LMFDB - Embedded newform 8007.2.a.f.1.44

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.a (trivial)

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:	yes
Analytic conductor:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$48$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.44
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.38551 q^{2} -1.00000 q^{3} +3.69065 q^{4} -1.70497 q^{5} -2.38551 q^{6} +3.54946 q^{7} +4.03306 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.38551 q^{2} -1.00000 q^{3} +3.69065 q^{4} -1.70497 q^{5} -2.38551 q^{6} +3.54946 q^{7} +4.03306 q^{8} +1.00000 q^{9} -4.06723 q^{10} +1.77305 q^{11} -3.69065 q^{12} -3.57101 q^{13} +8.46726 q^{14} +1.70497 q^{15} +2.23960 q^{16} -1.00000 q^{17} +2.38551 q^{18} -2.97373 q^{19} -6.29246 q^{20} -3.54946 q^{21} +4.22961 q^{22} -9.54123 q^{23} -4.03306 q^{24} -2.09307 q^{25} -8.51867 q^{26} -1.00000 q^{27} +13.0998 q^{28} -2.09288 q^{29} +4.06723 q^{30} +3.69825 q^{31} -2.72353 q^{32} -1.77305 q^{33} -2.38551 q^{34} -6.05173 q^{35} +3.69065 q^{36} -3.61193 q^{37} -7.09385 q^{38} +3.57101 q^{39} -6.87626 q^{40} -1.21726 q^{41} -8.46726 q^{42} -2.45179 q^{43} +6.54369 q^{44} -1.70497 q^{45} -22.7607 q^{46} -5.08516 q^{47} -2.23960 q^{48} +5.59865 q^{49} -4.99303 q^{50} +1.00000 q^{51} -13.1793 q^{52} +3.39762 q^{53} -2.38551 q^{54} -3.02299 q^{55} +14.3152 q^{56} +2.97373 q^{57} -4.99259 q^{58} -1.11134 q^{59} +6.29246 q^{60} +4.38285 q^{61} +8.82221 q^{62} +3.54946 q^{63} -10.9762 q^{64} +6.08847 q^{65} -4.22961 q^{66} -7.67085 q^{67} -3.69065 q^{68} +9.54123 q^{69} -14.4364 q^{70} +1.07669 q^{71} +4.03306 q^{72} -8.02295 q^{73} -8.61628 q^{74} +2.09307 q^{75} -10.9750 q^{76} +6.29335 q^{77} +8.51867 q^{78} +0.700468 q^{79} -3.81846 q^{80} +1.00000 q^{81} -2.90379 q^{82} +8.64683 q^{83} -13.0998 q^{84} +1.70497 q^{85} -5.84878 q^{86} +2.09288 q^{87} +7.15080 q^{88} +8.82373 q^{89} -4.06723 q^{90} -12.6751 q^{91} -35.2133 q^{92} -3.69825 q^{93} -12.1307 q^{94} +5.07012 q^{95} +2.72353 q^{96} -19.2592 q^{97} +13.3556 q^{98} +1.77305 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9}+O(q^{10}) $ 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9} - 20 q^{10} + 5 q^{11} - 45 q^{12} - 8 q^{13} + 4 q^{14} - q^{15} + 39 q^{16} - 48 q^{17} - q^{18} - 6 q^{19} + 6 q^{20} + 13 q^{21} - 35 q^{22} - 8 q^{23} + 6 q^{24} + 13 q^{25} + 17 q^{26} - 48 q^{27} - 38 q^{28} + q^{29} + 20 q^{30} - 21 q^{31} - 3 q^{32} - 5 q^{33} + q^{34} + 19 q^{35} + 45 q^{36} - 58 q^{37} - 14 q^{38} + 8 q^{39} - 54 q^{40} - 3 q^{41} - 4 q^{42} - 33 q^{43} + 2 q^{44} + q^{45} - 26 q^{46} + 9 q^{47} - 39 q^{48} + 11 q^{49} + 4 q^{50} + 48 q^{51} - 31 q^{52} - 33 q^{53} + q^{54} - 21 q^{55} + 6 q^{57} - 55 q^{58} + 77 q^{59} - 6 q^{60} - 29 q^{61} - 46 q^{62} - 13 q^{63} + 24 q^{64} - 49 q^{65} + 35 q^{66} - 44 q^{67} - 45 q^{68} + 8 q^{69} + 4 q^{70} + 22 q^{71} - 6 q^{72} - 63 q^{73} - 16 q^{74} - 13 q^{75} - 46 q^{76} - 30 q^{77} - 17 q^{78} - 46 q^{79} - 14 q^{80} + 48 q^{81} - 75 q^{82} + 11 q^{83} + 38 q^{84} - q^{85} + 8 q^{86} - q^{87} - 116 q^{88} + 10 q^{89} - 20 q^{90} - 67 q^{91} - 64 q^{92} + 21 q^{93} - 16 q^{94} - 8 q^{95} + 3 q^{96} - 96 q^{97} - 46 q^{98} + 5 q^{99}+O(q^{100}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9 - 20 * q^10 + 5 * q^11 - 45 * q^12 - 8 * q^13 + 4 * q^14 - q^15 + 39 * q^16 - 48 * q^17 - q^18 - 6 * q^19 + 6 * q^20 + 13 * q^21 - 35 * q^22 - 8 * q^23 + 6 * q^24 + 13 * q^25 + 17 * q^26 - 48 * q^27 - 38 * q^28 + q^29 + 20 * q^30 - 21 * q^31 - 3 * q^32 - 5 * q^33 + q^34 + 19 * q^35 + 45 * q^36 - 58 * q^37 - 14 * q^38 + 8 * q^39 - 54 * q^40 - 3 * q^41 - 4 * q^42 - 33 * q^43 + 2 * q^44 + q^45 - 26 * q^46 + 9 * q^47 - 39 * q^48 + 11 * q^49 + 4 * q^50 + 48 * q^51 - 31 * q^52 - 33 * q^53 + q^54 - 21 * q^55 + 6 * q^57 - 55 * q^58 + 77 * q^59 - 6 * q^60 - 29 * q^61 - 46 * q^62 - 13 * q^63 + 24 * q^64 - 49 * q^65 + 35 * q^66 - 44 * q^67 - 45 * q^68 + 8 * q^69 + 4 * q^70 + 22 * q^71 - 6 * q^72 - 63 * q^73 - 16 * q^74 - 13 * q^75 - 46 * q^76 - 30 * q^77 - 17 * q^78 - 46 * q^79 - 14 * q^80 + 48 * q^81 - 75 * q^82 + 11 * q^83 + 38 * q^84 - q^85 + 8 * q^86 - q^87 - 116 * q^88 + 10 * q^89 - 20 * q^90 - 67 * q^91 - 64 * q^92 + 21 * q^93 - 16 * q^94 - 8 * q^95 + 3 * q^96 - 96 * q^97 - 46 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.38551	1.68681	0.843405	−	0.537279i	$-0.180548\pi$
$2$	2.38551	1.68681	0.843405	+	0.537279i	$0.180548\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.69065	1.84533
$5$	−1.70497	−0.762487	−0.381243	−	0.924475i	$-0.624504\pi$
$5$	−1.70497	−0.762487	−0.381243	+	0.924475i	$0.624504\pi$
$6$	−2.38551	−0.973880
$7$	3.54946	1.34157	0.670784	−	0.741652i	$-0.265958\pi$
$7$	3.54946	1.34157	0.670784	+	0.741652i	$0.265958\pi$
$8$	4.03306	1.42590
$9$	1.00000	0.333333
$10$	−4.06723	−1.28617
$11$	1.77305	0.534593	0.267297	−	0.963614i	$-0.413870\pi$
$11$	1.77305	0.534593	0.267297	+	0.963614i	$0.413870\pi$
$12$	−3.69065	−1.06540
$13$	−3.57101	−0.990419	−0.495210	−	0.868773i	$-0.664909\pi$
$13$	−3.57101	−0.990419	−0.495210	+	0.868773i	$0.664909\pi$
$14$	8.46726	2.26297
$15$	1.70497	0.440222
$16$	2.23960	0.559901
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.38551	0.562270
$19$	−2.97373	−0.682220	−0.341110	−	0.940023i	$-0.610803\pi$
$19$	−2.97373	−0.682220	−0.341110	+	0.940023i	$0.610803\pi$
$20$	−6.29246	−1.40704
$21$	−3.54946	−0.774555
$22$	4.22961	0.901757
$23$	−9.54123	−1.98948	−0.994742	−	0.102417i	$-0.967342\pi$
$23$	−9.54123	−1.98948	−0.994742	+	0.102417i	$0.967342\pi$
$24$	−4.03306	−0.823245
$25$	−2.09307	−0.418614
$26$	−8.51867	−1.67065
$27$	−1.00000	−0.192450
$28$	13.0998	2.47563
$29$	−2.09288	−0.388639	−0.194319	−	0.980938i	$-0.562250\pi$
$29$	−2.09288	−0.388639	−0.194319	+	0.980938i	$0.562250\pi$
$30$	4.06723	0.742570
$31$	3.69825	0.664226	0.332113	−	0.943240i	$-0.392239\pi$
$31$	3.69825	0.664226	0.332113	+	0.943240i	$0.392239\pi$
$32$	−2.72353	−0.481457
$33$	−1.77305	−0.308648
$34$	−2.38551	−0.409111
$35$	−6.05173	−1.02293
$36$	3.69065	0.615108
$37$	−3.61193	−0.593797	−0.296898	−	0.954909i	$-0.595952\pi$
$37$	−3.61193	−0.593797	−0.296898	+	0.954909i	$0.595952\pi$
$38$	−7.09385	−1.15077
$39$	3.57101	0.571819
$40$	−6.87626	−1.08723
$41$	−1.21726	−0.190105	−0.0950523	−	0.995472i	$-0.530302\pi$
$41$	−1.21726	−0.190105	−0.0950523	+	0.995472i	$0.530302\pi$
$42$	−8.46726	−1.30653
$43$	−2.45179	−0.373895	−0.186948	−	0.982370i	$-0.559859\pi$
$43$	−2.45179	−0.373895	−0.186948	+	0.982370i	$0.559859\pi$
$44$	6.54369	0.986499
$45$	−1.70497	−0.254162
$46$	−22.7607	−3.35588
$47$	−5.08516	−0.741747	−0.370873	−	0.928683i	$-0.620942\pi$
$47$	−5.08516	−0.741747	−0.370873	+	0.928683i	$0.620942\pi$
$48$	−2.23960	−0.323259
$49$	5.59865	0.799807
$50$	−4.99303	−0.706122
$51$	1.00000	0.140028
$52$	−13.1793	−1.82765
$53$	3.39762	0.466699	0.233349	−	0.972393i	$-0.425031\pi$
$53$	3.39762	0.466699	0.233349	+	0.972393i	$0.425031\pi$
$54$	−2.38551	−0.324627
$55$	−3.02299	−0.407620
$56$	14.3152	1.91295
$57$	2.97373	0.393880
$58$	−4.99259	−0.655560
$59$	−1.11134	−0.144685	−0.0723423	−	0.997380i	$-0.523047\pi$
$59$	−1.11134	−0.144685	−0.0723423	+	0.997380i	$0.523047\pi$
$60$	6.29246	0.812353
$61$	4.38285	0.561167	0.280583	−	0.959830i	$-0.409472\pi$
$61$	4.38285	0.561167	0.280583	+	0.959830i	$0.409472\pi$
$62$	8.82221	1.12042
$63$	3.54946	0.447190
$64$	−10.9762	−1.37203
$65$	6.08847	0.755182
$66$	−4.22961	−0.520630
$67$	−7.67085	−0.937144	−0.468572	−	0.883425i	$-0.655231\pi$
$67$	−7.67085	−0.937144	−0.468572	+	0.883425i	$0.655231\pi$
$68$	−3.69065	−0.447557
$69$	9.54123	1.14863
$70$	−14.4364	−1.72549
$71$	1.07669	0.127779	0.0638895	−	0.997957i	$-0.479649\pi$
$71$	1.07669	0.127779	0.0638895	+	0.997957i	$0.479649\pi$
$72$	4.03306	0.475301
$73$	−8.02295	−0.939015	−0.469508	−	0.882928i	$-0.655569\pi$
$73$	−8.02295	−0.939015	−0.469508	+	0.882928i	$0.655569\pi$
$74$	−8.61628	−1.00162
$75$	2.09307	0.241687
$76$	−10.9750	−1.25892
$77$	6.29335	0.717194
$78$	8.51867	0.964549
$79$	0.700468	0.0788088	0.0394044	−	0.999223i	$-0.487454\pi$
$79$	0.700468	0.0788088	0.0394044	+	0.999223i	$0.487454\pi$
$80$	−3.81846	−0.426917
$81$	1.00000	0.111111
$82$	−2.90379	−0.320670
$83$	8.64683	0.949113	0.474557	−	0.880225i	$-0.342608\pi$
$83$	8.64683	0.949113	0.474557	+	0.880225i	$0.342608\pi$
$84$	−13.0998	−1.42931
$85$	1.70497	0.184930
$86$	−5.84878	−0.630690
$87$	2.09288	0.224381
$88$	7.15080	0.762278
$89$	8.82373	0.935314	0.467657	−	0.883910i	$-0.345098\pi$
$89$	8.82373	0.935314	0.467657	+	0.883910i	$0.345098\pi$
$90$	−4.06723	−0.428723
$91$	−12.6751	−1.32872
$92$	−35.2133	−3.67124
$93$	−3.69825	−0.383491
$94$	−12.1307	−1.25119
$95$	5.07012	0.520183
$96$	2.72353	0.277970
$97$	−19.2592	−1.95548	−0.977738	−	0.209831i	$-0.932709\pi$
$97$	−19.2592	−1.95548	−0.977738	+	0.209831i	$0.932709\pi$
$98$	13.3556	1.34912
$99$	1.77305	0.178198
$100$	−7.72479	−0.772479
$101$	−5.15830	−0.513270	−0.256635	−	0.966508i	$-0.582614\pi$
$101$	−5.15830	−0.513270	−0.256635	+	0.966508i	$0.582614\pi$
$102$	2.38551	0.236201
$103$	18.7119	1.84374	0.921870	−	0.387500i	$-0.126661\pi$
$103$	18.7119	1.84374	0.921870	+	0.387500i	$0.126661\pi$
$104$	−14.4021	−1.41224
$105$	6.05173	0.590588
$106$	8.10505	0.787232
$107$	−6.27139	−0.606278	−0.303139	−	0.952946i	$-0.598035\pi$
$107$	−6.27139	−0.606278	−0.303139	+	0.952946i	$0.598035\pi$
$108$	−3.69065	−0.355133
$109$	−20.0664	−1.92201	−0.961006	−	0.276529i	$-0.910816\pi$
$109$	−20.0664	−1.92201	−0.961006	+	0.276529i	$0.910816\pi$
$110$	−7.21138	−0.687578
$111$	3.61193	0.342829
$112$	7.94937	0.751145
$113$	17.2022	1.61825	0.809125	−	0.587636i	$-0.199941\pi$
$113$	17.2022	1.61825	0.809125	+	0.587636i	$0.199941\pi$
$114$	7.09385	0.664400
$115$	16.2675	1.51695
$116$	−7.72411	−0.717165
$117$	−3.57101	−0.330140
$118$	−2.65112	−0.244055
$119$	−3.54946	−0.325378
$120$	6.87626	0.627714
$121$	−7.85631	−0.714210
$122$	10.4553	0.946581
$123$	1.21726	0.109757
$124$	13.6490	1.22571
$125$	12.0935	1.08167
$126$	8.46726	0.754324
$127$	−1.55436	−0.137927	−0.0689637	−	0.997619i	$-0.521969\pi$
$127$	−1.55436	−0.137927	−0.0689637	+	0.997619i	$0.521969\pi$
$128$	−20.7368	−1.83289
$129$	2.45179	0.215868
$130$	14.5241	1.27385
$131$	13.3128	1.16315	0.581574	−	0.813494i	$-0.302437\pi$
$131$	13.3128	1.16315	0.581574	+	0.813494i	$0.302437\pi$
$132$	−6.54369	−0.569555
$133$	−10.5551	−0.915245
$134$	−18.2989	−1.58078
$135$	1.70497	0.146741
$136$	−4.03306	−0.345832
$137$	10.3314	0.882670	0.441335	−	0.897342i	$-0.354505\pi$
$137$	10.3314	0.882670	0.441335	+	0.897342i	$0.354505\pi$
$138$	22.7607	1.93752
$139$	16.3890	1.39010	0.695049	−	0.718962i	$-0.255383\pi$
$139$	16.3890	1.39010	0.695049	+	0.718962i	$0.255383\pi$
$140$	−22.3348	−1.88764
$141$	5.08516	0.428248
$142$	2.56844	0.215539
$143$	−6.33156	−0.529472
$144$	2.23960	0.186634
$145$	3.56831	0.296332
$146$	−19.1388	−1.58394
$147$	−5.59865	−0.461769
$148$	−13.3304	−1.09575
$149$	4.58577	0.375681	0.187840	−	0.982200i	$-0.439851\pi$
$149$	4.58577	0.375681	0.187840	+	0.982200i	$0.439851\pi$
$150$	4.99303	0.407680
$151$	−14.6053	−1.18856	−0.594280	−	0.804258i	$-0.702563\pi$
$151$	−14.6053	−1.18856	−0.594280	+	0.804258i	$0.702563\pi$
$152$	−11.9932	−0.972779
$153$	−1.00000	−0.0808452
$154$	15.0128	1.20977
$155$	−6.30542	−0.506463
$156$	13.1793	1.05519
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	1.67097	0.132935
$159$	−3.39762	−0.269449
$160$	4.64355	0.367105
$161$	−33.8662	−2.66903
$162$	2.38551	0.187423
$163$	5.03718	0.394542	0.197271	−	0.980349i	$-0.436792\pi$
$163$	5.03718	0.394542	0.197271	+	0.980349i	$0.436792\pi$
$164$	−4.49249	−0.350805
$165$	3.02299	0.235340
$166$	20.6271	1.60097
$167$	−13.9889	−1.08249	−0.541247	−	0.840863i	$-0.682048\pi$
$167$	−13.9889	−1.08249	−0.541247	+	0.840863i	$0.682048\pi$
$168$	−14.3152	−1.10444
$169$	−0.247902	−0.0190694
$170$	4.06723	0.311942
$171$	−2.97373	−0.227407
$172$	−9.04872	−0.689958
$173$	9.10778	0.692452	0.346226	−	0.938151i	$-0.387463\pi$
$173$	9.10778	0.692452	0.346226	+	0.938151i	$0.387463\pi$
$174$	4.99259	0.378488
$175$	−7.42926	−0.561599
$176$	3.97092	0.299319
$177$	1.11134	0.0835337
$178$	21.0491	1.57770
$179$	13.0024	0.971845	0.485922	−	0.874002i	$-0.338484\pi$
$179$	13.0024	0.971845	0.485922	+	0.874002i	$0.338484\pi$
$180$	−6.29246	−0.469012
$181$	−4.06356	−0.302042	−0.151021	−	0.988531i	$-0.548256\pi$
$181$	−4.06356	−0.302042	−0.151021	+	0.988531i	$0.548256\pi$
$182$	−30.2367	−2.24129
$183$	−4.38285	−0.323990
$184$	−38.4804	−2.83681
$185$	6.15823	0.452762
$186$	−8.82221	−0.646876
$187$	−1.77305	−0.129658
$188$	−18.7675	−1.36876
$189$	−3.54946	−0.258185
$190$	12.0948	0.877450
$191$	−16.1191	−1.16634	−0.583168	−	0.812351i	$-0.698187\pi$
$191$	−16.1191	−1.16634	−0.583168	+	0.812351i	$0.698187\pi$
$192$	10.9762	0.792140
$193$	−13.1424	−0.946008	−0.473004	−	0.881060i	$-0.656830\pi$
$193$	−13.1424	−0.946008	−0.473004	+	0.881060i	$0.656830\pi$
$194$	−45.9430	−3.29851
$195$	−6.08847	−0.436004
$196$	20.6627	1.47590
$197$	15.3852	1.09615	0.548075	−	0.836429i	$-0.315361\pi$
$197$	15.3852	1.09615	0.548075	+	0.836429i	$0.315361\pi$
$198$	4.22961	0.300586
$199$	−15.5015	−1.09888	−0.549438	−	0.835535i	$-0.685158\pi$
$199$	−15.5015	−1.09888	−0.549438	+	0.835535i	$0.685158\pi$
$200$	−8.44148	−0.596903
$201$	7.67085	0.541060
$202$	−12.3052	−0.865788
$203$	−7.42860	−0.521386
$204$	3.69065	0.258397
$205$	2.07540	0.144952
$206$	44.6374	3.11004
$207$	−9.54123	−0.663161
$208$	−7.99764	−0.554536
$209$	−5.27255	−0.364710
$210$	14.4364	0.996209
$211$	−3.80749	−0.262119	−0.131059	−	0.991375i	$-0.541838\pi$
$211$	−3.80749	−0.262119	−0.131059	+	0.991375i	$0.541838\pi$
$212$	12.5394	0.861211
$213$	−1.07669	−0.0737733
$214$	−14.9605	−1.02268
$215$	4.18024	0.285090
$216$	−4.03306	−0.274415
$217$	13.1268	0.891104
$218$	−47.8685	−3.24207
$219$	8.02295	0.542141
$220$	−11.1568	−0.752192
$221$	3.57101	0.240212
$222$	8.61628	0.578287
$223$	21.5201	1.44109	0.720547	−	0.693406i	$-0.243891\pi$
$223$	21.5201	1.44109	0.720547	+	0.693406i	$0.243891\pi$
$224$	−9.66707	−0.645908
$225$	−2.09307	−0.139538
$226$	41.0361	2.72968
$227$	−12.1500	−0.806423	−0.403212	−	0.915107i	$-0.632106\pi$
$227$	−12.1500	−0.806423	−0.403212	+	0.915107i	$0.632106\pi$
$228$	10.9750	0.726836
$229$	29.2181	1.93078	0.965392	−	0.260804i	$-0.0839875\pi$
$229$	29.2181	1.93078	0.965392	+	0.260804i	$0.0839875\pi$
$230$	38.8063	2.55881
$231$	−6.29335	−0.414072
$232$	−8.44073	−0.554161
$233$	−16.9434	−1.11000	−0.554999	−	0.831851i	$-0.687281\pi$
$233$	−16.9434	−1.11000	−0.554999	+	0.831851i	$0.687281\pi$
$234$	−8.51867	−0.556883
$235$	8.67006	0.565572
$236$	−4.10158	−0.266990
$237$	−0.700468	−0.0455003
$238$	−8.46726	−0.548851
$239$	−24.3448	−1.57474	−0.787368	−	0.616483i	$-0.788557\pi$
$239$	−24.3448	−1.57474	−0.787368	+	0.616483i	$0.788557\pi$
$240$	3.81846	0.246480
$241$	2.56042	0.164931	0.0824657	−	0.996594i	$-0.473720\pi$
$241$	2.56042	0.164931	0.0824657	+	0.996594i	$0.473720\pi$
$242$	−18.7413	−1.20474
$243$	−1.00000	−0.0641500
$244$	16.1756	1.03553
$245$	−9.54554	−0.609842
$246$	2.90379	0.185139
$247$	10.6192	0.675684
$248$	14.9153	0.947121
$249$	−8.64683	−0.547971
$250$	28.8491	1.82458
$251$	−18.2472	−1.15175	−0.575876	−	0.817537i	$-0.695339\pi$
$251$	−18.2472	−1.15175	−0.575876	+	0.817537i	$0.695339\pi$
$252$	13.0998	0.825210
$253$	−16.9170	−1.06356
$254$	−3.70795	−0.232657
$255$	−1.70497	−0.106770
$256$	−27.5154	−1.71971
$257$	6.42815	0.400977	0.200488	−	0.979696i	$-0.435747\pi$
$257$	6.42815	0.400977	0.200488	+	0.979696i	$0.435747\pi$
$258$	5.84878	0.364129
$259$	−12.8204	−0.796619
$260$	22.4704	1.39356
$261$	−2.09288	−0.129546
$262$	31.7579	1.96201
$263$	10.3439	0.637830	0.318915	−	0.947783i	$-0.396682\pi$
$263$	10.3439	0.637830	0.318915	+	0.947783i	$0.396682\pi$
$264$	−7.15080	−0.440101
$265$	−5.79285	−0.355852
$266$	−25.1793	−1.54384
$267$	−8.82373	−0.540004
$268$	−28.3104	−1.72934
$269$	3.22110	0.196394	0.0981970	−	0.995167i	$-0.468692\pi$
$269$	3.22110	0.196394	0.0981970	+	0.995167i	$0.468692\pi$
$270$	4.06723	0.247523
$271$	8.40771	0.510732	0.255366	−	0.966844i	$-0.417804\pi$
$271$	8.40771	0.510732	0.255366	+	0.966844i	$0.417804\pi$
$272$	−2.23960	−0.135796
$273$	12.6751	0.767134
$274$	24.6456	1.48890
$275$	−3.71111	−0.223788
$276$	35.2133	2.11959
$277$	−20.6339	−1.23977	−0.619885	−	0.784693i	$-0.712821\pi$
$277$	−20.6339	−1.23977	−0.619885	+	0.784693i	$0.712821\pi$
$278$	39.0961	2.34483
$279$	3.69825	0.221409
$280$	−24.4070	−1.45860
$281$	16.6593	0.993812	0.496906	−	0.867804i	$-0.334469\pi$
$281$	16.6593	0.993812	0.496906	+	0.867804i	$0.334469\pi$
$282$	12.1307	0.722372
$283$	−7.82793	−0.465322	−0.232661	−	0.972558i	$-0.574743\pi$
$283$	−7.82793	−0.465322	−0.232661	+	0.972558i	$0.574743\pi$
$284$	3.97367	0.235794
$285$	−5.07012	−0.300328
$286$	−15.1040	−0.893118
$287$	−4.32062	−0.255038
$288$	−2.72353	−0.160486
$289$	1.00000	0.0588235
$290$	8.51223	0.499856
$291$	19.2592	1.12899
$292$	−29.6099	−1.73279
$293$	4.88097	0.285149	0.142575	−	0.989784i	$-0.454462\pi$
$293$	4.88097	0.285149	0.142575	+	0.989784i	$0.454462\pi$
$294$	−13.3556	−0.778916
$295$	1.89481	0.110320
$296$	−14.5671	−0.846697
$297$	−1.77305	−0.102883
$298$	10.9394	0.633702
$299$	34.0718	1.97042
$300$	7.72479	0.445991
$301$	−8.70254	−0.501606
$302$	−34.8410	−2.00488
$303$	5.15830	0.296336
$304$	−6.65996	−0.381975
$305$	−7.47264	−0.427882
$306$	−2.38551	−0.136370
$307$	−10.3444	−0.590389	−0.295194	−	0.955437i	$-0.595384\pi$
$307$	−10.3444	−0.590389	−0.295194	+	0.955437i	$0.595384\pi$
$308$	23.2266	1.32346
$309$	−18.7119	−1.06448
$310$	−15.0416	−0.854307
$311$	12.0298	0.682146	0.341073	−	0.940037i	$-0.389210\pi$
$311$	12.0298	0.682146	0.341073	+	0.940037i	$0.389210\pi$
$312$	14.4021	0.815358
$313$	−21.9162	−1.23878	−0.619389	−	0.785085i	$-0.712619\pi$
$313$	−21.9162	−1.23878	−0.619389	+	0.785085i	$0.712619\pi$
$314$	−2.38551	−0.134622
$315$	−6.05173	−0.340976
$316$	2.58518	0.145428
$317$	−14.7341	−0.827547	−0.413773	−	0.910380i	$-0.635789\pi$
$317$	−14.7341	−0.827547	−0.413773	+	0.910380i	$0.635789\pi$
$318$	−8.10505	−0.454509
$319$	−3.71078	−0.207764
$320$	18.7141	1.04615
$321$	6.27139	0.350035
$322$	−80.7880	−4.50214
$323$	2.97373	0.165463
$324$	3.69065	0.205036
$325$	7.47437	0.414603
$326$	12.0162	0.665518
$327$	20.0664	1.10967
$328$	−4.90930	−0.271071
$329$	−18.0496	−0.995104
$330$	7.21138	0.396973
$331$	−17.9044	−0.984116	−0.492058	−	0.870562i	$-0.663755\pi$
$331$	−17.9044	−0.984116	−0.492058	+	0.870562i	$0.663755\pi$
$332$	31.9124	1.75142
$333$	−3.61193	−0.197932
$334$	−33.3707	−1.82596
$335$	13.0786	0.714560
$336$	−7.94937	−0.433674
$337$	−4.44466	−0.242116	−0.121058	−	0.992645i	$-0.538629\pi$
$337$	−4.44466	−0.242116	−0.121058	+	0.992645i	$0.538629\pi$
$338$	−0.591373	−0.0321665
$339$	−17.2022	−0.934297
$340$	6.29246	0.341256
$341$	6.55717	0.355091
$342$	−7.09385	−0.383591
$343$	−4.97404	−0.268573
$344$	−9.88824	−0.533138
$345$	−16.2675	−0.875814
$346$	21.7267	1.16803
$347$	−23.1104	−1.24063	−0.620316	−	0.784352i	$-0.712996\pi$
$347$	−23.1104	−1.24063	−0.620316	+	0.784352i	$0.712996\pi$
$348$	7.72411	0.414056
$349$	3.77827	0.202246	0.101123	−	0.994874i	$-0.467756\pi$
$349$	3.77827	0.202246	0.101123	+	0.994874i	$0.467756\pi$
$350$	−17.7226	−0.947311
$351$	3.57101	0.190606
$352$	−4.82895	−0.257384
$353$	−10.2795	−0.547123	−0.273561	−	0.961855i	$-0.588202\pi$
$353$	−10.2795	−0.547123	−0.273561	+	0.961855i	$0.588202\pi$
$354$	2.65112	0.140905
$355$	−1.83572	−0.0974299
$356$	32.5653	1.72596
$357$	3.54946	0.187857
$358$	31.0173	1.63932
$359$	−20.0306	−1.05717	−0.528587	−	0.848879i	$-0.677278\pi$
$359$	−20.0306	−1.05717	−0.528587	+	0.848879i	$0.677278\pi$
$360$	−6.87626	−0.362411
$361$	−10.1570	−0.534576
$362$	−9.69367	−0.509488
$363$	7.85631	0.412349
$364$	−46.7795	−2.45191
$365$	13.6789	0.715987
$366$	−10.4553	−0.546509
$367$	−11.1774	−0.583456	−0.291728	−	0.956501i	$-0.594230\pi$
$367$	−11.1774	−0.583456	−0.291728	+	0.956501i	$0.594230\pi$
$368$	−21.3685	−1.11391
$369$	−1.21726	−0.0633682
$370$	14.6905	0.763724
$371$	12.0597	0.626109
$372$	−13.6490	−0.707665
$373$	17.3225	0.896923	0.448462	−	0.893802i	$-0.351972\pi$
$373$	17.3225	0.896923	0.448462	+	0.893802i	$0.351972\pi$
$374$	−4.22961	−0.218708
$375$	−12.0935	−0.624505
$376$	−20.5088	−1.05766
$377$	7.47371	0.384916
$378$	−8.46726	−0.435509
$379$	−2.96921	−0.152518	−0.0762590	−	0.997088i	$-0.524298\pi$
$379$	−2.96921	−0.152518	−0.0762590	+	0.997088i	$0.524298\pi$
$380$	18.7120	0.959908
$381$	1.55436	0.0796325
$382$	−38.4522	−1.96739
$383$	−9.07459	−0.463690	−0.231845	−	0.972753i	$-0.574476\pi$
$383$	−9.07459	−0.463690	−0.231845	+	0.972753i	$0.574476\pi$
$384$	20.7368	1.05822
$385$	−10.7300	−0.546851
$386$	−31.3512	−1.59574
$387$	−2.45179	−0.124632
$388$	−71.0790	−3.60849
$389$	27.0056	1.36924	0.684619	−	0.728901i	$-0.259969\pi$
$389$	27.0056	1.36924	0.684619	+	0.728901i	$0.259969\pi$
$390$	−14.5241	−0.735456
$391$	9.54123	0.482521
$392$	22.5797	1.14045
$393$	−13.3128	−0.671543
$394$	36.7015	1.84899
$395$	−1.19428	−0.0600907
$396$	6.54369	0.328833
$397$	8.15106	0.409090	0.204545	−	0.978857i	$-0.434428\pi$
$397$	8.15106	0.409090	0.204545	+	0.978857i	$0.434428\pi$
$398$	−36.9791	−1.85359
$399$	10.5551	0.528417
$400$	−4.68764	−0.234382
$401$	4.37982	0.218718	0.109359	−	0.994002i	$-0.465120\pi$
$401$	4.37982	0.218718	0.109359	+	0.994002i	$0.465120\pi$
$402$	18.2989	0.912665
$403$	−13.2065	−0.657862
$404$	−19.0375	−0.947149
$405$	−1.70497	−0.0847208
$406$	−17.7210	−0.879478
$407$	−6.40411	−0.317440
$408$	4.03306	0.199666
$409$	13.1244	0.648958	0.324479	−	0.945893i	$-0.394811\pi$
$409$	13.1244	0.648958	0.324479	+	0.945893i	$0.394811\pi$
$410$	4.95088	0.244507
$411$	−10.3314	−0.509610
$412$	69.0591	3.40230
$413$	−3.94467	−0.194104
$414$	−22.7607	−1.11863
$415$	−14.7426	−0.723686
$416$	9.72576	0.476845
$417$	−16.3890	−0.802574
$418$	−12.5777	−0.615196
$419$	22.2969	1.08927	0.544637	−	0.838672i	$-0.316667\pi$
$419$	22.2969	1.08927	0.544637	+	0.838672i	$0.316667\pi$
$420$	22.3348	1.08983
$421$	15.3130	0.746308	0.373154	−	0.927769i	$-0.378276\pi$
$421$	15.3130	0.746308	0.373154	+	0.927769i	$0.378276\pi$
$422$	−9.08281	−0.442144
$423$	−5.08516	−0.247249
$424$	13.7028	0.665467
$425$	2.09307	0.101529
$426$	−2.56844	−0.124441
$427$	15.5567	0.752843
$428$	−23.1455	−1.11878
$429$	6.33156	0.305691
$430$	9.97200	0.480893
$431$	8.59089	0.413809	0.206904	−	0.978361i	$-0.433661\pi$
$431$	8.59089	0.413809	0.206904	+	0.978361i	$0.433661\pi$
$432$	−2.23960	−0.107753
$433$	−27.5537	−1.32415	−0.662073	−	0.749439i	$-0.730323\pi$
$433$	−27.5537	−1.32415	−0.662073	+	0.749439i	$0.730323\pi$
$434$	31.3141	1.50312
$435$	−3.56831	−0.171087
$436$	−74.0580	−3.54674
$437$	28.3730	1.35726
$438$	19.1388	0.914488
$439$	−17.7187	−0.845670	−0.422835	−	0.906207i	$-0.638965\pi$
$439$	−17.7187	−0.845670	−0.422835	+	0.906207i	$0.638965\pi$
$440$	−12.1919	−0.581227
$441$	5.59865	0.266602
$442$	8.51867	0.405192
$443$	0.00601453	0.000285759 0	0.000142879	−	1.00000i	$-0.499955\pi$
$443$	0.00601453	0.000285759 0	0.000142879		1.00000i	$0.499955\pi$
$444$	13.3304	0.632631
$445$	−15.0442	−0.713165
$446$	51.3364	2.43085
$447$	−4.58577	−0.216899
$448$	−38.9596	−1.84067
$449$	−20.4710	−0.966088	−0.483044	−	0.875596i	$-0.660469\pi$
$449$	−20.4710	−0.966088	−0.483044	+	0.875596i	$0.660469\pi$
$450$	−4.99303	−0.235374
$451$	−2.15826	−0.101629
$452$	63.4875	2.98620
$453$	14.6053	0.686216
$454$	−28.9839	−1.36028
$455$	21.6108	1.01313
$456$	11.9932	0.561634
$457$	17.3731	0.812678	0.406339	−	0.913722i	$-0.366805\pi$
$457$	17.3731	0.812678	0.406339	+	0.913722i	$0.366805\pi$
$458$	69.6999	3.25686
$459$	1.00000	0.0466760
$460$	60.0378	2.79927
$461$	12.9555	0.603396	0.301698	−	0.953404i	$-0.402447\pi$
$461$	12.9555	0.603396	0.301698	+	0.953404i	$0.402447\pi$
$462$	−15.0128	−0.698460
$463$	−35.9451	−1.67051	−0.835255	−	0.549862i	$-0.814680\pi$
$463$	−35.9451	−1.67051	−0.835255	+	0.549862i	$0.814680\pi$
$464$	−4.68723	−0.217599
$465$	6.30542	0.292407
$466$	−40.4186	−1.87236
$467$	−4.61657	−0.213629	−0.106815	−	0.994279i	$-0.534065\pi$
$467$	−4.61657	−0.213629	−0.106815	+	0.994279i	$0.534065\pi$
$468$	−13.1793	−0.609215
$469$	−27.2274	−1.25724
$470$	20.6825	0.954012
$471$	1.00000	0.0460776
$472$	−4.48212	−0.206306
$473$	−4.34714	−0.199882
$474$	−1.67097	−0.0767503
$475$	6.22422	0.285587
$476$	−13.0998	−0.600429
$477$	3.39762	0.155566
$478$	−58.0748	−2.65628
$479$	−15.1629	−0.692810	−0.346405	−	0.938085i	$-0.612598\pi$
$479$	−15.1629	−0.692810	−0.346405	+	0.938085i	$0.612598\pi$
$480$	−4.64355	−0.211948
$481$	12.8982	0.588108
$482$	6.10792	0.278208
$483$	33.8662	1.54096
$484$	−28.9949	−1.31795
$485$	32.8364	1.49102
$486$	−2.38551	−0.108209
$487$	5.78646	0.262210	0.131105	−	0.991369i	$-0.458148\pi$
$487$	5.78646	0.262210	0.131105	+	0.991369i	$0.458148\pi$
$488$	17.6763	0.800169
$489$	−5.03718	−0.227789
$490$	−22.7710	−1.02869
$491$	2.33360	0.105314	0.0526568	−	0.998613i	$-0.483231\pi$
$491$	2.33360	0.105314	0.0526568	+	0.998613i	$0.483231\pi$
$492$	4.49249	0.202537
$493$	2.09288	0.0942588
$494$	25.3322	1.13975
$495$	−3.02299	−0.135873
$496$	8.28261	0.371900
$497$	3.82165	0.171424
$498$	−20.6271	−0.924322
$499$	8.75409	0.391887	0.195943	−	0.980615i	$-0.437223\pi$
$499$	8.75409	0.391887	0.195943	+	0.980615i	$0.437223\pi$
$500$	44.6328	1.99604
$501$	13.9889	0.624979
$502$	−43.5288	−1.94278
$503$	4.09764	0.182705	0.0913523	−	0.995819i	$-0.470881\pi$
$503$	4.09764	0.182705	0.0913523	+	0.995819i	$0.470881\pi$
$504$	14.3152	0.637649
$505$	8.79475	0.391361
$506$	−40.3557	−1.79403
$507$	0.247902	0.0110097
$508$	−5.73661	−0.254521
$509$	3.94586	0.174897	0.0874485	−	0.996169i	$-0.472129\pi$
$509$	3.94586	0.174897	0.0874485	+	0.996169i	$0.472129\pi$
$510$	−4.06723	−0.180100
$511$	−28.4771	−1.25975
$512$	−24.1645	−1.06793
$513$	2.97373	0.131293
$514$	15.3344	0.676372
$515$	−31.9033	−1.40583
$516$	9.04872	0.398348
$517$	−9.01622	−0.396533
$518$	−30.5831	−1.34374
$519$	−9.10778	−0.399787
$520$	24.5552	1.07682
$521$	1.11211	0.0487224	0.0243612	−	0.999703i	$-0.492245\pi$
$521$	1.11211	0.0487224	0.0243612	+	0.999703i	$0.492245\pi$
$522$	−4.99259	−0.218520
$523$	17.2277	0.753314	0.376657	−	0.926353i	$-0.377074\pi$
$523$	17.2277	0.753314	0.376657	+	0.926353i	$0.377074\pi$
$524$	49.1330	2.14638
$525$	7.42926	0.324240
$526$	24.6754	1.07590
$527$	−3.69825	−0.161098
$528$	−3.97092	−0.172812
$529$	68.0350	2.95804
$530$	−13.8189	−0.600254
$531$	−1.11134	−0.0482282
$532$	−38.9552	−1.68892
$533$	4.34686	0.188283
$534$	−21.0491	−0.910883
$535$	10.6925	0.462279
$536$	−30.9370	−1.33628
$537$	−13.0024	−0.561095
$538$	7.68396	0.331279
$539$	9.92666	0.427571
$540$	6.29246	0.270784
$541$	17.9738	0.772756	0.386378	−	0.922341i	$-0.373726\pi$
$541$	17.9738	0.772756	0.386378	+	0.922341i	$0.373726\pi$
$542$	20.0567	0.861508
$543$	4.06356	0.174384
$544$	2.72353	0.116771
$545$	34.2126	1.46551
$546$	30.2367	1.29401
$547$	−24.7584	−1.05859	−0.529297	−	0.848436i	$-0.677544\pi$
$547$	−24.7584	−1.05859	−0.529297	+	0.848436i	$0.677544\pi$
$548$	38.1296	1.62881
$549$	4.38285	0.187056
$550$	−8.85288	−0.377488
$551$	6.22367	0.265137
$552$	38.4804	1.63783
$553$	2.48628	0.105727
$554$	−49.2223	−2.09125
$555$	−6.15823	−0.261402
$556$	60.4861	2.56518
$557$	43.5762	1.84638	0.923192	−	0.384340i	$-0.125571\pi$
$557$	43.5762	1.84638	0.923192	+	0.384340i	$0.125571\pi$
$558$	8.82221	0.373474
$559$	8.75538	0.370313
$560$	−13.5535	−0.572738
$561$	1.77305	0.0748580
$562$	39.7410	1.67637
$563$	−4.08073	−0.171982	−0.0859912	−	0.996296i	$-0.527406\pi$
$563$	−4.08073	−0.171982	−0.0859912	+	0.996296i	$0.527406\pi$
$564$	18.7675	0.790256
$565$	−29.3293	−1.23389
$566$	−18.6736	−0.784910
$567$	3.54946	0.149063
$568$	4.34234	0.182201
$569$	2.79788	0.117293	0.0586467	−	0.998279i	$-0.481321\pi$
$569$	2.79788	0.117293	0.0586467	+	0.998279i	$0.481321\pi$
$570$	−12.0948	−0.506596
$571$	8.04086	0.336500	0.168250	−	0.985744i	$-0.446188\pi$
$571$	8.04086	0.336500	0.168250	+	0.985744i	$0.446188\pi$
$572$	−23.3676	−0.977047
$573$	16.1191	0.673385
$574$	−10.3069	−0.430201
$575$	19.9704	0.832825
$576$	−10.9762	−0.457342
$577$	−5.22192	−0.217391	−0.108696	−	0.994075i	$-0.534667\pi$
$577$	−5.22192	−0.217391	−0.108696	+	0.994075i	$0.534667\pi$
$578$	2.38551	0.0992241
$579$	13.1424	0.546178
$580$	13.1694	0.546829
$581$	30.6916	1.27330
$582$	45.9430	1.90440
$583$	6.02413	0.249494
$584$	−32.3571	−1.33894
$585$	6.08847	0.251727
$586$	11.6436	0.480992
$587$	−4.36699	−0.180245	−0.0901226	−	0.995931i	$-0.528726\pi$
$587$	−4.36699	−0.180245	−0.0901226	+	0.995931i	$0.528726\pi$
$588$	−20.6627	−0.852113
$589$	−10.9976	−0.453148
$590$	4.52009	0.186089
$591$	−15.3852	−0.632862
$592$	−8.08927	−0.332467
$593$	18.8680	0.774814	0.387407	−	0.921909i	$-0.373371\pi$
$593$	18.8680	0.774814	0.387407	+	0.921909i	$0.373371\pi$
$594$	−4.22961	−0.173543
$595$	6.05173	0.248097
$596$	16.9245	0.693253
$597$	15.5015	0.634436
$598$	81.2786	3.32373
$599$	32.6871	1.33556	0.667780	−	0.744359i	$-0.267245\pi$
$599$	32.6871	1.33556	0.667780	+	0.744359i	$0.267245\pi$
$600$	8.44148	0.344622
$601$	37.8540	1.54410	0.772049	−	0.635563i	$-0.219232\pi$
$601$	37.8540	1.54410	0.772049	+	0.635563i	$0.219232\pi$
$602$	−20.7600	−0.846114
$603$	−7.67085	−0.312381
$604$	−53.9030	−2.19328
$605$	13.3948	0.544576
$606$	12.3052	0.499863
$607$	−32.1324	−1.30421	−0.652107	−	0.758127i	$-0.726115\pi$
$607$	−32.1324	−1.30421	−0.652107	+	0.758127i	$0.726115\pi$
$608$	8.09905	0.328460
$609$	7.42860	0.301022
$610$	−17.8260	−0.721755
$611$	18.1591	0.734640
$612$	−3.69065	−0.149186
$613$	−5.85646	−0.236540	−0.118270	−	0.992981i	$-0.537735\pi$
$613$	−5.85646	−0.236540	−0.118270	+	0.992981i	$0.537735\pi$
$614$	−24.6768	−0.995874
$615$	−2.07540	−0.0836882
$616$	25.3815	1.02265
$617$	2.36074	0.0950398	0.0475199	−	0.998870i	$-0.484868\pi$
$617$	2.36074	0.0950398	0.0475199	+	0.998870i	$0.484868\pi$
$618$	−44.6374	−1.79558
$619$	16.8877	0.678773	0.339386	−	0.940647i	$-0.389781\pi$
$619$	16.8877	0.678773	0.339386	+	0.940647i	$0.389781\pi$
$620$	−23.2711	−0.934589
$621$	9.54123	0.382876
$622$	28.6971	1.15065
$623$	31.3195	1.25479
$624$	7.99764	0.320162
$625$	−10.1537	−0.406149
$626$	−52.2813	−2.08958
$627$	5.27255	0.210565
$628$	−3.69065	−0.147273
$629$	3.61193	0.144017
$630$	−14.4364	−0.575162
$631$	−8.41241	−0.334893	−0.167446	−	0.985881i	$-0.553552\pi$
$631$	−8.41241	−0.334893	−0.167446	+	0.985881i	$0.553552\pi$
$632$	2.82503	0.112374
$633$	3.80749	0.151334
$634$	−35.1482	−1.39591
$635$	2.65015	0.105168
$636$	−12.5394	−0.497220
$637$	−19.9928	−0.792144
$638$	−8.85210	−0.350458
$639$	1.07669	0.0425930
$640$	35.3557	1.39756
$641$	31.5324	1.24545	0.622727	−	0.782439i	$-0.286025\pi$
$641$	31.5324	1.24545	0.622727	+	0.782439i	$0.286025\pi$
$642$	14.9605	0.590442
$643$	−33.3957	−1.31700	−0.658499	−	0.752582i	$-0.728808\pi$
$643$	−33.3957	−1.31700	−0.658499	+	0.752582i	$0.728808\pi$
$644$	−124.988	−4.92523
$645$	−4.18024	−0.164597
$646$	7.09385	0.279104
$647$	−24.6816	−0.970335	−0.485168	−	0.874421i	$-0.661241\pi$
$647$	−24.6816	−0.970335	−0.485168	+	0.874421i	$0.661241\pi$
$648$	4.03306	0.158434
$649$	−1.97046	−0.0773474
$650$	17.8302	0.699357
$651$	−13.1268	−0.514479
$652$	18.5905	0.728059
$653$	−36.2354	−1.41800	−0.709001	−	0.705207i	$-0.750854\pi$
$653$	−36.2354	−1.41800	−0.709001	+	0.705207i	$0.750854\pi$
$654$	47.8685	1.87181
$655$	−22.6980	−0.886884
$656$	−2.72618	−0.106440
$657$	−8.02295	−0.313005
$658$	−43.0574	−1.67855
$659$	13.6153	0.530376	0.265188	−	0.964197i	$-0.414566\pi$
$659$	13.6153	0.530376	0.265188	+	0.964197i	$0.414566\pi$
$660$	11.1568	0.434278
$661$	46.2084	1.79730	0.898649	−	0.438669i	$-0.144550\pi$
$661$	46.2084	1.79730	0.898649	+	0.438669i	$0.144550\pi$
$662$	−42.7111	−1.66002
$663$	−3.57101	−0.138686
$664$	34.8732	1.35334
$665$	17.9962	0.697862
$666$	−8.61628	−0.333874
$667$	19.9687	0.773191
$668$	−51.6282	−1.99755
$669$	−21.5201	−0.832016
$670$	31.1991	1.20533
$671$	7.77099	0.299996
$672$	9.66707	0.372915
$673$	6.46465	0.249194	0.124597	−	0.992207i	$-0.460236\pi$
$673$	6.46465	0.249194	0.124597	+	0.992207i	$0.460236\pi$
$674$	−10.6028	−0.408404
$675$	2.09307	0.0805623
$676$	−0.914921	−0.0351893
$677$	10.8392	0.416583	0.208292	−	0.978067i	$-0.433210\pi$
$677$	10.8392	0.416583	0.208292	+	0.978067i	$0.433210\pi$
$678$	−41.0361	−1.57598
$679$	−68.3597	−2.62340
$680$	6.87626	0.263692
$681$	12.1500	0.465589
$682$	15.6422	0.598970
$683$	29.5459	1.13054	0.565271	−	0.824905i	$-0.308772\pi$
$683$	29.5459	1.13054	0.565271	+	0.824905i	$0.308772\pi$
$684$	−10.9750	−0.419639
$685$	−17.6147	−0.673025
$686$	−11.8656	−0.453031
$687$	−29.2181	−1.11474
$688$	−5.49104	−0.209344
$689$	−12.1329	−0.462228
$690$	−38.8063	−1.47733
$691$	5.30148	0.201678	0.100839	−	0.994903i	$-0.467847\pi$
$691$	5.30148	0.201678	0.100839	+	0.994903i	$0.467847\pi$
$692$	33.6136	1.27780
$693$	6.29335	0.239065
$694$	−55.1301	−2.09271
$695$	−27.9428	−1.05993
$696$	8.44073	0.319945
$697$	1.21726	0.0461071
$698$	9.01310	0.341151
$699$	16.9434	0.640858
$700$	−27.4188	−1.03633
$701$	44.3341	1.67448	0.837238	−	0.546839i	$-0.184169\pi$
$701$	44.3341	1.67448	0.837238	+	0.546839i	$0.184169\pi$
$702$	8.51867	0.321516
$703$	10.7409	0.405100
$704$	−19.4613	−0.733477
$705$	−8.67006	−0.326533
$706$	−24.5218	−0.922891
$707$	−18.3091	−0.688586
$708$	4.10158	0.154147
$709$	−23.0112	−0.864202	−0.432101	−	0.901825i	$-0.642228\pi$
$709$	−23.0112	−0.864202	−0.432101	+	0.901825i	$0.642228\pi$
$710$	−4.37912	−0.164346
$711$	0.700468	0.0262696
$712$	35.5867	1.33367
$713$	−35.2859	−1.32147
$714$	8.46726	0.316879
$715$	10.7951	0.403715
$716$	47.9873	1.79337
$717$	24.3448	0.909174
$718$	−47.7831	−1.78325
$719$	−41.5951	−1.55124	−0.775618	−	0.631202i	$-0.782562\pi$
$719$	−41.5951	−1.55124	−0.775618	+	0.631202i	$0.782562\pi$
$720$	−3.81846	−0.142306
$721$	66.4171	2.47350
$722$	−24.2295	−0.901728
$723$	−2.56042	−0.0952232
$724$	−14.9972	−0.557367
$725$	4.38055	0.162690
$726$	18.7413	0.695555
$727$	−13.3162	−0.493870	−0.246935	−	0.969032i	$-0.579423\pi$
$727$	−13.3162	−0.493870	−0.246935	+	0.969032i	$0.579423\pi$
$728$	−51.1196	−1.89462
$729$	1.00000	0.0370370
$730$	32.6312	1.20773
$731$	2.45179	0.0906829
$732$	−16.1756	−0.597866
$733$	48.9618	1.80844	0.904222	−	0.427062i	$-0.140452\pi$
$733$	48.9618	1.80844	0.904222	+	0.427062i	$0.140452\pi$
$734$	−26.6638	−0.984178
$735$	9.54554	0.352093
$736$	25.9859	0.957851
$737$	−13.6008	−0.500991
$738$	−2.90379	−0.106890
$739$	31.5144	1.15928	0.579638	−	0.814874i	$-0.303194\pi$
$739$	31.5144	1.15928	0.579638	+	0.814874i	$0.303194\pi$
$740$	22.7279	0.835494
$741$	−10.6192	−0.390106
$742$	28.7685	1.05613
$743$	−15.7545	−0.577977	−0.288988	−	0.957333i	$-0.593319\pi$
$743$	−15.7545	−0.577977	−0.288988	+	0.957333i	$0.593319\pi$
$744$	−14.9153	−0.546821
$745$	−7.81861	−0.286452
$746$	41.3229	1.51294
$747$	8.64683	0.316371
$748$	−6.54369	−0.239261
$749$	−22.2600	−0.813364
$750$	−28.8491	−1.05342
$751$	−37.0370	−1.35150	−0.675750	−	0.737131i	$-0.736180\pi$
$751$	−37.0370	−1.35150	−0.675750	+	0.737131i	$0.736180\pi$
$752$	−11.3887	−0.415304
$753$	18.2472	0.664964
$754$	17.8286	0.649279
$755$	24.9016	0.906262
$756$	−13.0998	−0.476435
$757$	−40.7252	−1.48018	−0.740091	−	0.672507i	$-0.765218\pi$
$757$	−40.7252	−1.48018	−0.740091	+	0.672507i	$0.765218\pi$
$758$	−7.08307	−0.257269
$759$	16.9170	0.614049
$760$	20.4481	0.741731
$761$	−24.6505	−0.893581	−0.446791	−	0.894639i	$-0.647433\pi$
$761$	−24.6505	−0.893581	−0.446791	+	0.894639i	$0.647433\pi$
$762$	3.70795	0.134325
$763$	−71.2248	−2.57851
$764$	−59.4899	−2.15227
$765$	1.70497	0.0616434
$766$	−21.6475	−0.782157
$767$	3.96862	0.143298
$768$	27.5154	0.992875
$769$	43.5837	1.57167	0.785834	−	0.618437i	$-0.212234\pi$
$769$	43.5837	1.57167	0.785834	+	0.618437i	$0.212234\pi$
$770$	−25.5965	−0.922433
$771$	−6.42815	−0.231504
$772$	−48.5039	−1.74569
$773$	−7.03034	−0.252864	−0.126432	−	0.991975i	$-0.540353\pi$
$773$	−7.03034	−0.252864	−0.126432	+	0.991975i	$0.540353\pi$
$774$	−5.84878	−0.210230
$775$	−7.74070	−0.278054
$776$	−77.6735	−2.78832
$777$	12.8204	0.459928
$778$	64.4221	2.30964
$779$	3.61981	0.129693
$780$	−22.4704	−0.804570
$781$	1.90901	0.0683098
$782$	22.7607	0.813920
$783$	2.09288	0.0747936
$784$	12.5387	0.447812
$785$	1.70497	0.0608531
$786$	−31.7579	−1.13277
$787$	−0.0746412	−0.00266067	−0.00133034	−	0.999999i	$-0.500423\pi$
$787$	−0.0746412	−0.00266067	−0.00133034	+	0.999999i	$0.500423\pi$
$788$	56.7814	2.02275
$789$	−10.3439	−0.368251
$790$	−2.84896	−0.101362
$791$	61.0586	2.17099
$792$	7.15080	0.254093
$793$	−15.6512	−0.555790
$794$	19.4444	0.690057
$795$	5.79285	0.205451
$796$	−57.2108	−2.02778
$797$	13.0746	0.463128	0.231564	−	0.972820i	$-0.425616\pi$
$797$	13.0746	0.463128	0.231564	+	0.972820i	$0.425616\pi$
$798$	25.1793	0.891338
$799$	5.08516	0.179900
$800$	5.70055	0.201545
$801$	8.82373	0.311771
$802$	10.4481	0.368936
$803$	−14.2251	−0.501991
$804$	28.3104	0.998432
$805$	57.7409	2.03510
$806$	−31.5042	−1.10969
$807$	−3.22110	−0.113388
$808$	−20.8037	−0.731872
$809$	−39.0955	−1.37452	−0.687262	−	0.726409i	$-0.741188\pi$
$809$	−39.0955	−1.37452	−0.687262	+	0.726409i	$0.741188\pi$
$810$	−4.06723	−0.142908
$811$	45.3798	1.59350	0.796751	−	0.604308i	$-0.206550\pi$
$811$	45.3798	1.59350	0.796751	+	0.604308i	$0.206550\pi$
$812$	−27.4164	−0.962127
$813$	−8.40771	−0.294871
$814$	−15.2771	−0.535460
$815$	−8.58825	−0.300833
$816$	2.23960	0.0784018
$817$	7.29097	0.255079
$818$	31.3083	1.09467
$819$	−12.6751	−0.442905
$820$	7.65958	0.267484
$821$	−27.4974	−0.959666	−0.479833	−	0.877360i	$-0.659303\pi$
$821$	−27.4974	−0.959666	−0.479833	+	0.877360i	$0.659303\pi$
$822$	−24.6456	−0.859615
$823$	43.6548	1.52171	0.760855	−	0.648921i	$-0.224780\pi$
$823$	43.6548	1.52171	0.760855	+	0.648921i	$0.224780\pi$
$824$	75.4663	2.62899
$825$	3.71111	0.129204
$826$	−9.41004	−0.327417
$827$	4.23486	0.147260	0.0736302	−	0.997286i	$-0.476542\pi$
$827$	4.23486	0.147260	0.0736302	+	0.997286i	$0.476542\pi$
$828$	−35.2133	−1.22375
$829$	−22.8852	−0.794835	−0.397418	−	0.917638i	$-0.630094\pi$
$829$	−22.8852	−0.794835	−0.397418	+	0.917638i	$0.630094\pi$
$830$	−35.1686	−1.22072
$831$	20.6339	0.715781
$832$	39.1962	1.35888
$833$	−5.59865	−0.193982
$834$	−39.0961	−1.35379
$835$	23.8507	0.825388
$836$	−19.4591	−0.673009
$837$	−3.69825	−0.127830
$838$	53.1894	1.83740
$839$	−49.9417	−1.72418	−0.862090	−	0.506755i	$-0.830845\pi$
$839$	−49.9417	−1.72418	−0.862090	+	0.506755i	$0.830845\pi$
$840$	24.4070	0.842121
$841$	−24.6198	−0.848960
$842$	36.5292	1.25888
$843$	−16.6593	−0.573778
$844$	−14.0521	−0.483694
$845$	0.422667	0.0145402
$846$	−12.1307	−0.417062
$847$	−27.8856	−0.958162
$848$	7.60931	0.261305
$849$	7.82793	0.268654
$850$	4.99303	0.171260
$851$	34.4622	1.18135
$852$	−3.97367	−0.136136
$853$	9.30315	0.318534	0.159267	−	0.987236i	$-0.449087\pi$
$853$	9.30315	0.318534	0.159267	+	0.987236i	$0.449087\pi$
$854$	37.1107	1.26990
$855$	5.07012	0.173394
$856$	−25.2929	−0.864494
$857$	−8.87623	−0.303206	−0.151603	−	0.988441i	$-0.548444\pi$
$857$	−8.87623	−0.303206	−0.151603	+	0.988441i	$0.548444\pi$
$858$	15.1040	0.515642
$859$	52.2447	1.78257	0.891283	−	0.453447i	$-0.149806\pi$
$859$	52.2447	1.78257	0.891283	+	0.453447i	$0.149806\pi$
$860$	15.4278	0.526084
$861$	4.32062	0.147246
$862$	20.4936	0.698016
$863$	37.8548	1.28859	0.644296	−	0.764776i	$-0.277150\pi$
$863$	37.8548	1.28859	0.644296	+	0.764776i	$0.277150\pi$
$864$	2.72353	0.0926565
$865$	−15.5285	−0.527985
$866$	−65.7296	−2.23358
$867$	−1.00000	−0.0339618
$868$	48.4464	1.64438
$869$	1.24196	0.0421307
$870$	−8.51223	−0.288592
$871$	27.3927	0.928165
$872$	−80.9290	−2.74060
$873$	−19.2592	−0.651825
$874$	67.6840	2.28945
$875$	42.9253	1.45114
$876$	29.6099	1.00043
$877$	−21.7686	−0.735072	−0.367536	−	0.930009i	$-0.619799\pi$
$877$	−21.7686	−0.735072	−0.367536	+	0.930009i	$0.619799\pi$
$878$	−42.2682	−1.42648
$879$	−4.88097	−0.164631
$880$	−6.77030	−0.228227
$881$	30.6408	1.03231	0.516157	−	0.856494i	$-0.327362\pi$
$881$	30.6408	1.03231	0.516157	+	0.856494i	$0.327362\pi$
$882$	13.3556	0.449707
$883$	20.9770	0.705932	0.352966	−	0.935636i	$-0.385173\pi$
$883$	20.9770	0.705932	0.352966	+	0.935636i	$0.385173\pi$
$884$	13.1793	0.443269
$885$	−1.89481	−0.0636934
$886$	0.0143477	0.000482021 0
$887$	4.63636	0.155674	0.0778369	−	0.996966i	$-0.475199\pi$
$887$	4.63636	0.155674	0.0778369	+	0.996966i	$0.475199\pi$
$888$	14.5671	0.488840
$889$	−5.51715	−0.185039
$890$	−35.8881	−1.20297
$891$	1.77305	0.0593993
$892$	79.4232	2.65929
$893$	15.1219	0.506034
$894$	−10.9394	−0.365868
$895$	−22.1687	−0.741019
$896$	−73.6044	−2.45895
$897$	−34.0718	−1.13762
$898$	−48.8338	−1.62961
$899$	−7.74001	−0.258144
$900$	−7.72479	−0.257493
$901$	−3.39762	−0.113191
$902$	−5.14855	−0.171428
$903$	8.70254	0.289602
$904$	69.3777	2.30747
$905$	6.92827	0.230303
$906$	34.8410	1.15752
$907$	21.4210	0.711273	0.355636	−	0.934624i	$-0.384264\pi$
$907$	21.4210	0.711273	0.355636	+	0.934624i	$0.384264\pi$
$908$	−44.8414	−1.48811
$909$	−5.15830	−0.171090
$910$	51.5527	1.70895
$911$	−8.15346	−0.270136	−0.135068	−	0.990836i	$-0.543125\pi$
$911$	−8.15346	−0.270136	−0.135068	+	0.990836i	$0.543125\pi$
$912$	6.65996	0.220533
$913$	15.3312	0.507389
$914$	41.4436	1.37083
$915$	7.47264	0.247038
$916$	107.834	3.56292
$917$	47.2533	1.56044
$918$	2.38551	0.0787335
$919$	−14.9931	−0.494576	−0.247288	−	0.968942i	$-0.579539\pi$
$919$	−14.9931	−0.494576	−0.247288	+	0.968942i	$0.579539\pi$
$920$	65.6079	2.16303
$921$	10.3444	0.340861
$922$	30.9054	1.01781
$923$	−3.84485	−0.126555
$924$	−23.2266	−0.764098
$925$	7.56001	0.248572
$926$	−85.7474	−2.81783
$927$	18.7119	0.614580
$928$	5.70004	0.187113
$929$	13.3305	0.437359	0.218679	−	0.975797i	$-0.429825\pi$
$929$	13.3305	0.437359	0.218679	+	0.975797i	$0.429825\pi$
$930$	15.0416	0.493234
$931$	−16.6488	−0.545644
$932$	−62.5321	−2.04831
$933$	−12.0298	−0.393837
$934$	−11.0129	−0.360352
$935$	3.02299	0.0988625
$936$	−14.4021	−0.470747
$937$	−27.7093	−0.905222	−0.452611	−	0.891708i	$-0.649507\pi$
$937$	−27.7093	−0.905222	−0.452611	+	0.891708i	$0.649507\pi$
$938$	−64.9511	−2.12073
$939$	21.9162	0.715208
$940$	31.9981	1.04366
$941$	−2.65246	−0.0864679	−0.0432339	−	0.999065i	$-0.513766\pi$
$941$	−2.65246	−0.0864679	−0.0432339	+	0.999065i	$0.513766\pi$
$942$	2.38551	0.0777241
$943$	11.6142	0.378210
$944$	−2.48897	−0.0810090
$945$	6.05173	0.196863
$946$	−10.3701	−0.337162
$947$	−24.1667	−0.785311	−0.392655	−	0.919686i	$-0.628444\pi$
$947$	−24.1667	−0.785311	−0.392655	+	0.919686i	$0.628444\pi$
$948$	−2.58518	−0.0839629
$949$	28.6500	0.930019
$950$	14.8479	0.481730
$951$	14.7341	0.477784
$952$	−14.3152	−0.463958
$953$	25.6950	0.832343	0.416172	−	0.909286i	$-0.363372\pi$
$953$	25.6950	0.832343	0.416172	+	0.909286i	$0.363372\pi$
$954$	8.10505	0.262411
$955$	27.4826	0.889316
$956$	−89.8482	−2.90590
$957$	3.71078	0.119952
$958$	−36.1712	−1.16864
$959$	36.6708	1.18416
$960$	−18.7141	−0.603997
$961$	−17.3229	−0.558804
$962$	30.7688	0.992026
$963$	−6.27139	−0.202093
$964$	9.44963	0.304352
$965$	22.4074	0.721319
$966$	80.7880	2.59931
$967$	3.76872	0.121194	0.0605969	−	0.998162i	$-0.480700\pi$
$967$	3.76872	0.121194	0.0605969	+	0.998162i	$0.480700\pi$
$968$	−31.6850	−1.01839
$969$	−2.97373	−0.0955299
$970$	78.3315	2.51507
$971$	60.7894	1.95082	0.975412	−	0.220390i	$-0.0707331\pi$
$971$	60.7894	1.95082	0.975412	+	0.220390i	$0.0707331\pi$
$972$	−3.69065	−0.118378
$973$	58.1721	1.86491
$974$	13.8037	0.442298
$975$	−7.47437	−0.239371
$976$	9.81584	0.314197
$977$	−1.18843	−0.0380213	−0.0190106	−	0.999819i	$-0.506052\pi$
$977$	−1.18843	−0.0380213	−0.0190106	+	0.999819i	$0.506052\pi$
$978$	−12.0162	−0.384237
$979$	15.6449	0.500013
$980$	−35.2293	−1.12536
$981$	−20.0664	−0.640670
$982$	5.56681	0.177644
$983$	21.0840	0.672476	0.336238	−	0.941777i	$-0.390845\pi$
$983$	21.0840	0.672476	0.336238	+	0.941777i	$0.390845\pi$
$984$	4.90930	0.156503
$985$	−26.2313	−0.835799
$986$	4.99259	0.158997
$987$	18.0496	0.574524
$988$	39.1918	1.24686
$989$	23.3931	0.743858
$990$	−7.21138	−0.229193
$991$	−4.95893	−0.157526	−0.0787629	−	0.996893i	$-0.525097\pi$
$991$	−4.95893	−0.157526	−0.0787629	+	0.996893i	$0.525097\pi$
$992$	−10.0723	−0.319796
$993$	17.9044	0.568180
$994$	9.11658	0.289160
$995$	26.4297	0.837878
$996$	−31.9124	−1.01118
$997$	−14.9758	−0.474288	−0.237144	−	0.971475i	$-0.576211\pi$
$997$	−14.9758	−0.474288	−0.237144	+	0.971475i	$0.576211\pi$
$998$	20.8830	0.661038
$999$	3.61193	0.114276

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.f.1.44	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.f.1.44	✓	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q+2.38551 q^{2} -1.00000 q^{3} +3.69065 q^{4} -1.70497 q^{5} -2.38551 q^{6} +3.54946 q^{7} +4.03306 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.38551 q^{2} -1.00000 q^{3} +3.69065 q^{4} -1.70497 q^{5} -2.38551 q^{6} +3.54946 q^{7} +4.03306 q^{8} +1.00000 q^{9} -4.06723 q^{10} +1.77305 q^{11} -3.69065 q^{12} -3.57101 q^{13} +8.46726 q^{14} +1.70497 q^{15} +2.23960 q^{16} -1.00000 q^{17} +2.38551 q^{18} -2.97373 q^{19} -6.29246 q^{20} -3.54946 q^{21} +4.22961 q^{22} -9.54123 q^{23} -4.03306 q^{24} -2.09307 q^{25} -8.51867 q^{26} -1.00000 q^{27} +13.0998 q^{28} -2.09288 q^{29} +4.06723 q^{30} +3.69825 q^{31} -2.72353 q^{32} -1.77305 q^{33} -2.38551 q^{34} -6.05173 q^{35} +3.69065 q^{36} -3.61193 q^{37} -7.09385 q^{38} +3.57101 q^{39} -6.87626 q^{40} -1.21726 q^{41} -8.46726 q^{42} -2.45179 q^{43} +6.54369 q^{44} -1.70497 q^{45} -22.7607 q^{46} -5.08516 q^{47} -2.23960 q^{48} +5.59865 q^{49} -4.99303 q^{50} +1.00000 q^{51} -13.1793 q^{52} +3.39762 q^{53} -2.38551 q^{54} -3.02299 q^{55} +14.3152 q^{56} +2.97373 q^{57} -4.99259 q^{58} -1.11134 q^{59} +6.29246 q^{60} +4.38285 q^{61} +8.82221 q^{62} +3.54946 q^{63} -10.9762 q^{64} +6.08847 q^{65} -4.22961 q^{66} -7.67085 q^{67} -3.69065 q^{68} +9.54123 q^{69} -14.4364 q^{70} +1.07669 q^{71} +4.03306 q^{72} -8.02295 q^{73} -8.61628 q^{74} +2.09307 q^{75} -10.9750 q^{76} +6.29335 q^{77} +8.51867 q^{78} +0.700468 q^{79} -3.81846 q^{80} +1.00000 q^{81} -2.90379 q^{82} +8.64683 q^{83} -13.0998 q^{84} +1.70497 q^{85} -5.84878 q^{86} +2.09288 q^{87} +7.15080 q^{88} +8.82373 q^{89} -4.06723 q^{90} -12.6751 q^{91} -35.2133 q^{92} -3.69825 q^{93} -12.1307 q^{94} +5.07012 q^{95} +2.72353 q^{96} -19.2592 q^{97} +13.3556 q^{98} +1.77305 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9}+O(q^{10}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9} - 20 q^{10} + 5 q^{11} - 45 q^{12} - 8 q^{13} + 4 q^{14} - q^{15} + 39 q^{16} - 48 q^{17} - q^{18} - 6 q^{19} + 6 q^{20} + 13 q^{21} - 35 q^{22} - 8 q^{23} + 6 q^{24} + 13 q^{25} + 17 q^{26} - 48 q^{27} - 38 q^{28} + q^{29} + 20 q^{30} - 21 q^{31} - 3 q^{32} - 5 q^{33} + q^{34} + 19 q^{35} + 45 q^{36} - 58 q^{37} - 14 q^{38} + 8 q^{39} - 54 q^{40} - 3 q^{41} - 4 q^{42} - 33 q^{43} + 2 q^{44} + q^{45} - 26 q^{46} + 9 q^{47} - 39 q^{48} + 11 q^{49} + 4 q^{50} + 48 q^{51} - 31 q^{52} - 33 q^{53} + q^{54} - 21 q^{55} + 6 q^{57} - 55 q^{58} + 77 q^{59} - 6 q^{60} - 29 q^{61} - 46 q^{62} - 13 q^{63} + 24 q^{64} - 49 q^{65} + 35 q^{66} - 44 q^{67} - 45 q^{68} + 8 q^{69} + 4 q^{70} + 22 q^{71} - 6 q^{72} - 63 q^{73} - 16 q^{74} - 13 q^{75} - 46 q^{76} - 30 q^{77} - 17 q^{78} - 46 q^{79} - 14 q^{80} + 48 q^{81} - 75 q^{82} + 11 q^{83} + 38 q^{84} - q^{85} + 8 q^{86} - q^{87} - 116 q^{88} + 10 q^{89} - 20 q^{90} - 67 q^{91} - 64 q^{92} + 21 q^{93} - 16 q^{94} - 8 q^{95} + 3 q^{96} - 96 q^{97} - 46 q^{98} + 5 q^{99}+O(q^{100}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9 - 20 * q^10 + 5 * q^11 - 45 * q^12 - 8 * q^13 + 4 * q^14 - q^15 + 39 * q^16 - 48 * q^17 - q^18 - 6 * q^19 + 6 * q^20 + 13 * q^21 - 35 * q^22 - 8 * q^23 + 6 * q^24 + 13 * q^25 + 17 * q^26 - 48 * q^27 - 38 * q^28 + q^29 + 20 * q^30 - 21 * q^31 - 3 * q^32 - 5 * q^33 + q^34 + 19 * q^35 + 45 * q^36 - 58 * q^37 - 14 * q^38 + 8 * q^39 - 54 * q^40 - 3 * q^41 - 4 * q^42 - 33 * q^43 + 2 * q^44 + q^45 - 26 * q^46 + 9 * q^47 - 39 * q^48 + 11 * q^49 + 4 * q^50 + 48 * q^51 - 31 * q^52 - 33 * q^53 + q^54 - 21 * q^55 + 6 * q^57 - 55 * q^58 + 77 * q^59 - 6 * q^60 - 29 * q^61 - 46 * q^62 - 13 * q^63 + 24 * q^64 - 49 * q^65 + 35 * q^66 - 44 * q^67 - 45 * q^68 + 8 * q^69 + 4 * q^70 + 22 * q^71 - 6 * q^72 - 63 * q^73 - 16 * q^74 - 13 * q^75 - 46 * q^76 - 30 * q^77 - 17 * q^78 - 46 * q^79 - 14 * q^80 + 48 * q^81 - 75 * q^82 + 11 * q^83 + 38 * q^84 - q^85 + 8 * q^86 - q^87 - 116 * q^88 + 10 * q^89 - 20 * q^90 - 67 * q^91 - 64 * q^92 + 21 * q^93 - 16 * q^94 - 8 * q^95 + 3 * q^96 - 96 * q^97 - 46 * q^98 + 5 * q^99

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