LMFDB - Embedded newform 48.9.l.a.43.27

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			43.27
Character	$\chi$	$=$	48.43
Dual form			48.9.l.a.19.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(13.9758 + 7.78963i) q^{2} +(33.0681 + 33.0681i) q^{3} +(134.643 + 217.732i) q^{4} +(-633.321 - 633.321i) q^{5} +(204.563 + 719.740i) q^{6} -416.943 q^{7} +(185.692 + 4091.79i) q^{8} +2187.00i q^{9} +O(q^{10})$	\(q+(13.9758 + 7.78963i) q^{2} +(33.0681 + 33.0681i) q^{3} +(134.643 + 217.732i) q^{4} +(-633.321 - 633.321i) q^{5} +(204.563 + 719.740i) q^{6} -416.943 q^{7} +(185.692 + 4091.79i) q^{8} +2187.00i q^{9} +(-3917.80 - 13784.5i) q^{10} +(-18182.2 + 18182.2i) q^{11} +(-2747.58 + 11652.4i) q^{12} +(-31986.0 + 31986.0i) q^{13} +(-5827.09 - 3247.83i) q^{14} -41885.5i q^{15} +(-29278.3 + 58632.3i) q^{16} +38570.1 q^{17} +(-17035.9 + 30565.0i) q^{18} +(-110715. - 110715. i) q^{19} +(52621.7 - 223167. i) q^{20} +(-13787.5 - 13787.5i) q^{21} +(-395742. + 112477. i) q^{22} +402176. q^{23} +(-129167. + 141448. i) q^{24} +411566. i q^{25} +(-696188. + 197869. i) q^{26} +(-72320.0 + 72320.0i) q^{27} +(-56138.6 - 90781.8i) q^{28} +(-161325. + 161325. i) q^{29} +(326272. - 585381. i) q^{30} -1.49144e6i q^{31} +(-865911. + 591363. i) q^{32} -1.20250e6 q^{33} +(539047. + 300447. i) q^{34} +(264059. + 264059. i) q^{35} +(-476180. + 294465. i) q^{36} +(2.01992e6 + 2.01992e6i) q^{37} +(-684895. - 2.40975e6i) q^{38} -2.11543e6 q^{39} +(2.47381e6 - 2.70902e6i) q^{40} -673071. i q^{41} +(-85291.3 - 300091. i) q^{42} +(-1.68237e6 + 1.68237e6i) q^{43} +(-6.40694e6 - 1.51073e6i) q^{44} +(1.38507e6 - 1.38507e6i) q^{45} +(5.62071e6 + 3.13280e6i) q^{46} +4.76508e6i q^{47} +(-2.90704e6 + 970680. i) q^{48} -5.59096e6 q^{49} +(-3.20595e6 + 5.75195e6i) q^{50} +(1.27544e6 + 1.27544e6i) q^{51} +(-1.12711e7 - 2.65767e6i) q^{52} +(6.94700e6 + 6.94700e6i) q^{53} +(-1.57407e6 + 447380. i) q^{54} +2.30303e7 q^{55} +(-77422.8 - 1.70604e6i) q^{56} -7.32225e6i q^{57} +(-3.51130e6 + 997976. i) q^{58} +(-2.99285e6 + 2.99285e6i) q^{59} +(9.11980e6 - 5.63960e6i) q^{60} +(1.22473e7 - 1.22473e7i) q^{61} +(1.16178e7 - 2.08440e7i) q^{62} -911854. i q^{63} +(-1.67083e7 + 1.51962e6i) q^{64} +4.05148e7 q^{65} +(-1.68058e7 - 9.36703e6i) q^{66} +(2.26628e6 + 2.26628e6i) q^{67} +(5.19321e6 + 8.39795e6i) q^{68} +(1.32992e7 + 1.32992e7i) q^{69} +(1.63350e6 + 5.74734e6i) q^{70} +6.83501e6 q^{71} +(-8.94874e6 + 406108. i) q^{72} +2.36939e7i q^{73} +(1.24954e7 + 4.39642e7i) q^{74} +(-1.36097e7 + 1.36097e7i) q^{75} +(9.19912e6 - 3.90131e7i) q^{76} +(7.58093e6 - 7.58093e6i) q^{77} +(-2.95648e7 - 1.64784e7i) q^{78} -4.91999e6i q^{79} +(5.56757e7 - 1.85905e7i) q^{80} -4.78297e6 q^{81} +(5.24298e6 - 9.40668e6i) q^{82} +(3.44710e6 + 3.44710e6i) q^{83} +(1.14558e6 - 4.85838e6i) q^{84} +(-2.44273e7 - 2.44273e7i) q^{85} +(-3.66174e7 + 1.04073e7i) q^{86} -1.06694e7 q^{87} +(-7.77739e7 - 7.10213e7i) q^{88} -7.21985e6i q^{89} +(3.01466e7 - 8.56823e6i) q^{90} +(1.33363e7 - 1.33363e7i) q^{91} +(5.41503e7 + 8.75666e7i) q^{92} +(4.93191e7 - 4.93191e7i) q^{93} +(-3.71182e7 + 6.65956e7i) q^{94} +1.40236e8i q^{95} +(-4.81893e7 - 9.07877e6i) q^{96} -7.27214e7 q^{97} +(-7.81379e7 - 4.35515e7i) q^{98} +(-3.97644e7 - 3.97644e7i) 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 $

$2$	13.9758	+	7.78963i	0.873485	+	0.486852i
$2$	13.9758	+	7.78963i	0.873485	+	0.486852i
$3$	33.0681	+	33.0681i	0.408248	+	0.408248i
$3$	33.0681	+	33.0681i	0.408248	+	0.408248i
$4$	134.643	+	217.732i	0.525951	+	0.850515i
$5$	−633.321	−	633.321i	−1.01331	−	1.01331i	−0.999910	−	0.0134036i	$-0.995733\pi$
$5$	−633.321	−	633.321i	−1.01331	−	1.01331i	−0.0134036	−	0.999910i	$-0.504267\pi$
$6$	204.563	+	719.740i	0.157842	+	0.555355i
$7$	−416.943			−0.173654			−0.0868269	−	0.996223i	$-0.527673\pi$
$7$	−416.943			−0.173654			−0.0868269	+	0.996223i	$0.527673\pi$
$8$	185.692	+	4091.79i	0.0453349	+	0.998972i
$9$			2187.00i			0.333333i
$10$	−3917.80	−	13784.5i	−0.391780	−	1.37845i
$11$	−18182.2	+	18182.2i	−1.24187	+	1.24187i	−0.282640	+	0.959226i	$0.591210\pi$
$11$	−18182.2	+	18182.2i	−1.24187	+	1.24187i	−0.959226	+	0.282640i	$0.908790\pi$
$12$	−2747.58	+	11652.4i	−0.132503	+	0.561940i
$13$	−31986.0	+	31986.0i	−1.11992	+	1.11992i	−0.128167	+	0.991753i	$0.540909\pi$
$13$	−31986.0	+	31986.0i	−1.11992	+	1.11992i	−0.991753	+	0.128167i	$0.959091\pi$
$14$	−5827.09	−	3247.83i	−0.151684	−	0.0845437i
$15$		−	41885.5i		−	0.827367i
$16$	−29278.3	+	58632.3i	−0.446752	+	0.894658i
$17$	38570.1			0.461802			0.230901	−	0.972977i	$-0.425833\pi$
$17$	38570.1			0.461802			0.230901	+	0.972977i	$0.425833\pi$
$18$	−17035.9	+	30565.0i	−0.162284	+	0.291162i
$19$	−110715.	−	110715.i	−0.849554	−	0.849554i	0.140524	−	0.990077i	$-0.455121\pi$
$19$	−110715.	−	110715.i	−0.849554	−	0.849554i	−0.990077	+	0.140524i	$0.955121\pi$
$20$	52621.7	−	223167.i	0.328886	−	1.39479i
$21$	−13787.5	−	13787.5i	−0.0708939	−	0.0708939i
$22$	−395742.	+	112477.i	−1.68936	+	0.480146i
$23$	402176.			1.43716			0.718580	−	0.695445i	$-0.244793\pi$
$23$	402176.			1.43716			0.718580	+	0.695445i	$0.244793\pi$
$24$	−129167.	+	141448.i	−0.389321	+	0.426336i
$25$			411566.i			1.05361i
$26$	−696188.	+	197869.i	−1.52347	+	0.432997i
$27$	−72320.0	+	72320.0i	−0.136083	+	0.136083i
$28$	−56138.6	−	90781.8i	−0.0913334	−	0.147695i
$29$	−161325.	+	161325.i	−0.228092	+	0.228092i	−0.811895	−	0.583803i	$-0.801564\pi$
$29$	−161325.	+	161325.i	−0.228092	+	0.228092i	0.583803	+	0.811895i	$0.301564\pi$
$30$	326272.	−	585381.i	0.402805	−	0.722692i
$31$		−	1.49144e6i		−	1.61495i	−0.589903	−	0.807474i	$-0.700834\pi$
$31$		−	1.49144e6i		−	1.61495i	0.589903	−	0.807474i	$-0.299166\pi$
$32$	−865911.	+	591363.i	−0.825797	+	0.563968i
$33$	−1.20250e6			−1.01398
$34$	539047.	+	300447.i	0.403377	+	0.224829i
$35$	264059.	+	264059.i	0.175966	+	0.175966i
$36$	−476180.	+	294465.i	−0.283505	+	0.175317i
$37$	2.01992e6	+	2.01992e6i	1.07777	+	1.07777i	0.996709	+	0.0810612i	$0.0258309\pi$
$37$	2.01992e6	+	2.01992e6i	1.07777	+	1.07777i	0.0810612	+	0.996709i	$0.474169\pi$
$38$	−684895.	−	2.40975e6i	−0.328465	−	1.15568i
$39$	−2.11543e6			−0.914410
$40$	2.47381e6	−	2.70902e6i	0.966333	−	1.05821i
$41$		−	673071.i		−	0.238191i	−0.992883	−	0.119096i	$-0.962001\pi$
$41$		−	673071.i		−	0.238191i	0.992883	−	0.119096i	$-0.0379995\pi$
$42$	−85291.3	−	300091.i	−0.0274099	−	0.0964395i
$43$	−1.68237e6	+	1.68237e6i	−0.492094	+	0.492094i	−0.908965	−	0.416872i	$-0.863126\pi$
$43$	−1.68237e6	+	1.68237e6i	−0.492094	+	0.492094i	0.416872	+	0.908965i	$0.363126\pi$
$44$	−6.40694e6	−	1.51073e6i	−1.70939	−	0.403066i
$45$	1.38507e6	−	1.38507e6i	0.337771	−	0.337771i
$46$	5.62071e6	+	3.13280e6i	1.25534	+	0.699684i
$47$			4.76508e6i			0.976515i	0.872700	+	0.488258i	$0.162367\pi$
$47$			4.76508e6i			0.976515i	−0.872700	+	0.488258i	$0.837633\pi$
$48$	−2.90704e6	+	970680.i	−0.547628	+	0.182857i
$49$	−5.59096e6			−0.969844
$50$	−3.20595e6	+	5.75195e6i	−0.512952	+	0.920312i
$51$	1.27544e6	+	1.27544e6i	0.188530	+	0.188530i
$52$	−1.12711e7	−	2.65767e6i	−1.54153	−	0.363486i
$53$	6.94700e6	+	6.94700e6i	0.880428	+	0.880428i	0.993578	−	0.113150i	$-0.0360940\pi$
$53$	6.94700e6	+	6.94700e6i	0.880428	+	0.880428i	−0.113150	+	0.993578i	$0.536094\pi$
$54$	−1.57407e6	+	447380.i	−0.185118	+	0.0526141i
$55$	2.30303e7			2.51680
$56$	−77422.8	−	1.70604e6i	−0.00787258	−	0.173475i
$57$		−	7.32225e6i		−	0.693658i
$58$	−3.51130e6	+	997976.i	−0.310282	+	0.0881877i
$59$	−2.99285e6	+	2.99285e6i	−0.246988	+	0.246988i	−0.819734	−	0.572745i	$-0.805878\pi$
$59$	−2.99285e6	+	2.99285e6i	−0.246988	+	0.246988i	0.572745	+	0.819734i	$0.305878\pi$
$60$	9.11980e6	−	5.63960e6i	0.703688	−	0.435154i
$61$	1.22473e7	−	1.22473e7i	0.884548	−	0.884548i	−0.109445	−	0.993993i	$-0.534907\pi$
$61$	1.22473e7	−	1.22473e7i	0.884548	−	0.884548i	0.993993	+	0.109445i	$0.0349074\pi$
$62$	1.16178e7	−	2.08440e7i	0.786241	−	1.41063i
$63$		−	911854.i		−	0.0578846i
$64$	−1.67083e7	+	1.51962e6i	−0.995889	+	0.0905765i
$65$	4.05148e7			2.26966
$66$	−1.68058e7	−	9.36703e6i	−0.885696	−	0.493658i
$67$	2.26628e6	+	2.26628e6i	0.112464	+	0.112464i	0.761099	−	0.648635i	$-0.224660\pi$
$67$	2.26628e6	+	2.26628e6i	0.112464	+	0.112464i	−0.648635	+	0.761099i	$0.724660\pi$
$68$	5.19321e6	+	8.39795e6i	0.242885	+	0.392769i
$69$	1.32992e7	+	1.32992e7i	0.586718	+	0.586718i
$70$	1.63350e6	+	5.74734e6i	0.0680342	+	0.239373i
$71$	6.83501e6			0.268971			0.134486	−	0.990916i	$-0.457062\pi$
$71$	6.83501e6			0.268971			0.134486	+	0.990916i	$0.457062\pi$
$72$	−8.94874e6	+	406108.i	−0.332991	+	0.0151116i
$73$			2.36939e7i			0.834343i	0.908828	+	0.417171i	$0.136978\pi$
$73$			2.36939e7i			0.834343i	−0.908828	+	0.417171i	$0.863022\pi$
$74$	1.24954e7	+	4.39642e7i	0.416701	+	1.46613i
$75$	−1.36097e7	+	1.36097e7i	−0.430134	+	0.430134i
$76$	9.19912e6	−	3.90131e7i	0.275735	−	1.16938i
$77$	7.58093e6	−	7.58093e6i	0.215655	−	0.215655i
$78$	−2.95648e7	−	1.64784e7i	−0.798723	−	0.445182i
$79$		−	4.91999e6i		−	0.126315i	−0.998004	−	0.0631576i	$-0.979883\pi$
$79$		−	4.91999e6i		−	0.126315i	0.998004	−	0.0631576i	$-0.0201171\pi$
$80$	5.56757e7	−	1.85905e7i	1.35927	−	0.453869i
$81$	−4.78297e6			−0.111111
$82$	5.24298e6	−	9.40668e6i	0.115964	−	0.208056i
$83$	3.44710e6	+	3.44710e6i	0.0726343	+	0.0726343i	0.742491	−	0.669856i	$-0.233644\pi$
$83$	3.44710e6	+	3.44710e6i	0.0726343	+	0.0726343i	−0.669856	+	0.742491i	$0.733644\pi$
$84$	1.14558e6	−	4.85838e6i	0.0230096	−	0.0975830i
$85$	−2.44273e7	−	2.44273e7i	−0.467950	−	0.467950i
$86$	−3.66174e7	+	1.04073e7i	−0.669413	+	0.190259i
$87$	−1.06694e7			−0.186236
$88$	−7.77739e7	−	7.10213e7i	−1.29689	−	1.18429i
$89$		−	7.21985e6i		−	0.115072i	−0.998343	−	0.0575358i	$-0.981676\pi$
$89$		−	7.21985e6i		−	0.115072i	0.998343	−	0.0575358i	$-0.0183243\pi$
$90$	3.01466e7	−	8.56823e6i	0.459483	−	0.130593i
$91$	1.33363e7	−	1.33363e7i	0.194478	−	0.194478i
$92$	5.41503e7	+	8.75666e7i	0.755875	+	1.22233i
$93$	4.93191e7	−	4.93191e7i	0.659300	−	0.659300i
$94$	−3.71182e7	+	6.65956e7i	−0.475418	+	0.852971i
$95$			1.40236e8i			1.72173i
$96$	−4.81893e7	−	9.07877e6i	−0.567369	−	0.106891i
$97$	−7.27214e7			−0.821439			−0.410720	−	0.911762i	$-0.634723\pi$
$97$	−7.27214e7			−0.821439			−0.410720	+	0.911762i	$0.634723\pi$
$98$	−7.81379e7	−	4.35515e7i	−0.847144	−	0.472170i
$99$	−3.97644e7	−	3.97644e7i	−0.413955	−	0.413955i
$100$	−8.96111e7	+	5.54147e7i	−0.896111	+	0.554147i
$101$	−1.98947e7	−	1.98947e7i	−0.191185	−	0.191185i	0.605023	−	0.796208i	$-0.293164\pi$
$101$	−1.98947e7	−	1.98947e7i	−0.191185	−	0.191185i	−0.796208	+	0.605023i	$0.793164\pi$
$102$	7.89004e6	+	2.77605e7i	0.0728918	+	0.256464i
$103$	−2.09210e8			−1.85880			−0.929401	−	0.369071i	$-0.879676\pi$
$103$	−2.09210e8			−1.85880			−0.929401	+	0.369071i	$0.879676\pi$
$104$	−1.36820e8	−	1.24940e8i	−1.16954	−	1.06800i
$105$			1.74638e7i			0.143676i
$106$	4.29750e7	+	1.51204e8i	0.340402	+	1.19768i
$107$	−1.32040e8	+	1.32040e8i	−1.00733	+	1.00733i	−0.00735246	+	0.999973i	$0.502340\pi$
$107$	−1.32040e8	+	1.32040e8i	−1.00733	+	1.00733i	−0.999973	+	0.00735246i	$0.997660\pi$
$108$	−2.54838e7	−	6.00896e6i	−0.187313	−	0.0441676i
$109$	5.14063e7	−	5.14063e7i	0.364175	−	0.364175i	−0.501172	−	0.865348i	$-0.667098\pi$
$109$	5.14063e7	−	5.14063e7i	0.364175	−	0.364175i	0.865348	+	0.501172i	$0.167098\pi$
$110$	3.21866e8	+	1.79397e8i	2.19839	+	1.22531i
$111$			1.33590e8i			0.879996i
$112$	1.22074e7	−	2.44463e7i	0.0775802	−	0.155361i
$113$	2.83372e8			1.73797			0.868986	−	0.494836i	$-0.164772\pi$
$113$	2.83372e8			1.73797			0.868986	+	0.494836i	$0.164772\pi$
$114$	5.70376e7	−	1.02334e8i	0.337708	−	0.605899i
$115$	−2.54707e8	−	2.54707e8i	−1.45629	−	1.45629i
$116$	−5.68469e7	−	1.34043e7i	−0.313961	−	0.0740305i
$117$	−6.99534e7	−	6.99534e7i	−0.373306	−	0.373306i
$118$	−6.51405e7	+	1.85141e7i	−0.335987	+	0.0954938i
$119$	−1.60816e7			−0.0801937
$120$	1.71386e8	−	7.77778e6i	0.826517	−	0.0375086i
$121$		−	4.46823e8i		−	2.08446i
$122$	2.66567e8	−	7.57634e7i	1.20328	−	0.341995i
$123$	2.22572e7	−	2.22572e7i	0.0972411	−	0.0972411i
$124$	3.24734e8	−	2.00812e8i	1.37354	−	0.849383i
$125$	1.32625e7	−	1.32625e7i	0.0543232	−	0.0543232i
$126$	7.10301e6	−	1.27438e7i	0.0281812	−	0.0505613i
$127$			1.67677e8i			0.644552i	0.946646	+	0.322276i	$0.104448\pi$
$127$			1.67677e8i			0.644552i	−0.946646	+	0.322276i	$0.895552\pi$
$128$	−2.45348e8	−	1.08913e8i	−0.913991	−	0.405733i
$129$	−1.11266e8			−0.401793
$130$	5.66225e8	+	3.15596e8i	1.98251	+	1.10499i
$131$	2.15735e8	+	2.15735e8i	0.732546	+	0.732546i	0.971124	−	0.238577i	$-0.0766810\pi$
$131$	2.15735e8	+	2.15735e8i	0.732546	+	0.732546i	−0.238577	+	0.971124i	$0.576681\pi$
$132$	−1.61909e8	−	2.61823e8i	−0.533303	−	0.862405i
$133$	4.61617e7	+	4.61617e7i	0.147528	+	0.147528i
$134$	1.40195e7	+	4.93264e7i	0.0434823	+	0.152989i
$135$	9.16035e7			0.275789
$136$	7.16216e6	+	1.57821e8i	0.0209357	+	0.461327i
$137$			1.94697e7i			0.0552683i	0.999618	+	0.0276341i	$0.00879734\pi$
$137$			1.94697e7i			0.0552683i	−0.999618	+	0.0276341i	$0.991203\pi$
$138$	8.22705e7	+	2.89462e8i	0.226844	+	0.798134i
$139$	−1.73700e8	+	1.73700e8i	−0.465308	+	0.465308i	−0.900391	−	0.435082i	$-0.856719\pi$
$139$	−1.73700e8	+	1.73700e8i	−0.465308	+	0.465308i	0.435082	+	0.900391i	$0.356719\pi$
$140$	−2.19403e7	+	9.30478e7i	−0.0571123	+	0.242211i
$141$	−1.57572e8	+	1.57572e8i	−0.398661	+	0.398661i
$142$	9.55244e7	+	5.32422e7i	0.234942	+	0.130949i
$143$		−	1.16315e9i		−	2.78158i
$144$	−1.28229e8	−	6.40317e7i	−0.298219	−	0.148917i
$145$	2.04341e8			0.462257
$146$	−1.84566e8	+	3.31140e8i	−0.406201	+	0.728785i
$147$	−1.84882e8	−	1.84882e8i	−0.395937	−	0.395937i
$148$	−1.67832e8	+	7.11768e8i	−0.349806	+	1.48351i
$149$	2.97244e8	+	2.97244e8i	0.603070	+	0.603070i	0.941126	−	0.338056i	$-0.109769\pi$
$149$	2.97244e8	+	2.97244e8i	0.603070	+	0.603070i	−0.338056	+	0.941126i	$0.609769\pi$
$150$	−2.96221e8	+	8.41914e7i	−0.585127	+	0.166304i
$151$	1.69208e8			0.325472			0.162736	−	0.986670i	$-0.447968\pi$
$151$	1.69208e8			0.325472			0.162736	+	0.986670i	$0.447968\pi$
$152$	4.32462e8	−	4.73580e8i	0.810166	−	0.887195i
$153$			8.43529e7i			0.153934i
$154$	1.65002e8	−	4.68965e7i	0.293363	−	0.0833792i
$155$	−9.44560e8	+	9.44560e8i	−1.63645	+	1.63645i
$156$	−2.84829e8	−	4.60597e8i	−0.480935	−	0.777720i
$157$	4.65606e8	−	4.65606e8i	0.766338	−	0.766338i	−0.211122	−	0.977460i	$-0.567712\pi$
$157$	4.65606e8	−	4.65606e8i	0.766338	−	0.766338i	0.977460	+	0.211122i	$0.0677117\pi$
$158$	3.83249e7	−	6.87605e7i	0.0614968	−	0.110334i
$159$			4.59448e8i			0.718867i
$160$	9.22922e8	+	1.73877e8i	1.40827	+	0.265315i
$161$	−1.67684e8			−0.249568
$162$	−6.68456e7	−	3.72576e7i	−0.0970538	−	0.0540946i
$163$	−1.69636e8	−	1.69636e8i	−0.240308	−	0.240308i	0.576670	−	0.816978i	$-0.304352\pi$
$163$	−1.69636e8	−	1.69636e8i	−0.240308	−	0.240308i	−0.816978	+	0.576670i	$0.804352\pi$
$164$	1.46549e8	−	9.06246e7i	0.202585	−	0.125277i
$165$	7.61568e8	+	7.61568e8i	1.02748	+	1.02748i
$166$	2.13242e7	+	7.50275e7i	0.0280828	+	0.0988071i
$167$	−3.51667e8			−0.452132			−0.226066	−	0.974112i	$-0.572587\pi$
$167$	−3.51667e8			−0.452132			−0.226066	+	0.974112i	$0.572587\pi$
$168$	5.38554e7	−	5.89758e7i	0.0676070	−	0.0740350i
$169$		−	1.23048e9i		−	1.50844i
$170$	−1.51110e8	−	5.31669e8i	−0.180925	−	0.636570i
$171$	2.42133e8	−	2.42133e8i	0.283185	−	0.283185i
$172$	−5.92825e8	−	1.39786e8i	−0.677350	−	0.159716i
$173$	−9.35933e8	+	9.35933e8i	−1.04487	+	1.04487i	−0.0459208	+	0.998945i	$0.514622\pi$
$173$	−9.35933e8	+	9.35933e8i	−1.04487	+	1.04487i	−0.998945	+	0.0459208i	$0.985378\pi$
$174$	−1.49113e8	−	8.31109e7i	−0.162674	−	0.0906694i
$175$		−	1.71600e8i		−	0.182963i
$176$	−5.33719e8	−	1.59841e9i	−0.556239	−	1.66585i
$177$	−1.97936e8			−0.201665
$178$	5.62399e7	−	1.00903e8i	0.0560228	−	0.100513i
$179$	−1.14320e7	−	1.14320e7i	−0.0111355	−	0.0111355i	0.701517	−	0.712653i	$-0.252506\pi$
$179$	−1.14320e7	−	1.14320e7i	−0.0111355	−	0.0111355i	−0.712653	+	0.701517i	$0.752506\pi$
$180$	4.88065e8	+	1.15084e8i	0.464931	+	0.109629i
$181$	3.43006e8	+	3.43006e8i	0.319586	+	0.319586i	0.848608	−	0.529022i	$-0.177441\pi$
$181$	3.43006e8	+	3.43006e8i	0.319586	+	0.319586i	−0.529022	+	0.848608i	$0.677441\pi$
$182$	2.90271e8	−	8.25003e7i	0.264556	−	0.0751917i
$183$	8.09991e8			0.722230
$184$	7.46808e7	+	1.64562e9i	0.0651535	+	1.43568i
$185$		−	2.55851e9i		−	2.18424i
$186$	1.07345e9	−	3.05094e8i	0.896870	−	0.254907i
$187$	−7.01289e8	+	7.01289e8i	−0.573496	+	0.573496i
$188$	−1.03751e9	+	6.41587e8i	−0.830541	+	0.513599i
$189$	3.01533e7	−	3.01533e7i	0.0236313	−	0.0236313i
$190$	−1.09239e9	+	1.95990e9i	−0.838227	+	1.50390i
$191$			1.29730e9i			0.974777i	0.873185	+	0.487389i	$0.162050\pi$
$191$			1.29730e9i			0.974777i	−0.873185	+	0.487389i	$0.837950\pi$
$192$	−6.02761e8	−	5.02259e8i	−0.443548	−	0.369592i
$193$	−6.78131e8			−0.488747			−0.244374	−	0.969681i	$-0.578582\pi$
$193$	−6.78131e8			−0.488747			−0.244374	+	0.969681i	$0.578582\pi$
$194$	−1.01634e9	−	5.66473e8i	−0.717515	−	0.399919i
$195$	1.33975e9	+	1.33975e9i	0.926584	+	0.926584i
$196$	−7.52786e8	−	1.21733e9i	−0.510090	−	0.824867i
$197$	2.76682e8	+	2.76682e8i	0.183703	+	0.183703i	0.792967	−	0.609264i	$-0.208535\pi$
$197$	2.76682e8	+	2.76682e8i	0.183703	+	0.183703i	−0.609264	+	0.792967i	$0.708535\pi$
$198$	−2.45987e8	−	8.65487e8i	−0.160049	−	0.563119i
$199$	1.69637e9			1.08170			0.540852	−	0.841118i	$-0.318102\pi$
$199$	1.69637e9			1.08170			0.540852	+	0.841118i	$0.318102\pi$
$200$	−1.68404e9	+	7.64244e7i	−1.05253	+	0.0477653i
$201$			1.49883e8i			0.0918265i
$202$	−1.23071e8	−	4.33017e8i	−0.0739182	−	0.260075i
$203$	6.72633e7	−	6.72633e7i	0.0396090	−	0.0396090i
$204$	−1.05975e8	+	4.49434e8i	−0.0611901	+	0.259505i
$205$	−4.26270e8	+	4.26270e8i	−0.241362	+	0.241362i
$206$	−2.92386e9	−	1.62967e9i	−1.62363	−	0.904961i
$207$			8.79559e8i			0.479053i
$208$	−9.38916e8	−	2.81191e9i	−0.501618	−	1.50227i
$209$	4.02607e9			2.11006
$210$	−1.36037e8	+	2.44070e8i	−0.0699487	+	0.125498i
$211$	−1.25271e9	−	1.25271e9i	−0.632006	−	0.632006i	0.316565	−	0.948571i	$-0.397471\pi$
$211$	−1.25271e9	−	1.25271e9i	−0.632006	−	0.632006i	−0.948571	+	0.316565i	$0.897471\pi$
$212$	−5.77216e8	+	2.44795e9i	−0.285756	+	1.21188i
$213$	2.26021e8	+	2.26021e8i	0.109807	+	0.109807i
$214$	−2.87390e9	+	8.16815e8i	−1.37030	+	0.389465i
$215$	2.13096e9			0.997290
$216$	−3.09347e8	−	2.82489e8i	−0.142112	−	0.129774i
$217$			6.21845e8i			0.280442i
$218$	1.11888e9	−	3.18006e8i	0.495401	−	0.140802i
$219$	−7.83511e8	+	7.83511e8i	−0.340619	+	0.340619i
$220$	3.10088e9	+	5.01443e9i	1.32371	+	2.14058i
$221$	−1.23371e9	+	1.23371e9i	−0.517181	+	0.517181i
$222$	−1.04061e9	+	1.86701e9i	−0.428428	+	0.768663i
$223$		−	2.92259e9i		−	1.18181i	−0.806740	−	0.590906i	$-0.798770\pi$
$223$		−	2.92259e9i		−	1.18181i	0.806740	−	0.590906i	$-0.201230\pi$
$224$	3.61035e8	−	2.46565e8i	0.143403	−	0.0979352i
$225$	−9.00095e8			−0.351203
$226$	3.96034e9	+	2.20736e9i	1.51809	+	0.846135i
$227$	−1.60301e9	−	1.60301e9i	−0.603716	−	0.603716i	0.337580	−	0.941297i	$-0.390391\pi$
$227$	−1.60301e9	−	1.60301e9i	−0.603716	−	0.603716i	−0.941297	+	0.337580i	$0.890391\pi$
$228$	1.59429e9	−	9.85892e8i	0.589966	−	0.364830i
$229$	−1.40792e9	−	1.40792e9i	−0.511961	−	0.511961i	0.403166	−	0.915127i	$-0.367910\pi$
$229$	−1.40792e9	−	1.40792e9i	−0.511961	−	0.511961i	−0.915127	+	0.403166i	$0.867910\pi$
$230$	−1.57565e9	−	5.54379e9i	−0.563051	−	1.98105i
$231$	5.01374e8			0.176081
$232$	−6.90064e8	−	6.30151e8i	−0.238198	−	0.217517i
$233$			4.60047e9i			1.56091i	0.625210	+	0.780457i	$0.285013\pi$
$233$			4.60047e9i			1.56091i	−0.625210	+	0.780457i	$0.714987\pi$
$234$	−4.32740e8	−	1.52256e9i	−0.144332	−	0.507822i
$235$	3.01783e9	−	3.01783e9i	0.989516	−	0.989516i
$236$	−1.05461e9	−	2.48671e8i	−0.339971	−	0.0801637i
$237$	1.62695e8	−	1.62695e8i	0.0515680	−	0.0515680i
$238$	−2.24752e8	−	1.25269e8i	−0.0700479	−	0.0390424i
$239$			3.36072e8i			0.103001i	0.998673	+	0.0515004i	$0.0164003\pi$
$239$			3.36072e8i			0.103001i	−0.998673	+	0.0515004i	$0.983600\pi$
$240$	2.45584e9	+	1.22634e9i	0.740211	+	0.369628i
$241$	−4.05929e9			−1.20332			−0.601662	−	0.798751i	$-0.705494\pi$
$241$	−4.05929e9			−1.20332			−0.601662	+	0.798751i	$0.705494\pi$
$242$	3.48059e9	−	6.24469e9i	1.01483	−	1.82075i
$243$	−1.58164e8	−	1.58164e8i	−0.0453609	−	0.0453609i
$244$	4.31565e9	+	1.01761e9i	1.21755	+	0.287093i
$245$	3.54087e9	+	3.54087e9i	0.982757	+	0.982757i
$246$	4.84436e8	−	1.37686e8i	0.132281	−	0.0375966i
$247$	7.08264e9			1.90286
$248$	6.10265e9	−	2.76948e8i	1.61329	−	0.0732135i
$249$			2.27978e8i			0.0593057i
$250$	2.88663e8	−	8.20434e7i	0.0738978	−	0.0210031i
$251$	9.17666e8	−	9.17666e8i	0.231201	−	0.231201i	−0.581993	−	0.813194i	$-0.697727\pi$
$251$	9.17666e8	−	9.17666e8i	0.231201	−	0.231201i	0.813194	+	0.581993i	$0.197727\pi$
$252$	1.98540e8	−	1.22775e8i	0.0492317	−	0.0304445i
$253$	−7.31243e9	+	7.31243e9i	−1.78476	+	1.78476i
$254$	−1.30614e9	+	2.34341e9i	−0.313801	+	0.563006i
$255$		−	1.61553e9i		−	0.382080i
$256$	−2.58053e9	−	3.43331e9i	−0.600825	−	0.799380i
$257$	−4.04434e9			−0.927075			−0.463537	−	0.886077i	$-0.653420\pi$
$257$	−4.04434e9			−0.927075			−0.463537	+	0.886077i	$0.653420\pi$
$258$	−1.55502e9	−	8.66718e8i	−0.350960	−	0.195614i
$259$	−8.42189e8	−	8.42189e8i	−0.187159	−	0.187159i
$260$	5.45505e9	+	8.82137e9i	1.19373	+	1.93038i
$261$	−3.52818e8	−	3.52818e8i	−0.0760306	−	0.0760306i
$262$	1.33456e9	+	4.69555e9i	0.283226	+	0.996509i
$263$	2.15926e9			0.451318			0.225659	−	0.974206i	$-0.427546\pi$
$263$	2.15926e9			0.451318			0.225659	+	0.974206i	$0.427546\pi$
$264$	−2.23294e8	−	4.92037e9i	−0.0459686	−	1.01294i
$265$		−	8.79936e9i		−	1.78430i
$266$	2.85562e8	+	1.00473e9i	0.0570393	+	0.200688i
$267$	2.38747e8	−	2.38747e8i	0.0469778	−	0.0469778i
$268$	−1.88302e8	+	7.98580e8i	−0.0365019	+	0.154803i
$269$	2.65608e9	−	2.65608e9i	0.507263	−	0.507263i	−0.406423	−	0.913685i	$-0.633224\pi$
$269$	2.65608e9	−	2.65608e9i	0.507263	−	0.507263i	0.913685	+	0.406423i	$0.133224\pi$
$270$	1.28023e9	+	7.13557e8i	0.240897	+	0.134268i
$271$		−	2.29858e9i		−	0.426170i	−0.977034	−	0.213085i	$-0.931649\pi$
$271$		−	2.29858e9i		−	0.426170i	0.977034	−	0.213085i	$-0.0683511\pi$
$272$	−1.12927e9	+	2.26146e9i	−0.206311	+	0.413155i
$273$	8.82015e8			0.158791
$274$	−1.51661e8	+	2.72103e8i	−0.0269075	+	0.0482760i
$275$	−7.48316e9	−	7.48316e9i	−1.30844	−	1.30844i
$276$	−1.10501e9	+	4.68631e9i	−0.190428	+	0.807597i
$277$	3.47866e9	+	3.47866e9i	0.590871	+	0.590871i	0.937867	−	0.346996i	$-0.112798\pi$
$277$	3.47866e9	+	3.47866e9i	0.590871	+	0.590871i	−0.346996	+	0.937867i	$0.612798\pi$
$278$	−3.78065e9	+	1.07453e9i	−0.632976	+	0.179903i
$279$	3.26178e9			0.538316
$280$	−1.03144e9	+	1.12951e9i	−0.167808	+	0.183762i
$281$		−	7.30786e9i		−	1.17210i	−0.810275	−	0.586050i	$-0.800682\pi$
$281$		−	7.30786e9i		−	1.17210i	0.810275	−	0.586050i	$-0.199318\pi$
$282$	−3.42962e9	+	9.74762e8i	−0.542313	+	0.154135i
$283$	−2.53028e9	+	2.53028e9i	−0.394478	+	0.394478i	−0.876280	−	0.481802i	$-0.839982\pi$
$283$	−2.53028e9	+	2.53028e9i	−0.394478	+	0.394478i	0.481802	+	0.876280i	$0.339982\pi$
$284$	9.20289e8	+	1.48820e9i	0.141466	+	0.228764i
$285$	−4.63734e9	+	4.63734e9i	−0.702893	+	0.702893i
$286$	9.06051e9	−	1.62559e10i	1.35422	−	2.42967i
$287$			2.80632e8i			0.0413628i
$288$	−1.29331e9	−	1.89375e9i	−0.187989	−	0.275266i
$289$	−5.48810e9			−0.786739
$290$	2.85582e9	+	1.59174e9i	0.403774	+	0.225051i
$291$	−2.40476e9	−	2.40476e9i	−0.335351	−	0.335351i
$292$	−5.15891e9	+	3.19022e9i	−0.709621	+	0.438823i
$293$	5.03826e9	+	5.03826e9i	0.683613	+	0.683613i	0.960812	−	0.277199i	$-0.0894063\pi$
$293$	5.03826e9	+	5.03826e9i	0.683613	+	0.683613i	−0.277199	+	0.960812i	$0.589406\pi$
$294$	−1.14371e9	−	4.02404e9i	−0.153082	−	0.538608i
$295$	3.79087e9			0.500553
$296$	−7.88998e9	+	8.64015e9i	−1.02780	+	1.12552i
$297$		−	2.62987e9i		−	0.337993i
$298$	1.83879e9	+	6.46963e9i	0.233167	+	0.820378i
$299$	−1.28640e10	+	1.28640e10i	−1.60950	+	1.60950i
$300$	−4.79573e9	−	1.13081e9i	−0.592065	−	0.139606i
$301$	7.01452e8	−	7.01452e8i	0.0854539	−	0.0854539i
$302$	2.36482e9	+	1.31807e9i	0.284295	+	0.158457i
$303$		−	1.31576e9i		−	0.156102i
$304$	9.73300e9	−	3.24991e9i	1.13960	−	0.380520i
$305$	−1.55130e10			−1.79265
$306$	−6.57078e8	+	1.17890e9i	−0.0749430	+	0.134459i
$307$	3.90750e9	+	3.90750e9i	0.439891	+	0.439891i	0.891975	−	0.452084i	$-0.149319\pi$
$307$	3.90750e9	+	3.90750e9i	0.439891	+	0.439891i	−0.452084	+	0.891975i	$0.649319\pi$
$308$	2.67133e9	+	6.29888e8i	0.296842	+	0.0699939i
$309$	−6.91817e9	−	6.91817e9i	−0.758853	−	0.758853i
$310$	−2.05587e10	+	5.84316e9i	−2.22612	+	0.632705i
$311$	1.53622e9			0.164215			0.0821075	−	0.996623i	$-0.473835\pi$
$311$	1.53622e9			0.164215			0.0821075	+	0.996623i	$0.473835\pi$
$312$	−3.92819e8	−	8.65591e9i	−0.0414547	−	0.913470i
$313$			4.01304e9i			0.418116i	0.977903	+	0.209058i	$0.0670397\pi$
$313$			4.01304e9i			0.418116i	−0.977903	+	0.209058i	$0.932960\pi$
$314$	1.01341e10	−	2.88030e9i	1.04248	−	0.296291i
$315$	−5.77496e8	+	5.77496e8i	−0.0586553	+	0.0586553i
$316$	1.07124e9	−	6.62443e8i	0.107433	−	0.0664355i
$317$	2.00031e9	−	2.00031e9i	0.198089	−	0.198089i	−0.601091	−	0.799180i	$-0.705267\pi$
$317$	2.00031e9	−	2.00031e9i	0.198089	−	0.198089i	0.799180	+	0.601091i	$0.205267\pi$
$318$	−3.57893e9	+	6.42114e9i	−0.349981	+	0.627919i
$319$		−	5.86647e9i		−	0.566519i
$320$	1.15441e10	+	9.61928e9i	1.10093	+	0.917366i
$321$	−8.73261e9			−0.822478
$322$	−2.34352e9	−	1.30620e9i	−0.217994	−	0.121503i
$323$	−4.27028e9	−	4.27028e9i	−0.392325	−	0.392325i
$324$	−6.43995e8	−	1.04140e9i	−0.0584390	−	0.0945017i
$325$	−1.31644e10	−	1.31644e10i	−1.17996	−	1.17996i
$326$	−1.04939e9	−	3.69220e9i	−0.0929109	−	0.326900i
$327$	3.39982e9			0.297348
$328$	2.75407e9	−	1.24984e8i	0.237946	−	0.0107984i
$329$		−	1.98677e9i		−	0.169576i
$330$	4.71116e9	+	1.65758e10i	0.397257	+	1.39772i
$331$	−1.63292e10	+	1.63292e10i	−1.36036	+	1.36036i	−0.486900	+	0.873457i	$0.661873\pi$
$331$	−1.63292e10	+	1.63292e10i	−1.36036	+	1.36036i	−0.873457	+	0.486900i	$0.838127\pi$
$332$	−2.86415e8	+	1.21467e9i	−0.0235745	+	0.0999787i
$333$	−4.41755e9	+	4.41755e9i	−0.359257	+	0.359257i
$334$	−4.91481e9	−	2.73935e9i	−0.394931	−	0.220121i
$335$		−	2.87056e9i		−	0.227923i
$336$	1.21207e9	−	4.04718e8i	0.0950978	−	0.0317538i
$337$	2.41937e10			1.87579			0.937894	−	0.346923i	$-0.112773\pi$
$337$	2.41937e10			1.87579			0.937894	+	0.346923i	$0.112773\pi$
$338$	9.58498e9	−	1.71969e10i	0.734386	−	1.31760i
$339$	9.37057e9	+	9.37057e9i	0.709524	+	0.709524i
$340$	2.02963e9	−	8.60757e9i	0.151880	−	0.644117i
$341$	2.71176e10	+	2.71176e10i	2.00555	+	2.00555i
$342$	5.27012e9	−	1.49786e9i	0.385226	−	0.109488i
$343$	4.73470e9			0.342071
$344$	−7.19630e9	−	6.57150e9i	−0.513897	−	0.469279i
$345$		−	1.68453e10i		−	1.18906i
$346$	−2.03709e10	+	5.78980e9i	−1.42137	+	0.403979i
$347$	1.68192e10	−	1.68192e10i	1.16008	−	1.16008i	0.175622	−	0.984458i	$-0.443806\pi$
$347$	1.68192e10	−	1.68192e10i	1.16008	−	1.16008i	0.984458	−	0.175622i	$-0.0561937\pi$
$348$	−1.43657e9	−	2.32307e9i	−0.0979510	−	0.158397i
$349$	−3.94825e9	+	3.94825e9i	−0.266136	+	0.266136i	−0.827541	−	0.561405i	$-0.810261\pi$
$349$	−3.94825e9	+	3.94825e9i	−0.266136	+	0.266136i	0.561405	+	0.827541i	$0.310261\pi$
$350$	1.33670e9	−	2.39823e9i	0.0890760	−	0.159816i
$351$		−	4.62645e9i		−	0.304803i
$352$	4.99187e9	−	2.64964e10i	0.325157	−	1.72590i
$353$	2.93567e10			1.89064			0.945320	−	0.326144i	$-0.105749\pi$
$353$	2.93567e10			1.89064			0.945320	+	0.326144i	$0.105749\pi$
$354$	−2.76630e9	−	1.54185e9i	−0.176151	−	0.0981811i
$355$	−4.32876e9	−	4.32876e9i	−0.272552	−	0.272552i
$356$	1.57199e9	−	9.72104e8i	0.0978701	−	0.0605219i
$357$	−5.31786e8	−	5.31786e8i	−0.0327389	−	0.0327389i
$358$	−7.07196e7	−	2.48821e8i	−0.00430534	−	0.0151480i
$359$	−1.25453e10			−0.755274			−0.377637	−	0.925954i	$-0.623263\pi$
$359$	−1.25453e10			−0.755274			−0.377637	+	0.925954i	$0.623263\pi$
$360$	5.92462e9	+	5.41023e9i	0.352737	+	0.322111i
$361$			7.53192e9i			0.443483i
$362$	2.12188e9	+	7.46565e9i	0.123562	+	0.434744i
$363$	1.47756e10	−	1.47756e10i	0.850979	−	0.850979i
$364$	4.69940e9	+	1.10810e9i	0.267693	+	0.0631208i
$365$	1.50058e10	−	1.50058e10i	0.845451	−	0.845451i
$366$	1.13202e10	+	6.30953e9i	0.630857	+	0.351619i
$367$			2.57066e10i			1.41703i	0.705694	+	0.708517i	$0.250635\pi$
$367$			2.57066e10i			1.41703i	−0.705694	+	0.708517i	$0.749365\pi$
$368$	−1.17750e10	+	2.35805e10i	−0.642054	+	1.28577i
$369$	1.47201e9			0.0793971
$370$	1.99298e10	−	3.57571e10i	1.06340	−	1.90790i
$371$	−2.89650e9	−	2.89650e9i	−0.152890	−	0.152890i
$372$	1.73788e10	+	4.09785e9i	0.907504	+	0.213985i
$373$	1.54914e10	+	1.54914e10i	0.800305	+	0.800305i	0.983143	−	0.182838i	$-0.0585285\pi$
$373$	1.54914e10	+	1.54914e10i	0.800305	+	0.800305i	−0.182838	+	0.983143i	$0.558528\pi$
$374$	−1.52638e10	+	4.33826e9i	−0.780148	+	0.221732i
$375$	8.77131e8			0.0443547
$376$	−1.94977e10	+	8.84836e8i	−0.975511	+	0.0442702i
$377$		−	1.03203e10i		−	0.510889i
$378$	6.56298e8	−	1.86532e8i	0.0321465	−	0.00913663i
$379$	1.62397e8	−	1.62397e8i	0.00787083	−	0.00787083i	−0.703160	−	0.711031i	$-0.748228\pi$
$379$	1.62397e8	−	1.62397e8i	0.00787083	−	0.00787083i	0.711031	+	0.703160i	$0.248228\pi$
$380$	−3.05338e10	+	1.88818e10i	−1.46436	+	0.905544i
$381$	−5.54476e9	+	5.54476e9i	−0.263137	+	0.263137i
$382$	−1.01054e10	+	1.81307e10i	−0.474572	+	0.851453i
$383$			2.40023e10i			1.11547i	0.830019	+	0.557736i	$0.188330\pi$
$383$			2.40023e10i			1.11547i	−0.830019	+	0.557736i	$0.811670\pi$
$384$	−4.51163e9	−	1.17147e10i	−0.207495	−	0.538775i
$385$	−9.60232e9			−0.437052
$386$	−9.47739e9	−	5.28239e9i	−0.426913	−	0.237948i
$387$	−3.67934e9	−	3.67934e9i	−0.164031	−	0.164031i
$388$	−9.79146e9	−	1.58338e10i	−0.432037	−	0.698647i
$389$	−1.54247e10	−	1.54247e10i	−0.673626	−	0.673626i	0.284924	−	0.958550i	$-0.408032\pi$
$389$	−1.54247e10	−	1.54247e10i	−0.673626	−	0.673626i	−0.958550	+	0.284924i	$0.908032\pi$
$390$	8.28785e9	+	2.91601e10i	0.358248	+	1.26047i
$391$	1.55120e10			0.663683
$392$	−1.03819e9	−	2.28770e10i	−0.0439678	−	0.968847i
$393$			1.42679e10i			0.598122i
$394$	1.71159e9	+	6.02208e9i	0.0710254	+	0.249897i
$395$	−3.11593e9	+	3.11593e9i	−0.127997	+	0.127997i
$396$	3.30396e9	−	1.40120e10i	0.134355	−	0.569795i
$397$	7.38423e9	−	7.38423e9i	0.297265	−	0.297265i	−0.542677	−	0.839942i	$-0.682589\pi$
$397$	7.38423e9	−	7.38423e9i	0.297265	−	0.297265i	0.839942	+	0.542677i	$0.182589\pi$
$398$	2.37080e10	+	1.32141e10i	0.944851	+	0.526629i
$399$			3.05296e9i			0.120456i
$400$	−2.41311e10	−	1.20500e10i	−0.942620	−	0.470702i
$401$	4.18550e10			1.61871			0.809357	−	0.587317i	$-0.199816\pi$
$401$	4.18550e10			1.61871			0.809357	+	0.587317i	$0.199816\pi$
$402$	−1.16753e9	+	2.09473e9i	−0.0447059	+	0.0802091i
$403$	4.77052e10	+	4.77052e10i	1.80861	+	1.80861i
$404$	1.65302e9	−	7.01041e9i	0.0620517	−	0.263159i
$405$	3.02916e9	+	3.02916e9i	0.112590	+	0.112590i
$406$	1.46401e9	−	4.16099e8i	0.0538816	−	0.0153141i
$407$	−7.34529e10			−2.67689
$408$	−4.98200e9	+	5.45568e9i	−0.179789	+	0.196883i
$409$			2.58790e9i			0.0924813i	0.998930	+	0.0462407i	$0.0147241\pi$
$409$			2.58790e9i			0.0924813i	−0.998930	+	0.0462407i	$0.985276\pi$
$410$	−9.27793e9	+	2.63696e9i	−0.328334	+	0.0933186i
$411$	−6.43825e8	+	6.43825e8i	−0.0225632	+	0.0225632i
$412$	−2.81687e10	−	4.55516e10i	−0.977638	−	1.58094i
$413$	1.24785e9	−	1.24785e9i	0.0428905	−	0.0428905i
$414$	−6.85144e9	+	1.22925e10i	−0.233228	+	0.418446i
$415$		−	4.36625e9i		−	0.147203i
$416$	8.78168e9	−	4.66124e10i	0.293227	−	1.55642i
$417$	−1.14879e10			−0.379922
$418$	5.62673e10	+	3.13616e10i	1.84311	+	1.02729i
$419$	−1.81531e10	−	1.81531e10i	−0.588972	−	0.588972i	0.348381	−	0.937353i	$-0.386732\pi$
$419$	−1.81531e10	−	1.81531e10i	−0.588972	−	0.588972i	−0.937353	+	0.348381i	$0.886732\pi$
$420$	−3.80244e9	+	2.35139e9i	−0.122198	+	0.0755662i
$421$	−1.86939e10	−	1.86939e10i	−0.595076	−	0.595076i	0.343922	−	0.938998i	$-0.388244\pi$
$421$	−1.86939e10	−	1.86939e10i	−0.595076	−	0.595076i	−0.938998	+	0.343922i	$0.888244\pi$
$422$	−7.74943e9	−	2.72658e10i	−0.244354	−	0.859741i
$423$	−1.04212e10			−0.325505
$424$	−2.71357e10	+	2.97157e10i	−0.839609	+	0.919437i
$425$			1.58742e10i			0.486559i
$426$	1.39819e9	+	4.91943e9i	0.0424550	+	0.149375i
$427$	−5.10643e9	+	5.10643e9i	−0.153605	+	0.153605i
$428$	−4.65276e10	−	1.09710e10i	−1.38655	−	0.326942i
$429$	3.84632e10	−	3.84632e10i	1.13558	−	1.13558i
$430$	2.97818e10	+	1.65994e10i	0.871118	+	0.485533i
$431$		−	3.00887e10i		−	0.871957i	−0.899957	−	0.435978i	$-0.856402\pi$
$431$		−	3.00887e10i		−	0.871957i	0.899957	−	0.435978i	$-0.143598\pi$
$432$	−2.12288e9	−	6.35769e9i	−0.0609523	−	0.182543i
$433$	4.86395e10			1.38369			0.691843	−	0.722048i	$-0.256799\pi$
$433$	4.86395e10			1.38369			0.691843	+	0.722048i	$0.256799\pi$
$434$	−4.84394e9	+	8.69075e9i	−0.136534	+	0.244962i
$435$	6.75717e9	+	6.75717e9i	0.188716	+	0.188716i
$436$	1.81143e10	+	4.27127e9i	0.501275	+	0.118198i
$437$	−4.45268e10	−	4.45268e10i	−1.22094	−	1.22094i
$438$	−1.70534e10	+	4.84690e9i	−0.463356	+	0.131694i
$439$	−1.37806e10			−0.371032			−0.185516	−	0.982641i	$-0.559396\pi$
$439$	−1.37806e10			−0.371032			−0.185516	+	0.982641i	$0.559396\pi$
$440$	4.27653e9	+	9.42351e10i	0.114099	+	2.51421i
$441$		−	1.22274e10i		−	0.323281i
$442$	−2.68521e10	+	7.63185e9i	−0.703540	+	0.199959i
$443$	−3.25924e10	+	3.25924e10i	−0.846254	+	0.846254i	−0.989663	−	0.143409i	$-0.954194\pi$
$443$	−3.25924e10	+	3.25924e10i	−0.846254	+	0.846254i	0.143409	+	0.989663i	$0.454194\pi$
$444$	−2.90867e10	+	1.79869e10i	−0.748450	+	0.462834i
$445$	−4.57248e9	+	4.57248e9i	−0.116604	+	0.116604i
$446$	2.27659e10	−	4.08454e10i	0.575367	−	1.03229i
$447$			1.96586e10i			0.492405i
$448$	6.96639e9	−	6.33596e8i	0.172940	−	0.0157290i
$449$	9.33153e9			0.229598			0.114799	−	0.993389i	$-0.463378\pi$
$449$	9.33153e9			0.229598			0.114799	+	0.993389i	$0.463378\pi$
$450$	−1.25795e10	−	7.01141e9i	−0.306771	−	0.170984i
$451$	1.22379e10	+	1.22379e10i	0.295802	+	0.295802i
$452$	3.81541e10	+	6.16991e10i	0.914088	+	1.47817i
$453$	5.59540e9	+	5.59540e9i	0.132874	+	0.132874i
$454$	−9.91642e9	−	3.48901e10i	−0.233416	−	0.821257i
$455$	−1.68924e10			−0.394135
$456$	2.99611e10	−	1.35968e9i	0.692944	−	0.0314469i
$457$			7.51376e10i			1.72263i	0.508070	+	0.861316i	$0.330359\pi$
$457$			7.51376e10i			1.72263i	−0.508070	+	0.861316i	$0.669641\pi$
$458$	−8.70959e9	−	3.06440e10i	−0.197941	−	0.696439i
$459$	−2.78939e9	+	2.78939e9i	−0.0628433	+	0.0628433i
$460$	2.11632e10	−	8.97523e10i	0.472661	−	2.00454i
$461$	1.10749e10	−	1.10749e10i	0.245209	−	0.245209i	−0.573792	−	0.819001i	$-0.694528\pi$
$461$	1.10749e10	−	1.10749e10i	0.245209	−	0.245209i	0.819001	+	0.573792i	$0.194528\pi$
$462$	7.00708e9	+	3.90552e9i	0.153804	+	0.0857256i
$463$		−	7.32144e9i		−	0.159321i	−0.996822	−	0.0796604i	$-0.974616\pi$
$463$		−	7.32144e9i		−	0.159321i	0.996822	−	0.0796604i	$-0.0253836\pi$
$464$	−4.73553e9	−	1.41822e10i	−0.102164	−	0.305965i
$465$	−6.24696e10			−1.33616
$466$	−3.58360e10	+	6.42951e10i	−0.759934	+	1.36343i
$467$	−5.20318e10	−	5.20318e10i	−1.09396	−	1.09396i	−0.995102	−	0.0988571i	$-0.968481\pi$
$467$	−5.20318e10	−	5.20318e10i	−1.09396	−	1.09396i	−0.0988571	−	0.995102i	$-0.531519\pi$
$468$	5.81233e9	−	2.46498e10i	0.121162	−	0.513843i
$469$	−9.44908e8	−	9.44908e8i	−0.0195298	−	0.0195298i
$470$	6.56842e10	−	1.86687e10i	1.34608	−	0.382579i
$471$	3.07934e10			0.625712
$472$	−1.28018e10	−	1.16904e10i	−0.257932	−	0.235537i
$473$		−	6.11783e10i		−	1.22223i
$474$	3.54111e9	−	1.00645e9i	0.0701498	−	0.0199379i
$475$	4.55664e10	−	4.55664e10i	0.895098	−	0.895098i
$476$	−2.16527e9	−	3.50147e9i	−0.0421779	−	0.0682059i
$477$	−1.51931e10	+	1.51931e10i	−0.293476	+	0.293476i
$478$	−2.61788e9	+	4.69686e9i	−0.0501461	+	0.0899696i
$479$		−	1.99480e10i		−	0.378929i	−0.981888	−	0.189464i	$-0.939325\pi$
$479$		−	1.99480e10i		−	0.378929i	0.981888	−	0.189464i	$-0.0606752\pi$
$480$	2.47695e10	+	3.62691e10i	0.466608	+	0.683237i
$481$	−1.29218e11			−2.41403
$482$	−5.67317e10	−	3.16204e10i	−1.05108	−	0.585840i
$483$	−5.54501e9	−	5.54501e9i	−0.101886	−	0.101886i
$484$	9.72877e10	−	6.01618e10i	1.77287	−	1.09633i
$485$	4.60560e10	+	4.60560e10i	0.832376	+	0.832376i
$486$	−9.78421e8	−	3.44249e9i	−0.0175380	−	0.0617061i
$487$	−1.69385e10			−0.301134			−0.150567	−	0.988600i	$-0.548110\pi$
$487$	−1.69385e10			−0.301134			−0.150567	+	0.988600i	$0.548110\pi$
$488$	5.23876e10	+	4.78392e10i	0.923739	+	0.843537i
$489$		−	1.12191e10i		−	0.196211i
$490$	2.19043e10	+	7.70684e10i	0.379966	+	1.33688i
$491$	−1.53810e10	+	1.53810e10i	−0.264642	+	0.264642i	−0.826937	−	0.562295i	$-0.809919\pi$
$491$	−1.53810e10	+	1.53810e10i	−0.264642	+	0.264642i	0.562295	+	0.826937i	$0.309919\pi$
$492$	7.84288e9	+	1.84932e9i	0.133849	+	0.0315610i
$493$	−6.22233e9	+	6.22233e9i	−0.105333	+	0.105333i
$494$	9.89853e10	+	5.51712e10i	1.66212	+	0.926412i
$495$			5.03673e10i			0.838933i
$496$	8.74465e10	+	4.36669e10i	1.44483	+	0.721482i
$497$	−2.84981e9			−0.0467079
$498$	−1.77587e9	+	3.18617e9i	−0.0288731	+	0.0518026i
$499$	−4.44021e10	−	4.44021e10i	−0.716146	−	0.716146i	0.251668	−	0.967814i	$-0.419021\pi$
$499$	−4.44021e10	−	4.44021e10i	−0.716146	−	0.716146i	−0.967814	+	0.251668i	$0.919021\pi$
$500$	4.67337e9	+	1.10196e9i	0.0747740	+	0.0176314i
$501$	−1.16290e10	−	1.16290e10i	−0.184582	−	0.184582i
$502$	1.99734e10	−	5.67680e9i	0.314511	−	0.0893899i
$503$	−8.46327e10			−1.32211			−0.661053	−	0.750339i	$-0.729890\pi$
$503$	−8.46327e10			−1.32211			−0.661053	+	0.750339i	$0.729890\pi$
$504$	3.73111e9	−	1.69324e8i	0.0578251	−	0.00262419i
$505$			2.51995e10i			0.387460i
$506$	−1.59158e11	+	4.52356e10i	−2.42787	+	0.690047i
$507$	4.06896e10	−	4.06896e10i	0.615817	−	0.615817i
$508$	−3.65086e10	+	2.25766e10i	−0.548201	+	0.339003i
$509$	1.37705e10	−	1.37705e10i	0.205153	−	0.205153i	−0.597051	−	0.802204i	$-0.703661\pi$
$509$	1.37705e10	−	1.37705e10i	0.205153	−	0.205153i	0.802204	+	0.597051i	$0.203661\pi$
$510$	1.25844e10	−	2.25782e10i	0.186016	−	0.333741i
$511$		−	9.87899e9i		−	0.144887i
$512$	−9.32056e9	−	6.80845e10i	−0.135632	−	0.990759i
$513$	1.60138e10			0.231219
$514$	−5.65226e10	−	3.15039e10i	−0.809785	−	0.451348i
$515$	1.32497e11	+	1.32497e11i	1.88355	+	1.88355i
$516$	−1.49812e10	−	2.42261e10i	−0.211323	−	0.341731i
$517$	−8.66395e10	−	8.66395e10i	−1.21270	−	1.21270i
$518$	−5.20989e9	−	1.83306e10i	−0.0723618	−	0.254599i
$519$	−6.18991e10			−0.853129
$520$	7.52327e9	+	1.65778e11i	0.102895	+	2.26733i
$521$			1.41914e11i			1.92608i	0.269361	+	0.963039i	$0.413188\pi$
$521$			1.41914e11i			1.92608i	−0.269361	+	0.963039i	$0.586812\pi$
$522$	−2.18257e9	−	7.67921e9i	−0.0293959	−	0.103427i
$523$	−9.09192e9	+	9.09192e9i	−0.121520	+	0.121520i	−0.765252	−	0.643731i	$-0.777385\pi$
$523$	−9.09192e9	+	9.09192e9i	−0.121520	+	0.121520i	0.643731	+	0.765252i	$0.277385\pi$
$524$	−1.79251e10	+	7.60196e10i	−0.237759	+	1.00832i
$525$	5.67447e9	−	5.67447e9i	0.0746945	−	0.0746945i
$526$	3.01774e10	+	1.68199e10i	0.394220	+	0.219725i
$527$		−	5.75250e10i		−	0.745786i
$528$	3.52072e10	−	7.05053e10i	0.452997	−	0.907165i
$529$	8.34346e10			1.06543
$530$	6.85438e10	−	1.22978e11i	0.868690	−	1.55856i
$531$	−6.54536e9	−	6.54536e9i	−0.0823295	−	0.0823295i
$532$	−3.83551e9	+	1.62662e10i	−0.0478824	+	0.203068i
$533$	2.15289e10	+	2.15289e10i	0.266755	+	0.266755i
$534$	5.19641e9	−	1.47692e9i	0.0639055	−	0.0181631i
$535$	1.67247e11			2.04147
$536$	−8.85230e9	+	9.69396e9i	−0.107250	+	0.117447i
$537$		−	7.56068e8i		−	0.00909209i
$538$	5.78107e10	−	1.64309e10i	0.690048	−	0.196124i
$539$	1.01656e11	−	1.01656e11i	1.20442	−	1.20442i
$540$	1.23338e10	+	1.99450e10i	0.145051	+	0.234563i
$541$	9.92149e10	−	9.92149e10i	1.15821	−	1.15821i	0.173352	−	0.984860i	$-0.444540\pi$
$541$	9.92149e10	−	9.92149e10i	1.15821	−	1.15821i	0.984860	−	0.173352i	$-0.0554598\pi$
$542$	1.79051e10	−	3.21244e10i	0.207482	−	0.372253i
$543$			2.26851e10i			0.260940i
$544$	−3.33983e10	+	2.28090e10i	−0.381354	+	0.260441i
$545$	−6.51134e10			−0.738048
$546$	1.23268e10	+	6.87057e9i	0.138701	+	0.0773076i
$547$	−3.02302e10	−	3.02302e10i	−0.337669	−	0.337669i	0.517820	−	0.855489i	$-0.326744\pi$
$547$	−3.02302e10	−	3.02302e10i	−0.337669	−	0.337669i	−0.855489	+	0.517820i	$0.826744\pi$
$548$	−4.23917e9	+	2.62146e9i	−0.0470065	+	0.0290684i
$549$	2.67849e10	+	2.67849e10i	0.294849	+	0.294849i
$550$	−4.62918e10	−	1.62874e11i	−0.505887	−	1.77992i
$551$	3.57221e10			0.387552
$552$	−5.19480e10	+	5.68871e10i	−0.559516	+	0.612713i
$553$			2.05135e9i			0.0219351i
$554$	2.15194e10	+	7.57143e10i	0.228450	+	0.803783i
$555$	8.46051e10	−	8.46051e10i	0.891712	−	0.891712i
$556$	−6.12076e10	−	1.44325e10i	−0.640481	−	0.151023i
$557$	8.88111e10	−	8.88111e10i	0.922671	−	0.922671i	−0.0745470	−	0.997218i	$-0.523751\pi$
$557$	8.88111e10	−	8.88111e10i	0.922671	−	0.922671i	0.997218	+	0.0745470i	$0.0237511\pi$
$558$	4.55858e10	+	2.54080e10i	0.470211	+	0.262080i
$559$		−	1.07625e11i		−	1.10221i
$560$	−2.32136e10	+	7.75117e9i	−0.236042	+	0.0788161i
$561$	−4.63806e10			−0.468258
$562$	5.69255e10	−	1.02133e11i	0.570639	−	1.02381i
$563$	1.26232e11	+	1.26232e11i	1.25642	+	1.25642i	0.952790	+	0.303631i	$0.0981989\pi$
$563$	1.26232e11	+	1.26232e11i	1.25642	+	1.25642i	0.303631	+	0.952790i	$0.401801\pi$
$564$	−5.55246e10	−	1.30924e10i	−0.548743	−	0.129391i
$565$	−1.79465e11	−	1.79465e11i	−1.76111	−	1.76111i
$566$	−5.50725e10	+	1.56526e10i	−0.536622	+	0.152518i
$567$	1.99423e9			0.0192949
$568$	1.26920e9	+	2.79674e10i	0.0121938	+	0.268695i
$569$			1.30998e11i			1.24973i	0.780734	+	0.624863i	$0.214845\pi$
$569$			1.30998e11i			1.24973i	−0.780734	+	0.624863i	$0.785155\pi$
$570$	−1.00933e11	+	2.86871e10i	−0.956171	+	0.271761i
$571$	−1.08171e11	+	1.08171e11i	−1.01758	+	1.01758i	−0.0177334	+	0.999843i	$0.505645\pi$
$571$	−1.08171e11	+	1.08171e11i	−1.01758	+	1.01758i	−0.999843	+	0.0177334i	$0.994355\pi$
$572$	2.53255e11	−	1.56610e11i	2.36578	−	1.46297i
$573$	−4.28991e10	+	4.28991e10i	−0.397951	+	0.397951i
$574$	−2.18602e9	+	3.92205e9i	−0.0201376	+	0.0361298i
$575$			1.65522e11i			1.51420i
$576$	−3.32341e9	−	3.65409e10i	−0.0301922	−	0.331963i
$577$	7.54218e10			0.680446			0.340223	−	0.940345i	$-0.389497\pi$
$577$	7.54218e10			0.680446			0.340223	+	0.940345i	$0.389497\pi$
$578$	−7.67003e10	−	4.27503e10i	−0.687204	−	0.383025i
$579$	−2.24245e10	−	2.24245e10i	−0.199530	−	0.199530i
$580$	2.75132e10	+	4.44916e10i	0.243124	+	0.393157i
$581$	−1.43725e9	−	1.43725e9i	−0.0126132	−	0.0126132i
$582$	−1.48761e10	−	5.23405e10i	−0.129658	−	0.456190i
$583$	−2.52623e11			−2.18675
$584$	−9.69503e10	+	4.39975e9i	−0.833485	+	0.0378248i
$585$			8.86059e10i			0.756553i
$586$	3.11673e10	+	1.09660e11i	0.264307	+	0.929944i
$587$	1.27999e11	−	1.27999e11i	1.07809	−	1.07809i	0.0814055	−	0.996681i	$-0.474059\pi$
$587$	1.27999e11	−	1.27999e11i	1.07809	−	1.07809i	0.996681	−	0.0814055i	$-0.0259409\pi$
$588$	1.53616e10	−	6.51480e10i	0.128507	−	0.544994i
$589$	−1.65124e11	+	1.65124e11i	−1.37199	+	1.37199i
$590$	5.29802e10	+	2.95294e10i	0.437226	+	0.243695i
$591$			1.82987e10i			0.149993i
$592$	−1.77572e11	+	5.92925e10i	−1.44573	+	0.482740i
$593$	2.29193e10			0.185346			0.0926728	−	0.995697i	$-0.470459\pi$
$593$	2.29193e10			0.185346			0.0926728	+	0.995697i	$0.470459\pi$
$594$	2.04857e10	−	3.67544e10i	0.164553	−	0.295232i
$595$	1.01848e10	+	1.01848e10i	0.0812613	+	0.0812613i
$596$	−2.46976e10	+	1.04741e11i	−0.195735	+	0.830105i
$597$	5.60957e10	+	5.60957e10i	0.441604	+	0.441604i
$598$	−2.79990e11	+	7.95784e10i	−2.18946	+	0.622286i
$599$	7.72494e10			0.600050			0.300025	−	0.953931i	$-0.403005\pi$
$599$	7.72494e10			0.600050			0.300025	+	0.953931i	$0.403005\pi$
$600$	−5.82153e10	−	5.31609e10i	−0.449192	−	0.410192i
$601$			1.99566e11i			1.52964i	0.644245	+	0.764819i	$0.277172\pi$
$601$			1.99566e11i			1.52964i	−0.644245	+	0.764819i	$0.722828\pi$
$602$	1.52674e10	−	4.33927e9i	0.116246	−	0.0330393i
$603$	−4.95635e9	+	4.95635e9i	−0.0374880	+	0.0374880i
$604$	2.27828e10	+	3.68421e10i	0.171182	+	0.276819i
$605$	−2.82983e11	+	2.82983e11i	−2.11222	+	2.11222i
$606$	1.02493e10	−	1.83888e10i	0.0759983	−	0.136352i
$607$		−	7.56809e10i		−	0.557483i	−0.960366	−	0.278742i	$-0.910083\pi$
$607$		−	7.56809e10i		−	0.557483i	0.960366	−	0.278742i	$-0.0899173\pi$
$608$	1.61342e11	+	3.03964e10i	1.18068	+	0.222438i
$609$	4.44854e9			0.0323406
$610$	−2.16805e11	−	1.20840e11i	−1.56585	−	0.872754i
$611$	−1.52416e11	−	1.52416e11i	−1.09362	−	1.09362i
$612$	−1.83663e10	+	1.13576e10i	−0.130923	+	0.0809616i
$613$	−1.05683e11	−	1.05683e11i	−0.748448	−	0.748448i	0.225740	−	0.974188i	$-0.427520\pi$
$613$	−1.05683e11	−	1.05683e11i	−0.748448	−	0.748448i	−0.974188	+	0.225740i	$0.927520\pi$
$614$	2.41723e10	+	8.50482e10i	0.170076	+	0.598400i
$615$	−2.81919e10			−0.197072
$616$	3.24273e10	+	2.96118e10i	0.225210	+	0.205656i
$617$		−	6.52442e10i		−	0.450196i	−0.974336	−	0.225098i	$-0.927730\pi$
$617$		−	6.52442e10i		−	0.450196i	0.974336	−	0.225098i	$-0.0722702\pi$
$618$	−4.27967e10	−	1.50577e11i	−0.293397	−	1.03230i
$619$	1.17485e11	−	1.17485e11i	0.800238	−	0.800238i	−0.182894	−	0.983133i	$-0.558547\pi$
$619$	1.17485e11	−	1.17485e11i	0.800238	−	0.800238i	0.983133	+	0.182894i	$0.0585466\pi$
$620$	−3.32840e11	−	7.84821e10i	−2.25252	−	0.531134i
$621$	−2.90854e10	+	2.90854e10i	−0.195573	+	0.195573i
$622$	2.14699e10	+	1.19666e10i	0.143439	+	0.0799483i
$623$			3.01026e9i			0.0199826i
$624$	6.19364e10	−	1.24033e11i	0.408515	−	0.818084i
$625$	1.43969e11			0.943517
$626$	−3.12601e10	+	5.60853e10i	−0.203560	+	0.365218i
$627$	1.33134e11	+	1.33134e11i	0.861430	+	0.861430i
$628$	1.64068e11	+	3.86865e10i	1.05484	+	0.248726i
$629$	7.79084e10	+	7.79084e10i	0.497716	+	0.497716i
$630$	−1.25694e10	+	3.57246e9i	−0.0797909	+	0.0226781i
$631$	1.58980e11			1.00283			0.501414	−	0.865208i	$-0.332813\pi$
$631$	1.58980e11			1.00283			0.501414	+	0.865208i	$0.332813\pi$
$632$	2.01315e10	−	9.13601e8i	0.126185	−	0.00572648i
$633$		−	8.28496e10i		−	0.516031i
$634$	4.35376e10	−	1.23742e10i	0.269468	−	0.0765878i
$635$	1.06193e11	−	1.06193e11i	0.653134	−	0.653134i
$636$	−1.00037e11	+	6.18617e10i	−0.611407	+	0.378088i
$637$	1.78833e11	−	1.78833e11i	1.08615	−	1.08615i
$638$	4.56977e10	−	8.19884e10i	0.275811	−	0.494846i
$639$			1.49482e10i			0.0896571i
$640$	8.64068e10	+	2.24361e11i	0.515025	+	1.33730i
$641$	−7.67986e10			−0.454905			−0.227453	−	0.973789i	$-0.573040\pi$
$641$	−7.67986e10			−0.454905			−0.227453	+	0.973789i	$0.573040\pi$
$642$	−1.22045e11	−	6.80238e10i	−0.718422	−	0.400425i
$643$	8.55288e10	+	8.55288e10i	0.500344	+	0.500344i	0.911545	−	0.411201i	$-0.134891\pi$
$643$	8.55288e10	+	8.55288e10i	0.500344	+	0.500344i	−0.411201	+	0.911545i	$0.634891\pi$
$644$	−2.25776e10	−	3.65103e10i	−0.131261	−	0.212262i
$645$	7.04668e10	+	7.04668e10i	0.407142	+	0.407142i
$646$	−2.64165e10	−	9.29443e10i	−0.151686	−	0.533694i
$647$	−3.11878e10			−0.177978			−0.0889892	−	0.996033i	$-0.528364\pi$
$647$	−3.11878e10			−0.177978			−0.0889892	+	0.996033i	$0.528364\pi$
$648$	−8.88158e8	−	1.95709e10i	−0.00503721	−	0.110997i
$649$		−	1.08833e11i		−	0.613453i
$650$	−8.14364e10	−	2.86527e11i	−0.456210	−	1.60514i
$651$	−2.05632e10	+	2.05632e10i	−0.114490	+	0.114490i
$652$	1.40948e10	−	5.97756e10i	0.0779954	−	0.330776i
$653$	7.98538e10	−	7.98538e10i	0.439181	−	0.439181i	−0.452556	−	0.891736i	$-0.649488\pi$
$653$	7.98538e10	−	7.98538e10i	0.439181	−	0.439181i	0.891736	+	0.452556i	$0.149488\pi$
$654$	4.75150e10	+	2.64833e10i	0.259729	+	0.144764i
$655$		−	2.73259e11i		−	1.48460i
$656$	3.94637e10	+	1.97064e10i	0.213100	+	0.106412i
$657$	−5.18185e10			−0.278114
$658$	1.54762e10	−	2.77666e10i	0.0825582	−	0.148122i
$659$	−1.26153e10	−	1.26153e10i	−0.0668892	−	0.0668892i	0.672871	−	0.739760i	$-0.265061\pi$
$659$	−1.26153e10	−	1.26153e10i	−0.0668892	−	0.0668892i	−0.739760	+	0.672871i	$0.765061\pi$
$660$	−6.32776e10	+	2.68358e11i	−0.333483	+	1.41429i
$661$	2.22512e11	+	2.22512e11i	1.16559	+	1.16559i	0.983232	+	0.182361i	$0.0583738\pi$
$661$	2.22512e11	+	2.22512e11i	1.16559	+	1.16559i	0.182361	+	0.983232i	$0.441626\pi$
$662$	−3.55411e11	+	1.01015e11i	−1.85054	+	0.525959i
$663$	−8.15926e10			−0.422276
$664$	−1.34647e10	+	1.47449e10i	−0.0692668	+	0.0758525i
$665$		−	5.84704e10i		−	0.298985i
$666$	−9.61498e10	+	2.73275e10i	−0.488710	+	0.138900i
$667$	−6.48811e10	+	6.48811e10i	−0.327804	+	0.327804i
$668$	−4.73496e10	−	7.65691e10i	−0.237799	−	0.384545i
$669$	9.66445e10	−	9.66445e10i	0.482473	−	0.482473i
$670$	2.23606e10	−	4.01183e10i	0.110965	−	0.199087i
$671$			4.45365e11i			2.19698i
$672$	2.00922e10	+	3.78533e9i	0.0985258	+	0.0185621i
$673$	1.84331e11			0.898543			0.449271	−	0.893395i	$-0.351684\pi$
$673$	1.84331e11			0.898543			0.449271	+	0.893395i	$0.351684\pi$
$674$	3.38126e11	+	1.88460e11i	1.63847	+	0.913230i
$675$	−2.97644e10	−	2.97644e10i	−0.143378	−	0.143378i
$676$	2.67915e11	−	1.65676e11i	1.28295	−	0.793364i
$677$	−1.73288e9	−	1.73288e9i	−0.00824924	−	0.00824924i	0.702970	−	0.711219i	$-0.251857\pi$
$677$	−1.73288e9	−	1.73288e9i	−0.00824924	−	0.00824924i	−0.711219	+	0.702970i	$0.751857\pi$
$678$	5.79675e10	+	2.03954e11i	0.274325	+	0.965192i
$679$	3.03207e10			0.142646
$680$	9.54154e10	−	1.04487e11i	0.446255	−	0.488683i
$681$		−	1.06017e11i		−	0.492932i
$682$	1.67753e11	+	5.90225e11i	0.775412	+	2.72822i
$683$	−3.44541e10	+	3.44541e10i	−0.158328	+	0.158328i	−0.781825	−	0.623497i	$-0.785711\pi$
$683$	−3.44541e10	+	3.44541e10i	−0.158328	+	0.158328i	0.623497	+	0.781825i	$0.285711\pi$
$684$	8.53217e10	+	2.01185e10i	0.389794	+	0.0919117i
$685$	1.23305e10	−	1.23305e10i	0.0560041	−	0.0560041i
$686$	6.61711e10	+	3.68816e10i	0.298794	+	0.166538i
$687$		−	9.31147e10i		−	0.418014i
$688$	−4.93842e10	−	1.47898e11i	−0.220412	−	0.660099i
$689$	−4.44414e11			−1.97202
$690$	1.31219e11	−	2.35426e11i	0.578895	−	1.03862i
$691$	1.13764e11	+	1.13764e11i	0.498992	+	0.498992i	0.911124	−	0.412132i	$-0.135216\pi$
$691$	1.13764e11	+	1.13764e11i	0.498992	+	0.498992i	−0.412132	+	0.911124i	$0.635216\pi$
$692$	−3.29800e11	−	7.77653e10i	−1.43822	−	0.339126i
$693$	1.65795e10	+	1.65795e10i	0.0718850	+	0.0718850i
$694$	3.66077e11	−	1.04046e11i	1.57810	−	0.448525i
$695$	2.20016e11			0.943006
$696$	−1.98122e9	−	4.36570e10i	−0.00844299	−	0.186045i
$697$		−	2.59605e10i		−	0.109997i
$698$	−8.59352e10	+	2.44244e10i	−0.362034	+	0.102897i
$699$	−1.52129e11	+	1.52129e11i	−0.637240	+	0.637240i
$700$	3.73627e10	−	2.31047e10i	0.155613	−	0.0962297i
$701$	1.65572e11	−	1.65572e11i	0.685669	−	0.685669i	−0.275603	−	0.961272i	$-0.588877\pi$
$701$	1.65572e11	−	1.65572e11i	0.685669	−	0.685669i	0.961272	+	0.275603i	$0.0888775\pi$
$702$	3.60384e10	−	6.46582e10i	0.148394	−	0.266241i
$703$		−	4.47268e11i		−	1.83125i
$704$	2.76162e11	−	3.31422e11i	1.12428	−	1.34925i
$705$	1.99588e11			0.807937
$706$	4.10282e11	+	2.28678e11i	1.65145	+	0.920462i
$707$	8.29497e9	+	8.29497e9i	0.0331999	+	0.0331999i
$708$	−2.66507e10	−	4.30969e10i	−0.106066	−	0.171519i
$709$	−1.22633e11	−	1.22633e11i	−0.485315	−	0.485315i	0.421509	−	0.906824i	$-0.361501\pi$
$709$	−1.22633e11	−	1.22633e11i	−0.485315	−	0.485315i	−0.906824	+	0.421509i	$0.861501\pi$
$710$	−2.67782e10	−	9.42171e10i	−0.105378	−	0.370763i
$711$	1.07600e10			0.0421051
$712$	2.95421e10	−	1.34067e9i	0.114953	−	0.00521675i
$713$		−	5.99821e11i		−	2.32094i
$714$	−3.28970e9	−	1.15745e10i	−0.0126579	−	0.0445360i
$715$	−7.36647e11	+	7.36647e11i	−2.81861	+	2.81861i
$716$	9.49866e8	−	4.02835e9i	0.00361418	−	0.0153276i
$717$	−1.11133e10	+	1.11133e10i	−0.0420499	+	0.0420499i
$718$	−1.75331e11	−	9.77236e10i	−0.659720	−	0.367707i
$719$			4.23478e10i			0.158458i	0.996856	+	0.0792291i	$0.0252459\pi$
$719$			4.23478e10i			0.158458i	−0.996856	+	0.0792291i	$0.974754\pi$
$720$	4.06574e10	+	1.21763e11i	0.151290	+	0.453090i
$721$	8.72286e10			0.322788
$722$	−5.86708e10	+	1.05264e11i	−0.215910	+	0.387375i
$723$	−1.34233e11	−	1.34233e11i	−0.491255	−	0.491255i
$724$	−2.84998e10	+	1.20867e11i	−0.103726	+	0.439899i
$725$	−6.63959e10	−	6.63959e10i	−0.240320	−	0.240320i
$726$	3.21597e11	−	9.14037e10i	1.15762	−	0.329016i
$727$	4.75387e9			0.0170180			0.00850902	−	0.999964i	$-0.497291\pi$
$727$	4.75387e9			0.0170180			0.00850902	+	0.999964i	$0.497291\pi$
$728$	5.70459e10	+	5.20930e10i	0.203095	+	0.185462i
$729$		−	1.04604e10i		−	0.0370370i
$730$	3.26607e11	−	9.28279e10i	1.15010	−	0.326879i
$731$	−6.48893e10	+	6.48893e10i	−0.227250	+	0.227250i
$732$	1.09060e11	+	1.76361e11i	0.379857	+	0.614268i
$733$	−3.63002e11	+	3.63002e11i	−1.25746	+	1.25746i	−0.305154	+	0.952303i	$0.598708\pi$
$733$	−3.63002e11	+	3.63002e11i	−1.25746	+	1.25746i	−0.952303	+	0.305154i	$0.901292\pi$
$734$	−2.00245e11	+	3.59269e11i	−0.689886	+	1.23776i
$735$			2.34180e11i			0.802417i
$736$	−3.48249e11	+	2.37832e11i	−1.18680	+	0.810512i
$737$	−8.24117e10			−0.279331
$738$	2.05724e10	+	1.14664e10i	0.0693521	+	0.0386546i
$739$	−1.93442e11	−	1.93442e11i	−0.648594	−	0.648594i	0.304059	−	0.952653i	$-0.401658\pi$
$739$	−1.93442e11	−	1.93442e11i	−0.648594	−	0.648594i	−0.952653	+	0.304059i	$0.901658\pi$
$740$	5.57069e11	−	3.44486e11i	1.85773	−	1.14880i
$741$	2.34210e11	+	2.34210e11i	0.776841	+	0.776841i
$742$	−1.79181e10	−	6.30435e10i	−0.0591122	−	0.207981i
$743$	−8.77353e10			−0.287885			−0.143942	−	0.989586i	$-0.545978\pi$
$743$	−8.77353e10			−0.287885			−0.143942	+	0.989586i	$0.545978\pi$
$744$	2.10961e11	+	1.92645e11i	0.688512	+	0.628733i
$745$		−	3.76502e11i		−	1.22220i
$746$	9.58317e10	+	3.37176e11i	0.309424	+	1.08868i
$747$	−7.53881e9	+	7.53881e9i	−0.0242114	+	0.0242114i
$748$	−2.47117e11	−	5.82690e10i	−0.789398	−	0.186136i
$749$	5.50531e10	−	5.50531e10i	0.174926	−	0.174926i
$750$	1.22586e10	+	6.83253e9i	0.0387431	+	0.0215942i
$751$			1.87508e11i			0.589467i	0.955580	+	0.294733i	$0.0952308\pi$
$751$			1.87508e11i			0.589467i	−0.955580	+	0.294733i	$0.904769\pi$
$752$	−2.79388e11	−	1.39514e11i	−0.873647	−	0.436260i
$753$	6.06910e10			0.188775
$754$	8.03912e10	−	1.44234e11i	0.248727	−	0.446253i
$755$	−1.07163e11	−	1.07163e11i	−0.329806	−	0.329806i
$756$	1.06253e10	+	2.50539e9i	0.0325277	+	0.00766988i
$757$	−3.03140e11	−	3.03140e11i	−0.923124	−	0.923124i	0.0741254	−	0.997249i	$-0.476384\pi$
$757$	−3.03140e11	−	3.03140e11i	−0.923124	−	0.923124i	−0.997249	+	0.0741254i	$0.976384\pi$
$758$	3.53463e9	−	1.00461e9i	0.0107070	−	0.00304312i
$759$	−4.83617e11			−1.45725
$760$	−5.73816e11	+	2.60406e10i	−1.71996	+	0.0780544i
$761$		−	9.64556e10i		−	0.287600i	−0.989607	−	0.143800i	$-0.954068\pi$
$761$		−	9.64556e10i		−	0.287600i	0.989607	−	0.143800i	$-0.0459322\pi$
$762$	−1.20684e11	+	3.43005e10i	−0.357955	+	0.101738i
$763$	−2.14335e10	+	2.14335e10i	−0.0632404	+	0.0632404i
$764$	−2.82463e11	+	1.74672e11i	−0.829063	+	0.512685i
$765$	5.34225e10	−	5.34225e10i	0.155983	−	0.155983i
$766$	−1.86969e11	+	3.35451e11i	−0.543069	+	0.974347i
$767$		−	1.91459e11i		−	0.553214i
$768$	2.82000e10	−	1.98866e11i	0.0810597	−	0.571632i
$769$	2.90372e11			0.830327			0.415163	−	0.909747i	$-0.363724\pi$
$769$	2.90372e11			0.830327			0.415163	+	0.909747i	$0.363724\pi$
$770$	−1.34200e11	−	7.47985e10i	−0.381758	−	0.212780i
$771$	−1.33739e11	−	1.33739e11i	−0.378477	−	0.378477i
$772$	−9.13059e10	−	1.47651e11i	−0.257057	−	0.415687i
$773$	4.56904e11	+	4.56904e11i	1.27970	+	1.27970i	0.940837	+	0.338859i	$0.110041\pi$
$773$	4.56904e11	+	4.56904e11i	1.27970	+	1.27970i	0.338859	+	0.940837i	$0.389959\pi$
$774$	−2.27609e10	−	8.00823e10i	−0.0634198	−	0.223138i
$775$	6.13826e11			1.70153
$776$	−1.35038e10	−	2.97561e11i	−0.0372399	−	0.820595i
$777$		−	5.56992e10i		−	0.152815i
$778$	−9.54192e10	−	3.35725e11i	−0.260446	−	0.916358i
$779$	−7.45189e10	+	7.45189e10i	−0.202356	+	0.202356i
$780$	−1.11318e11	+	4.72094e11i	−0.300736	+	1.27541i
$781$	−1.24275e11	+	1.24275e11i	−0.334026	+	0.334026i
$782$	2.16792e11	+	1.20833e11i	0.579717	+	0.323115i
$783$		−	2.33340e10i		−	0.0620787i
$784$	1.63694e11	−	3.27811e11i	0.433280	−	0.867679i
$785$	−5.89757e11			−1.55308
$786$	−1.11142e11	+	1.99404e11i	−0.291197	+	0.522450i
$787$	−4.52290e11	−	4.52290e11i	−1.17901	−	1.17901i	−0.979996	−	0.199015i	$-0.936226\pi$
$787$	−4.52290e11	−	4.52290e11i	−1.17901	−	1.17901i	−0.199015	−	0.979996i	$-0.563774\pi$
$788$	−2.29891e10	+	9.74957e10i	−0.0596233	+	0.252860i
$789$	7.14028e10	+	7.14028e10i	0.184250	+	0.184250i
$790$	−6.78194e10	+	1.92755e10i	−0.174119	+	0.0494878i
$791$	−1.18150e11			−0.301806
$792$	1.55324e11	−	1.70091e11i	0.394763	−	0.432296i
$793$			7.83485e11i			1.98124i
$794$	1.60721e11	−	4.56798e10i	0.404380	−	0.114932i
$795$	2.90978e11	−	2.90978e11i	0.728437	−	0.728437i
$796$	2.28405e11	+	3.69354e11i	0.568923	+	0.920005i
$797$	−1.40672e9	+	1.40672e9i	−0.00348638	+	0.00348638i	−0.708848	−	0.705361i	$-0.750785\pi$
$797$	−1.40672e9	+	1.40672e9i	−0.00348638	+	0.00348638i	0.705361	+	0.708848i	$0.250785\pi$
$798$	−2.37814e10	+	4.26674e10i	−0.0586444	+	0.105217i
$799$			1.83790e11i			0.450957i
$800$	−2.43385e11	−	3.56380e11i	−0.594202	−	0.870067i
$801$	1.57898e10			0.0383572
$802$	5.84955e11	+	3.26035e11i	1.41392	+	0.788074i
$803$	−4.30806e11	−	4.30806e11i	−1.03614	−	1.03614i
$804$	−3.26343e10	+	2.01808e10i	−0.0780999	+	0.0482962i
$805$	1.06198e11	+	1.06198e11i	0.252891	+	0.252891i
$806$	2.95110e11	+	1.03832e12i	0.699269	+	2.46032i
$807$	1.75663e11			0.414178
$808$	7.77108e10	−	8.50994e10i	0.182321	−	0.199655i
$809$		−	2.75364e11i		−	0.642855i	−0.946934	−	0.321428i	$-0.895837\pi$
$809$		−	2.75364e11i		−	0.642855i	0.946934	−	0.321428i	$-0.104163\pi$
$810$	1.87387e10	+	6.59307e10i	0.0435311	+	0.153161i
$811$	−3.12224e11	+	3.12224e11i	−0.721743	+	0.721743i	−0.968960	−	0.247217i	$-0.920484\pi$
$811$	−3.12224e11	+	3.12224e11i	−0.721743	+	0.721743i	0.247217	+	0.968960i	$0.420484\pi$
$812$	2.37019e10	+	5.58881e9i	0.0545205	+	0.0128557i
$813$	7.60098e10	−	7.60098e10i	0.173983	−	0.173983i
$814$	−1.02656e12	−	5.72171e11i	−2.33823	−	1.30325i
$815$			2.14868e11i			0.487015i
$816$	−1.12125e11	+	3.74393e10i	−0.252896	+	0.0844436i
$817$	3.72526e11			0.836120
$818$	−2.01588e10	+	3.61678e10i	−0.0450247	+	0.0807810i
$819$	2.91666e10	+	2.91666e10i	0.0648261	+	0.0648261i
$820$	−1.50207e11	−	3.54182e10i	−0.332227	−	0.0783377i
$821$	−3.59055e11	−	3.59055e11i	−0.790293	−	0.790293i	0.191248	−	0.981542i	$-0.438746\pi$
$821$	−3.59055e11	−	3.59055e11i	−0.790293	−	0.790293i	−0.981542	+	0.191248i	$0.938746\pi$
$822$	−1.40131e10	+	3.98278e9i	−0.0306935	+	0.00872367i
$823$	2.23649e11			0.487492			0.243746	−	0.969839i	$-0.421624\pi$
$823$	2.23649e11			0.487492			0.243746	+	0.969839i	$0.421624\pi$
$824$	−3.88485e10	−	8.56042e11i	−0.0842686	−	1.85689i
$825$		−	4.94908e11i		−	1.06834i
$826$	2.71599e10	−	7.71933e9i	0.0583455	−	0.0165829i
$827$	3.38704e11	−	3.38704e11i	0.724099	−	0.724099i	−0.245338	−	0.969438i	$-0.578899\pi$
$827$	3.38704e11	−	3.38704e11i	0.724099	−	0.724099i	0.969438	+	0.245338i	$0.0788991\pi$
$828$	−1.91508e11	+	1.18427e11i	−0.407442	+	0.251958i
$829$	4.92090e11	−	4.92090e11i	1.04190	−	1.04190i	0.0428172	−	0.999083i	$-0.486367\pi$
$829$	4.92090e11	−	4.92090e11i	1.04190	−	1.04190i	0.999083	−	0.0428172i	$-0.0136333\pi$
$830$	3.40114e10	−	6.10216e10i	0.0716659	−	0.128579i
$831$			2.30065e11i			0.482444i
$832$	4.85824e11	−	5.83037e11i	1.01388	−	1.21675i
$833$	−2.15644e11			−0.447876
$834$	−1.60552e11	−	8.94862e10i	−0.331856	−	0.184966i
$835$	2.22718e11	+	2.22718e11i	0.458152	+	0.458152i
$836$	5.42083e11	+	8.76603e11i	1.10979	+	1.79464i
$837$	1.07861e11	+	1.07861e11i	0.219767	+	0.219767i
$838$	−1.12297e11	−	3.95109e11i	−0.227716	−	0.801200i
$839$	2.28053e11			0.460244			0.230122	−	0.973162i	$-0.426087\pi$
$839$	2.28053e11			0.460244			0.230122	+	0.973162i	$0.426087\pi$
$840$	−7.14584e10	+	3.24289e9i	−0.143528	+	0.00651351i
$841$			4.48195e11i			0.895948i
$842$	−1.15643e11	−	4.06880e11i	−0.230076	−	0.809503i
$843$	2.41657e11	−	2.41657e11i	0.478508	−	0.478508i
$844$	1.04086e11	−	4.41425e11i	0.205127	−	0.869935i
$845$	−7.79289e11	+	7.79289e11i	−1.52852	+	1.52852i
$846$	−1.45645e11	−	8.11776e10i	−0.284324	−	0.158473i
$847$			1.86300e11i			0.361975i
$848$	−6.10715e11	+	2.03922e11i	−1.18101	+	0.394349i
$849$	−1.67343e11			−0.322090
$850$	−1.23654e11	+	2.21853e11i	−0.236882	+	0.425002i
$851$	8.12362e11	+	8.12362e11i	1.54893	+	1.54893i
$852$	−1.87797e10	+	7.96442e10i	−0.0356395	+	0.151146i
$853$	3.03106e11	+	3.03106e11i	0.572530	+	0.572530i	0.932835	−	0.360305i	$-0.117327\pi$
$853$	3.03106e11	+	3.03106e11i	0.572530	+	0.572530i	−0.360305	+	0.932835i	$0.617327\pi$
$854$	−1.11143e11	+	3.15890e10i	−0.208955	+	0.0593888i
$855$	−3.06696e11			−0.573910
$856$	−5.64798e11	−	5.15760e11i	−1.05196	−	0.960623i
$857$		−	1.91924e11i		−	0.355801i	−0.984049	−	0.177900i	$-0.943070\pi$
$857$		−	1.91924e11i		−	0.355801i	0.984049	−	0.177900i	$-0.0569305\pi$
$858$	8.37166e11	−	2.37938e11i	1.54476	−	0.439051i
$859$	−3.73858e11	+	3.73858e11i	−0.686647	+	0.686647i	−0.961489	−	0.274842i	$-0.911374\pi$
$859$	−3.73858e11	+	3.73858e11i	−0.686647	+	0.686647i	0.274842	+	0.961489i	$0.411374\pi$
$860$	2.86920e11	+	4.63978e11i	0.524525	+	0.848210i
$861$	−9.27998e9	+	9.27998e9i	−0.0168863	+	0.0168863i
$862$	2.34380e11	−	4.20513e11i	0.424514	−	0.761641i
$863$		−	5.72749e11i		−	1.03257i	−0.856416	−	0.516287i	$-0.827314\pi$
$863$		−	5.72749e11i		−	1.03257i	0.856416	−	0.516287i	$-0.172686\pi$
$864$	1.98553e10	−	1.05390e11i	0.0356304	−	0.189123i
$865$	1.18549e12			2.11755
$866$	6.79773e11	+	3.78884e11i	1.20863	+	0.673650i
$867$	−1.81481e11	−	1.81481e11i	−0.321185	−	0.321185i
$868$	−1.35395e11	+	8.37273e10i	−0.238520	+	0.147499i
$869$	8.94560e10	+	8.94560e10i	0.156867	+	0.156867i
$870$	4.18007e10	+	1.47072e11i	0.0729637	+	0.256717i
$871$	−1.44978e11			−0.251901
$872$	2.19890e11	+	2.00798e11i	0.380311	+	0.347291i
$873$		−	1.59042e11i		−	0.273813i
$874$	−2.75448e11	−	9.69143e11i	−0.472057	−	1.66089i
$875$	−5.52970e9	+	5.52970e9i	−0.00943343	+	0.00943343i
$876$	−2.76090e11	−	6.51008e10i	−0.468850	−	0.110553i
$877$	3.15632e11	−	3.15632e11i	0.533559	−	0.533559i	−0.388071	−	0.921630i	$-0.626858\pi$
$877$	3.15632e11	−	3.15632e11i	0.533559	−	0.533559i	0.921630	+	0.388071i	$0.126858\pi$
$878$	−1.92595e11	−	1.07346e11i	−0.324090	−	0.180637i
$879$			3.33212e11i			0.558168i
$880$	−6.74289e11	+	1.35032e12i	−1.12439	+	2.25168i
$881$	6.52202e11			1.08263			0.541313	−	0.840821i	$-0.317927\pi$
$881$	6.52202e11			1.08263			0.541313	+	0.840821i	$0.317927\pi$
$882$	9.52471e10	−	1.70888e11i	0.157390	−	0.282381i
$883$	−2.27532e11	−	2.27532e11i	−0.374283	−	0.374283i	0.494752	−	0.869034i	$-0.335259\pi$
$883$	−2.27532e11	−	2.27532e11i	−0.374283	−	0.374283i	−0.869034	+	0.494752i	$0.835259\pi$
$884$	−4.34727e11	−	1.02507e11i	−0.711882	−	0.167859i
$885$	1.25357e11	+	1.25357e11i	0.204350	+	0.204350i
$886$	−7.09385e11	+	2.01620e11i	−1.15119	+	0.327190i
$887$	1.08067e12			1.74581			0.872907	−	0.487886i	$-0.162232\pi$
$887$	1.08067e12			1.74581			0.872907	+	0.487886i	$0.162232\pi$
$888$	−5.46620e11	+	2.48065e10i	−0.879091	+	0.0398945i
$889$		−	6.99117e10i		−	0.111929i
$890$	−9.95218e10	+	2.82859e10i	−0.158620	+	0.0450828i
$891$	8.69647e10	−	8.69647e10i	0.137985	−	0.137985i
$892$	6.36341e11	−	3.93507e11i	1.00515	−	0.621575i
$893$	5.27565e11	−	5.27565e11i	0.829602	−	0.829602i
$894$	−1.53133e11	+	2.74744e11i	−0.239728	+	0.430108i
$895$			1.44802e10i			0.0225675i
$896$	1.02296e11	+	4.54106e10i	0.158718	+	0.0704572i
$897$	−8.50777e11			−1.31415
$898$	1.30415e11	+	7.26891e10i	0.200550	+	0.111780i
$899$	2.40606e11	+	2.40606e11i	0.368357	+	0.368357i
$900$	−1.21192e11	−	1.95979e11i	−0.184716	−	0.298704i
$901$	2.67947e11	+	2.67947e11i	0.406583	+	0.406583i
$902$	7.57051e10	+	2.66362e11i	0.114367	+	0.402390i
$903$	4.63914e10			0.0697729
$904$	5.26198e10	+	1.15950e12i	0.0787908	+	1.73619i
$905$		−	4.34466e11i		−	0.647681i
$906$	3.46139e10	+	1.21786e11i	0.0513733	+	0.180753i
$907$	−6.66950e11	+	6.66950e11i	−0.985516	+	0.985516i	−0.999897	−	0.0143803i	$-0.995422\pi$
$907$	−6.66950e11	+	6.66950e11i	−0.985516	+	0.985516i	0.0143803	+	0.999897i	$0.495422\pi$
$908$	1.33192e11	−	5.64861e11i	0.195945	−	0.830995i
$909$	4.35098e10	−	4.35098e10i	0.0637282	−	0.0637282i
$910$	−2.36084e11	−	1.31585e11i	−0.344271	−	0.191885i
$911$			4.27457e11i			0.620611i	0.950637	+	0.310305i	$0.100431\pi$
$911$			4.27457e11i			0.620611i	−0.950637	+	0.310305i	$0.899569\pi$
$912$	4.29320e11	+	2.14383e11i	0.620586	+	0.309893i
$913$	−1.25352e11			−0.180404
$914$	−5.85294e11	+	1.05010e12i	−0.838666	+	1.50469i
$915$	−5.12984e11	−	5.12984e11i	−0.731846	−	0.731846i
$916$	1.16982e11	−	4.96117e11i	0.166164	−	0.704697i
$917$	−8.99491e10	−	8.99491e10i	−0.127209	−	0.127209i
$918$	−6.07122e10	+	1.72555e10i	−0.0854880	+	0.0242973i
$919$	1.19432e12			1.67440			0.837200	−	0.546896i	$-0.184191\pi$
$919$	1.19432e12			1.67440			0.837200	+	0.546896i	$0.184191\pi$
$920$	9.94909e11	−	1.08950e12i	1.38878	−	1.52082i
$921$			2.58427e11i			0.359170i
$922$	2.41049e11	−	6.85107e10i	0.333566	−	0.0948057i
$923$	−2.18625e11	+	2.18625e11i	−0.301226	+	0.301226i
$924$	6.75066e10	+	1.09165e11i	0.0926102	+	0.149760i
$925$	−8.31329e11	+	8.31329e11i	−1.13555	+	1.13555i
$926$	5.70313e10	−	1.02323e11i	0.0775657	−	0.139164i
$927$		−	4.57542e11i		−	0.619601i
$928$	4.42914e10	−	2.35095e11i	0.0597210	−	0.316994i
$929$	−5.95261e10			−0.0799180			−0.0399590	−	0.999201i	$-0.512723\pi$
$929$	−5.95261e10			−0.0799180			−0.0399590	+	0.999201i	$0.512723\pi$
$930$	−8.73060e11	−	4.86615e11i	−1.16711	−	0.650510i
$931$	6.19001e11	+	6.19001e11i	0.823935	+	0.823935i
$932$	−1.00167e12	+	6.19423e11i	−1.32758	+	0.820963i
$933$	5.08000e10	+	5.08000e10i	0.0670405	+	0.0670405i
$934$	−3.21875e11	−	1.13249e12i	−0.422960	−	1.48815i
$935$	8.88282e11			1.16226
$936$	2.73245e11	−	2.99224e11i	0.355999	−	0.389846i
$937$		−	3.73172e11i		−	0.484117i	−0.970262	−	0.242059i	$-0.922177\pi$
$937$		−	3.73172e11i		−	0.484117i	0.970262	−	0.242059i	$-0.0778227\pi$
$938$	−5.84532e9	−	2.05663e10i	−0.00755087	−	0.0265671i
$939$	−1.32704e11	+	1.32704e11i	−0.170695	+	0.170695i
$940$	1.06341e12	+	2.50747e11i	1.36204	+	0.321162i
$941$	−8.19790e11	+	8.19790e11i	−1.04555	+	1.04555i	−0.0466361	+	0.998912i	$0.514850\pi$
$941$	−8.19790e11	+	8.19790e11i	−1.04555	+	1.04555i	−0.998912	+	0.0466361i	$0.985150\pi$
$942$	4.30362e11	+	2.39869e11i	0.546550	+	0.304629i
$943$		−	2.70693e11i		−	0.342319i
$944$	−8.78519e10	−	2.63103e11i	−0.110628	−	0.331313i
$945$	−3.81934e10			−0.0478918
$946$	4.76556e11	−	8.55012e11i	0.595044	−	1.06760i
$947$	5.00862e11	+	5.00862e11i	0.622756	+	0.622756i	0.946235	−	0.323479i	$-0.104853\pi$
$947$	5.00862e11	+	5.00862e11i	0.622756	+	0.622756i	−0.323479	+	0.946235i	$0.604853\pi$
$948$	5.73296e10	+	1.35181e10i	0.0709815	+	0.0167371i
$949$	−7.57872e11	−	7.57872e11i	−0.934396	−	0.934396i
$950$	9.91770e11	−	2.81879e11i	1.21763	−	0.346074i
$951$	1.32293e11			0.161739
$952$	−2.98621e9	−	6.58023e10i	−0.00363557	−	0.0801112i
$953$			4.81880e11i			0.584208i	0.956387	+	0.292104i	$0.0943553\pi$
$953$			4.81880e11i			0.584208i	−0.956387	+	0.292104i	$0.905645\pi$
$954$	−3.30683e11	+	9.39863e10i	−0.399226	+	0.113467i
$955$	8.21604e11	−	8.21604e11i	0.987755	−	0.987755i
$956$	−7.31736e10	+	4.52499e10i	−0.0876038	+	0.0541733i
$957$	1.93993e11	−	1.93993e11i	0.231280	−	0.231280i
$958$	1.55388e11	−	2.78789e11i	0.184482	−	0.330988i
$959$		−	8.11774e9i		−	0.00959755i
$960$	6.36501e10	+	6.99833e11i	0.0749401	+	0.823966i
$961$	−1.37150e12			−1.60806
$962$	−1.80592e12	−	1.00656e12i	−2.10862	−	1.17528i
$963$	−2.88771e11	−	2.88771e11i	−0.335775	−	0.335775i
$964$	−5.46557e11	−	8.83838e11i	−0.632889	−	1.02344i
$965$	4.29475e11	+	4.29475e11i	0.495255	+	0.495255i
$966$	−3.43021e10	−	1.20689e11i	−0.0393924	−	0.138599i
$967$	−8.15496e11			−0.932644			−0.466322	−	0.884615i	$-0.654421\pi$
$967$	−8.15496e11			−0.932644			−0.466322	+	0.884615i	$0.654421\pi$
$968$	1.82831e12	−	8.29714e10i	2.08232	−	0.0944989i
$969$		−	2.82420e11i		−	0.320332i
$970$	2.84908e11	+	1.00243e12i	0.321824	+	1.13231i
$971$	1.05256e12	−	1.05256e12i	1.18405	−	1.18405i	0.205367	−	0.978685i	$-0.434161\pi$
$971$	1.05256e12	−	1.05256e12i	1.18405	−	1.18405i	0.978685	−	0.205367i	$-0.0658387\pi$
$972$	1.31416e10	−	5.57330e10i	0.0147225	−	0.0624378i
$973$	7.24230e10	−	7.24230e10i	0.0808026	−	0.0808026i
$974$	−2.36729e11	−	1.31945e11i	−0.263036	−	0.146608i
$975$		−	8.70641e11i		−	0.963431i
$976$	3.59507e11	+	1.07667e12i	0.396194	+	1.18654i
$977$	2.81012e10			0.0308423			0.0154211	−	0.999881i	$-0.495091\pi$
$977$	2.81012e10			0.0308423			0.0154211	+	0.999881i	$0.495091\pi$
$978$	8.73926e10	−	1.56795e11i	0.0955255	−	0.171387i
$979$	1.31272e11	+	1.31272e11i	0.142903	+	0.142903i
$980$	−2.94206e11	+	1.24772e12i	−0.318968	+	1.35273i
$981$	1.12426e11	+	1.12426e11i	0.121392	+	0.121392i
$982$	−3.34773e11	+	9.51487e10i	−0.360002	+	0.102319i
$983$	−1.47422e12			−1.57887			−0.789437	−	0.613832i	$-0.789627\pi$
$983$	−1.47422e12			−1.57887			−0.789437	+	0.613832i	$0.789627\pi$
$984$	9.52047e10	+	8.69388e10i	0.101550	+	0.0927327i
$985$		−	3.50457e11i		−	0.372297i
$986$	−1.35431e11	+	3.84921e10i	−0.143289	+	0.0407253i
$987$	6.56987e10	−	6.56987e10i	0.0692290	−	0.0692290i
$988$	9.53631e11	+	1.54212e12i	1.00081	+	1.61841i
$989$	−6.76609e11	+	6.76609e11i	−0.707217	+	0.707217i
$990$	−3.92342e11	+	7.03920e11i	−0.408436	+	0.732795i
$991$		−	1.51182e12i		−	1.56749i	−0.621082	−	0.783745i	$-0.713307\pi$
$991$		−	1.51182e12i		−	1.56749i	0.621082	−	0.783745i	$-0.286693\pi$
$992$	8.81982e11	+	1.29145e12i	0.910779	+	1.33362i
$993$	−1.07995e12			−1.11073
$994$	−3.98282e10	−	2.21990e10i	−0.0407986	−	0.0227398i
$995$	−1.07435e12	−	1.07435e12i	−1.09610	−	1.09610i
$996$	−4.96382e10	+	3.06958e10i	−0.0504404	+	0.0311919i
$997$	1.17934e12	+	1.17934e12i	1.19360	+	1.19360i	0.976049	+	0.217552i	$0.0698073\pi$
$997$	1.17934e12	+	1.17934e12i	1.19360	+	1.19360i	0.217552	+	0.976049i	$0.430193\pi$
$998$	−2.74677e11	−	9.66429e11i	−0.276885	−	0.974199i
$999$	−2.92160e11			−0.293332

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.9.l.a.43.27	yes	64
4.3	odd	2		192.9.l.a.79.2		64
16.3	odd	4	inner	48.9.l.a.19.27	✓	64
16.13	even	4		192.9.l.a.175.2		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.27	✓	64	16.3	odd	4	inner
48.9.l.a.43.27	yes	64	1.1	even	1	trivial
192.9.l.a.79.2		64	4.3	odd	2
192.9.l.a.175.2		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)

\(f(q)\)	\(=\)	\(q+(13.9758 + 7.78963i) q^{2} +(33.0681 + 33.0681i) q^{3} +(134.643 + 217.732i) q^{4} +(-633.321 - 633.321i) q^{5} +(204.563 + 719.740i) q^{6} -416.943 q^{7} +(185.692 + 4091.79i) q^{8} +2187.00i q^{9} +O(q^{10})\)	\(q+(13.9758 + 7.78963i) q^{2} +(33.0681 + 33.0681i) q^{3} +(134.643 + 217.732i) q^{4} +(-633.321 - 633.321i) q^{5} +(204.563 + 719.740i) q^{6} -416.943 q^{7} +(185.692 + 4091.79i) q^{8} +2187.00i q^{9} +(-3917.80 - 13784.5i) q^{10} +(-18182.2 + 18182.2i) q^{11} +(-2747.58 + 11652.4i) q^{12} +(-31986.0 + 31986.0i) q^{13} +(-5827.09 - 3247.83i) q^{14} -41885.5i q^{15} +(-29278.3 + 58632.3i) q^{16} +38570.1 q^{17} +(-17035.9 + 30565.0i) q^{18} +(-110715. - 110715. i) q^{19} +(52621.7 - 223167. i) q^{20} +(-13787.5 - 13787.5i) q^{21} +(-395742. + 112477. i) q^{22} +402176. q^{23} +(-129167. + 141448. i) q^{24} +411566. i q^{25} +(-696188. + 197869. i) q^{26} +(-72320.0 + 72320.0i) q^{27} +(-56138.6 - 90781.8i) q^{28} +(-161325. + 161325. i) q^{29} +(326272. - 585381. i) q^{30} -1.49144e6i q^{31} +(-865911. + 591363. i) q^{32} -1.20250e6 q^{33} +(539047. + 300447. i) q^{34} +(264059. + 264059. i) q^{35} +(-476180. + 294465. i) q^{36} +(2.01992e6 + 2.01992e6i) q^{37} +(-684895. - 2.40975e6i) q^{38} -2.11543e6 q^{39} +(2.47381e6 - 2.70902e6i) q^{40} -673071. i q^{41} +(-85291.3 - 300091. i) q^{42} +(-1.68237e6 + 1.68237e6i) q^{43} +(-6.40694e6 - 1.51073e6i) q^{44} +(1.38507e6 - 1.38507e6i) q^{45} +(5.62071e6 + 3.13280e6i) q^{46} +4.76508e6i q^{47} +(-2.90704e6 + 970680. i) q^{48} -5.59096e6 q^{49} +(-3.20595e6 + 5.75195e6i) q^{50} +(1.27544e6 + 1.27544e6i) q^{51} +(-1.12711e7 - 2.65767e6i) q^{52} +(6.94700e6 + 6.94700e6i) q^{53} +(-1.57407e6 + 447380. i) q^{54} +2.30303e7 q^{55} +(-77422.8 - 1.70604e6i) q^{56} -7.32225e6i q^{57} +(-3.51130e6 + 997976. i) q^{58} +(-2.99285e6 + 2.99285e6i) q^{59} +(9.11980e6 - 5.63960e6i) q^{60} +(1.22473e7 - 1.22473e7i) q^{61} +(1.16178e7 - 2.08440e7i) q^{62} -911854. i q^{63} +(-1.67083e7 + 1.51962e6i) q^{64} +4.05148e7 q^{65} +(-1.68058e7 - 9.36703e6i) q^{66} +(2.26628e6 + 2.26628e6i) q^{67} +(5.19321e6 + 8.39795e6i) q^{68} +(1.32992e7 + 1.32992e7i) q^{69} +(1.63350e6 + 5.74734e6i) q^{70} +6.83501e6 q^{71} +(-8.94874e6 + 406108. i) q^{72} +2.36939e7i q^{73} +(1.24954e7 + 4.39642e7i) q^{74} +(-1.36097e7 + 1.36097e7i) q^{75} +(9.19912e6 - 3.90131e7i) q^{76} +(7.58093e6 - 7.58093e6i) q^{77} +(-2.95648e7 - 1.64784e7i) q^{78} -4.91999e6i q^{79} +(5.56757e7 - 1.85905e7i) q^{80} -4.78297e6 q^{81} +(5.24298e6 - 9.40668e6i) q^{82} +(3.44710e6 + 3.44710e6i) q^{83} +(1.14558e6 - 4.85838e6i) q^{84} +(-2.44273e7 - 2.44273e7i) q^{85} +(-3.66174e7 + 1.04073e7i) q^{86} -1.06694e7 q^{87} +(-7.77739e7 - 7.10213e7i) q^{88} -7.21985e6i q^{89} +(3.01466e7 - 8.56823e6i) q^{90} +(1.33363e7 - 1.33363e7i) q^{91} +(5.41503e7 + 8.75666e7i) q^{92} +(4.93191e7 - 4.93191e7i) q^{93} +(-3.71182e7 + 6.65956e7i) q^{94} +1.40236e8i q^{95} +(-4.81893e7 - 9.07877e6i) q^{96} -7.27214e7 q^{97} +(-7.81379e7 - 4.35515e7i) q^{98} +(-3.97644e7 - 3.97644e7i) 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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