LMFDB - Embedded newform 48.9.l.a.43.16

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			43.16
Character	$\chi$	$=$	48.43
Dual form			48.9.l.a.19.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.76142 - 15.9027i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-249.795 + 56.0230i) q^{4} +(47.4496 + 47.4496i) q^{5} +(467.627 - 584.121i) q^{6} -2246.74 q^{7} +(1330.91 + 3873.74i) q^{8} +2187.00i q^{9} +O(q^{10})$	\(q+(-1.76142 - 15.9027i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-249.795 + 56.0230i) q^{4} +(47.4496 + 47.4496i) q^{5} +(467.627 - 584.121i) q^{6} -2246.74 q^{7} +(1330.91 + 3873.74i) q^{8} +2187.00i q^{9} +(670.999 - 838.157i) q^{10} +(17865.3 - 17865.3i) q^{11} +(-10112.8 - 6407.67i) q^{12} +(-16949.9 + 16949.9i) q^{13} +(3957.46 + 35729.3i) q^{14} +3138.13i q^{15} +(59258.9 - 27988.5i) q^{16} +141614. q^{17} +(34779.3 - 3852.23i) q^{18} +(165898. + 165898. i) q^{19} +(-14510.9 - 9194.39i) q^{20} +(-74295.4 - 74295.4i) q^{21} +(-315577. - 252640. i) q^{22} +64910.8 q^{23} +(-84086.6 + 172108. i) q^{24} -386122. i q^{25} +(299406. + 239694. i) q^{26} +(-72320.0 + 72320.0i) q^{27} +(561224. - 125869. i) q^{28} +(67177.4 - 67177.4i) q^{29} +(49905.0 - 5527.58i) q^{30} -1.30939e6i q^{31} +(-549474. - 893079. i) q^{32} +1.18155e6 q^{33} +(-249443. - 2.25206e6i) q^{34} +(-106607. - 106607. i) q^{35} +(-122522. - 546301. i) q^{36} +(2.03671e6 + 2.03671e6i) q^{37} +(2.34601e6 - 2.93044e6i) q^{38} -1.12100e6 q^{39} +(-120656. + 246959. i) q^{40} -1.65048e6i q^{41} +(-1.05064e6 + 1.31237e6i) q^{42} +(1.66741e6 - 1.66741e6i) q^{43} +(-3.46180e6 + 5.46354e6i) q^{44} +(-103772. + 103772. i) q^{45} +(-114336. - 1.03226e6i) q^{46} +9.60354e6i q^{47} +(2.88510e6 + 1.03405e6i) q^{48} -716963. q^{49} +(-6.14040e6 + 680125. i) q^{50} +(4.68292e6 + 4.68292e6i) q^{51} +(3.28441e6 - 5.18358e6i) q^{52} +(1.35090e6 + 1.35090e6i) q^{53} +(1.27747e6 + 1.02270e6i) q^{54} +1.69541e6 q^{55} +(-2.99022e6 - 8.70329e6i) q^{56} +1.09718e7i q^{57} +(-1.18663e6 - 949978. i) q^{58} +(-4.17057e6 + 4.17057e6i) q^{59} +(-175808. - 783889. i) q^{60} +(5.53048e6 - 5.53048e6i) q^{61} +(-2.08229e7 + 2.30639e6i) q^{62} -4.91362e6i q^{63} +(-1.32346e7 + 1.03112e7i) q^{64} -1.60853e6 q^{65} +(-2.08120e6 - 1.87898e7i) q^{66} +(1.60468e7 + 1.60468e7i) q^{67} +(-3.53745e7 + 7.93365e6i) q^{68} +(2.14648e6 + 2.14648e6i) q^{69} +(-1.50756e6 + 1.88312e6i) q^{70} +1.51290e7 q^{71} +(-8.47188e6 + 2.91071e6i) q^{72} -9.31022e6i q^{73} +(2.88017e7 - 3.59768e7i) q^{74} +(1.27683e7 - 1.27683e7i) q^{75} +(-5.07344e7 - 3.21463e7i) q^{76} +(-4.01388e7 + 4.01388e7i) q^{77} +(1.97456e6 + 1.78270e7i) q^{78} +4.17784e7i q^{79} +(4.13985e6 + 1.48377e6i) q^{80} -4.78297e6 q^{81} +(-2.62472e7 + 2.90720e6i) q^{82} +(1.25940e7 + 1.25940e7i) q^{83} +(2.27209e7 + 1.43964e7i) q^{84} +(6.71953e6 + 6.71953e6i) q^{85} +(-2.94534e7 - 2.35794e7i) q^{86} +4.44286e6 q^{87} +(9.29830e7 + 4.54285e7i) q^{88} -4.99268e7i q^{89} +(1.83305e6 + 1.46748e6i) q^{90} +(3.80820e7 - 3.80820e7i) q^{91} +(-1.62144e7 + 3.63650e6i) q^{92} +(4.32991e7 - 4.32991e7i) q^{93} +(1.52723e8 - 1.69159e7i) q^{94} +1.57435e7i q^{95} +(1.13624e7 - 4.77025e7i) q^{96} -4.98508e7 q^{97} +(1.26288e6 + 1.14017e7i) q^{98} +(3.90715e7 + 3.90715e7i) 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 $

$2$	−1.76142	−	15.9027i	−0.110089	−	0.993922i
$2$	−1.76142	−	15.9027i	−0.110089	−	0.993922i
$3$	33.0681	+	33.0681i	0.408248	+	0.408248i
$3$	33.0681	+	33.0681i	0.408248	+	0.408248i
$4$	−249.795	+	56.0230i	−0.975761	+	0.218840i
$5$	47.4496	+	47.4496i	0.0759193	+	0.0759193i	0.744047	−	0.668128i	$-0.232904\pi$
$5$	47.4496	+	47.4496i	0.0759193	+	0.0759193i	−0.668128	+	0.744047i	$0.732904\pi$
$6$	467.627	−	584.121i	0.360823	−	0.450710i
$7$	−2246.74			−0.935751			−0.467876	−	0.883794i	$-0.654981\pi$
$7$	−2246.74			−0.935751			−0.467876	+	0.883794i	$0.654981\pi$
$8$	1330.91	+	3873.74i	0.324930	+	0.945738i
$9$			2187.00i			0.333333i
$10$	670.999	−	838.157i	0.0670999	−	0.0838157i
$11$	17865.3	−	17865.3i	1.22023	−	1.22023i	0.252676	−	0.967551i	$-0.418689\pi$
$11$	17865.3	−	17865.3i	1.22023	−	1.22023i	0.967551	−	0.252676i	$-0.0813108\pi$
$12$	−10112.8	−	6407.67i	−0.487694	−	0.309012i
$13$	−16949.9	+	16949.9i	−0.593463	+	0.593463i	−0.938565	−	0.345102i	$-0.887844\pi$
$13$	−16949.9	+	16949.9i	−0.593463	+	0.593463i	0.345102	+	0.938565i	$0.387844\pi$
$14$	3957.46	+	35729.3i	0.103016	+	0.930064i
$15$			3138.13i			0.0619878i
$16$	59258.9	−	27988.5i	0.904218	−	0.427070i
$17$	141614.			1.69555			0.847777	−	0.530354i	$-0.177941\pi$
$17$	141614.			1.69555			0.847777	+	0.530354i	$0.177941\pi$
$18$	34779.3	−	3852.23i	0.331307	−	0.0366963i
$19$	165898.	+	165898.i	1.27299	+	1.27299i	0.944511	+	0.328481i	$0.106537\pi$
$19$	165898.	+	165898.i	1.27299	+	1.27299i	0.328481	+	0.944511i	$0.393463\pi$
$20$	−14510.9	−	9194.39i	−0.0906932	−	0.0574649i
$21$	−74295.4	−	74295.4i	−0.382019	−	0.382019i
$22$	−315577.	−	252640.i	−1.34714	−	1.07848i
$23$	64910.8			0.231956			0.115978	−	0.993252i	$-0.463000\pi$
$23$	64910.8			0.231956			0.115978	+	0.993252i	$0.463000\pi$
$24$	−84086.6	+	172108.i	−0.253444	+	0.518748i
$25$		−	386122.i		−	0.988473i
$26$	299406.	+	239694.i	0.655190	+	0.524522i
$27$	−72320.0	+	72320.0i	−0.136083	+	0.136083i
$28$	561224.	−	125869.i	0.913070	−	0.204780i
$29$	67177.4	−	67177.4i	0.0949798	−	0.0949798i	−0.658020	−	0.753000i	$-0.728606\pi$
$29$	67177.4	−	67177.4i	0.0949798	−	0.0949798i	0.753000	+	0.658020i	$0.228606\pi$
$30$	49905.0	−	5527.58i	0.0616111	−	0.00682418i
$31$		−	1.30939e6i		−	1.41783i	−0.705296	−	0.708913i	$-0.749186\pi$
$31$		−	1.30939e6i		−	1.41783i	0.705296	−	0.708913i	$-0.250814\pi$
$32$	−549474.	−	893079.i	−0.524019	−	0.851707i
$33$	1.18155e6			0.996311
$34$	−249443.	−	2.25206e6i	−0.186662	−	1.68525i
$35$	−106607.	−	106607.i	−0.0710416	−	0.0710416i
$36$	−122522.	−	546301.i	−0.0729466	−	0.325254i
$37$	2.03671e6	+	2.03671e6i	1.08673	+	1.08673i	0.995863	+	0.0908676i	$0.0289640\pi$
$37$	2.03671e6	+	2.03671e6i	1.08673	+	1.08673i	0.0908676	+	0.995863i	$0.471036\pi$
$38$	2.34601e6	−	2.93044e6i	1.12511	−	1.40540i
$39$	−1.12100e6			−0.484561
$40$	−120656.	+	246959.i	−0.0471313	+	0.0964682i
$41$		−	1.65048e6i		−	0.584085i	−0.956405	−	0.292043i	$-0.905665\pi$
$41$		−	1.65048e6i		−	0.584085i	0.956405	−	0.292043i	$-0.0943349\pi$
$42$	−1.05064e6	+	1.31237e6i	−0.337641	+	0.421753i
$43$	1.66741e6	−	1.66741e6i	0.487717	−	0.487717i	−0.419868	−	0.907585i	$-0.637924\pi$
$43$	1.66741e6	−	1.66741e6i	0.487717	−	0.487717i	0.907585	+	0.419868i	$0.137924\pi$
$44$	−3.46180e6	+	5.46354e6i	−0.923616	+	1.45768i
$45$	−103772.	+	103772.i	−0.0253064	+	0.0253064i
$46$	−114336.	−	1.03226e6i	−0.0255358	−	0.230546i
$47$			9.60354e6i			1.96807i	0.177986	+	0.984033i	$0.443042\pi$
$47$			9.60354e6i			1.96807i	−0.177986	+	0.984033i	$0.556958\pi$
$48$	2.88510e6	+	1.03405e6i	0.543496	+	0.194795i
$49$	−716963.			−0.124369
$50$	−6.14040e6	+	680125.i	−0.982464	+	0.108820i
$51$	4.68292e6	+	4.68292e6i	0.692207	+	0.692207i
$52$	3.28441e6	−	5.18358e6i	0.449205	−	0.708952i
$53$	1.35090e6	+	1.35090e6i	0.171207	+	0.171207i	0.787509	−	0.616303i	$-0.211370\pi$
$53$	1.35090e6	+	1.35090e6i	0.171207	+	0.171207i	−0.616303	+	0.787509i	$0.711370\pi$
$54$	1.27747e6	+	1.02270e6i	0.150237	+	0.120274i
$55$	1.69541e6			0.185278
$56$	−2.99022e6	−	8.70329e6i	−0.304054	−	0.884976i
$57$			1.09718e7i			1.03939i
$58$	−1.18663e6	−	949978.i	−0.104859	−	0.0839463i
$59$	−4.17057e6	+	4.17057e6i	−0.344181	+	0.344181i	−0.857937	−	0.513756i	$-0.828254\pi$
$59$	−4.17057e6	+	4.17057e6i	−0.344181	+	0.344181i	0.513756	+	0.857937i	$0.328254\pi$
$60$	−175808.	−	783889.i	−0.0135654	−	0.0604853i
$61$	5.53048e6	−	5.53048e6i	0.399432	−	0.399432i	−0.478600	−	0.878033i	$-0.658856\pi$
$61$	5.53048e6	−	5.53048e6i	0.399432	−	0.399432i	0.878033	+	0.478600i	$0.158856\pi$
$62$	−2.08229e7	+	2.30639e6i	−1.40921	+	0.156087i
$63$		−	4.91362e6i		−	0.311917i
$64$	−1.32346e7	+	1.03112e7i	−0.788841	+	0.614597i
$65$	−1.60853e6			−0.0901106
$66$	−2.08120e6	−	1.87898e7i	−0.109683	−	0.990255i
$67$	1.60468e7	+	1.60468e7i	0.796322	+	0.796322i	0.982513	−	0.186192i	$-0.0596146\pi$
$67$	1.60468e7	+	1.60468e7i	0.796322	+	0.796322i	−0.186192	+	0.982513i	$0.559615\pi$
$68$	−3.53745e7	+	7.93365e6i	−1.65445	+	0.371054i
$69$	2.14648e6	+	2.14648e6i	0.0946957	+	0.0946957i
$70$	−1.50756e6	+	1.88312e6i	−0.0627889	+	0.0784307i
$71$	1.51290e7			0.595354			0.297677	−	0.954667i	$-0.403788\pi$
$71$	1.51290e7			0.595354			0.297677	+	0.954667i	$0.403788\pi$
$72$	−8.47188e6	+	2.91071e6i	−0.315246	+	0.108310i
$73$		−	9.31022e6i		−	0.327845i	−0.986473	−	0.163923i	$-0.947585\pi$
$73$		−	9.31022e6i		−	0.327845i	0.986473	−	0.163923i	$-0.0524147\pi$
$74$	2.88017e7	−	3.59768e7i	0.960488	−	1.19976i
$75$	1.27683e7	−	1.27683e7i	0.403542	−	0.403542i
$76$	−5.07344e7	−	3.21463e7i	−1.52072	−	0.963554i
$77$	−4.01388e7	+	4.01388e7i	−1.14183	+	1.14183i
$78$	1.97456e6	+	1.78270e7i	0.0533448	+	0.481615i
$79$			4.17784e7i			1.07261i	0.844023	+	0.536307i	$0.180181\pi$
$79$			4.17784e7i			1.07261i	−0.844023	+	0.536307i	$0.819819\pi$
$80$	4.13985e6	+	1.48377e6i	0.101070	+	0.0362247i
$81$	−4.78297e6			−0.111111
$82$	−2.62472e7	+	2.90720e6i	−0.580535	+	0.0643013i
$83$	1.25940e7	+	1.25940e7i	0.265371	+	0.265371i	0.827232	−	0.561861i	$-0.189914\pi$
$83$	1.25940e7	+	1.25940e7i	0.265371	+	0.265371i	−0.561861	+	0.827232i	$0.689914\pi$
$84$	2.27209e7	+	1.43964e7i	0.456360	+	0.289158i
$85$	6.71953e6	+	6.71953e6i	0.128725	+	0.128725i
$86$	−2.94534e7	−	2.35794e7i	−0.538445	−	0.431061i
$87$	4.44286e6			0.0775507
$88$	9.29830e7	+	4.54285e7i	1.55050	+	0.757527i
$89$		−	4.99268e7i		−	0.795745i	−0.917441	−	0.397872i	$-0.869749\pi$
$89$		−	4.99268e7i		−	0.795745i	0.917441	−	0.397872i	$-0.130251\pi$
$90$	1.83305e6	+	1.46748e6i	0.0279386	+	0.0223666i
$91$	3.80820e7	−	3.80820e7i	0.555334	−	0.555334i
$92$	−1.62144e7	+	3.63650e6i	−0.226334	+	0.0507612i
$93$	4.32991e7	−	4.32991e7i	0.578825	−	0.578825i
$94$	1.52723e8	−	1.69159e7i	1.95610	−	0.216662i
$95$			1.57435e7i			0.193289i
$96$	1.13624e7	−	4.77025e7i	0.133778	−	0.561638i
$97$	−4.98508e7			−0.563099			−0.281550	−	0.959547i	$-0.590848\pi$
$97$	−4.98508e7			−0.563099			−0.281550	+	0.959547i	$0.590848\pi$
$98$	1.26288e6	+	1.14017e7i	0.0136917	+	0.123613i
$99$	3.90715e7	+	3.90715e7i	0.406742	+	0.406742i
$100$	2.16317e7	+	9.64513e7i	0.216317	+	0.964513i
$101$	−9.87694e7	−	9.87694e7i	−0.949155	−	0.949155i	0.0496137	−	0.998768i	$-0.484201\pi$
$101$	−9.87694e7	−	9.87694e7i	−0.949155	−	0.949155i	−0.998768	+	0.0496137i	$0.984201\pi$
$102$	6.62226e7	−	8.27199e7i	0.611795	−	0.764204i
$103$	1.41838e8			1.26021			0.630106	−	0.776509i	$-0.283011\pi$
$103$	1.41838e8			1.26021			0.630106	+	0.776509i	$0.283011\pi$
$104$	−8.82184e7	−	4.31007e7i	−0.754095	−	0.368427i
$105$		−	7.05057e6i		−	0.0580052i
$106$	1.91036e7	−	2.38626e7i	0.151318	−	0.189014i
$107$	6.86007e7	−	6.86007e7i	0.523351	−	0.523351i	−0.395231	−	0.918582i	$-0.629335\pi$
$107$	6.86007e7	−	6.86007e7i	0.523351	−	0.523351i	0.918582	+	0.395231i	$0.129335\pi$
$108$	1.40136e7	−	2.21167e7i	0.103004	−	0.162565i
$109$	−6.22635e7	+	6.22635e7i	−0.441091	+	0.441091i	−0.892378	−	0.451288i	$-0.850965\pi$
$109$	−6.22635e7	+	6.22635e7i	−0.441091	+	0.441091i	0.451288	+	0.892378i	$0.350965\pi$
$110$	−2.98633e6	−	2.69616e7i	−0.0203970	−	0.184151i
$111$			1.34700e8i			0.887312i
$112$	−1.33139e8	+	6.28828e7i	−0.846124	+	0.399632i
$113$	−1.50898e8			−0.925488			−0.462744	−	0.886492i	$-0.653135\pi$
$113$	−1.50898e8			−0.925488			−0.462744	+	0.886492i	$0.653135\pi$
$114$	1.74482e8	−	1.93261e7i	1.03308	−	0.114426i
$115$	3.07999e6	+	3.07999e6i	0.0176099	+	0.0176099i
$116$	−1.30171e7	+	2.05441e7i	−0.0718923	+	0.113463i
$117$	−3.70694e7	−	3.70694e7i	−0.197821	−	0.197821i
$118$	7.36696e7	+	5.89773e7i	0.379980	+	0.304199i
$119$	−3.18170e8			−1.58662
$120$	−1.21563e7	+	4.17658e6i	−0.0586243	+	0.0201417i
$121$		−	4.23982e8i		−	1.97791i
$122$	−9.76913e7	−	7.82083e7i	−0.440978	−	0.353031i
$123$	5.45784e7	−	5.45784e7i	0.238452	−	0.238452i
$124$	7.33560e7	+	3.27079e8i	0.310276	+	1.38346i
$125$	3.68563e7	−	3.68563e7i	0.150963	−	0.150963i
$126$	−7.81400e7	+	8.65496e6i	−0.310021	+	0.0343386i
$127$		−	2.66738e8i		−	1.02534i	−0.858584	−	0.512672i	$-0.828656\pi$
$127$		−	2.66738e8i		−	1.02534i	0.858584	−	0.512672i	$-0.171344\pi$
$128$	1.87289e8	+	1.92303e8i	0.697704	+	0.716386i
$129$	1.10276e8			0.398220
$130$	2.83330e6	+	2.55801e7i	0.00992018	+	0.0895629i
$131$	1.66446e8	+	1.66446e8i	0.565183	+	0.565183i	0.930775	−	0.365592i	$-0.119134\pi$
$131$	1.66446e8	+	1.66446e8i	0.565183	+	0.565183i	−0.365592	+	0.930775i	$0.619134\pi$
$132$	−2.95144e8	+	6.61937e7i	−0.972162	+	0.218032i
$133$	−3.72728e8	−	3.72728e8i	−1.19120	−	1.19120i
$134$	2.26923e8	−	2.83453e8i	0.703815	−	0.879148i
$135$	−6.86310e6			−0.0206626
$136$	1.88476e8	+	5.48577e8i	0.550936	+	1.60355i
$137$			3.14642e8i			0.893170i	0.894741	+	0.446585i	$0.147360\pi$
$137$			3.14642e8i			0.893170i	−0.894741	+	0.446585i	$0.852640\pi$
$138$	3.03541e7	−	3.79158e7i	0.0836952	−	0.104545i
$139$	−1.39232e8	+	1.39232e8i	−0.372976	+	0.372976i	−0.868560	−	0.495584i	$-0.834954\pi$
$139$	−1.39232e8	+	1.39232e8i	−0.372976	+	0.372976i	0.495584	+	0.868560i	$0.334954\pi$
$140$	3.26022e7	+	2.06574e7i	0.0848663	+	0.0537729i
$141$	−3.17571e8	+	3.17571e8i	−0.803460	+	0.803460i
$142$	−2.66485e7	−	2.40592e8i	−0.0655420	−	0.591736i
$143$			6.05632e8i			1.44832i
$144$	6.12108e7	+	1.29599e8i	0.142357	+	0.301406i
$145$	6.37508e6			0.0144216
$146$	−1.48058e8	+	1.63992e7i	−0.325852	+	0.0360921i
$147$	−2.37086e7	−	2.37086e7i	−0.0507735	−	0.0507735i
$148$	−6.22861e8	−	3.94657e8i	−1.29821	−	0.822569i
$149$	−4.59473e8	−	4.59473e8i	−0.932213	−	0.932213i	0.0656314	−	0.997844i	$-0.479094\pi$
$149$	−4.59473e8	−	4.59473e8i	−0.932213	−	0.932213i	−0.997844	+	0.0656314i	$0.979094\pi$
$150$	−2.25542e8	−	1.80561e8i	−0.445515	−	0.356664i
$151$	1.41862e8			0.272871			0.136435	−	0.990649i	$-0.456435\pi$
$151$	1.41862e8			0.272871			0.136435	+	0.990649i	$0.456435\pi$
$152$	−4.21849e8	+	8.63440e8i	−0.790283	+	1.61755i
$153$			3.09710e8i			0.565184i
$154$	7.09018e8	+	5.67615e8i	1.26059	+	1.00919i
$155$	6.21300e7	−	6.21300e7i	0.107640	−	0.107640i
$156$	2.80021e8	−	6.28019e7i	0.472815	−	0.106041i
$157$	2.30405e8	−	2.30405e8i	0.379221	−	0.379221i	−0.491600	−	0.870821i	$-0.663588\pi$
$157$	2.30405e8	−	2.30405e8i	0.379221	−	0.379221i	0.870821	+	0.491600i	$0.163588\pi$
$158$	6.64392e8	−	7.35895e7i	1.06609	−	0.118083i
$159$			8.93437e7i			0.139790i
$160$	1.63039e7	−	6.84485e7i	0.0248778	−	0.104444i
$161$	−1.45838e8			−0.217053
$162$	8.42483e6	+	7.60623e7i	0.0122321	+	0.110436i
$163$	−7.28740e8	−	7.28740e8i	−1.03234	−	1.03234i	−0.999459	−	0.0328796i	$-0.989532\pi$
$163$	−7.28740e8	−	7.28740e8i	−1.03234	−	1.03234i	−0.0328796	−	0.999459i	$-0.510468\pi$
$164$	9.24650e7	+	4.12282e8i	0.127821	+	0.569927i
$165$	5.60638e7	+	5.60638e7i	0.0756392	+	0.0756392i
$166$	1.78096e8	−	2.22463e8i	0.234543	−	0.292972i
$167$	1.08061e9			1.38932			0.694661	−	0.719337i	$-0.255554\pi$
$167$	1.08061e9			1.38932			0.694661	+	0.719337i	$0.255554\pi$
$168$	1.88921e8	−	3.86682e8i	0.237160	−	0.485419i
$169$			2.41132e8i			0.295603i
$170$	9.50231e7	−	1.18695e8i	0.113772	−	0.142114i
$171$	−3.62818e8	+	3.62818e8i	−0.424330	+	0.424330i
$172$	−3.23097e8	+	5.09923e8i	−0.369164	+	0.582627i
$173$	2.32974e8	−	2.32974e8i	0.260089	−	0.260089i	−0.565001	−	0.825090i	$-0.691124\pi$
$173$	2.32974e8	−	2.32974e8i	0.260089	−	0.260089i	0.825090	+	0.565001i	$0.191124\pi$
$174$	−7.82576e6	−	7.06537e7i	−0.00853748	−	0.0770793i
$175$			8.67516e8i			0.924965i
$176$	5.58656e8	−	1.55870e9i	0.582229	−	1.62447i
$177$	−2.75826e8			−0.281023
$178$	−7.93974e8	+	8.79423e7i	−0.790908	+	0.0876027i
$179$	8.47329e8	+	8.47329e8i	0.825354	+	0.825354i	0.986870	−	0.161516i	$-0.0516384\pi$
$179$	8.47329e8	+	8.47329e8i	0.825354	+	0.825354i	−0.161516	+	0.986870i	$0.551638\pi$
$180$	2.01081e7	−	3.17354e7i	0.0191550	−	0.0302311i
$181$	−9.37914e8	−	9.37914e8i	−0.873874	−	0.873874i	0.119018	−	0.992892i	$-0.462025\pi$
$181$	−9.37914e8	−	9.37914e8i	−0.873874	−	0.873874i	−0.992892	+	0.119018i	$0.962025\pi$
$182$	−6.72687e8	−	5.38530e8i	−0.613095	−	0.490822i
$183$	3.65765e8			0.326135
$184$	8.63907e7	+	2.51448e8i	0.0753695	+	0.219370i
$185$			1.93282e8i			0.165008i
$186$	−7.64843e8	−	6.12307e8i	−0.639029	−	0.511584i
$187$	2.52999e9	−	2.52999e9i	2.06896	−	2.06896i
$188$	−5.38018e8	−	2.39891e9i	−0.430691	−	1.92036i
$189$	1.62484e8	−	1.62484e8i	0.127340	−	0.127340i
$190$	2.50365e8	−	2.77310e7i	0.192114	−	0.0212790i
$191$			9.91150e8i			0.744742i	0.928084	+	0.372371i	$0.121455\pi$
$191$			9.91150e8i			0.744742i	−0.928084	+	0.372371i	$0.878545\pi$
$192$	−7.78615e8	−	9.66688e7i	−0.572951	−	0.0711347i
$193$	9.32199e8			0.671861			0.335930	−	0.941887i	$-0.390949\pi$
$193$	9.32199e8			0.671861			0.335930	+	0.941887i	$0.390949\pi$
$194$	8.78083e7	+	7.92764e8i	0.0619910	+	0.559676i
$195$	−5.31911e7	−	5.31911e7i	−0.0367875	−	0.0367875i
$196$	1.79094e8	−	4.01664e7i	0.121355	−	0.0272169i
$197$	1.05900e8	+	1.05900e8i	0.0703120	+	0.0703120i	0.741388	−	0.671076i	$-0.234168\pi$
$197$	1.05900e8	+	1.05900e8i	0.0703120	+	0.0703120i	−0.671076	+	0.741388i	$0.734168\pi$
$198$	5.52523e8	−	6.90166e8i	0.359492	−	0.449048i
$199$	−1.52250e9			−0.970835			−0.485418	−	0.874282i	$-0.661332\pi$
$199$	−1.52250e9			−0.970835			−0.485418	+	0.874282i	$0.661332\pi$
$200$	1.49574e9	−	5.13895e8i	0.934836	−	0.321184i
$201$			1.06127e9i			0.650194i
$202$	−1.39673e9	+	1.74468e9i	−0.838894	+	1.04788i
$203$	−1.50930e8	+	1.50930e8i	−0.0888775	+	0.0888775i
$204$	−1.43212e9	−	9.07417e8i	−0.826910	−	0.523946i
$205$	7.83148e7	−	7.83148e7i	0.0443433	−	0.0443433i
$206$	−2.49837e8	−	2.25561e9i	−0.138736	−	1.25255i
$207$			1.41960e8i			0.0773187i
$208$	−5.30030e8	+	1.47883e9i	−0.283170	+	0.790071i
$209$	5.92763e9			3.10668
$210$	−1.12123e8	+	1.24190e7i	−0.0576526	+	0.00638573i
$211$	2.13500e8	+	2.13500e8i	0.107713	+	0.107713i	0.758909	−	0.651196i	$-0.225733\pi$
$211$	2.13500e8	+	2.13500e8i	0.107713	+	0.107713i	−0.651196	+	0.758909i	$0.725733\pi$
$212$	−4.13130e8	−	2.61767e8i	−0.204524	−	0.129590i
$213$	5.00286e8	+	5.00286e8i	0.243052	+	0.243052i
$214$	−1.21177e9	−	9.70104e8i	−0.577785	−	0.462555i
$215$	1.58236e8			0.0740543
$216$	−3.76401e8	−	1.83897e8i	−0.172916	−	0.0844813i
$217$			2.94186e9i			1.32673i
$218$	1.09983e9	+	8.80489e8i	0.486969	+	0.389850i
$219$	3.07871e8	−	3.07871e8i	0.133842	−	0.133842i
$220$	−4.23503e8	+	9.49816e7i	−0.180787	+	0.0405461i
$221$	−2.40035e9	+	2.40035e9i	−1.00625	+	1.00625i
$222$	2.14210e9	−	2.37264e8i	0.881918	−	0.0976832i
$223$		−	1.72171e9i		−	0.696209i	−0.937456	−	0.348105i	$-0.886825\pi$
$223$		−	1.72171e9i		−	0.696209i	0.937456	−	0.348105i	$-0.113175\pi$
$224$	1.23452e9	+	2.00652e9i	0.490352	+	0.796986i
$225$	8.44449e8			0.329491
$226$	2.65796e8	+	2.39970e9i	0.101886	+	0.919863i
$227$	−7.69801e8	−	7.69801e8i	−0.289918	−	0.289918i	0.547130	−	0.837048i	$-0.315720\pi$
$227$	−7.69801e8	−	7.69801e8i	−0.289918	−	0.289918i	−0.837048	+	0.547130i	$0.815720\pi$
$228$	−6.14675e8	−	2.74071e9i	−0.227460	−	1.01420i
$229$	−5.44692e8	−	5.44692e8i	−0.198065	−	0.198065i	0.601105	−	0.799170i	$-0.294727\pi$
$229$	−5.44692e8	−	5.44692e8i	−0.198065	−	0.198065i	−0.799170	+	0.601105i	$0.794727\pi$
$230$	4.35551e7	−	5.44055e7i	0.0155642	−	0.0194416i
$231$	−2.65463e9			−0.932300
$232$	3.49635e8	+	1.70821e8i	0.120688	+	0.0589643i
$233$		−	1.66872e9i		−	0.566188i	−0.959092	−	0.283094i	$-0.908639\pi$
$233$		−	1.66872e9i		−	0.566188i	0.959092	−	0.283094i	$-0.0913608\pi$
$234$	−5.24211e8	+	6.54801e8i	−0.174841	+	0.218397i
$235$	−4.55683e8	+	4.55683e8i	−0.149414	+	0.149414i
$236$	8.08138e8	−	1.27543e9i	0.260518	−	0.411159i
$237$	−1.38153e9	+	1.38153e9i	−0.437893	+	0.437893i
$238$	5.60433e8	+	5.05978e9i	0.174669	+	1.57697i
$239$			5.04593e9i			1.54650i	0.634102	+	0.773249i	$0.281370\pi$
$239$			5.04593e9i			1.54650i	−0.634102	+	0.773249i	$0.718630\pi$
$240$	8.78316e7	+	1.85962e8i	0.0264732	+	0.0560505i
$241$	2.03267e9			0.602557			0.301278	−	0.953536i	$-0.402587\pi$
$241$	2.03267e9			0.602557			0.301278	+	0.953536i	$0.402587\pi$
$242$	−6.74248e9	+	7.46812e8i	−1.96589	+	0.217746i
$243$	−1.58164e8	−	1.58164e8i	−0.0453609	−	0.0453609i
$244$	−1.07165e9	+	1.69132e9i	−0.302339	+	0.477162i
$245$	−3.40196e7	−	3.40196e7i	−0.00944202	−	0.00944202i
$246$	−9.64082e8	−	7.71811e8i	−0.263253	−	0.210751i
$247$	−5.62389e9			−1.51095
$248$	5.07225e9	−	1.74269e9i	1.34089	−	0.460694i
$249$			8.32922e8i			0.216674i
$250$	−6.51036e8	−	5.21197e8i	−0.166665	−	0.133426i
$251$	2.27923e9	−	2.27923e9i	0.574239	−	0.574239i	−0.359071	−	0.933310i	$-0.616906\pi$
$251$	2.27923e9	−	2.27923e9i	0.574239	−	0.574239i	0.933310	+	0.359071i	$0.116906\pi$
$252$	2.75275e8	+	1.22740e9i	0.0682598	+	0.304357i
$253$	1.15965e9	−	1.15965e9i	0.283039	−	0.283039i
$254$	−4.24187e9	+	4.69838e8i	−1.01911	+	0.112879i
$255$			4.44405e8i			0.105104i
$256$	2.72826e9	−	3.31713e9i	0.635222	−	0.772330i
$257$	−3.55390e9			−0.814652			−0.407326	−	0.913283i	$-0.633539\pi$
$257$	−3.55390e9			−0.814652			−0.407326	+	0.913283i	$0.633539\pi$
$258$	−1.94243e8	−	1.75369e9i	−0.0438396	−	0.395799i
$259$	−4.57595e9	−	4.57595e9i	−1.01691	−	1.01691i
$260$	4.01803e8	−	9.01146e7i	0.0879264	−	0.0197198i
$261$	1.46917e8	+	1.46917e8i	0.0316599	+	0.0316599i
$262$	2.35377e9	−	2.94013e9i	0.499527	−	0.623968i
$263$	−7.80529e9			−1.63142			−0.815711	−	0.578460i	$-0.803654\pi$
$263$	−7.80529e9			−1.63142			−0.815711	+	0.578460i	$0.803654\pi$
$264$	1.57254e9	+	4.57701e9i	0.323731	+	0.942250i
$265$			1.28200e8i			0.0259958i
$266$	−5.27087e9	+	6.58394e9i	−1.05282	+	1.31510i
$267$	1.65099e9	−	1.65099e9i	0.324861	−	0.324861i
$268$	−4.90739e9	−	3.10941e9i	−0.951286	−	0.602753i
$269$	3.28256e9	−	3.28256e9i	0.626907	−	0.626907i	−0.320381	−	0.947289i	$-0.603811\pi$
$269$	3.28256e9	−	3.28256e9i	0.626907	−	0.626907i	0.947289	+	0.320381i	$0.103811\pi$
$270$	1.20888e7	+	1.09142e8i	0.00227473	+	0.0205370i
$271$			2.72532e9i			0.505289i	0.967559	+	0.252644i	$0.0813003\pi$
$271$			2.72532e9i			0.505289i	−0.967559	+	0.252644i	$0.918700\pi$
$272$	8.39190e9	−	3.96357e9i	1.53315	−	0.724120i
$273$	2.51860e9			0.453428
$274$	5.00367e9	−	5.54218e8i	0.887741	−	0.0983282i
$275$	−6.89820e9	−	6.89820e9i	−1.20616	−	1.20616i
$276$	−6.56431e8	−	4.15927e8i	−0.113124	−	0.0716772i
$277$	−1.81149e9	−	1.81149e9i	−0.307692	−	0.307692i	0.536321	−	0.844014i	$-0.319813\pi$
$277$	−1.81149e9	−	1.81149e9i	−0.307692	−	0.307692i	−0.844014	+	0.536321i	$0.819813\pi$
$278$	2.45942e9	+	1.96893e9i	0.411769	+	0.329648i
$279$	2.86364e9			0.472608
$280$	2.71083e8	−	5.54852e8i	0.0441032	−	0.0902703i
$281$			6.37253e9i			1.02208i	0.859556	+	0.511042i	$0.170740\pi$
$281$			6.37253e9i			1.02208i	−0.859556	+	0.511042i	$0.829260\pi$
$282$	5.60962e9	+	4.49087e9i	0.887028	+	0.710124i
$283$	7.66787e9	−	7.66787e9i	1.19544	−	1.19544i	0.219926	−	0.975517i	$-0.429418\pi$
$283$	7.66787e9	−	7.66787e9i	1.19544	−	1.19544i	0.975517	−	0.219926i	$-0.0705816\pi$
$284$	−3.77913e9	+	8.47569e8i	−0.580924	+	0.130287i
$285$	−5.20609e8	+	5.20609e8i	−0.0789100	+	0.0789100i
$286$	9.63121e9	−	1.06677e9i	1.43952	−	0.159444i
$287$			3.70821e9i			0.546558i
$288$	1.95316e9	−	1.20170e9i	0.283902	−	0.174673i
$289$	1.30788e10			1.87490
$290$	−1.12292e7	−	1.01381e8i	−0.00158766	−	0.0143339i
$291$	−1.64847e9	−	1.64847e9i	−0.229884	−	0.229884i
$292$	5.21586e8	+	2.32564e9i	0.0717455	+	0.319898i
$293$	−7.56090e9	−	7.56090e9i	−1.02590	−	1.02590i	−0.999656	−	0.0262398i	$-0.991647\pi$
$293$	−7.56090e9	−	7.56090e9i	−1.02590	−	1.02590i	−0.0262398	−	0.999656i	$-0.508353\pi$
$294$	−3.35271e8	+	4.18793e8i	−0.0448753	+	0.0560545i
$295$	−3.95783e8			−0.0522600
$296$	−5.17900e9	+	1.06004e10i	−0.674651	+	1.38087i
$297$			2.58404e9i			0.332104i
$298$	−6.49756e9	+	8.11621e9i	−0.823920	+	1.02917i
$299$	−1.10023e9	+	1.10023e9i	−0.137657	+	0.137657i
$300$	−2.47414e9	+	3.90478e9i	−0.305450	+	0.482072i
$301$	−3.74623e9	+	3.74623e9i	−0.456382	+	0.456382i
$302$	−2.49878e8	−	2.25599e9i	−0.0300401	−	0.271212i
$303$		−	6.53224e9i		−	0.774982i
$304$	1.44741e10	+	5.18768e9i	1.69472	+	0.607405i
$305$	5.24837e8			0.0606492
$306$	4.92525e9	−	5.45531e8i	0.561749	−	0.0622206i
$307$	−5.51929e9	−	5.51929e9i	−0.621340	−	0.621340i	0.324534	−	0.945874i	$-0.394793\pi$
$307$	−5.51929e9	−	5.51929e9i	−0.621340	−	0.621340i	−0.945874	+	0.324534i	$0.894793\pi$
$308$	7.77776e9	−	1.22751e10i	0.864275	−	1.36403i
$309$	4.69032e9	+	4.69032e9i	0.514480	+	0.514480i
$310$	−1.09748e9	−	8.78601e8i	−0.118836	−	0.0951360i
$311$	−5.46409e9			−0.584086			−0.292043	−	0.956405i	$-0.594335\pi$
$311$	−5.46409e9			−0.584086			−0.292043	+	0.956405i	$0.594335\pi$
$312$	−1.49196e9	−	4.34248e9i	−0.157448	−	0.458268i
$313$		−	4.15814e7i		−	0.00433234i	−0.999998	−	0.00216617i	$-0.999310\pi$
$313$		−	4.15814e7i		−	0.00433234i	0.999998	−	0.00216617i	$-0.000689513\pi$
$314$	−4.06991e9	−	3.25823e9i	−0.418664	−	0.335168i
$315$	2.33149e8	−	2.33149e8i	0.0236805	−	0.0236805i
$316$	−2.34055e9	−	1.04360e10i	−0.234731	−	1.04662i
$317$	3.47349e9	−	3.47349e9i	0.343977	−	0.343977i	−0.513883	−	0.857860i	$-0.671794\pi$
$317$	3.47349e9	−	3.47349e9i	0.343977	−	0.343977i	0.857860	+	0.513883i	$0.171794\pi$
$318$	1.42081e9	−	1.57372e8i	0.138940	−	0.0153893i
$319$		−	2.40030e9i		−	0.231794i
$320$	−1.11724e9	−	1.38710e8i	−0.106548	−	0.0132285i
$321$	4.53699e9			0.427314
$322$	2.56882e8	+	2.31922e9i	0.0238952	+	0.215734i
$323$	2.34935e10	+	2.34935e10i	2.15842	+	2.15842i
$324$	1.19476e9	−	2.67956e8i	0.108418	−	0.0243155i
$325$	6.54473e9	+	6.54473e9i	0.586622	+	0.586622i
$326$	−1.03054e10	+	1.28726e10i	−0.912415	+	1.13971i
$327$	−4.11787e9			−0.360149
$328$	6.39355e9	−	2.19665e9i	0.552391	−	0.189787i
$329$		−	2.15766e10i		−	1.84162i
$330$	7.92817e8	−	9.90321e8i	0.0668524	−	0.0835065i
$331$	3.27124e9	−	3.27124e9i	0.272521	−	0.272521i	−0.557593	−	0.830114i	$-0.688275\pi$
$331$	3.27124e9	−	3.27124e9i	0.272521	−	0.272521i	0.830114	+	0.557593i	$0.188275\pi$
$332$	−3.85148e9	−	2.44037e9i	−0.317012	−	0.200865i
$333$	−4.45428e9	+	4.45428e9i	−0.362244	+	0.362244i
$334$	−1.90341e9	−	1.71847e10i	−0.152949	−	1.38088i
$335$			1.52282e9i			0.120912i
$336$	−6.48208e9	−	2.32325e9i	−0.508578	−	0.182280i
$337$	−1.87990e10			−1.45752			−0.728761	−	0.684768i	$-0.759903\pi$
$337$	−1.87990e10			−1.45752			−0.728761	+	0.684768i	$0.759903\pi$
$338$	3.83466e9	−	4.24736e8i	0.293806	−	0.0325426i
$339$	−4.98992e9	−	4.98992e9i	−0.377829	−	0.377829i
$340$	−2.05495e9	−	1.30206e9i	−0.153775	−	0.0974348i
$341$	−2.33927e10	−	2.33927e10i	−1.73007	−	1.73007i
$342$	6.40888e9	+	5.13073e9i	0.468465	+	0.375037i
$343$	1.45628e10			1.05213
$344$	8.67829e9	+	4.23994e9i	0.619727	+	0.302779i
$345$			2.03699e8i			0.0143785i
$346$	−4.11529e9	−	3.29456e9i	−0.287142	−	0.229876i
$347$	−3.94626e9	+	3.94626e9i	−0.272187	+	0.272187i	−0.829980	−	0.557793i	$-0.811648\pi$
$347$	−3.94626e9	+	3.94626e9i	−0.272187	+	0.272187i	0.557793	+	0.829980i	$0.311648\pi$
$348$	−1.10980e9	+	2.48902e8i	−0.0756710	+	0.0169712i
$349$	−1.22506e10	+	1.22506e10i	−0.825766	+	0.825766i	−0.986928	−	0.161162i	$-0.948476\pi$
$349$	−1.22506e10	+	1.22506e10i	−0.825766	+	0.825766i	0.161162	+	0.986928i	$0.448476\pi$
$350$	1.37959e10	−	1.52806e9i	0.919342	−	0.101828i
$351$		−	2.45163e9i		−	0.161520i
$352$	−2.57717e10	−	6.13863e9i	−1.67870	−	0.399853i
$353$	8.23971e9			0.530656			0.265328	−	0.964158i	$-0.414520\pi$
$353$	8.23971e9			0.530656			0.265328	+	0.964158i	$0.414520\pi$
$354$	4.85846e8	+	4.38638e9i	0.0309375	+	0.279315i
$355$	7.17862e8	+	7.17862e8i	0.0451989	+	0.0451989i
$356$	2.79705e9	+	1.24715e10i	0.174141	+	0.776457i
$357$	−1.05213e10	−	1.05213e10i	−0.647733	−	0.647733i
$358$	1.19824e10	−	1.49674e10i	0.729475	−	0.911199i
$359$	−1.03833e9			−0.0625113			−0.0312557	−	0.999511i	$-0.509951\pi$
$359$	−1.03833e9			−0.0625113			−0.0312557	+	0.999511i	$0.509951\pi$
$360$	−5.40098e8	−	2.63875e8i	−0.0321561	−	0.0157104i
$361$			3.80604e10i			2.24101i
$362$	−1.32633e10	+	1.65675e10i	−0.772358	+	0.964766i
$363$	1.40203e10	−	1.40203e10i	0.807478	−	0.807478i
$364$	−7.37922e9	+	1.16462e10i	−0.420344	+	0.663402i
$365$	4.41766e8	−	4.41766e8i	0.0248898	−	0.0248898i
$366$	−6.44267e8	−	5.81667e9i	−0.0359039	−	0.324153i
$367$			3.12066e10i			1.72021i	0.510115	+	0.860106i	$0.329603\pi$
$367$			3.12066e10i			1.72021i	−0.510115	+	0.860106i	$0.670397\pi$
$368$	3.84654e9	−	1.81676e9i	0.209739	−	0.0990616i
$369$	3.60961e9			0.194695
$370$	3.07371e9	−	3.40451e8i	0.164005	−	0.0181655i
$371$	−3.03513e9	−	3.03513e9i	−0.160207	−	0.160207i
$372$	−8.39015e9	+	1.32416e10i	−0.438125	+	0.691464i
$373$	2.09805e10	+	2.09805e10i	1.08388	+	1.08388i	0.996144	+	0.0877333i	$0.0279623\pi$
$373$	2.09805e10	+	2.09805e10i	1.08388	+	1.08388i	0.0877333	+	0.996144i	$0.472038\pi$
$374$	−4.46901e10	−	3.57774e10i	−2.28415	−	1.82861i
$375$	2.43754e9			0.123261
$376$	−3.72016e10	+	1.27815e10i	−1.86128	+	0.639484i
$377$			2.27730e9i			0.112734i
$378$	−2.87015e9	−	2.29774e9i	−0.140584	−	0.112547i
$379$	−1.72306e10	+	1.72306e10i	−0.835109	+	0.835109i	−0.988210	−	0.153102i	$-0.951074\pi$
$379$	−1.72306e10	+	1.72306e10i	−0.835109	+	0.835109i	0.153102	+	0.988210i	$0.451074\pi$
$380$	−8.81999e8	−	3.93265e9i	−0.0422993	−	0.188604i
$381$	8.82052e9	−	8.82052e9i	0.418595	−	0.418595i
$382$	1.57620e10	−	1.74584e9i	0.740216	−	0.0819879i
$383$			3.09945e10i			1.44042i	0.693756	+	0.720210i	$0.255954\pi$
$383$			3.09945e10i			1.44042i	−0.693756	+	0.720210i	$0.744046\pi$
$384$	−1.65829e8	+	1.25524e10i	−0.00762666	+	0.577300i
$385$	−3.80913e9			−0.173374
$386$	−1.64200e9	−	1.48245e10i	−0.0739645	−	0.667777i
$387$	3.64662e9	+	3.64662e9i	0.162572	+	0.162572i
$388$	1.24525e10	−	2.79279e9i	0.549450	−	0.123228i
$389$	−3.19222e8	−	3.19222e8i	−0.0139410	−	0.0139410i	0.700102	−	0.714043i	$-0.253138\pi$
$389$	−3.19222e8	−	3.19222e8i	−0.0139410	−	0.0139410i	−0.714043	+	0.700102i	$0.753138\pi$
$390$	−7.52192e8	+	9.39576e8i	−0.0325140	+	0.0406138i
$391$	9.19230e9			0.393294
$392$	−9.54216e8	−	2.77733e9i	−0.0404113	−	0.117621i
$393$			1.10081e10i			0.461470i
$394$	1.49756e9	−	1.87063e9i	0.0621440	−	0.0776252i
$395$	−1.98237e9	+	1.98237e9i	−0.0814321	+	0.0814321i
$396$	−1.19488e10	−	7.57096e9i	−0.485895	−	0.307872i
$397$	1.76535e10	−	1.76535e10i	0.710672	−	0.710672i	−0.256004	−	0.966676i	$-0.582406\pi$
$397$	1.76535e10	−	1.76535e10i	0.710672	−	0.710672i	0.966676	+	0.256004i	$0.0824059\pi$
$398$	2.68177e9	+	2.42120e10i	0.106878	+	0.964934i
$399$		−	2.46509e10i		−	0.972614i
$400$	−1.08070e10	−	2.28812e10i	−0.422147	−	0.893795i
$401$	3.74095e8			0.0144679			0.00723393	−	0.999974i	$-0.497697\pi$
$401$	3.74095e8			0.0144679			0.00723393	+	0.999974i	$0.497697\pi$
$402$	1.68772e10	−	1.86935e9i	0.646242	−	0.0715792i
$403$	2.21941e10	+	2.21941e10i	0.841427	+	0.841427i
$404$	3.02054e10	+	1.91387e10i	1.13386	+	0.718435i
$405$	−2.26950e8	−	2.26950e8i	−0.00843548	−	0.00843548i
$406$	2.66606e9	+	2.13435e9i	0.0981217	+	0.0785529i
$407$	7.27730e10			2.65212
$408$	−1.19079e10	+	2.43730e10i	−0.429727	+	0.879565i
$409$		−	3.00482e10i		−	1.07380i	−0.843645	−	0.536902i	$-0.819595\pi$
$409$		−	3.00482e10i		−	1.07380i	0.843645	−	0.536902i	$-0.180405\pi$
$410$	−1.38337e9	−	1.10747e9i	−0.0489555	−	0.0391921i
$411$	−1.04046e10	+	1.04046e10i	−0.364635	+	0.364635i
$412$	−3.54304e10	+	7.94618e9i	−1.22967	+	0.275784i
$413$	9.37018e9	−	9.37018e9i	0.322068	−	0.322068i
$414$	2.25755e9	−	2.50052e8i	0.0768488	−	0.00851194i
$415$			1.19516e9i			0.0402935i
$416$	2.44511e10	+	5.82408e9i	0.816443	+	0.194471i
$417$	−9.20830e9			−0.304534
$418$	−1.04411e10	−	9.42657e10i	−0.342011	−	3.08779i
$419$	6.04082e9	+	6.04082e9i	0.195993	+	0.195993i	0.798280	−	0.602287i	$-0.205744\pi$
$419$	6.04082e9	+	6.04082e9i	0.195993	+	0.195993i	−0.602287	+	0.798280i	$0.705744\pi$
$420$	3.94994e8	+	1.76120e9i	0.0126938	+	0.0565992i
$421$	−7.29767e9	−	7.29767e9i	−0.232304	−	0.232304i	0.581350	−	0.813654i	$-0.302525\pi$
$421$	−7.29767e9	−	7.29767e9i	−0.232304	−	0.232304i	−0.813654	+	0.581350i	$0.802525\pi$
$422$	3.01917e9	−	3.77129e9i	0.0952001	−	0.118916i
$423$	−2.10029e10			−0.656022
$424$	−3.43512e9	+	7.03099e9i	−0.106287	+	0.217547i
$425$		−	5.46804e10i		−	1.67601i
$426$	7.07471e9	−	8.83714e9i	0.214818	−	0.268332i
$427$	−1.24255e10	+	1.24255e10i	−0.373769	+	0.373769i
$428$	−1.32929e10	+	2.09793e10i	−0.396136	+	0.625196i
$429$	−2.00271e10	+	2.00271e10i	−0.591274	+	0.591274i
$430$	−2.78720e8	−	2.51638e9i	−0.00815256	−	0.0736042i
$431$		−	2.69990e10i		−	0.782418i	−0.920302	−	0.391209i	$-0.872057\pi$
$431$		−	2.69990e10i		−	0.782418i	0.920302	−	0.391209i	$-0.127943\pi$
$432$	−2.26147e9	+	6.30972e9i	−0.0649316	+	0.181165i
$433$	−2.67958e10			−0.762282			−0.381141	−	0.924517i	$-0.624469\pi$
$433$	−2.67958e10			−0.762282			−0.381141	+	0.924517i	$0.624469\pi$
$434$	4.67837e10	−	5.18186e9i	1.31867	−	0.146059i
$435$	2.10812e8	+	2.10812e8i	0.00588759	+	0.00588759i
$436$	1.20649e10	−	1.90413e10i	0.333871	−	0.526927i
$437$	1.07685e10	+	1.07685e10i	0.295278	+	0.295278i
$438$	−5.43829e9	−	4.35371e9i	−0.147763	−	0.118294i
$439$	3.38996e8			0.00912717			0.00456358	−	0.999990i	$-0.498547\pi$
$439$	3.38996e8			0.00912717			0.00456358	+	0.999990i	$0.498547\pi$
$440$	2.25644e9	+	6.56756e9i	0.0602022	+	0.175224i
$441$		−	1.56800e9i		−	0.0414564i
$442$	4.24002e10	+	3.39441e10i	1.11091	+	0.889355i
$443$	−7.03554e9	+	7.03554e9i	−0.182676	+	0.182676i	−0.792521	−	0.609845i	$-0.791232\pi$
$443$	−7.03554e9	+	7.03554e9i	−0.182676	+	0.182676i	0.609845	+	0.792521i	$0.291232\pi$
$444$	−7.54630e9	−	3.36474e10i	−0.194179	−	0.865804i
$445$	2.36900e9	−	2.36900e9i	0.0604124	−	0.0604124i
$446$	−2.73799e10	+	3.03266e9i	−0.691977	+	0.0766450i
$447$		−	3.03878e10i		−	0.761148i
$448$	2.97346e10	−	2.31667e10i	0.738159	−	0.575110i
$449$	−2.61244e10			−0.642778			−0.321389	−	0.946947i	$-0.604150\pi$
$449$	−2.61244e10			−0.642778			−0.321389	+	0.946947i	$0.604150\pi$
$450$	−1.48743e9	−	1.34291e10i	−0.0362733	−	0.327488i
$451$	−2.94865e10	−	2.94865e10i	−0.712716	−	0.712716i
$452$	3.76936e10	−	8.45377e9i	0.903055	−	0.202533i
$453$	4.69109e9	+	4.69109e9i	0.111399	+	0.111399i
$454$	−1.08860e10	+	1.35979e10i	−0.256239	+	0.320073i
$455$	3.61395e9			0.0843211
$456$	−4.25021e10	+	1.46026e10i	−0.982994	+	0.337730i
$457$			5.77079e10i			1.32303i	0.749931	+	0.661516i	$0.230087\pi$
$457$			5.77079e10i			1.32303i	−0.749931	+	0.661516i	$0.769913\pi$
$458$	−7.70266e9	+	9.62152e9i	−0.175057	+	0.218666i
$459$	−1.02415e10	+	1.02415e10i	−0.230736	+	0.230736i
$460$	−9.41916e8	−	5.96815e8i	−0.0210369	−	0.0133293i
$461$	8.63048e9	−	8.63048e9i	0.191087	−	0.191087i	−0.605079	−	0.796166i	$-0.706858\pi$
$461$	8.63048e9	−	8.63048e9i	0.191087	−	0.191087i	0.796166	+	0.605079i	$0.206858\pi$
$462$	4.67592e9	+	4.22159e10i	0.102636	+	0.926633i
$463$		−	5.35776e10i		−	1.16589i	−0.812510	−	0.582947i	$-0.801900\pi$
$463$		−	5.35776e10i		−	1.16589i	0.812510	−	0.582947i	$-0.198100\pi$
$464$	2.10066e9	−	5.86105e9i	0.0453194	−	0.126446i
$465$	4.10905e9			0.0878879
$466$	−2.65373e10	+	2.93933e9i	−0.562746	+	0.0623310i
$467$	4.91477e10	+	4.91477e10i	1.03332	+	1.03332i	0.999425	+	0.0338964i	$0.0107916\pi$
$467$	4.91477e10	+	4.91477e10i	1.03332	+	1.03332i	0.0338964	+	0.999425i	$0.489208\pi$
$468$	1.13365e10	+	7.18301e9i	0.236317	+	0.149735i
$469$	−3.60529e10	−	3.60529e10i	−0.745159	−	0.745159i
$470$	8.04927e9	+	6.44397e9i	0.164955	+	0.132057i
$471$	1.52381e10			0.309633
$472$	−2.17064e10	−	1.06050e10i	−0.437340	−	0.213670i
$473$		−	5.95777e10i		−	1.19025i
$474$	2.44036e10	+	1.95367e10i	0.483439	+	0.387024i
$475$	6.40567e10	−	6.40567e10i	1.25832	−	1.25832i
$476$	7.94773e10	−	1.78248e10i	1.54816	−	0.347215i
$477$	−2.95443e9	+	2.95443e9i	−0.0570689	+	0.0570689i
$478$	8.02441e10	−	8.88802e9i	1.53710	−	0.170252i
$479$			2.87792e10i			0.546684i	0.961917	+	0.273342i	$0.0881291\pi$
$479$			2.87792e10i			0.546684i	−0.961917	+	0.273342i	$0.911871\pi$
$480$	2.80260e9	−	1.72432e9i	0.0527954	−	0.0324828i
$481$	−6.90440e10			−1.28987
$482$	−3.58039e9	−	3.23250e10i	−0.0663349	−	0.598894i
$483$	−4.82258e9	−	4.82258e9i	−0.0886117	−	0.0886117i
$484$	2.37527e10	+	1.05909e11i	0.432845	+	1.92997i
$485$	−2.36540e9	−	2.36540e9i	−0.0427501	−	0.0427501i
$486$	−2.23664e9	+	2.79383e9i	−0.0400915	+	0.0500789i
$487$	−1.35906e10			−0.241614			−0.120807	−	0.992676i	$-0.538548\pi$
$487$	−1.35906e10			−0.241614			−0.120807	+	0.992676i	$0.538548\pi$
$488$	2.87842e10	+	1.40631e10i	0.507546	+	0.247971i
$489$		−	4.81961e10i		−	0.842901i
$490$	−4.81082e8	+	6.00928e8i	−0.00834516	+	0.0104241i
$491$	−7.35880e10	+	7.35880e10i	−1.26614	+	1.26614i	−0.318072	+	0.948067i	$0.603035\pi$
$491$	−7.35880e10	+	7.35880e10i	−1.26614	+	1.26614i	−0.948067	+	0.318072i	$0.896965\pi$
$492$	−1.05758e10	+	1.66910e10i	−0.180489	+	0.284855i
$493$	9.51329e9	−	9.51329e9i	0.161043	−	0.161043i
$494$	9.90606e9	+	8.94354e10i	0.166339	+	1.50176i
$495$			3.70785e9i			0.0617592i
$496$	−3.66479e10	−	7.75930e10i	−0.605511	−	1.28202i
$497$	−3.39908e10			−0.557104
$498$	1.32458e10	−	1.46713e9i	0.215357	−	0.0238534i
$499$	−1.81053e10	−	1.81053e10i	−0.292015	−	0.292015i	0.545861	−	0.837876i	$-0.316203\pi$
$499$	−1.81053e10	−	1.81053e10i	−0.292015	−	0.292015i	−0.837876	+	0.545861i	$0.816203\pi$
$500$	−7.14171e9	+	1.12713e10i	−0.114267	+	0.180341i
$501$	3.57337e10	+	3.57337e10i	0.567188	+	0.567188i
$502$	−4.02607e10	−	3.22313e10i	−0.633967	−	0.507532i
$503$	−1.08311e11			−1.69200			−0.846002	−	0.533179i	$-0.820997\pi$
$503$	−1.08311e11			−1.69200			−0.846002	+	0.533179i	$0.820997\pi$
$504$	1.90341e10	−	6.53960e9i	0.294992	−	0.101351i
$505$		−	9.37313e9i		−	0.144118i
$506$	−2.04843e10	−	1.63991e10i	−0.312478	−	0.250159i
$507$	−7.97379e9	+	7.97379e9i	−0.120679	+	0.120679i
$508$	1.49434e10	+	6.66297e10i	0.224386	+	1.00049i
$509$	−1.04729e10	+	1.04729e10i	−0.156025	+	0.156025i	−0.780803	−	0.624778i	$-0.785190\pi$
$509$	−1.04729e10	+	1.04729e10i	−0.156025	+	0.156025i	0.624778	+	0.780803i	$0.285190\pi$
$510$	7.06725e9	−	7.82785e8i	0.104465	−	0.0115708i
$511$			2.09176e10i			0.306781i
$512$	−5.75571e10	−	3.75439e10i	−0.837566	−	0.546336i
$513$	−2.39954e10			−0.346464
$514$	6.25992e9	+	5.65167e10i	0.0896842	+	0.809701i
$515$	6.73015e9	+	6.73015e9i	0.0956744	+	0.0956744i
$516$	−2.75464e10	+	6.17799e9i	−0.388567	+	0.0871462i
$517$	1.71570e11	+	1.71570e11i	2.40149	+	2.40149i
$518$	−6.47100e10	+	8.08304e10i	−0.898778	+	1.12268i
$519$	1.54080e10			0.212362
$520$	−2.14081e9	−	6.23103e9i	−0.0292796	−	0.0852210i
$521$		−	4.54812e10i		−	0.617278i	−0.951179	−	0.308639i	$-0.900127\pi$
$521$		−	4.54812e10i		−	0.617278i	0.951179	−	0.308639i	$-0.0998734\pi$
$522$	2.07760e9	−	2.59517e9i	0.0279821	−	0.0349529i
$523$	−2.83198e10	+	2.83198e10i	−0.378515	+	0.378515i	−0.870566	−	0.492051i	$-0.836247\pi$
$523$	−2.83198e10	+	2.83198e10i	−0.378515	+	0.378515i	0.492051	+	0.870566i	$0.336247\pi$
$524$	−5.09022e10	−	3.22526e10i	−0.675167	−	0.427799i
$525$	−2.86871e10	+	2.86871e10i	−0.377615	+	0.377615i
$526$	1.37484e10	+	1.24126e11i	0.179602	+	1.62151i
$527$		−	1.85429e11i		−	2.40400i
$528$	7.00171e10	−	3.30697e10i	0.900883	−	0.425495i
$529$	−7.40976e10			−0.946196
$530$	2.03873e9	−	2.25814e8i	0.0258378	−	0.00286185i
$531$	−9.12103e9	−	9.12103e9i	−0.114727	−	0.114727i
$532$	1.13987e11	+	7.22243e10i	1.42301	+	0.901647i
$533$	2.79756e10	+	2.79756e10i	0.346633	+	0.346633i
$534$	−2.91633e10	−	2.33471e10i	−0.358651	−	0.287123i
$535$	6.51014e9			0.0794649
$536$	−4.08042e10	+	8.35179e10i	−0.494363	+	1.01186i
$537$			5.60392e10i			0.673898i
$538$	−5.79837e10	−	4.64197e10i	−0.692112	−	0.554081i
$539$	−1.28088e10	+	1.28088e10i	−0.151759	+	0.151759i
$540$	1.71437e9	−	3.84491e8i	0.0201618	−	0.00452180i
$541$	2.92862e10	−	2.92862e10i	0.341881	−	0.341881i	−0.515193	−	0.857074i	$-0.672280\pi$
$541$	2.92862e10	−	2.92862e10i	0.341881	−	0.341881i	0.857074	+	0.515193i	$0.172280\pi$
$542$	4.33400e10	−	4.80043e9i	0.502217	−	0.0556267i
$543$		−	6.20301e10i		−	0.713515i
$544$	−7.78133e10	−	1.26473e11i	−0.888502	−	1.44411i
$545$	−5.90875e9			−0.0669745
$546$	−4.43632e9	−	4.00527e10i	−0.0499175	−	0.450672i
$547$	−1.03888e11	−	1.03888e11i	−1.16042	−	1.16042i	−0.984383	−	0.176039i	$-0.943672\pi$
$547$	−1.03888e11	−	1.03888e11i	−1.16042	−	1.16042i	−0.176039	−	0.984383i	$-0.556328\pi$
$548$	−1.76272e10	−	7.85959e10i	−0.195461	−	0.871520i
$549$	1.20952e10	+	1.20952e10i	0.133144	+	0.133144i
$550$	−9.75497e10	+	1.21851e11i	−1.06604	+	1.33161i
$551$	2.22891e10			0.241817
$552$	−5.45813e9	+	1.11717e10i	−0.0587879	+	0.120327i
$553$		−	9.38652e10i		−	1.00370i
$554$	−2.56169e10	+	3.19985e10i	−0.271949	+	0.339696i
$555$	−6.39146e9	+	6.39146e9i	−0.0673641	+	0.0673641i
$556$	2.69793e10	−	4.25797e10i	0.282313	−	0.445557i
$557$	−4.16797e10	+	4.16797e10i	−0.433016	+	0.433016i	−0.889653	−	0.456637i	$-0.849054\pi$
$557$	−4.16797e10	+	4.16797e10i	−0.433016	+	0.433016i	0.456637	+	0.889653i	$0.349054\pi$
$558$	−5.04408e9	−	4.55397e10i	−0.0520290	−	0.469736i
$559$			5.65248e10i			0.578885i
$560$	−9.30116e9	−	3.33363e9i	−0.0945769	−	0.0338974i
$561$	1.67324e11			1.68930
$562$	1.01341e11	−	1.12247e10i	1.01587	−	0.112520i
$563$	7.81306e10	+	7.81306e10i	0.777656	+	0.777656i	0.979432	−	0.201776i	$-0.0646712\pi$
$563$	7.81306e10	+	7.81306e10i	0.777656	+	0.777656i	−0.201776	+	0.979432i	$0.564671\pi$
$564$	6.15363e10	−	9.71188e10i	0.608156	−	0.959813i
$565$	−7.16006e9	−	7.16006e9i	−0.0702624	−	0.0702624i
$566$	−1.35446e11	−	1.08434e11i	−1.31978	−	1.05657i
$567$	1.07461e10			0.103972
$568$	2.01353e10	+	5.86057e10i	0.193449	+	0.563049i
$569$			1.34862e11i			1.28659i	0.765618	+	0.643296i	$0.222434\pi$
$569$			1.34862e11i			1.28659i	−0.765618	+	0.643296i	$0.777566\pi$
$570$	9.19612e9	+	7.36210e9i	0.0871175	+	0.0697432i
$571$	−6.56636e10	+	6.56636e10i	−0.617704	+	0.617704i	−0.944942	−	0.327238i	$-0.893882\pi$
$571$	−6.56636e10	+	6.56636e10i	−0.617704	+	0.617704i	0.327238	+	0.944942i	$0.393882\pi$
$572$	−3.39293e10	−	1.51284e11i	−0.316950	−	1.41321i
$573$	−3.27755e10	+	3.27755e10i	−0.304040	+	0.304040i
$574$	5.89707e10	−	6.53173e9i	0.543236	−	0.0601701i
$575$		−	2.50635e10i		−	0.229282i
$576$	−2.25507e10	−	2.89440e10i	−0.204866	−	0.262947i
$577$	4.11217e10			0.370995			0.185498	−	0.982645i	$-0.440610\pi$
$577$	4.11217e10			0.370995			0.185498	+	0.982645i	$0.440610\pi$
$578$	−2.30374e10	−	2.07990e11i	−0.206406	−	1.86350i
$579$	3.08261e10	+	3.08261e10i	0.274286	+	0.274286i
$580$	−1.59246e9	+	3.57151e8i	−0.0140720	+	0.00315602i
$581$	−2.82955e10	−	2.82955e10i	−0.248321	−	0.248321i
$582$	−2.33116e10	+	2.91189e10i	−0.203179	+	0.253795i
$583$	4.82687e10			0.417822
$584$	3.60654e10	−	1.23911e10i	0.310056	−	0.106527i
$585$		−	3.51786e9i		−	0.0300369i
$586$	−1.06921e11	+	1.33557e11i	−0.906720	+	1.13260i
$587$	−6.41428e10	+	6.41428e10i	−0.540251	+	0.540251i	−0.923603	−	0.383352i	$-0.874770\pi$
$587$	−6.41428e10	+	6.41428e10i	−0.540251	+	0.540251i	0.383352	+	0.923603i	$0.374770\pi$
$588$	7.25052e9	+	4.59406e9i	0.0606540	+	0.0384315i
$589$	2.17225e11	−	2.17225e11i	1.80488	−	1.80488i
$590$	6.97142e8	+	6.29404e9i	0.00575325	+	0.0519423i
$591$			7.00380e9i			0.0574095i
$592$	1.77697e11	+	6.36886e10i	1.44675	+	0.518531i
$593$	1.17104e11			0.947005			0.473502	−	0.880793i	$-0.342990\pi$
$593$	1.17104e11			0.947005			0.473502	+	0.880793i	$0.342990\pi$
$594$	4.10934e10	−	4.55159e9i	0.330085	−	0.0365610i
$595$	−1.50970e10	−	1.50970e10i	−0.120455	−	0.120455i
$596$	1.40515e11	+	8.90329e10i	1.11362	+	0.705611i
$597$	−5.03463e10	−	5.03463e10i	−0.396342	−	0.396342i
$598$	1.94347e10	+	1.55587e10i	0.151975	+	0.121666i
$599$	−6.59737e10			−0.512464			−0.256232	−	0.966615i	$-0.582481\pi$
$599$	−6.59737e10			−0.512464			−0.256232	+	0.966615i	$0.582481\pi$
$600$	6.64548e10	+	3.24677e10i	0.512768	+	0.250522i
$601$		−	1.57761e10i		−	0.120921i	−0.998171	−	0.0604606i	$-0.980743\pi$
$601$		−	1.57761e10i		−	0.120921i	0.998171	−	0.0604606i	$-0.0192570\pi$
$602$	6.61741e10	+	5.29767e10i	0.503851	+	0.403366i
$603$	−3.50943e10	+	3.50943e10i	−0.265441	+	0.265441i
$604$	−3.54363e10	+	7.94750e9i	−0.266257	+	0.0597149i
$605$	2.01178e10	−	2.01178e10i	0.150161	−	0.150161i
$606$	−1.03881e11	+	1.15060e10i	−0.770271	+	0.0853169i
$607$		−	9.67141e10i		−	0.712418i	−0.934406	−	0.356209i	$-0.884069\pi$
$607$		−	9.67141e10i		−	0.712418i	0.934406	−	0.356209i	$-0.115931\pi$
$608$	5.70033e10	−	2.39316e11i	0.417144	−	1.75129i
$609$	−9.98195e9			−0.0725682
$610$	−9.24461e8	−	8.34635e9i	−0.00667681	−	0.0602806i
$611$	−1.62779e11	−	1.62779e11i	−1.16797	−	1.16797i
$612$	−1.73509e10	−	7.73641e10i	−0.123685	−	0.551485i
$613$	1.45465e11	+	1.45465e11i	1.03019	+	1.03019i	0.999530	+	0.0306587i	$0.00976051\pi$
$613$	1.45465e11	+	1.45465e11i	1.03019	+	1.03019i	0.0306587	+	0.999530i	$0.490239\pi$
$614$	−7.80500e10	+	9.74936e10i	−0.549161	+	0.685966i
$615$	5.17944e9			0.0362062
$616$	−2.08909e11	−	1.02066e11i	−1.45089	−	0.708857i
$617$			1.57319e11i			1.08553i	0.839885	+	0.542764i	$0.182622\pi$
$617$			1.57319e11i			1.08553i	−0.839885	+	0.542764i	$0.817378\pi$
$618$	6.63273e10	−	8.28505e10i	0.454714	−	0.567991i
$619$	1.53017e11	−	1.53017e11i	1.04226	−	1.04226i	0.0431963	−	0.999067i	$-0.486246\pi$
$619$	1.53017e11	−	1.53017e11i	1.04226	−	1.04226i	0.999067	−	0.0431963i	$-0.0137541\pi$
$620$	−1.20390e10	+	1.90005e10i	−0.0814752	+	0.128587i
$621$	−4.69435e9	+	4.69435e9i	−0.0315652	+	0.0315652i
$622$	9.62458e9	+	8.68941e10i	0.0643014	+	0.580535i
$623$			1.12173e11i			0.744619i
$624$	−6.64293e10	+	3.13752e10i	−0.438149	+	0.206942i
$625$	−1.47331e11			−0.965550
$626$	−6.61259e8	+	7.32425e7i	−0.00430600	+	0.000476943i
$627$	1.96016e11	+	1.96016e11i	1.26830	+	1.26830i
$628$	−4.46459e10	+	7.04618e10i	−0.287040	+	0.453018i
$629$	2.88427e11	+	2.88427e11i	1.84261	+	1.84261i
$630$	−4.11838e9	−	3.29704e9i	−0.0261436	−	0.0209296i
$631$	1.00191e11			0.631992			0.315996	−	0.948761i	$-0.397661\pi$
$631$	1.00191e11			0.631992			0.315996	+	0.948761i	$0.397661\pi$
$632$	−1.61839e11	+	5.56035e10i	−1.01441	+	0.348525i
$633$			1.41201e10i			0.0879471i
$634$	−6.13564e10	−	4.91198e10i	−0.379754	−	0.304018i
$635$	1.26566e10	−	1.26566e10i	0.0778434	−	0.0778434i
$636$	−5.00530e9	−	2.23176e10i	−0.0305915	−	0.136401i
$637$	1.21525e10	−	1.21525e10i	0.0738085	−	0.0738085i
$638$	−3.81713e10	+	4.22794e9i	−0.230385	+	0.0255180i
$639$			3.30870e10i			0.198451i
$640$	−2.37948e8	+	1.80115e10i	−0.00141828	+	0.107357i
$641$	9.02125e10			0.534361			0.267180	−	0.963647i	$-0.413908\pi$
$641$	9.02125e10			0.534361			0.267180	+	0.963647i	$0.413908\pi$
$642$	−7.99156e9	−	7.21506e10i	−0.0470426	−	0.424717i
$643$	−9.84072e10	−	9.84072e10i	−0.575682	−	0.575682i	0.358028	−	0.933711i	$-0.383449\pi$
$643$	−9.84072e10	−	9.84072e10i	−0.575682	−	0.575682i	−0.933711	+	0.358028i	$0.883449\pi$
$644$	3.64295e10	−	8.17026e9i	0.211792	−	0.0474999i
$645$	5.23255e9	+	5.23255e9i	0.0302325	+	0.0302325i
$646$	3.32229e11	−	4.14992e11i	1.90769	−	2.38292i
$647$	1.45755e11			0.831775			0.415888	−	0.909416i	$-0.363471\pi$
$647$	1.45755e11			0.831775			0.415888	+	0.909416i	$0.363471\pi$
$648$	−6.36572e9	−	1.85280e10i	−0.0361033	−	0.105082i
$649$			1.49017e11i			0.839958i
$650$	9.25512e10	−	1.15607e11i	0.518476	−	0.647637i
$651$	−9.72818e10	+	9.72818e10i	−0.541636	+	0.541636i
$652$	2.22862e11	+	1.41209e11i	1.23323	+	0.781399i
$653$	−6.37258e10	+	6.37258e10i	−0.350480	+	0.350480i	−0.860288	−	0.509808i	$-0.829716\pi$
$653$	−6.37258e10	+	6.37258e10i	−0.350480	+	0.350480i	0.509808	+	0.860288i	$0.329716\pi$
$654$	7.25332e9	+	6.54855e10i	0.0396484	+	0.357960i
$655$			1.57956e10i			0.0858165i
$656$	−4.61946e10	−	9.78058e10i	−0.249445	−	0.528140i
$657$	2.03615e10			0.109282
$658$	−3.43128e11	+	3.80056e10i	−1.83043	+	0.202742i
$659$	−1.81802e10	−	1.81802e10i	−0.0963958	−	0.0963958i	0.657264	−	0.753660i	$-0.271714\pi$
$659$	−1.81802e10	−	1.81802e10i	−0.0963958	−	0.0963958i	−0.753660	+	0.657264i	$0.771714\pi$
$660$	−1.71453e10	−	1.08636e10i	−0.0903587	−	0.0572529i
$661$	−2.15596e11	−	2.15596e11i	−1.12937	−	1.12937i	−0.990280	−	0.139089i	$-0.955583\pi$
$661$	−2.15596e11	−	2.15596e11i	−1.12937	−	1.12937i	−0.139089	−	0.990280i	$-0.544417\pi$
$662$	−5.77837e10	−	4.62596e10i	−0.300866	−	0.240863i
$663$	−1.58750e11			−0.821598
$664$	−3.20245e10	+	6.55477e10i	−0.164744	+	0.337198i
$665$		−	3.53716e10i		−	0.180871i
$666$	7.86812e10	+	6.29894e10i	0.399921	+	0.320163i
$667$	4.36054e9	−	4.36054e9i	0.0220312	−	0.0220312i
$668$	−2.69931e11	+	6.05390e10i	−1.35565	+	0.304039i
$669$	5.69336e10	−	5.69336e10i	0.284226	−	0.284226i
$670$	2.42171e10	−	2.68234e9i	0.120177	−	0.0133111i
$671$		−	1.97608e11i		−	0.974796i
$672$	−2.55283e10	+	1.07175e11i	−0.125183	+	0.525553i
$673$	−4.19618e10			−0.204547			−0.102274	−	0.994756i	$-0.532612\pi$
$673$	−4.19618e10			−0.204547			−0.102274	+	0.994756i	$0.532612\pi$
$674$	3.31130e10	+	2.98956e11i	0.160457	+	1.44866i
$675$	2.79243e10	+	2.79243e10i	0.134514	+	0.134514i
$676$	−1.35089e10	−	6.02336e10i	−0.0646896	−	0.288438i
$677$	−2.76576e11	−	2.76576e11i	−1.31662	−	1.31662i	−0.916437	−	0.400180i	$-0.868948\pi$
$677$	−2.76576e11	−	2.76576e11i	−1.31662	−	1.31662i	−0.400180	−	0.916437i	$-0.631052\pi$
$678$	−7.05641e10	+	8.81429e10i	−0.333938	+	0.417127i
$679$	1.12002e11			0.526921
$680$	−1.70866e10	+	3.49729e10i	−0.0799136	+	0.163567i
$681$		−	5.09117e10i		−	0.236717i
$682$	−3.30804e11	+	4.13213e11i	−1.52909	+	1.91001i
$683$	3.63771e9	−	3.63771e9i	0.0167165	−	0.0167165i	−0.698699	−	0.715416i	$-0.746237\pi$
$683$	3.63771e9	−	3.63771e9i	0.0167165	−	0.0167165i	0.715416	+	0.698699i	$0.246237\pi$
$684$	7.03039e10	−	1.10956e11i	0.321185	−	0.506905i
$685$	−1.49296e10	+	1.49296e10i	−0.0678088	+	0.0678088i
$686$	−2.56513e10	−	2.31589e11i	−0.115828	−	1.04573i
$687$		−	3.60238e10i		−	0.161720i
$688$	5.21405e10	−	1.45477e11i	0.232713	−	0.649293i
$689$	−4.57954e10			−0.203210
$690$	3.23937e9	−	3.58800e8i	0.0142911	−	0.00158291i
$691$	−1.13936e11	−	1.13936e11i	−0.499745	−	0.499745i	0.411613	−	0.911359i	$-0.364965\pi$
$691$	−1.13936e11	−	1.13936e11i	−0.499745	−	0.499745i	−0.911359	+	0.411613i	$0.864965\pi$
$692$	−4.51438e10	+	7.12475e10i	−0.196867	+	0.310703i
$693$	−8.77835e10	−	8.77835e10i	−0.380610	−	0.380610i
$694$	6.97074e10	+	5.58053e10i	0.300498	+	0.240568i
$695$	−1.32130e10			−0.0566321
$696$	5.91306e9	+	1.72105e10i	0.0251986	+	0.0733427i
$697$		−	2.33732e11i		−	0.990347i
$698$	2.16397e11	+	1.73240e11i	0.911655	+	0.729839i
$699$	5.51815e10	−	5.51815e10i	0.231145	−	0.231145i
$700$	−4.86008e10	−	2.16701e11i	−0.202419	−	0.902544i
$701$	−3.28579e11	+	3.28579e11i	−1.36071	+	1.36071i	−0.487708	+	0.873007i	$0.662167\pi$
$701$	−3.28579e11	+	3.28579e11i	−1.36071	+	1.36071i	−0.873007	+	0.487708i	$0.837833\pi$
$702$	−3.89877e10	+	4.31836e9i	−0.160538	+	0.0177816i
$703$			6.75770e11i			2.76680i
$704$	−5.22262e10	+	4.20654e11i	−0.212617	+	1.71251i
$705$	−3.01372e10			−0.121996
$706$	−1.45136e10	−	1.31034e11i	−0.0584194	−	0.527431i
$707$	2.21909e11	+	2.21909e11i	0.888173	+	0.888173i
$708$	6.88998e10	−	1.54526e10i	0.274211	−	0.0614989i
$709$	−2.44267e11	−	2.44267e11i	−0.966676	−	0.966676i	0.0327868	−	0.999462i	$-0.489562\pi$
$709$	−2.44267e11	−	2.44267e11i	−0.966676	−	0.966676i	−0.999462	+	0.0327868i	$0.989562\pi$
$710$	1.01515e10	−	1.26804e10i	0.0399483	−	0.0499001i
$711$	−9.13694e10			−0.357538
$712$	1.93404e11	−	6.64483e10i	0.752566	−	0.258561i
$713$		−	8.49937e10i		−	0.328873i
$714$	−1.48785e11	+	1.85850e11i	−0.572488	+	0.715105i
$715$	−2.87370e10	+	2.87370e10i	−0.109955	+	0.109955i
$716$	−2.59128e11	−	1.64189e11i	−0.985968	−	0.624728i
$717$	−1.66859e11	+	1.66859e11i	−0.631355	+	0.631355i
$718$	1.82894e9	+	1.65123e10i	0.00688181	+	0.0621313i
$719$		−	1.63434e11i		−	0.611544i	−0.952105	−	0.305772i	$-0.901086\pi$
$719$		−	1.63434e11i		−	0.611544i	0.952105	−	0.305772i	$-0.0989145\pi$
$720$	−3.24499e9	+	9.05385e9i	−0.0120749	+	0.0336902i
$721$	−3.18673e11			−1.17925
$722$	6.05265e11	−	6.70405e10i	2.22739	−	0.246711i
$723$	6.72164e10	+	6.72164e10i	0.245993	+	0.245993i
$724$	2.86831e11	+	1.81741e11i	1.04393	+	0.661454i
$725$	−2.59387e10	−	2.59387e10i	−0.0938850	−	0.0938850i
$726$	−2.47657e11	−	1.98266e11i	−0.891464	−	0.713675i
$727$	7.56518e9			0.0270821			0.0135410	−	0.999908i	$-0.495690\pi$
$727$	7.56518e9			0.0270821			0.0135410	+	0.999908i	$0.495690\pi$
$728$	1.98204e11	+	9.68361e10i	0.705645	+	0.344756i
$729$		−	1.04604e10i		−	0.0370370i
$730$	−7.80343e9	−	6.24715e9i	−0.0274786	−	0.0219984i
$731$	2.36129e11	−	2.36129e11i	0.826951	−	0.826951i
$732$	−9.13661e10	+	2.04912e10i	−0.318230	+	0.0713713i
$733$	1.76671e11	−	1.76671e11i	0.611996	−	0.611996i	−0.331470	−	0.943466i	$-0.607544\pi$
$733$	1.76671e11	−	1.76671e11i	0.611996	−	0.611996i	0.943466	+	0.331470i	$0.107544\pi$
$734$	4.96271e11	−	5.49680e10i	1.70976	−	0.189376i
$735$		−	2.24993e9i		−	0.00770937i
$736$	−3.56668e10	−	5.79705e10i	−0.121549	−	0.197559i
$737$	5.73362e11			1.94339
$738$	−6.35805e9	−	5.74027e10i	−0.0214338	−	0.193512i
$739$	7.52469e10	+	7.52469e10i	0.252296	+	0.252296i	0.821912	−	0.569615i	$-0.192908\pi$
$739$	7.52469e10	+	7.52469e10i	0.252296	+	0.252296i	−0.569615	+	0.821912i	$0.692908\pi$
$740$	−1.08282e10	−	4.82808e10i	−0.0361102	−	0.161008i
$741$	−1.85972e11	−	1.85972e11i	−0.616842	−	0.616842i
$742$	−4.29208e10	+	5.36131e10i	−0.141596	+	0.176870i
$743$	−2.55902e11			−0.839687			−0.419844	−	0.907596i	$-0.637915\pi$
$743$	−2.55902e11			−0.839687			−0.419844	+	0.907596i	$0.637915\pi$
$744$	2.25357e11	+	1.10102e11i	0.735494	+	0.359339i
$745$		−	4.36036e10i		−	0.141546i
$746$	2.96692e11	−	3.70603e11i	0.957966	−	1.19661i
$747$	−2.75432e10	+	2.75432e10i	−0.0884569	+	0.0884569i
$748$	−4.90240e11	+	7.73715e11i	−1.56604	+	2.47158i
$749$	−1.54128e11	+	1.54128e11i	−0.489727	+	0.489727i
$750$	−4.29353e9	−	3.87635e10i	−0.0135697	−	0.122512i
$751$		−	7.66881e10i		−	0.241084i	−0.992708	−	0.120542i	$-0.961537\pi$
$751$		−	7.66881e10i		−	0.241084i	0.992708	−	0.120542i	$-0.0384632\pi$
$752$	2.68788e11	+	5.69095e11i	0.840503	+	1.77956i
$753$	1.50740e11			0.468865
$754$	3.62154e10	−	4.01129e9i	0.112049	−	0.0124108i
$755$	6.73127e9	+	6.73127e9i	0.0207161	+	0.0207161i
$756$	−3.14848e10	+	4.96905e10i	−0.0963861	+	0.152120i
$757$	1.92715e11	+	1.92715e11i	0.586857	+	0.586857i	0.936779	−	0.349922i	$-0.113792\pi$
$757$	1.92715e11	+	1.92715e11i	0.586857	+	0.586857i	−0.349922	+	0.936779i	$0.613792\pi$
$758$	3.04364e11	+	2.43663e11i	0.921969	+	0.738096i
$759$	7.66952e10			0.231101
$760$	−6.09864e10	+	2.09533e10i	−0.182801	+	0.0628055i
$761$			3.82780e11i			1.14133i	0.821183	+	0.570665i	$0.193314\pi$
$761$			3.82780e11i			1.14133i	−0.821183	+	0.570665i	$0.806686\pi$
$762$	−1.55807e11	−	1.24734e11i	−0.462134	−	0.369968i
$763$	1.39890e11	−	1.39890e11i	0.412751	−	0.412751i
$764$	−5.55272e10	−	2.47584e11i	−0.162979	−	0.726690i
$765$	−1.46956e10	+	1.46956e10i	−0.0429084	+	0.0429084i
$766$	4.92897e11	−	5.45944e10i	1.43166	−	0.158574i
$767$		−	1.41381e11i		−	0.408518i
$768$	1.99910e11	−	1.94729e10i	0.574631	−	0.0559740i
$769$	−6.55771e11			−1.87520			−0.937598	−	0.347722i	$-0.886955\pi$
$769$	−6.55771e11			−1.87520			−0.937598	+	0.347722i	$0.886955\pi$
$770$	6.70950e9	+	6.05757e10i	0.0190865	+	0.172320i
$771$	−1.17521e11	−	1.17521e11i	−0.332580	−	0.332580i
$772$	−2.32858e11	+	5.22245e10i	−0.655575	+	0.147030i
$773$	−2.91283e11	−	2.91283e11i	−0.815826	−	0.815826i	0.169675	−	0.985500i	$-0.445728\pi$
$773$	−2.91283e11	−	2.91283e11i	−0.815826	−	0.815826i	−0.985500	+	0.169675i	$0.945728\pi$
$774$	5.15681e10	−	6.44146e10i	0.143687	−	0.179482i
$775$	−5.05585e11			−1.40148
$776$	−6.63470e10	−	1.93109e11i	−0.182968	−	0.532544i
$777$		−	3.02636e11i		−	0.830303i
$778$	−4.51422e9	+	5.63879e9i	−0.0123215	+	0.0153910i
$779$	2.73811e11	−	2.73811e11i	0.743535	−	0.743535i
$780$	1.62668e10	+	1.03069e10i	0.0439464	+	0.0278452i
$781$	2.70284e11	−	2.70284e11i	0.726468	−	0.726468i
$782$	−1.61915e10	−	1.46183e11i	−0.0432973	−	0.390903i
$783$			9.71654e9i			0.0258502i
$784$	−4.24864e10	+	2.00667e10i	−0.112457	+	0.0531144i
$785$	2.18652e10			0.0575804
$786$	1.75059e11	−	1.93900e10i	0.458665	−	0.0508027i
$787$	−2.10330e11	−	2.10330e11i	−0.548279	−	0.548279i	0.377664	−	0.925943i	$-0.376728\pi$
$787$	−2.10330e11	−	2.10330e11i	−0.548279	−	0.548279i	−0.925943	+	0.377664i	$0.876728\pi$
$788$	−3.23860e10	−	2.05204e10i	−0.0839947	−	0.0532206i
$789$	−2.58106e11	−	2.58106e11i	−0.666025	−	0.666025i
$790$	3.50169e10	+	2.80333e10i	0.0899019	+	0.0719724i
$791$	3.39029e11			0.866027
$792$	−9.93522e10	+	2.03354e11i	−0.252509	+	0.516835i
$793$			1.87482e11i			0.474097i
$794$	−3.11835e11	−	2.49644e11i	−0.784590	−	0.628115i
$795$	−4.23932e9	+	4.23932e9i	−0.0106127	+	0.0106127i
$796$	3.80313e11	−	8.52950e10i	0.947303	−	0.212457i
$797$	4.56045e11	−	4.56045e11i	1.13025	−	1.13025i	0.140114	−	0.990135i	$-0.455253\pi$
$797$	4.56045e11	−	4.56045e11i	1.13025	−	1.13025i	0.990135	−	0.140114i	$-0.0447470\pi$
$798$	−3.92016e11	+	4.34206e10i	−0.966702	+	0.107074i
$799$			1.36000e12i			3.33696i
$800$	−3.44838e11	+	2.12164e11i	−0.841889	+	0.517978i
$801$	1.09190e11			0.265248
$802$	−6.58940e8	−	5.94914e9i	−0.00159275	−	0.0143799i
$803$	−1.66330e11	−	1.66330e11i	−0.400045	−	0.400045i
$804$	−5.94556e10	−	2.65100e11i	−0.142288	−	0.634434i
$805$	−6.91994e9	−	6.91994e9i	−0.0164785	−	0.0164785i
$806$	3.13853e11	−	3.92040e11i	0.743681	−	0.928945i
$807$	2.17096e11			0.511868
$808$	2.51154e11	−	5.14061e11i	0.589243	−	1.20606i
$809$		−	1.82376e11i		−	0.425768i	−0.977077	−	0.212884i	$-0.931714\pi$
$809$		−	1.82376e11i		−	0.425768i	0.977077	−	0.212884i	$-0.0682857\pi$
$810$	−3.20937e9	+	4.00888e9i	−0.00745555	+	0.00931286i
$811$	3.52659e11	−	3.52659e11i	0.815213	−	0.815213i	−0.170197	−	0.985410i	$-0.554440\pi$
$811$	3.52659e11	−	3.52659e11i	0.815213	−	0.815213i	0.985410	+	0.170197i	$0.0544403\pi$
$812$	2.92460e10	−	4.61571e10i	0.0672733	−	0.106173i
$813$	−9.01210e10	+	9.01210e10i	−0.206283	+	0.206283i
$814$	−1.28184e11	−	1.15729e12i	−0.291969	−	2.63600i
$815$		−	6.91568e10i		−	0.156749i
$816$	4.08572e11	+	1.46437e11i	0.921527	+	0.330285i
$817$	5.53238e11			1.24172
$818$	−4.77848e11	+	5.29276e10i	−1.06728	+	0.118214i
$819$	8.32854e10	+	8.32854e10i	0.185111	+	0.185111i
$820$	−1.51752e10	+	2.39500e10i	−0.0335644	+	0.0529725i
$821$	−2.25647e11	−	2.25647e11i	−0.496658	−	0.496658i	0.413738	−	0.910396i	$-0.364223\pi$
$821$	−2.25647e11	−	2.25647e11i	−0.496658	−	0.496658i	−0.910396	+	0.413738i	$0.864223\pi$
$822$	1.83789e11	+	1.47135e11i	0.402561	+	0.322277i
$823$	8.52445e11			1.85809			0.929045	−	0.369966i	$-0.120631\pi$
$823$	8.52445e11			1.85809			0.929045	+	0.369966i	$0.120631\pi$
$824$	1.88774e11	+	5.49444e11i	0.409481	+	1.19183i
$825$		−	4.56221e11i		−	0.984826i
$826$	−1.65516e11	−	1.32507e11i	−0.355566	−	0.284654i
$827$	1.73742e11	−	1.73742e11i	0.371436	−	0.371436i	−0.496564	−	0.868000i	$-0.665405\pi$
$827$	1.73742e11	−	1.73742e11i	0.371436	−	0.371436i	0.868000	+	0.496564i	$0.165405\pi$
$828$	−7.95302e9	−	3.54609e10i	−0.0169204	−	0.0754446i
$829$	−2.84585e11	+	2.84585e11i	−0.602550	+	0.602550i	−0.940989	−	0.338438i	$-0.890101\pi$
$829$	−2.84585e11	+	2.84585e11i	−0.602550	+	0.602550i	0.338438	+	0.940989i	$0.390101\pi$
$830$	1.90064e10	−	2.10519e9i	0.0400486	−	0.00443587i
$831$		−	1.19805e11i		−	0.251230i
$832$	4.95500e10	−	3.99099e11i	0.103407	−	0.832889i
$833$	−1.01532e11			−0.210874
$834$	1.62197e10	+	1.46437e11i	0.0335258	+	0.302683i
$835$	5.12744e10	+	5.12744e10i	0.105476	+	0.105476i
$836$	−1.48069e12	+	3.32084e11i	−3.03137	+	0.679864i
$837$	9.46951e10	+	9.46951e10i	0.192942	+	0.192942i
$838$	8.54252e10	−	1.06706e11i	0.173225	−	0.216378i
$839$	−9.13957e11			−1.84450			−0.922248	−	0.386598i	$-0.873650\pi$
$839$	−9.13957e11			−1.84450			−0.922248	+	0.386598i	$0.873650\pi$
$840$	2.73121e10	−	9.38370e9i	0.0548577	−	0.0188476i
$841$			4.91221e11i			0.981958i
$842$	−1.03199e11	+	1.28907e11i	−0.205318	+	0.256466i
$843$	−2.10728e11	+	2.10728e11i	−0.417264	+	0.417264i
$844$	−6.52920e10	−	4.13702e10i	−0.128674	−	0.0815301i
$845$	−1.14416e10	+	1.14416e10i	−0.0224419	+	0.0224419i
$846$	3.69951e10	+	3.34004e11i	0.0722208	+	0.652035i
$847$			9.52578e11i			1.85083i
$848$	1.17863e11	+	4.22433e10i	0.227926	+	0.0816910i
$849$	5.07124e11			0.976075
$850$	−8.69569e11	+	9.63154e10i	−1.66582	+	0.184510i
$851$	1.32204e11	+	1.32204e11i	0.252074	+	0.252074i
$852$	−1.52996e11	−	9.69413e10i	−0.290351	−	0.183972i
$853$	−1.99237e11	−	1.99237e11i	−0.376335	−	0.376335i	0.493443	−	0.869778i	$-0.335738\pi$
$853$	−1.99237e11	−	1.99237e11i	−0.376335	−	0.376335i	−0.869778	+	0.493443i	$0.835738\pi$
$854$	2.19487e11	+	1.75714e11i	0.412645	+	0.330350i
$855$	−3.44311e10			−0.0644297
$856$	3.57043e11	+	1.74440e11i	0.665006	+	0.324901i
$857$			3.49315e11i			0.647580i	0.946129	+	0.323790i	$0.104957\pi$
$857$			3.49315e11i			0.647580i	−0.946129	+	0.323790i	$0.895043\pi$
$858$	3.53762e11	+	2.83210e11i	0.652773	+	0.522587i
$859$	3.89887e11	−	3.89887e11i	0.716088	−	0.716088i	−0.251714	−	0.967802i	$-0.580994\pi$
$859$	3.89887e11	−	3.89887e11i	0.716088	−	0.716088i	0.967802	+	0.251714i	$0.0809941\pi$
$860$	−3.95264e10	+	8.86482e9i	−0.0722593	+	0.0162060i
$861$	−1.22623e11	+	1.22623e11i	−0.223132	+	0.223132i
$862$	−4.29359e11	+	4.75567e10i	−0.777663	+	0.0861356i
$863$		−	1.65970e11i		−	0.299218i	−0.988745	−	0.149609i	$-0.952199\pi$
$863$		−	1.65970e11i		−	0.299218i	0.988745	−	0.149609i	$-0.0478014\pi$
$864$	1.04325e11	+	2.48495e10i	0.187213	+	0.0445926i
$865$	2.21090e10			0.0394916
$866$	4.71988e10	+	4.26127e11i	0.0839188	+	0.757648i
$867$	4.32493e11	+	4.32493e11i	0.765425	+	0.765425i
$868$	−1.64812e11	−	7.34862e11i	−0.290342	−	1.29457i
$869$	7.46386e11	+	7.46386e11i	1.30883	+	1.30883i
$870$	2.98116e9	−	3.72382e9i	0.00520365	−	0.00649997i
$871$	−5.43982e11			−0.945175
$872$	−3.24060e11	−	1.58326e11i	−0.560480	−	0.273833i
$873$		−	1.09024e11i		−	0.187700i
$874$	1.52282e11	−	1.90217e11i	0.260977	−	0.325990i
$875$	−8.28065e10	+	8.28065e10i	−0.141264	+	0.141264i
$876$	−5.96568e10	+	9.41525e10i	−0.101308	+	0.159888i
$877$	−3.63425e10	+	3.63425e10i	−0.0614352	+	0.0614352i	−0.737157	−	0.675722i	$-0.763832\pi$
$877$	−3.63425e10	+	3.63425e10i	−0.0614352	+	0.0614352i	0.675722	+	0.737157i	$0.263832\pi$
$878$	−5.97115e8	−	5.39096e9i	−0.00100480	−	0.00907169i
$879$		−	5.00049e11i		−	0.837640i
$880$	1.00468e11	−	4.74518e10i	0.167531	−	0.0791265i
$881$	2.60623e11			0.432622			0.216311	−	0.976324i	$-0.430597\pi$
$881$	2.60623e11			0.432622			0.216311	+	0.976324i	$0.430597\pi$
$882$	−2.49355e10	+	2.76191e9i	−0.0412044	+	0.00456389i
$883$	2.51693e11	+	2.51693e11i	0.414027	+	0.414027i	0.883139	−	0.469112i	$-0.155426\pi$
$883$	2.51693e11	+	2.51693e11i	0.414027	+	0.414027i	−0.469112	+	0.883139i	$0.655426\pi$
$884$	4.65120e11	−	7.34069e11i	0.761651	−	1.20206i
$885$	−1.30878e10	−	1.30878e10i	−0.0213350	−	0.0213350i
$886$	1.24277e11	+	9.94918e10i	0.201677	+	0.161455i
$887$	7.54905e9			0.0121955			0.00609773	−	0.999981i	$-0.498059\pi$
$887$	7.54905e9			0.0121955			0.00609773	+	0.999981i	$0.498059\pi$
$888$	−5.21794e11	+	1.79274e11i	−0.839165	+	0.288314i
$889$			5.99290e11i			0.959468i
$890$	−4.18465e10	−	3.35009e10i	−0.0666959	−	0.0533944i
$891$	−8.54494e10	+	8.54494e10i	−0.135581	+	0.135581i
$892$	9.64551e10	+	4.30073e11i	0.152358	+	0.679334i
$893$	−1.59320e12	+	1.59320e12i	−2.50533	+	2.50533i
$894$	−4.83250e11	+	5.35258e10i	−0.756522	+	0.0837940i
$895$			8.04108e10i			0.125321i
$896$	−4.20789e11	−	4.32055e11i	−0.652878	−	0.670359i
$897$	−7.27652e10			−0.112397
$898$	4.60162e10	+	4.15450e11i	0.0707628	+	0.638871i
$899$	−8.79616e10	−	8.79616e10i	−0.134665	−	0.134665i
$900$	−2.10939e11	+	4.73085e10i	−0.321504	+	0.0721057i
$901$	1.91307e11	+	1.91307e11i	0.290290	+	0.290290i
$902$	−4.16978e11	+	5.20854e11i	−0.629922	+	0.786847i
$903$	−2.47762e11			−0.372635
$904$	−2.00833e11	−	5.84541e11i	−0.300719	−	0.875269i
$905$		−	8.90072e10i		−	0.132688i
$906$	6.63383e10	−	8.28643e10i	0.0984581	−	0.122986i
$907$	−1.55079e11	+	1.55079e11i	−0.229152	+	0.229152i	−0.812338	−	0.583187i	$-0.801806\pi$
$907$	−1.55079e11	+	1.55079e11i	−0.229152	+	0.229152i	0.583187	+	0.812338i	$0.301806\pi$
$908$	2.35419e11	+	1.49166e11i	0.346336	+	0.219445i
$909$	2.16009e11	−	2.16009e11i	0.316385	−	0.316385i
$910$	−6.36570e9	−	5.74717e10i	−0.00928283	−	0.0838086i
$911$		−	3.98458e11i		−	0.578507i	−0.957253	−	0.289254i	$-0.906593\pi$
$911$		−	3.98458e11i		−	0.578507i	0.957253	−	0.289254i	$-0.0934071\pi$
$912$	3.07085e11	+	6.50178e11i	0.443894	+	0.939838i
$913$	4.49994e11			0.647625
$914$	9.17714e11	−	1.01648e11i	1.31499	−	0.145651i
$915$	1.73554e10	+	1.73554e10i	0.0247599	+	0.0247599i
$916$	1.66576e11	+	1.05546e11i	0.236609	+	0.149920i
$917$	−3.73961e11	−	3.73961e11i	−0.528870	−	0.528870i
$918$	1.80908e11	+	1.44829e11i	0.254735	+	0.203932i
$919$	−2.48640e11			−0.348585			−0.174292	−	0.984694i	$-0.555764\pi$
$919$	−2.48640e11			−0.348585			−0.174292	+	0.984694i	$0.555764\pi$
$920$	−7.83189e9	+	1.60303e10i	−0.0109324	+	0.0223764i
$921$		−	3.65025e11i		−	0.507322i
$922$	−1.52450e11	−	1.22046e11i	−0.210962	−	0.168889i
$923$	−2.56434e11	+	2.56434e11i	−0.353321	+	0.353321i
$924$	6.63112e11	−	1.48720e11i	0.909702	−	0.204024i
$925$	7.86418e11	−	7.86418e11i	1.07420	−	1.07420i
$926$	−8.52030e11	+	9.43728e10i	−1.15881	+	0.128352i
$927$			3.10200e11i			0.420071i
$928$	−9.69070e10	−	2.30825e10i	−0.130666	−	0.0311237i
$929$	7.69981e11			1.03375			0.516877	−	0.856060i	$-0.327094\pi$
$929$	7.69981e11			1.03375			0.516877	+	0.856060i	$0.327094\pi$
$930$	−7.23777e9	−	6.53451e10i	−0.00967549	−	0.0873537i
$931$	−1.18942e11	−	1.18942e11i	−0.158321	−	0.158321i
$932$	9.34867e10	+	4.16838e11i	0.123904	+	0.552464i
$933$	−1.80687e11	−	1.80687e11i	−0.238452	−	0.238452i
$934$	6.95013e11	−	8.68153e11i	0.913284	−	1.14080i
$935$	2.40094e11			0.314148
$936$	9.42613e10	−	1.92934e11i	0.122809	−	0.251365i
$937$			1.30062e11i			0.168730i	0.996435	+	0.0843650i	$0.0268862\pi$
$937$			1.30062e11i			0.168730i	−0.996435	+	0.0843650i	$0.973114\pi$
$938$	−5.09836e11	+	6.36845e11i	−0.658596	+	0.822664i
$939$	1.37502e9	−	1.37502e9i	0.00176867	−	0.00176867i
$940$	8.82986e10	−	1.39356e11i	0.113095	−	0.178490i
$941$	4.72398e11	−	4.72398e11i	0.602490	−	0.602490i	−0.338483	−	0.940973i	$-0.609914\pi$
$941$	4.72398e11	−	4.72398e11i	0.602490	−	0.602490i	0.940973	+	0.338483i	$0.109914\pi$
$942$	−2.68407e10	−	2.42327e11i	−0.0340871	−	0.307751i
$943$		−	1.07134e11i		−	0.135482i
$944$	−1.30415e11	+	3.63871e11i	−0.164225	+	0.458204i
$945$	1.54196e10			0.0193351
$946$	−9.47448e11	+	1.04941e11i	−1.18302	+	0.131034i
$947$	−8.20303e11	−	8.20303e11i	−1.01994	−	1.01994i	−0.999797	−	0.0201428i	$-0.993588\pi$
$947$	−8.20303e11	−	8.20303e11i	−1.01994	−	1.01994i	−0.0201428	−	0.999797i	$-0.506412\pi$
$948$	2.67702e11	−	4.22497e11i	0.331450	−	0.523107i
$949$	1.57807e11	+	1.57807e11i	0.194564	+	0.194564i
$950$	−1.13151e12	−	9.05846e11i	−1.38920	−	1.11214i
$951$	2.29724e11			0.280856
$952$	−4.23457e11	−	1.23251e12i	−0.515539	−	1.50052i
$953$			6.58637e11i			0.798499i	0.916842	+	0.399249i	$0.130729\pi$
$953$			6.58637e11i			0.798499i	−0.916842	+	0.399249i	$0.869271\pi$
$954$	5.21875e10	+	4.17795e10i	0.0630047	+	0.0504394i
$955$	−4.70296e10	+	4.70296e10i	−0.0565403	+	0.0565403i
$956$	−2.82688e11	−	1.26045e12i	−0.338435	−	1.50901i
$957$	7.93733e10	−	7.93733e10i	0.0946295	−	0.0946295i
$958$	4.57668e11	−	5.06924e10i	0.543362	−	0.0601839i
$959$		−	7.06918e11i		−	0.835785i
$960$	−3.23580e10	−	4.15318e10i	−0.0380976	−	0.0488985i
$961$	−8.61615e11			−1.01023
$962$	1.21616e11	+	1.09799e12i	0.142000	+	1.28203i
$963$	1.50030e11	+	1.50030e11i	0.174450	+	0.174450i
$964$	−5.07750e11	+	1.13876e11i	−0.587951	+	0.131863i
$965$	4.42324e10	+	4.42324e10i	0.0510072	+	0.0510072i
$966$	−6.81977e10	+	8.51869e10i	−0.0783179	+	0.0978282i
$967$	5.65580e11			0.646826			0.323413	−	0.946258i	$-0.395170\pi$
$967$	5.65580e11			0.646826			0.323413	+	0.946258i	$0.395170\pi$
$968$	1.64240e12	−	5.64284e11i	1.87058	−	0.642682i
$969$			1.55377e12i			1.76235i
$970$	−3.34498e10	+	4.17828e10i	−0.0377839	+	0.0471965i
$971$	2.05378e11	−	2.05378e11i	0.231034	−	0.231034i	−0.582090	−	0.813124i	$-0.697765\pi$
$971$	2.05378e11	−	2.05378e11i	0.231034	−	0.231034i	0.813124	+	0.582090i	$0.197765\pi$
$972$	4.83693e10	+	3.06477e10i	0.0541882	+	0.0343346i
$973$	3.12819e11	−	3.12819e11i	0.349013	−	0.349013i
$974$	2.39387e10	+	2.16127e11i	0.0265990	+	0.240145i
$975$			4.32844e11i			0.478975i
$976$	1.72940e11	−	4.82519e11i	0.190588	−	0.531760i
$977$	4.40237e11			0.483179			0.241589	−	0.970379i	$-0.422331\pi$
$977$	4.40237e11			0.483179			0.241589	+	0.970379i	$0.422331\pi$
$978$	−7.66451e11	+	8.48938e10i	−0.837778	+	0.0927941i
$979$	−8.91960e11	−	8.91960e11i	−0.970989	−	0.970989i
$980$	1.04038e10	+	6.59204e9i	0.0112794	+	0.00714686i
$981$	−1.36170e11	−	1.36170e11i	−0.147030	−	0.147030i
$982$	1.29987e12	+	1.04063e12i	1.39783	+	1.11905i
$983$	−1.88557e11			−0.201943			−0.100971	−	0.994889i	$-0.532195\pi$
$983$	−1.88557e11			−0.201943			−0.100971	+	0.994889i	$0.532195\pi$
$984$	2.84062e11	+	1.38784e11i	0.302993	+	0.148033i
$985$			1.00498e10i			0.0106761i
$986$	−1.68044e11	−	1.34530e11i	−0.177794	−	0.142335i
$987$	7.13499e11	−	7.13499e11i	0.751839	−	0.751839i
$988$	1.40482e12	−	3.15067e11i	1.47432	−	0.330655i
$989$	1.08233e11	−	1.08233e11i	0.113129	−	0.113129i
$990$	5.89650e10	−	6.53110e9i	0.0613838	−	0.00679900i
$991$		−	1.09480e12i		−	1.13512i	−0.823332	−	0.567560i	$-0.807888\pi$
$991$		−	1.09480e12i		−	1.13512i	0.823332	−	0.567560i	$-0.192112\pi$
$992$	−1.16939e12	+	7.19476e11i	−1.20757	+	0.742967i
$993$	2.16347e11			0.222513
$994$	5.98722e10	+	5.40548e11i	0.0613310	+	0.553718i
$995$	−7.22420e10	−	7.22420e10i	−0.0737051	−	0.0737051i
$996$	−4.66628e10	−	2.08060e11i	−0.0474169	−	0.211422i
$997$	1.24391e12	+	1.24391e12i	1.25895	+	1.25895i	0.951597	+	0.307348i	$0.0994416\pi$
$997$	1.24391e12	+	1.24391e12i	1.25895	+	1.25895i	0.307348	+	0.951597i	$0.400558\pi$
$998$	−2.56034e11	+	3.19816e11i	−0.258092	+	0.322387i
$999$	−2.94589e11			−0.295771

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.9.l.a.43.16	yes	64
4.3	odd	2		192.9.l.a.79.11		64
16.3	odd	4	inner	48.9.l.a.19.16	✓	64
16.13	even	4		192.9.l.a.175.11		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.16	✓	64	16.3	odd	4	inner
48.9.l.a.43.16	yes	64	1.1	even	1	trivial
192.9.l.a.79.11		64	4.3	odd	2
192.9.l.a.175.11		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)

\(f(q)\)	\(=\)	\(q+(-1.76142 - 15.9027i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-249.795 + 56.0230i) q^{4} +(47.4496 + 47.4496i) q^{5} +(467.627 - 584.121i) q^{6} -2246.74 q^{7} +(1330.91 + 3873.74i) q^{8} +2187.00i q^{9} +O(q^{10})\)	\(q+(-1.76142 - 15.9027i) q^{2} +(33.0681 + 33.0681i) q^{3} +(-249.795 + 56.0230i) q^{4} +(47.4496 + 47.4496i) q^{5} +(467.627 - 584.121i) q^{6} -2246.74 q^{7} +(1330.91 + 3873.74i) q^{8} +2187.00i q^{9} +(670.999 - 838.157i) q^{10} +(17865.3 - 17865.3i) q^{11} +(-10112.8 - 6407.67i) q^{12} +(-16949.9 + 16949.9i) q^{13} +(3957.46 + 35729.3i) q^{14} +3138.13i q^{15} +(59258.9 - 27988.5i) q^{16} +141614. q^{17} +(34779.3 - 3852.23i) q^{18} +(165898. + 165898. i) q^{19} +(-14510.9 - 9194.39i) q^{20} +(-74295.4 - 74295.4i) q^{21} +(-315577. - 252640. i) q^{22} +64910.8 q^{23} +(-84086.6 + 172108. i) q^{24} -386122. i q^{25} +(299406. + 239694. i) q^{26} +(-72320.0 + 72320.0i) q^{27} +(561224. - 125869. i) q^{28} +(67177.4 - 67177.4i) q^{29} +(49905.0 - 5527.58i) q^{30} -1.30939e6i q^{31} +(-549474. - 893079. i) q^{32} +1.18155e6 q^{33} +(-249443. - 2.25206e6i) q^{34} +(-106607. - 106607. i) q^{35} +(-122522. - 546301. i) q^{36} +(2.03671e6 + 2.03671e6i) q^{37} +(2.34601e6 - 2.93044e6i) q^{38} -1.12100e6 q^{39} +(-120656. + 246959. i) q^{40} -1.65048e6i q^{41} +(-1.05064e6 + 1.31237e6i) q^{42} +(1.66741e6 - 1.66741e6i) q^{43} +(-3.46180e6 + 5.46354e6i) q^{44} +(-103772. + 103772. i) q^{45} +(-114336. - 1.03226e6i) q^{46} +9.60354e6i q^{47} +(2.88510e6 + 1.03405e6i) q^{48} -716963. q^{49} +(-6.14040e6 + 680125. i) q^{50} +(4.68292e6 + 4.68292e6i) q^{51} +(3.28441e6 - 5.18358e6i) q^{52} +(1.35090e6 + 1.35090e6i) q^{53} +(1.27747e6 + 1.02270e6i) q^{54} +1.69541e6 q^{55} +(-2.99022e6 - 8.70329e6i) q^{56} +1.09718e7i q^{57} +(-1.18663e6 - 949978. i) q^{58} +(-4.17057e6 + 4.17057e6i) q^{59} +(-175808. - 783889. i) q^{60} +(5.53048e6 - 5.53048e6i) q^{61} +(-2.08229e7 + 2.30639e6i) q^{62} -4.91362e6i q^{63} +(-1.32346e7 + 1.03112e7i) q^{64} -1.60853e6 q^{65} +(-2.08120e6 - 1.87898e7i) q^{66} +(1.60468e7 + 1.60468e7i) q^{67} +(-3.53745e7 + 7.93365e6i) q^{68} +(2.14648e6 + 2.14648e6i) q^{69} +(-1.50756e6 + 1.88312e6i) q^{70} +1.51290e7 q^{71} +(-8.47188e6 + 2.91071e6i) q^{72} -9.31022e6i q^{73} +(2.88017e7 - 3.59768e7i) q^{74} +(1.27683e7 - 1.27683e7i) q^{75} +(-5.07344e7 - 3.21463e7i) q^{76} +(-4.01388e7 + 4.01388e7i) q^{77} +(1.97456e6 + 1.78270e7i) q^{78} +4.17784e7i q^{79} +(4.13985e6 + 1.48377e6i) q^{80} -4.78297e6 q^{81} +(-2.62472e7 + 2.90720e6i) q^{82} +(1.25940e7 + 1.25940e7i) q^{83} +(2.27209e7 + 1.43964e7i) q^{84} +(6.71953e6 + 6.71953e6i) q^{85} +(-2.94534e7 - 2.35794e7i) q^{86} +4.44286e6 q^{87} +(9.29830e7 + 4.54285e7i) q^{88} -4.99268e7i q^{89} +(1.83305e6 + 1.46748e6i) q^{90} +(3.80820e7 - 3.80820e7i) q^{91} +(-1.62144e7 + 3.63650e6i) q^{92} +(4.32991e7 - 4.32991e7i) q^{93} +(1.52723e8 - 1.69159e7i) q^{94} +1.57435e7i q^{95} +(1.13624e7 - 4.77025e7i) q^{96} -4.98508e7 q^{97} +(1.26288e6 + 1.14017e7i) q^{98} +(3.90715e7 + 3.90715e7i) 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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