LMFDB - Embedded newform 8041.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$60$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.78000 q^{2} -1.81181 q^{3} +5.72839 q^{4} +1.28422 q^{5} +5.03683 q^{6} +3.89203 q^{7} -10.3649 q^{8} +0.282655 q^{9} +O(q^{10})$	\(q-2.78000 q^{2} -1.81181 q^{3} +5.72839 q^{4} +1.28422 q^{5} +5.03683 q^{6} +3.89203 q^{7} -10.3649 q^{8} +0.282655 q^{9} -3.57012 q^{10} +1.00000 q^{11} -10.3787 q^{12} -0.124526 q^{13} -10.8198 q^{14} -2.32676 q^{15} +17.3576 q^{16} +1.00000 q^{17} -0.785780 q^{18} +3.07733 q^{19} +7.35648 q^{20} -7.05162 q^{21} -2.78000 q^{22} -1.35465 q^{23} +18.7792 q^{24} -3.35079 q^{25} +0.346182 q^{26} +4.92331 q^{27} +22.2950 q^{28} -7.41748 q^{29} +6.46837 q^{30} -5.45872 q^{31} -27.5244 q^{32} -1.81181 q^{33} -2.78000 q^{34} +4.99820 q^{35} +1.61916 q^{36} -0.235379 q^{37} -8.55496 q^{38} +0.225618 q^{39} -13.3108 q^{40} +0.226441 q^{41} +19.6035 q^{42} -1.00000 q^{43} +5.72839 q^{44} +0.362990 q^{45} +3.76591 q^{46} +2.95635 q^{47} -31.4487 q^{48} +8.14789 q^{49} +9.31519 q^{50} -1.81181 q^{51} -0.713333 q^{52} +4.07225 q^{53} -13.6868 q^{54} +1.28422 q^{55} -40.3405 q^{56} -5.57553 q^{57} +20.6206 q^{58} +4.09710 q^{59} -13.3285 q^{60} +4.54927 q^{61} +15.1752 q^{62} +1.10010 q^{63} +41.8024 q^{64} -0.159918 q^{65} +5.03683 q^{66} -11.7681 q^{67} +5.72839 q^{68} +2.45436 q^{69} -13.8950 q^{70} +4.78726 q^{71} -2.92969 q^{72} +6.61123 q^{73} +0.654354 q^{74} +6.07099 q^{75} +17.6281 q^{76} +3.89203 q^{77} -0.627216 q^{78} -12.0207 q^{79} +22.2909 q^{80} -9.76807 q^{81} -0.629505 q^{82} -4.74008 q^{83} -40.3944 q^{84} +1.28422 q^{85} +2.78000 q^{86} +13.4391 q^{87} -10.3649 q^{88} -17.1277 q^{89} -1.00911 q^{90} -0.484659 q^{91} -7.75993 q^{92} +9.89015 q^{93} -8.21864 q^{94} +3.95195 q^{95} +49.8689 q^{96} +5.08118 q^{97} -22.6511 q^{98} +0.282655 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) $ 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * 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 $

$2$	−2.78000	−1.96575	−0.982877	−	0.184260i	$-0.941011\pi$
$2$	−2.78000	−1.96575	−0.982877	+	0.184260i	$0.941011\pi$
$3$	−1.81181	−1.04605	−0.523024	−	0.852318i	$-0.675196\pi$
$3$	−1.81181	−1.04605	−0.523024	+	0.852318i	$0.675196\pi$
$4$	5.72839	2.86419
$5$	1.28422	0.574319	0.287159	−	0.957883i	$-0.407289\pi$
$5$	1.28422	0.574319	0.287159	+	0.957883i	$0.407289\pi$
$6$	5.03683	2.05628
$7$	3.89203	1.47105	0.735524	−	0.677498i	$-0.236936\pi$
$7$	3.89203	1.47105	0.735524	+	0.677498i	$0.236936\pi$
$8$	−10.3649	−3.66455
$9$	0.282655	0.0942183
$10$	−3.57012	−1.12897
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−10.3787	−2.99609
$13$	−0.124526	−0.0345373	−0.0172687	−	0.999851i	$-0.505497\pi$
$13$	−0.124526	−0.0345373	−0.0172687	+	0.999851i	$0.505497\pi$
$14$	−10.8198	−2.89172
$15$	−2.32676	−0.600766
$16$	17.3576	4.33941
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.785780	−0.185210
$19$	3.07733	0.705988	0.352994	−	0.935626i	$-0.385164\pi$
$19$	3.07733	0.705988	0.352994	+	0.935626i	$0.385164\pi$
$20$	7.35648	1.64496
$21$	−7.05162	−1.53879
$22$	−2.78000	−0.592697
$23$	−1.35465	−0.282463	−0.141232	−	0.989977i	$-0.545106\pi$
$23$	−1.35465	−0.282463	−0.141232	+	0.989977i	$0.545106\pi$
$24$	18.7792	3.83329
$25$	−3.35079	−0.670158
$26$	0.346182	0.0678919
$27$	4.92331	0.947492
$28$	22.2950	4.21337
$29$	−7.41748	−1.37739	−0.688696	−	0.725050i	$-0.741816\pi$
$29$	−7.41748	−1.37739	−0.688696	+	0.725050i	$0.741816\pi$
$30$	6.46837	1.18096
$31$	−5.45872	−0.980414	−0.490207	−	0.871606i	$-0.663079\pi$
$31$	−5.45872	−0.980414	−0.490207	+	0.871606i	$0.663079\pi$
$32$	−27.5244	−4.86567
$33$	−1.81181	−0.315396
$34$	−2.78000	−0.476766
$35$	4.99820	0.844851
$36$	1.61916	0.269859
$37$	−0.235379	−0.0386961	−0.0193481	−	0.999813i	$-0.506159\pi$
$37$	−0.235379	−0.0386961	−0.0193481	+	0.999813i	$0.506159\pi$
$38$	−8.55496	−1.38780
$39$	0.225618	0.0361277
$40$	−13.3108	−2.10462
$41$	0.226441	0.0353641	0.0176821	−	0.999844i	$-0.494371\pi$
$41$	0.226441	0.0353641	0.0176821	+	0.999844i	$0.494371\pi$
$42$	19.6035	3.02488
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	5.72839	0.863587
$45$	0.362990	0.0541113
$46$	3.76591	0.555253
$47$	2.95635	0.431228	0.215614	−	0.976479i	$-0.430825\pi$
$47$	2.95635	0.431228	0.215614	+	0.976479i	$0.430825\pi$
$48$	−31.4487	−4.53923
$49$	8.14789	1.16398
$50$	9.31519	1.31737
$51$	−1.81181	−0.253704
$52$	−0.713333	−0.0989215
$53$	4.07225	0.559366	0.279683	−	0.960092i	$-0.409771\pi$
$53$	4.07225	0.559366	0.279683	+	0.960092i	$0.409771\pi$
$54$	−13.6868	−1.86254
$55$	1.28422	0.173164
$56$	−40.3405	−5.39072
$57$	−5.57553	−0.738497
$58$	20.6206	2.70761
$59$	4.09710	0.533397	0.266698	−	0.963780i	$-0.414067\pi$
$59$	4.09710	0.533397	0.266698	+	0.963780i	$0.414067\pi$
$60$	−13.3285	−1.72071
$61$	4.54927	0.582474	0.291237	−	0.956651i	$-0.405933\pi$
$61$	4.54927	0.582474	0.291237	+	0.956651i	$0.405933\pi$
$62$	15.1752	1.92725
$63$	1.10010	0.138600
$64$	41.8024	5.22530
$65$	−0.159918	−0.0198354
$66$	5.03683	0.619990
$67$	−11.7681	−1.43770	−0.718849	−	0.695166i	$-0.755331\pi$
$67$	−11.7681	−1.43770	−0.718849	+	0.695166i	$0.755331\pi$
$68$	5.72839	0.694669
$69$	2.45436	0.295470
$70$	−13.8950	−1.66077
$71$	4.78726	0.568144	0.284072	−	0.958803i	$-0.408315\pi$
$71$	4.78726	0.568144	0.284072	+	0.958803i	$0.408315\pi$
$72$	−2.92969	−0.345267
$73$	6.61123	0.773786	0.386893	−	0.922125i	$-0.373548\pi$
$73$	6.61123	0.773786	0.386893	+	0.922125i	$0.373548\pi$
$74$	0.654354	0.0760671
$75$	6.07099	0.701018
$76$	17.6281	2.02208
$77$	3.89203	0.443538
$78$	−0.627216	−0.0710183
$79$	−12.0207	−1.35244	−0.676220	−	0.736700i	$-0.736383\pi$
$79$	−12.0207	−1.35244	−0.676220	+	0.736700i	$0.736383\pi$
$80$	22.2909	2.49220
$81$	−9.76807	−1.08534
$82$	−0.629505	−0.0695172
$83$	−4.74008	−0.520291	−0.260146	−	0.965569i	$-0.583771\pi$
$83$	−4.74008	−0.520291	−0.260146	+	0.965569i	$0.583771\pi$
$84$	−40.3944	−4.40739
$85$	1.28422	0.139293
$86$	2.78000	0.299775
$87$	13.4391	1.44082
$88$	−10.3649	−1.10490
$89$	−17.1277	−1.81553	−0.907764	−	0.419481i	$-0.862212\pi$
$89$	−17.1277	−1.81553	−0.907764	+	0.419481i	$0.862212\pi$
$90$	−1.00911	−0.106370
$91$	−0.484659	−0.0508061
$92$	−7.75993	−0.809029
$93$	9.89015	1.02556
$94$	−8.21864	−0.847688
$95$	3.95195	0.405462
$96$	49.8689	5.08972
$97$	5.08118	0.515915	0.257958	−	0.966156i	$-0.416951\pi$
$97$	5.08118	0.515915	0.257958	+	0.966156i	$0.416951\pi$
$98$	−22.6511	−2.28811
$99$	0.282655	0.0284079
$100$	−19.1946	−1.91946
$101$	−7.35102	−0.731454	−0.365727	−	0.930722i	$-0.619180\pi$
$101$	−7.35102	−0.731454	−0.365727	+	0.930722i	$0.619180\pi$
$102$	5.03683	0.498720
$103$	15.9064	1.56731	0.783653	−	0.621199i	$-0.213354\pi$
$103$	15.9064	1.56731	0.783653	+	0.621199i	$0.213354\pi$
$104$	1.29070	0.126564
$105$	−9.05580	−0.883755
$106$	−11.3208	−1.09958
$107$	−2.34553	−0.226751	−0.113375	−	0.993552i	$-0.536166\pi$
$107$	−2.34553	−0.226751	−0.113375	+	0.993552i	$0.536166\pi$
$108$	28.2026	2.71380
$109$	6.60301	0.632454	0.316227	−	0.948684i	$-0.397584\pi$
$109$	6.60301	0.632454	0.316227	+	0.948684i	$0.397584\pi$
$110$	−3.57012	−0.340397
$111$	0.426463	0.0404781
$112$	67.5564	6.38348
$113$	−2.91245	−0.273980	−0.136990	−	0.990572i	$-0.543743\pi$
$113$	−2.91245	−0.273980	−0.136990	+	0.990572i	$0.543743\pi$
$114$	15.5000	1.45171
$115$	−1.73966	−0.162224
$116$	−42.4902	−3.94511
$117$	−0.0351979	−0.00325405
$118$	−11.3899	−1.04853
$119$	3.89203	0.356782
$120$	24.1166	2.20153
$121$	1.00000	0.0909091
$122$	−12.6470	−1.14500
$123$	−0.410268	−0.0369926
$124$	−31.2696	−2.80810
$125$	−10.7242	−0.959203
$126$	−3.05828	−0.272453
$127$	12.8960	1.14434	0.572169	−	0.820135i	$-0.306102\pi$
$127$	12.8960	1.14434	0.572169	+	0.820135i	$0.306102\pi$
$128$	−61.1618	−5.40599
$129$	1.81181	0.159521
$130$	0.444573	0.0389916
$131$	−17.4257	−1.52249	−0.761247	−	0.648462i	$-0.775412\pi$
$131$	−17.4257	−1.52249	−0.761247	+	0.648462i	$0.775412\pi$
$132$	−10.3787	−0.903354
$133$	11.9770	1.03854
$134$	32.7152	2.82616
$135$	6.32260	0.544162
$136$	−10.3649	−0.888783
$137$	−18.1600	−1.55151	−0.775756	−	0.631033i	$-0.782631\pi$
$137$	−18.1600	−1.55151	−0.775756	+	0.631033i	$0.782631\pi$
$138$	−6.82312	−0.580822
$139$	−6.71350	−0.569431	−0.284716	−	0.958612i	$-0.591899\pi$
$139$	−6.71350	−0.569431	−0.284716	+	0.958612i	$0.591899\pi$
$140$	28.6316	2.41982
$141$	−5.35634	−0.451085
$142$	−13.3086	−1.11683
$143$	−0.124526	−0.0104134
$144$	4.90622	0.408851
$145$	−9.52565	−0.791062
$146$	−18.3792	−1.52107
$147$	−14.7624	−1.21758
$148$	−1.34834	−0.110833
$149$	−6.79554	−0.556713	−0.278356	−	0.960478i	$-0.589790\pi$
$149$	−6.79554	−0.556713	−0.278356	+	0.960478i	$0.589790\pi$
$150$	−16.8773	−1.37803
$151$	1.44983	0.117985	0.0589927	−	0.998258i	$-0.481211\pi$
$151$	1.44983	0.117985	0.0589927	+	0.998258i	$0.481211\pi$
$152$	−31.8962	−2.58712
$153$	0.282655	0.0228513
$154$	−10.8198	−0.871887
$155$	−7.01017	−0.563070
$156$	1.29242	0.103477
$157$	−1.94386	−0.155137	−0.0775685	−	0.996987i	$-0.524716\pi$
$157$	−1.94386	−0.155137	−0.0775685	+	0.996987i	$0.524716\pi$
$158$	33.4176	2.65856
$159$	−7.37813	−0.585124
$160$	−35.3472	−2.79444
$161$	−5.27232	−0.415517
$162$	27.1552	2.13351
$163$	13.6640	1.07025	0.535124	−	0.844773i	$-0.320265\pi$
$163$	13.6640	1.07025	0.535124	+	0.844773i	$0.320265\pi$
$164$	1.29714	0.101290
$165$	−2.32676	−0.181138
$166$	13.1774	1.02277
$167$	−14.7035	−1.13779	−0.568895	−	0.822410i	$-0.692629\pi$
$167$	−14.7035	−1.13779	−0.568895	+	0.822410i	$0.692629\pi$
$168$	73.0893	5.63896
$169$	−12.9845	−0.998807
$170$	−3.57012	−0.273815
$171$	0.869822	0.0665169
$172$	−5.72839	−0.436785
$173$	−14.7443	−1.12099	−0.560495	−	0.828158i	$-0.689389\pi$
$173$	−14.7443	−1.12099	−0.560495	+	0.828158i	$0.689389\pi$
$174$	−37.3606	−2.83230
$175$	−13.0414	−0.985835
$176$	17.3576	1.30838
$177$	−7.42316	−0.557959
$178$	47.6149	3.56888
$179$	−22.6445	−1.69253	−0.846263	−	0.532765i	$-0.821153\pi$
$179$	−22.6445	−1.69253	−0.846263	+	0.532765i	$0.821153\pi$
$180$	2.07935	0.154985
$181$	−9.74396	−0.724263	−0.362132	−	0.932127i	$-0.617951\pi$
$181$	−9.74396	−0.724263	−0.362132	+	0.932127i	$0.617951\pi$
$182$	1.34735	0.0998723
$183$	−8.24241	−0.609296
$184$	14.0408	1.03510
$185$	−0.302278	−0.0222239
$186$	−27.4946	−2.01600
$187$	1.00000	0.0731272
$188$	16.9351	1.23512
$189$	19.1617	1.39381
$190$	−10.9864	−0.797039
$191$	−6.55402	−0.474232	−0.237116	−	0.971481i	$-0.576202\pi$
$191$	−6.55402	−0.474232	−0.237116	+	0.971481i	$0.576202\pi$
$192$	−75.7380	−5.46592
$193$	−7.40857	−0.533280	−0.266640	−	0.963796i	$-0.585914\pi$
$193$	−7.40857	−0.533280	−0.266640	+	0.963796i	$0.585914\pi$
$194$	−14.1257	−1.01416
$195$	0.289742	0.0207488
$196$	46.6742	3.33387
$197$	−2.40818	−0.171576	−0.0857880	−	0.996313i	$-0.527341\pi$
$197$	−2.40818	−0.171576	−0.0857880	+	0.996313i	$0.527341\pi$
$198$	−0.785780	−0.0558429
$199$	−4.79545	−0.339940	−0.169970	−	0.985449i	$-0.554367\pi$
$199$	−4.79545	−0.339940	−0.169970	+	0.985449i	$0.554367\pi$
$200$	34.7306	2.45582
$201$	21.3215	1.50390
$202$	20.4358	1.43786
$203$	−28.8690	−2.02621
$204$	−10.3787	−0.726657
$205$	0.290799	0.0203103
$206$	−44.2198	−3.08094
$207$	−0.382897	−0.0266132
$208$	−2.16148	−0.149871
$209$	3.07733	0.212863
$210$	25.1751	1.73725
$211$	9.38124	0.645831	0.322916	−	0.946428i	$-0.395337\pi$
$211$	9.38124	0.645831	0.322916	+	0.946428i	$0.395337\pi$
$212$	23.3274	1.60213
$213$	−8.67361	−0.594306
$214$	6.52057	0.445737
$215$	−1.28422	−0.0875828
$216$	−51.0297	−3.47213
$217$	−21.2455	−1.44224
$218$	−18.3563	−1.24325
$219$	−11.9783	−0.809418
$220$	7.35648	0.495974
$221$	−0.124526	−0.00837653
$222$	−1.18557	−0.0795700
$223$	−4.14575	−0.277620	−0.138810	−	0.990319i	$-0.544328\pi$
$223$	−4.14575	−0.277620	−0.138810	+	0.990319i	$0.544328\pi$
$224$	−107.126	−7.15763
$225$	−0.947117	−0.0631411
$226$	8.09660	0.538578
$227$	9.18572	0.609678	0.304839	−	0.952404i	$-0.401397\pi$
$227$	9.18572	0.609678	0.304839	+	0.952404i	$0.401397\pi$
$228$	−31.9388	−2.11520
$229$	−19.1505	−1.26550	−0.632750	−	0.774356i	$-0.718074\pi$
$229$	−19.1505	−1.26550	−0.632750	+	0.774356i	$0.718074\pi$
$230$	4.83624	0.318892
$231$	−7.05162	−0.463962
$232$	76.8815	5.04751
$233$	−26.1889	−1.71569	−0.857844	−	0.513909i	$-0.828197\pi$
$233$	−26.1889	−1.71569	−0.857844	+	0.513909i	$0.828197\pi$
$234$	0.0978501	0.00639666
$235$	3.79659	0.247662
$236$	23.4698	1.52775
$237$	21.7793	1.41472
$238$	−10.8198	−0.701345
$239$	28.2312	1.82613	0.913063	−	0.407818i	$-0.133710\pi$
$239$	28.2312	1.82613	0.913063	+	0.407818i	$0.133710\pi$
$240$	−40.3869	−2.60697
$241$	−8.74562	−0.563355	−0.281677	−	0.959509i	$-0.590891\pi$
$241$	−8.74562	−0.563355	−0.281677	+	0.959509i	$0.590891\pi$
$242$	−2.78000	−0.178705
$243$	2.92795	0.187828
$244$	26.0600	1.66832
$245$	10.4636	0.668498
$246$	1.14054	0.0727184
$247$	−0.383208	−0.0243829
$248$	56.5790	3.59277
$249$	8.58813	0.544250
$250$	29.8133	1.88556
$251$	−1.17114	−0.0739218	−0.0369609	−	0.999317i	$-0.511768\pi$
$251$	−1.17114	−0.0739218	−0.0369609	+	0.999317i	$0.511768\pi$
$252$	6.30180	0.396976
$253$	−1.35465	−0.0851658
$254$	−35.8510	−2.24949
$255$	−2.32676	−0.145707
$256$	86.4249	5.40156
$257$	−11.2675	−0.702845	−0.351423	−	0.936217i	$-0.614302\pi$
$257$	−11.2675	−0.702845	−0.351423	+	0.936217i	$0.614302\pi$
$258$	−5.03683	−0.313579
$259$	−0.916104	−0.0569239
$260$	−0.916074	−0.0568125
$261$	−2.09659	−0.129775
$262$	48.4435	2.99285
$263$	16.0944	0.992423	0.496212	−	0.868202i	$-0.334724\pi$
$263$	16.0944	0.992423	0.496212	+	0.868202i	$0.334724\pi$
$264$	18.7792	1.15578
$265$	5.22964	0.321254
$266$	−33.2962	−2.04152
$267$	31.0321	1.89913
$268$	−67.4120	−4.11785
$269$	6.27112	0.382357	0.191178	−	0.981555i	$-0.438769\pi$
$269$	6.27112	0.382357	0.191178	+	0.981555i	$0.438769\pi$
$270$	−17.5768	−1.06969
$271$	16.0379	0.974234	0.487117	−	0.873337i	$-0.338049\pi$
$271$	16.0379	0.974234	0.487117	+	0.873337i	$0.338049\pi$
$272$	17.3576	1.05246
$273$	0.878110	0.0531456
$274$	50.4847	3.04989
$275$	−3.35079	−0.202060
$276$	14.0595	0.846284
$277$	20.9373	1.25800	0.629000	−	0.777405i	$-0.283464\pi$
$277$	20.9373	1.25800	0.629000	+	0.777405i	$0.283464\pi$
$278$	18.6635	1.11936
$279$	−1.54293	−0.0923729
$280$	−51.8059	−3.09599
$281$	0.873133	0.0520868	0.0260434	−	0.999661i	$-0.491709\pi$
$281$	0.873133	0.0520868	0.0260434	+	0.999661i	$0.491709\pi$
$282$	14.8906	0.886723
$283$	27.9764	1.66302	0.831512	−	0.555507i	$-0.187476\pi$
$283$	27.9764	1.66302	0.831512	+	0.555507i	$0.187476\pi$
$284$	27.4233	1.62727
$285$	−7.16019	−0.424133
$286$	0.346182	0.0204702
$287$	0.881314	0.0520223
$288$	−7.77989	−0.458435
$289$	1.00000	0.0588235
$290$	26.4813	1.55503
$291$	−9.20612	−0.539673
$292$	37.8717	2.21627
$293$	18.7078	1.09292	0.546459	−	0.837486i	$-0.315975\pi$
$293$	18.7078	1.09292	0.546459	+	0.837486i	$0.315975\pi$
$294$	41.0395	2.39347
$295$	5.26156	0.306340
$296$	2.43969	0.141804
$297$	4.92331	0.285680
$298$	18.8916	1.09436
$299$	0.168689	0.00975552
$300$	34.7770	2.00785
$301$	−3.89203	−0.224333
$302$	−4.03052	−0.231930
$303$	13.3187	0.765137
$304$	53.4151	3.06357
$305$	5.84224	0.334526
$306$	−0.785780	−0.0449200
$307$	−17.7447	−1.01274	−0.506371	−	0.862316i	$-0.669013\pi$
$307$	−17.7447	−1.01274	−0.506371	+	0.862316i	$0.669013\pi$
$308$	22.2950	1.27038
$309$	−28.8194	−1.63948
$310$	19.4883	1.10686
$311$	12.8637	0.729435	0.364718	−	0.931118i	$-0.381166\pi$
$311$	12.8637	0.729435	0.364718	+	0.931118i	$0.381166\pi$
$312$	−2.33850	−0.132392
$313$	−9.89641	−0.559378	−0.279689	−	0.960091i	$-0.590231\pi$
$313$	−9.89641	−0.559378	−0.279689	+	0.960091i	$0.590231\pi$
$314$	5.40393	0.304961
$315$	1.41277	0.0796004
$316$	−68.8595	−3.87365
$317$	−6.37692	−0.358163	−0.179082	−	0.983834i	$-0.557313\pi$
$317$	−6.37692	−0.358163	−0.179082	+	0.983834i	$0.557313\pi$
$318$	20.5112	1.15021
$319$	−7.41748	−0.415299
$320$	53.6833	3.00099
$321$	4.24965	0.237193
$322$	14.6570	0.816805
$323$	3.07733	0.171227
$324$	−55.9553	−3.10863
$325$	0.417261	0.0231455
$326$	−37.9859	−2.10385
$327$	−11.9634	−0.661577
$328$	−2.34704	−0.129593
$329$	11.5062	0.634357
$330$	6.46837	0.356072
$331$	1.67659	0.0921539	0.0460769	−	0.998938i	$-0.485328\pi$
$331$	1.67659	0.0921539	0.0460769	+	0.998938i	$0.485328\pi$
$332$	−27.1530	−1.49022
$333$	−0.0665312	−0.00364588
$334$	40.8757	2.23662
$335$	−15.1127	−0.825697
$336$	−122.399	−6.67743
$337$	17.0515	0.928854	0.464427	−	0.885612i	$-0.346260\pi$
$337$	17.0515	0.928854	0.464427	+	0.885612i	$0.346260\pi$
$338$	36.0969	1.96341
$339$	5.27680	0.286597
$340$	7.35648	0.398961
$341$	−5.45872	−0.295606
$342$	−2.41810	−0.130756
$343$	4.46760	0.241228
$344$	10.3649	0.558838
$345$	3.15193	0.169694
$346$	40.9891	2.20359
$347$	5.88261	0.315795	0.157897	−	0.987456i	$-0.449528\pi$
$347$	5.88261	0.315795	0.157897	+	0.987456i	$0.449528\pi$
$348$	76.9841	4.12678
$349$	−15.7897	−0.845201	−0.422601	−	0.906316i	$-0.638883\pi$
$349$	−15.7897	−0.845201	−0.422601	+	0.906316i	$0.638883\pi$
$350$	36.2550	1.93791
$351$	−0.613081	−0.0327238
$352$	−27.5244	−1.46705
$353$	15.8171	0.841859	0.420929	−	0.907093i	$-0.361704\pi$
$353$	15.8171	0.841859	0.420929	+	0.907093i	$0.361704\pi$
$354$	20.6364	1.09681
$355$	6.14788	0.326296
$356$	−98.1138	−5.20002
$357$	−7.05162	−0.373211
$358$	62.9515	3.32709
$359$	17.7078	0.934581	0.467290	−	0.884104i	$-0.345230\pi$
$359$	17.7078	0.934581	0.467290	+	0.884104i	$0.345230\pi$
$360$	−3.76235	−0.198293
$361$	−9.53005	−0.501582
$362$	27.0882	1.42372
$363$	−1.81181	−0.0950954
$364$	−2.77631	−0.145518
$365$	8.49025	0.444400
$366$	22.9139	1.19773
$367$	−14.8965	−0.777593	−0.388797	−	0.921324i	$-0.627109\pi$
$367$	−14.8965	−0.777593	−0.388797	+	0.921324i	$0.627109\pi$
$368$	−23.5134	−1.22572
$369$	0.0640046	0.00333195
$370$	0.840332	0.0436868
$371$	15.8493	0.822854
$372$	56.6546	2.93740
$373$	33.2188	1.72000	0.860001	−	0.510292i	$-0.170463\pi$
$373$	33.2188	1.72000	0.860001	+	0.510292i	$0.170463\pi$
$374$	−2.78000	−0.143750
$375$	19.4302	1.00337
$376$	−30.6422	−1.58025
$377$	0.923670	0.0475714
$378$	−53.2694	−2.73988
$379$	−37.7035	−1.93670	−0.968348	−	0.249604i	$-0.919700\pi$
$379$	−37.7035	−1.93670	−0.968348	+	0.249604i	$0.919700\pi$
$380$	22.6383	1.16132
$381$	−23.3652	−1.19703
$382$	18.2202	0.932225
$383$	−34.8743	−1.78199	−0.890997	−	0.454008i	$-0.849994\pi$
$383$	−34.8743	−1.78199	−0.890997	+	0.454008i	$0.849994\pi$
$384$	110.814	5.65493
$385$	4.99820	0.254732
$386$	20.5958	1.04830
$387$	−0.282655	−0.0143682
$388$	29.1069	1.47768
$389$	18.7224	0.949265	0.474633	−	0.880184i	$-0.342581\pi$
$389$	18.7224	0.949265	0.474633	+	0.880184i	$0.342581\pi$
$390$	−0.805481	−0.0407871
$391$	−1.35465	−0.0685074
$392$	−84.4520	−4.26547
$393$	31.5721	1.59260
$394$	6.69474	0.337276
$395$	−15.4372	−0.776731
$396$	1.61916	0.0813656
$397$	21.7967	1.09394	0.546972	−	0.837151i	$-0.315780\pi$
$397$	21.7967	1.09394	0.546972	+	0.837151i	$0.315780\pi$
$398$	13.3313	0.668240
$399$	−21.7001	−1.08637
$400$	−58.1618	−2.90809
$401$	20.9145	1.04442	0.522210	−	0.852817i	$-0.325108\pi$
$401$	20.9145	1.04442	0.522210	+	0.852817i	$0.325108\pi$
$402$	−59.2737	−2.95630
$403$	0.679752	0.0338609
$404$	−42.1095	−2.09502
$405$	−12.5443	−0.623332
$406$	80.2559	3.98303
$407$	−0.235379	−0.0116673
$408$	18.7792	0.929710
$409$	−38.3966	−1.89859	−0.949294	−	0.314389i	$-0.898200\pi$
$409$	−38.3966	−1.89859	−0.949294	+	0.314389i	$0.898200\pi$
$410$	−0.808421	−0.0399250
$411$	32.9024	1.62296
$412$	91.1181	4.48907
$413$	15.9460	0.784652
$414$	1.06445	0.0523150
$415$	−6.08729	−0.298813
$416$	3.42750	0.168047
$417$	12.1636	0.595653
$418$	−8.55496	−0.418437
$419$	25.5099	1.24624	0.623120	−	0.782126i	$-0.285865\pi$
$419$	25.5099	1.24624	0.623120	+	0.782126i	$0.285865\pi$
$420$	−51.8751	−2.53125
$421$	−17.6733	−0.861346	−0.430673	−	0.902508i	$-0.641724\pi$
$421$	−17.6733	−0.861346	−0.430673	+	0.902508i	$0.641724\pi$
$422$	−26.0798	−1.26955
$423$	0.835626	0.0406295
$424$	−42.2084	−2.04982
$425$	−3.35079	−0.162537
$426$	24.1126	1.16826
$427$	17.7059	0.856848
$428$	−13.4361	−0.649458
$429$	0.225618	0.0108929
$430$	3.57012	0.172166
$431$	−22.3153	−1.07489	−0.537444	−	0.843299i	$-0.680610\pi$
$431$	−22.3153	−1.07489	−0.537444	+	0.843299i	$0.680610\pi$
$432$	85.4570	4.11155
$433$	−11.0444	−0.530758	−0.265379	−	0.964144i	$-0.585497\pi$
$433$	−11.0444	−0.530758	−0.265379	+	0.964144i	$0.585497\pi$
$434$	59.0624	2.83508
$435$	17.2587	0.827489
$436$	37.8246	1.81147
$437$	−4.16869	−0.199415
$438$	33.2996	1.59112
$439$	16.1376	0.770206	0.385103	−	0.922874i	$-0.374166\pi$
$439$	16.1376	0.770206	0.385103	+	0.922874i	$0.374166\pi$
$440$	−13.3108	−0.634566
$441$	2.30304	0.109669
$442$	0.346182	0.0164662
$443$	−23.5081	−1.11690	−0.558452	−	0.829537i	$-0.688605\pi$
$443$	−23.5081	−1.11690	−0.558452	+	0.829537i	$0.688605\pi$
$444$	2.44294	0.115937
$445$	−21.9956	−1.04269
$446$	11.5252	0.545733
$447$	12.3122	0.582349
$448$	162.696	7.68667
$449$	−5.39785	−0.254740	−0.127370	−	0.991855i	$-0.540654\pi$
$449$	−5.39785	−0.254740	−0.127370	+	0.991855i	$0.540654\pi$
$450$	2.63298	0.124120
$451$	0.226441	0.0106627
$452$	−16.6836	−0.784732
$453$	−2.62682	−0.123419
$454$	−25.5363	−1.19848
$455$	−0.622407	−0.0291789
$456$	57.7899	2.70626
$457$	29.9425	1.40065	0.700325	−	0.713824i	$-0.253038\pi$
$457$	29.9425	1.40065	0.700325	+	0.713824i	$0.253038\pi$
$458$	53.2383	2.48766
$459$	4.92331	0.229801
$460$	−9.96543	−0.464641
$461$	−19.4175	−0.904363	−0.452181	−	0.891926i	$-0.649354\pi$
$461$	−19.4175	−0.904363	−0.452181	+	0.891926i	$0.649354\pi$
$462$	19.6035	0.912036
$463$	26.8379	1.24726	0.623632	−	0.781718i	$-0.285656\pi$
$463$	26.8379	1.24726	0.623632	+	0.781718i	$0.285656\pi$
$464$	−128.750	−5.97706
$465$	12.7011	0.588999
$466$	72.8050	3.37262
$467$	−5.91222	−0.273585	−0.136792	−	0.990600i	$-0.543679\pi$
$467$	−5.91222	−0.273585	−0.136792	+	0.990600i	$0.543679\pi$
$468$	−0.201627	−0.00932022
$469$	−45.8017	−2.11492
$470$	−10.5545	−0.486843
$471$	3.52191	0.162281
$472$	−42.4660	−1.95466
$473$	−1.00000	−0.0459800
$474$	−60.5464	−2.78099
$475$	−10.3115	−0.473123
$476$	22.2950	1.02189
$477$	1.15104	0.0527025
$478$	−78.4827	−3.58972
$479$	34.6848	1.58479	0.792393	−	0.610010i	$-0.208835\pi$
$479$	34.6848	1.58479	0.792393	+	0.610010i	$0.208835\pi$
$480$	64.0424	2.92312
$481$	0.0293109	0.00133646
$482$	24.3128	1.10742
$483$	9.55244	0.434651
$484$	5.72839	0.260381
$485$	6.52533	0.296300
$486$	−8.13969	−0.369224
$487$	2.61411	0.118457	0.0592284	−	0.998244i	$-0.481136\pi$
$487$	2.61411	0.118457	0.0592284	+	0.998244i	$0.481136\pi$
$488$	−47.1527	−2.13450
$489$	−24.7566	−1.11953
$490$	−29.0889	−1.31410
$491$	−10.4756	−0.472758	−0.236379	−	0.971661i	$-0.575961\pi$
$491$	−10.4756	−0.472758	−0.236379	+	0.971661i	$0.575961\pi$
$492$	−2.35017	−0.105954
$493$	−7.41748	−0.334067
$494$	1.06532	0.0479308
$495$	0.362990	0.0163152
$496$	−94.7503	−4.25442
$497$	18.6322	0.835767
$498$	−23.8750	−1.06986
$499$	−10.4316	−0.466982	−0.233491	−	0.972359i	$-0.575015\pi$
$499$	−10.4316	−0.466982	−0.233491	+	0.972359i	$0.575015\pi$
$500$	−61.4324	−2.74734
$501$	26.6399	1.19018
$502$	3.25577	0.145312
$503$	−34.2177	−1.52569	−0.762847	−	0.646579i	$-0.776199\pi$
$503$	−34.2177	−1.52569	−0.762847	+	0.646579i	$0.776199\pi$
$504$	−11.4024	−0.507905
$505$	−9.44030	−0.420088
$506$	3.76591	0.167415
$507$	23.5254	1.04480
$508$	73.8735	3.27761
$509$	23.3418	1.03461	0.517304	−	0.855801i	$-0.326935\pi$
$509$	23.3418	1.03461	0.517304	+	0.855801i	$0.326935\pi$
$510$	6.46837	0.286424
$511$	25.7311	1.13828
$512$	−117.937	−5.21214
$513$	15.1506	0.668918
$514$	31.3235	1.38162
$515$	20.4273	0.900133
$516$	10.3787	0.456899
$517$	2.95635	0.130020
$518$	2.54677	0.111898
$519$	26.7139	1.17261
$520$	1.65754	0.0726879
$521$	−11.1780	−0.489718	−0.244859	−	0.969559i	$-0.578742\pi$
$521$	−11.1780	−0.489718	−0.244859	+	0.969559i	$0.578742\pi$
$522$	5.82851	0.255107
$523$	−7.27272	−0.318014	−0.159007	−	0.987277i	$-0.550829\pi$
$523$	−7.27272	−0.318014	−0.159007	+	0.987277i	$0.550829\pi$
$524$	−99.8213	−4.36071
$525$	23.6285	1.03123
$526$	−44.7424	−1.95086
$527$	−5.45872	−0.237785
$528$	−31.4487	−1.36863
$529$	−21.1649	−0.920215
$530$	−14.5384	−0.631507
$531$	1.15806	0.0502557
$532$	68.6092	2.97458
$533$	−0.0281978	−0.00122138
$534$	−86.2691	−3.73323
$535$	−3.01217	−0.130227
$536$	121.975	5.26851
$537$	41.0275	1.77047
$538$	−17.4337	−0.751620
$539$	8.14789	0.350954
$540$	36.2183	1.55859
$541$	−2.51627	−0.108183	−0.0540915	−	0.998536i	$-0.517226\pi$
$541$	−2.51627	−0.108183	−0.0540915	+	0.998536i	$0.517226\pi$
$542$	−44.5853	−1.91510
$543$	17.6542	0.757615
$544$	−27.5244	−1.18010
$545$	8.47969	0.363230
$546$	−2.44114	−0.104471
$547$	17.4729	0.747086	0.373543	−	0.927613i	$-0.378143\pi$
$547$	17.4729	0.747086	0.373543	+	0.927613i	$0.378143\pi$
$548$	−104.027	−4.44383
$549$	1.28587	0.0548797
$550$	9.31519	0.397201
$551$	−22.8260	−0.972421
$552$	−25.4392	−1.08276
$553$	−46.7851	−1.98950
$554$	−58.2056	−2.47292
$555$	0.547670	0.0232473
$556$	−38.4575	−1.63096
$557$	43.9443	1.86198	0.930989	−	0.365048i	$-0.118947\pi$
$557$	43.9443	1.86198	0.930989	+	0.365048i	$0.118947\pi$
$558$	4.28935	0.181583
$559$	0.124526	0.00526689
$560$	86.7570	3.66615
$561$	−1.81181	−0.0764947
$562$	−2.42731	−0.102390
$563$	−34.5081	−1.45434	−0.727172	−	0.686455i	$-0.759166\pi$
$563$	−34.5081	−1.45434	−0.727172	+	0.686455i	$0.759166\pi$
$564$	−30.6832	−1.29199
$565$	−3.74021	−0.157352
$566$	−77.7743	−3.26910
$567$	−38.0176	−1.59659
$568$	−49.6195	−2.08199
$569$	8.24136	0.345496	0.172748	−	0.984966i	$-0.444735\pi$
$569$	8.24136	0.345496	0.172748	+	0.984966i	$0.444735\pi$
$570$	19.9053	0.833742
$571$	−41.9816	−1.75687	−0.878437	−	0.477859i	$-0.841413\pi$
$571$	−41.9816	−1.75687	−0.878437	+	0.477859i	$0.841413\pi$
$572$	−0.713333	−0.0298260
$573$	11.8746	0.496070
$574$	−2.45005	−0.102263
$575$	4.53913	0.189295
$576$	11.8156	0.492319
$577$	−23.3013	−0.970044	−0.485022	−	0.874502i	$-0.661188\pi$
$577$	−23.3013	−0.970044	−0.485022	+	0.874502i	$0.661188\pi$
$578$	−2.78000	−0.115633
$579$	13.4229	0.557837
$580$	−54.5666	−2.26575
$581$	−18.4485	−0.765374
$582$	25.5930	1.06086
$583$	4.07225	0.168655
$584$	−68.5247	−2.83557
$585$	−0.0452017	−0.00186886
$586$	−52.0075	−2.14841
$587$	36.7290	1.51597	0.757984	−	0.652273i	$-0.226184\pi$
$587$	36.7290	1.51597	0.757984	+	0.652273i	$0.226184\pi$
$588$	−84.5648	−3.48739
$589$	−16.7983	−0.692160
$590$	−14.6271	−0.602189
$591$	4.36317	0.179477
$592$	−4.08563	−0.167918
$593$	4.94777	0.203180	0.101590	−	0.994826i	$-0.467607\pi$
$593$	4.94777	0.203180	0.101590	+	0.994826i	$0.467607\pi$
$594$	−13.6868	−0.561576
$595$	4.99820	0.204906
$596$	−38.9275	−1.59453
$597$	8.68844	0.355594
$598$	−0.468954	−0.0191770
$599$	8.47010	0.346079	0.173039	−	0.984915i	$-0.444641\pi$
$599$	8.47010	0.346079	0.173039	+	0.984915i	$0.444641\pi$
$600$	−62.9252	−2.56891
$601$	−30.8255	−1.25740	−0.628699	−	0.777649i	$-0.716412\pi$
$601$	−30.8255	−1.25740	−0.628699	+	0.777649i	$0.716412\pi$
$602$	10.8198	0.440983
$603$	−3.32630	−0.135457
$604$	8.30518	0.337933
$605$	1.28422	0.0522108
$606$	−37.0258	−1.50407
$607$	11.4239	0.463683	0.231842	−	0.972754i	$-0.425525\pi$
$607$	11.4239	0.463683	0.231842	+	0.972754i	$0.425525\pi$
$608$	−84.7015	−3.43510
$609$	52.3052	2.11951
$610$	−16.2414	−0.657596
$611$	−0.368142	−0.0148934
$612$	1.61916	0.0654505
$613$	22.8038	0.921036	0.460518	−	0.887650i	$-0.347664\pi$
$613$	22.8038	0.921036	0.460518	+	0.887650i	$0.347664\pi$
$614$	49.3301	1.99080
$615$	−0.526873	−0.0212456
$616$	−40.3405	−1.62536
$617$	22.7436	0.915623	0.457812	−	0.889049i	$-0.348633\pi$
$617$	22.7436	0.915623	0.457812	+	0.889049i	$0.348633\pi$
$618$	80.1179	3.22281
$619$	−41.2592	−1.65835	−0.829173	−	0.558992i	$-0.811188\pi$
$619$	−41.2592	−1.65835	−0.829173	+	0.558992i	$0.811188\pi$
$620$	−40.1569	−1.61274
$621$	−6.66934	−0.267632
$622$	−35.7611	−1.43389
$623$	−66.6613	−2.67073
$624$	3.91619	0.156773
$625$	2.98174	0.119269
$626$	27.5120	1.09960
$627$	−5.57553	−0.222665
$628$	−11.1352	−0.444342
$629$	−0.235379	−0.00938519
$630$	−3.92749	−0.156475
$631$	−0.197835	−0.00787567	−0.00393784	−	0.999992i	$-0.501253\pi$
$631$	−0.197835	−0.00787567	−0.00393784	+	0.999992i	$0.501253\pi$
$632$	124.594	4.95608
$633$	−16.9970	−0.675571
$634$	17.7278	0.704061
$635$	16.5613	0.657215
$636$	−42.2648	−1.67591
$637$	−1.01462	−0.0402009
$638$	20.6206	0.816376
$639$	1.35314	0.0535295
$640$	−78.5450	−3.10476
$641$	−31.1508	−1.23038	−0.615192	−	0.788377i	$-0.710922\pi$
$641$	−31.1508	−1.23038	−0.615192	+	0.788377i	$0.710922\pi$
$642$	−11.8140	−0.466263
$643$	−18.7005	−0.737475	−0.368737	−	0.929534i	$-0.620210\pi$
$643$	−18.7005	−0.737475	−0.368737	+	0.929534i	$0.620210\pi$
$644$	−30.2019	−1.19012
$645$	2.32676	0.0916159
$646$	−8.55496	−0.336591
$647$	30.0847	1.18275	0.591377	−	0.806396i	$-0.298585\pi$
$647$	30.0847	1.18275	0.591377	+	0.806396i	$0.298585\pi$
$648$	101.245	3.97728
$649$	4.09710	0.160825
$650$	−1.15998	−0.0454983
$651$	38.4928	1.50865
$652$	78.2727	3.06540
$653$	−12.4659	−0.487830	−0.243915	−	0.969797i	$-0.578432\pi$
$653$	−12.4659	−0.487830	−0.243915	+	0.969797i	$0.578432\pi$
$654$	33.2582	1.30050
$655$	−22.3784	−0.874397
$656$	3.93048	0.153459
$657$	1.86870	0.0729048
$658$	−31.9872	−1.24699
$659$	−2.35336	−0.0916740	−0.0458370	−	0.998949i	$-0.514595\pi$
$659$	−2.35336	−0.0916740	−0.0458370	+	0.998949i	$0.514595\pi$
$660$	−13.3285	−0.518813
$661$	0.449724	0.0174922	0.00874612	−	0.999962i	$-0.497216\pi$
$661$	0.449724	0.0174922	0.00874612	+	0.999962i	$0.497216\pi$
$662$	−4.66092	−0.181152
$663$	0.225618	0.00876226
$664$	49.1305	1.90663
$665$	15.3811	0.596454
$666$	0.184956	0.00716692
$667$	10.0481	0.389062
$668$	−84.2272	−3.25885
$669$	7.51131	0.290404
$670$	42.0134	1.62312
$671$	4.54927	0.175623
$672$	194.091	7.48723
$673$	−4.79284	−0.184750	−0.0923752	−	0.995724i	$-0.529446\pi$
$673$	−4.79284	−0.184750	−0.0923752	+	0.995724i	$0.529446\pi$
$674$	−47.4031	−1.82590
$675$	−16.4970	−0.634969
$676$	−74.3802	−2.86078
$677$	21.2983	0.818560	0.409280	−	0.912409i	$-0.365780\pi$
$677$	21.2983	0.818560	0.409280	+	0.912409i	$0.365780\pi$
$678$	−14.6695	−0.563379
$679$	19.7761	0.758936
$680$	−13.3108	−0.510445
$681$	−16.6428	−0.637753
$682$	15.1752	0.581089
$683$	23.8477	0.912507	0.456253	−	0.889850i	$-0.349191\pi$
$683$	23.8477	0.912507	0.456253	+	0.889850i	$0.349191\pi$
$684$	4.98267	0.190517
$685$	−23.3213	−0.891062
$686$	−12.4199	−0.474195
$687$	34.6970	1.32377
$688$	−17.3576	−0.661753
$689$	−0.507101	−0.0193190
$690$	−8.76235	−0.333577
$691$	35.5467	1.35226	0.676130	−	0.736782i	$-0.263656\pi$
$691$	35.5467	1.35226	0.676130	+	0.736782i	$0.263656\pi$
$692$	−84.4611	−3.21073
$693$	1.10010	0.0417894
$694$	−16.3536	−0.620775
$695$	−8.62158	−0.327035
$696$	−139.295	−5.27995
$697$	0.226441	0.00857706
$698$	43.8952	1.66146
$699$	47.4492	1.79469
$700$	−74.7060	−2.82362
$701$	43.8457	1.65603	0.828015	−	0.560706i	$-0.189470\pi$
$701$	43.8457	1.65603	0.828015	+	0.560706i	$0.189470\pi$
$702$	1.70436	0.0643270
$703$	−0.724340	−0.0273190
$704$	41.8024	1.57549
$705$	−6.87870	−0.259067
$706$	−43.9715	−1.65489
$707$	−28.6104	−1.07600
$708$	−42.5227	−1.59810
$709$	−33.7264	−1.26662	−0.633311	−	0.773897i	$-0.718305\pi$
$709$	−33.7264	−1.26662	−0.633311	+	0.773897i	$0.718305\pi$
$710$	−17.0911	−0.641417
$711$	−3.39772	−0.127425
$712$	177.527	6.65309
$713$	7.39463	0.276931
$714$	19.6035	0.733642
$715$	−0.159918	−0.00598061
$716$	−129.716	−4.84772
$717$	−51.1496	−1.91022
$718$	−49.2276	−1.83716
$719$	−37.2019	−1.38740	−0.693699	−	0.720265i	$-0.744020\pi$
$719$	−37.2019	−1.38740	−0.693699	+	0.720265i	$0.744020\pi$
$720$	6.30064	0.234811
$721$	61.9082	2.30558
$722$	26.4935	0.985986
$723$	15.8454	0.589297
$724$	−55.8172	−2.07443
$725$	24.8544	0.923070
$726$	5.03683	0.186934
$727$	−12.0953	−0.448590	−0.224295	−	0.974521i	$-0.572008\pi$
$727$	−12.0953	−0.448590	−0.224295	+	0.974521i	$0.572008\pi$
$728$	5.02344	0.186181
$729$	23.9993	0.888864
$730$	−23.6029	−0.873581
$731$	−1.00000	−0.0369863
$732$	−47.2157	−1.74514
$733$	−47.2012	−1.74342	−0.871708	−	0.490026i	$-0.836987\pi$
$733$	−47.2012	−1.74342	−0.871708	+	0.490026i	$0.836987\pi$
$734$	41.4124	1.52856
$735$	−18.9581	−0.699281
$736$	37.2858	1.37437
$737$	−11.7681	−0.433482
$738$	−0.177933	−0.00654979
$739$	29.7244	1.09343	0.546716	−	0.837318i	$-0.315878\pi$
$739$	29.7244	1.09343	0.546716	+	0.837318i	$0.315878\pi$
$740$	−1.73157	−0.0636536
$741$	0.694299	0.0255057
$742$	−44.0610	−1.61753
$743$	30.1347	1.10553	0.552767	−	0.833336i	$-0.313572\pi$
$743$	30.1347	1.10553	0.552767	+	0.833336i	$0.313572\pi$
$744$	−102.510	−3.75822
$745$	−8.72695	−0.319731
$746$	−92.3481	−3.38110
$747$	−1.33981	−0.0490210
$748$	5.72839	0.209451
$749$	−9.12887	−0.333562
$750$	−54.0160	−1.97239
$751$	−25.0333	−0.913479	−0.456739	−	0.889601i	$-0.650983\pi$
$751$	−25.0333	−0.913479	−0.456739	+	0.889601i	$0.650983\pi$
$752$	51.3152	1.87127
$753$	2.12189	0.0773258
$754$	−2.56780	−0.0935137
$755$	1.86189	0.0677613
$756$	109.765	3.99213
$757$	18.3098	0.665481	0.332740	−	0.943018i	$-0.392027\pi$
$757$	18.3098	0.665481	0.332740	+	0.943018i	$0.392027\pi$
$758$	104.815	3.80707
$759$	2.45436	0.0890876
$760$	−40.9616	−1.48583
$761$	37.1745	1.34758	0.673788	−	0.738925i	$-0.264666\pi$
$761$	37.1745	1.34758	0.673788	+	0.738925i	$0.264666\pi$
$762$	64.9551	2.35308
$763$	25.6991	0.930370
$764$	−37.5440	−1.35829
$765$	0.362990	0.0131239
$766$	96.9505	3.50297
$767$	−0.510195	−0.0184221
$768$	−156.585	−5.65029
$769$	15.4434	0.556903	0.278452	−	0.960450i	$-0.410179\pi$
$769$	15.4434	0.556903	0.278452	+	0.960450i	$0.410179\pi$
$770$	−13.8950	−0.500741
$771$	20.4145	0.735211
$772$	−42.4391	−1.52742
$773$	−21.0784	−0.758136	−0.379068	−	0.925369i	$-0.623755\pi$
$773$	−21.0784	−0.758136	−0.379068	+	0.925369i	$0.623755\pi$
$774$	0.785780	0.0282443
$775$	18.2910	0.657032
$776$	−52.6659	−1.89060
$777$	1.65981	0.0595452
$778$	−52.0483	−1.86602
$779$	0.696833	0.0249666
$780$	1.65975	0.0594287
$781$	4.78726	0.171302
$782$	3.76591	0.134669
$783$	−36.5186	−1.30507
$784$	141.428	5.05100
$785$	−2.49634	−0.0890981
$786$	−87.7704	−3.13067
$787$	−6.51008	−0.232059	−0.116030	−	0.993246i	$-0.537017\pi$
$787$	−6.51008	−0.232059	−0.116030	+	0.993246i	$0.537017\pi$
$788$	−13.7950	−0.491426
$789$	−29.1600	−1.03812
$790$	42.9155	1.52686
$791$	−11.3353	−0.403038
$792$	−2.92969	−0.104102
$793$	−0.566503	−0.0201171
$794$	−60.5947	−2.15043
$795$	−9.47512	−0.336048
$796$	−27.4702	−0.973655
$797$	−34.5873	−1.22515	−0.612573	−	0.790414i	$-0.709866\pi$
$797$	−34.5873	−1.22515	−0.612573	+	0.790414i	$0.709866\pi$
$798$	60.3263	2.13553
$799$	2.95635	0.104588
$800$	92.2283	3.26076
$801$	−4.84122	−0.171056
$802$	−58.1422	−2.05307
$803$	6.61123	0.233305
$804$	122.138	4.30747
$805$	−6.77080	−0.238639
$806$	−1.88971	−0.0665622
$807$	−11.3621	−0.399964
$808$	76.1926	2.68045
$809$	−5.61256	−0.197327	−0.0986636	−	0.995121i	$-0.531457\pi$
$809$	−5.61256	−0.197327	−0.0986636	+	0.995121i	$0.531457\pi$
$810$	34.8732	1.22532
$811$	−15.9414	−0.559780	−0.279890	−	0.960032i	$-0.590298\pi$
$811$	−15.9414	−0.559780	−0.279890	+	0.960032i	$0.590298\pi$
$812$	−165.373	−5.80345
$813$	−29.0576	−1.01910
$814$	0.654354	0.0229351
$815$	17.5475	0.614664
$816$	−31.4487	−1.10093
$817$	−3.07733	−0.107662
$818$	106.742	3.73216
$819$	−0.136991	−0.00478686
$820$	1.66581	0.0581726
$821$	10.3839	0.362400	0.181200	−	0.983446i	$-0.442002\pi$
$821$	10.3839	0.362400	0.181200	+	0.983446i	$0.442002\pi$
$822$	−91.4686	−3.19034
$823$	−11.2782	−0.393134	−0.196567	−	0.980490i	$-0.562979\pi$
$823$	−11.2782	−0.393134	−0.196567	+	0.980490i	$0.562979\pi$
$824$	−164.868	−5.74347
$825$	6.07099	0.211365
$826$	−44.3299	−1.54243
$827$	−18.8334	−0.654903	−0.327452	−	0.944868i	$-0.606190\pi$
$827$	−18.8334	−0.654903	−0.327452	+	0.944868i	$0.606190\pi$
$828$	−2.19338	−0.0762253
$829$	−19.0001	−0.659900	−0.329950	−	0.943998i	$-0.607032\pi$
$829$	−19.0001	−0.659900	−0.329950	+	0.943998i	$0.607032\pi$
$830$	16.9226	0.587394
$831$	−37.9344	−1.31593
$832$	−5.20549	−0.180468
$833$	8.14789	0.282307
$834$	−33.8147	−1.17091
$835$	−18.8825	−0.653454
$836$	17.6281	0.609681
$837$	−26.8750	−0.928935
$838$	−70.9175	−2.44980
$839$	−5.51910	−0.190540	−0.0952702	−	0.995451i	$-0.530372\pi$
$839$	−5.51910	−0.190540	−0.0952702	+	0.995451i	$0.530372\pi$
$840$	93.8624	3.23856
$841$	26.0190	0.897207
$842$	49.1318	1.69319
$843$	−1.58195	−0.0544853
$844$	53.7394	1.84979
$845$	−16.6749	−0.573634
$846$	−2.32304	−0.0798677
$847$	3.89203	0.133732
$848$	70.6845	2.42732
$849$	−50.6879	−1.73960
$850$	9.31519	0.319508
$851$	0.318856	0.0109302
$852$	−49.6858	−1.70221
$853$	−11.6254	−0.398045	−0.199022	−	0.979995i	$-0.563777\pi$
$853$	−11.6254	−0.398045	−0.199022	+	0.979995i	$0.563777\pi$
$854$	−49.2223	−1.68435
$855$	1.11704	0.0382019
$856$	24.3112	0.830939
$857$	45.0407	1.53856	0.769281	−	0.638911i	$-0.220615\pi$
$857$	45.0407	1.53856	0.769281	+	0.638911i	$0.220615\pi$
$858$	−0.627216	−0.0214128
$859$	−38.3082	−1.30706	−0.653529	−	0.756902i	$-0.726712\pi$
$859$	−38.3082	−1.30706	−0.653529	+	0.756902i	$0.726712\pi$
$860$	−7.35648	−0.250854
$861$	−1.59677	−0.0544179
$862$	62.0364	2.11297
$863$	−50.8148	−1.72976	−0.864878	−	0.501981i	$-0.832605\pi$
$863$	−50.8148	−1.72976	−0.864878	+	0.501981i	$0.832605\pi$
$864$	−135.511	−4.61018
$865$	−18.9349	−0.643805
$866$	30.7033	1.04334
$867$	−1.81181	−0.0615323
$868$	−121.702	−4.13084
$869$	−12.0207	−0.407776
$870$	−47.9790	−1.62664
$871$	1.46543	0.0496543
$872$	−68.4395	−2.31766
$873$	1.43622	0.0486086
$874$	11.5889	0.392002
$875$	−41.7390	−1.41103
$876$	−68.6163	−2.31833
$877$	44.5515	1.50440	0.752199	−	0.658935i	$-0.228993\pi$
$877$	44.5515	1.50440	0.752199	+	0.658935i	$0.228993\pi$
$878$	−44.8625	−1.51404
$879$	−33.8949	−1.14325
$880$	22.2909	0.751428
$881$	20.3559	0.685808	0.342904	−	0.939370i	$-0.388589\pi$
$881$	20.3559	0.685808	0.342904	+	0.939370i	$0.388589\pi$
$882$	−6.40244	−0.215581
$883$	30.7993	1.03648	0.518239	−	0.855236i	$-0.326588\pi$
$883$	30.7993	1.03648	0.518239	+	0.855236i	$0.326588\pi$
$884$	−0.713333	−0.0239920
$885$	−9.53294	−0.320446
$886$	65.3525	2.19556
$887$	−20.0482	−0.673152	−0.336576	−	0.941656i	$-0.609269\pi$
$887$	−20.0482	−0.673152	−0.336576	+	0.941656i	$0.609269\pi$
$888$	−4.42025	−0.148334
$889$	50.1918	1.68338
$890$	61.1478	2.04968
$891$	−9.76807	−0.327243
$892$	−23.7485	−0.795157
$893$	9.09765	0.304441
$894$	−34.2280	−1.14475
$895$	−29.0804	−0.972050
$896$	−238.043	−7.95248
$897$	−0.305632	−0.0102048
$898$	15.0060	0.500757
$899$	40.4899	1.35041
$900$	−5.42545	−0.180848
$901$	4.07225	0.135666
$902$	−0.629505	−0.0209602
$903$	7.05162	0.234663
$904$	30.1873	1.00401
$905$	−12.5134	−0.415958
$906$	7.30254	0.242611
$907$	4.05403	0.134612	0.0673060	−	0.997732i	$-0.478560\pi$
$907$	4.05403	0.134612	0.0673060	+	0.997732i	$0.478560\pi$
$908$	52.6194	1.74623
$909$	−2.07780	−0.0689163
$910$	1.73029	0.0573585
$911$	−36.1847	−1.19885	−0.599427	−	0.800429i	$-0.704605\pi$
$911$	−36.1847	−1.19885	−0.599427	+	0.800429i	$0.704605\pi$
$912$	−96.7780	−3.20464
$913$	−4.74008	−0.156874
$914$	−83.2401	−2.75334
$915$	−10.5850	−0.349930
$916$	−109.701	−3.62463
$917$	−67.8214	−2.23966
$918$	−13.6868	−0.451732
$919$	−16.8988	−0.557438	−0.278719	−	0.960373i	$-0.589910\pi$
$919$	−16.8988	−0.557438	−0.278719	+	0.960373i	$0.589910\pi$
$920$	18.0314	0.594477
$921$	32.1499	1.05938
$922$	53.9806	1.77776
$923$	−0.596139	−0.0196222
$924$	−40.3944	−1.32888
$925$	0.788707	0.0259325
$926$	−74.6094	−2.45182
$927$	4.49603	0.147669
$928$	204.161	6.70193
$929$	18.7543	0.615308	0.307654	−	0.951498i	$-0.400456\pi$
$929$	18.7543	0.615308	0.307654	+	0.951498i	$0.400456\pi$
$930$	−35.3090	−1.15783
$931$	25.0737	0.821758
$932$	−150.020	−4.91406
$933$	−23.3066	−0.763025
$934$	16.4359	0.537801
$935$	1.28422	0.0419984
$936$	0.364823	0.0119246
$937$	28.1105	0.918330	0.459165	−	0.888351i	$-0.348149\pi$
$937$	28.1105	0.918330	0.459165	+	0.888351i	$0.348149\pi$
$938$	127.328	4.15742
$939$	17.9304	0.585137
$940$	21.7483	0.709352
$941$	10.0835	0.328713	0.164357	−	0.986401i	$-0.447445\pi$
$941$	10.0835	0.328713	0.164357	+	0.986401i	$0.447445\pi$
$942$	−9.79089	−0.319004
$943$	−0.306747	−0.00998906
$944$	71.1159	2.31462
$945$	24.6077	0.800489
$946$	2.78000	0.0903855
$947$	−53.6734	−1.74415	−0.872076	−	0.489371i	$-0.837226\pi$
$947$	−53.6734	−1.74415	−0.872076	+	0.489371i	$0.837226\pi$
$948$	124.760	4.05202
$949$	−0.823271	−0.0267245
$950$	28.6659	0.930044
$951$	11.5538	0.374656
$952$	−40.3405	−1.30744
$953$	−48.2393	−1.56262	−0.781312	−	0.624141i	$-0.785449\pi$
$953$	−48.2393	−1.56262	−0.781312	+	0.624141i	$0.785449\pi$
$954$	−3.19989	−0.103600
$955$	−8.41678	−0.272361
$956$	161.719	5.23038
$957$	13.4391	0.434423
$958$	−96.4235	−3.11530
$959$	−70.6791	−2.28235
$960$	−97.2639	−3.13918
$961$	−1.20243	−0.0387880
$962$	−0.0814842	−0.00262716
$963$	−0.662975	−0.0213641
$964$	−50.0983	−1.61356
$965$	−9.51420	−0.306273
$966$	−26.5558	−0.854418
$967$	14.3708	0.462133	0.231067	−	0.972938i	$-0.425778\pi$
$967$	14.3708	0.462133	0.231067	+	0.972938i	$0.425778\pi$
$968$	−10.3649	−0.333141
$969$	−5.57553	−0.179112
$970$	−18.1404	−0.582453
$971$	14.7981	0.474895	0.237447	−	0.971400i	$-0.423689\pi$
$971$	14.7981	0.474895	0.237447	+	0.971400i	$0.423689\pi$
$972$	16.7724	0.537976
$973$	−26.1291	−0.837661
$974$	−7.26722	−0.232857
$975$	−0.755997	−0.0242113
$976$	78.9645	2.52759
$977$	42.6576	1.36474	0.682368	−	0.731009i	$-0.260950\pi$
$977$	42.6576	1.36474	0.682368	+	0.731009i	$0.260950\pi$
$978$	68.8233	2.20073
$979$	−17.1277	−0.547402
$980$	59.9398	1.91471
$981$	1.86637	0.0595887
$982$	29.1222	0.929326
$983$	−22.5333	−0.718702	−0.359351	−	0.933202i	$-0.617002\pi$
$983$	−22.5333	−0.718702	−0.359351	+	0.933202i	$0.617002\pi$
$984$	4.25239	0.135561
$985$	−3.09263	−0.0985393
$986$	20.6206	0.656693
$987$	−20.8470	−0.663568
$988$	−2.19516	−0.0698374
$989$	1.35465	0.0430752
$990$	−1.00911	−0.0320716
$991$	−32.8975	−1.04502	−0.522511	−	0.852633i	$-0.675005\pi$
$991$	−32.8975	−1.04502	−0.522511	+	0.852633i	$0.675005\pi$
$992$	150.248	4.77037
$993$	−3.03767	−0.0963975
$994$	−51.7974	−1.64291
$995$	−6.15839	−0.195234
$996$	49.1961	1.55884
$997$	17.8624	0.565707	0.282854	−	0.959163i	$-0.408719\pi$
$997$	17.8624	0.565707	0.282854	+	0.959163i	$0.408719\pi$
$998$	28.9998	0.917971
$999$	−1.15885	−0.0366643

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.c.1.1	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.c.1.1	✓	60	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.78000 q^{2} -1.81181 q^{3} +5.72839 q^{4} +1.28422 q^{5} +5.03683 q^{6} +3.89203 q^{7} -10.3649 q^{8} +0.282655 q^{9} +O(q^{10})\)	\(q-2.78000 q^{2} -1.81181 q^{3} +5.72839 q^{4} +1.28422 q^{5} +5.03683 q^{6} +3.89203 q^{7} -10.3649 q^{8} +0.282655 q^{9} -3.57012 q^{10} +1.00000 q^{11} -10.3787 q^{12} -0.124526 q^{13} -10.8198 q^{14} -2.32676 q^{15} +17.3576 q^{16} +1.00000 q^{17} -0.785780 q^{18} +3.07733 q^{19} +7.35648 q^{20} -7.05162 q^{21} -2.78000 q^{22} -1.35465 q^{23} +18.7792 q^{24} -3.35079 q^{25} +0.346182 q^{26} +4.92331 q^{27} +22.2950 q^{28} -7.41748 q^{29} +6.46837 q^{30} -5.45872 q^{31} -27.5244 q^{32} -1.81181 q^{33} -2.78000 q^{34} +4.99820 q^{35} +1.61916 q^{36} -0.235379 q^{37} -8.55496 q^{38} +0.225618 q^{39} -13.3108 q^{40} +0.226441 q^{41} +19.6035 q^{42} -1.00000 q^{43} +5.72839 q^{44} +0.362990 q^{45} +3.76591 q^{46} +2.95635 q^{47} -31.4487 q^{48} +8.14789 q^{49} +9.31519 q^{50} -1.81181 q^{51} -0.713333 q^{52} +4.07225 q^{53} -13.6868 q^{54} +1.28422 q^{55} -40.3405 q^{56} -5.57553 q^{57} +20.6206 q^{58} +4.09710 q^{59} -13.3285 q^{60} +4.54927 q^{61} +15.1752 q^{62} +1.10010 q^{63} +41.8024 q^{64} -0.159918 q^{65} +5.03683 q^{66} -11.7681 q^{67} +5.72839 q^{68} +2.45436 q^{69} -13.8950 q^{70} +4.78726 q^{71} -2.92969 q^{72} +6.61123 q^{73} +0.654354 q^{74} +6.07099 q^{75} +17.6281 q^{76} +3.89203 q^{77} -0.627216 q^{78} -12.0207 q^{79} +22.2909 q^{80} -9.76807 q^{81} -0.629505 q^{82} -4.74008 q^{83} -40.3944 q^{84} +1.28422 q^{85} +2.78000 q^{86} +13.4391 q^{87} -10.3649 q^{88} -17.1277 q^{89} -1.00911 q^{90} -0.484659 q^{91} -7.75993 q^{92} +9.89015 q^{93} -8.21864 q^{94} +3.95195 q^{95} +49.8689 q^{96} +5.08118 q^{97} -22.6511 q^{98} +0.282655 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * q^99

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