LMFDB - Embedded newform 6019.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$1$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77092 q^{2} -0.383319 q^{3} +5.67797 q^{4} -1.00861 q^{5} +1.06214 q^{6} +0.495501 q^{7} -10.1914 q^{8} -2.85307 q^{9} +O(q^{10})$	\(q-2.77092 q^{2} -0.383319 q^{3} +5.67797 q^{4} -1.00861 q^{5} +1.06214 q^{6} +0.495501 q^{7} -10.1914 q^{8} -2.85307 q^{9} +2.79476 q^{10} -3.62859 q^{11} -2.17647 q^{12} +1.00000 q^{13} -1.37299 q^{14} +0.386618 q^{15} +16.8834 q^{16} +0.116211 q^{17} +7.90561 q^{18} +3.01305 q^{19} -5.72684 q^{20} -0.189935 q^{21} +10.0545 q^{22} +0.738431 q^{23} +3.90654 q^{24} -3.98271 q^{25} -2.77092 q^{26} +2.24359 q^{27} +2.81344 q^{28} -3.86163 q^{29} -1.07129 q^{30} +2.83022 q^{31} -26.3999 q^{32} +1.39091 q^{33} -0.322010 q^{34} -0.499766 q^{35} -16.1996 q^{36} +3.91508 q^{37} -8.34890 q^{38} -0.383319 q^{39} +10.2791 q^{40} +4.86990 q^{41} +0.526293 q^{42} -9.41041 q^{43} -20.6031 q^{44} +2.87762 q^{45} -2.04613 q^{46} +3.26752 q^{47} -6.47174 q^{48} -6.75448 q^{49} +11.0358 q^{50} -0.0445457 q^{51} +5.67797 q^{52} +2.32997 q^{53} -6.21680 q^{54} +3.65982 q^{55} -5.04983 q^{56} -1.15496 q^{57} +10.7003 q^{58} +11.0599 q^{59} +2.19521 q^{60} +14.6834 q^{61} -7.84231 q^{62} -1.41370 q^{63} +39.3849 q^{64} -1.00861 q^{65} -3.85409 q^{66} +9.62836 q^{67} +0.659841 q^{68} -0.283054 q^{69} +1.38481 q^{70} -11.8246 q^{71} +29.0766 q^{72} +9.51276 q^{73} -10.8484 q^{74} +1.52665 q^{75} +17.1080 q^{76} -1.79797 q^{77} +1.06214 q^{78} -7.42313 q^{79} -17.0287 q^{80} +7.69919 q^{81} -13.4941 q^{82} +8.52610 q^{83} -1.07844 q^{84} -0.117211 q^{85} +26.0755 q^{86} +1.48024 q^{87} +36.9803 q^{88} -2.51878 q^{89} -7.97365 q^{90} +0.495501 q^{91} +4.19279 q^{92} -1.08488 q^{93} -9.05404 q^{94} -3.03898 q^{95} +10.1196 q^{96} -6.38672 q^{97} +18.7161 q^{98} +10.3526 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) $ 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * 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 $

$2$	−2.77092	−1.95933	−0.979667	−	0.200632i	$-0.935700\pi$
$2$	−2.77092	−1.95933	−0.979667	+	0.200632i	$0.935700\pi$
$3$	−0.383319	−0.221309	−0.110655	−	0.993859i	$-0.535295\pi$
$3$	−0.383319	−0.221309	−0.110655	+	0.993859i	$0.535295\pi$
$4$	5.67797	2.83899
$5$	−1.00861	−0.451063	−0.225531	−	0.974236i	$-0.572412\pi$
$5$	−1.00861	−0.451063	−0.225531	+	0.974236i	$0.572412\pi$
$6$	1.06214	0.433618
$7$	0.495501	0.187282	0.0936409	−	0.995606i	$-0.470149\pi$
$7$	0.495501	0.187282	0.0936409	+	0.995606i	$0.470149\pi$
$8$	−10.1914	−3.60319
$9$	−2.85307	−0.951022
$10$	2.79476	0.883782
$11$	−3.62859	−1.09406	−0.547031	−	0.837112i	$-0.684242\pi$
$11$	−3.62859	−1.09406	−0.547031	+	0.837112i	$0.684242\pi$
$12$	−2.17647	−0.628294
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.37299	−0.366947
$15$	0.386618	0.0998243
$16$	16.8834	4.22086
$17$	0.116211	0.0281852	0.0140926	−	0.999901i	$-0.495514\pi$
$17$	0.116211	0.0281852	0.0140926	+	0.999901i	$0.495514\pi$
$18$	7.90561	1.86337
$19$	3.01305	0.691240	0.345620	−	0.938375i	$-0.387669\pi$
$19$	3.01305	0.691240	0.345620	+	0.938375i	$0.387669\pi$
$20$	−5.72684	−1.28056
$21$	−0.189935	−0.0414472
$22$	10.0545	2.14363
$23$	0.738431	0.153973	0.0769867	−	0.997032i	$-0.475470\pi$
$23$	0.738431	0.153973	0.0769867	+	0.997032i	$0.475470\pi$
$24$	3.90654	0.797418
$25$	−3.98271	−0.796543
$26$	−2.77092	−0.543421
$27$	2.24359	0.431779
$28$	2.81344	0.531691
$29$	−3.86163	−0.717087	−0.358543	−	0.933513i	$-0.616726\pi$
$29$	−3.86163	−0.717087	−0.358543	+	0.933513i	$0.616726\pi$
$30$	−1.07129	−0.195589
$31$	2.83022	0.508323	0.254161	−	0.967162i	$-0.418201\pi$
$31$	2.83022	0.508323	0.254161	+	0.967162i	$0.418201\pi$
$32$	−26.3999	−4.66688
$33$	1.39091	0.242126
$34$	−0.322010	−0.0552242
$35$	−0.499766	−0.0844758
$36$	−16.1996	−2.69994
$37$	3.91508	0.643635	0.321818	−	0.946802i	$-0.395706\pi$
$37$	3.91508	0.643635	0.321818	+	0.946802i	$0.395706\pi$
$38$	−8.34890	−1.35437
$39$	−0.383319	−0.0613801
$40$	10.2791	1.62526
$41$	4.86990	0.760551	0.380275	−	0.924873i	$-0.375829\pi$
$41$	4.86990	0.760551	0.380275	+	0.924873i	$0.375829\pi$
$42$	0.526293	0.0812088
$43$	−9.41041	−1.43507	−0.717537	−	0.696520i	$-0.754731\pi$
$43$	−9.41041	−1.43507	−0.717537	+	0.696520i	$0.754731\pi$
$44$	−20.6031	−3.10603
$45$	2.87762	0.428970
$46$	−2.04613	−0.301685
$47$	3.26752	0.476617	0.238309	−	0.971189i	$-0.423407\pi$
$47$	3.26752	0.476617	0.238309	+	0.971189i	$0.423407\pi$
$48$	−6.47174	−0.934115
$49$	−6.75448	−0.964926
$50$	11.0358	1.56069
$51$	−0.0445457	−0.00623764
$52$	5.67797	0.787393
$53$	2.32997	0.320045	0.160023	−	0.987113i	$-0.448843\pi$
$53$	2.32997	0.320045	0.160023	+	0.987113i	$0.448843\pi$
$54$	−6.21680	−0.845999
$55$	3.65982	0.493490
$56$	−5.04983	−0.674811
$57$	−1.15496	−0.152978
$58$	10.7003	1.40501
$59$	11.0599	1.43988	0.719939	−	0.694037i	$-0.244170\pi$
$59$	11.0599	1.43988	0.719939	+	0.694037i	$0.244170\pi$
$60$	2.19521	0.283400
$61$	14.6834	1.88002	0.940008	−	0.341152i	$-0.110817\pi$
$61$	14.6834	1.88002	0.940008	+	0.341152i	$0.110817\pi$
$62$	−7.84231	−0.995974
$63$	−1.41370	−0.178109
$64$	39.3849	4.92312
$65$	−1.00861	−0.125102
$66$	−3.85409	−0.474405
$67$	9.62836	1.17629	0.588145	−	0.808755i	$-0.299858\pi$
$67$	9.62836	1.17629	0.588145	+	0.808755i	$0.299858\pi$
$68$	0.659841	0.0800174
$69$	−0.283054	−0.0340757
$70$	1.38481	0.165516
$71$	−11.8246	−1.40332	−0.701661	−	0.712511i	$-0.747558\pi$
$71$	−11.8246	−1.40332	−0.701661	+	0.712511i	$0.747558\pi$
$72$	29.0766	3.42671
$73$	9.51276	1.11338	0.556692	−	0.830719i	$-0.312070\pi$
$73$	9.51276	1.11338	0.556692	+	0.830719i	$0.312070\pi$
$74$	−10.8484	−1.26110
$75$	1.52665	0.176282
$76$	17.1080	1.96242
$77$	−1.79797	−0.204898
$78$	1.06214	0.120264
$79$	−7.42313	−0.835167	−0.417583	−	0.908639i	$-0.637123\pi$
$79$	−7.42313	−0.835167	−0.417583	+	0.908639i	$0.637123\pi$
$80$	−17.0287	−1.90387
$81$	7.69919	0.855466
$82$	−13.4941	−1.49017
$83$	8.52610	0.935861	0.467930	−	0.883765i	$-0.345000\pi$
$83$	8.52610	0.935861	0.467930	+	0.883765i	$0.345000\pi$
$84$	−1.07844	−0.117668
$85$	−0.117211	−0.0127133
$86$	26.0755	2.81179
$87$	1.48024	0.158698
$88$	36.9803	3.94211
$89$	−2.51878	−0.266991	−0.133495	−	0.991049i	$-0.542620\pi$
$89$	−2.51878	−0.266991	−0.133495	+	0.991049i	$0.542620\pi$
$90$	−7.97365	−0.840496
$91$	0.495501	0.0519426
$92$	4.19279	0.437129
$93$	−1.08488	−0.112497
$94$	−9.05404	−0.933852
$95$	−3.03898	−0.311793
$96$	10.1196	1.03282
$97$	−6.38672	−0.648473	−0.324236	−	0.945976i	$-0.605107\pi$
$97$	−6.38672	−0.648473	−0.324236	+	0.945976i	$0.605107\pi$
$98$	18.7161	1.89061
$99$	10.3526	1.04048
$100$	−22.6137	−2.26137
$101$	−10.0485	−0.999862	−0.499931	−	0.866065i	$-0.666641\pi$
$101$	−10.0485	−0.999862	−0.499931	+	0.866065i	$0.666641\pi$
$102$	0.123432	0.0122216
$103$	7.38045	0.727217	0.363609	−	0.931552i	$-0.381545\pi$
$103$	7.38045	0.727217	0.363609	+	0.931552i	$0.381545\pi$
$104$	−10.1914	−0.999344
$105$	0.191569	0.0186953
$106$	−6.45614	−0.627076
$107$	−2.31775	−0.224066	−0.112033	−	0.993705i	$-0.535736\pi$
$107$	−2.31775	−0.224066	−0.112033	+	0.993705i	$0.535736\pi$
$108$	12.7390	1.22582
$109$	8.25109	0.790311	0.395156	−	0.918614i	$-0.370691\pi$
$109$	8.25109	0.790311	0.395156	+	0.918614i	$0.370691\pi$
$110$	−10.1411	−0.966912
$111$	−1.50072	−0.142442
$112$	8.36576	0.790490
$113$	−4.11370	−0.386985	−0.193492	−	0.981102i	$-0.561981\pi$
$113$	−4.11370	−0.386985	−0.193492	+	0.981102i	$0.561981\pi$
$114$	3.20029	0.299734
$115$	−0.744786	−0.0694517
$116$	−21.9262	−2.03580
$117$	−2.85307	−0.263766
$118$	−30.6461	−2.82120
$119$	0.0575825	0.00527858
$120$	−3.94016	−0.359686
$121$	2.16669	0.196971
$122$	−40.6864	−3.68358
$123$	−1.86672	−0.168317
$124$	16.0699	1.44312
$125$	9.06002	0.810353
$126$	3.91724	0.348975
$127$	1.40466	0.124643	0.0623217	−	0.998056i	$-0.480150\pi$
$127$	1.40466	0.124643	0.0623217	+	0.998056i	$0.480150\pi$
$128$	−56.3326	−4.97914
$129$	3.60719	0.317595
$130$	2.79476	0.245117
$131$	−5.55929	−0.485718	−0.242859	−	0.970062i	$-0.578085\pi$
$131$	−5.55929	−0.485718	−0.242859	+	0.970062i	$0.578085\pi$
$132$	7.89754	0.687392
$133$	1.49297	0.129457
$134$	−26.6794	−2.30475
$135$	−2.26290	−0.194759
$136$	−1.18434	−0.101557
$137$	−4.67793	−0.399662	−0.199831	−	0.979830i	$-0.564039\pi$
$137$	−4.67793	−0.399662	−0.199831	+	0.979830i	$0.564039\pi$
$138$	0.784320	0.0667657
$139$	−10.3472	−0.877640	−0.438820	−	0.898575i	$-0.644603\pi$
$139$	−10.3472	−0.877640	−0.438820	+	0.898575i	$0.644603\pi$
$140$	−2.83766	−0.239826
$141$	−1.25250	−0.105480
$142$	32.7650	2.74958
$143$	−3.62859	−0.303438
$144$	−48.1696	−4.01413
$145$	3.89487	0.323451
$146$	−26.3590	−2.18149
$147$	2.58912	0.213547
$148$	22.2297	1.82727
$149$	2.47246	0.202552	0.101276	−	0.994858i	$-0.467707\pi$
$149$	2.47246	0.202552	0.101276	+	0.994858i	$0.467707\pi$
$150$	−4.23021	−0.345396
$151$	6.24386	0.508118	0.254059	−	0.967189i	$-0.418234\pi$
$151$	6.24386	0.508118	0.254059	+	0.967189i	$0.418234\pi$
$152$	−30.7070	−2.49067
$153$	−0.331557	−0.0268048
$154$	4.98203	0.401463
$155$	−2.85458	−0.229285
$156$	−2.17647	−0.174257
$157$	1.59010	0.126903	0.0634517	−	0.997985i	$-0.479789\pi$
$157$	1.59010	0.126903	0.0634517	+	0.997985i	$0.479789\pi$
$158$	20.5689	1.63637
$159$	−0.893120	−0.0708290
$160$	26.6271	2.10506
$161$	0.365893	0.0288364
$162$	−21.3338	−1.67614
$163$	−3.51122	−0.275020	−0.137510	−	0.990500i	$-0.543910\pi$
$163$	−3.51122	−0.275020	−0.137510	+	0.990500i	$0.543910\pi$
$164$	27.6512	2.15919
$165$	−1.40288	−0.109214
$166$	−23.6251	−1.83366
$167$	−8.49691	−0.657511	−0.328755	−	0.944415i	$-0.606629\pi$
$167$	−8.49691	−0.657511	−0.328755	+	0.944415i	$0.606629\pi$
$168$	1.93569	0.149342
$169$	1.00000	0.0769231
$170$	0.324781	0.0249096
$171$	−8.59642	−0.657385
$172$	−53.4321	−4.07416
$173$	−5.93521	−0.451246	−0.225623	−	0.974215i	$-0.572442\pi$
$173$	−5.93521	−0.451246	−0.225623	+	0.974215i	$0.572442\pi$
$174$	−4.10161	−0.310942
$175$	−1.97344	−0.149178
$176$	−61.2631	−4.61788
$177$	−4.23947	−0.318658
$178$	6.97934	0.523123
$179$	−8.55524	−0.639449	−0.319724	−	0.947511i	$-0.603590\pi$
$179$	−8.55524	−0.639449	−0.319724	+	0.947511i	$0.603590\pi$
$180$	16.3391	1.21784
$181$	3.18904	0.237040	0.118520	−	0.992952i	$-0.462185\pi$
$181$	3.18904	0.237040	0.118520	+	0.992952i	$0.462185\pi$
$182$	−1.37299	−0.101773
$183$	−5.62842	−0.416065
$184$	−7.52561	−0.554795
$185$	−3.94877	−0.290320
$186$	3.00610	0.220418
$187$	−0.421681	−0.0308364
$188$	18.5529	1.35311
$189$	1.11170	0.0808644
$190$	8.42075	0.610906
$191$	11.1945	0.810003	0.405002	−	0.914316i	$-0.367271\pi$
$191$	11.1945	0.810003	0.405002	+	0.914316i	$0.367271\pi$
$192$	−15.0970	−1.08953
$193$	4.77584	0.343772	0.171886	−	0.985117i	$-0.445014\pi$
$193$	4.77584	0.343772	0.171886	+	0.985117i	$0.445014\pi$
$194$	17.6971	1.27057
$195$	0.386618	0.0276863
$196$	−38.3518	−2.73941
$197$	17.0176	1.21245	0.606226	−	0.795292i	$-0.292683\pi$
$197$	17.0176	1.21245	0.606226	+	0.795292i	$0.292683\pi$
$198$	−28.6862	−2.03864
$199$	−13.3182	−0.944104	−0.472052	−	0.881571i	$-0.656487\pi$
$199$	−13.3182	−0.944104	−0.472052	+	0.881571i	$0.656487\pi$
$200$	40.5892	2.87009
$201$	−3.69073	−0.260324
$202$	27.8435	1.95906
$203$	−1.91344	−0.134297
$204$	−0.252929	−0.0177086
$205$	−4.91181	−0.343056
$206$	−20.4506	−1.42486
$207$	−2.10679	−0.146432
$208$	16.8834	1.17066
$209$	−10.9331	−0.756260
$210$	−0.530823	−0.0366303
$211$	10.8147	0.744516	0.372258	−	0.928129i	$-0.378584\pi$
$211$	10.8147	0.744516	0.372258	+	0.928129i	$0.378584\pi$
$212$	13.2295	0.908605
$213$	4.53259	0.310568
$214$	6.42230	0.439019
$215$	9.49140	0.647308
$216$	−22.8652	−1.55578
$217$	1.40238	0.0951996
$218$	−22.8631	−1.54848
$219$	−3.64642	−0.246402
$220$	20.7804	1.40101
$221$	0.116211	0.00781717
$222$	4.15838	0.279092
$223$	−13.9311	−0.932897	−0.466448	−	0.884548i	$-0.654467\pi$
$223$	−13.9311	−0.932897	−0.466448	+	0.884548i	$0.654467\pi$
$224$	−13.0812	−0.874022
$225$	11.3629	0.757530
$226$	11.3987	0.758232
$227$	−1.36806	−0.0908014	−0.0454007	−	0.998969i	$-0.514456\pi$
$227$	−1.36806	−0.0908014	−0.0454007	+	0.998969i	$0.514456\pi$
$228$	−6.55782	−0.434302
$229$	4.34618	0.287203	0.143602	−	0.989636i	$-0.454132\pi$
$229$	4.34618	0.287203	0.143602	+	0.989636i	$0.454132\pi$
$230$	2.06374	0.136079
$231$	0.689196	0.0453458
$232$	39.3552	2.58380
$233$	3.04070	0.199203	0.0996015	−	0.995027i	$-0.468243\pi$
$233$	3.04070	0.199203	0.0996015	+	0.995027i	$0.468243\pi$
$234$	7.90561	0.516806
$235$	−3.29565	−0.214984
$236$	62.7979	4.08779
$237$	2.84542	0.184830
$238$	−0.159556	−0.0103425
$239$	3.77609	0.244255	0.122128	−	0.992514i	$-0.461028\pi$
$239$	3.77609	0.244255	0.122128	+	0.992514i	$0.461028\pi$
$240$	6.52744	0.421344
$241$	−16.1080	−1.03761	−0.518803	−	0.854894i	$-0.673622\pi$
$241$	−16.1080	−1.03761	−0.518803	+	0.854894i	$0.673622\pi$
$242$	−6.00370	−0.385933
$243$	−9.68201	−0.621101
$244$	83.3719	5.33734
$245$	6.81261	0.435242
$246$	5.17253	0.329789
$247$	3.01305	0.191716
$248$	−28.8438	−1.83158
$249$	−3.26821	−0.207115
$250$	−25.1046	−1.58775
$251$	−5.07913	−0.320592	−0.160296	−	0.987069i	$-0.551245\pi$
$251$	−5.07913	−0.320592	−0.160296	+	0.987069i	$0.551245\pi$
$252$	−8.02694	−0.505650
$253$	−2.67946	−0.168457
$254$	−3.89219	−0.244218
$255$	0.0449291	0.00281357
$256$	77.3230	4.83269
$257$	−28.0709	−1.75102	−0.875509	−	0.483202i	$-0.839474\pi$
$257$	−28.0709	−1.75102	−0.875509	+	0.483202i	$0.839474\pi$
$258$	−9.99521	−0.622275
$259$	1.93993	0.120541
$260$	−5.72684	−0.355164
$261$	11.0175	0.681966
$262$	15.4043	0.951683
$263$	19.6718	1.21302	0.606509	−	0.795077i	$-0.292570\pi$
$263$	19.6718	1.21302	0.606509	+	0.795077i	$0.292570\pi$
$264$	−14.1752	−0.872425
$265$	−2.35002	−0.144361
$266$	−4.13689	−0.253649
$267$	0.965497	0.0590875
$268$	54.6696	3.33947
$269$	−27.0842	−1.65135	−0.825675	−	0.564146i	$-0.809206\pi$
$269$	−27.0842	−1.65135	−0.825675	+	0.564146i	$0.809206\pi$
$270$	6.27030	0.381598
$271$	−13.2837	−0.806928	−0.403464	−	0.914996i	$-0.632194\pi$
$271$	−13.2837	−0.806928	−0.403464	+	0.914996i	$0.632194\pi$
$272$	1.96203	0.118966
$273$	−0.189935	−0.0114954
$274$	12.9621	0.783072
$275$	14.4516	0.871467
$276$	−1.60718	−0.0967406
$277$	17.2231	1.03484	0.517418	−	0.855733i	$-0.326893\pi$
$277$	17.2231	1.03484	0.517418	+	0.855733i	$0.326893\pi$
$278$	28.6713	1.71959
$279$	−8.07481	−0.483426
$280$	5.09329	0.304382
$281$	−10.2183	−0.609575	−0.304788	−	0.952420i	$-0.598586\pi$
$281$	−10.2183	−0.609575	−0.304788	+	0.952420i	$0.598586\pi$
$282$	3.47058	0.206670
$283$	−4.33656	−0.257782	−0.128891	−	0.991659i	$-0.541142\pi$
$283$	−4.33656	−0.257782	−0.128891	+	0.991659i	$0.541142\pi$
$284$	−67.1398	−3.98401
$285$	1.16490	0.0690025
$286$	10.0545	0.594537
$287$	2.41304	0.142437
$288$	75.3206	4.43831
$289$	−16.9865	−0.999206
$290$	−10.7923	−0.633748
$291$	2.44815	0.143513
$292$	54.0132	3.16088
$293$	18.3957	1.07469	0.537344	−	0.843363i	$-0.319428\pi$
$293$	18.3957	1.07469	0.537344	+	0.843363i	$0.319428\pi$
$294$	−7.17423	−0.418409
$295$	−11.1551	−0.649475
$296$	−39.9000	−2.31914
$297$	−8.14107	−0.472393
$298$	−6.85098	−0.396867
$299$	0.738431	0.0427046
$300$	8.66827	0.500463
$301$	−4.66287	−0.268763
$302$	−17.3012	−0.995572
$303$	3.85177	0.221279
$304$	50.8706	2.91763
$305$	−14.8098	−0.848005
$306$	0.918715	0.0525195
$307$	−5.81971	−0.332148	−0.166074	−	0.986113i	$-0.553109\pi$
$307$	−5.81971	−0.332148	−0.166074	+	0.986113i	$0.553109\pi$
$308$	−10.2088	−0.581702
$309$	−2.82906	−0.160940
$310$	7.90980	0.449247
$311$	13.5397	0.767767	0.383883	−	0.923382i	$-0.374586\pi$
$311$	13.5397	0.767767	0.383883	+	0.923382i	$0.374586\pi$
$312$	3.90654	0.221164
$313$	30.1824	1.70601	0.853004	−	0.521904i	$-0.174778\pi$
$313$	30.1824	1.70601	0.853004	+	0.521904i	$0.174778\pi$
$314$	−4.40602	−0.248646
$315$	1.42586	0.0803384
$316$	−42.1483	−2.37103
$317$	−19.1396	−1.07499	−0.537494	−	0.843268i	$-0.680629\pi$
$317$	−19.1396	−1.07499	−0.537494	+	0.843268i	$0.680629\pi$
$318$	2.47476	0.138778
$319$	14.0123	0.784537
$320$	−39.7239	−2.22063
$321$	0.888438	0.0495878
$322$	−1.01386	−0.0565002
$323$	0.350148	0.0194828
$324$	43.7158	2.42866
$325$	−3.98271	−0.220921
$326$	9.72930	0.538856
$327$	−3.16280	−0.174903
$328$	−49.6309	−2.74041
$329$	1.61906	0.0892618
$330$	3.88726	0.213986
$331$	−13.5278	−0.743554	−0.371777	−	0.928322i	$-0.621251\pi$
$331$	−13.5278	−0.743554	−0.371777	+	0.928322i	$0.621251\pi$
$332$	48.4110	2.65690
$333$	−11.1700	−0.612111
$334$	23.5442	1.28828
$335$	−9.71122	−0.530581
$336$	−3.20675	−0.174943
$337$	19.4172	1.05772	0.528860	−	0.848709i	$-0.322619\pi$
$337$	19.4172	1.05772	0.528860	+	0.848709i	$0.322619\pi$
$338$	−2.77092	−0.150718
$339$	1.57686	0.0856433
$340$	−0.665520	−0.0360929
$341$	−10.2697	−0.556137
$342$	23.8200	1.28804
$343$	−6.81536	−0.367995
$344$	95.9048	5.17084
$345$	0.285490	0.0153703
$346$	16.4460	0.884141
$347$	3.71008	0.199168	0.0995838	−	0.995029i	$-0.468249\pi$
$347$	3.71008	0.199168	0.0995838	+	0.995029i	$0.468249\pi$
$348$	8.40474	0.450541
$349$	1.69000	0.0904636	0.0452318	−	0.998977i	$-0.485597\pi$
$349$	1.69000	0.0904636	0.0452318	+	0.998977i	$0.485597\pi$
$350$	5.46823	0.292289
$351$	2.24359	0.119754
$352$	95.7944	5.10586
$353$	24.9104	1.32585	0.662924	−	0.748686i	$-0.269315\pi$
$353$	24.9104	1.32585	0.662924	+	0.748686i	$0.269315\pi$
$354$	11.7472	0.624358
$355$	11.9264	0.632986
$356$	−14.3016	−0.757983
$357$	−0.0220724	−0.00116820
$358$	23.7059	1.25289
$359$	−7.23157	−0.381668	−0.190834	−	0.981622i	$-0.561119\pi$
$359$	−7.23157	−0.381668	−0.190834	+	0.981622i	$0.561119\pi$
$360$	−29.3269	−1.54566
$361$	−9.92155	−0.522187
$362$	−8.83657	−0.464440
$363$	−0.830531	−0.0435916
$364$	2.81344	0.147464
$365$	−9.59463	−0.502206
$366$	15.5959	0.815209
$367$	−8.06040	−0.420749	−0.210375	−	0.977621i	$-0.567468\pi$
$367$	−8.06040	−0.420749	−0.210375	+	0.977621i	$0.567468\pi$
$368$	12.4672	0.649900
$369$	−13.8942	−0.723301
$370$	10.9417	0.568833
$371$	1.15450	0.0599387
$372$	−6.15990	−0.319376
$373$	−22.5911	−1.16972	−0.584862	−	0.811133i	$-0.698851\pi$
$373$	−22.5911	−1.16972	−0.584862	+	0.811133i	$0.698851\pi$
$374$	1.16844	0.0604187
$375$	−3.47288	−0.179339
$376$	−33.3005	−1.71734
$377$	−3.86163	−0.198884
$378$	−3.08043	−0.158440
$379$	−4.17440	−0.214425	−0.107212	−	0.994236i	$-0.534192\pi$
$379$	−4.17440	−0.214425	−0.107212	+	0.994236i	$0.534192\pi$
$380$	−17.2552	−0.885175
$381$	−0.538432	−0.0275847
$382$	−31.0189	−1.58707
$383$	28.5823	1.46048	0.730242	−	0.683188i	$-0.239407\pi$
$383$	28.5823	1.46048	0.730242	+	0.683188i	$0.239407\pi$
$384$	21.5933	1.10193
$385$	1.81345	0.0924217
$386$	−13.2334	−0.673564
$387$	26.8485	1.36479
$388$	−36.2636	−1.84101
$389$	31.9173	1.61827	0.809137	−	0.587620i	$-0.199935\pi$
$389$	31.9173	1.61827	0.809137	+	0.587620i	$0.199935\pi$
$390$	−1.07129	−0.0542466
$391$	0.0858135	0.00433977
$392$	68.8373	3.47681
$393$	2.13098	0.107494
$394$	−47.1543	−2.37560
$395$	7.48701	0.376712
$396$	58.7819	2.95390
$397$	3.82887	0.192166	0.0960828	−	0.995373i	$-0.469369\pi$
$397$	3.82887	0.192166	0.0960828	+	0.995373i	$0.469369\pi$
$398$	36.9037	1.84981
$399$	−0.572282	−0.0286500
$400$	−67.2419	−3.36209
$401$	19.9031	0.993915	0.496958	−	0.867775i	$-0.334450\pi$
$401$	19.9031	0.993915	0.496958	+	0.867775i	$0.334450\pi$
$402$	10.2267	0.510061
$403$	2.83022	0.140983
$404$	−57.0550	−2.83859
$405$	−7.76545	−0.385868
$406$	5.30199	0.263133
$407$	−14.2062	−0.704177
$408$	0.453981	0.0224754
$409$	−20.7672	−1.02687	−0.513437	−	0.858127i	$-0.671628\pi$
$409$	−20.7672	−1.02687	−0.513437	+	0.858127i	$0.671628\pi$
$410$	13.6102	0.672161
$411$	1.79314	0.0884489
$412$	41.9060	2.06456
$413$	5.48020	0.269663
$414$	5.83774	0.286909
$415$	−8.59948	−0.422132
$416$	−26.3999	−1.29436
$417$	3.96628	0.194230
$418$	30.2948	1.48176
$419$	−27.3934	−1.33826	−0.669128	−	0.743147i	$-0.733332\pi$
$419$	−27.3934	−1.33826	−0.669128	+	0.743147i	$0.733332\pi$
$420$	1.08773	0.0530756
$421$	−22.7325	−1.10792	−0.553958	−	0.832545i	$-0.686883\pi$
$421$	−22.7325	−1.10792	−0.553958	+	0.832545i	$0.686883\pi$
$422$	−29.9667	−1.45875
$423$	−9.32247	−0.453274
$424$	−23.7455	−1.15318
$425$	−0.462833	−0.0224507
$426$	−12.5594	−0.608506
$427$	7.27564	0.352093
$428$	−13.1601	−0.636119
$429$	1.39091	0.0671536
$430$	−26.2999	−1.26829
$431$	−22.1591	−1.06737	−0.533683	−	0.845685i	$-0.679192\pi$
$431$	−22.1591	−1.06737	−0.533683	+	0.845685i	$0.679192\pi$
$432$	37.8795	1.82248
$433$	−5.73650	−0.275678	−0.137839	−	0.990455i	$-0.544016\pi$
$433$	−5.73650	−0.275678	−0.137839	+	0.990455i	$0.544016\pi$
$434$	−3.88587	−0.186528
$435$	−1.49297	−0.0715827
$436$	46.8495	2.24368
$437$	2.22493	0.106433
$438$	10.1039	0.482784
$439$	−36.0072	−1.71853	−0.859265	−	0.511530i	$-0.829079\pi$
$439$	−36.0072	−1.71853	−0.859265	+	0.511530i	$0.829079\pi$
$440$	−37.2985	−1.77814
$441$	19.2710	0.917666
$442$	−0.322010	−0.0153164
$443$	7.73534	0.367517	0.183758	−	0.982971i	$-0.441174\pi$
$443$	7.73534	0.367517	0.183758	+	0.982971i	$0.441174\pi$
$444$	−8.52107	−0.404392
$445$	2.54046	0.120429
$446$	38.6020	1.82786
$447$	−0.947741	−0.0448266
$448$	19.5153	0.922010
$449$	−0.497023	−0.0234560	−0.0117280	−	0.999931i	$-0.503733\pi$
$449$	−0.497023	−0.0234560	−0.0117280	+	0.999931i	$0.503733\pi$
$450$	−31.4858	−1.48425
$451$	−17.6709	−0.832090
$452$	−23.3575	−1.09864
$453$	−2.39339	−0.112451
$454$	3.79078	0.177910
$455$	−0.499766	−0.0234294
$456$	11.7706	0.551208
$457$	10.2017	0.477215	0.238607	−	0.971116i	$-0.423309\pi$
$457$	10.2017	0.477215	0.238607	+	0.971116i	$0.423309\pi$
$458$	−12.0429	−0.562727
$459$	0.260729	0.0121698
$460$	−4.22888	−0.197172
$461$	2.77483	0.129237	0.0646183	−	0.997910i	$-0.479417\pi$
$461$	2.77483	0.129237	0.0646183	+	0.997910i	$0.479417\pi$
$462$	−1.90970	−0.0888475
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	−65.1976	−3.02672
$465$	1.09421	0.0507430
$466$	−8.42553	−0.390305
$467$	13.3627	0.618352	0.309176	−	0.951005i	$-0.399947\pi$
$467$	13.3627	0.618352	0.309176	+	0.951005i	$0.399947\pi$
$468$	−16.1996	−0.748829
$469$	4.77086	0.220298
$470$	9.13196	0.421226
$471$	−0.609513	−0.0280849
$472$	−112.715	−5.18815
$473$	34.1466	1.57006
$474$	−7.88443	−0.362144
$475$	−12.0001	−0.550602
$476$	0.326952	0.0149858
$477$	−6.64755	−0.304370
$478$	−10.4632	−0.478577
$479$	−18.8321	−0.860461	−0.430231	−	0.902719i	$-0.641568\pi$
$479$	−18.8321	−0.860461	−0.430231	+	0.902719i	$0.641568\pi$
$480$	−10.2067	−0.465868
$481$	3.91508	0.178512
$482$	44.6339	2.03302
$483$	−0.140254	−0.00638177
$484$	12.3024	0.559199
$485$	6.44168	0.292502
$486$	26.8280	1.21694
$487$	20.9182	0.947896	0.473948	−	0.880553i	$-0.342829\pi$
$487$	20.9182	0.947896	0.473948	+	0.880553i	$0.342829\pi$
$488$	−149.644	−6.77405
$489$	1.34592	0.0608645
$490$	−18.8772	−0.852784
$491$	−24.1671	−1.09065	−0.545323	−	0.838226i	$-0.683593\pi$
$491$	−24.1671	−1.09065	−0.545323	+	0.838226i	$0.683593\pi$
$492$	−10.5992	−0.477849
$493$	−0.448762	−0.0202112
$494$	−8.34890	−0.375635
$495$	−10.4417	−0.469320
$496$	47.7839	2.14556
$497$	−5.85910	−0.262817
$498$	9.05594	0.405806
$499$	−13.5760	−0.607747	−0.303874	−	0.952712i	$-0.598280\pi$
$499$	−13.5760	−0.607747	−0.303874	+	0.952712i	$0.598280\pi$
$500$	51.4426	2.30058
$501$	3.25703	0.145513
$502$	14.0738	0.628146
$503$	9.24691	0.412299	0.206150	−	0.978520i	$-0.433907\pi$
$503$	9.24691	0.412299	0.206150	+	0.978520i	$0.433907\pi$
$504$	14.4075	0.641761
$505$	10.1350	0.451000
$506$	7.42457	0.330062
$507$	−0.383319	−0.0170238
$508$	7.97562	0.353861
$509$	−5.09777	−0.225955	−0.112977	−	0.993598i	$-0.536039\pi$
$509$	−5.09777	−0.225955	−0.112977	+	0.993598i	$0.536039\pi$
$510$	−0.124495	−0.00551272
$511$	4.71358	0.208517
$512$	−101.590	−4.48970
$513$	6.76004	0.298463
$514$	77.7822	3.43083
$515$	−7.44397	−0.328020
$516$	20.4815	0.901648
$517$	−11.8565	−0.521449
$518$	−5.37537	−0.236180
$519$	2.27508	0.0998648
$520$	10.2791	0.450767
$521$	−0.832601	−0.0364769	−0.0182385	−	0.999834i	$-0.505806\pi$
$521$	−0.832601	−0.0364769	−0.0182385	+	0.999834i	$0.505806\pi$
$522$	−30.5285	−1.33620
$523$	22.5835	0.987508	0.493754	−	0.869602i	$-0.335624\pi$
$523$	22.5835	0.987508	0.493754	+	0.869602i	$0.335624\pi$
$524$	−31.5655	−1.37895
$525$	0.756456	0.0330144
$526$	−54.5090	−2.37671
$527$	0.328902	0.0143272
$528$	23.4833	1.02198
$529$	−22.4547	−0.976292
$530$	6.51170	0.282850
$531$	−31.5547	−1.36936
$532$	8.47703	0.367526
$533$	4.86990	0.210939
$534$	−2.67531	−0.115772
$535$	2.33770	0.101068
$536$	−98.1260	−4.23840
$537$	3.27938	0.141516
$538$	75.0479	3.23555
$539$	24.5093	1.05569
$540$	−12.8487	−0.552919
$541$	−16.5529	−0.711663	−0.355831	−	0.934550i	$-0.615802\pi$
$541$	−16.5529	−0.711663	−0.355831	+	0.934550i	$0.615802\pi$
$542$	36.8080	1.58104
$543$	−1.22242	−0.0524591
$544$	−3.06794	−0.131537
$545$	−8.32210	−0.356480
$546$	0.526293	0.0225233
$547$	−34.4386	−1.47249	−0.736245	−	0.676715i	$-0.763403\pi$
$547$	−34.4386	−1.47249	−0.736245	+	0.676715i	$0.763403\pi$
$548$	−26.5611	−1.13464
$549$	−41.8927	−1.78794
$550$	−40.0443	−1.70749
$551$	−11.6353	−0.495679
$552$	2.88471	0.122781
$553$	−3.67817	−0.156412
$554$	−47.7238	−2.02759
$555$	1.51364	0.0642504
$556$	−58.7512	−2.49161
$557$	−36.8843	−1.56284	−0.781420	−	0.624006i	$-0.785504\pi$
$557$	−36.8843	−1.56284	−0.781420	+	0.624006i	$0.785504\pi$
$558$	22.3746	0.947194
$559$	−9.41041	−0.398018
$560$	−8.43776	−0.356560
$561$	0.161638	0.00682437
$562$	28.3142	1.19436
$563$	−23.4772	−0.989445	−0.494722	−	0.869051i	$-0.664730\pi$
$563$	−23.4772	−0.989445	−0.494722	+	0.869051i	$0.664730\pi$
$564$	−7.11168	−0.299456
$565$	4.14911	0.174554
$566$	12.0162	0.505081
$567$	3.81496	0.160213
$568$	120.509	5.05643
$569$	23.7348	0.995013	0.497507	−	0.867460i	$-0.334249\pi$
$569$	23.7348	0.995013	0.497507	+	0.867460i	$0.334249\pi$
$570$	−3.22783	−0.135199
$571$	37.6779	1.57677	0.788386	−	0.615181i	$-0.210917\pi$
$571$	37.6779	1.57677	0.788386	+	0.615181i	$0.210917\pi$
$572$	−20.6031	−0.861457
$573$	−4.29105	−0.179261
$574$	−6.68633	−0.279082
$575$	−2.94096	−0.122646
$576$	−112.368	−4.68199
$577$	−30.7899	−1.28180	−0.640899	−	0.767625i	$-0.721438\pi$
$577$	−30.7899	−1.28180	−0.640899	+	0.767625i	$0.721438\pi$
$578$	47.0681	1.95778
$579$	−1.83067	−0.0760799
$580$	22.1149	0.918273
$581$	4.22469	0.175270
$582$	−6.78361	−0.281190
$583$	−8.45450	−0.350150
$584$	−96.9479	−4.01173
$585$	2.87762	0.118975
$586$	−50.9730	−2.10567
$587$	15.8346	0.653564	0.326782	−	0.945100i	$-0.394036\pi$
$587$	15.8346	0.653564	0.326782	+	0.945100i	$0.394036\pi$
$588$	14.7009	0.606257
$589$	8.52759	0.351373
$590$	30.9098	1.27254
$591$	−6.52316	−0.268327
$592$	66.1000	2.71669
$593$	−10.9265	−0.448697	−0.224349	−	0.974509i	$-0.572025\pi$
$593$	−10.9265	−0.448697	−0.224349	+	0.974509i	$0.572025\pi$
$594$	22.5582	0.925575
$595$	−0.0580780	−0.00238097
$596$	14.0386	0.575042
$597$	5.10512	0.208939
$598$	−2.04613	−0.0836725
$599$	−10.7391	−0.438788	−0.219394	−	0.975636i	$-0.570408\pi$
$599$	−10.7391	−0.438788	−0.219394	+	0.975636i	$0.570408\pi$
$600$	−15.5586	−0.635178
$601$	2.67400	0.109075	0.0545373	−	0.998512i	$-0.482632\pi$
$601$	2.67400	0.109075	0.0545373	+	0.998512i	$0.482632\pi$
$602$	12.9204	0.526597
$603$	−27.4703	−1.11868
$604$	35.4525	1.44254
$605$	−2.18533	−0.0888464
$606$	−10.6729	−0.433558
$607$	−15.4017	−0.625135	−0.312567	−	0.949896i	$-0.601189\pi$
$607$	−15.4017	−0.625135	−0.312567	+	0.949896i	$0.601189\pi$
$608$	−79.5440	−3.22594
$609$	0.733458	0.0297212
$610$	41.0366	1.66152
$611$	3.26752	0.132190
$612$	−1.88257	−0.0760984
$613$	13.9508	0.563468	0.281734	−	0.959493i	$-0.409090\pi$
$613$	13.9508	0.563468	0.281734	+	0.959493i	$0.409090\pi$
$614$	16.1259	0.650789
$615$	1.88279	0.0759214
$616$	18.3238	0.738286
$617$	3.63760	0.146444	0.0732222	−	0.997316i	$-0.476672\pi$
$617$	3.63760	0.146444	0.0732222	+	0.997316i	$0.476672\pi$
$618$	7.83910	0.315335
$619$	−3.18143	−0.127873	−0.0639363	−	0.997954i	$-0.520365\pi$
$619$	−3.18143	−0.127873	−0.0639363	+	0.997954i	$0.520365\pi$
$620$	−16.2082	−0.650938
$621$	1.65674	0.0664825
$622$	−37.5174	−1.50431
$623$	−1.24806	−0.0500025
$624$	−6.47174	−0.259077
$625$	10.7756	0.431023
$626$	−83.6328	−3.34264
$627$	4.19087	0.167367
$628$	9.02852	0.360277
$629$	0.454974	0.0181410
$630$	−3.95095	−0.157410
$631$	24.7678	0.985991	0.492995	−	0.870032i	$-0.335902\pi$
$631$	24.7678	0.985991	0.492995	+	0.870032i	$0.335902\pi$
$632$	75.6517	3.00926
$633$	−4.14548	−0.164768
$634$	53.0343	2.10626
$635$	−1.41675	−0.0562220
$636$	−5.07111	−0.201083
$637$	−6.75448	−0.267622
$638$	−38.8269	−1.53717
$639$	33.7364	1.33459
$640$	56.8174	2.24591
$641$	−29.1956	−1.15316	−0.576578	−	0.817042i	$-0.695612\pi$
$641$	−29.1956	−1.15316	−0.576578	+	0.817042i	$0.695612\pi$
$642$	−2.46179	−0.0971590
$643$	−11.2866	−0.445100	−0.222550	−	0.974921i	$-0.571438\pi$
$643$	−11.2866	−0.445100	−0.222550	+	0.974921i	$0.571438\pi$
$644$	2.07753	0.0818662
$645$	−3.63823	−0.143255
$646$	−0.970230	−0.0381732
$647$	−14.6084	−0.574316	−0.287158	−	0.957883i	$-0.592711\pi$
$647$	−14.6084	−0.574316	−0.287158	+	0.957883i	$0.592711\pi$
$648$	−78.4652	−3.08240
$649$	−40.1319	−1.57532
$650$	11.0358	0.432858
$651$	−0.537558	−0.0210686
$652$	−19.9366	−0.780778
$653$	−10.5754	−0.413849	−0.206924	−	0.978357i	$-0.566345\pi$
$653$	−10.5754	−0.413849	−0.206924	+	0.978357i	$0.566345\pi$
$654$	8.76384	0.342693
$655$	5.60714	0.219089
$656$	82.2207	3.21018
$657$	−27.1405	−1.05885
$658$	−4.48628	−0.174894
$659$	40.4228	1.57465	0.787325	−	0.616539i	$-0.211466\pi$
$659$	40.4228	1.57465	0.787325	+	0.616539i	$0.211466\pi$
$660$	−7.96551	−0.310057
$661$	−38.7744	−1.50815	−0.754074	−	0.656790i	$-0.771914\pi$
$661$	−38.7744	−1.50815	−0.754074	+	0.656790i	$0.771914\pi$
$662$	37.4844	1.45687
$663$	−0.0445457	−0.00173001
$664$	−86.8925	−3.37208
$665$	−1.50582	−0.0583931
$666$	30.9511	1.19933
$667$	−2.85155	−0.110412
$668$	−48.2452	−1.86666
$669$	5.34006	0.206459
$670$	26.9090	1.03958
$671$	−53.2801	−2.05685
$672$	5.01425	0.193429
$673$	−19.3777	−0.746956	−0.373478	−	0.927639i	$-0.621835\pi$
$673$	−19.3777	−0.746956	−0.373478	+	0.927639i	$0.621835\pi$
$674$	−53.8034	−2.07243
$675$	−8.93558	−0.343930
$676$	5.67797	0.218384
$677$	14.4421	0.555054	0.277527	−	0.960718i	$-0.410485\pi$
$677$	14.4421	0.555054	0.277527	+	0.960718i	$0.410485\pi$
$678$	−4.36935	−0.167804
$679$	−3.16462	−0.121447
$680$	1.19454	0.0458084
$681$	0.524404	0.0200952
$682$	28.4565	1.08966
$683$	−39.6431	−1.51690	−0.758451	−	0.651730i	$-0.774044\pi$
$683$	−39.6431	−1.51690	−0.758451	+	0.651730i	$0.774044\pi$
$684$	−48.8103	−1.86631
$685$	4.71819	0.180273
$686$	18.8848	0.721024
$687$	−1.66597	−0.0635607
$688$	−158.880	−6.05725
$689$	2.32997	0.0887646
$690$	−0.791070	−0.0301155
$691$	−44.5644	−1.69531	−0.847656	−	0.530547i	$-0.821987\pi$
$691$	−44.5644	−1.69531	−0.847656	+	0.530547i	$0.821987\pi$
$692$	−33.7000	−1.28108
$693$	5.12973	0.194862
$694$	−10.2803	−0.390236
$695$	10.4363	0.395870
$696$	−15.0856	−0.571818
$697$	0.565934	0.0214363
$698$	−4.68285	−0.177248
$699$	−1.16556	−0.0440854
$700$	−11.2051	−0.423514
$701$	−3.58601	−0.135442	−0.0677208	−	0.997704i	$-0.521573\pi$
$701$	−3.58601	−0.135442	−0.0677208	+	0.997704i	$0.521573\pi$
$702$	−6.21680	−0.234638
$703$	11.7963	0.444907
$704$	−142.912	−5.38619
$705$	1.26328	0.0475780
$706$	−69.0247	−2.59778
$707$	−4.97904	−0.187256
$708$	−24.0716	−0.904666
$709$	44.4344	1.66877	0.834384	−	0.551184i	$-0.185824\pi$
$709$	44.4344	1.66877	0.834384	+	0.551184i	$0.185824\pi$
$710$	−33.0470	−1.24023
$711$	21.1787	0.794262
$712$	25.6698	0.962017
$713$	2.08992	0.0782683
$714$	0.0611609	0.00228889
$715$	3.65982	0.136870
$716$	−48.5764	−1.81539
$717$	−1.44745	−0.0540559
$718$	20.0381	0.747814
$719$	44.0193	1.64164	0.820822	−	0.571185i	$-0.193516\pi$
$719$	44.0193	1.64164	0.820822	+	0.571185i	$0.193516\pi$
$720$	48.5841	1.81062
$721$	3.65702	0.136195
$722$	27.4918	1.02314
$723$	6.17449	0.229632
$724$	18.1073	0.672953
$725$	15.3798	0.571190
$726$	2.30133	0.0854105
$727$	−24.7184	−0.916756	−0.458378	−	0.888757i	$-0.651569\pi$
$727$	−24.7184	−0.916756	−0.458378	+	0.888757i	$0.651569\pi$
$728$	−5.04983	−0.187159
$729$	−19.3863	−0.718010
$730$	26.5859	0.983988
$731$	−1.09359	−0.0404479
$732$	−31.9580	−1.18120
$733$	−30.9692	−1.14387	−0.571937	−	0.820297i	$-0.693808\pi$
$733$	−30.9692	−1.14387	−0.571937	+	0.820297i	$0.693808\pi$
$734$	22.3347	0.824388
$735$	−2.61140	−0.0963230
$736$	−19.4945	−0.718576
$737$	−34.9374	−1.28694
$738$	38.4995	1.41719
$739$	−25.2355	−0.928302	−0.464151	−	0.885756i	$-0.653641\pi$
$739$	−25.2355	−0.928302	−0.464151	+	0.885756i	$0.653641\pi$
$740$	−22.4210	−0.824214
$741$	−1.15496	−0.0424284
$742$	−3.19902	−0.117440
$743$	51.9171	1.90466	0.952328	−	0.305077i	$-0.0986822\pi$
$743$	51.9171	1.90466	0.952328	+	0.305077i	$0.0986822\pi$
$744$	11.0564	0.405346
$745$	−2.49374	−0.0913636
$746$	62.5981	2.29188
$747$	−24.3255	−0.890025
$748$	−2.39429	−0.0875440
$749$	−1.14845	−0.0419634
$750$	9.62305	0.351384
$751$	31.6194	1.15381	0.576905	−	0.816812i	$-0.304260\pi$
$751$	31.6194	1.15381	0.576905	+	0.816812i	$0.304260\pi$
$752$	55.1670	2.01174
$753$	1.94693	0.0709499
$754$	10.7003	0.389680
$755$	−6.29760	−0.229193
$756$	6.31221	0.229573
$757$	13.8339	0.502803	0.251401	−	0.967883i	$-0.419109\pi$
$757$	13.8339	0.502803	0.251401	+	0.967883i	$0.419109\pi$
$758$	11.5669	0.420129
$759$	1.02709	0.0372810
$760$	30.9713	1.12345
$761$	−25.8418	−0.936763	−0.468381	−	0.883526i	$-0.655163\pi$
$761$	−25.8418	−0.936763	−0.468381	+	0.883526i	$0.655163\pi$
$762$	1.49195	0.0540477
$763$	4.08842	0.148011
$764$	63.5619	2.29959
$765$	0.334410	0.0120906
$766$	−79.1990	−2.86158
$767$	11.0599	0.399350
$768$	−29.6394	−1.06952
$769$	−25.3392	−0.913755	−0.456877	−	0.889530i	$-0.651032\pi$
$769$	−25.3392	−0.913755	−0.456877	+	0.889530i	$0.651032\pi$
$770$	−5.02490	−0.181085
$771$	10.7601	0.387516
$772$	27.1171	0.975965
$773$	6.86858	0.247046	0.123523	−	0.992342i	$-0.460581\pi$
$773$	6.86858	0.247046	0.123523	+	0.992342i	$0.460581\pi$
$774$	−74.3950	−2.67407
$775$	−11.2720	−0.404901
$776$	65.0893	2.33657
$777$	−0.743610	−0.0266769
$778$	−88.4403	−3.17074
$779$	14.6732	0.525723
$780$	2.19521	0.0786009
$781$	42.9067	1.53532
$782$	−0.237782	−0.00850306
$783$	−8.66392	−0.309623
$784$	−114.039	−4.07281
$785$	−1.60378	−0.0572414
$786$	−5.90477	−0.210616
$787$	31.6527	1.12830	0.564149	−	0.825673i	$-0.309204\pi$
$787$	31.6527	1.12830	0.564149	+	0.825673i	$0.309204\pi$
$788$	96.6254	3.44214
$789$	−7.54058	−0.268452
$790$	−20.7459	−0.738105
$791$	−2.03835	−0.0724752
$792$	−105.507	−3.74903
$793$	14.6834	0.521423
$794$	−10.6095	−0.376517
$795$	0.900806	0.0319483
$796$	−75.6205	−2.68030
$797$	43.5563	1.54284	0.771422	−	0.636324i	$-0.219546\pi$
$797$	43.5563	1.54284	0.771422	+	0.636324i	$0.219546\pi$
$798$	1.58575	0.0561348
$799$	0.379721	0.0134336
$800$	105.143	3.71737
$801$	7.18626	0.253914
$802$	−55.1499	−1.94741
$803$	−34.5179	−1.21811
$804$	−20.9559	−0.739056
$805$	−0.369042	−0.0130070
$806$	−7.84231	−0.276234
$807$	10.3819	0.365459
$808$	102.408	3.60269
$809$	−42.7859	−1.50427	−0.752136	−	0.659008i	$-0.770976\pi$
$809$	−42.7859	−1.50427	−0.752136	+	0.659008i	$0.770976\pi$
$810$	21.5174	0.756045
$811$	23.3959	0.821541	0.410771	−	0.911739i	$-0.365260\pi$
$811$	23.3959	0.821541	0.410771	+	0.911739i	$0.365260\pi$
$812$	−10.8645	−0.381268
$813$	5.09189	0.178581
$814$	39.3643	1.37972
$815$	3.54144	0.124051
$816$	−0.752084	−0.0263282
$817$	−28.3540	−0.991981
$818$	57.5442	2.01199
$819$	−1.41370	−0.0493986
$820$	−27.8891	−0.973931
$821$	−24.6447	−0.860105	−0.430053	−	0.902804i	$-0.641505\pi$
$821$	−24.6447	−0.860105	−0.430053	+	0.902804i	$0.641505\pi$
$822$	−4.96863	−0.173301
$823$	22.5922	0.787514	0.393757	−	0.919215i	$-0.371175\pi$
$823$	22.5922	0.787514	0.393757	+	0.919215i	$0.371175\pi$
$824$	−75.2167	−2.62030
$825$	−5.53959	−0.192864
$826$	−15.1852	−0.528360
$827$	−4.88500	−0.169868	−0.0849340	−	0.996387i	$-0.527068\pi$
$827$	−4.88500	−0.169868	−0.0849340	+	0.996387i	$0.527068\pi$
$828$	−11.9623	−0.415719
$829$	−37.6934	−1.30915	−0.654573	−	0.755999i	$-0.727152\pi$
$829$	−37.6934	−1.30915	−0.654573	+	0.755999i	$0.727152\pi$
$830$	23.8284	0.827097
$831$	−6.60194	−0.229019
$832$	39.3849	1.36543
$833$	−0.784942	−0.0271966
$834$	−10.9902	−0.380561
$835$	8.57004	0.296579
$836$	−62.0780	−2.14701
$837$	6.34986	0.219483
$838$	75.9048	2.62209
$839$	−11.6645	−0.402704	−0.201352	−	0.979519i	$-0.564534\pi$
$839$	−11.6645	−0.402704	−0.201352	+	0.979519i	$0.564534\pi$
$840$	−1.95235	−0.0673626
$841$	−14.0878	−0.485786
$842$	62.9899	2.17078
$843$	3.91688	0.134905
$844$	61.4057	2.11367
$845$	−1.00861	−0.0346971
$846$	25.8318	0.888115
$847$	1.07360	0.0368892
$848$	39.3378	1.35087
$849$	1.66229	0.0570495
$850$	1.28247	0.0439884
$851$	2.89102	0.0991027
$852$	25.7359	0.881699
$853$	−31.7477	−1.08702	−0.543511	−	0.839402i	$-0.682905\pi$
$853$	−31.7477	−1.08702	−0.543511	+	0.839402i	$0.682905\pi$
$854$	−20.1602	−0.689867
$855$	8.67041	0.296522
$856$	23.6210	0.807350
$857$	−43.9228	−1.50037	−0.750187	−	0.661226i	$-0.770036\pi$
$857$	−43.9228	−1.50037	−0.750187	+	0.661226i	$0.770036\pi$
$858$	−3.85409	−0.131576
$859$	−6.48159	−0.221149	−0.110575	−	0.993868i	$-0.535269\pi$
$859$	−6.48159	−0.221149	−0.110575	+	0.993868i	$0.535269\pi$
$860$	53.8919	1.83770
$861$	−0.924964	−0.0315227
$862$	61.4010	2.09133
$863$	1.24017	0.0422159	0.0211080	−	0.999777i	$-0.493281\pi$
$863$	1.24017	0.0422159	0.0211080	+	0.999777i	$0.493281\pi$
$864$	−59.2305	−2.01506
$865$	5.98629	0.203540
$866$	15.8954	0.540146
$867$	6.51124	0.221133
$868$	7.96267	0.270271
$869$	26.9355	0.913724
$870$	4.13691	0.140254
$871$	9.62836	0.326244
$872$	−84.0898	−2.84764
$873$	18.2217	0.616712
$874$	−6.16508	−0.208537
$875$	4.48925	0.151764
$876$	−20.7043	−0.699532
$877$	−7.21603	−0.243668	−0.121834	−	0.992550i	$-0.538878\pi$
$877$	−7.21603	−0.243668	−0.121834	+	0.992550i	$0.538878\pi$
$878$	99.7729	3.36717
$879$	−7.05142	−0.237839
$880$	61.7904	2.08295
$881$	−10.0331	−0.338023	−0.169012	−	0.985614i	$-0.554058\pi$
$881$	−10.0331	−0.338023	−0.169012	+	0.985614i	$0.554058\pi$
$882$	−53.3983	−1.79801
$883$	−58.5098	−1.96901	−0.984505	−	0.175355i	$-0.943893\pi$
$883$	−58.5098	−1.96901	−0.984505	+	0.175355i	$0.943893\pi$
$884$	0.659841	0.0221928
$885$	4.27596	0.143735
$886$	−21.4340	−0.720088
$887$	−33.0872	−1.11096	−0.555480	−	0.831530i	$-0.687466\pi$
$887$	−33.0872	−1.11096	−0.555480	+	0.831530i	$0.687466\pi$
$888$	15.2944	0.513247
$889$	0.696010	0.0233434
$890$	−7.03940	−0.235961
$891$	−27.9372	−0.935932
$892$	−79.1005	−2.64848
$893$	9.84520	0.329457
$894$	2.62611	0.0878303
$895$	8.62887	0.288431
$896$	−27.9129	−0.932503
$897$	−0.283054	−0.00945091
$898$	1.37721	0.0459581
$899$	−10.9293	−0.364512
$900$	64.5185	2.15062
$901$	0.270767	0.00902055
$902$	48.9645	1.63034
$903$	1.78736	0.0594798
$904$	41.9242	1.39438
$905$	−3.21649	−0.106920
$906$	6.63187	0.220329
$907$	12.7758	0.424213	0.212106	−	0.977247i	$-0.431968\pi$
$907$	12.7758	0.424213	0.212106	+	0.977247i	$0.431968\pi$
$908$	−7.76782	−0.257784
$909$	28.6690	0.950891
$910$	1.38481	0.0459059
$911$	33.1847	1.09946	0.549730	−	0.835343i	$-0.314731\pi$
$911$	33.1847	1.09946	0.549730	+	0.835343i	$0.314731\pi$
$912$	−19.4996	−0.645698
$913$	−30.9377	−1.02389
$914$	−28.2680	−0.935023
$915$	5.67686	0.187671
$916$	24.6775	0.815366
$917$	−2.75463	−0.0909661
$918$	−0.722458	−0.0238447
$919$	11.5804	0.382003	0.191001	−	0.981590i	$-0.438827\pi$
$919$	11.5804	0.382003	0.191001	+	0.981590i	$0.438827\pi$
$920$	7.59038	0.250247
$921$	2.23080	0.0735075
$922$	−7.68882	−0.253218
$923$	−11.8246	−0.389212
$924$	3.91324	0.128736
$925$	−15.5926	−0.512683
$926$	−2.77092	−0.0910579
$927$	−21.0569	−0.691600
$928$	101.947	3.34656
$929$	−29.5014	−0.967910	−0.483955	−	0.875093i	$-0.660800\pi$
$929$	−29.5014	−0.967910	−0.483955	+	0.875093i	$0.660800\pi$
$930$	−3.03198	−0.0994224
$931$	−20.3516	−0.666995
$932$	17.2650	0.565535
$933$	−5.19003	−0.169914
$934$	−37.0269	−1.21156
$935$	0.425310	0.0139091
$936$	29.0766	0.950399
$937$	36.8219	1.20292	0.601460	−	0.798903i	$-0.294586\pi$
$937$	36.8219	1.20292	0.601460	+	0.798903i	$0.294586\pi$
$938$	−13.2197	−0.431637
$939$	−11.5695	−0.377555
$940$	−18.7126	−0.610338
$941$	−17.0231	−0.554937	−0.277469	−	0.960735i	$-0.589495\pi$
$941$	−17.0231	−0.554937	−0.277469	+	0.960735i	$0.589495\pi$
$942$	1.68891	0.0550277
$943$	3.59608	0.117105
$944$	186.729	6.07752
$945$	−1.12127	−0.0364749
$946$	−94.6172	−3.07627
$947$	15.3578	0.499062	0.249531	−	0.968367i	$-0.419723\pi$
$947$	15.3578	0.499062	0.249531	+	0.968367i	$0.419723\pi$
$948$	16.1562	0.524730
$949$	9.51276	0.308797
$950$	33.2513	1.07881
$951$	7.33657	0.237905
$952$	−0.586843	−0.0190197
$953$	53.4543	1.73156	0.865778	−	0.500428i	$-0.166824\pi$
$953$	53.4543	1.73156	0.865778	+	0.500428i	$0.166824\pi$
$954$	18.4198	0.596363
$955$	−11.2908	−0.365362
$956$	21.4406	0.693437
$957$	−5.37117	−0.173625
$958$	52.1822	1.68593
$959$	−2.31792	−0.0748495
$960$	15.2269	0.491446
$961$	−22.9898	−0.741608
$962$	−10.8484	−0.349765
$963$	6.61270	0.213091
$964$	−91.4607	−2.94575
$965$	−4.81694	−0.155063
$966$	0.388631	0.0125040
$967$	30.1643	0.970019	0.485010	−	0.874509i	$-0.338816\pi$
$967$	30.1643	0.970019	0.485010	+	0.874509i	$0.338816\pi$
$968$	−22.0815	−0.709725
$969$	−0.134218	−0.00431171
$970$	−17.8494	−0.573108
$971$	−9.02055	−0.289483	−0.144742	−	0.989469i	$-0.546235\pi$
$971$	−9.02055	−0.289483	−0.144742	+	0.989469i	$0.546235\pi$
$972$	−54.9742	−1.76330
$973$	−5.12706	−0.164366
$974$	−57.9627	−1.85724
$975$	1.52665	0.0488919
$976$	247.906	7.93528
$977$	−32.4597	−1.03848	−0.519238	−	0.854629i	$-0.673784\pi$
$977$	−32.4597	−1.03848	−0.519238	+	0.854629i	$0.673784\pi$
$978$	−3.72942	−0.119254
$979$	9.13964	0.292104
$980$	38.6818	1.23565
$981$	−23.5409	−0.751603
$982$	66.9650	2.13694
$983$	14.5131	0.462896	0.231448	−	0.972847i	$-0.425654\pi$
$983$	14.5131	0.462896	0.231448	+	0.972847i	$0.425654\pi$
$984$	19.0244	0.606477
$985$	−17.1640	−0.546892
$986$	1.24348	0.0396006
$987$	−0.620617	−0.0197544
$988$	17.1080	0.544278
$989$	−6.94894	−0.220963
$990$	28.9331	0.919555
$991$	−36.2232	−1.15067	−0.575334	−	0.817919i	$-0.695128\pi$
$991$	−36.2232	−1.15067	−0.575334	+	0.817919i	$0.695128\pi$
$992$	−74.7175	−2.37228
$993$	5.18545	0.164555
$994$	16.2351	0.514945
$995$	13.4328	0.425850
$996$	−18.5568	−0.587996
$997$	−32.8528	−1.04046	−0.520230	−	0.854026i	$-0.674154\pi$
$997$	−32.8528	−1.04046	−0.520230	+	0.854026i	$0.674154\pi$
$998$	37.6181	1.19078
$999$	8.78383	0.277908

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.b.1.1	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.b.1.1	✓	101	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.77092 q^{2} -0.383319 q^{3} +5.67797 q^{4} -1.00861 q^{5} +1.06214 q^{6} +0.495501 q^{7} -10.1914 q^{8} -2.85307 q^{9} +O(q^{10})\)	\(q-2.77092 q^{2} -0.383319 q^{3} +5.67797 q^{4} -1.00861 q^{5} +1.06214 q^{6} +0.495501 q^{7} -10.1914 q^{8} -2.85307 q^{9} +2.79476 q^{10} -3.62859 q^{11} -2.17647 q^{12} +1.00000 q^{13} -1.37299 q^{14} +0.386618 q^{15} +16.8834 q^{16} +0.116211 q^{17} +7.90561 q^{18} +3.01305 q^{19} -5.72684 q^{20} -0.189935 q^{21} +10.0545 q^{22} +0.738431 q^{23} +3.90654 q^{24} -3.98271 q^{25} -2.77092 q^{26} +2.24359 q^{27} +2.81344 q^{28} -3.86163 q^{29} -1.07129 q^{30} +2.83022 q^{31} -26.3999 q^{32} +1.39091 q^{33} -0.322010 q^{34} -0.499766 q^{35} -16.1996 q^{36} +3.91508 q^{37} -8.34890 q^{38} -0.383319 q^{39} +10.2791 q^{40} +4.86990 q^{41} +0.526293 q^{42} -9.41041 q^{43} -20.6031 q^{44} +2.87762 q^{45} -2.04613 q^{46} +3.26752 q^{47} -6.47174 q^{48} -6.75448 q^{49} +11.0358 q^{50} -0.0445457 q^{51} +5.67797 q^{52} +2.32997 q^{53} -6.21680 q^{54} +3.65982 q^{55} -5.04983 q^{56} -1.15496 q^{57} +10.7003 q^{58} +11.0599 q^{59} +2.19521 q^{60} +14.6834 q^{61} -7.84231 q^{62} -1.41370 q^{63} +39.3849 q^{64} -1.00861 q^{65} -3.85409 q^{66} +9.62836 q^{67} +0.659841 q^{68} -0.283054 q^{69} +1.38481 q^{70} -11.8246 q^{71} +29.0766 q^{72} +9.51276 q^{73} -10.8484 q^{74} +1.52665 q^{75} +17.1080 q^{76} -1.79797 q^{77} +1.06214 q^{78} -7.42313 q^{79} -17.0287 q^{80} +7.69919 q^{81} -13.4941 q^{82} +8.52610 q^{83} -1.07844 q^{84} -0.117211 q^{85} +26.0755 q^{86} +1.48024 q^{87} +36.9803 q^{88} -2.51878 q^{89} -7.97365 q^{90} +0.495501 q^{91} +4.19279 q^{92} -1.08488 q^{93} -9.05404 q^{94} -3.03898 q^{95} +10.1196 q^{96} -6.38672 q^{97} +18.7161 q^{98} +10.3526 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * q^99

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