570463i	0.904697	+	0.426055i	$0.140097\pi$
$410$	−2.58224e13	+	1.49085e13i	−0.110074	+	0.0635512i
$411$	2.10820e14	+	2.08951e14i	0.886709	+	0.878851i
$412$		−	1.17878e14i		−	0.489214i
$413$	−8.31185e13	+	1.76212e14i	−0.340386	+	0.721622i
$414$	1.29411e14	+	7.31876e13i	0.522962	+	0.295757i
$415$	1.25648e14	−	2.17629e14i	0.501061	−	0.867864i
$416$	8.54096e11	+	1.47934e12i	0.00336119	+	0.00582175i
$417$	2.04278e14	−	5.57118e13i	0.793366	−	0.216371i
$418$	−3.11965e13	−	1.80113e13i	−0.119574	−	0.0690360i
$419$	3.46229e14			1.30974			0.654871	−	0.755741i	$-0.272723\pi$
$419$	3.46229e14			1.30974			0.654871	+	0.755741i	$0.272723\pi$
$420$	−7.93605e13	+	9.45847e13i	−0.296301	+	0.353142i
$421$	−1.52531e14			−0.562090			−0.281045	−	0.959695i	$-0.590681\pi$
$421$	−1.52531e14			−0.562090			−0.281045	+	0.959695i	$0.590681\pi$
$422$	2.16265e14	+	1.24861e14i	0.786625	+	0.454158i
$423$	−2.21476e11	−	2.48806e13i	−0.000795161	−	0.0893284i
$424$	8.51428e13	+	1.47472e14i	0.301742	+	0.522633i
$425$	−3.32161e13	+	5.75320e13i	−0.116201	+	0.201266i
$426$	−1.33515e14	−	3.51392e13i	−0.461082	−	0.121350i
$427$	−1.11683e13	−	1.34493e14i	−0.0380743	−	0.458508i
$428$			1.92444e14i			0.647684i
$429$	−1.82419e12	+	1.84050e12i	−0.00606115	+	0.00611535i
$430$	−2.22753e14	+	1.28607e14i	−0.730714	+	0.421878i
$431$	3.53153e14	−	2.03893e14i	1.14377	−	0.660355i	0.196407	−	0.980523i	$-0.437073\pi$
$431$	3.53153e14	−	2.03893e14i	1.14377	−	0.660355i	0.947361	+	0.320168i	$0.103739\pi$
$432$	7.52400e13	−	2.12412e13i	0.240596	−	0.0679232i
$433$			4.84121e14i			1.52852i	0.644910	+	0.764259i	$0.276895\pi$
$433$			4.84121e14i			1.52852i	−0.644910	+	0.764259i	$0.723105\pi$
$434$	−2.14500e14	−	3.09236e14i	−0.668704	−	0.964044i
$435$	4.74255e12	−	1.80199e13i	0.0145989	−	0.0554703i
$436$	−3.24549e13	+	5.62136e13i	−0.0986517	+	0.170870i
$437$	−1.22059e14	−	2.11413e14i	−0.366373	−	0.634576i
$438$	1.05294e14	+	3.86081e14i	0.312102	+	1.14438i
$439$	−1.58341e14	−	9.14185e13i	−0.463489	−	0.267596i	0.250021	−	0.968240i	$-0.419562\pi$
$439$	−1.58341e14	−	9.14185e13i	−0.463489	−	0.267596i	−0.713510	+	0.700645i	$0.752896\pi$
$440$	−2.55312e13			−0.0738043
$441$	−6.08483e13	−	3.44952e14i	−0.173715	−	0.984796i
$442$	1.47774e13			0.0416655
$443$	2.02304e14	+	1.16800e14i	0.563357	+	0.325254i	0.754492	−	0.656310i	$-0.227883\pi$
$443$	2.02304e14	+	1.16800e14i	0.563357	+	0.325254i	−0.191135	+	0.981564i	$0.561217\pi$
$444$	2.37050e13	+	8.69188e13i	0.0651978	+	0.239060i
$445$	−2.81768e14	−	4.88036e14i	−0.765441	−	1.32578i
$446$	1.06391e14	−	1.84275e14i	0.285473	−	0.494453i
$447$	−4.18341e13	+	1.58954e14i	−0.110877	+	0.421288i
$448$	−2.72131e13	−	3.92320e13i	−0.0712441	−	0.102710i
$449$		−	3.69553e14i		−	0.955700i	−0.878441	−	0.477850i	$-0.841416\pi$
$449$		−	3.69553e14i		−	0.955700i	0.878441	−	0.477850i	$-0.158584\pi$
$450$	−2.10765e13	−	3.57665e13i	−0.0538430	−	0.0913708i
$451$	1.51485e13	−	8.74601e12i	0.0382296	−	0.0220719i
$452$	−1.36473e14	+	7.87929e13i	−0.340241	+	0.196438i
$453$	−6.75492e13	+	6.81532e13i	−0.166372	+	0.167860i
$454$		−	2.12757e14i		−	0.517698i
$455$	−1.20689e12	−	1.45339e13i	−0.00290138	−	0.0349397i
$456$	−1.24144e14	−	3.26728e13i	−0.294862	−	0.0776032i
$457$	−3.88192e14	+	6.72368e14i	−0.910976	+	1.57786i	−0.0982887	+	0.995158i	$0.531337\pi$
$457$	−3.88192e14	+	6.72368e14i	−0.910976	+	1.57786i	−0.812688	+	0.582699i	$0.801996\pi$
$458$	−1.64086e14	−	2.84205e14i	−0.380461	−	0.658979i
$459$	1.66311e14	−	6.55570e14i	0.381022	−	1.50193i
$460$	−1.49840e14	−	8.65102e13i	−0.339203	−	0.195839i
$461$	−7.50947e13			−0.167979			−0.0839893	−	0.996467i	$-0.526766\pi$
$461$	−7.50947e13			−0.167979			−0.0839893	+	0.996467i	$0.526766\pi$
$462$	4.65564e13	−	5.54876e13i	0.102908	−	0.122649i
$463$	4.48992e14			0.980715			0.490357	−	0.871521i	$-0.336866\pi$
$463$	4.48992e14			0.980715			0.490357	+	0.871521i	$0.336866\pi$
$464$	6.24036e12	+	3.60287e12i	0.0134698	+	0.00777679i
$465$	−6.91889e14	+	1.88695e14i	−1.47586	+	0.402504i
$466$	−9.19586e13	−	1.59277e14i	−0.193852	−	0.335761i
$467$	−1.51249e14	+	2.61971e14i	−0.315101	+	0.545771i	−0.979459	−	0.201644i	$-0.935372\pi$
$467$	−1.51249e14	+	2.61971e14i	−0.315101	+	0.545771i	0.664358	+	0.747415i	$0.268705\pi$
$468$	−4.54596e12	+	8.03822e12i	−0.00935994	+	0.0165504i
$469$	−1.63417e14	+	3.46446e14i	−0.332543	+	0.704994i
$470$			2.89563e13i			0.0582378i
$471$	7.66123e13	+	7.59333e13i	0.152294	+	0.150945i
$472$	−1.24337e14	+	7.17860e13i	−0.244298	+	0.141045i
$473$	1.30677e14	−	7.54464e13i	0.253783	−	0.146522i
$474$	2.03243e14	+	2.01442e14i	0.390152	+	0.386695i
$475$			6.81662e13i			0.129346i
$476$	−4.11632e14	+	3.41818e13i	−0.772095	+	0.0641145i
$477$	−4.53176e14	+	8.01312e14i	−0.840264	+	1.48577i
$478$	7.40108e13	−	1.28190e14i	0.135657	−	0.234965i
$479$	3.92365e14	+	6.79595e14i	0.710959	+	1.23142i	0.964498	+	0.264092i	$0.0850722\pi$
$479$	3.92365e14	+	6.79595e14i	0.710959	+	1.23142i	−0.253539	+	0.967325i	$0.581595\pi$
$480$	−8.77782e13	+	2.39393e13i	−0.157239	+	0.0428830i
$481$	−9.21602e12	−	5.32087e12i	−0.0163209	−	0.00942290i
$482$	−2.64415e14			−0.462943
$483$	4.61249e14	−	1.67899e14i	0.798411	−	0.290628i
$484$	−2.77181e14			−0.474367
$485$	−5.16752e14	−	2.98347e14i	−0.874384	−	0.504826i
$486$	3.05437e14	+	2.92137e14i	0.511002	+	0.488750i
$487$	3.72678e14	+	6.45498e14i	0.616489	+	1.06779i	0.990121	+	0.140213i	$0.0447787\pi$
$487$	3.72678e14	+	6.45498e14i	0.616489	+	1.06779i	−0.373633	+	0.927577i	$0.621888\pi$
$488$	4.97248e13	−	8.61259e13i	0.0813325	−	0.140872i
$489$	9.34657e14	+	2.45987e14i	1.51166	+	0.397845i
$490$	6.72369e13	+	4.02057e14i	0.107530	+	0.642997i
$491$		−	4.35501e13i		−	0.0688718i	−0.999407	−	0.0344359i	$-0.989037\pi$
$491$		−	4.35501e13i		−	0.0688718i	0.999407	−	0.0344359i	$-0.0109635\pi$
$492$	4.38811e13	−	4.42734e13i	0.0686229	−	0.0692365i
$493$	5.39849e13	−	3.11682e13i	0.0834861	−	0.0482007i
$494$	1.31317e13	−	7.58156e12i	0.0200827	−	0.0115947i
$495$	−7.00734e13	−	1.18913e14i	−0.105980	−	0.179847i
$496$		−	2.77332e14i		−	0.414811i
$497$	−3.74540e14	+	2.59798e14i	−0.554036	+	0.384304i
$498$	−1.33712e14	+	5.08055e14i	−0.195619	+	0.743275i
$499$	−4.28214e14	+	7.41689e14i	−0.619595	+	1.07317i	0.369964	+	0.929046i	$0.379370\pi$
$499$	−4.28214e14	+	7.41689e14i	−0.619595	+	1.07317i	−0.989560	+	0.144125i	$0.953963\pi$
$500$	1.85217e14	+	3.20805e14i	0.265061	+	0.459099i
$501$	−1.85609e14	−	6.80570e14i	−0.262718	−	0.963309i
$502$	−2.55406e14	−	1.47459e14i	−0.357570	−	0.206443i
$503$	1.46656e13			0.0203084			0.0101542	−	0.999948i	$-0.496768\pi$
$503$	1.46656e13			0.0203084			0.0101542	+	0.999948i	$0.496768\pi$
$504$	1.08036e14	−	2.34424e14i	0.147980	−	0.321095i
$505$	8.19270e14			1.11000
$506$	8.79028e13	+	5.07507e13i	0.117808	+	0.0680165i
$507$	1.98181e14	+	7.26669e14i	0.262735	+	0.963369i
$508$	−3.04477e14	−	5.27369e14i	−0.399304	−	0.691615i
$509$	−2.41682e13	+	4.18605e13i	−0.0313542	+	0.0543071i	−0.881277	−	0.472601i	$-0.843315\pi$
$509$	−2.41682e13	+	4.18605e13i	−0.0313542	+	0.0543071i	0.849922	+	0.526908i	$0.176649\pi$
$510$	−2.00330e14	+	7.61175e14i	−0.257104	+	0.976897i
$511$	1.19497e15	+	5.63661e14i	1.51719	+	0.715654i
$512$		−	3.51844e13i		−	0.0441942i
$513$	−1.88552e14	−	6.67884e14i	−0.234307	−	0.829957i
$514$	9.73516e14	−	5.62060e14i	1.19687	−	0.691012i
$515$	−6.42262e14	+	3.70810e14i	−0.781219	+	0.451037i
$516$	3.78534e14	−	3.81919e14i	0.455546	−	0.459619i
$517$		−	1.69871e13i		−	0.0202265i
$518$	2.69024e14	+	1.26898e14i	0.316940	+	0.149500i
$519$	−8.26193e14	−	2.17441e14i	−0.963078	−	0.253467i
$520$	5.37347e12	−	9.30713e12i	0.00619779	−	0.0107349i
$521$	−3.87655e14	−	6.71438e14i	−0.442423	−	0.766299i	0.555446	−	0.831553i	$-0.312548\pi$
$521$	−3.87655e14	−	6.71438e14i	−0.442423	−	0.766299i	−0.997869	+	0.0652539i	$0.979214\pi$
$522$	3.46746e11	+	3.89534e13i	0.000391583	+	0.0439904i
$523$	−1.06756e15	−	6.16358e14i	−1.19298	−	0.688769i	−0.234002	−	0.972236i	$-0.575182\pi$
$523$	−1.06756e15	−	6.16358e14i	−1.19298	−	0.688769i	−0.958982	+	0.283467i	$0.908515\pi$
$524$	4.50226e14			0.497861
$525$	−1.34982e14	−	2.37963e13i	−0.147707	−	0.0260396i
$526$	−1.19197e13			−0.0129076
$527$	−2.07775e15	−	1.19959e15i	−2.22656	−	1.28550i
$528$	5.14946e13	−	1.40439e13i	0.0546103	−	0.0148936i
$529$	−1.32477e14	−	2.29456e14i	−0.139038	−	0.240821i
$530$	5.35669e14	−	9.27806e14i	0.556390	−	0.963696i
$531$	−6.75606e14	−	3.82084e14i	−0.694502	−	0.392770i
$532$	−3.48251e14	+	2.41563e14i	−0.354306	+	0.245763i
$533$			7.36298e12i			0.00741402i
$534$	8.36757e14	+	8.29342e14i	0.833916	+	0.826526i
$535$	1.04853e15	−	6.05372e14i	1.03428	−	0.597140i
$536$	−2.44456e14	+	1.41137e14i	−0.238668	+	0.137795i
$537$	7.09395e14	+	7.03109e14i	0.685535	+	0.679460i
$538$			6.26964e14i			0.599708i
$539$	−3.94441e13	−	2.35864e14i	−0.0373460	−	0.223318i
$540$	−3.52416e14	−	3.43129e14i	−0.330286	−	0.321582i
$541$	1.07424e15	−	1.86064e15i	0.996591	−	1.72615i	0.426846	−	0.904325i	$-0.359625\pi$
$541$	1.07424e15	−	1.86064e15i	0.996591	−	1.72615i	0.569745	−	0.821821i	$-0.307042\pi$
$542$	−4.66077e14	−	8.07269e14i	−0.428018	−	0.741348i
$543$	7.34479e14	−	2.00311e14i	0.667698	−	0.182098i
$544$	−2.63598e14	−	1.52189e14i	−0.237219	−	0.136958i
$545$	4.08375e14			0.363813
$546$	1.04288e13	+	2.86499e13i	0.00919761	+	0.0252676i
$547$	−1.60383e15			−1.40032			−0.700160	−	0.713986i	$-0.746888\pi$
$547$	−1.60383e15			−1.40032			−0.700160	+	0.713986i	$0.746888\pi$
$548$	6.25411e14	+	3.61081e14i	0.540596	+	0.312113i
$549$	5.37613e14	−	4.78559e12i	0.460068	−	0.00409531i
$550$	−1.41713e13	−	2.45454e13i	−0.0120065	−	0.0207958i
$551$	3.19817e13	−	5.53939e13i	0.0268267	−	0.0464652i
$552$	3.49802e14	+	9.20626e13i	0.290508	+	0.0764572i
$553$	9.41533e14	−	7.81846e13i	0.774190	−	0.0642884i
$554$			2.45214e14i			0.199637i
$555$	3.99011e14	−	4.02578e14i	0.321642	−	0.324518i
$556$	4.46133e14	−	2.57575e14i	0.356084	−	0.205585i
$557$	−2.68302e14	+	1.54904e14i	−0.212041	+	0.122422i	−0.602260	−	0.798300i	$-0.705733\pi$
$557$	−2.68302e14	+	1.54904e14i	−0.212041	+	0.122422i	0.390219	+	0.920722i	$0.372399\pi$
$558$	1.29169e15	−	7.61169e14i	1.01081	−	0.595653i
$559$			6.35158e13i			0.0492172i
$560$	−1.28152e14	+	2.71684e14i	−0.0983313	+	0.208463i
$561$	1.17522e14	−	4.46539e14i	0.0892944	−	0.339284i
$562$	8.64090e14	−	1.49665e15i	0.650144	−	1.12608i
$563$	−8.25955e14	−	1.43060e15i	−0.615404	−	1.06591i	−0.990314	−	0.138849i	$-0.955660\pi$
$563$	−8.25955e14	−	1.43060e15i	−0.615404	−	1.06591i	0.374910	−	0.927061i	$-0.377674\pi$
$564$	−1.59279e13	−	5.84027e13i	−0.0117523	−	0.0430921i
$565$	8.58610e14	+	4.95719e14i	0.627378	+	0.362217i
$566$	6.16551e14			0.446148
$567$	1.38836e15	−	1.40216e14i	0.994939	−	0.100482i
$568$	−3.35898e14			−0.238392
$569$	−4.60776e14	−	2.66029e14i	−0.323871	−	0.186987i	0.329246	−	0.944244i	$-0.393206\pi$
$569$	−4.60776e14	−	2.66029e14i	−0.323871	−	0.186987i	−0.653117	+	0.757257i	$0.726539\pi$
$570$	2.12502e14	+	7.79181e14i	0.147929	+	0.542409i
$571$	7.73728e14	+	1.34014e15i	0.533445	+	0.923954i	0.999237	+	0.0390597i	$0.0124363\pi$
$571$	7.73728e14	+	1.34014e15i	0.533445	+	0.923954i	−0.465792	+	0.884894i	$0.654230\pi$
$572$	−3.15232e12	+	5.45997e12i	−0.00215254	+	0.00372831i
$573$	−1.13850e14	+	4.32585e14i	−0.0769984	+	0.292564i
$574$	−1.70314e13	−	2.05099e14i	−0.0114086	−	0.137388i
$575$		−	1.92073e14i		−	0.127436i
$576$	1.63874e14	−	9.65676e13i	0.107693	−	0.0634611i
$577$	3.68443e14	−	2.12721e14i	0.239830	−	0.138466i	−0.375269	−	0.926916i	$-0.622450\pi$
$577$	3.68443e14	−	2.12721e14i	0.239830	−	0.138466i	0.615099	+	0.788450i	$0.289116\pi$
$578$	−1.33060e15	+	7.68221e14i	−0.857914	+	0.495317i
$579$	−1.17975e15	+	1.19030e15i	−0.753458	+	0.760195i
$580$		−	4.53344e13i		−	0.0286796i
$581$	9.88588e14	+	1.42521e15i	0.619507	+	0.893118i
$582$	1.20636e15	+	3.17495e14i	0.748859	+	0.197088i
$583$	−3.14247e14	+	5.44292e14i	−0.193239	+	0.334699i
$584$	4.86811e14	+	8.43181e14i	0.296544	+	0.513630i
$585$	5.80967e13	−	5.17151e11i	0.0350586	−	0.000312076i
$586$	−1.87347e15	−	1.08165e15i	−1.11998	−	0.646618i
$587$	2.93512e14			0.173827			0.0869133	−	0.996216i	$-0.472300\pi$
$587$	2.93512e14			0.173827			0.0869133	+	0.996216i	$0.472300\pi$
$588$	−3.56770e14	−	7.73933e14i	−0.209321	−	0.454076i
$589$	−2.46179e15			−1.43093
$590$	7.82256e14	+	4.51636e14i	0.450467	+	0.260077i
$591$	−1.80530e14	+	4.92350e13i	−0.102995	+	0.0280894i
$592$	1.09596e14	+	1.89826e14i	0.0619479	+	0.107297i
$593$	−2.41806e12	+	4.18820e12i	−0.00135415	+	0.00234545i	−0.866702	−	0.498827i	$-0.833764\pi$
$593$	−2.41806e12	+	4.18820e12i	−0.00135415	+	0.00234545i	0.865348	+	0.501172i	$0.167098\pi$
$594$	2.06743e14	+	2.01295e14i	0.114711	+	0.111688i
$595$	1.48111e15	+	2.13526e15i	0.814227	+	1.17384i
$596$			3.99895e14i			0.217817i
$597$	−1.79322e15	−	1.77732e15i	−0.967774	−	0.959197i
$598$	−3.70012e13	+	2.13627e13i	−0.0197861	+	0.0114235i
$599$	−1.15539e15	+	6.67064e14i	−0.612182	+	0.353443i	−0.773819	−	0.633407i	$-0.781656\pi$
$599$	−1.15539e15	+	6.67064e14i	−0.612182	+	0.353443i	0.161637	+	0.986850i	$0.448323\pi$
$600$	−7.17370e13	−	7.11012e13i	−0.0376627	−	0.0373289i
$601$			3.47430e15i			1.80741i	0.428151	+	0.903707i	$0.359165\pi$
$601$			3.47430e15i			1.80741i	−0.428151	+	0.903707i	$0.640835\pi$
$602$	−1.46919e14	−	1.76926e15i	−0.0757350	−	0.912035i
$603$	−1.32829e15	−	7.51207e14i	−0.678499	−	0.383720i
$604$	−1.16729e14	+	2.02181e14i	−0.0590849	+	0.102338i
$605$	8.71932e14	+	1.51023e15i	0.437349	+	0.757510i
$606$	−1.65241e15	+	4.50652e14i	−0.821329	+	0.223997i
$607$	−2.06798e15	−	1.19395e15i	−1.01861	−	0.588096i	−0.104910	−	0.994482i	$-0.533456\pi$
$607$	−2.06798e15	−	1.19395e15i	−1.01861	−	0.588096i	−0.913702	+	0.406386i	$0.866789\pi$
$608$	−3.12322e14			−0.152452
$609$	9.85261e13	+	8.26676e13i	0.0476603	+	0.0399890i
$610$	−6.25679e14			−0.299942
$611$	6.19245e12	+	3.57521e12i	0.00294195	+	0.00169854i
$612$	−1.46469e13	−	1.64543e15i	−0.00689623	−	0.774722i
$613$	−5.24528e14	−	9.08509e14i	−0.244757	−	0.423932i	0.717306	−	0.696758i	$-0.245375\pi$
$613$	−5.24528e14	−	9.08509e14i	−0.244757	−	0.423932i	−0.962063	+	0.272826i	$0.912042\pi$
$614$	1.20373e15	−	2.08493e15i	0.556678	−	0.964194i
$615$	−3.79262e14	−	9.98159e13i	−0.173831	−	0.0457495i
$616$	7.51797e13	−	1.59382e14i	0.0341513	−	0.0724010i
$617$		−	3.58079e14i		−	0.161217i	−0.996746	−	0.0806084i	$-0.974314\pi$
$617$		−	3.58079e14i		−	0.161217i	0.996746	−	0.0806084i	$-0.0256863\pi$
$618$	1.09142e15	−	1.10118e15i	0.487032	−	0.491386i
$619$	−2.08818e15	+	1.20561e15i	−0.923567	+	0.533222i	−0.884771	−	0.466025i	$-0.845686\pi$
$619$	−2.08818e15	+	1.20561e15i	−0.923567	+	0.533222i	−0.0387958	+	0.999247i	$0.512352\pi$
$620$	−1.51105e15	+	8.72405e14i	−0.662406	+	0.382440i
$621$	5.31285e14	+	1.88191e15i	0.230847	+	0.817701i
$622$			2.70374e15i			1.16444i
$623$	3.87632e15	−	3.21888e14i	1.65476	−	0.137411i
$624$	−5.71836e12	+	2.17275e13i	−0.00241967	+	0.00919381i
$625$	9.86481e14	−	1.70863e15i	0.413760	−	0.716653i
$626$	4.84601e14	+	8.39354e14i	0.201477	+	0.348968i
$627$	−1.24663e14	−	4.57102e14i	−0.0513768	−	0.188383i
$628$	2.27276e14	+	1.31218e14i	0.0928484	+	0.0536061i
$629$	1.89622e15			0.767909
$630$	−1.61711e15	+	1.48789e14i	−0.649184	+	0.0597309i
$631$	−2.36463e15			−0.941028			−0.470514	−	0.882393i	$-0.655931\pi$
$631$	−2.36463e15			−0.941028			−0.470514	+	0.882393i	$0.655931\pi$
$632$	6.02933e14	+	3.48104e14i	0.237862	+	0.137330i
$633$	8.64210e14	+	3.16879e15i	0.337986	+	1.23929i
$634$	−1.22130e15	−	2.11535e15i	−0.473511	−	0.820145i
$635$	−1.91559e15	+	3.31790e15i	−0.736287	+	1.27529i
$636$	−5.70050e14	+	2.16597e15i	−0.217219	+	0.825350i
$637$	9.42834e13	+	3.52627e13i	0.0356179	+	0.0133213i
$638$			2.65951e13i			0.00996067i
$639$	−9.21910e14	−	1.56447e15i	−0.342321	−	0.580914i
$640$	−1.91703e14	+	1.10680e14i	−0.0705731	+	0.0407454i
$641$	2.28339e15	−	1.31831e15i	0.833413	−	0.481171i	−0.0216069	−	0.999767i	$-0.506878\pi$
$641$	2.28339e15	−	1.31831e15i	0.833413	−	0.481171i	0.855020	+	0.518595i	$0.173545\pi$
$642$	−1.78182e15	+	1.79775e15i	−0.644795	+	0.650560i
$643$			2.28595e14i			0.0820173i	0.999159	+	0.0410087i	$0.0130571\pi$
$643$			2.28595e14i			0.0820173i	−0.999159	+	0.0410087i	$0.986943\pi$
$644$	9.81272e14	−	6.80655e14i	0.349074	−	0.242133i
$645$	−3.27166e15	−	8.61049e14i	−1.15396	−	0.303703i
$646$	−1.35093e15	+	2.33989e15i	−0.472450	+	0.818307i
$647$	−7.55679e14	−	1.30888e15i	−0.262038	−	0.453863i	0.704745	−	0.709460i	$-0.251061\pi$
$647$	−7.55679e14	−	1.30888e15i	−0.262038	−	0.453863i	−0.966783	+	0.255597i	$0.917728\pi$
$648$	8.99541e14	+	4.98213e14i	0.309285	+	0.171298i
$649$	−4.58906e14	−	2.64950e14i	−0.156451	−	0.0903270i
$650$	1.19304e13			0.00403302
$651$	8.59395e14	−	4.87483e15i	0.288070	−	1.63405i
$652$	2.35141e15			0.781568
$653$	2.88975e15	+	1.66840e15i	0.952440	+	0.549892i	0.893838	−	0.448390i	$-0.148002\pi$
$653$	2.88975e15	+	1.66840e15i	0.952440	+	0.549892i	0.0586020	+	0.998281i	$0.481336\pi$
$654$	−8.23661e14	+	2.24633e14i	−0.269198	+	0.0734169i
$655$	−1.41628e15	−	2.45307e15i	−0.459009	−	0.795028i
$656$	7.58292e13	−	1.31340e14i	0.0243706	−	0.0422111i
$657$	−2.59107e15	+	4.58157e15i	−0.825790	+	1.46017i
$658$	−1.80763e14	−	8.52653e13i	−0.0571305	−	0.0269482i
$659$		−	8.58039e14i		−	0.268929i	−0.990918	−	0.134464i	$-0.957069\pi$
$659$		−	8.58039e14i		−	0.268929i	0.990918	−	0.134464i	$-0.0429314\pi$
$660$	−2.38505e14	−	2.36392e14i	−0.0741321	−	0.0734751i
$661$	1.14074e15	−	6.58609e14i	0.351625	−	0.203011i	−0.313776	−	0.949497i	$-0.601594\pi$
$661$	1.14074e15	−	6.58609e14i	0.351625	−	0.203011i	0.665401	+	0.746486i	$0.268261\pi$
$662$	−3.68620e15	+	2.12823e15i	−1.12683	+	0.650577i
$663$	1.38046e14	+	1.36823e14i	0.0418505	+	0.0414796i
$664$			1.27817e15i			0.384293i
$665$	2.41166e15	+	1.13757e15i	0.719112	+	0.339202i
$666$	−5.83330e14	+	1.03145e15i	−0.172507	+	0.305029i
$667$	−9.01152e13	+	1.56084e14i	−0.0264305	+	0.0457790i
$668$	−8.58133e14	−	1.48633e15i	−0.249623	−	0.432359i
$669$	2.70007e15	−	7.36376e14i	0.778988	−	0.212450i
$670$	1.53798e15	+	8.87951e14i	0.440087	+	0.254084i
$671$	3.67051e14			0.104172
$672$	1.09029e14	−	6.18458e14i	0.0306911	−	0.174092i
$673$	−2.60116e13			−0.00726246			−0.00363123	−	0.999993i	$-0.501156\pi$
$673$	−2.60116e13			−0.00726246			−0.00363123	+	0.999993i	$0.501156\pi$
$674$	1.82698e15	+	1.05480e15i	0.505945	+	0.292107i
$675$	1.34269e14	−	5.29266e14i	0.0368811	−	0.145379i
$676$	9.16259e14	+	1.58701e15i	0.249638	+	0.432387i
$677$	−1.94152e15	+	3.36280e15i	−0.524691	+	0.908791i	0.474896	+	0.880042i	$0.342486\pi$
$677$	−1.94152e15	+	3.36280e15i	−0.524691	+	0.908791i	−0.999587	+	0.0287489i	$0.990848\pi$
$678$	−2.00443e15	−	5.27535e14i	−0.537313	−	0.141413i
$679$	3.38410e15	−	2.34737e15i	0.899828	−	0.624162i
$680$			1.91496e15i			0.505082i
$681$	1.96990e15	−	1.98751e15i	0.515389	−	0.519997i
$682$	8.86449e14	−	5.11791e14i	0.230059	−	0.132825i
$683$	4.49772e15	−	2.59676e15i	1.15792	−	0.668525i	0.207115	−	0.978317i	$-0.433593\pi$
$683$	4.49772e15	−	2.59676e15i	1.15792	−	0.668525i	0.950804	+	0.309792i	$0.100259\pi$
$684$	−8.57202e14	−	1.45466e15i	−0.218915	−	0.371495i
$685$		−	4.54343e15i		−	1.15103i
$686$	−2.70787e15	−	7.64170e14i	−0.680528	−	0.192047i
$687$	1.09859e15	−	4.17422e15i	0.273888	−	1.04067i
$688$	6.54131e14	−	1.13299e15i	0.161781	−	0.280214i
$689$	−1.32277e14	−	2.29111e14i	−0.0324548	−	0.0562134i
$690$	−5.98771e14	−	2.19551e15i	−0.145744	−	0.534399i
$691$	3.85121e15	+	2.22350e15i	0.929968	+	0.536918i	0.886802	−	0.462150i	$-0.152922\pi$
$691$	3.85121e15	+	2.22350e15i	0.929968	+	0.536918i	0.0431669	+	0.999068i	$0.486255\pi$
$692$	−2.07854e15			−0.497937
$693$	9.48671e14	−	8.72864e13i	0.225467	−	0.0207450i
$694$	−2.17548e15			−0.512954
$695$	−2.80681e15	−	1.62051e15i	−0.656593	−	0.379084i
$696$	2.49369e13	+	9.14360e13i	0.00578751	+	0.0212210i
$697$	−6.55993e14	−	1.13621e15i	−0.151049	−	0.261625i
$698$	2.46819e15	−	4.27502e15i	0.563862	−	0.976638i
$699$	6.15683e14	−	2.33936e15i	0.139551	−	0.530239i
$700$	−3.32326e14	+	2.75962e13i	−0.0747351	+	0.00620597i
$701$			4.22211e15i			0.942064i	0.882116	+	0.471032i	$0.156118\pi$
$701$			4.22211e15i			0.942064i	−0.882116	+	0.471032i	$0.843882\pi$
$702$	−1.16892e14	+	3.30001e13i	−0.0258781	+	0.00730569i
$703$	1.68503e15	−	9.72854e14i	0.370130	−	0.213695i
$704$	1.12461e14	−	6.49297e13i	0.0245106	−	0.0141512i
$705$	−2.68104e14	+	2.70501e14i	−0.0579781	+	0.0584964i
$706$		−	8.33616e14i		−	0.178871i
$707$	−2.41244e15	+	5.11439e15i	−0.513629	+	1.08890i
$708$	−1.82618e15	−	4.80623e14i	−0.385799	−	0.101536i
$709$	−7.07511e13	+	1.22545e14i	−0.0148313	+	0.0256886i	−0.873346	−	0.487101i	$-0.838054\pi$
$709$	−7.07511e13	+	1.22545e14i	−0.0148313	+	0.0256886i	0.858515	+	0.512789i	$0.171388\pi$
$710$	1.05664e15	+	1.83015e15i	0.219788	+	0.380685i
$711$	3.35020e13	+	3.76362e15i	0.00691493	+	0.776824i
$712$	2.48230e15	+	1.43315e15i	0.508410	+	0.293530i
$713$	6.93663e15			1.40980
$714$	−4.16183e15	−	3.49195e15i	−0.839353	−	0.704252i
$715$	3.96651e13			0.00793826
$716$	2.10447e15	+	1.21502e15i	0.417947	+	0.241302i
$717$	1.87829e15	−	5.12258e14i	0.370176	−	0.100956i
$718$	2.02166e15	+	3.50162e15i	0.395388	+	0.684832i
$719$	2.92451e15	−	5.06540e15i	0.567603	−	0.983117i	−0.429199	−	0.903210i	$-0.641204\pi$
$719$	2.92451e15	−	5.06540e15i	0.567603	−	0.983117i	0.996802	−	0.0799073i	$-0.0254624\pi$
$720$	−1.04165e15	−	5.89097e14i	−0.200629	−	0.113464i
$721$	−4.23609e14	−	5.10129e15i	−0.0809695	−	0.975071i
$722$		−	9.55300e14i		−	0.181211i
$723$	−2.47009e15	−	2.44820e15i	−0.464999	−	0.460878i
$724$	1.60406e15	−	9.26107e14i	0.299681	−	0.173021i
$725$	4.35839e13	−	2.51632e13i	0.00808104	−	0.00466559i
$726$	−2.58935e15	−	2.56640e15i	−0.476474	−	0.472251i
$727$			3.20154e15i			0.584682i	0.956314	+	0.292341i	$0.0944342\pi$
$727$			3.20154e15i			0.584682i	−0.956314	+	0.292341i	$0.905566\pi$
$728$	4.22780e13	+	6.09505e13i	0.00766288	+	0.0110473i
$729$	1.48431e14	+	5.55708e15i	0.0267008	+	0.999643i
$730$	3.06273e15	−	5.30481e15i	0.546806	−	0.947095i
$731$	−5.65884e15	−	9.80140e15i	−1.00272	−	1.73677i
$732$	1.26195e15	−	3.44165e14i	0.221937	−	0.0605279i
$733$	5.38978e15	+	3.11179e15i	0.940805	+	0.543174i	0.890213	−	0.455545i	$-0.150556\pi$
$733$	5.38978e15	+	3.11179e15i	0.940805	+	0.543174i	0.0505924	+	0.998719i	$0.483889\pi$
$734$	−3.36233e15			−0.582521
$735$	−3.09450e15	+	4.37844e15i	−0.532121	+	0.752903i
$736$	8.80033e14			0.150200
$737$	−9.02245e14	−	5.20912e14i	−0.152846	−	0.0882456i
$738$	8.19848e14	−	7.29791e12i	0.137855	−	0.00122712i
$739$	−3.78337e15	−	6.55299e15i	−0.631444	−	1.09369i	−0.987257	−	0.159136i	$-0.949129\pi$
$739$	−3.78337e15	−	6.55299e15i	−0.631444	−	1.09369i	0.355813	−	0.934557i	$-0.384204\pi$
$740$	6.89516e14	−	1.19428e15i	0.114227	−	0.197847i
$741$	1.92869e14	+	5.07602e13i	0.0317148	+	0.00834686i
$742$	4.21460e15	+	6.07601e15i	0.687915	+	0.991739i
$743$		−	2.66450e15i		−	0.431695i	−0.976427	−	0.215848i	$-0.930749\pi$
$743$		−	2.66450e15i		−	0.431695i	0.976427	−	0.215848i	$-0.0692514\pi$
$744$	2.56779e15	−	2.59075e15i	0.412961	−	0.416653i
$745$	2.17884e15	−	1.25795e15i	0.347829	−	0.200819i
$746$	−5.49917e15	+	3.17494e15i	−0.871432	+	0.503121i
$747$	−5.95315e15	+	3.50807e15i	−0.936447	+	0.551830i
$748$		−	1.12340e15i		−	0.175419i
$749$	6.91570e14	+	8.32819e15i	0.107198	+	1.29092i
$750$	−1.24007e15	+	4.71177e15i	−0.190813	+	0.725016i
$751$	−3.54975e15	+	6.14835e15i	−0.542223	+	0.939158i	0.456553	+	0.889696i	$0.349084\pi$
$751$	−3.54975e15	+	6.14835e15i	−0.542223	+	0.939158i	−0.998776	+	0.0494618i	$0.984249\pi$
$752$	−7.36402e13	−	1.27549e14i	−0.0111665	−	0.0193409i
$753$	−1.02062e15	−	3.74230e15i	−0.153635	−	0.563335i
$754$	−9.69497e12	−	5.59739e12i	−0.00144879	−	0.000836457i
$755$	1.46879e15			0.217896
$756$	3.17975e15	−	1.18962e15i	0.468300	−	0.175201i
$757$	8.44083e14			0.123412			0.0617061	−	0.998094i	$-0.480346\pi$
$757$	8.44083e14			0.123412			0.0617061	+	0.998094i	$0.480346\pi$
$758$	4.37402e15	+	2.52534e15i	0.634892	+	0.366555i
$759$	3.51265e14	+	1.28798e15i	0.0506181	+	0.185601i
$760$	9.82472e14	+	1.70169e15i	0.140555	+	0.243448i
$761$	−8.90473e14	+	1.54234e15i	−0.126475	+	0.219061i	−0.922309	−	0.386454i	$-0.873700\pi$
$761$	−8.90473e14	+	1.54234e15i	−0.126475	+	0.219061i	0.795833	+	0.605516i	$0.207033\pi$
$762$	2.03854e15	−	7.74566e15i	0.287453	−	1.09221i
$763$	−1.20251e15	+	2.54933e15i	−0.168346	+	0.356895i
$764$			1.08830e15i			0.151263i
$765$	−8.91908e15	+	5.25584e15i	−1.23079	+	0.725278i
$766$	−4.72774e15	+	2.72956e15i	−0.647732	+	0.373968i
$767$	1.93169e14	−	1.11526e14i	0.0262762	−	0.0151706i
$768$	3.25769e14	−	3.28682e14i	0.0439970	−	0.0443904i
$769$		−	2.71335e15i		−	0.363841i	−0.983313	−	0.181920i	$-0.941769\pi$
$769$		−	2.71335e15i		−	0.363841i	0.983313	−	0.181920i	$-0.0582313\pi$
$770$	−1.10489e15	+	9.17496e13i	−0.147102	+	0.0122153i
$771$	1.42984e16	+	3.76311e15i	1.89011	+	0.497448i
$772$	−2.03869e15	+	3.53111e15i	−0.267581	+	0.463465i
$773$	−2.63341e15	−	4.56119e15i	−0.343187	−	0.594417i	0.641836	−	0.766842i	$-0.278173\pi$
$773$	−2.63341e15	−	4.56119e15i	−0.343187	−	0.594417i	−0.985023	+	0.172425i	$0.944840\pi$
$774$	7.07232e15	−	6.29545e13i	0.915138	−	0.00814614i
$775$	−1.67744e15	−	9.68471e14i	−0.215520	−	0.124431i
$776$	3.03496e15			0.387180
$777$	1.33821e15	+	3.67631e15i	0.169515	+	0.465690i
$778$	−7.28276e14			−0.0916027
$779$	−1.16587e15	−	6.73114e14i	−0.145611	−	0.0840684i
$780$	1.36371e14	−	3.71919e13i	0.0169123	−	0.00461241i
$781$	−6.19870e14	−	1.07365e15i	−0.0763343	−	0.132215i
$782$	3.80655e15	−	6.59313e15i	0.465473	−	0.806222i
$783$	−3.57428e14	+	3.67102e14i	−0.0434009	+	0.0445756i
$784$	−1.31866e15	−	1.60001e15i	−0.158999	−	0.192923i
$785$		−	1.65109e15i		−	0.197691i
$786$	4.20588e15	+	4.16860e15i	0.500072	+	0.495640i
$787$	−4.19434e15	+	2.42160e15i	−0.495225	+	0.285918i	−0.726739	−	0.686913i	$-0.758965\pi$
$787$	−4.19434e15	+	2.42160e15i	−0.495225	+	0.285918i	0.231515	+	0.972831i	$0.425632\pi$
$788$	−3.94267e14	+	2.27630e14i	−0.0462271	+	0.0266892i
$789$	−1.11350e14	−	1.10364e14i	−0.0129649	−	0.0128500i
$790$		−	4.38013e15i		−	0.506452i
$791$	−5.62286e15	+	3.90027e15i	−0.645635	+	0.447841i
$792$	6.11078e14	+	3.45590e14i	0.0696800	+	0.0394070i
$793$	−7.72520e13	+	1.33804e14i	−0.00874797	+	0.0151519i
$794$	1.17589e15	+	2.03670e15i	0.132237	+	0.229041i
$795$	1.35945e16	−	3.70757e15i	1.51826	−	0.414067i
$796$	−5.31970e15	−	3.07133e15i	−0.590018	−	0.340647i
$797$	5.77447e15			0.636050			0.318025	−	0.948082i	$-0.396980\pi$
$797$	5.77447e15			0.636050			0.318025	+	0.948082i	$0.396980\pi$
$798$	−5.48987e15	−	9.67822e14i	−0.600546	−	0.105872i
$799$	−1.27411e15			−0.138420
$800$	−2.12813e14	−	1.22867e14i	−0.0229616	−	0.0132569i
$801$	1.37929e14	+	1.54949e16i	0.0147801	+	1.66039i
$802$	1.05434e15	+	1.82617e15i	0.112207	+	0.194348i
$803$	−1.79673e15	+	3.11203e15i	−0.189910	+	0.328934i
$804$	−3.59042e15	−	9.44942e14i	−0.376909	−	0.0991967i
$805$	−6.79536e15	−	3.20535e15i	−0.708493	−	0.334193i
$806$			4.30860e14i			0.0446163i
$807$	−5.80501e15	+	5.85691e15i	−0.597033	+	0.602372i
$808$	−3.60877e15	+	2.08352e15i	−0.368635	+	0.212832i
$809$	−1.41977e16	+	8.19706e15i	−1.44046	+	0.831651i	−0.997880	−	0.0650776i	$-0.979271\pi$
$809$	−1.41977e16	+	8.19706e15i	−1.44046	+	0.831651i	−0.442581	+	0.896728i	$0.645937\pi$
$810$	−1.15167e14	−	6.46840e15i	−0.0116054	−	0.651823i
$811$		−	2.49306e15i		−	0.249527i	−0.992187	−	0.124764i	$-0.960183\pi$
$811$		−	2.49306e15i		−	0.249527i	0.992187	−	0.124764i	$-0.0398172\pi$
$812$	2.83005e14	+	1.33492e14i	0.0281343	+	0.0132708i
$813$	3.12049e15	−	1.18566e16i	0.308123	−	1.17075i
$814$	−4.04501e14	+	7.00615e14i	−0.0396721	+	0.0687140i
$815$	−7.39685e15	−	1.28117e16i	−0.720576	−	1.24807i
$816$	−1.05336e15	−	3.86234e15i	−0.101925	−	0.373727i
$817$	−1.00572e16	−	5.80654e15i	−0.966622	−	0.558079i
$818$	8.45057e15			0.806757
$819$	−1.67844e14	+	3.64199e14i	−0.0159164	+	0.0345364i
$820$	−9.54147e14			−0.0898750
$821$	−1.42794e16	−	8.24421e15i	−1.33605	−	0.771368i	−0.349830	−	0.936813i	$-0.613761\pi$
$821$	−1.42794e16	−	8.24421e15i	−1.33605	−	0.771368i	−0.986219	+	0.165445i	$0.947094\pi$
$822$	2.49918e15	+	9.16375e15i	0.232275	+	0.851683i
$823$	−1.81011e15	−	3.13520e15i	−0.167111	−	0.289445i	0.770292	−	0.637692i	$-0.220111\pi$
$823$	−1.81011e15	−	3.13520e15i	−0.167111	−	0.289445i	−0.937403	+	0.348247i	$0.886777\pi$
$824$	1.88605e15	−	3.26673e15i	0.172963	−	0.299581i
$825$	9.48800e13	−	3.60507e14i	0.00864327	−	0.0328411i
$826$	−5.12284e15	+	3.55343e15i	−0.463575	+	0.321557i
$827$		−	2.76850e15i		−	0.248865i	−0.992228	−	0.124432i	$-0.960289\pi$
$827$		−	2.76850e15i		−	0.248865i	0.992228	−	0.124432i	$-0.0397110\pi$
$828$	2.41535e15	+	4.09882e15i	0.215682	+	0.366009i
$829$	−1.08020e16	+	6.23655e15i	−0.958198	+	0.553216i	−0.895618	−	0.444824i	$-0.853266\pi$
$829$	−1.08020e16	+	6.23655e15i	−0.958198	+	0.553216i	−0.0625798	+	0.998040i	$0.519933\pi$
$830$	6.96412e15	−	4.02074e15i	0.613672	−	0.354304i
$831$	−2.27041e15	+	2.29072e15i	−0.198747	+	0.200524i
$832$			5.46621e13i			0.00475344i
$833$	−1.76910e16	+	2.95850e15i	−1.52828	+	0.255578i
$834$	6.55251e15	+	1.72452e15i	0.562334	+	0.147998i
$835$	−5.39887e15	+	9.35113e15i	−0.460286	+	0.797238i
$836$	−5.76362e14	−	9.98288e14i	−0.0488158	−	0.0845515i
$837$	1.91142e16	+	4.84906e15i	1.60830	+	0.408007i
$838$	9.59497e15	+	5.53966e15i	0.802050	+	0.463064i
$839$	−6.58933e14			−0.0547205			−0.0273603	−	0.999626i	$-0.508710\pi$
$839$	−6.58933e14			−0.0547205			−0.0273603	+	0.999626i	$0.508710\pi$
$840$	−3.71266e15	+	1.35144e15i	−0.306301	+	0.111496i
$841$	1.21533e16			0.996129
$842$	−4.22706e15	−	2.44049e15i	−0.344209	−	0.198729i
$843$	2.19294e16	−	5.98070e15i	1.77409	−	0.483839i
$844$	3.99554e15	+	6.92048e15i	0.321138	+	0.556228i
$845$	5.76457e15	−	9.98453e15i	0.460315	−	0.797289i
$846$	3.91953e14	−	6.93056e14i	0.0310954	−	0.0549834i
$847$	−1.19953e16	+	9.96085e14i	−0.945480	+	0.0785123i
$848$			5.44914e15i			0.426728i
$849$	5.75964e15	+	5.70860e15i	0.448129	+	0.444158i
$850$	−1.84102e15	+	1.06292e15i	−0.142317	+	0.0821665i
$851$	−4.74794e15	+	2.74123e15i	−0.364664	+	0.210539i
$852$	−3.13786e15	−	3.11005e15i	−0.239450	−	0.237328i
$853$			4.28445e15i			0.324844i	0.986721	+	0.162422i	$0.0519306\pi$
$853$			4.28445e15i			0.324844i	−0.986721	+	0.162422i	$0.948069\pi$
$854$	1.84239e15	−	3.90588e15i	0.138791	−	0.294239i
$855$	−5.22924e15	+	9.24643e15i	−0.391404	+	0.692086i
$856$	−3.07910e15	+	5.33316e15i	−0.228991	+	0.396624i
$857$	−3.17413e15	−	5.49776e15i	−0.234547	−	0.406248i	0.724594	−	0.689176i	$-0.242027\pi$
$857$	−3.17413e15	−	5.49776e15i	−0.234547	−	0.406248i	−0.959141	+	0.282928i	$0.908694\pi$
$858$	−8.00015e13	+	2.18184e13i	−0.00587378	+	0.00160193i
$859$	−6.45134e15	−	3.72468e15i	−0.470638	−	0.271723i	0.245869	−	0.969303i	$-0.420927\pi$
$859$	−6.45134e15	−	3.72468e15i	−0.470638	−	0.271723i	−0.716507	+	0.697580i	$0.754260\pi$
$860$	−8.23083e15			−0.596626
$861$	1.73989e15	−	2.07367e15i	0.125316	−	0.149356i
$862$	1.30491e16			0.933882
$863$	2.11534e16	+	1.22129e16i	1.50425	+	0.868479i	0.999988	+	0.00492813i	$0.00156868\pi$
$863$	2.11534e16	+	1.22129e16i	1.50425	+	0.868479i	0.504262	+	0.863551i	$0.331765\pi$
$864$	2.42497e15	+	6.15188e14i	0.171349	+	0.0434693i
$865$	6.53847e15	+	1.13250e16i	0.459079	+	0.795148i
$866$	−7.74594e15	+	1.34164e16i	−0.540413	+	0.936022i
$867$	−1.95430e16	−	5.14341e15i	−1.35483	−	0.356571i
$868$	−9.96625e14	−	1.20018e16i	−0.0686552	−	0.826777i
$869$			2.56958e15i			0.175895i
$870$	4.19747e14	−	4.23500e14i	0.0285517	−	0.0288070i
$871$	3.79785e14	−	2.19269e14i	0.0256707	−	0.0148210i
$872$	−1.79883e15	+	1.03856e15i	−0.120823	+	0.0697573i
$873$	8.32979e15	+	1.41355e16i	0.555976	+	0.943483i
$874$		−	7.81180e15i		−	0.518129i
$875$	9.16829e15	+	1.32176e16i	0.604288	+	0.871178i
$876$	−3.25930e15	+	1.23841e16i	−0.213478	+	0.811132i
$877$	1.30164e16	−	2.25451e16i	0.847215	−	1.46742i	−0.0364695	−	0.999335i	$-0.511611\pi$
$877$	1.30164e16	−	2.25451e16i	0.847215	−	1.46742i	0.883684	−	0.468084i	$-0.155055\pi$
$878$	−2.92539e15	−	5.06693e15i	−0.189219	−	0.327736i
$879$	−7.48649e15	−	2.74507e16i	−0.481215	−	1.76447i
$880$	−7.07542e14	−	4.08500e14i	−0.0451957	−	0.0260938i
$881$	1.18729e15			0.0753684			0.0376842	−	0.999290i	$-0.488002\pi$
$881$	1.18729e15			0.0753684			0.0376842	+	0.999290i	$0.488002\pi$
$882$	3.83295e15	−	1.05332e16i	0.241800	−	0.664479i
$883$	2.34944e16			1.47293			0.736463	−	0.676477i	$-0.236494\pi$
$883$	2.34944e16			1.47293			0.736463	+	0.676477i	$0.236494\pi$
$884$	4.09524e14	+	2.36439e14i	0.0255148	+	0.0147310i
$885$	3.12595e15	+	1.14619e16i	0.193550	+	0.709690i
$886$	3.73761e15	+	6.47372e15i	0.229989	+	0.398353i
$887$	−1.19962e16	+	2.07780e16i	−0.733606	+	1.27064i	0.221726	+	0.975109i	$0.428831\pi$
$887$	−1.19962e16	+	2.07780e16i	−0.733606	+	1.27064i	−0.955332	+	0.295534i	$0.904502\pi$
$888$	−7.33771e14	+	2.78804e15i	−0.0445953	+	0.169445i
$889$	−1.50717e16	−	2.17283e16i	−0.910338	−	1.31240i
$890$		−	1.80331e16i		−	1.08250i
$891$	6.75619e13	+	3.79465e15i	0.00403064	+	0.226383i
$892$	5.89681e15	−	3.40452e15i	0.349631	−	0.201860i
$893$	−1.13221e15	+	6.53683e14i	−0.0667182	+	0.0385198i
$894$	−3.70260e15	+	3.73571e15i	−0.216845	+	0.218784i
$895$		−	1.52883e16i		−	0.889885i
$896$	−1.26439e14	−	1.52264e15i	−0.00731456	−	0.0880852i
$897$	−5.43450e14	−	1.43028e14i	−0.0312465	−	0.00822360i
$898$	5.91284e15	−	1.02413e16i	0.337891	−	0.585244i
$899$	9.08759e14	+	1.57402e15i	0.0516144	+	0.0893987i
$900$	−1.18249e13	−	1.32841e15i	−0.000667521	−	0.0749893i
$901$	4.08245e16	+	2.35700e16i	2.29052	+	1.32243i
$902$	5.59745e14			0.0312143
$903$	1.50090e16	−	1.78882e16i	0.831895	−	0.991482i
$904$	−5.04274e15			−0.277805
$905$	−1.00918e16	−	5.82653e15i	−0.552590	−	0.319038i
$906$	−2.96243e15	+	8.07929e14i	−0.161229	+	0.0439712i
$907$	9.48785e15	+	1.64334e16i	0.513249	+	0.888973i	0.999882	+	0.0153664i	$0.00489149\pi$
$907$	9.48785e15	+	1.64334e16i	0.513249	+	0.888973i	−0.486633	+	0.873606i	$0.661775\pi$
$908$	3.40411e15	−	5.89609e15i	0.183034	−	0.317024i
$909$	−1.96088e16	−	1.10896e16i	−1.04797	−	0.592674i
$910$	1.99096e14	−	4.22085e14i	0.0105763	−	0.0224219i
$911$		−	3.72765e16i		−	1.96827i	−0.177427	−	0.984134i	$-0.556777\pi$
$911$		−	3.72765e16i		−	1.96827i	0.177427	−	0.984134i	$-0.443223\pi$
$912$	−2.91762e15	−	2.89176e15i	−0.153129	−	0.151772i
$913$	−4.08546e15	+	2.35874e15i	−0.213133	+	0.123053i
$914$	−2.15158e16	+	1.24221e16i	−1.11571	+	0.644158i
$915$	−5.84491e15	−	5.79311e15i	−0.301274	−	0.298604i
$916$		−	1.05015e16i		−	0.538054i
$917$	1.94840e16	−	1.61794e15i	0.992307	−	0.0824008i
$918$	1.50981e16	−	1.55067e16i	0.764340	−	0.785028i
$919$	−1.21826e16	+	2.11010e16i	−0.613064	+	1.06186i	0.377656	+	0.925946i	$0.376730\pi$
$919$	−1.21826e16	+	2.11010e16i	−0.613064	+	1.06186i	−0.990721	+	0.135913i	$0.956603\pi$
$920$	−2.76833e15	−	4.79488e15i	−0.138479	−	0.239853i
$921$	3.05491e16	−	8.33150e15i	1.51904	−	0.414281i
$922$	−2.08109e15	−	1.20152e15i	−0.102866	−	0.0593894i
$923$	5.21848e14			0.0256410
$924$	2.17801e15	−	7.92814e14i	0.106381	−	0.0387236i
$925$	1.53089e15			0.0743298
$926$	1.24428e16	+	7.18386e15i	0.600563	+	0.346735i
$927$	2.03915e16	−	1.81516e14i	0.978389	−	0.00870917i
$928$	1.15292e14	+	1.99692e14i	0.00549902	+	0.00952458i
$929$	1.53945e16	−	2.66641e16i	0.729927	−	1.26427i	−0.226987	−	0.973898i	$-0.572887\pi$
$929$	1.53945e16	−	2.66641e16i	0.729927	−	1.26427i	0.956914	−	0.290373i	$-0.0937793\pi$
$930$	−2.21933e16	−	5.84094e15i	−1.04608	−	0.275313i
$931$	−1.42028e16	+	1.17054e16i	−0.665506	+	0.548481i
$932$		−	5.88535e15i		−	0.274148i
$933$	−2.50337e16	+	2.52575e16i	−1.15925	+	1.16961i
$934$	−8.38307e15	+	4.83997e15i	−0.385918	+	0.222810i
$935$	−6.12089e15	+	3.53390e15i	−0.280124	+	0.161730i
$936$	−2.54593e14	+	1.50027e14i	−0.0115832	+	0.00682576i
$937$		−	3.06873e16i		−	1.38801i	−0.719972	−	0.694003i	$-0.755846\pi$
$937$		−	3.06873e16i		−	1.38801i	0.719972	−	0.694003i	$-0.244154\pi$
$938$	−1.00719e16	+	6.98633e15i	−0.452893	+	0.314147i
$939$	−3.24451e15	+	1.23279e16i	−0.145040	+	0.551096i
$940$	−4.63301e14	+	8.02461e14i	−0.0205902	+	0.0356632i
$941$	−1.88681e15	−	3.26805e15i	−0.0833651	−	0.144393i	0.821328	−	0.570456i	$-0.193233\pi$
$941$	−1.88681e15	−	3.26805e15i	−0.0833651	−	0.144393i	−0.904693	+	0.426063i	$0.859900\pi$
$942$	9.08208e14	+	3.33012e15i	0.0398938	+	0.146278i
$943$	3.28508e15	+	1.89664e15i	0.143460	+	0.0828269i
$944$	−4.59431e15			−0.199468
$945$	−1.64842e16	−	1.35828e16i	−0.711531	−	0.586292i
$946$	4.82857e15			0.207213
$947$	2.35239e16	+	1.35815e16i	1.00365	+	0.579460i	0.909328	−	0.416081i	$-0.136597\pi$
$947$	2.35239e16	+	1.35815e16i	1.00365	+	0.579460i	0.0943272	+	0.995541i	$0.469930\pi$
$948$	2.40936e15	+	8.83439e15i	0.102201	+	0.374741i
$949$	−7.56305e14	−	1.30996e15i	−0.0318958	−	0.0552451i
$950$	−1.09066e15	+	1.88908e15i	−0.0457308	+	0.0792081i
$951$	8.17684e15	−	3.10688e16i	0.340873	−	1.29519i
$952$	−1.19544e16	−	5.63884e15i	−0.495478	−	0.233715i
$953$		−	1.96766e16i		−	0.810846i	−0.914129	−	0.405423i	$-0.867124\pi$
$953$		−	1.96766e16i		−	0.810846i	0.914129	−	0.405423i	$-0.132876\pi$
$954$	−2.53798e16	+	1.49558e16i	−1.03985	+	0.612764i
$955$	5.92961e15	−	3.42346e15i	0.241550	−	0.139459i
$956$	4.10210e15	−	2.36835e15i	0.166145	−	0.0959239i
$957$	−2.46242e14	+	2.48444e14i	−0.00991624	+	0.0100049i
$958$			2.51113e16i			1.00545i
$959$	2.83629e16	+	1.33787e16i	1.12914	+	0.532611i
$960$	−2.81561e15	−	7.41025e14i	−0.111450	−	0.0293320i
$961$	2.22717e16	−	3.85757e16i	0.876546	−	1.51822i
$962$	−1.70268e14	−	2.94912e14i	−0.00666300	−	0.0115406i
$963$	−3.32905e16	+	2.96337e14i	−1.29532	+	0.0115303i
$964$	−7.32769e15	−	4.23064e15i	−0.283494	−	0.163675i
$965$	2.56525e16			0.986800
$966$	1.54689e16	+	2.72704e15i	0.591677	+	0.104308i
$967$	1.37805e16			0.524108			0.262054	−	0.965053i	$-0.415600\pi$
$967$	1.37805e16			0.524108			0.262054	+	0.965053i	$0.415600\pi$
$968$	−7.68148e15	−	4.43490e15i	−0.290489	−	0.167714i
$969$	−3.42849e16	+	9.35034e15i	−1.28920	+	0.351598i
$970$	−9.54709e15	−	1.65361e16i	−0.356966	−	0.618283i
$971$	3.05209e15	−	5.28637e15i	0.113473	−	0.196541i	−0.803695	−	0.595041i	$-0.797136\pi$
$971$	3.05209e15	−	5.28637e15i	0.113473	−	0.196541i	0.917168	+	0.398500i	$0.130469\pi$
$972$	3.79033e15	+	1.29829e16i	0.140124	+	0.479964i
$973$	1.83812e16	−	1.27500e16i	0.675700	−	0.468696i
$974$			2.38514e16i			0.871847i
$975$	1.11450e14	+	1.10462e14i	0.00405093	+	0.00401503i
$976$	2.75603e15	−	1.59119e15i	0.0996116	−	0.0575108i
$977$	−2.74613e16	+	1.58548e16i	−0.986962	+	0.569823i	−0.904365	−	0.426760i	$-0.859655\pi$
$977$	−2.74613e16	+	1.58548e16i	−0.986962	+	0.569823i	−0.0825975	+	0.996583i	$0.526322\pi$
$978$	2.19662e16	+	2.17715e16i	0.785038	+	0.778081i
$979$			1.05790e16i			0.375960i
$980$	−4.56958e15	+	1.22179e16i	−0.161485	+	0.431771i
$981$	−9.77426e15	−	5.52776e15i	−0.343482	−	0.194254i
$982$	6.96802e14	−	1.20690e15i	0.0243499	−	0.0421752i
$983$	3.61149e15	+	6.25528e15i	0.125499	+	0.217371i	0.921928	−	0.387361i	$-0.126613\pi$
$983$	3.61149e15	+	6.25528e15i	0.125499	+	0.217371i	−0.796429	+	0.604733i	$0.793280\pi$
$984$	1.92444e15	−	5.24844e14i	0.0665016	−	0.0181366i
$985$	2.48050e15	+	1.43212e15i	0.0852393	+	0.0492130i
$986$	1.99476e15			0.0681661
$987$	−8.99172e14	−	2.47020e15i	−0.0305562	−	0.0839435i
$988$	4.85220e14			0.0163974
$989$	2.83384e16	+	1.63612e16i	0.952347	+	0.549838i
$990$	−3.93146e13	−	4.41660e15i	−0.00131389	−	0.147603i
$991$	1.35586e16	+	2.34841e16i	0.450618	+	0.780494i	0.998425	−	0.0561115i	$-0.0178702\pi$
$991$	1.35586e16	+	2.34841e16i	0.450618	+	0.780494i	−0.547806	+	0.836605i	$0.684537\pi$
$992$	4.43731e15	−	7.68564e15i	0.146658	−	0.254019i
$993$	−5.41405e16	−	1.42489e16i	−1.77951	−	0.468340i
$994$	−1.45363e16	+	1.20709e15i	−0.475148	+	0.0394561i
$995$			3.86460e16i			1.25625i
$996$	−1.18344e16	+	1.19402e16i	−0.382579	+	0.386000i
$997$	−2.99627e16	+	1.72990e16i	−0.963290	+	0.556156i	−0.897184	−	0.441657i	$-0.854391\pi$
$997$	−2.99627e16	+	1.72990e16i	−0.963290	+	0.556156i	−0.0661060	+	0.997813i	$0.521058\pi$
$998$	−2.37340e16	+	1.37029e16i	−0.758846	+	0.438120i
$999$	−1.49994e16	+	4.23452e15i	−0.476941	+	0.134646i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.12.f.a.5.24	yes	60
3.2	odd	2	inner	42.12.f.a.5.4	✓	60
7.3	odd	6	inner	42.12.f.a.17.4	yes	60
21.17	even	6	inner	42.12.f.a.17.24	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.12.f.a.5.4	✓	60	3.2	odd	2	inner
42.12.f.a.5.24	yes	60	1.1	even	1	trivial
42.12.f.a.17.4	yes	60	7.3	odd	6	inner
42.12.f.a.17.24	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} +(110.742 + 406.058i) q^{3} +(512.000 + 886.810i) q^{4} +(3221.21 - 5579.29i) q^{5} +(-3427.95 + 13024.9i) q^{6} +(25344.2 + 36537.6i) q^{7} +32768.0i q^{8} +(-152619. + 89935.6i) q^{9} +(178537. - 103079. i) q^{10} +(-104738. + 60470.5i) q^{11} +(-303396. + 306109. i) q^{12} -50908.1i q^{13} +(117756. + 1.41807e6i) q^{14} +(2.62224e6 + 690133. i) q^{15} +(-524288. + 908093. i) q^{16} +(4.53557e6 + 7.85584e6i) q^{17} +(-5.66848e6 + 50458.2i) q^{18} +(8.06088e6 + 4.65395e6i) q^{19} +6.59703e6 q^{20} +(-1.20297e7 + 1.43375e7i) q^{21} -3.87011e6 q^{22} +(-2.27133e7 - 1.31135e7i) q^{23} +(-1.33057e7 + 3.62880e6i) q^{24} +(3.66173e6 + 6.34231e6i) q^{25} +(814529. - 1.41081e6i) q^{26} +(-5.34205e7 - 5.20126e7i) q^{27} +(-1.94257e7 + 4.11827e7i) q^{28} -6.87194e6i q^{29} +(6.16275e7 + 6.10814e7i) q^{30} +(-2.29050e8 + 1.32242e8i) q^{31} +(-2.90590e7 + 1.67772e7i) q^{32} +(-3.61534e7 - 3.58330e7i) q^{33} +2.90277e8i q^{34} +(2.85493e8 - 2.37072e7i) q^{35} +(-1.57897e8 - 8.92973e7i) q^{36} +(1.04519e8 - 1.81032e8i) q^{37} +(1.48927e8 + 2.57948e8i) q^{38} +(2.06716e7 - 5.63767e6i) q^{39} +(1.82822e8 + 1.05552e8i) q^{40} -1.44633e8 q^{41} +(-5.62777e8 + 2.04856e8i) q^{42} -1.24766e9 q^{43} +(-1.07252e8 - 6.19217e7i) q^{44} +(1.01585e7 + 1.14121e9i) q^{45} +(-4.19632e8 - 7.26824e8i) q^{46} +(-7.02288e7 + 1.21640e8i) q^{47} +(-4.26800e8 - 1.12327e8i) q^{48} +(-6.92673e8 + 1.85203e9i) q^{49} +2.34351e8i q^{50} +(-2.68765e9 + 2.71168e9i) q^{51} +(4.51458e7 - 2.60649e7i) q^{52} +(4.50048e9 - 2.59835e9i) q^{53} +(-6.48229e8 - 2.29614e9i) q^{54} +7.79151e8i q^{55} +(-1.19727e9 + 8.30478e8i) q^{56} +(-9.97095e8 + 3.78858e9i) q^{57} +(1.09951e8 - 1.90441e8i) q^{58} +(2.19074e9 + 3.79447e9i) q^{59} +(7.30570e8 + 2.67878e9i) q^{60} +(-2.62835e9 - 1.51748e9i) q^{61} -8.46349e9 q^{62} +(-7.15404e9 - 3.29701e9i) q^{63} -1.07374e9 q^{64} +(-2.84031e8 - 1.63985e8i) q^{65} +(-4.28585e8 - 1.57149e9i) q^{66} +(4.30716e9 + 7.46022e9i) q^{67} +(-4.64443e9 + 8.04439e9i) q^{68} +(2.80953e9 - 1.06751e10i) q^{69} +(8.29113e9 + 3.91089e9i) q^{70} +1.02508e10i q^{71} +(-2.94701e9 - 5.00103e9i) q^{72} +(2.57319e10 - 1.48563e10i) q^{73} +(5.79304e9 - 3.34461e9i) q^{74} +(-2.16984e9 + 2.18924e9i) q^{75} +9.53130e9i q^{76} +(-4.86394e9 - 2.29430e9i) q^{77} +(6.63072e8 + 1.74510e8i) q^{78} +(1.06233e10 - 1.84001e10i) q^{79} +(3.37768e9 + 5.85031e9i) q^{80} +(1.52043e10 - 2.74518e10i) q^{81} +(-4.00818e9 - 2.31412e9i) q^{82} +3.90065e10 q^{83} +(-1.88738e10 - 3.32731e9i) q^{84} +5.84401e10 q^{85} +(-3.45761e10 - 1.99625e10i) q^{86} +(2.79041e9 - 7.61014e8i) q^{87} +(-1.98150e9 - 3.43205e9i) q^{88} +(4.37364e10 - 7.57537e10i) q^{89} +(-1.79778e10 + 3.17886e10i) q^{90} +(1.86006e9 - 1.29022e9i) q^{91} -2.68565e10i q^{92} +(-7.90635e10 - 7.83628e10i) q^{93} +(-3.89247e9 + 2.24732e9i) q^{94} +(5.19315e10 - 2.99827e10i) q^{95} +(-1.00306e10 - 9.94169e9i) q^{96} -9.26196e10i q^{97} +(-4.88284e10 + 4.02423e10i) q^{98} +(1.05466e10 - 1.86486e10i) 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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