LMFDB - Embedded newform 48.9.l.a.43.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,9,Mod(19,48)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	48.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$19.5541732829$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.15
Character	$\chi$	$=$	48.43
Dual form			48.9.l.a.19.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.37796 + 15.8223i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-244.691 - 75.2496i) q^{4} +(508.668 + 508.668i) q^{5} +(-601.848 + 444.579i) q^{6} -3253.34 q^{7} +(1772.49 - 3692.63i) q^{8} +2187.00i q^{9} +O(q^{10})$	\(q+(-2.37796 + 15.8223i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-244.691 - 75.2496i) q^{4} +(508.668 + 508.668i) q^{5} +(-601.848 + 444.579i) q^{6} -3253.34 q^{7} +(1772.49 - 3692.63i) q^{8} +2187.00i q^{9} +(-9257.88 + 6838.70i) q^{10} +(6777.24 - 6777.24i) q^{11} +(-5603.10 - 10579.8i) q^{12} +(-26051.9 + 26051.9i) q^{13} +(7736.30 - 51475.3i) q^{14} +33641.4i q^{15} +(54211.0 + 36825.7i) q^{16} -155108. q^{17} +(-34603.4 - 5200.60i) q^{18} +(-98189.8 - 98189.8i) q^{19} +(-86189.2 - 162743. i) q^{20} +(-107582. - 107582. i) q^{21} +(91115.6 + 123348. i) q^{22} +440378. q^{23} +(180721. - 63495.5i) q^{24} +126860. i q^{25} +(-350251. - 474152. i) q^{26} +(-72320.0 + 72320.0i) q^{27} +(796061. + 244812. i) q^{28} +(480071. - 480071. i) q^{29} +(-532284. - 79997.7i) q^{30} -627305. i q^{31} +(-711579. + 770173. i) q^{32} +448221. q^{33} +(368839. - 2.45416e6i) q^{34} +(-1.65487e6 - 1.65487e6i) q^{35} +(164571. - 535138. i) q^{36} +(-1.48337e6 - 1.48337e6i) q^{37} +(1.78708e6 - 1.32010e6i) q^{38} -1.72298e6 q^{39} +(2.77993e6 - 976715. i) q^{40} +42321.1i q^{41} +(1.95802e6 - 1.44637e6i) q^{42} +(-1.53336e6 + 1.53336e6i) q^{43} +(-2.16831e6 + 1.14834e6i) q^{44} +(-1.11246e6 + 1.11246e6i) q^{45} +(-1.04720e6 + 6.96779e6i) q^{46} +8.84396e6i q^{47} +(574898. + 3.01041e6i) q^{48} +4.81940e6 q^{49} +(-2.00722e6 - 301669. i) q^{50} +(-5.12911e6 - 5.12911e6i) q^{51} +(8.33505e6 - 4.41426e6i) q^{52} +(-6.41564e6 - 6.41564e6i) q^{53} +(-972295. - 1.31624e6i) q^{54} +6.89473e6 q^{55} +(-5.76649e6 + 1.20134e7i) q^{56} -6.49390e6i q^{57} +(6.45424e6 + 8.73742e6i) q^{58} +(-9.15868e6 + 9.15868e6i) q^{59} +(2.53150e6 - 8.23172e6i) q^{60} +(-1.53578e7 + 1.53578e7i) q^{61} +(9.92541e6 + 1.49170e6i) q^{62} -7.11505e6i q^{63} +(-1.04938e7 - 1.30903e7i) q^{64} -2.65035e7 q^{65} +(-1.06585e6 + 7.09189e6i) q^{66} +(9.64762e6 + 9.64762e6i) q^{67} +(3.79534e7 + 1.16718e7i) q^{68} +(1.45625e7 + 1.45625e7i) q^{69} +(3.01190e7 - 2.22486e7i) q^{70} -9.00590e6 q^{71} +(8.07578e6 + 3.87643e6i) q^{72} +1.17210e7i q^{73} +(2.69977e7 - 1.99429e7i) q^{74} +(-4.19503e6 + 4.19503e6i) q^{75} +(1.66374e7 + 3.14148e7i) q^{76} +(-2.20486e7 + 2.20486e7i) q^{77} +(4.09716e6 - 2.72614e7i) q^{78} -3.38546e6i q^{79} +(8.84332e6 + 4.63074e7i) q^{80} -4.78297e6 q^{81} +(-669618. - 100638. i) q^{82} +(1.31997e7 + 1.31997e7i) q^{83} +(1.82288e7 + 3.44197e7i) q^{84} +(-7.88982e7 - 7.88982e7i) q^{85} +(-2.06150e7 - 2.79076e7i) q^{86} +3.17501e7 q^{87} +(-1.30133e7 - 3.70384e7i) q^{88} +6.91877e7i q^{89} +(-1.49562e7 - 2.02470e7i) q^{90} +(8.47556e7 - 8.47556e7i) q^{91} +(-1.07756e8 - 3.31382e7i) q^{92} +(2.07438e7 - 2.07438e7i) q^{93} +(-1.39932e8 - 2.10306e7i) q^{94} -9.98919e7i q^{95} +(-4.89988e7 + 1.93758e6i) q^{96} -1.04598e8 q^{97} +(-1.14603e7 + 7.62540e7i) q^{98} +(1.48218e7 + 1.48218e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 372 q^{4} + 17460 q^{8}+O(q^{10}) $ 64 * q - 372 * q^4 + 17460 * q^8	\( 64 q - 372 q^{4} + 17460 q^{8} - 13784 q^{10} + 39552 q^{11} - 22680 q^{12} + 116772 q^{14} - 161824 q^{16} - 26244 q^{18} - 167552 q^{19} + 690000 q^{20} - 1252768 q^{22} + 1691136 q^{23} - 74844 q^{24} - 1682100 q^{26} + 678600 q^{28} - 2132352 q^{29} - 2054808 q^{30} + 1407840 q^{32} - 3704544 q^{34} - 2415744 q^{35} - 1041012 q^{36} - 4720512 q^{37} + 2413320 q^{38} - 3544848 q^{40} + 9436500 q^{42} - 7244672 q^{43} - 3982056 q^{44} + 11165992 q^{46} - 9467280 q^{48} + 52706752 q^{49} + 17072676 q^{50} + 13862016 q^{51} - 22890864 q^{52} - 5358720 q^{53} - 4960116 q^{54} - 46326784 q^{55} - 9637152 q^{56} + 25732944 q^{58} + 44938752 q^{59} + 40927032 q^{60} + 24476032 q^{61} - 17024868 q^{62} - 116303448 q^{64} + 29941632 q^{65} - 56828952 q^{66} - 44244736 q^{67} - 12614400 q^{68} - 8636544 q^{69} - 60922560 q^{70} + 159664128 q^{71} - 18502020 q^{72} + 140654028 q^{74} + 12918528 q^{75} + 204842760 q^{76} - 94964352 q^{77} + 14001660 q^{78} + 38076648 q^{80} - 306110016 q^{81} - 260917000 q^{82} + 209328000 q^{83} - 127862712 q^{84} + 106960000 q^{85} - 123451824 q^{86} + 104240736 q^{88} + 53520264 q^{90} - 45401472 q^{91} + 351567216 q^{92} + 208488216 q^{94} + 49597920 q^{96} - 681890712 q^{98} + 86500224 q^{99}+O(q^{100}) \) 64 * q - 372 * q^4 + 17460 * q^8 - 13784 * q^10 + 39552 * q^11 - 22680 * q^12 + 116772 * q^14 - 161824 * q^16 - 26244 * q^18 - 167552 * q^19 + 690000 * q^20 - 1252768 * q^22 + 1691136 * q^23 - 74844 * q^24 - 1682100 * q^26 + 678600 * q^28 - 2132352 * q^29 - 2054808 * q^30 + 1407840 * q^32 - 3704544 * q^34 - 2415744 * q^35 - 1041012 * q^36 - 4720512 * q^37 + 2413320 * q^38 - 3544848 * q^40 + 9436500 * q^42 - 7244672 * q^43 - 3982056 * q^44 + 11165992 * q^46 - 9467280 * q^48 + 52706752 * q^49 + 17072676 * q^50 + 13862016 * q^51 - 22890864 * q^52 - 5358720 * q^53 - 4960116 * q^54 - 46326784 * q^55 - 9637152 * q^56 + 25732944 * q^58 + 44938752 * q^59 + 40927032 * q^60 + 24476032 * q^61 - 17024868 * q^62 - 116303448 * q^64 + 29941632 * q^65 - 56828952 * q^66 - 44244736 * q^67 - 12614400 * q^68 - 8636544 * q^69 - 60922560 * q^70 + 159664128 * q^71 - 18502020 * q^72 + 140654028 * q^74 + 12918528 * q^75 + 204842760 * q^76 - 94964352 * q^77 + 14001660 * q^78 + 38076648 * q^80 - 306110016 * q^81 - 260917000 * q^82 + 209328000 * q^83 - 127862712 * q^84 + 106960000 * q^85 - 123451824 * q^86 + 104240736 * q^88 + 53520264 * q^90 - 45401472 * q^91 + 351567216 * q^92 + 208488216 * q^94 + 49597920 * q^96 - 681890712 * q^98 + 86500224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−2.37796	+	15.8223i	−0.148622	+	0.988894i
$2$	−2.37796	+	15.8223i	−0.148622	+	0.988894i
$3$	33.0681	+	33.0681i	0.408248	+	0.408248i
$3$	33.0681	+	33.0681i	0.408248	+	0.408248i
$4$	−244.691	−	75.2496i	−0.955823	−	0.293944i
$5$	508.668	+	508.668i	0.813868	+	0.813868i	0.985211	−	0.171343i	$-0.0548107\pi$
$5$	508.668	+	508.668i	0.813868	+	0.813868i	−0.171343	+	0.985211i	$0.554811\pi$
$6$	−601.848	+	444.579i	−0.464389	+	0.343039i
$7$	−3253.34			−1.35499			−0.677496	−	0.735526i	$-0.736935\pi$
$7$	−3253.34			−1.35499			−0.677496	+	0.735526i	$0.736935\pi$
$8$	1772.49	−	3692.63i	0.432736	−	0.901521i
$9$			2187.00i			0.333333i
$10$	−9257.88	+	6838.70i	−0.925788	+	0.683870i
$11$	6777.24	−	6777.24i	0.462895	−	0.462895i	−0.436708	−	0.899603i	$-0.643856\pi$
$11$	6777.24	−	6777.24i	0.462895	−	0.462895i	0.899603	+	0.436708i	$0.143856\pi$
$12$	−5603.10	−	10579.8i	−0.270211	−	0.510215i
$13$	−26051.9	+	26051.9i	−0.912150	+	0.912150i	−0.996441	−	0.0842912i	$-0.973137\pi$
$13$	−26051.9	+	26051.9i	−0.912150	+	0.912150i	0.0842912	+	0.996441i	$0.473137\pi$
$14$	7736.30	−	51475.3i	0.201382	−	1.33994i
$15$			33641.4i			0.664521i
$16$	54211.0	+	36825.7i	0.827194	+	0.561916i
$17$	−155108.			−1.85711			−0.928554	−	0.371197i	$-0.878947\pi$
$17$	−155108.			−1.85711			−0.928554	+	0.371197i	$0.878947\pi$
$18$	−34603.4	−	5200.60i	−0.329631	−	0.0495408i
$19$	−98189.8	−	98189.8i	−0.753445	−	0.753445i	0.221675	−	0.975121i	$-0.428848\pi$
$19$	−98189.8	−	98189.8i	−0.753445	−	0.753445i	−0.975121	+	0.221675i	$0.928848\pi$
$20$	−86189.2	−	162743.i	−0.538682	−	1.01714i
$21$	−107582.	−	107582.i	−0.553173	−	0.553173i
$22$	91115.6	+	123348.i	0.388957	+	0.526550i
$23$	440378.			1.57367			0.786835	−	0.617163i	$-0.211718\pi$
$23$	440378.			1.57367			0.786835	+	0.617163i	$0.211718\pi$
$24$	180721.	−	63495.5i	0.544708	−	0.191381i
$25$			126860.i			0.324763i
$26$	−350251.	−	474152.i	−0.766454	−	1.03759i
$27$	−72320.0	+	72320.0i	−0.136083	+	0.136083i
$28$	796061.	+	244812.i	1.29513	+	0.398291i
$29$	480071.	−	480071.i	0.678756	−	0.678756i	−0.280963	−	0.959719i	$-0.590654\pi$
$29$	480071.	−	480071.i	0.678756	−	0.678756i	0.959719	+	0.280963i	$0.0906537\pi$
$30$	−532284.	−	79997.7i	−0.657140	−	0.0987626i
$31$		−	627305.i		−	0.679253i	−0.940560	−	0.339627i	$-0.889699\pi$
$31$		−	627305.i		−	0.679253i	0.940560	−	0.339627i	$-0.110301\pi$
$32$	−711579.	+	770173.i	−0.678615	+	0.734494i
$33$	448221.			0.377952
$34$	368839.	−	2.45416e6i	0.276008	−	1.83648i
$35$	−1.65487e6	−	1.65487e6i	−1.10279	−	1.10279i
$36$	164571.	−	535138.i	0.0979812	−	0.318608i
$37$	−1.48337e6	−	1.48337e6i	−0.791484	−	0.791484i	0.190251	−	0.981735i	$-0.439070\pi$
$37$	−1.48337e6	−	1.48337e6i	−0.791484	−	0.791484i	−0.981735	+	0.190251i	$0.939070\pi$
$38$	1.78708e6	−	1.32010e6i	0.857056	−	0.633099i
$39$	−1.72298e6			−0.744767
$40$	2.77993e6	−	976715.i	1.08591	−	0.381529i
$41$			42321.1i			0.0149769i	0.999972	+	0.00748845i	$0.00238367\pi$
$41$			42321.1i			0.0149769i	−0.999972	+	0.00748845i	$0.997616\pi$
$42$	1.95802e6	−	1.44637e6i	0.629244	−	0.464816i
$43$	−1.53336e6	+	1.53336e6i	−0.448508	+	0.448508i	−0.894858	−	0.446350i	$-0.852724\pi$
$43$	−1.53336e6	+	1.53336e6i	−0.448508	+	0.448508i	0.446350	+	0.894858i	$0.352724\pi$
$44$	−2.16831e6	+	1.14834e6i	−0.578510	+	0.306380i
$45$	−1.11246e6	+	1.11246e6i	−0.271289	+	0.271289i
$46$	−1.04720e6	+	6.96779e6i	−0.233883	+	1.55619i
$47$			8.84396e6i			1.81241i	0.422844	+	0.906203i	$0.361032\pi$
$47$			8.84396e6i			1.81241i	−0.422844	+	0.906203i	$0.638968\pi$
$48$	574898.	+	3.01041e6i	0.108299	+	0.567102i
$49$	4.81940e6			0.836004
$50$	−2.00722e6	−	301669.i	−0.321156	−	0.0482670i
$51$	−5.12911e6	−	5.12911e6i	−0.758161	−	0.758161i
$52$	8.33505e6	−	4.41426e6i	1.13997	−	0.603733i
$53$	−6.41564e6	−	6.41564e6i	−0.813086	−	0.813086i	0.172010	−	0.985095i	$-0.444974\pi$
$53$	−6.41564e6	−	6.41564e6i	−0.813086	−	0.813086i	−0.985095	+	0.172010i	$0.944974\pi$
$54$	−972295.	−	1.31624e6i	−0.114346	−	0.154796i
$55$	6.89473e6			0.753470
$56$	−5.76649e6	+	1.20134e7i	−0.586354	+	1.22155i
$57$		−	6.49390e6i		−	0.615186i
$58$	6.45424e6	+	8.73742e6i	0.570339	+	0.772096i
$59$	−9.15868e6	+	9.15868e6i	−0.755831	+	0.755831i	−0.975561	−	0.219730i	$-0.929482\pi$
$59$	−9.15868e6	+	9.15868e6i	−0.755831	+	0.755831i	0.219730	+	0.975561i	$0.429482\pi$
$60$	2.53150e6	−	8.23172e6i	0.195332	−	0.635164i
$61$	−1.53578e7	+	1.53578e7i	−1.10920	+	1.10920i	−0.115946	+	0.993256i	$0.536990\pi$
$61$	−1.53578e7	+	1.53578e7i	−1.10920	+	1.10920i	−0.993256	+	0.115946i	$0.963010\pi$
$62$	9.92541e6	+	1.49170e6i	0.671710	+	0.100952i
$63$		−	7.11505e6i		−	0.451664i
$64$	−1.04938e7	−	1.30903e7i	−0.625479	−	0.780241i
$65$	−2.65035e7			−1.48474
$66$	−1.06585e6	+	7.09189e6i	−0.0561721	+	0.373754i
$67$	9.64762e6	+	9.64762e6i	0.478764	+	0.478764i	0.904736	−	0.425972i	$-0.140068\pi$
$67$	9.64762e6	+	9.64762e6i	0.478764	+	0.478764i	−0.425972	+	0.904736i	$0.640068\pi$
$68$	3.79534e7	+	1.16718e7i	1.77507	+	0.545885i
$69$	1.45625e7	+	1.45625e7i	0.642448	+	0.642448i
$70$	3.01190e7	−	2.22486e7i	1.25444	−	0.926639i
$71$	−9.00590e6			−0.354400			−0.177200	−	0.984175i	$-0.556704\pi$
$71$	−9.00590e6			−0.354400			−0.177200	+	0.984175i	$0.556704\pi$
$72$	8.07578e6	+	3.87643e6i	0.300507	+	0.144245i
$73$			1.17210e7i			0.412736i	0.978474	+	0.206368i	$0.0661644\pi$
$73$			1.17210e7i			0.412736i	−0.978474	+	0.206368i	$0.933836\pi$
$74$	2.69977e7	−	1.99429e7i	0.900326	−	0.665062i
$75$	−4.19503e6	+	4.19503e6i	−0.132584	+	0.132584i
$76$	1.66374e7	+	3.14148e7i	0.498690	+	0.941631i
$77$	−2.20486e7	+	2.20486e7i	−0.627219	+	0.627219i
$78$	4.09716e6	−	2.72614e7i	0.110689	−	0.736496i
$79$		−	3.38546e6i		−	0.0869179i	−0.999055	−	0.0434590i	$-0.986162\pi$
$79$		−	3.38546e6i		−	0.0869179i	0.999055	−	0.0434590i	$-0.0138378\pi$
$80$	8.84332e6	+	4.63074e7i	0.215901	+	1.13055i
$81$	−4.78297e6			−0.111111
$82$	−669618.	−	100638.i	−0.0148106	−	0.00222590i
$83$	1.31997e7	+	1.31997e7i	0.278132	+	0.278132i	0.832363	−	0.554231i	$-0.186987\pi$
$83$	1.31997e7	+	1.31997e7i	0.278132	+	0.278132i	−0.554231	+	0.832363i	$0.686987\pi$
$84$	1.82288e7	+	3.44197e7i	0.366134	+	0.691337i
$85$	−7.88982e7	−	7.88982e7i	−1.51144	−	1.51144i
$86$	−2.06150e7	−	2.79076e7i	−0.376869	−	0.510186i
$87$	3.17501e7			0.554202
$88$	−1.30133e7	−	3.70384e7i	−0.216998	−	0.617620i
$89$			6.91877e7i			1.10273i	0.834264	+	0.551365i	$0.185893\pi$
$89$			6.91877e7i			1.10273i	−0.834264	+	0.551365i	$0.814107\pi$
$90$	−1.49562e7	−	2.02470e7i	−0.227957	−	0.308596i
$91$	8.47556e7	−	8.47556e7i	1.23596	−	1.23596i
$92$	−1.07756e8	−	3.31382e7i	−1.50415	−	0.462570i
$93$	2.07438e7	−	2.07438e7i	0.277304	−	0.277304i
$94$	−1.39932e8	−	2.10306e7i	−1.79228	−	0.269364i
$95$		−	9.98919e7i		−	1.22641i
$96$	−4.89988e7	+	1.93758e6i	−0.576899	+	0.0228125i
$97$	−1.04598e8			−1.18151			−0.590755	−	0.806851i	$-0.701170\pi$
$97$	−1.04598e8			−1.18151			−0.590755	+	0.806851i	$0.701170\pi$
$98$	−1.14603e7	+	7.62540e7i	−0.124249	+	0.826720i
$99$	1.48218e7	+	1.48218e7i	0.154298	+	0.154298i
$100$	9.54619e6	−	3.10415e7i	0.0954619	−	0.310415i
$101$	−754525.	−	754525.i	−0.00725084	−	0.00725084i	0.703472	−	0.710723i	$-0.251632\pi$
$101$	−754525.	−	754525.i	−0.00725084	−	0.00725084i	−0.710723	+	0.703472i	$0.751632\pi$
$102$	9.33512e7	−	6.89576e7i	0.862421	−	0.637061i
$103$	5.75624e7			0.511435			0.255717	−	0.966752i	$-0.417688\pi$
$103$	5.75624e7			0.511435			0.255717	+	0.966752i	$0.417688\pi$
$104$	5.00234e7	+	1.42377e8i	0.427602	+	1.21704i
$105$		−	1.09447e8i		−	0.900420i
$106$	1.16766e8	−	8.62540e7i	0.924898	−	0.683213i
$107$	−1.43345e8	+	1.43345e8i	−1.09357	+	1.09357i	−0.0984243	+	0.995145i	$0.531380\pi$
$107$	−1.43345e8	+	1.43345e8i	−1.09357	+	1.09357i	−0.995145	+	0.0984243i	$0.968620\pi$
$108$	2.31381e7	−	1.22540e7i	0.170072	−	0.0900703i
$109$	9.63597e7	−	9.63597e7i	0.682637	−	0.682637i	−0.277957	−	0.960594i	$-0.589657\pi$
$109$	9.63597e7	−	9.63597e7i	0.682637	−	0.682637i	0.960594	+	0.277957i	$0.0896572\pi$
$110$	−1.63954e7	+	1.09090e8i	−0.111983	+	0.745102i
$111$		−	9.81044e7i		−	0.646244i
$112$	−1.76367e8	−	1.19806e8i	−1.12084	−	0.761392i
$113$	−1.40687e8			−0.862861			−0.431431	−	0.902146i	$-0.641991\pi$
$113$	−1.40687e8			−0.862861			−0.431431	+	0.902146i	$0.641991\pi$
$114$	1.02748e8	+	1.54422e7i	0.608353	+	0.0914304i
$115$	2.24006e8	+	2.24006e8i	1.28076	+	1.28076i
$116$	−1.53594e8	+	8.13438e7i	−0.848286	+	0.449254i
$117$	−5.69755e7	−	5.69755e7i	−0.304050	−	0.304050i
$118$	−1.23132e8	−	1.66690e8i	−0.635103	−	0.859770i
$119$	5.04617e8			2.51637
$120$	1.24225e8	+	5.96288e7i	0.599079	+	0.287562i
$121$			1.22497e8i			0.571457i
$122$	−2.06476e8	−	2.79516e8i	−0.932030	−	1.26173i
$123$	−1.39948e6	+	1.39948e6i	−0.00611429	+	0.00611429i
$124$	−4.72044e7	+	1.53496e8i	−0.199662	+	0.649246i
$125$	1.34169e8	−	1.34169e8i	0.549554	−	0.549554i
$126$	1.12576e8	+	1.69193e7i	0.446648	+	0.0671274i
$127$			1.18604e8i			0.455916i	0.973671	+	0.227958i	$0.0732048\pi$
$127$			1.18604e8i			0.455916i	−0.973671	+	0.227958i	$0.926795\pi$
$128$	2.32072e8	−	1.34908e8i	0.864536	−	0.502572i
$129$	−1.01411e8			−0.366206
$130$	6.30243e7	−	4.19347e8i	0.220666	−	1.46825i
$131$	−7.63451e7	−	7.63451e7i	−0.259236	−	0.259236i	0.565507	−	0.824743i	$-0.308680\pi$
$131$	−7.63451e7	−	7.63451e7i	−0.259236	−	0.259236i	−0.824743	+	0.565507i	$0.808680\pi$
$132$	−1.09676e8	−	3.37285e7i	−0.361255	−	0.111097i
$133$	3.19444e8	+	3.19444e8i	1.02091	+	1.02091i
$134$	−1.75589e8	+	1.29706e8i	−0.544602	+	0.402291i
$135$	−7.35736e7			−0.221507
$136$	−2.74926e8	+	5.72755e8i	−0.803637	+	1.67422i
$137$		−	2.67355e7i		−	0.0758938i	−0.999280	−	0.0379469i	$-0.987918\pi$
$137$		−	2.67355e7i		−	0.0758938i	0.999280	−	0.0379469i	$-0.0120818\pi$
$138$	−2.65040e8	+	1.95783e8i	−0.730796	+	0.539831i
$139$	1.90673e8	−	1.90673e8i	0.510776	−	0.510776i	−0.403988	−	0.914764i	$-0.632376\pi$
$139$	1.90673e8	−	1.90673e8i	0.510776	−	0.510776i	0.914764	+	0.403988i	$0.132376\pi$
$140$	2.80402e8	+	5.29458e8i	0.729910	+	1.37822i
$141$	−2.92453e8	+	2.92453e8i	−0.739911	+	0.739911i
$142$	2.14157e7	−	1.42494e8i	0.0526718	−	0.350464i
$143$			3.53120e8i			0.844459i
$144$	−8.05379e7	+	1.18559e8i	−0.187305	+	0.275731i
$145$	4.88393e8			1.10484
$146$	−1.85453e8	−	2.78720e7i	−0.408152	−	0.0613418i
$147$	1.59368e8	+	1.59368e8i	0.341297	+	0.341297i
$148$	2.51344e8	+	4.74589e8i	0.523867	+	0.989170i
$149$	−2.87068e8	−	2.87068e8i	−0.582424	−	0.582424i	0.353145	−	0.935569i	$-0.385112\pi$
$149$	−2.87068e8	−	2.87068e8i	−0.582424	−	0.582424i	−0.935569	+	0.353145i	$0.885112\pi$
$150$	−5.63995e7	−	7.63507e7i	−0.111406	−	0.150816i
$151$	2.73453e7			0.0525986			0.0262993	−	0.999654i	$-0.491628\pi$
$151$	2.73453e7			0.0525986			0.0262993	+	0.999654i	$0.491628\pi$
$152$	−5.36618e8	+	1.88538e8i	−1.00529	+	0.353204i
$153$		−	3.39220e8i		−	0.619036i
$154$	−2.96430e8	−	4.01291e8i	−0.527034	−	0.713472i
$155$	3.19090e8	−	3.19090e8i	0.552823	−	0.552823i
$156$	4.21596e8	+	1.29653e8i	0.711866	+	0.218920i
$157$	−3.95872e8	+	3.95872e8i	−0.651562	+	0.651562i	−0.953369	−	0.301807i	$-0.902410\pi$
$157$	−3.95872e8	+	3.95872e8i	−0.651562	+	0.651562i	0.301807	+	0.953369i	$0.402410\pi$
$158$	5.35658e7	+	8.05049e6i	0.0859526	+	0.0129180i
$159$		−	4.24306e8i		−	0.663882i
$160$	−7.53719e8	+	2.98046e7i	−1.15008	+	0.0454782i
$161$	−1.43270e9			−2.13231
$162$	1.13737e7	−	7.56776e7i	0.0165136	−	0.109877i
$163$	7.13925e8	+	7.13925e8i	1.01135	+	1.01135i	0.999935	+	0.0114165i	$0.00363407\pi$
$163$	7.13925e8	+	7.13925e8i	1.01135	+	1.01135i	0.0114165	+	0.999935i	$0.496366\pi$
$164$	3.18465e6	−	1.03556e7i	0.00440237	−	0.0143153i
$165$	2.27996e8	+	2.27996e8i	0.307603	+	0.307603i
$166$	−2.40238e8	+	1.77461e8i	−0.316380	+	0.233707i
$167$	6.13122e8			0.788281			0.394140	−	0.919050i	$-0.371042\pi$
$167$	6.13122e8			0.788281			0.394140	+	0.919050i	$0.371042\pi$
$168$	−5.87946e8	+	2.06572e8i	−0.738075	+	0.259319i
$169$		−	5.41674e8i		−	0.664035i
$170$	1.43597e9	−	1.06073e9i	1.71929	−	1.27002i
$171$	2.14741e8	−	2.14741e8i	0.251148	−	0.251148i
$172$	4.90584e8	−	2.59814e8i	0.560531	−	0.296858i
$173$	−9.63205e7	+	9.63205e7i	−0.107531	+	0.107531i	−0.758825	−	0.651294i	$-0.774226\pi$
$173$	−9.63205e7	+	9.63205e7i	−0.107531	+	0.107531i	0.651294	+	0.758825i	$0.274226\pi$
$174$	−7.55004e7	+	5.02360e8i	−0.0823668	+	0.548047i
$175$		−	4.12719e8i		−	0.440051i
$176$	6.16978e8	−	1.17824e8i	0.643012	−	0.122796i
$177$	−6.05720e8			−0.617133
$178$	−1.09471e9	−	1.64526e8i	−1.09048	−	0.163890i
$179$	−1.44620e7	−	1.44620e7i	−0.0140870	−	0.0140870i	0.700028	−	0.714115i	$-0.253171\pi$
$179$	−1.44620e7	−	1.44620e7i	−0.0140870	−	0.0140870i	−0.714115	+	0.700028i	$0.753171\pi$
$180$	3.55919e8	−	1.88496e8i	0.339048	−	0.179561i
$181$	1.15314e9	+	1.15314e9i	1.07440	+	1.07440i	0.997000	+	0.0774047i	$0.0246634\pi$
$181$	1.15314e9	+	1.15314e9i	1.07440	+	1.07440i	0.0774047	+	0.997000i	$0.475337\pi$
$182$	1.13948e9	+	1.54258e9i	1.03854	+	1.40592i
$183$	−1.01571e9			−0.905659
$184$	7.80563e8	−	1.62615e9i	0.680984	−	1.41870i
$185$		−	1.50908e9i		−	1.28833i
$186$	2.78887e8	+	3.77542e8i	0.233011	+	0.315438i
$187$	−1.05120e9	+	1.05120e9i	−0.859645	+	0.859645i
$188$	6.65504e8	−	2.16403e9i	0.532745	−	1.73234i
$189$	2.35281e8	−	2.35281e8i	0.184391	−	0.184391i
$190$	1.58052e9	+	2.37539e8i	1.21279	+	0.182272i
$191$		−	1.91013e9i		−	1.43526i	−0.696426	−	0.717629i	$-0.745228\pi$
$191$		−	1.91013e9i		−	1.43526i	0.696426	−	0.717629i	$-0.254772\pi$
$192$	8.58601e7	−	7.79881e8i	0.0631810	−	0.573883i
$193$	−9.12672e8			−0.657788			−0.328894	−	0.944367i	$-0.606676\pi$
$193$	−9.12672e8			−0.657788			−0.328894	+	0.944367i	$0.606676\pi$
$194$	2.48730e8	−	1.65499e9i	0.175599	−	1.16839i
$195$	−8.76422e8	−	8.76422e8i	−0.606142	−	0.606142i
$196$	−1.17926e9	−	3.62658e8i	−0.799072	−	0.245738i
$197$	−6.71398e8	−	6.71398e8i	−0.445775	−	0.445775i	0.448172	−	0.893947i	$-0.352075\pi$
$197$	−6.71398e8	−	6.71398e8i	−0.445775	−	0.445775i	−0.893947	+	0.448172i	$0.852075\pi$
$198$	−2.69761e8	+	1.99270e8i	−0.175517	+	0.129652i
$199$	2.52411e7			0.0160952			0.00804758	−	0.999968i	$-0.497438\pi$
$199$	2.52411e7			0.0160952			0.00804758	+	0.999968i	$0.497438\pi$
$200$	4.68448e8	+	2.24858e8i	0.292780	+	0.140536i
$201$			6.38057e8i			0.390909i
$202$	1.37326e7	−	1.01441e7i	0.00824795	−	0.00609268i
$203$	−1.56183e9	+	1.56183e9i	−0.919709	+	0.919709i
$204$	8.69082e8	+	1.64101e9i	0.501811	+	0.947524i
$205$	−2.15274e7	+	2.15274e7i	−0.0121892	+	0.0121892i
$206$	−1.36881e8	+	9.10770e8i	−0.0760107	+	0.505755i
$207$			9.63106e8i			0.524557i
$208$	−2.37168e9	+	4.52920e8i	−1.26708	+	0.241973i
$209$	−1.33091e9			−0.697532
$210$	1.73170e9	+	2.60260e8i	0.890420	+	0.133823i
$211$	−6.60490e8	−	6.60490e8i	−0.333224	−	0.333224i	0.520585	−	0.853810i	$-0.325714\pi$
$211$	−6.60490e8	−	6.60490e8i	−0.333224	−	0.333224i	−0.853810	+	0.520585i	$0.825714\pi$
$212$	1.08707e9	+	2.05262e9i	0.538164	+	1.01617i
$213$	−2.97808e8	−	2.97808e8i	−0.144683	−	0.144683i
$214$	−1.92717e9	−	2.60891e9i	−0.918895	−	1.24395i
$215$	−1.55994e9			−0.730053
$216$	1.38865e8	+	3.95237e8i	0.0637936	+	0.181569i
$217$			2.04083e9i			0.920383i
$218$	1.29549e9	+	1.75377e9i	0.573600	+	0.776510i
$219$	−3.87590e8	+	3.87590e8i	−0.168499	+	0.168499i
$220$	−1.68707e9	−	5.18825e8i	−0.720184	−	0.221478i
$221$	4.04085e9	−	4.04085e9i	1.69396	−	1.69396i
$222$	1.55224e9	+	2.33288e8i	0.639067	+	0.0960463i
$223$		−	2.95254e9i		−	1.19392i	−0.802269	−	0.596962i	$-0.796374\pi$
$223$		−	2.95254e9i		−	1.19392i	0.802269	−	0.596962i	$-0.203626\pi$
$224$	2.31501e9	−	2.50563e9i	0.919518	−	0.995234i
$225$	−2.77444e8			−0.108254
$226$	3.34549e8	−	2.22600e9i	0.128241	−	0.853278i
$227$	1.18789e9	+	1.18789e9i	0.447378	+	0.447378i	0.894482	−	0.447104i	$-0.147545\pi$
$227$	1.18789e9	+	1.18789e9i	0.447378	+	0.447378i	−0.447104	+	0.894482i	$0.647545\pi$
$228$	−4.88663e8	+	1.58900e9i	−0.180830	+	0.588008i
$229$	3.55495e9	+	3.55495e9i	1.29268	+	1.29268i	0.933122	+	0.359559i	$0.117073\pi$
$229$	3.55495e9	+	3.55495e9i	1.29268	+	1.29268i	0.359559	+	0.933122i	$0.382927\pi$
$230$	−4.07696e9	+	3.01161e9i	−1.45689	+	1.07619i
$231$	−1.45821e9			−0.512122
$232$	−9.21805e8	−	2.62364e9i	−0.318191	−	0.905635i
$233$			2.60000e9i			0.882165i	0.897467	+	0.441082i	$0.145405\pi$
$233$			2.60000e9i			0.882165i	−0.897467	+	0.441082i	$0.854595\pi$
$234$	1.03697e9	−	7.65999e8i	0.345862	−	0.255485i
$235$	−4.49864e9	+	4.49864e9i	−1.47506	+	1.47506i
$236$	2.93023e9	−	1.55186e9i	0.944612	−	0.500269i
$237$	1.11951e8	−	1.11951e8i	0.0354841	−	0.0354841i
$238$	−1.19996e9	+	7.98420e9i	−0.373989	+	2.48842i
$239$		−	1.22584e9i		−	0.375701i	−0.982198	−	0.187850i	$-0.939848\pi$
$239$		−	1.22584e9i		−	0.375701i	0.982198	−	0.187850i	$-0.0601520\pi$
$240$	−1.23887e9	+	1.82373e9i	−0.373405	+	0.549688i
$241$	−5.38574e9			−1.59653			−0.798265	−	0.602307i	$-0.794248\pi$
$241$	−5.38574e9			−1.59653			−0.798265	+	0.602307i	$0.794248\pi$
$242$	−1.93818e9	−	2.91293e8i	−0.565110	−	0.0849313i
$243$	−1.58164e8	−	1.58164e8i	−0.0453609	−	0.0453609i
$244$	4.91359e9	−	2.60225e9i	1.38624	−	0.734157i
$245$	2.45147e9	+	2.45147e9i	0.680397	+	0.680397i
$246$	−1.88151e7	−	2.54709e7i	−0.00513767	−	0.00695511i
$247$	5.11606e9			1.37451
$248$	−2.31640e9	−	1.11189e9i	−0.612361	−	0.293937i
$249$			8.72978e8i			0.227094i
$250$	1.80381e9	+	2.44190e9i	0.461775	+	0.625127i
$251$	−2.62200e8	+	2.62200e8i	−0.0660599	+	0.0660599i	−0.739365	−	0.673305i	$-0.764874\pi$
$251$	−2.62200e8	+	2.62200e8i	−0.0660599	+	0.0660599i	0.673305	+	0.739365i	$0.264874\pi$
$252$	−5.35404e8	+	1.74099e9i	−0.132764	+	0.431711i
$253$	2.98454e9	−	2.98454e9i	0.728444	−	0.728444i
$254$	−1.87659e9	−	2.82035e8i	−0.450852	−	0.0677593i
$255$		−	5.21803e9i		−	1.23409i
$256$	1.58270e9	+	3.99272e9i	0.368501	+	0.929627i
$257$	2.42435e9			0.555728			0.277864	−	0.960620i	$-0.410373\pi$
$257$	2.42435e9			0.555728			0.277864	+	0.960620i	$0.410373\pi$
$258$	2.41150e8	−	1.60455e9i	0.0544264	−	0.362138i
$259$	4.82590e9	+	4.82590e9i	1.07245	+	1.07245i
$260$	6.48516e9	+	1.99438e9i	1.41915	+	0.436430i
$261$	1.04992e9	+	1.04992e9i	0.226252	+	0.226252i
$262$	1.38950e9	−	1.02641e9i	0.294886	−	0.217829i
$263$	−3.25783e9			−0.680934			−0.340467	−	0.940256i	$-0.610585\pi$
$263$	−3.25783e9			−0.680934			−0.340467	+	0.940256i	$0.610585\pi$
$264$	7.94466e8	−	1.65511e9i	0.163553	−	0.340732i
$265$		−	6.52685e9i		−	1.32349i
$266$	−5.81397e9	+	4.29472e9i	−1.16130	+	0.857844i
$267$	−2.28791e9	+	2.28791e9i	−0.450188	+	0.450188i
$268$	−1.63470e9	−	3.08666e9i	−0.316884	−	0.598343i
$269$	−1.83290e9	+	1.83290e9i	−0.350050	+	0.350050i	−0.860128	−	0.510078i	$-0.829617\pi$
$269$	−1.83290e9	+	1.83290e9i	−0.350050	+	0.350050i	0.510078	+	0.860128i	$0.329617\pi$
$270$	1.74955e8	−	1.16410e9i	0.0329209	−	0.219047i
$271$		−	4.10341e9i		−	0.760796i	−0.924823	−	0.380398i	$-0.875787\pi$
$271$		−	4.10341e9i		−	0.760796i	0.924823	−	0.380398i	$-0.124213\pi$
$272$	−8.40853e9	−	5.71195e9i	−1.53619	−	1.04354i
$273$	5.60542e9			1.00915
$274$	4.23017e8	+	6.35759e7i	0.0750509	+	0.0112795i
$275$	8.59763e8	+	8.59763e8i	0.150331	+	0.150331i
$276$	−2.46748e9	−	4.65911e9i	−0.425223	−	0.802910i
$277$	4.59144e9	+	4.59144e9i	0.779884	+	0.779884i	0.979811	−	0.199927i	$-0.0640705\pi$
$277$	4.59144e9	+	4.59144e9i	0.779884	+	0.779884i	−0.199927	+	0.979811i	$0.564070\pi$
$278$	2.56348e9	+	3.47030e9i	0.429191	+	0.581016i
$279$	1.37192e9			0.226418
$280$	−9.04404e9	+	3.17758e9i	−1.47140	+	0.516969i
$281$		−	6.54546e9i		−	1.04982i	−0.851157	−	0.524910i	$-0.824099\pi$
$281$		−	6.54546e9i		−	1.04982i	0.851157	−	0.524910i	$-0.175901\pi$
$282$	−3.93184e9	−	5.32272e9i	−0.621727	−	0.841661i
$283$	1.57393e9	−	1.57393e9i	0.245381	−	0.245381i	−0.573691	−	0.819072i	$-0.694489\pi$
$283$	1.57393e9	−	1.57393e9i	0.245381	−	0.245381i	0.819072	+	0.573691i	$0.194489\pi$
$284$	2.20366e9	+	6.77690e8i	0.338744	+	0.104174i
$285$	3.30324e9	−	3.30324e9i	0.500680	−	0.500680i
$286$	−5.58718e9	−	8.39705e8i	−0.835080	−	0.125506i
$287$		−	1.37685e8i		−	0.0202936i
$288$	−1.68437e9	−	1.55622e9i	−0.244831	−	0.226205i
$289$	1.70826e10			2.44885
$290$	−1.16138e9	+	7.72751e9i	−0.164203	+	1.09257i
$291$	−3.45887e9	−	3.45887e9i	−0.482350	−	0.482350i
$292$	8.81998e8	−	2.86801e9i	0.121321	−	0.394502i
$293$	1.77618e9	+	1.77618e9i	0.240999	+	0.240999i	0.817263	−	0.576264i	$-0.195490\pi$
$293$	1.77618e9	+	1.77618e9i	0.240999	+	0.240999i	−0.576264	+	0.817263i	$0.695490\pi$
$294$	−2.90055e9	+	2.14260e9i	−0.388231	+	0.286782i
$295$	−9.31744e9			−1.23029
$296$	−8.10678e9	+	2.84828e9i	−1.05604	+	0.371036i
$297$			9.80260e8i			0.125984i
$298$	5.22471e9	−	3.85944e9i	0.662517	−	0.489394i
$299$	−1.14727e10	+	1.14727e10i	−1.43542	+	1.43542i
$300$	1.34216e9	−	7.10811e8i	0.165699	−	0.0877544i
$301$	4.98854e9	−	4.98854e9i	0.607725	−	0.607725i
$302$	−6.50259e7	+	4.32665e8i	−0.00781733	+	0.0520144i
$303$		−	4.99015e7i		−	0.00592029i
$304$	−1.70706e9	−	8.93887e9i	−0.199873	−	1.04662i
$305$	−1.56241e10			−1.80549
$306$	5.36724e9	+	8.06652e8i	0.612161	+	0.0920026i
$307$	−1.15353e10	−	1.15353e10i	−1.29860	−	1.29860i	−0.929319	−	0.369278i	$-0.879605\pi$
$307$	−1.15353e10	−	1.15353e10i	−1.29860	−	1.29860i	−0.369278	−	0.929319i	$-0.620395\pi$
$308$	7.05425e9	−	3.73595e9i	0.783877	−	0.415143i
$309$	1.90348e9	+	1.90348e9i	0.208792	+	0.208792i
$310$	4.28995e9	+	5.80751e9i	0.464521	+	0.628845i
$311$	1.19033e10			1.27241			0.636204	−	0.771521i	$-0.280504\pi$
$311$	1.19033e10			1.27241			0.636204	+	0.771521i	$0.280504\pi$
$312$	−3.05395e9	+	6.36231e9i	−0.322287	+	0.671423i
$313$			1.72755e10i			1.79992i	0.435968	+	0.899962i	$0.356406\pi$
$313$			1.72755e10i			1.79992i	−0.435968	+	0.899962i	$0.643594\pi$
$314$	−5.32224e9	−	7.20497e9i	−0.547489	−	0.741163i
$315$	3.61919e9	−	3.61919e9i	0.367595	−	0.367595i
$316$	−2.54754e8	+	8.28391e8i	−0.0255490	+	0.0830781i
$317$	−4.29968e9	+	4.29968e9i	−0.425794	+	0.425794i	−0.887193	−	0.461399i	$-0.847348\pi$
$317$	−4.29968e9	+	4.29968e9i	−0.425794	+	0.425794i	0.461399	+	0.887193i	$0.347348\pi$
$318$	6.71350e9	+	1.00898e9i	0.656509	+	0.0986677i
$319$		−	6.50712e9i		−	0.628385i
$320$	1.32074e9	−	1.19965e10i	0.125955	−	1.14407i
$321$	−9.48027e9			−0.892895
$322$	3.40689e9	−	2.26686e10i	0.316909	−	2.10863i
$323$	1.52300e10	+	1.52300e10i	1.39923	+	1.39923i
$324$	1.17035e9	+	3.59916e8i	0.106203	+	0.0326604i
$325$	−3.30496e9	−	3.30496e9i	−0.296232	−	0.296232i
$326$	−1.29936e10	+	9.59825e9i	−1.15043	+	0.849810i
$327$	6.37287e9			0.557370
$328$	1.56276e8	+	7.50136e7i	0.0135020	+	0.00648104i
$329$		−	2.87724e10i		−	2.45580i
$330$	−4.14958e9	+	3.06525e9i	−0.349903	+	0.258470i
$331$	4.94130e9	−	4.94130e9i	0.411651	−	0.411651i	−0.470663	−	0.882313i	$-0.655985\pi$
$331$	4.94130e9	−	4.94130e9i	0.411651	−	0.411651i	0.882313	+	0.470663i	$0.155985\pi$
$332$	−2.23657e9	−	4.22311e9i	−0.184090	−	0.347600i
$333$	3.24413e9	−	3.24413e9i	0.263828	−	0.263828i
$334$	−1.45798e9	+	9.70100e9i	−0.117156	+	0.779526i
$335$			9.81487e9i			0.779301i
$336$	−1.87034e9	−	9.79389e9i	−0.146745	−	0.768419i
$337$	−9.65157e9			−0.748305			−0.374152	−	0.927367i	$-0.622066\pi$
$337$	−9.65157e9			−0.748305			−0.374152	+	0.927367i	$0.622066\pi$
$338$	8.57053e9	+	1.28808e9i	0.656660	+	0.0986905i
$339$	−4.65226e9	−	4.65226e9i	−0.352262	−	0.352262i
$340$	1.33686e10	+	2.52427e10i	1.00039	+	1.88895i
$341$	−4.25140e9	−	4.25140e9i	−0.314423	−	0.314423i
$342$	2.88705e9	+	3.90834e9i	0.211033	+	0.285685i
$343$	3.07571e9			0.222213
$344$	2.94427e9	+	8.37999e9i	0.210254	+	0.598425i
$345$			1.48149e10i			1.04574i
$346$	−1.29497e9	−	1.75306e9i	−0.0903554	−	0.122318i
$347$	1.26738e10	−	1.26738e10i	0.874154	−	0.874154i	−0.118768	−	0.992922i	$-0.537894\pi$
$347$	1.26738e10	−	1.26738e10i	0.874154	−	0.874154i	0.992922	+	0.118768i	$0.0378944\pi$
$348$	−7.76895e9	−	2.38918e9i	−0.529719	−	0.162904i
$349$	−5.75442e9	+	5.75442e9i	−0.387882	+	0.387882i	−0.873931	−	0.486049i	$-0.838438\pi$
$349$	−5.75442e9	+	5.75442e9i	−0.387882	+	0.387882i	0.486049	+	0.873931i	$0.338438\pi$
$350$	6.53017e9	+	9.81430e8i	0.435164	+	0.0654014i
$351$		−	3.76815e9i		−	0.248256i
$352$	3.97102e8	+	1.00422e10i	0.0258661	+	0.654121i
$353$	−9.23615e9			−0.594829			−0.297415	−	0.954748i	$-0.596124\pi$
$353$	−9.23615e9			−0.594829			−0.297415	+	0.954748i	$0.596124\pi$
$354$	1.44038e9	−	9.58389e9i	0.0917199	−	0.610279i
$355$	−4.58101e9	−	4.58101e9i	−0.288435	−	0.288435i
$356$	5.20635e9	−	1.69296e10i	0.324140	−	1.05401i
$357$	1.66867e10	+	1.66867e10i	1.02730	+	1.02730i
$358$	2.63213e8	−	1.94433e8i	0.0160241	−	0.0118369i
$359$	1.95347e10			1.17606			0.588029	−	0.808840i	$-0.299904\pi$
$359$	1.95347e10			1.17606			0.588029	+	0.808840i	$0.299904\pi$
$360$	2.13607e9	+	6.07970e9i	0.127176	+	0.361970i
$361$			2.29889e9i			0.135360i
$362$	−2.09875e10	+	1.55032e10i	−1.22215	+	0.902792i
$363$	−4.05074e9	+	4.05074e9i	−0.233296	+	0.233296i
$364$	−2.71167e10	+	1.43611e10i	−1.54466	+	0.818054i
$365$	−5.96208e9	+	5.96208e9i	−0.335913	+	0.335913i
$366$	2.41531e9	−	1.60708e10i	0.134601	−	0.895601i
$367$		−	2.69559e10i		−	1.48590i	−0.669346	−	0.742951i	$-0.733426\pi$
$367$		−	2.69559e10i		−	1.48590i	0.669346	−	0.742951i	$-0.266574\pi$
$368$	2.38733e10	+	1.62172e10i	1.30173	+	0.884271i
$369$	−9.25563e7			−0.00499230
$370$	2.38772e10	+	3.58854e9i	1.27402	+	0.191474i
$371$	2.08722e10	+	2.08722e10i	1.10172	+	1.10172i
$372$	−6.63677e9	+	3.51485e9i	−0.346565	+	0.183542i
$373$	−2.16781e10	−	2.16781e10i	−1.11992	−	1.11992i	−0.991753	−	0.128166i	$-0.959091\pi$
$373$	−2.16781e10	−	2.16781e10i	−1.11992	−	1.11992i	−0.128166	−	0.991753i	$-0.540909\pi$
$374$	−1.41327e10	−	1.91321e10i	−0.722336	−	0.977861i
$375$	8.87340e9			0.448709
$376$	3.26575e10	+	1.56758e10i	1.63392	+	0.784293i
$377$			2.50135e10i			1.23825i
$378$	3.16320e9	+	4.28218e9i	0.154939	+	0.209748i
$379$	−2.36973e10	+	2.36973e10i	−1.14853	+	1.14853i	−0.161686	+	0.986842i	$0.551693\pi$
$379$	−2.36973e10	+	2.36973e10i	−1.14853	+	1.14853i	−0.986842	+	0.161686i	$0.948307\pi$
$380$	−7.51682e9	+	2.44426e10i	−0.360496	+	1.17223i
$381$	−3.92201e9	+	3.92201e9i	−0.186127	+	0.186127i
$382$	3.02227e10	+	4.54221e9i	1.41932	+	0.213311i
$383$			2.26683e10i			1.05348i	0.850028	+	0.526738i	$0.176585\pi$
$383$			2.26683e10i			1.05348i	−0.850028	+	0.526738i	$0.823415\pi$
$384$	1.21353e10	+	3.21303e9i	0.558119	+	0.147771i
$385$	−2.24309e10			−1.02095
$386$	2.17030e9	−	1.44406e10i	0.0977620	−	0.650482i
$387$	−3.35346e9	−	3.35346e9i	−0.149503	−	0.149503i
$388$	2.55942e10	+	7.87098e9i	1.12931	+	0.347298i
$389$	−1.99758e9	−	1.99758e9i	−0.0872379	−	0.0872379i	0.662141	−	0.749379i	$-0.269648\pi$
$389$	−1.99758e9	−	1.99758e9i	−0.0872379	−	0.0872379i	−0.749379	+	0.662141i	$0.769648\pi$
$390$	1.59511e10	−	1.17829e10i	0.689497	−	0.509324i
$391$	−6.83059e10			−2.92248
$392$	8.54232e9	−	1.77963e10i	0.361769	−	0.753675i
$393$		−	5.04918e9i		−	0.211666i
$394$	1.22196e10	−	9.02651e9i	0.507076	−	0.374572i
$395$	1.72207e9	−	1.72207e9i	0.0707397	−	0.0707397i
$396$	−2.51143e9	−	4.74210e9i	−0.102127	−	0.192837i
$397$	−1.46535e10	+	1.46535e10i	−0.589900	+	0.589900i	−0.937604	−	0.347704i	$-0.886961\pi$
$397$	−1.46535e10	+	1.46535e10i	−0.589900	+	0.589900i	0.347704	+	0.937604i	$0.386961\pi$
$398$	−6.00222e7	+	3.99372e8i	−0.00239210	+	0.0159164i
$399$			2.11268e10i			0.833572i
$400$	−4.67173e9	+	6.87723e9i	−0.182489	+	0.268642i
$401$	−3.06109e10			−1.18385			−0.591927	−	0.805991i	$-0.701633\pi$
$401$	−3.06109e10			−1.18385			−0.591927	+	0.805991i	$0.701633\pi$
$402$	−1.00955e10	−	1.51727e9i	−0.386567	−	0.0580978i
$403$	1.63425e10	+	1.63425e10i	0.619581	+	0.619581i
$404$	1.27848e8	+	2.41403e8i	0.00479918	+	0.00906186i
$405$	−2.43294e9	−	2.43294e9i	−0.0904298	−	0.0904298i
$406$	−2.09978e10	−	2.84258e10i	−0.772805	−	1.04618i
$407$	−2.01063e10			−0.732748
$408$	−2.80312e10	+	9.84863e9i	−1.01158	+	0.355415i
$409$		−	4.58595e10i		−	1.63884i	−0.573194	−	0.819420i	$-0.694296\pi$
$409$		−	4.58595e10i		−	1.63884i	0.573194	−	0.819420i	$-0.305704\pi$
$410$	−2.89422e8	−	3.91804e8i	−0.0102423	−	0.0138654i
$411$	8.84093e8	−	8.84093e8i	0.0309835	−	0.0309835i
$412$	−1.40850e10	−	4.33155e9i	−0.488841	−	0.150333i
$413$	2.97963e10	−	2.97963e10i	1.02415	−	1.02415i
$414$	−1.52386e10	−	2.29023e9i	−0.518731	−	0.0779609i
$415$			1.34285e10i			0.452726i
$416$	−1.52647e9	−	3.86025e10i	−0.0509701	−	1.28897i
$417$	1.26104e10			0.417047
$418$	3.16485e9	−	2.10581e10i	0.103669	−	0.689785i
$419$	−8.22572e9	−	8.22572e9i	−0.266881	−	0.266881i	0.560961	−	0.827842i	$-0.310432\pi$
$419$	−8.22572e9	−	8.22572e9i	−0.266881	−	0.266881i	−0.827842	+	0.560961i	$0.810432\pi$
$420$	−8.23581e9	+	2.67806e10i	−0.264673	+	0.860642i
$421$	1.63287e10	+	1.63287e10i	0.519784	+	0.519784i	0.917506	−	0.397722i	$-0.130199\pi$
$421$	1.63287e10	+	1.63287e10i	0.519784	+	0.519784i	−0.397722	+	0.917506i	$0.630199\pi$
$422$	1.20211e10	−	8.87986e9i	0.379048	−	0.279999i
$423$	−1.93417e10			−0.604135
$424$	−3.50622e10	+	1.23189e10i	−1.08486	+	0.381162i
$425$		−	1.96770e10i		−	0.603119i
$426$	5.42019e9	−	4.00384e9i	0.164580	−	0.121573i
$427$	4.99642e10	−	4.99642e10i	1.50296	−	1.50296i
$428$	4.58617e10	−	2.42885e10i	1.36671	−	0.723810i
$429$	−1.16770e10	+	1.16770e10i	−0.344749	+	0.344749i
$430$	3.70948e9	−	2.46819e10i	0.108502	−	0.721945i
$431$		−	1.42893e9i		−	0.0414098i	−0.999786	−	0.0207049i	$-0.993409\pi$
$431$		−	1.42893e9i		−	0.0414098i	0.999786	−	0.0207049i	$-0.00659105\pi$
$432$	−6.58377e9	+	1.25730e9i	−0.189034	+	0.0360998i
$433$	2.04819e10			0.582664			0.291332	−	0.956622i	$-0.405902\pi$
$433$	2.04819e10			0.582664			0.291332	+	0.956622i	$0.405902\pi$
$434$	−3.22907e10	−	4.85302e9i	−0.910161	−	0.136790i
$435$	1.61502e10	+	1.61502e10i	0.451047	+	0.451047i
$436$	−3.08294e10	+	1.63273e10i	−0.853136	+	0.451823i
$437$	−4.32406e10	−	4.32406e10i	−1.18567	−	1.18567i
$438$	−5.21090e9	−	7.05425e9i	−0.141585	−	0.191670i
$439$	5.67014e10			1.52664			0.763318	−	0.646023i	$-0.223569\pi$
$439$	5.67014e10			1.52664			0.763318	+	0.646023i	$0.223569\pi$
$440$	1.22208e10	−	2.54597e10i	0.326054	−	0.679269i
$441$			1.05400e10i			0.278668i
$442$	5.43266e10	+	7.35445e10i	1.42339	+	1.92691i
$443$	3.09800e10	−	3.09800e10i	0.804389	−	0.804389i	−0.179389	−	0.983778i	$-0.557412\pi$
$443$	3.09800e10	−	3.09800e10i	0.804389	−	0.804389i	0.983778	+	0.179389i	$0.0574121\pi$
$444$	−7.38231e9	+	2.40052e10i	−0.189959	+	0.617695i
$445$	−3.51936e10	+	3.51936e10i	−0.897477	+	0.897477i
$446$	4.67160e10	+	7.02103e9i	1.18066	+	0.177444i
$447$		−	1.89856e10i		−	0.475547i
$448$	3.41399e10	+	4.25870e10i	0.847520	+	1.05722i
$449$	3.06686e10			0.754587			0.377293	−	0.926094i	$-0.376855\pi$
$449$	3.06686e10			0.754587			0.377293	+	0.926094i	$0.376855\pi$
$450$	6.59749e8	−	4.38980e9i	0.0160890	−	0.107052i
$451$	2.86821e8	+	2.86821e8i	0.00693273	+	0.00693273i
$452$	3.44249e10	+	1.05867e10i	0.824743	+	0.253633i
$453$	9.04256e8	+	9.04256e8i	0.0214733	+	0.0214733i
$454$	−2.16200e10	+	1.59705e10i	−0.508900	+	0.375919i
$455$	8.62249e10			2.01181
$456$	−2.39796e10	−	1.15103e10i	−0.554603	−	0.266213i
$457$			9.64047e9i			0.221021i	0.993875	+	0.110510i	$0.0352486\pi$
$457$			9.64047e9i			0.221021i	−0.993875	+	0.110510i	$0.964751\pi$
$458$	−6.47010e10	+	4.77940e10i	−1.47045	+	1.08620i
$459$	1.12174e10	−	1.12174e10i	0.252720	−	0.252720i
$460$	−3.79558e10	−	7.16685e10i	−0.847708	−	1.60065i
$461$	3.69566e9	−	3.69566e9i	0.0818255	−	0.0818255i	−0.665009	−	0.746835i	$-0.731572\pi$
$461$	3.69566e9	−	3.69566e9i	0.0818255	−	0.0818255i	0.746835	+	0.665009i	$0.231572\pi$
$462$	3.46757e9	−	2.30723e10i	0.0761128	−	0.506434i
$463$			5.80756e9i			0.126377i	0.998002	+	0.0631887i	$0.0201270\pi$
$463$			5.80756e9i			0.126377i	−0.998002	+	0.0631887i	$0.979873\pi$
$464$	4.37041e10	−	8.34617e9i	0.942867	−	0.180059i
$465$	2.11034e10			0.451378
$466$	−4.11380e10	−	6.18269e9i	−0.872368	−	0.131109i
$467$	−4.63321e10	−	4.63321e10i	−0.974125	−	0.974125i	0.0255490	−	0.999674i	$-0.491867\pi$
$467$	−4.63321e10	−	4.63321e10i	−0.974125	−	0.974125i	−0.999674	+	0.0255490i	$0.991867\pi$
$468$	9.65399e9	+	1.82288e10i	0.201244	+	0.379991i
$469$	−3.13870e10	−	3.13870e10i	−0.648721	−	0.648721i
$470$	−6.04812e10	−	8.18763e10i	−1.23945	−	1.67790i
$471$	−2.61815e10			−0.531999
$472$	1.75860e10	+	5.00532e10i	0.354322	+	1.00847i
$473$			2.07839e10i			0.415224i
$474$	1.50511e9	+	2.03753e9i	0.0298163	+	0.0403637i
$475$	1.24564e10	−	1.24564e10i	0.244691	−	0.244691i
$476$	−1.23475e11	−	3.79722e10i	−2.40520	−	0.739670i
$477$	1.40310e10	−	1.40310e10i	0.271029	−	0.271029i
$478$	1.93956e10	+	2.91500e9i	0.371528	+	0.0558375i
$479$			9.25763e10i			1.75856i	0.476302	+	0.879282i	$0.341977\pi$
$479$			9.25763e10i			1.75856i	−0.476302	+	0.879282i	$0.658023\pi$
$480$	−2.59097e10	−	2.39385e10i	−0.488086	−	0.450954i
$481$	7.72892e10			1.44390
$482$	1.28071e10	−	8.52148e10i	0.237280	−	1.57880i
$483$	−4.73766e10	−	4.73766e10i	−0.870513	−	0.870513i
$484$	9.21784e9	−	2.99738e10i	0.167976	−	0.546212i
$485$	−5.32058e10	−	5.32058e10i	−0.961594	−	0.961594i
$486$	2.87862e9	−	2.12641e9i	0.0515988	−	0.0381155i
$487$	4.07553e10			0.724550			0.362275	−	0.932071i	$-0.382000\pi$
$487$	4.07553e10			0.724550			0.362275	+	0.932071i	$0.382000\pi$
$488$	2.94892e10	+	8.39323e10i	0.519977	+	1.47996i
$489$			4.72163e10i			0.825765i
$490$	−4.46174e10	+	3.29584e10i	−0.773963	+	0.571718i
$491$	−2.12853e10	+	2.12853e10i	−0.366229	+	0.366229i	−0.866100	−	0.499871i	$-0.833381\pi$
$491$	−2.12853e10	+	2.12853e10i	−0.366229	+	0.366229i	0.499871	+	0.866100i	$0.333381\pi$
$492$	4.47750e8	−	2.37129e8i	0.00764144	−	0.00404692i
$493$	−7.44626e10	+	7.44626e10i	−1.26052	+	1.26052i
$494$	−1.21658e10	+	8.09479e10i	−0.204283	+	1.35924i
$495$			1.50788e10i			0.251157i
$496$	2.31010e10	−	3.40068e10i	0.381683	−	0.561874i
$497$	2.92992e10			0.480209
$498$	−1.38125e10	−	2.07591e9i	−0.224572	−	0.0337513i
$499$	−6.20782e8	−	6.20782e8i	−0.0100124	−	0.0100124i	0.702083	−	0.712095i	$-0.252254\pi$
$499$	−6.20782e8	−	6.20782e8i	−0.0100124	−	0.0100124i	−0.712095	+	0.702083i	$0.752254\pi$
$500$	−4.29259e10	+	2.27337e10i	−0.686814	+	0.363738i
$501$	2.02748e10	+	2.02748e10i	0.321814	+	0.321814i
$502$	−3.52511e9	−	4.77211e9i	−0.0555083	−	0.0751442i
$503$	5.71269e10			0.892419			0.446210	−	0.894928i	$-0.352774\pi$
$503$	5.71269e10			0.892419			0.446210	+	0.894928i	$0.352774\pi$
$504$	−2.62732e10	−	1.26113e10i	−0.407185	−	0.195451i
$505$		−	7.67605e8i		−	0.0118025i
$506$	4.01253e10	+	5.43195e10i	0.612091	+	0.828617i
$507$	1.79121e10	−	1.79121e10i	0.271091	−	0.271091i
$508$	8.92490e9	−	2.90213e10i	0.134013	−	0.435774i
$509$	7.08210e9	−	7.08210e9i	0.105509	−	0.105509i	−0.652381	−	0.757891i	$-0.726230\pi$
$509$	7.08210e9	−	7.08210e9i	0.105509	−	0.105509i	0.757891	+	0.652381i	$0.226230\pi$
$510$	8.25612e10	+	1.24083e10i	1.22038	+	0.183413i
$511$		−	3.81323e10i		−	0.559254i
$512$	−6.69376e10	+	1.55474e10i	−0.974071	+	0.226245i
$513$	1.42022e10			0.205062
$514$	−5.76500e9	+	3.83588e10i	−0.0825937	+	0.549557i
$515$	2.92801e10	+	2.92801e10i	0.416240	+	0.416240i
$516$	2.48142e10	+	7.63111e9i	0.350028	+	0.107644i
$517$	5.99377e10	+	5.99377e10i	0.838953	+	0.838953i
$518$	−8.78326e10	+	6.48810e10i	−1.21993	+	0.901153i
$519$	−6.37027e9			−0.0877988
$520$	−4.69771e10	+	9.78677e10i	−0.642500	+	1.33852i
$521$			7.39836e10i			1.00412i	0.864833	+	0.502059i	$0.167424\pi$
$521$			7.39836e10i			1.00412i	−0.864833	+	0.502059i	$0.832576\pi$
$522$	−1.91087e10	+	1.41154e10i	−0.257365	+	0.190113i
$523$	−4.85141e10	+	4.85141e10i	−0.648427	+	0.648427i	−0.952613	−	0.304186i	$-0.901616\pi$
$523$	−4.85141e10	+	4.85141e10i	−0.648427	+	0.648427i	0.304186	+	0.952613i	$0.401616\pi$
$524$	1.29360e10	+	2.44259e10i	0.171583	+	0.323985i
$525$	1.36479e10	−	1.36479e10i	0.179650	−	0.179650i
$526$	7.74698e9	−	5.15463e10i	0.101202	−	0.673372i
$527$			9.72997e10i			1.26145i
$528$	2.42985e10	+	1.65061e10i	0.312640	+	0.212377i
$529$	1.15621e11			1.47644
$530$	1.03270e11	+	1.55206e10i	1.30879	+	0.196700i
$531$	−2.00300e10	−	2.00300e10i	−0.251944	−	0.251944i
$532$	−5.41270e10	−	1.02203e11i	−0.675721	−	1.27590i
$533$	−1.10255e9	−	1.10255e9i	−0.0136612	−	0.0136612i
$534$	−3.07594e10	−	4.16405e10i	−0.378280	−	0.512096i
$535$	−1.45829e11			−1.78004
$536$	5.27254e10	−	1.85248e10i	0.638794	−	0.224437i
$537$		−	9.56464e8i		−	0.0115019i
$538$	−2.46422e10	−	3.33593e10i	−0.294137	−	0.398188i
$539$	3.26622e10	−	3.26622e10i	0.386982	−	0.386982i
$540$	1.80028e10	+	5.53638e9i	0.211721	+	0.0651105i
$541$	7.14242e10	−	7.14242e10i	0.833789	−	0.833789i	−0.154244	−	0.988033i	$-0.549294\pi$
$541$	7.14242e10	−	7.14242e10i	0.833789	−	0.833789i	0.988033	+	0.154244i	$0.0492941\pi$
$542$	6.49255e10	+	9.75775e9i	0.752346	+	0.113071i
$543$			7.62643e10i			0.877248i
$544$	1.10371e11	−	1.19460e11i	1.26026	−	1.36403i
$545$	9.80301e10			1.11115
$546$	−1.33295e10	+	8.86906e10i	−0.149983	+	0.997946i
$547$	−4.85657e10	−	4.85657e10i	−0.542476	−	0.542476i	0.381778	−	0.924254i	$-0.375312\pi$
$547$	−4.85657e10	−	4.85657e10i	−0.542476	−	0.542476i	−0.924254	+	0.381778i	$0.875312\pi$
$548$	−2.01184e9	+	6.54193e9i	−0.0223085	+	0.0725410i
$549$	−3.35876e10	−	3.35876e10i	−0.369734	−	0.369734i
$550$	−1.56479e10	+	1.15590e10i	−0.171004	+	0.126319i
$551$	−9.42761e10			−1.02281
$552$	7.95855e10	−	2.79620e10i	0.857191	−	0.301170i
$553$			1.10140e10i			0.117773i
$554$	−8.35654e10	+	6.17289e10i	−0.887131	+	0.655314i
$555$	4.99025e10	−	4.99025e10i	0.525957	−	0.525957i
$556$	−6.10040e10	+	3.23079e10i	−0.638351	+	0.338072i
$557$	2.15340e10	−	2.15340e10i	0.223720	−	0.223720i	−0.586343	−	0.810063i	$-0.699433\pi$
$557$	2.15340e10	−	2.15340e10i	0.223720	−	0.223720i	0.810063	+	0.586343i	$0.199433\pi$
$558$	−3.26236e9	+	2.17069e10i	−0.0336508	+	0.223903i
$559$		−	7.98940e10i		−	0.818214i
$560$	−2.87703e10	−	1.50654e11i	−0.292545	−	1.53189i
$561$	−6.95225e10			−0.701898
$562$	1.03564e11	+	1.55648e10i	1.03816	+	0.156027i
$563$	−6.79499e10	−	6.79499e10i	−0.676325	−	0.676325i	0.282842	−	0.959167i	$-0.408723\pi$
$563$	−6.79499e10	−	6.79499e10i	−0.676325	−	0.676325i	−0.959167	+	0.282842i	$0.908723\pi$
$564$	9.35675e10	−	4.95536e10i	0.924716	−	0.489732i
$565$	−7.15631e10	−	7.15631e10i	−0.702255	−	0.702255i
$566$	2.11605e10	+	2.86460e10i	0.206187	+	0.279125i
$567$	1.55606e10			0.150555
$568$	−1.59628e10	+	3.32555e10i	−0.153362	+	0.319499i
$569$			5.33123e10i			0.508603i	0.967125	+	0.254301i	$0.0818455\pi$
$569$			5.33123e10i			0.508603i	−0.967125	+	0.254301i	$0.918155\pi$
$570$	4.44098e10	+	6.01198e10i	0.420707	+	0.569532i
$571$	−4.45623e10	+	4.45623e10i	−0.419202	+	0.419202i	−0.884929	−	0.465727i	$-0.845793\pi$
$571$	−4.45623e10	+	4.45623e10i	−0.419202	+	0.419202i	0.465727	+	0.884929i	$0.345793\pi$
$572$	2.65721e10	−	8.64052e10i	0.248223	−	0.807153i
$573$	6.31644e10	−	6.31644e10i	0.585941	−	0.585941i
$574$	2.17849e9	+	3.27409e8i	0.0200682	+	0.00301608i
$575$			5.58665e10i			0.511069i
$576$	2.86284e10	−	2.29499e10i	0.260080	−	0.208493i
$577$	1.92831e11			1.73969			0.869847	−	0.493322i	$-0.164218\pi$
$577$	1.92831e11			1.73969			0.869847	+	0.493322i	$0.164218\pi$
$578$	−4.06217e10	+	2.70286e11i	−0.363954	+	2.42165i
$579$	−3.01804e10	−	3.01804e10i	−0.268541	−	0.268541i
$580$	−1.19505e11	−	3.67514e10i	−1.05603	−	0.324759i
$581$	−4.29430e10	−	4.29430e10i	−0.376867	−	0.376867i
$582$	6.29523e10	−	4.65022e10i	0.548681	−	0.405305i
$583$	−8.69606e10			−0.752746
$584$	4.32812e10	+	2.07753e10i	0.372090	+	0.178606i
$585$		−	5.79632e10i		−	0.494913i
$586$	−3.23269e10	+	2.38795e10i	−0.274141	+	0.202505i
$587$	−1.57969e10	+	1.57969e10i	−0.133051	+	0.133051i	−0.770496	−	0.637445i	$-0.779991\pi$
$587$	−1.57969e10	+	1.57969e10i	−0.133051	+	0.133051i	0.637445	+	0.770496i	$0.279991\pi$
$588$	−2.70035e10	−	5.09884e10i	−0.225898	−	0.426542i
$589$	−6.15949e10	+	6.15949e10i	−0.511780	+	0.511780i
$590$	2.21565e10	−	1.47423e11i	0.182849	−	1.21663i
$591$		−	4.44038e10i		−	0.363973i
$592$	−2.57888e10	−	1.35041e11i	−0.209963	−	1.09946i
$593$	−1.82931e11			−1.47934			−0.739669	−	0.672970i	$-0.765018\pi$
$593$	−1.82931e11			−1.47934			−0.739669	+	0.672970i	$0.765018\pi$
$594$	−1.55100e10	−	2.33102e9i	−0.124585	−	0.0187240i
$595$	2.56682e11	+	2.56682e11i	2.04799	+	2.04799i
$596$	4.86411e10	+	9.18445e10i	0.385494	+	0.727894i
$597$	8.34674e8	+	8.34674e8i	0.00657082	+	0.00657082i
$598$	−1.54243e11	−	2.08806e11i	−1.20615	−	1.63282i
$599$	−1.91701e11			−1.48908			−0.744538	−	0.667580i	$-0.767330\pi$
$599$	−1.91701e11			−1.48908			−0.744538	+	0.667580i	$0.767330\pi$
$600$	8.05506e9	+	2.29263e10i	0.0621533	+	0.176901i
$601$		−	9.59781e10i		−	0.735655i	−0.929894	−	0.367828i	$-0.880102\pi$
$601$		−	9.59781e10i		−	0.735655i	0.929894	−	0.367828i	$-0.119898\pi$
$602$	6.70676e10	+	9.07927e10i	0.510654	+	0.691298i
$603$	−2.10994e10	+	2.10994e10i	−0.159588	+	0.159588i
$604$	−6.69113e9	−	2.05772e9i	−0.0502749	−	0.0154610i
$605$	−6.23102e10	+	6.23102e10i	−0.465091	+	0.465091i
$606$	7.89556e8	+	1.18664e8i	0.00585454	+	0.000879887i
$607$			8.08524e10i			0.595577i	0.954632	+	0.297789i	$0.0962491\pi$
$607$			8.08524e10i			0.595577i	−0.954632	+	0.297789i	$0.903751\pi$
$608$	1.45493e11	−	5.75328e9i	1.06470	−	0.0421018i
$609$	−1.03294e11			−0.750939
$610$	3.71534e10	−	2.47209e11i	0.268336	−	1.78544i
$611$	−2.30402e11	−	2.30402e11i	−1.65319	−	1.65319i
$612$	−2.55262e10	+	8.30040e10i	−0.181962	+	0.591689i
$613$	8.34407e10	+	8.34407e10i	0.590930	+	0.590930i	0.937883	−	0.346953i	$-0.112784\pi$
$613$	8.34407e10	+	8.34407e10i	0.590930	+	0.590930i	−0.346953	+	0.937883i	$0.612784\pi$
$614$	2.09945e11	−	1.55084e11i	1.47718	−	1.09117i
$615$	−1.42374e9			−0.00995246
$616$	4.23366e10	+	1.20498e11i	0.294031	+	0.836871i
$617$		−	2.09834e11i		−	1.44789i	−0.689859	−	0.723943i	$-0.742328\pi$
$617$		−	2.09834e11i		−	1.44789i	0.689859	−	0.723943i	$-0.257672\pi$
$618$	−3.46439e10	+	2.55911e10i	−0.237505	+	0.175442i
$619$	2.75000e10	−	2.75000e10i	0.187314	−	0.187314i	−0.607220	−	0.794534i	$-0.707715\pi$
$619$	2.75000e10	−	2.75000e10i	0.187314	−	0.187314i	0.794534	+	0.607220i	$0.207715\pi$
$620$	−1.02090e11	+	5.40669e10i	−0.690899	+	0.365902i
$621$	−3.18481e10	+	3.18481e10i	−0.214149	+	0.214149i
$622$	−2.83056e10	+	1.88338e11i	−0.189108	+	1.25828i
$623$		−	2.25091e11i		−	1.49419i
$624$	−9.34042e10	−	6.34498e10i	−0.616067	−	0.418497i
$625$	1.86049e11			1.21929
$626$	−2.73339e11	−	4.10805e10i	−1.77993	−	0.267509i
$627$	−4.40107e10	−	4.40107e10i	−0.284766	−	0.284766i
$628$	1.26655e11	−	6.70770e10i	0.814301	−	0.431256i
$629$	2.30082e11	+	2.30082e11i	1.46987	+	1.46987i
$630$	4.86577e10	+	6.58703e10i	0.308880	+	0.418145i
$631$	−1.92278e11			−1.21286			−0.606432	−	0.795135i	$-0.707400\pi$
$631$	−1.92278e11			−1.21286			−0.606432	+	0.795135i	$0.707400\pi$
$632$	−1.25013e10	−	6.00068e9i	−0.0783583	−	0.0376125i
$633$		−	4.36823e10i		−	0.272076i
$634$	−5.78064e10	−	7.82553e10i	−0.357782	−	0.484347i
$635$	−6.03300e10	+	6.03300e10i	−0.371055	+	0.371055i
$636$	−3.19288e10	+	1.03824e11i	−0.195144	+	0.634553i
$637$	−1.25555e11	+	1.25555e11i	−0.762561	+	0.762561i
$638$	1.02958e11	+	1.54737e10i	0.621406	+	0.0933921i
$639$		−	1.96959e10i		−	0.118133i
$640$	1.86671e11	+	4.94242e10i	1.11264	+	0.294591i
$641$	−2.38418e11			−1.41223			−0.706117	−	0.708095i	$-0.749555\pi$
$641$	−2.38418e11			−1.41223			−0.706117	+	0.708095i	$0.749555\pi$
$642$	2.25437e10	−	1.50000e11i	0.132704	−	0.882979i
$643$	−4.68691e10	−	4.68691e10i	−0.274184	−	0.274184i	0.556598	−	0.830782i	$-0.312106\pi$
$643$	−4.68691e10	−	4.68691e10i	−0.274184	−	0.274184i	−0.830782	+	0.556598i	$0.812106\pi$
$644$	3.50567e11	+	1.07810e11i	2.03811	+	0.626779i
$645$	−5.15843e10	−	5.15843e10i	−0.298043	−	0.298043i
$646$	−2.77189e11	+	2.04757e11i	−1.59165	+	1.17573i
$647$	−9.62172e10			−0.549080			−0.274540	−	0.961576i	$-0.588526\pi$
$647$	−9.62172e10			−0.549080			−0.274540	+	0.961576i	$0.588526\pi$
$648$	−8.47774e9	+	1.76617e10i	−0.0480818	+	0.100169i
$649$			1.24141e11i			0.699740i
$650$	6.01511e10	−	4.44330e10i	0.336969	−	0.248915i
$651$	−6.74865e10	+	6.74865e10i	−0.375745	+	0.375745i
$652$	−1.20968e11	−	2.28413e11i	−0.669392	−	1.26395i
$653$	1.55526e11	−	1.55526e11i	0.855360	−	0.855360i	−0.135427	−	0.990787i	$-0.543241\pi$
$653$	1.55526e11	−	1.55526e11i	0.855360	−	0.855360i	0.990787	+	0.135427i	$0.0432407\pi$
$654$	−1.51544e10	+	1.00833e11i	−0.0828378	+	0.551180i
$655$		−	7.76685e10i		−	0.421968i
$656$	−1.55851e9	+	2.29427e9i	−0.00841576	+	0.0123888i
$657$	−2.56338e10			−0.137579
$658$	4.55245e11	+	6.84195e10i	2.42852	+	0.364986i
$659$	7.24722e10	+	7.24722e10i	0.384264	+	0.384264i	0.872636	−	0.488372i	$-0.162409\pi$
$659$	7.24722e10	+	7.24722e10i	0.384264	+	0.384264i	−0.488372	+	0.872636i	$0.662409\pi$
$660$	−3.86318e10	−	7.29449e10i	−0.203596	−	0.384432i
$661$	−1.45594e11	−	1.45594e11i	−0.762673	−	0.762673i	0.214132	−	0.976805i	$-0.431308\pi$
$661$	−1.45594e11	−	1.45594e11i	−0.762673	−	0.762673i	−0.976805	+	0.214132i	$0.931308\pi$
$662$	6.64325e10	+	8.99329e10i	0.345898	+	0.468259i
$663$	2.67246e11			1.38311
$664$	7.21378e10	−	2.53453e10i	0.371100	−	0.130384i
$665$			3.24982e11i			1.66178i
$666$	4.36152e10	+	5.90440e10i	0.221687	+	0.300109i
$667$	2.11413e11	−	2.11413e11i	1.06814	−	1.06814i
$668$	−1.50025e11	−	4.61372e10i	−0.753457	−	0.231710i
$669$	9.76350e10	−	9.76350e10i	0.487418	−	0.487418i
$670$	−1.55294e11	−	2.33393e10i	−0.770646	−	0.115822i
$671$			2.08167e11i			1.02689i
$672$	1.59409e11	−	6.30359e9i	0.781694	−	0.0309108i
$673$	−5.95017e10			−0.290048			−0.145024	−	0.989428i	$-0.546326\pi$
$673$	−5.95017e10			−0.290048			−0.145024	+	0.989428i	$0.546326\pi$
$674$	2.29510e10	−	1.52710e11i	0.111215	−	0.739994i
$675$	−9.17454e9	−	9.17454e9i	−0.0441946	−	0.0441946i
$676$	−4.07607e10	+	1.32542e11i	−0.195189	+	0.634700i
$677$	6.38020e10	+	6.38020e10i	0.303724	+	0.303724i	0.842469	−	0.538745i	$-0.181101\pi$
$677$	6.38020e10	+	6.38020e10i	0.303724	+	0.303724i	−0.538745	+	0.842469i	$0.681101\pi$
$678$	8.46724e10	−	6.25466e10i	0.400703	−	0.295995i
$679$	3.40293e11			1.60094
$680$	−4.31188e11	+	1.51496e11i	−2.01665	+	0.708541i
$681$			7.85629e10i			0.365283i
$682$	7.73765e10	−	5.71572e10i	0.357661	−	0.264201i
$683$	9.14398e10	−	9.14398e10i	0.420196	−	0.420196i	−0.465075	−	0.885271i	$-0.653973\pi$
$683$	9.14398e10	−	9.14398e10i	0.420196	−	0.420196i	0.885271	+	0.465075i	$0.153973\pi$
$684$	−6.87043e10	+	3.63859e10i	−0.313877	+	0.166230i
$685$	1.35995e10	−	1.35995e10i	0.0617675	−	0.0617675i
$686$	−7.31392e9	+	4.86649e10i	−0.0330258	+	0.219745i
$687$			2.35111e11i			1.05547i
$688$	−1.39592e11	+	2.66579e10i	−0.623028	+	0.118980i
$689$	3.34279e11			1.48331
$690$	−2.34406e11	−	3.52292e10i	−1.03412	−	0.155420i
$691$	2.29971e11	+	2.29971e11i	1.00870	+	1.00870i	0.999962	+	0.00873733i	$0.00278121\pi$
$691$	2.29971e11	+	2.29971e11i	1.00870	+	1.00870i	0.00873733	+	0.999962i	$0.497219\pi$
$692$	3.08168e10	−	1.63206e10i	0.134389	−	0.0711726i
$693$	−4.82204e10	−	4.82204e10i	−0.209073	−	0.209073i
$694$	1.70391e11	+	2.30666e11i	0.734527	+	0.994365i
$695$	1.93979e11			0.831408
$696$	5.62766e10	−	1.17241e11i	0.239823	−	0.499625i
$697$		−	6.56433e9i		−	0.0278137i
$698$	−7.73644e10	−	1.04732e11i	−0.325926	−	0.441222i
$699$	−8.59771e10	+	8.59771e10i	−0.360142	+	0.360142i
$700$	−3.10570e10	+	1.00989e11i	−0.129350	+	0.420611i
$701$	−2.53372e11	+	2.53372e11i	−1.04927	+	1.04927i	−0.0505476	+	0.998722i	$0.516097\pi$
$701$	−2.53372e11	+	2.53372e11i	−1.04927	+	1.04927i	−0.998722	+	0.0505476i	$0.983903\pi$
$702$	5.96208e10	+	8.96050e9i	0.245499	+	0.0368964i
$703$			2.91303e11i			1.19268i
$704$	−1.59835e11	−	1.75969e10i	−0.650700	−	0.0716381i
$705$	−2.97523e11			−1.20438
$706$	2.19632e10	−	1.46137e11i	0.0884050	−	0.588223i
$707$	2.45473e9	+	2.45473e9i	0.00982483	+	0.00982483i
$708$	1.48214e11	+	4.55802e10i	0.589870	+	0.181402i
$709$	−1.66916e11	−	1.66916e11i	−0.660561	−	0.660561i	0.294951	−	0.955512i	$-0.404697\pi$
$709$	−1.66916e11	−	1.66916e11i	−0.660561	−	0.660561i	−0.955512	+	0.294951i	$0.904697\pi$
$710$	8.33756e10	−	6.15887e10i	0.328099	−	0.242364i
$711$	7.40400e9			0.0289726
$712$	2.55485e11	+	1.22634e11i	0.994134	+	0.477191i
$713$		−	2.76251e11i		−	1.06892i
$714$	−3.03703e11	+	2.24342e11i	−1.16857	+	0.863213i
$715$	−1.79621e11	+	1.79621e11i	−0.687278	+	0.687278i
$716$	2.45046e9	+	4.62698e9i	0.00932386	+	0.0176054i
$717$	4.05362e10	−	4.05362e10i	0.153379	−	0.153379i
$718$	−4.64527e10	+	3.09084e11i	−0.174789	+	1.16300i
$719$		−	4.08434e11i		−	1.52829i	−0.645042	−	0.764147i	$-0.723160\pi$
$719$		−	4.08434e11i		−	1.52829i	0.645042	−	0.764147i	$-0.276840\pi$
$720$	−1.01274e11	+	1.93403e10i	−0.376851	+	0.0719672i
$721$	−1.87270e11			−0.692990
$722$	−3.63738e10	−	5.46667e9i	−0.133857	−	0.0201175i
$723$	−1.78096e11	−	1.78096e11i	−0.651780	−	0.651780i
$724$	−1.95389e11	−	3.68936e11i	−0.711126	−	1.34275i
$725$	6.09020e10	+	6.09020e10i	0.220434	+	0.220434i
$726$	−5.44596e10	−	7.37245e10i	−0.196032	−	0.265378i
$727$	1.75647e11			0.628785			0.314392	−	0.949293i	$-0.398199\pi$
$727$	1.75647e11			0.628785			0.314392	+	0.949293i	$0.398199\pi$
$728$	−1.62743e11	−	4.63199e11i	−0.579398	−	1.64908i
$729$		−	1.04604e10i		−	0.0370370i
$730$	−8.01562e10	−	1.08511e11i	−0.282258	−	0.382106i
$731$	2.37836e11	−	2.37836e11i	0.832929	−	0.832929i
$732$	2.48534e11	+	7.64316e10i	0.865649	+	0.266213i
$733$	−2.15517e11	+	2.15517e11i	−0.746563	+	0.746563i	−0.973832	−	0.227269i	$-0.927020\pi$
$733$	−2.15517e11	+	2.15517e11i	−0.746563	+	0.746563i	0.227269	+	0.973832i	$0.427020\pi$
$734$	4.26505e11	+	6.41001e10i	1.46940	+	0.220838i
$735$			1.62131e11i			0.555542i
$736$	−3.13364e11	+	3.39167e11i	−1.06792	+	1.15585i
$737$	1.30769e11			0.443234
$738$	2.20095e8	−	1.46445e9i	0.000741968	−	0.00493686i
$739$	2.36391e11	+	2.36391e11i	0.792598	+	0.792598i	0.981916	−	0.189318i	$-0.0606276\pi$
$739$	2.36391e11	+	2.36391e11i	0.792598	+	0.792598i	−0.189318	+	0.981916i	$0.560628\pi$
$740$	−1.13558e11	+	3.69258e11i	−0.378696	+	1.23141i
$741$	1.69179e11	+	1.69179e11i	0.561141	+	0.561141i
$742$	−3.79880e11	+	2.80613e11i	−1.25323	+	0.925748i
$743$	8.00989e10			0.262828			0.131414	−	0.991328i	$-0.458048\pi$
$743$	8.00989e10			0.262828			0.131414	+	0.991328i	$0.458048\pi$
$744$	−3.98310e10	−	1.13367e11i	−0.129996	−	0.369995i
$745$		−	2.92044e11i		−	0.948033i
$746$	3.94548e11	−	2.91448e11i	1.27393	−	0.941036i
$747$	−2.88677e10	+	2.88677e10i	−0.0927108	+	0.0927108i
$748$	3.36321e11	−	1.78117e11i	1.07436	−	0.568981i
$749$	4.66348e11	−	4.66348e11i	1.48178	−	1.48178i
$750$	−2.11006e10	+	1.40398e11i	−0.0666882	+	0.443726i
$751$		−	4.40769e11i		−	1.38564i	−0.721110	−	0.692821i	$-0.756368\pi$
$751$		−	4.40769e11i		−	1.38564i	0.721110	−	0.692821i	$-0.243632\pi$
$752$	−3.25685e11	+	4.79440e11i	−1.01842	+	1.49921i
$753$	−1.73409e10			−0.0539377
$754$	−3.95772e11	−	5.94812e10i	−1.22450	−	0.184032i
$755$	1.39096e10	+	1.39096e10i	0.0428083	+	0.0428083i
$756$	−7.52759e10	+	3.98663e10i	−0.230446	+	0.122045i
$757$	3.82170e11	+	3.82170e11i	1.16379	+	1.16379i	0.983640	+	0.180147i	$0.0576575\pi$
$757$	3.82170e11	+	3.82170e11i	1.16379	+	1.16379i	0.180147	+	0.983640i	$0.442343\pi$
$758$	−3.18595e11	−	4.31297e11i	−0.965076	−	1.30647i
$759$	1.97387e11			0.594772
$760$	−3.68864e11	−	1.77057e11i	−1.10563	−	0.530712i
$761$		−	4.89963e10i		−	0.146092i	−0.997329	−	0.0730458i	$-0.976728\pi$
$761$		−	4.89963e10i		−	0.146092i	0.997329	−	0.0730458i	$-0.0232719\pi$
$762$	−5.27289e10	−	7.13816e10i	−0.156397	−	0.211722i
$763$	−3.13491e11	+	3.13491e11i	−0.924967	+	0.924967i
$764$	−1.43737e11	+	4.67391e11i	−0.421885	+	1.37185i
$765$	1.72550e11	−	1.72550e11i	0.503814	−	0.503814i
$766$	−3.58665e11	−	5.39044e10i	−1.04178	−	0.156570i
$767$		−	4.77202e11i		−	1.37886i
$768$	−7.96948e10	+	1.84369e11i	−0.229079	+	0.529959i
$769$	−4.61794e11			−1.32051			−0.660257	−	0.751040i	$-0.729553\pi$
$769$	−4.61794e11			−1.32051			−0.660257	+	0.751040i	$0.729553\pi$
$770$	5.33397e10	−	3.54908e11i	0.151736	−	1.00961i
$771$	8.01686e10	+	8.01686e10i	0.226875	+	0.226875i
$772$	2.23322e11	+	6.86782e10i	0.628728	+	0.193353i
$773$	1.57922e11	+	1.57922e11i	0.442307	+	0.442307i	0.892787	−	0.450480i	$-0.148747\pi$
$773$	1.57922e11	+	1.57922e11i	0.442307	+	0.442307i	−0.450480	+	0.892787i	$0.648747\pi$
$774$	6.10339e10	−	4.50851e10i	0.170062	−	0.125623i
$775$	7.95801e10			0.220596
$776$	−1.85399e11	+	3.86243e11i	−0.511282	+	1.06516i
$777$			3.19167e11i			0.875656i
$778$	3.63564e10	−	2.68561e10i	0.0992345	−	0.0733035i
$779$	4.15550e9	−	4.15550e9i	0.0112843	−	0.0112843i
$780$	1.48502e11	+	2.80402e11i	0.401193	+	0.757536i
$781$	−6.10352e10	+	6.10352e10i	−0.164050	+	0.164050i
$782$	1.62429e11	−	1.08076e12i	0.434346	−	2.89002i
$783$			6.94375e10i			0.184734i
$784$	2.61264e11	+	1.77478e11i	0.691538	+	0.469764i
$785$	−4.02734e11			−1.06057
$786$	7.98896e10	+	1.20067e10i	0.209315	+	0.0314583i
$787$	3.89880e11	+	3.89880e11i	1.01632	+	1.01632i	0.999865	+	0.0164595i	$0.00523946\pi$
$787$	3.89880e11	+	3.89880e11i	1.01632	+	1.01632i	0.0164595	+	0.999865i	$0.494761\pi$
$788$	1.13762e11	+	2.14807e11i	0.295049	+	0.557114i
$789$	−1.07730e11	−	1.07730e11i	−0.277990	−	0.277990i
$790$	2.31522e10	+	3.13422e10i	0.0594406	+	0.0804676i
$791$	4.57703e11			1.16917
$792$	8.10030e10	−	2.84600e10i	0.205873	−	0.0723327i
$793$		−	8.00201e11i		−	2.02352i
$794$	−1.97006e11	−	2.66697e11i	−0.495676	−	0.671021i
$795$	2.15831e11	−	2.15831e11i	0.540312	−	0.540312i
$796$	−6.17625e9	−	1.89938e9i	−0.0153841	−	0.00473107i
$797$	−1.28611e11	+	1.28611e11i	−0.318745	+	0.318745i	−0.848285	−	0.529540i	$-0.822365\pi$
$797$	−1.28611e11	+	1.28611e11i	−0.318745	+	0.318745i	0.529540	+	0.848285i	$0.322365\pi$
$798$	−3.34275e11	−	5.02388e10i	−0.824314	−	0.123887i
$799$		−	1.37176e12i		−	3.36583i
$800$	−9.77044e10	−	9.02712e10i	−0.238536	−	0.220389i
$801$	−1.51314e11			−0.367577
$802$	7.27914e10	−	4.84335e11i	0.175947	−	1.17071i
$803$	7.94359e10	+	7.94359e10i	0.191053	+	0.191053i
$804$	4.80135e10	−	1.56127e11i	0.114905	−	0.373640i
$805$	−7.28766e11	−	7.28766e11i	−1.73542	−	1.73542i
$806$	−2.97438e11	+	2.19714e11i	−0.704783	+	0.520616i
$807$	−1.21221e11			−0.285815
$808$	−4.12357e9	+	1.44880e9i	−0.00967448	+	0.00339909i
$809$			3.20778e11i			0.748877i	0.927252	+	0.374439i	$0.122165\pi$
$809$			3.20778e11i			0.748877i	−0.927252	+	0.374439i	$0.877835\pi$
$810$	4.42802e10	−	3.27093e10i	0.102865	−	0.0759856i
$811$	−1.06682e11	+	1.06682e11i	−0.246608	+	0.246608i	−0.819577	−	0.572969i	$-0.805792\pi$
$811$	−1.06682e11	+	1.06682e11i	−0.246608	+	0.246608i	0.572969	+	0.819577i	$0.305792\pi$
$812$	4.99693e11	−	2.64639e11i	1.14942	−	0.608736i
$813$	1.35692e11	−	1.35692e11i	0.310594	−	0.310594i
$814$	4.78119e10	−	3.18128e11i	0.108903	−	0.724610i
$815$			7.26301e11i			1.64621i
$816$	−8.91710e10	−	4.66938e11i	−0.201124	−	1.05317i
$817$	3.01121e11			0.675853
$818$	7.25603e11	+	1.09052e11i	1.62064	+	0.243568i
$819$	1.85361e11	+	1.85361e11i	0.411985	+	0.411985i
$820$	6.88748e9	−	3.64762e9i	0.0152337	−	0.00806779i
$821$	4.40491e11	+	4.40491e11i	0.969537	+	0.969537i	0.999550	−	0.0300127i	$-0.00955477\pi$
$821$	4.40491e11	+	4.40491e11i	0.969537	+	0.969537i	−0.0300127	+	0.999550i	$0.509555\pi$
$822$	1.18861e10	+	1.60907e10i	0.0260346	+	0.0352443i
$823$	−3.96401e11			−0.864042			−0.432021	−	0.901864i	$-0.642199\pi$
$823$	−3.96401e11			−0.864042			−0.432021	+	0.901864i	$0.642199\pi$
$824$	1.02029e11	−	2.12557e11i	0.221316	−	0.461069i
$825$			5.68615e10i			0.122745i
$826$	4.00591e11	+	5.42300e11i	0.860560	+	1.16498i
$827$	−4.18792e11	+	4.18792e11i	−0.895316	+	0.895316i	−0.995017	−	0.0997016i	$-0.968211\pi$
$827$	−4.18792e11	+	4.18792e11i	−0.895316	+	0.895316i	0.0997016	+	0.995017i	$0.468211\pi$
$828$	7.24733e10	−	2.35663e11i	0.154190	−	0.501383i
$829$	−3.69338e11	+	3.69338e11i	−0.781999	+	0.781999i	−0.980168	−	0.198169i	$-0.936501\pi$
$829$	−3.69338e11	+	3.69338e11i	−0.781999	+	0.781999i	0.198169	+	0.980168i	$0.436501\pi$
$830$	−2.12470e11	−	3.19324e10i	−0.447698	−	0.0672852i
$831$			3.03661e11i			0.636773i
$832$	6.14410e11	+	6.76428e10i	1.28223	+	0.141165i
$833$	−7.47525e11			−1.55255
$834$	−2.99870e10	+	1.99526e11i	−0.0619825	+	0.412415i
$835$	3.11875e11	+	3.11875e11i	0.641557	+	0.641557i
$836$	3.25662e11	+	1.00151e11i	0.666717	+	0.205035i
$837$	4.53666e10	+	4.53666e10i	0.0924347	+	0.0924347i
$838$	1.49710e11	−	1.10589e11i	0.303582	−	0.224253i
$839$	−5.35390e11			−1.08049			−0.540247	−	0.841506i	$-0.681669\pi$
$839$	−5.35390e11			−1.08049			−0.540247	+	0.841506i	$0.681669\pi$
$840$	−4.04146e11	−	1.93993e11i	−0.811748	−	0.389644i
$841$			3.93097e10i			0.0785807i
$842$	−2.97186e11	+	2.19529e11i	−0.591263	+	0.436760i
$843$	2.16446e11	−	2.16446e11i	0.428588	−	0.428588i
$844$	1.11914e11	+	2.11317e11i	0.220554	+	0.416452i
$845$	2.75532e11	−	2.75532e11i	0.540437	−	0.540437i
$846$	4.59939e10	−	3.06031e11i	0.0897880	−	0.597426i
$847$		−	3.98524e11i		−	0.774320i
$848$	−1.11538e11	−	5.84059e11i	−0.215694	−	1.12947i
$849$	1.04094e11			0.200353
$850$	3.11335e11	+	4.67911e10i	0.596421	+	0.0896370i
$851$	−6.53242e11	−	6.53242e11i	−1.24554	−	1.24554i
$852$	5.04609e10	+	9.52808e10i	0.0957628	+	0.180820i
$853$	−1.25669e11	−	1.25669e11i	−0.237373	−	0.237373i	0.578388	−	0.815762i	$-0.303682\pi$
$853$	−1.25669e11	−	1.25669e11i	−0.237373	−	0.237373i	−0.815762	+	0.578388i	$0.803682\pi$
$854$	6.71736e11	+	9.09361e11i	1.26289	+	1.70964i
$855$	2.18464e11			0.408803
$856$	2.75242e11	+	7.83395e11i	0.512649	+	1.45910i
$857$			9.60332e11i			1.78032i	0.455648	+	0.890160i	$0.349407\pi$
$857$			9.60332e11i			1.78032i	−0.455648	+	0.890160i	$0.650593\pi$
$858$	−1.56990e11	−	2.12525e11i	−0.289683	−	0.392157i
$859$	−3.78436e11	+	3.78436e11i	−0.695056	+	0.695056i	−0.963340	−	0.268284i	$-0.913543\pi$
$859$	−3.78436e11	+	3.78436e11i	−0.695056	+	0.695056i	0.268284	+	0.963340i	$0.413543\pi$
$860$	3.81703e11	+	1.17385e11i	0.697802	+	0.214595i
$861$	4.55298e9	−	4.55298e9i	0.00828482	−	0.00828482i
$862$	2.26090e10	+	3.39795e9i	0.0409499	+	0.00615443i
$863$		−	2.22812e11i		−	0.401693i	−0.979623	−	0.200847i	$-0.935631\pi$
$863$		−	2.22812e11i		−	0.401693i	0.979623	−	0.200847i	$-0.0643693\pi$
$864$	−4.23748e9	−	1.07160e11i	−0.00760418	−	0.192300i
$865$	−9.79902e10			−0.175032
$866$	−4.87051e10	+	3.24071e11i	−0.0865970	+	0.576193i
$867$	5.64889e11	+	5.64889e11i	0.999739	+	0.999739i
$868$	1.53572e11	−	4.99373e11i	0.270541	−	0.879723i
$869$	−2.29441e10	−	2.29441e10i	−0.0402339	−	0.0402339i
$870$	−2.93939e11	+	2.17129e11i	−0.513074	+	0.379002i
$871$	−5.02678e11			−0.873408
$872$	−1.85024e11	−	5.26617e11i	−0.320010	−	0.910812i
$873$		−	2.28756e11i		−	0.393837i
$874$	7.86990e11	−	5.81341e11i	1.34872	−	0.996289i
$875$	−4.36495e11	+	4.36495e11i	−0.744642	+	0.744642i
$876$	1.24006e11	−	6.56737e10i	0.210584	−	0.111526i
$877$	2.02917e10	−	2.02917e10i	0.0343021	−	0.0343021i	−0.689748	−	0.724050i	$-0.742279\pi$
$877$	2.02917e10	−	2.02917e10i	0.0343021	−	0.0343021i	0.724050	+	0.689748i	$0.242279\pi$
$878$	−1.34834e11	+	8.97147e11i	−0.226892	+	1.50968i
$879$			1.17470e11i			0.196775i
$880$	3.73770e11	+	2.53903e11i	0.623266	+	0.423387i
$881$	−5.75202e11			−0.954809			−0.477405	−	0.878684i	$-0.658422\pi$
$881$	−5.75202e11			−0.954809			−0.477405	+	0.878684i	$0.658422\pi$
$882$	−1.66767e11	−	2.50637e10i	−0.275573	−	0.0414163i
$883$	−9.76084e10	−	9.76084e10i	−0.160563	−	0.160563i	0.622253	−	0.782816i	$-0.286217\pi$
$883$	−9.76084e10	−	9.76084e10i	−0.160563	−	0.160563i	−0.782816	+	0.622253i	$0.786217\pi$
$884$	−1.29283e12	+	6.84685e11i	−2.11706	+	1.12120i
$885$	−3.08110e11	−	3.08110e11i	−0.502265	−	0.502265i
$886$	4.16505e11	+	5.63844e11i	0.675905	+	0.915006i
$887$	8.61421e11			1.39162			0.695811	−	0.718225i	$-0.255045\pi$
$887$	8.61421e11			1.39162			0.695811	+	0.718225i	$0.255045\pi$
$888$	−3.62263e11	−	1.73889e11i	−0.582602	−	0.279653i
$889$		−	3.85859e11i		−	0.617762i
$890$	−4.73154e11	−	6.40532e11i	−0.754124	−	1.02089i
$891$	−3.24153e10	+	3.24153e10i	−0.0514327	+	0.0514327i
$892$	−2.22178e11	+	7.22460e11i	−0.350947	+	1.14118i
$893$	8.68386e11	−	8.68386e11i	1.36555	−	1.36555i
$894$	3.00396e11	+	4.51469e10i	0.470266	+	0.0706770i
$895$		−	1.47127e10i		−	0.0229298i
$896$	−7.55008e11	+	4.38901e11i	−1.17144	+	0.680981i
$897$	−7.58760e11			−1.17202
$898$	−7.29288e10	+	4.85249e11i	−0.112149	+	0.746206i
$899$	−3.01151e11	−	3.01151e11i	−0.461047	−	0.461047i
$900$	6.78879e10	+	2.08775e10i	0.103472	+	0.0318206i
$901$	9.95113e11	+	9.95113e11i	1.50999	+	1.50999i
$902$	−5.22021e9	+	3.85612e9i	−0.00788609	+	0.00582537i
$903$	3.29923e11			0.496206
$904$	−2.49366e11	+	5.19506e11i	−0.373391	+	0.777887i
$905$			1.17313e12i			1.74885i
$906$	−1.64577e10	+	1.21571e10i	−0.0244262	+	0.0180434i
$907$	−7.63561e11	+	7.63561e11i	−1.12827	+	1.12827i	−0.137817	+	0.990458i	$0.544009\pi$
$907$	−7.63561e11	+	7.63561e11i	−1.12827	+	1.12827i	−0.990458	+	0.137817i	$0.955991\pi$
$908$	−2.01278e11	−	3.80055e11i	−0.296110	−	0.559118i
$909$	1.65015e9	−	1.65015e9i	0.00241695	−	0.00241695i
$910$	−2.05039e11	+	1.36428e12i	−0.299000	+	1.98947i
$911$		−	1.00379e11i		−	0.145736i	−0.997342	−	0.0728682i	$-0.976785\pi$
$911$		−	1.00379e11i		−	0.145736i	0.997342	−	0.0728682i	$-0.0232153\pi$
$912$	2.39143e11	−	3.52041e11i	0.345683	−	0.508878i
$913$	1.78915e11			0.257492
$914$	−1.52534e11	−	2.29246e10i	−0.218566	−	0.0328487i
$915$	−5.16658e11	−	5.16658e11i	−0.737087	−	0.737087i
$916$	−6.02354e11	−	1.13737e12i	−0.855599	−	1.61555i
$917$	2.48376e11	+	2.48376e11i	0.351263	+	0.351263i
$918$	1.50810e11	+	2.04159e11i	0.212354	+	0.287474i
$919$	4.24302e10			0.0594858			0.0297429	−	0.999558i	$-0.490531\pi$
$919$	4.24302e10			0.0594858			0.0297429	+	0.999558i	$0.490531\pi$
$920$	1.22422e12	−	4.30123e11i	1.70886	−	0.600401i
$921$		−	7.62900e11i		−	1.06030i
$922$	4.96858e10	+	6.72620e10i	0.0687556	+	0.0930779i
$923$	2.34621e11	−	2.34621e11i	0.323266	−	0.323266i
$924$	3.56811e11	+	1.09730e11i	0.489498	+	0.150535i
$925$	1.88181e11	−	1.88181e11i	0.257044	−	0.257044i
$926$	−9.18890e10	−	1.38101e10i	−0.124974	−	0.0187825i
$927$			1.25889e11i			0.170478i
$928$	2.81290e10	+	7.11347e11i	0.0379283	+	0.959156i
$929$	1.03495e12			1.38949			0.694745	−	0.719256i	$-0.255517\pi$
$929$	1.03495e12			1.38949			0.694745	+	0.719256i	$0.255517\pi$
$930$	−5.01830e10	+	3.33904e11i	−0.0670849	+	0.446365i
$931$	−4.73216e11	−	4.73216e11i	−0.629884	−	0.629884i
$932$	1.95649e11	−	6.36196e11i	0.259307	−	0.843193i
$933$	3.93620e11	+	3.93620e11i	0.519458	+	0.519458i
$934$	8.43257e11	−	6.22905e11i	1.10808	−	0.818529i
$935$	−1.06942e12			−1.39928
$936$	−3.11378e11	+	1.09401e11i	−0.405681	+	0.142534i
$937$		−	8.71654e11i		−	1.13080i	−0.824817	−	0.565400i	$-0.808722\pi$
$937$		−	8.71654e11i		−	1.13080i	0.824817	−	0.565400i	$-0.191278\pi$
$938$	5.71251e11	−	4.21977e11i	0.737931	−	0.545102i
$939$	−5.71269e11	+	5.71269e11i	−0.734816	+	0.734816i
$940$	1.43929e12	−	7.62254e11i	1.84348	−	0.976311i
$941$	−8.26055e11	+	8.26055e11i	−1.05354	+	1.05354i	−0.0550553	+	0.998483i	$0.517533\pi$
$941$	−8.26055e11	+	8.26055e11i	−1.05354	+	1.05354i	−0.998483	+	0.0550553i	$0.982467\pi$
$942$	6.22585e10	−	4.14251e11i	0.0790669	−	0.526090i
$943$			1.86373e10i			0.0235687i
$944$	−8.33776e11	+	1.59226e11i	−1.04993	+	0.200505i
$945$	2.39360e11			0.300140
$946$	−3.28849e11	−	4.94233e10i	−0.410613	−	0.0617116i
$947$	−2.32021e11	−	2.32021e11i	−0.288487	−	0.288487i	0.547994	−	0.836482i	$-0.315391\pi$
$947$	−2.32021e11	−	2.32021e11i	−0.288487	−	0.288487i	−0.836482	+	0.547994i	$0.815391\pi$
$948$	−3.58176e10	+	1.89691e10i	−0.0443468	+	0.0234862i
$949$	−3.05354e11	−	3.05354e11i	−0.376477	−	0.376477i
$950$	1.67468e11	+	2.26710e11i	0.205607	+	0.278340i
$951$	−2.84365e11			−0.347659
$952$	8.94426e11	−	1.86336e12i	1.08892	−	2.26856i
$953$			1.33518e10i			0.0161871i	0.999967	+	0.00809355i	$0.00257628\pi$
$953$			1.33518e10i			0.0161871i	−0.999967	+	0.00809355i	$0.997424\pi$
$954$	1.88638e11	+	2.55368e11i	0.227738	+	0.308299i
$955$	9.71622e11	−	9.71622e11i	1.16811	−	1.16811i
$956$	−9.22439e10	+	2.99951e11i	−0.110435	+	0.359103i
$957$	2.15178e11	−	2.15178e11i	0.256537	−	0.256537i
$958$	−1.46477e12	−	2.20143e11i	−1.73903	−	0.261362i
$959$			8.69796e10i			0.102836i
$960$	4.40374e11	−	3.53026e11i	0.518486	−	0.415644i
$961$	4.59380e11			0.538615
$962$	−1.83790e11	+	1.22289e12i	−0.214597	+	1.42787i
$963$	−3.13495e11	−	3.13495e11i	−0.364523	−	0.364523i
$964$	1.31784e12	+	4.05274e11i	1.52600	+	0.469290i
$965$	−4.64247e11	−	4.64247e11i	−0.535352	−	0.535352i
$966$	8.62266e11	−	6.36947e11i	0.990222	−	0.731467i
$967$	−6.56705e11			−0.751042			−0.375521	−	0.926814i	$-0.622536\pi$
$967$	−6.56705e11			−0.751042			−0.375521	+	0.926814i	$0.622536\pi$
$968$	4.52336e11	+	2.17124e11i	0.515180	+	0.247290i
$969$			1.00725e12i			1.14247i
$970$	9.68359e11	−	7.15317e11i	1.09383	−	0.808000i
$971$	9.77017e10	−	9.77017e10i	0.109907	−	0.109907i	−0.650015	−	0.759922i	$-0.725237\pi$
$971$	9.77017e10	−	9.77017e10i	0.109907	−	0.109907i	0.759922	+	0.650015i	$0.225237\pi$
$972$	2.67994e10	+	5.06029e10i	0.0300234	+	0.0566906i
$973$	−6.20324e11	+	6.20324e11i	−0.692097	+	0.692097i
$974$	−9.69144e10	+	6.44843e11i	−0.107684	+	0.716503i
$975$		−	2.18577e11i		−	0.241873i
$976$	−1.39813e12	+	2.67000e11i	−1.54080	+	0.294247i
$977$	8.10989e11			0.890095			0.445048	−	0.895507i	$-0.353187\pi$
$977$	8.10989e11			0.890095			0.445048	+	0.895507i	$0.353187\pi$
$978$	−7.47071e11	−	1.12278e11i	−0.816594	−	0.122727i
$979$	4.68902e11	+	4.68902e11i	0.510448	+	0.510448i
$980$	−4.15380e11	−	7.84324e11i	−0.450341	−	0.850338i
$981$	2.10739e11	+	2.10739e11i	0.227546	+	0.227546i
$982$	−2.86166e11	−	3.87397e11i	−0.307732	−	0.416592i
$983$	5.69686e11			0.610129			0.305064	−	0.952332i	$-0.401322\pi$
$983$	5.69686e11			0.610129			0.305064	+	0.952332i	$0.401322\pi$
$984$	2.68720e9	+	7.64832e9i	0.00286629	+	0.00815804i
$985$		−	6.83037e11i		−	0.725604i
$986$	−1.00110e12	−	1.35524e12i	−1.05918	−	1.43387i
$987$	9.51448e11	−	9.51448e11i	1.00257	−	1.00257i
$988$	−1.25185e12	−	3.84981e11i	−1.31379	−	0.404029i
$989$	−6.75258e11	+	6.75258e11i	−0.705804	+	0.705804i
$990$	−2.38581e11	−	3.58567e10i	−0.248367	−	0.0373275i
$991$			1.31899e12i			1.36757i	0.729685	+	0.683783i	$0.239667\pi$
$991$			1.31899e12i			1.36757i	−0.729685	+	0.683783i	$0.760333\pi$
$992$	4.83133e11	+	4.46377e11i	0.498908	+	0.460951i
$993$	3.26799e11			0.336111
$994$	−6.96724e10	+	4.63581e11i	−0.0713699	+	0.474876i
$995$	1.28393e10	+	1.28393e10i	0.0130993	+	0.0130993i
$996$	6.56912e10	−	2.13609e11i	0.0667529	−	0.217062i
$997$	4.63158e10	+	4.63158e10i	0.0468758	+	0.0468758i	0.730156	−	0.683280i	$-0.239447\pi$
$997$	4.63158e10	+	4.63158e10i	0.0468758	+	0.0468758i	−0.683280	+	0.730156i	$0.739447\pi$
$998$	1.12984e10	−	8.34601e9i	0.0113892	−	0.00841311i
$999$	2.14554e11			0.215415

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.9.l.a.43.15	yes	64
4.3	odd	2		192.9.l.a.79.12		64
16.3	odd	4	inner	48.9.l.a.19.15	✓	64
16.13	even	4		192.9.l.a.175.12		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.15	✓	64	16.3	odd	4	inner
48.9.l.a.43.15	yes	64	1.1	even	1	trivial
192.9.l.a.79.12		64	4.3	odd	2
192.9.l.a.175.12		64	16.13	even	4

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.37796 + 15.8223i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-244.691 - 75.2496i) q^{4} +(508.668 + 508.668i) q^{5} +(-601.848 + 444.579i) q^{6} -3253.34 q^{7} +(1772.49 - 3692.63i) q^{8} +2187.00i q^{9} +O(q^{10})\)	\(q+(-2.37796 + 15.8223i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-244.691 - 75.2496i) q^{4} +(508.668 + 508.668i) q^{5} +(-601.848 + 444.579i) q^{6} -3253.34 q^{7} +(1772.49 - 3692.63i) q^{8} +2187.00i q^{9} +(-9257.88 + 6838.70i) q^{10} +(6777.24 - 6777.24i) q^{11} +(-5603.10 - 10579.8i) q^{12} +(-26051.9 + 26051.9i) q^{13} +(7736.30 - 51475.3i) q^{14} +33641.4i q^{15} +(54211.0 + 36825.7i) q^{16} -155108. q^{17} +(-34603.4 - 5200.60i) q^{18} +(-98189.8 - 98189.8i) q^{19} +(-86189.2 - 162743. i) q^{20} +(-107582. - 107582. i) q^{21} +(91115.6 + 123348. i) q^{22} +440378. q^{23} +(180721. - 63495.5i) q^{24} +126860. i q^{25} +(-350251. - 474152. i) q^{26} +(-72320.0 + 72320.0i) q^{27} +(796061. + 244812. i) q^{28} +(480071. - 480071. i) q^{29} +(-532284. - 79997.7i) q^{30} -627305. i q^{31} +(-711579. + 770173. i) q^{32} +448221. q^{33} +(368839. - 2.45416e6i) q^{34} +(-1.65487e6 - 1.65487e6i) q^{35} +(164571. - 535138. i) q^{36} +(-1.48337e6 - 1.48337e6i) q^{37} +(1.78708e6 - 1.32010e6i) q^{38} -1.72298e6 q^{39} +(2.77993e6 - 976715. i) q^{40} +42321.1i q^{41} +(1.95802e6 - 1.44637e6i) q^{42} +(-1.53336e6 + 1.53336e6i) q^{43} +(-2.16831e6 + 1.14834e6i) q^{44} +(-1.11246e6 + 1.11246e6i) q^{45} +(-1.04720e6 + 6.96779e6i) q^{46} +8.84396e6i q^{47} +(574898. + 3.01041e6i) q^{48} +4.81940e6 q^{49} +(-2.00722e6 - 301669. i) q^{50} +(-5.12911e6 - 5.12911e6i) q^{51} +(8.33505e6 - 4.41426e6i) q^{52} +(-6.41564e6 - 6.41564e6i) q^{53} +(-972295. - 1.31624e6i) q^{54} +6.89473e6 q^{55} +(-5.76649e6 + 1.20134e7i) q^{56} -6.49390e6i q^{57} +(6.45424e6 + 8.73742e6i) q^{58} +(-9.15868e6 + 9.15868e6i) q^{59} +(2.53150e6 - 8.23172e6i) q^{60} +(-1.53578e7 + 1.53578e7i) q^{61} +(9.92541e6 + 1.49170e6i) q^{62} -7.11505e6i q^{63} +(-1.04938e7 - 1.30903e7i) q^{64} -2.65035e7 q^{65} +(-1.06585e6 + 7.09189e6i) q^{66} +(9.64762e6 + 9.64762e6i) q^{67} +(3.79534e7 + 1.16718e7i) q^{68} +(1.45625e7 + 1.45625e7i) q^{69} +(3.01190e7 - 2.22486e7i) q^{70} -9.00590e6 q^{71} +(8.07578e6 + 3.87643e6i) q^{72} +1.17210e7i q^{73} +(2.69977e7 - 1.99429e7i) q^{74} +(-4.19503e6 + 4.19503e6i) q^{75} +(1.66374e7 + 3.14148e7i) q^{76} +(-2.20486e7 + 2.20486e7i) q^{77} +(4.09716e6 - 2.72614e7i) q^{78} -3.38546e6i q^{79} +(8.84332e6 + 4.63074e7i) q^{80} -4.78297e6 q^{81} +(-669618. - 100638. i) q^{82} +(1.31997e7 + 1.31997e7i) q^{83} +(1.82288e7 + 3.44197e7i) q^{84} +(-7.88982e7 - 7.88982e7i) q^{85} +(-2.06150e7 - 2.79076e7i) q^{86} +3.17501e7 q^{87} +(-1.30133e7 - 3.70384e7i) q^{88} +6.91877e7i q^{89} +(-1.49562e7 - 2.02470e7i) q^{90} +(8.47556e7 - 8.47556e7i) q^{91} +(-1.07756e8 - 3.31382e7i) q^{92} +(2.07438e7 - 2.07438e7i) q^{93} +(-1.39932e8 - 2.10306e7i) q^{94} -9.98919e7i q^{95} +(-4.89988e7 + 1.93758e6i) q^{96} -1.04598e8 q^{97} +(-1.14603e7 + 7.62540e7i) q^{98} +(1.48218e7 + 1.48218e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 372 q^{4} + 17460 q^{8}+O(q^{10}) \) 64 * q - 372 * q^4 + 17460 * q^8	\( 64 q - 372 q^{4} + 17460 q^{8} - 13784 q^{10} + 39552 q^{11} - 22680 q^{12} + 116772 q^{14} - 161824 q^{16} - 26244 q^{18} - 167552 q^{19} + 690000 q^{20} - 1252768 q^{22} + 1691136 q^{23} - 74844 q^{24} - 1682100 q^{26} + 678600 q^{28} - 2132352 q^{29} - 2054808 q^{30} + 1407840 q^{32} - 3704544 q^{34} - 2415744 q^{35} - 1041012 q^{36} - 4720512 q^{37} + 2413320 q^{38} - 3544848 q^{40} + 9436500 q^{42} - 7244672 q^{43} - 3982056 q^{44} + 11165992 q^{46} - 9467280 q^{48} + 52706752 q^{49} + 17072676 q^{50} + 13862016 q^{51} - 22890864 q^{52} - 5358720 q^{53} - 4960116 q^{54} - 46326784 q^{55} - 9637152 q^{56} + 25732944 q^{58} + 44938752 q^{59} + 40927032 q^{60} + 24476032 q^{61} - 17024868 q^{62} - 116303448 q^{64} + 29941632 q^{65} - 56828952 q^{66} - 44244736 q^{67} - 12614400 q^{68} - 8636544 q^{69} - 60922560 q^{70} + 159664128 q^{71} - 18502020 q^{72} + 140654028 q^{74} + 12918528 q^{75} + 204842760 q^{76} - 94964352 q^{77} + 14001660 q^{78} + 38076648 q^{80} - 306110016 q^{81} - 260917000 q^{82} + 209328000 q^{83} - 127862712 q^{84} + 106960000 q^{85} - 123451824 q^{86} + 104240736 q^{88} + 53520264 q^{90} - 45401472 q^{91} + 351567216 q^{92} + 208488216 q^{94} + 49597920 q^{96} - 681890712 q^{98} + 86500224 q^{99}+O(q^{100}) \) 64 * q - 372 * q^4 + 17460 * q^8 - 13784 * q^10 + 39552 * q^11 - 22680 * q^12 + 116772 * q^14 - 161824 * q^16 - 26244 * q^18 - 167552 * q^19 + 690000 * q^20 - 1252768 * q^22 + 1691136 * q^23 - 74844 * q^24 - 1682100 * q^26 + 678600 * q^28 - 2132352 * q^29 - 2054808 * q^30 + 1407840 * q^32 - 3704544 * q^34 - 2415744 * q^35 - 1041012 * q^36 - 4720512 * q^37 + 2413320 * q^38 - 3544848 * q^40 + 9436500 * q^42 - 7244672 * q^43 - 3982056 * q^44 + 11165992 * q^46 - 9467280 * q^48 + 52706752 * q^49 + 17072676 * q^50 + 13862016 * q^51 - 22890864 * q^52 - 5358720 * q^53 - 4960116 * q^54 - 46326784 * q^55 - 9637152 * q^56 + 25732944 * q^58 + 44938752 * q^59 + 40927032 * q^60 + 24476032 * q^61 - 17024868 * q^62 - 116303448 * q^64 + 29941632 * q^65 - 56828952 * q^66 - 44244736 * q^67 - 12614400 * q^68 - 8636544 * q^69 - 60922560 * q^70 + 159664128 * q^71 - 18502020 * q^72 + 140654028 * q^74 + 12918528 * q^75 + 204842760 * q^76 - 94964352 * q^77 + 14001660 * q^78 + 38076648 * q^80 - 306110016 * q^81 - 260917000 * q^82 + 209328000 * q^83 - 127862712 * q^84 + 106960000 * q^85 - 123451824 * q^86 + 104240736 * q^88 + 53520264 * q^90 - 45401472 * q^91 + 351567216 * q^92 + 208488216 * q^94 + 49597920 * q^96 - 681890712 * q^98 + 86500224 * q^99

Introduction

L-functions

Modular forms

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