LMFDB - Embedded newform 8018.2.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$47$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.13813 q^{3} +1.00000 q^{4} +2.17673 q^{5} -3.13813 q^{6} +2.94096 q^{7} +1.00000 q^{8} +6.84787 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.13813 q^{3} +1.00000 q^{4} +2.17673 q^{5} -3.13813 q^{6} +2.94096 q^{7} +1.00000 q^{8} +6.84787 q^{9} +2.17673 q^{10} -0.677923 q^{11} -3.13813 q^{12} -1.92598 q^{13} +2.94096 q^{14} -6.83085 q^{15} +1.00000 q^{16} -0.0568742 q^{17} +6.84787 q^{18} -1.00000 q^{19} +2.17673 q^{20} -9.22911 q^{21} -0.677923 q^{22} -7.41334 q^{23} -3.13813 q^{24} -0.261866 q^{25} -1.92598 q^{26} -12.0751 q^{27} +2.94096 q^{28} +3.72430 q^{29} -6.83085 q^{30} +6.43359 q^{31} +1.00000 q^{32} +2.12741 q^{33} -0.0568742 q^{34} +6.40166 q^{35} +6.84787 q^{36} +3.10884 q^{37} -1.00000 q^{38} +6.04397 q^{39} +2.17673 q^{40} +4.25069 q^{41} -9.22911 q^{42} +0.0900971 q^{43} -0.677923 q^{44} +14.9059 q^{45} -7.41334 q^{46} -9.35894 q^{47} -3.13813 q^{48} +1.64923 q^{49} -0.261866 q^{50} +0.178479 q^{51} -1.92598 q^{52} +9.62968 q^{53} -12.0751 q^{54} -1.47565 q^{55} +2.94096 q^{56} +3.13813 q^{57} +3.72430 q^{58} -2.91543 q^{59} -6.83085 q^{60} +7.57892 q^{61} +6.43359 q^{62} +20.1393 q^{63} +1.00000 q^{64} -4.19232 q^{65} +2.12741 q^{66} +7.50104 q^{67} -0.0568742 q^{68} +23.2640 q^{69} +6.40166 q^{70} -4.17053 q^{71} +6.84787 q^{72} +14.8152 q^{73} +3.10884 q^{74} +0.821770 q^{75} -1.00000 q^{76} -1.99374 q^{77} +6.04397 q^{78} +12.2510 q^{79} +2.17673 q^{80} +17.3497 q^{81} +4.25069 q^{82} +14.2160 q^{83} -9.22911 q^{84} -0.123800 q^{85} +0.0900971 q^{86} -11.6873 q^{87} -0.677923 q^{88} -2.98084 q^{89} +14.9059 q^{90} -5.66422 q^{91} -7.41334 q^{92} -20.1895 q^{93} -9.35894 q^{94} -2.17673 q^{95} -3.13813 q^{96} +1.69741 q^{97} +1.64923 q^{98} -4.64233 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.13813	−1.81180	−0.905901	−	0.423490i	$-0.860805\pi$
$3$	−3.13813	−1.81180	−0.905901	+	0.423490i	$0.860805\pi$
$4$	1.00000	0.500000
$5$	2.17673	0.973461	0.486731	−	0.873552i	$-0.338189\pi$
$5$	2.17673	0.973461	0.486731	+	0.873552i	$0.338189\pi$
$6$	−3.13813	−1.28114
$7$	2.94096	1.11158	0.555789	−	0.831324i	$-0.312416\pi$
$7$	2.94096	1.11158	0.555789	+	0.831324i	$0.312416\pi$
$8$	1.00000	0.353553
$9$	6.84787	2.28262
$10$	2.17673	0.688341
$11$	−0.677923	−0.204401	−0.102201	−	0.994764i	$-0.532588\pi$
$11$	−0.677923	−0.204401	−0.102201	+	0.994764i	$0.532588\pi$
$12$	−3.13813	−0.905901
$13$	−1.92598	−0.534170	−0.267085	−	0.963673i	$-0.586060\pi$
$13$	−1.92598	−0.534170	−0.267085	+	0.963673i	$0.586060\pi$
$14$	2.94096	0.786004
$15$	−6.83085	−1.76372
$16$	1.00000	0.250000
$17$	−0.0568742	−0.0137940	−0.00689701	−	0.999976i	$-0.502195\pi$
$17$	−0.0568742	−0.0137940	−0.00689701	+	0.999976i	$0.502195\pi$
$18$	6.84787	1.61406
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	2.17673	0.486731
$21$	−9.22911	−2.01396
$22$	−0.677923	−0.144534
$23$	−7.41334	−1.54579	−0.772894	−	0.634535i	$-0.781192\pi$
$23$	−7.41334	−1.54579	−0.772894	+	0.634535i	$0.781192\pi$
$24$	−3.13813	−0.640569
$25$	−0.261866	−0.0523732
$26$	−1.92598	−0.377715
$27$	−12.0751	−2.32386
$28$	2.94096	0.555789
$29$	3.72430	0.691585	0.345793	−	0.938311i	$-0.387610\pi$
$29$	3.72430	0.691585	0.345793	+	0.938311i	$0.387610\pi$
$30$	−6.83085	−1.24714
$31$	6.43359	1.15551	0.577753	−	0.816211i	$-0.303930\pi$
$31$	6.43359	1.15551	0.577753	+	0.816211i	$0.303930\pi$
$32$	1.00000	0.176777
$33$	2.12741	0.370335
$34$	−0.0568742	−0.00975384
$35$	6.40166	1.08208
$36$	6.84787	1.14131
$37$	3.10884	0.511090	0.255545	−	0.966797i	$-0.417745\pi$
$37$	3.10884	0.511090	0.255545	+	0.966797i	$0.417745\pi$
$38$	−1.00000	−0.162221
$39$	6.04397	0.967810
$40$	2.17673	0.344171
$41$	4.25069	0.663847	0.331923	−	0.943306i	$-0.392302\pi$
$41$	4.25069	0.663847	0.331923	+	0.943306i	$0.392302\pi$
$42$	−9.22911	−1.42408
$43$	0.0900971	0.0137397	0.00686984	−	0.999976i	$-0.497813\pi$
$43$	0.0900971	0.0137397	0.00686984	+	0.999976i	$0.497813\pi$
$44$	−0.677923	−0.102201
$45$	14.9059	2.22205
$46$	−7.41334	−1.09304
$47$	−9.35894	−1.36514	−0.682571	−	0.730819i	$-0.739138\pi$
$47$	−9.35894	−1.36514	−0.682571	+	0.730819i	$0.739138\pi$
$48$	−3.13813	−0.452950
$49$	1.64923	0.235605
$50$	−0.261866	−0.0370334
$51$	0.178479	0.0249920
$52$	−1.92598	−0.267085
$53$	9.62968	1.32274	0.661369	−	0.750061i	$-0.269976\pi$
$53$	9.62968	1.32274	0.661369	+	0.750061i	$0.269976\pi$
$54$	−12.0751	−1.64322
$55$	−1.47565	−0.198977
$56$	2.94096	0.393002
$57$	3.13813	0.415656
$58$	3.72430	0.489025
$59$	−2.91543	−0.379557	−0.189779	−	0.981827i	$-0.560777\pi$
$59$	−2.91543	−0.379557	−0.189779	+	0.981827i	$0.560777\pi$
$60$	−6.83085	−0.881859
$61$	7.57892	0.970381	0.485190	−	0.874409i	$-0.338750\pi$
$61$	7.57892	0.970381	0.485190	+	0.874409i	$0.338750\pi$
$62$	6.43359	0.817067
$63$	20.1393	2.53731
$64$	1.00000	0.125000
$65$	−4.19232	−0.519994
$66$	2.12741	0.261866
$67$	7.50104	0.916398	0.458199	−	0.888850i	$-0.348495\pi$
$67$	7.50104	0.916398	0.458199	+	0.888850i	$0.348495\pi$
$68$	−0.0568742	−0.00689701
$69$	23.2640	2.80066
$70$	6.40166	0.765144
$71$	−4.17053	−0.494951	−0.247475	−	0.968894i	$-0.579601\pi$
$71$	−4.17053	−0.494951	−0.247475	+	0.968894i	$0.579601\pi$
$72$	6.84787	0.807030
$73$	14.8152	1.73398	0.866991	−	0.498323i	$-0.166051\pi$
$73$	14.8152	1.73398	0.866991	+	0.498323i	$0.166051\pi$
$74$	3.10884	0.361395
$75$	0.821770	0.0948898
$76$	−1.00000	−0.114708
$77$	−1.99374	−0.227208
$78$	6.04397	0.684345
$79$	12.2510	1.37835	0.689173	−	0.724597i	$-0.257974\pi$
$79$	12.2510	1.37835	0.689173	+	0.724597i	$0.257974\pi$
$80$	2.17673	0.243365
$81$	17.3497	1.92775
$82$	4.25069	0.469410
$83$	14.2160	1.56041	0.780205	−	0.625523i	$-0.215115\pi$
$83$	14.2160	1.56041	0.780205	+	0.625523i	$0.215115\pi$
$84$	−9.22911	−1.00698
$85$	−0.123800	−0.0134279
$86$	0.0900971	0.00971542
$87$	−11.6873	−1.25301
$88$	−0.677923	−0.0722668
$89$	−2.98084	−0.315968	−0.157984	−	0.987442i	$-0.550499\pi$
$89$	−2.98084	−0.315968	−0.157984	+	0.987442i	$0.550499\pi$
$90$	14.9059	1.57122
$91$	−5.66422	−0.593771
$92$	−7.41334	−0.772894
$93$	−20.1895	−2.09355
$94$	−9.35894	−0.965301
$95$	−2.17673	−0.223327
$96$	−3.13813	−0.320284
$97$	1.69741	0.172346	0.0861729	−	0.996280i	$-0.472536\pi$
$97$	1.69741	0.172346	0.0861729	+	0.996280i	$0.472536\pi$
$98$	1.64923	0.166598
$99$	−4.64233	−0.466572
$100$	−0.261866	−0.0261866
$101$	−14.0189	−1.39493	−0.697466	−	0.716618i	$-0.745689\pi$
$101$	−14.0189	−1.39493	−0.697466	+	0.716618i	$0.745689\pi$
$102$	0.178479	0.0176720
$103$	6.57765	0.648115	0.324058	−	0.946037i	$-0.394953\pi$
$103$	6.57765	0.648115	0.324058	+	0.946037i	$0.394953\pi$
$104$	−1.92598	−0.188858
$105$	−20.0892	−1.96051
$106$	9.62968	0.935317
$107$	6.18607	0.598030	0.299015	−	0.954248i	$-0.403342\pi$
$107$	6.18607	0.598030	0.299015	+	0.954248i	$0.403342\pi$
$108$	−12.0751	−1.16193
$109$	6.65064	0.637015	0.318508	−	0.947920i	$-0.396818\pi$
$109$	6.65064	0.637015	0.318508	+	0.947920i	$0.396818\pi$
$110$	−1.47565	−0.140698
$111$	−9.75595	−0.925994
$112$	2.94096	0.277894
$113$	−0.172612	−0.0162380	−0.00811900	−	0.999967i	$-0.502584\pi$
$113$	−0.172612	−0.0162380	−0.00811900	+	0.999967i	$0.502584\pi$
$114$	3.13813	0.293913
$115$	−16.1368	−1.50477
$116$	3.72430	0.345793
$117$	−13.1889	−1.21931
$118$	−2.91543	−0.268387
$119$	−0.167265	−0.0153331
$120$	−6.83085	−0.623569
$121$	−10.5404	−0.958220
$122$	7.57892	0.686163
$123$	−13.3392	−1.20276
$124$	6.43359	0.577753
$125$	−11.4536	−1.02444
$126$	20.1393	1.79415
$127$	−0.0366627	−0.00325329	−0.00162664	−	0.999999i	$-0.500518\pi$
$127$	−0.0366627	−0.00325329	−0.00162664	+	0.999999i	$0.500518\pi$
$128$	1.00000	0.0883883
$129$	−0.282737	−0.0248936
$130$	−4.19232	−0.367691
$131$	−15.5217	−1.35614	−0.678068	−	0.734999i	$-0.737183\pi$
$131$	−15.5217	−1.35614	−0.678068	+	0.734999i	$0.737183\pi$
$132$	2.12741	0.185167
$133$	−2.94096	−0.255013
$134$	7.50104	0.647991
$135$	−26.2842	−2.26219
$136$	−0.0568742	−0.00487692
$137$	−0.603727	−0.0515799	−0.0257899	−	0.999667i	$-0.508210\pi$
$137$	−0.603727	−0.0515799	−0.0257899	+	0.999667i	$0.508210\pi$
$138$	23.2640	1.98037
$139$	−7.67314	−0.650827	−0.325413	−	0.945572i	$-0.605503\pi$
$139$	−7.67314	−0.650827	−0.325413	+	0.945572i	$0.605503\pi$
$140$	6.40166	0.541039
$141$	29.3696	2.47337
$142$	−4.17053	−0.349983
$143$	1.30566	0.109185
$144$	6.84787	0.570656
$145$	8.10678	0.673231
$146$	14.8152	1.22611
$147$	−5.17551	−0.426869
$148$	3.10884	0.255545
$149$	17.8478	1.46214	0.731072	−	0.682300i	$-0.239020\pi$
$149$	17.8478	1.46214	0.731072	+	0.682300i	$0.239020\pi$
$150$	0.821770	0.0670972
$151$	1.96512	0.159920	0.0799598	−	0.996798i	$-0.474521\pi$
$151$	1.96512	0.159920	0.0799598	+	0.996798i	$0.474521\pi$
$152$	−1.00000	−0.0811107
$153$	−0.389467	−0.0314866
$154$	−1.99374	−0.160660
$155$	14.0042	1.12484
$156$	6.04397	0.483905
$157$	20.4528	1.63231	0.816155	−	0.577832i	$-0.196101\pi$
$157$	20.4528	1.63231	0.816155	+	0.577832i	$0.196101\pi$
$158$	12.2510	0.974637
$159$	−30.2192	−2.39654
$160$	2.17673	0.172085
$161$	−21.8023	−1.71826
$162$	17.3497	1.36312
$163$	−1.83432	−0.143675	−0.0718377	−	0.997416i	$-0.522886\pi$
$163$	−1.83432	−0.143675	−0.0718377	+	0.997416i	$0.522886\pi$
$164$	4.25069	0.331923
$165$	4.63079	0.360507
$166$	14.2160	1.10338
$167$	−5.63314	−0.435906	−0.217953	−	0.975959i	$-0.569938\pi$
$167$	−5.63314	−0.435906	−0.217953	+	0.975959i	$0.569938\pi$
$168$	−9.22911	−0.712042
$169$	−9.29061	−0.714662
$170$	−0.123800	−0.00949499
$171$	−6.84787	−0.523670
$172$	0.0900971	0.00686984
$173$	18.5062	1.40700	0.703499	−	0.710697i	$-0.251620\pi$
$173$	18.5062	1.40700	0.703499	+	0.710697i	$0.251620\pi$
$174$	−11.6873	−0.886015
$175$	−0.770136	−0.0582168
$176$	−0.677923	−0.0511004
$177$	9.14902	0.687682
$178$	−2.98084	−0.223423
$179$	10.1095	0.755621	0.377810	−	0.925883i	$-0.376677\pi$
$179$	10.1095	0.755621	0.377810	+	0.925883i	$0.376677\pi$
$180$	14.9059	1.11102
$181$	−14.1473	−1.05156	−0.525780	−	0.850621i	$-0.676226\pi$
$181$	−14.1473	−1.05156	−0.525780	+	0.850621i	$0.676226\pi$
$182$	−5.66422	−0.419860
$183$	−23.7836	−1.75814
$184$	−7.41334	−0.546519
$185$	6.76709	0.497527
$186$	−20.1895	−1.48036
$187$	0.0385563	0.00281952
$188$	−9.35894	−0.682571
$189$	−35.5125	−2.58315
$190$	−2.17673	−0.157916
$191$	−7.02060	−0.507993	−0.253997	−	0.967205i	$-0.581745\pi$
$191$	−7.02060	−0.507993	−0.253997	+	0.967205i	$0.581745\pi$
$192$	−3.13813	−0.226475
$193$	8.20378	0.590521	0.295260	−	0.955417i	$-0.404594\pi$
$193$	8.20378	0.590521	0.295260	+	0.955417i	$0.404594\pi$
$194$	1.69741	0.121867
$195$	13.1561	0.942126
$196$	1.64923	0.117802
$197$	17.7254	1.26288	0.631441	−	0.775424i	$-0.282464\pi$
$197$	17.7254	1.26288	0.631441	+	0.775424i	$0.282464\pi$
$198$	−4.64233	−0.329916
$199$	13.9359	0.987890	0.493945	−	0.869493i	$-0.335554\pi$
$199$	13.9359	0.987890	0.493945	+	0.869493i	$0.335554\pi$
$200$	−0.261866	−0.0185167
$201$	−23.5392	−1.66033
$202$	−14.0189	−0.986366
$203$	10.9530	0.768750
$204$	0.178479	0.0124960
$205$	9.25259	0.646229
$206$	6.57765	0.458287
$207$	−50.7656	−3.52845
$208$	−1.92598	−0.133543
$209$	0.677923	0.0468929
$210$	−20.0892	−1.38629
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	9.62968	0.661369
$213$	13.0877	0.896753
$214$	6.18607	0.422871
$215$	0.196117	0.0133750
$216$	−12.0751	−0.821609
$217$	18.9209	1.28444
$218$	6.65064	0.450438
$219$	−46.4919	−3.14163
$220$	−1.47565	−0.0994884
$221$	0.109538	0.00736835
$222$	−9.75595	−0.654777
$223$	22.6646	1.51774	0.758868	−	0.651245i	$-0.225753\pi$
$223$	22.6646	1.51774	0.758868	+	0.651245i	$0.225753\pi$
$224$	2.94096	0.196501
$225$	−1.79322	−0.119548
$226$	−0.172612	−0.0114820
$227$	−27.0609	−1.79609	−0.898047	−	0.439899i	$-0.855014\pi$
$227$	−27.0609	−1.79609	−0.898047	+	0.439899i	$0.855014\pi$
$228$	3.13813	0.207828
$229$	−17.9654	−1.18718	−0.593592	−	0.804766i	$-0.702291\pi$
$229$	−17.9654	−1.18718	−0.593592	+	0.804766i	$0.702291\pi$
$230$	−16.1368	−1.06403
$231$	6.25663	0.411656
$232$	3.72430	0.244512
$233$	12.5585	0.822736	0.411368	−	0.911469i	$-0.365051\pi$
$233$	12.5585	0.822736	0.411368	+	0.911469i	$0.365051\pi$
$234$	−13.1889	−0.862182
$235$	−20.3718	−1.32891
$236$	−2.91543	−0.189779
$237$	−38.4453	−2.49729
$238$	−0.167265	−0.0108422
$239$	1.08193	0.0699840	0.0349920	−	0.999388i	$-0.488859\pi$
$239$	1.08193	0.0699840	0.0349920	+	0.999388i	$0.488859\pi$
$240$	−6.83085	−0.440930
$241$	7.91764	0.510020	0.255010	−	0.966938i	$-0.417921\pi$
$241$	7.91764	0.510020	0.255010	+	0.966938i	$0.417921\pi$
$242$	−10.5404	−0.677564
$243$	−18.2204	−1.16884
$244$	7.57892	0.485190
$245$	3.58993	0.229352
$246$	−13.3392	−0.850479
$247$	1.92598	0.122547
$248$	6.43359	0.408533
$249$	−44.6117	−2.82715
$250$	−11.4536	−0.724392
$251$	−1.15591	−0.0729601	−0.0364801	−	0.999334i	$-0.511615\pi$
$251$	−1.15591	−0.0729601	−0.0364801	+	0.999334i	$0.511615\pi$
$252$	20.1393	1.26866
$253$	5.02567	0.315961
$254$	−0.0366627	−0.00230042
$255$	0.388499	0.0243288
$256$	1.00000	0.0625000
$257$	25.7438	1.60585	0.802926	−	0.596079i	$-0.203275\pi$
$257$	25.7438	1.60585	0.802926	+	0.596079i	$0.203275\pi$
$258$	−0.282737	−0.0176024
$259$	9.14297	0.568117
$260$	−4.19232	−0.259997
$261$	25.5035	1.57863
$262$	−15.5217	−0.958933
$263$	9.07220	0.559416	0.279708	−	0.960085i	$-0.409762\pi$
$263$	9.07220	0.559416	0.279708	+	0.960085i	$0.409762\pi$
$264$	2.12741	0.130933
$265$	20.9612	1.28763
$266$	−2.94096	−0.180322
$267$	9.35426	0.572472
$268$	7.50104	0.458199
$269$	−1.42081	−0.0866282	−0.0433141	−	0.999062i	$-0.513792\pi$
$269$	−1.42081	−0.0866282	−0.0433141	+	0.999062i	$0.513792\pi$
$270$	−26.2842	−1.59961
$271$	0.387319	0.0235279	0.0117640	−	0.999931i	$-0.496255\pi$
$271$	0.387319	0.0235279	0.0117640	+	0.999931i	$0.496255\pi$
$272$	−0.0568742	−0.00344850
$273$	17.7751	1.07580
$274$	−0.603727	−0.0364725
$275$	0.177525	0.0107052
$276$	23.2640	1.40033
$277$	−21.4747	−1.29029	−0.645145	−	0.764060i	$-0.723203\pi$
$277$	−21.4747	−1.29029	−0.645145	+	0.764060i	$0.723203\pi$
$278$	−7.67314	−0.460204
$279$	44.0564	2.63759
$280$	6.40166	0.382572
$281$	−6.86911	−0.409777	−0.204889	−	0.978785i	$-0.565683\pi$
$281$	−6.86911	−0.409777	−0.204889	+	0.978785i	$0.565683\pi$
$282$	29.3696	1.74893
$283$	−23.6913	−1.40830	−0.704151	−	0.710050i	$-0.748672\pi$
$283$	−23.6913	−1.40830	−0.704151	+	0.710050i	$0.748672\pi$
$284$	−4.17053	−0.247475
$285$	6.83085	0.404625
$286$	1.30566	0.0772056
$287$	12.5011	0.737917
$288$	6.84787	0.403515
$289$	−16.9968	−0.999810
$290$	8.10678	0.476046
$291$	−5.32670	−0.312256
$292$	14.8152	0.866991
$293$	18.2346	1.06528	0.532639	−	0.846342i	$-0.321200\pi$
$293$	18.2346	1.06528	0.532639	+	0.846342i	$0.321200\pi$
$294$	−5.17551	−0.301842
$295$	−6.34610	−0.369484
$296$	3.10884	0.180698
$297$	8.18601	0.475000
$298$	17.8478	1.03389
$299$	14.2779	0.825714
$300$	0.821770	0.0474449
$301$	0.264972	0.0152727
$302$	1.96512	0.113080
$303$	43.9931	2.52734
$304$	−1.00000	−0.0573539
$305$	16.4972	0.944628
$306$	−0.389467	−0.0222644
$307$	19.7289	1.12599	0.562993	−	0.826461i	$-0.309650\pi$
$307$	19.7289	1.12599	0.562993	+	0.826461i	$0.309650\pi$
$308$	−1.99374	−0.113604
$309$	−20.6415	−1.17426
$310$	14.0042	0.795383
$311$	−16.4419	−0.932337	−0.466169	−	0.884696i	$-0.654366\pi$
$311$	−16.4419	−0.932337	−0.466169	+	0.884696i	$0.654366\pi$
$312$	6.04397	0.342173
$313$	30.1407	1.70365	0.851827	−	0.523824i	$-0.175495\pi$
$313$	30.1407	1.70365	0.851827	+	0.523824i	$0.175495\pi$
$314$	20.4528	1.15422
$315$	43.8377	2.46998
$316$	12.2510	0.689173
$317$	2.60261	0.146177	0.0730886	−	0.997325i	$-0.476714\pi$
$317$	2.60261	0.146177	0.0730886	+	0.997325i	$0.476714\pi$
$318$	−30.2192	−1.69461
$319$	−2.52479	−0.141361
$320$	2.17673	0.121683
$321$	−19.4127	−1.08351
$322$	−21.8023	−1.21500
$323$	0.0568742	0.00316457
$324$	17.3497	0.963875
$325$	0.504348	0.0279762
$326$	−1.83432	−0.101594
$327$	−20.8706	−1.15415
$328$	4.25069	0.234705
$329$	−27.5243	−1.51746
$330$	4.63079	0.254917
$331$	15.7023	0.863078	0.431539	−	0.902094i	$-0.357971\pi$
$331$	15.7023	0.863078	0.431539	+	0.902094i	$0.357971\pi$
$332$	14.2160	0.780205
$333$	21.2890	1.16663
$334$	−5.63314	−0.308232
$335$	16.3277	0.892078
$336$	−9.22911	−0.503489
$337$	−7.79959	−0.424871	−0.212435	−	0.977175i	$-0.568139\pi$
$337$	−7.79959	−0.424871	−0.212435	+	0.977175i	$0.568139\pi$
$338$	−9.29061	−0.505343
$339$	0.541680	0.0294200
$340$	−0.123800	−0.00671397
$341$	−4.36148	−0.236187
$342$	−6.84787	−0.370291
$343$	−15.7364	−0.849685
$344$	0.0900971	0.00485771
$345$	50.6394	2.72634
$346$	18.5062	0.994897
$347$	−0.207988	−0.0111654	−0.00558268	−	0.999984i	$-0.501777\pi$
$347$	−0.207988	−0.0111654	−0.00558268	+	0.999984i	$0.501777\pi$
$348$	−11.6873	−0.626507
$349$	8.01503	0.429035	0.214517	−	0.976720i	$-0.431182\pi$
$349$	8.01503	0.429035	0.214517	+	0.976720i	$0.431182\pi$
$350$	−0.770136	−0.0411655
$351$	23.2564	1.24134
$352$	−0.677923	−0.0361334
$353$	1.32594	0.0705726	0.0352863	−	0.999377i	$-0.488766\pi$
$353$	1.32594	0.0705726	0.0352863	+	0.999377i	$0.488766\pi$
$354$	9.14902	0.486265
$355$	−9.07810	−0.481816
$356$	−2.98084	−0.157984
$357$	0.524898	0.0277806
$358$	10.1095	0.534305
$359$	32.4982	1.71519	0.857595	−	0.514325i	$-0.171958\pi$
$359$	32.4982	1.71519	0.857595	+	0.514325i	$0.171958\pi$
$360$	14.9059	0.785612
$361$	1.00000	0.0526316
$362$	−14.1473	−0.743565
$363$	33.0772	1.73610
$364$	−5.66422	−0.296886
$365$	32.2485	1.68796
$366$	−23.7836	−1.24319
$367$	−13.7239	−0.716382	−0.358191	−	0.933648i	$-0.616606\pi$
$367$	−13.7239	−0.716382	−0.358191	+	0.933648i	$0.616606\pi$
$368$	−7.41334	−0.386447
$369$	29.1082	1.51531
$370$	6.76709	0.351804
$371$	28.3205	1.47033
$372$	−20.1895	−1.04677
$373$	9.46516	0.490087	0.245044	−	0.969512i	$-0.421198\pi$
$373$	9.46516	0.490087	0.245044	+	0.969512i	$0.421198\pi$
$374$	0.0385563	0.00199370
$375$	35.9430	1.85609
$376$	−9.35894	−0.482651
$377$	−7.17292	−0.369424
$378$	−35.5125	−1.82656
$379$	20.3600	1.04582	0.522911	−	0.852387i	$-0.324846\pi$
$379$	20.3600	1.04582	0.522911	+	0.852387i	$0.324846\pi$
$380$	−2.17673	−0.111664
$381$	0.115052	0.00589431
$382$	−7.02060	−0.359205
$383$	−24.3490	−1.24418	−0.622088	−	0.782948i	$-0.713715\pi$
$383$	−24.3490	−1.24418	−0.622088	+	0.782948i	$0.713715\pi$
$384$	−3.13813	−0.160142
$385$	−4.33983	−0.221178
$386$	8.20378	0.417561
$387$	0.616974	0.0313625
$388$	1.69741	0.0861729
$389$	−24.8707	−1.26099	−0.630496	−	0.776192i	$-0.717149\pi$
$389$	−24.8707	−1.26099	−0.630496	+	0.776192i	$0.717149\pi$
$390$	13.1561	0.666183
$391$	0.421628	0.0213226
$392$	1.64923	0.0832988
$393$	48.7091	2.45705
$394$	17.7254	0.892993
$395$	26.6671	1.34177
$396$	−4.64233	−0.233286
$397$	5.94481	0.298362	0.149181	−	0.988810i	$-0.452336\pi$
$397$	5.94481	0.298362	0.149181	+	0.988810i	$0.452336\pi$
$398$	13.9359	0.698544
$399$	9.22911	0.462034
$400$	−0.261866	−0.0130933
$401$	−32.5793	−1.62693	−0.813467	−	0.581611i	$-0.802423\pi$
$401$	−32.5793	−1.62693	−0.813467	+	0.581611i	$0.802423\pi$
$402$	−23.5392	−1.17403
$403$	−12.3910	−0.617237
$404$	−14.0189	−0.697466
$405$	37.7656	1.87659
$406$	10.9530	0.543589
$407$	−2.10755	−0.104468
$408$	0.178479	0.00883601
$409$	−8.21196	−0.406055	−0.203028	−	0.979173i	$-0.565078\pi$
$409$	−8.21196	−0.406055	−0.203028	+	0.979173i	$0.565078\pi$
$410$	9.25259	0.456953
$411$	1.89458	0.0934525
$412$	6.57765	0.324058
$413$	−8.57417	−0.421907
$414$	−50.7656	−2.49499
$415$	30.9444	1.51900
$416$	−1.92598	−0.0944288
$417$	24.0793	1.17917
$418$	0.677923	0.0331583
$419$	6.67006	0.325854	0.162927	−	0.986638i	$-0.447907\pi$
$419$	6.67006	0.325854	0.162927	+	0.986638i	$0.447907\pi$
$420$	−20.0892	−0.980255
$421$	31.9362	1.55647	0.778237	−	0.627970i	$-0.216114\pi$
$421$	31.9362	1.55647	0.778237	+	0.627970i	$0.216114\pi$
$422$	−1.00000	−0.0486792
$423$	−64.0888	−3.11611
$424$	9.62968	0.467658
$425$	0.0148934	0.000722437 0
$426$	13.0877	0.634100
$427$	22.2893	1.07865
$428$	6.18607	0.299015
$429$	−4.09735	−0.197822
$430$	0.196117	0.00945759
$431$	3.40300	0.163917	0.0819584	−	0.996636i	$-0.473883\pi$
$431$	3.40300	0.163917	0.0819584	+	0.996636i	$0.473883\pi$
$432$	−12.0751	−0.580965
$433$	32.9384	1.58292	0.791460	−	0.611221i	$-0.209321\pi$
$433$	32.9384	1.58292	0.791460	+	0.611221i	$0.209321\pi$
$434$	18.9209	0.908233
$435$	−25.4401	−1.21976
$436$	6.65064	0.318508
$437$	7.41334	0.354628
$438$	−46.4919	−2.22147
$439$	−36.8895	−1.76064	−0.880319	−	0.474382i	$-0.842672\pi$
$439$	−36.8895	−1.76064	−0.880319	+	0.474382i	$0.842672\pi$
$440$	−1.47565	−0.0703490
$441$	11.2937	0.537797
$442$	0.109538	0.00521021
$443$	5.25207	0.249534	0.124767	−	0.992186i	$-0.460182\pi$
$443$	5.25207	0.249534	0.124767	+	0.992186i	$0.460182\pi$
$444$	−9.75595	−0.462997
$445$	−6.48847	−0.307583
$446$	22.6646	1.07320
$447$	−56.0086	−2.64912
$448$	2.94096	0.138947
$449$	−16.5954	−0.783184	−0.391592	−	0.920139i	$-0.628075\pi$
$449$	−16.5954	−0.783184	−0.391592	+	0.920139i	$0.628075\pi$
$450$	−1.79322	−0.0845334
$451$	−2.88164	−0.135691
$452$	−0.172612	−0.00811900
$453$	−6.16682	−0.289743
$454$	−27.0609	−1.27003
$455$	−12.3295	−0.578014
$456$	3.13813	0.146956
$457$	21.1449	0.989119	0.494559	−	0.869144i	$-0.335329\pi$
$457$	21.1449	0.989119	0.494559	+	0.869144i	$0.335329\pi$
$458$	−17.9654	−0.839466
$459$	0.686764	0.0320554
$460$	−16.1368	−0.752383
$461$	3.07268	0.143109	0.0715544	−	0.997437i	$-0.477204\pi$
$461$	3.07268	0.143109	0.0715544	+	0.997437i	$0.477204\pi$
$462$	6.25663	0.291085
$463$	27.7827	1.29117	0.645587	−	0.763687i	$-0.276613\pi$
$463$	27.7827	1.29117	0.645587	+	0.763687i	$0.276613\pi$
$464$	3.72430	0.172896
$465$	−43.9469	−2.03799
$466$	12.5585	0.581763
$467$	−4.37619	−0.202506	−0.101253	−	0.994861i	$-0.532285\pi$
$467$	−4.37619	−0.202506	−0.101253	+	0.994861i	$0.532285\pi$
$468$	−13.1889	−0.609655
$469$	22.0602	1.01865
$470$	−20.3718	−0.939683
$471$	−64.1836	−2.95742
$472$	−2.91543	−0.134194
$473$	−0.0610789	−0.00280841
$474$	−38.4453	−1.76585
$475$	0.261866	0.0120152
$476$	−0.167265	−0.00766656
$477$	65.9428	3.01931
$478$	1.08193	0.0494862
$479$	−12.2778	−0.560989	−0.280494	−	0.959856i	$-0.590498\pi$
$479$	−12.2778	−0.560989	−0.280494	+	0.959856i	$0.590498\pi$
$480$	−6.83085	−0.311784
$481$	−5.98756	−0.273009
$482$	7.91764	0.360639
$483$	68.4186	3.11315
$484$	−10.5404	−0.479110
$485$	3.69480	0.167772
$486$	−18.2204	−0.826493
$487$	−18.3877	−0.833226	−0.416613	−	0.909084i	$-0.636783\pi$
$487$	−18.3877	−0.833226	−0.416613	+	0.909084i	$0.636783\pi$
$488$	7.57892	0.343081
$489$	5.75635	0.260311
$490$	3.58993	0.162176
$491$	29.5824	1.33503	0.667517	−	0.744595i	$-0.267357\pi$
$491$	29.5824	1.33503	0.667517	+	0.744595i	$0.267357\pi$
$492$	−13.3392	−0.601379
$493$	−0.211817	−0.00953974
$494$	1.92598	0.0866538
$495$	−10.1051	−0.454189
$496$	6.43359	0.288877
$497$	−12.2654	−0.550176
$498$	−44.6117	−1.99910
$499$	10.7603	0.481696	0.240848	−	0.970563i	$-0.422574\pi$
$499$	10.7603	0.481696	0.240848	+	0.970563i	$0.422574\pi$
$500$	−11.4536	−0.512222
$501$	17.6775	0.789775
$502$	−1.15591	−0.0515906
$503$	−6.26370	−0.279284	−0.139642	−	0.990202i	$-0.544595\pi$
$503$	−6.26370	−0.279284	−0.139642	+	0.990202i	$0.544595\pi$
$504$	20.1393	0.897076
$505$	−30.5153	−1.35791
$506$	5.02567	0.223418
$507$	29.1552	1.29483
$508$	−0.0366627	−0.00162664
$509$	43.2024	1.91491	0.957455	−	0.288581i	$-0.0931836\pi$
$509$	43.2024	1.91491	0.957455	+	0.288581i	$0.0931836\pi$
$510$	0.388499	0.0172030
$511$	43.5707	1.92746
$512$	1.00000	0.0441942
$513$	12.0751	0.533130
$514$	25.7438	1.13551
$515$	14.3177	0.630915
$516$	−0.282737	−0.0124468
$517$	6.34464	0.279037
$518$	9.14297	0.401719
$519$	−58.0748	−2.54920
$520$	−4.19232	−0.183846
$521$	−23.2818	−1.01999	−0.509997	−	0.860176i	$-0.670354\pi$
$521$	−23.2818	−1.01999	−0.509997	+	0.860176i	$0.670354\pi$
$522$	25.5035	1.11626
$523$	−10.0037	−0.437431	−0.218715	−	0.975789i	$-0.570187\pi$
$523$	−10.0037	−0.437431	−0.218715	+	0.975789i	$0.570187\pi$
$524$	−15.5217	−0.678068
$525$	2.41679	0.105477
$526$	9.07220	0.395567
$527$	−0.365905	−0.0159391
$528$	2.12741	0.0925837
$529$	31.9576	1.38946
$530$	20.9612	0.910495
$531$	−19.9645	−0.866387
$532$	−2.94096	−0.127507
$533$	−8.18674	−0.354607
$534$	9.35426	0.404799
$535$	13.4654	0.582159
$536$	7.50104	0.323996
$537$	−31.7250	−1.36904
$538$	−1.42081	−0.0612554
$539$	−1.11805	−0.0481579
$540$	−26.2842	−1.13109
$541$	16.1434	0.694061	0.347030	−	0.937854i	$-0.387190\pi$
$541$	16.1434	0.694061	0.347030	+	0.937854i	$0.387190\pi$
$542$	0.387319	0.0166368
$543$	44.3960	1.90522
$544$	−0.0568742	−0.00243846
$545$	14.4766	0.620110
$546$	17.7751	0.760703
$547$	8.59487	0.367490	0.183745	−	0.982974i	$-0.441178\pi$
$547$	8.59487	0.367490	0.183745	+	0.982974i	$0.441178\pi$
$548$	−0.603727	−0.0257899
$549$	51.8995	2.21501
$550$	0.177525	0.00756969
$551$	−3.72430	−0.158661
$552$	23.2640	0.990184
$553$	36.0297	1.53214
$554$	−21.4747	−0.912373
$555$	−21.2360	−0.901420
$556$	−7.67314	−0.325413
$557$	22.5177	0.954104	0.477052	−	0.878875i	$-0.341705\pi$
$557$	22.5177	0.954104	0.477052	+	0.878875i	$0.341705\pi$
$558$	44.0564	1.86506
$559$	−0.173525	−0.00733933
$560$	6.40166	0.270519
$561$	−0.120995	−0.00510841
$562$	−6.86911	−0.289756
$563$	−37.5767	−1.58367	−0.791835	−	0.610736i	$-0.790874\pi$
$563$	−37.5767	−1.58367	−0.791835	+	0.610736i	$0.790874\pi$
$564$	29.3696	1.23668
$565$	−0.375730	−0.0158071
$566$	−23.6913	−0.995821
$567$	51.0249	2.14284
$568$	−4.17053	−0.174992
$569$	3.93013	0.164760	0.0823798	−	0.996601i	$-0.473748\pi$
$569$	3.93013	0.164760	0.0823798	+	0.996601i	$0.473748\pi$
$570$	6.83085	0.286113
$571$	7.07265	0.295981	0.147991	−	0.988989i	$-0.452719\pi$
$571$	7.07265	0.295981	0.147991	+	0.988989i	$0.452719\pi$
$572$	1.30566	0.0545926
$573$	22.0316	0.920383
$574$	12.5011	0.521786
$575$	1.94130	0.0809579
$576$	6.84787	0.285328
$577$	−11.7591	−0.489537	−0.244768	−	0.969582i	$-0.578712\pi$
$577$	−11.7591	−0.489537	−0.244768	+	0.969582i	$0.578712\pi$
$578$	−16.9968	−0.706972
$579$	−25.7445	−1.06991
$580$	8.10678	0.336616
$581$	41.8087	1.73452
$582$	−5.32670	−0.220799
$583$	−6.52818	−0.270369
$584$	14.8152	0.613055
$585$	−28.7085	−1.18695
$586$	18.2346	0.753265
$587$	8.29118	0.342214	0.171107	−	0.985252i	$-0.445266\pi$
$587$	8.29118	0.342214	0.171107	+	0.985252i	$0.445266\pi$
$588$	−5.17551	−0.213434
$589$	−6.43359	−0.265091
$590$	−6.34610	−0.261265
$591$	−55.6246	−2.28809
$592$	3.10884	0.127773
$593$	−10.3414	−0.424669	−0.212334	−	0.977197i	$-0.568107\pi$
$593$	−10.3414	−0.424669	−0.212334	+	0.977197i	$0.568107\pi$
$594$	8.18601	0.335876
$595$	−0.364089	−0.0149262
$596$	17.8478	0.731072
$597$	−43.7327	−1.78986
$598$	14.2779	0.583868
$599$	40.2651	1.64519	0.822594	−	0.568629i	$-0.192526\pi$
$599$	40.2651	1.64519	0.822594	+	0.568629i	$0.192526\pi$
$600$	0.821770	0.0335486
$601$	−22.1721	−0.904420	−0.452210	−	0.891912i	$-0.649364\pi$
$601$	−22.1721	−0.904420	−0.452210	+	0.891912i	$0.649364\pi$
$602$	0.264972	0.0107994
$603$	51.3662	2.09179
$604$	1.96512	0.0799598
$605$	−22.9436	−0.932790
$606$	43.9931	1.78710
$607$	−22.3686	−0.907912	−0.453956	−	0.891024i	$-0.649988\pi$
$607$	−22.3686	−0.907912	−0.453956	+	0.891024i	$0.649988\pi$
$608$	−1.00000	−0.0405554
$609$	−34.3720	−1.39282
$610$	16.4972	0.667953
$611$	18.0251	0.729218
$612$	−0.389467	−0.0157433
$613$	32.2960	1.30442	0.652211	−	0.758037i	$-0.273842\pi$
$613$	32.2960	1.30442	0.652211	+	0.758037i	$0.273842\pi$
$614$	19.7289	0.796193
$615$	−29.0359	−1.17084
$616$	−1.99374	−0.0803302
$617$	8.60952	0.346606	0.173303	−	0.984869i	$-0.444556\pi$
$617$	8.60952	0.346606	0.173303	+	0.984869i	$0.444556\pi$
$618$	−20.6415	−0.830325
$619$	2.71059	0.108948	0.0544739	−	0.998515i	$-0.482652\pi$
$619$	2.71059	0.108948	0.0544739	+	0.998515i	$0.482652\pi$
$620$	14.0042	0.562421
$621$	89.5171	3.59220
$622$	−16.4419	−0.659262
$623$	−8.76652	−0.351223
$624$	6.04397	0.241953
$625$	−23.6221	−0.944884
$626$	30.1407	1.20467
$627$	−2.12741	−0.0849606
$628$	20.4528	0.816155
$629$	−0.176813	−0.00704999
$630$	43.8377	1.74654
$631$	−14.7800	−0.588381	−0.294190	−	0.955747i	$-0.595050\pi$
$631$	−14.7800	−0.588381	−0.294190	+	0.955747i	$0.595050\pi$
$632$	12.2510	0.487319
$633$	3.13813	0.124730
$634$	2.60261	0.103363
$635$	−0.0798046	−0.00316695
$636$	−30.2192	−1.19827
$637$	−3.17638	−0.125853
$638$	−2.52479	−0.0999573
$639$	−28.5593	−1.12979
$640$	2.17673	0.0860426
$641$	−10.9253	−0.431524	−0.215762	−	0.976446i	$-0.569223\pi$
$641$	−10.9253	−0.431524	−0.215762	+	0.976446i	$0.569223\pi$
$642$	−19.4127	−0.766158
$643$	−6.49059	−0.255964	−0.127982	−	0.991776i	$-0.540850\pi$
$643$	−6.49059	−0.255964	−0.127982	+	0.991776i	$0.540850\pi$
$644$	−21.8023	−0.859132
$645$	−0.615440	−0.0242329
$646$	0.0568742	0.00223769
$647$	33.8660	1.33141	0.665705	−	0.746215i	$-0.268131\pi$
$647$	33.8660	1.33141	0.665705	+	0.746215i	$0.268131\pi$
$648$	17.3497	0.681562
$649$	1.97644	0.0775820
$650$	0.504348	0.0197821
$651$	−59.3763	−2.32714
$652$	−1.83432	−0.0718377
$653$	20.3926	0.798024	0.399012	−	0.916946i	$-0.369353\pi$
$653$	20.3926	0.798024	0.399012	+	0.916946i	$0.369353\pi$
$654$	−20.8706	−0.816104
$655$	−33.7865	−1.32015
$656$	4.25069	0.165962
$657$	101.452	3.95803
$658$	−27.5243	−1.07301
$659$	−10.3240	−0.402165	−0.201083	−	0.979574i	$-0.564446\pi$
$659$	−10.3240	−0.402165	−0.201083	+	0.979574i	$0.564446\pi$
$660$	4.63079	0.180253
$661$	−0.578727	−0.0225099	−0.0112549	−	0.999937i	$-0.503583\pi$
$661$	−0.578727	−0.0225099	−0.0112549	+	0.999937i	$0.503583\pi$
$662$	15.7023	0.610288
$663$	−0.343746	−0.0133500
$664$	14.2160	0.551689
$665$	−6.40166	−0.248246
$666$	21.2890	0.824930
$667$	−27.6095	−1.06904
$668$	−5.63314	−0.217953
$669$	−71.1246	−2.74983
$670$	16.3277	0.630794
$671$	−5.13792	−0.198347
$672$	−9.22911	−0.356021
$673$	15.0961	0.581910	0.290955	−	0.956737i	$-0.406027\pi$
$673$	15.0961	0.581910	0.290955	+	0.956737i	$0.406027\pi$
$674$	−7.79959	−0.300429
$675$	3.16206	0.121708
$676$	−9.29061	−0.357331
$677$	47.2522	1.81605	0.908025	−	0.418916i	$-0.137590\pi$
$677$	47.2522	1.81605	0.908025	+	0.418916i	$0.137590\pi$
$678$	0.541680	0.0208031
$679$	4.99201	0.191576
$680$	−0.123800	−0.00474750
$681$	84.9207	3.25417
$682$	−4.36148	−0.167010
$683$	−35.4713	−1.35727	−0.678636	−	0.734475i	$-0.737429\pi$
$683$	−35.4713	−1.35727	−0.678636	+	0.734475i	$0.737429\pi$
$684$	−6.84787	−0.261835
$685$	−1.31415	−0.0502110
$686$	−15.7364	−0.600818
$687$	56.3777	2.15094
$688$	0.0900971	0.00343492
$689$	−18.5465	−0.706567
$690$	50.6394	1.92781
$691$	4.43469	0.168704	0.0843519	−	0.996436i	$-0.473118\pi$
$691$	4.43469	0.168704	0.0843519	+	0.996436i	$0.473118\pi$
$692$	18.5062	0.703499
$693$	−13.6529	−0.518631
$694$	−0.207988	−0.00789510
$695$	−16.7023	−0.633555
$696$	−11.6873	−0.443008
$697$	−0.241755	−0.00915711
$698$	8.01503	0.303373
$699$	−39.4103	−1.49064
$700$	−0.770136	−0.0291084
$701$	10.8854	0.411136	0.205568	−	0.978643i	$-0.434096\pi$
$701$	10.8854	0.411136	0.205568	+	0.978643i	$0.434096\pi$
$702$	23.2564	0.877758
$703$	−3.10884	−0.117252
$704$	−0.677923	−0.0255502
$705$	63.9295	2.40773
$706$	1.32594	0.0499023
$707$	−41.2290	−1.55057
$708$	9.14902	0.343841
$709$	−39.3745	−1.47874	−0.739370	−	0.673299i	$-0.764877\pi$
$709$	−39.3745	−1.47874	−0.739370	+	0.673299i	$0.764877\pi$
$710$	−9.07810	−0.340695
$711$	83.8933	3.14624
$712$	−2.98084	−0.111712
$713$	−47.6944	−1.78617
$714$	0.524898	0.0196438
$715$	2.84207	0.106288
$716$	10.1095	0.377810
$717$	−3.39523	−0.126797
$718$	32.4982	1.21282
$719$	9.68910	0.361342	0.180671	−	0.983544i	$-0.442173\pi$
$719$	9.68910	0.361342	0.180671	+	0.983544i	$0.442173\pi$
$720$	14.9059	0.555512
$721$	19.3446	0.720431
$722$	1.00000	0.0372161
$723$	−24.8466	−0.924055
$724$	−14.1473	−0.525780
$725$	−0.975267	−0.0362205
$726$	33.0772	1.22761
$727$	−38.6933	−1.43506	−0.717528	−	0.696530i	$-0.754726\pi$
$727$	−38.6933	−1.43506	−0.717528	+	0.696530i	$0.754726\pi$
$728$	−5.66422	−0.209930
$729$	5.12874	0.189954
$730$	32.2485	1.19357
$731$	−0.00512420	−0.000189525 0
$732$	−23.7836	−0.879069
$733$	−41.7858	−1.54339	−0.771696	−	0.635991i	$-0.780591\pi$
$733$	−41.7858	−1.54339	−0.771696	+	0.635991i	$0.780591\pi$
$734$	−13.7239	−0.506558
$735$	−11.2657	−0.415540
$736$	−7.41334	−0.273259
$737$	−5.08513	−0.187313
$738$	29.1082	1.07149
$739$	−12.2027	−0.448882	−0.224441	−	0.974488i	$-0.572056\pi$
$739$	−12.2027	−0.448882	−0.224441	+	0.974488i	$0.572056\pi$
$740$	6.76709	0.248763
$741$	−6.04397	−0.222031
$742$	28.3205	1.03968
$743$	−42.9444	−1.57548	−0.787738	−	0.616011i	$-0.788748\pi$
$743$	−42.9444	−1.57548	−0.787738	+	0.616011i	$0.788748\pi$
$744$	−20.1895	−0.740181
$745$	38.8497	1.42334
$746$	9.46516	0.346544
$747$	97.3495	3.56183
$748$	0.0385563	0.00140976
$749$	18.1930	0.664757
$750$	35.9430	1.31245
$751$	−7.76923	−0.283503	−0.141752	−	0.989902i	$-0.545273\pi$
$751$	−7.76923	−0.283503	−0.141752	+	0.989902i	$0.545273\pi$
$752$	−9.35894	−0.341285
$753$	3.62738	0.132189
$754$	−7.17292	−0.261222
$755$	4.27754	0.155676
$756$	−35.5125	−1.29158
$757$	9.84299	0.357749	0.178875	−	0.983872i	$-0.442754\pi$
$757$	9.84299	0.357749	0.178875	+	0.983872i	$0.442754\pi$
$758$	20.3600	0.739508
$759$	−15.7712	−0.572459
$760$	−2.17673	−0.0789581
$761$	19.2000	0.695999	0.348000	−	0.937495i	$-0.386861\pi$
$761$	19.2000	0.695999	0.348000	+	0.937495i	$0.386861\pi$
$762$	0.115052	0.00416791
$763$	19.5592	0.708092
$764$	−7.02060	−0.253997
$765$	−0.847763	−0.0306510
$766$	−24.3490	−0.879765
$767$	5.61506	0.202748
$768$	−3.13813	−0.113238
$769$	−6.79690	−0.245102	−0.122551	−	0.992462i	$-0.539108\pi$
$769$	−6.79690	−0.245102	−0.122551	+	0.992462i	$0.539108\pi$
$770$	−4.33983	−0.156397
$771$	−80.7873	−2.90948
$772$	8.20378	0.295260
$773$	−11.9514	−0.429862	−0.214931	−	0.976629i	$-0.568953\pi$
$773$	−11.9514	−0.429862	−0.214931	+	0.976629i	$0.568953\pi$
$774$	0.616974	0.0221767
$775$	−1.68474	−0.0605176
$776$	1.69741	0.0609335
$777$	−28.6919	−1.02931
$778$	−24.8707	−0.891656
$779$	−4.25069	−0.152297
$780$	13.1561	0.471063
$781$	2.82730	0.101169
$782$	0.421628	0.0150774
$783$	−44.9714	−1.60715
$784$	1.64923	0.0589011
$785$	44.5201	1.58899
$786$	48.7091	1.73740
$787$	35.1604	1.25333	0.626667	−	0.779287i	$-0.284419\pi$
$787$	35.1604	1.25333	0.626667	+	0.779287i	$0.284419\pi$
$788$	17.7254	0.631441
$789$	−28.4698	−1.01355
$790$	26.6671	0.948772
$791$	−0.507645	−0.0180498
$792$	−4.64233	−0.164958
$793$	−14.5968	−0.518348
$794$	5.94481	0.210974
$795$	−65.7789	−2.33294
$796$	13.9359	0.493945
$797$	−7.07338	−0.250552	−0.125276	−	0.992122i	$-0.539982\pi$
$797$	−7.07338	−0.250552	−0.125276	+	0.992122i	$0.539982\pi$
$798$	9.22911	0.326707
$799$	0.532282	0.0188308
$800$	−0.261866	−0.00925836
$801$	−20.4124	−0.721237
$802$	−32.5793	−1.15042
$803$	−10.0435	−0.354429
$804$	−23.5392	−0.830165
$805$	−47.4577	−1.67266
$806$	−12.3910	−0.436453
$807$	4.45868	0.156953
$808$	−14.0189	−0.493183
$809$	−19.5805	−0.688415	−0.344208	−	0.938894i	$-0.611852\pi$
$809$	−19.5805	−0.688415	−0.344208	+	0.938894i	$0.611852\pi$
$810$	37.7656	1.32695
$811$	−20.4619	−0.718514	−0.359257	−	0.933239i	$-0.616970\pi$
$811$	−20.4619	−0.718514	−0.359257	+	0.933239i	$0.616970\pi$
$812$	10.9530	0.384375
$813$	−1.21546	−0.0426279
$814$	−2.10755	−0.0738698
$815$	−3.99282	−0.139862
$816$	0.178479	0.00624801
$817$	−0.0900971	−0.00315210
$818$	−8.21196	−0.287124
$819$	−38.7879	−1.35536
$820$	9.25259	0.323115
$821$	33.9776	1.18583	0.592913	−	0.805267i	$-0.297978\pi$
$821$	33.9776	1.18583	0.592913	+	0.805267i	$0.297978\pi$
$822$	1.89458	0.0660809
$823$	−20.7767	−0.724232	−0.362116	−	0.932133i	$-0.617946\pi$
$823$	−20.7767	−0.724232	−0.362116	+	0.932133i	$0.617946\pi$
$824$	6.57765	0.229143
$825$	−0.557096	−0.0193956
$826$	−8.57417	−0.298334
$827$	25.4596	0.885316	0.442658	−	0.896691i	$-0.354036\pi$
$827$	25.4596	0.885316	0.442658	+	0.896691i	$0.354036\pi$
$828$	−50.7656	−1.76423
$829$	−23.4750	−0.815322	−0.407661	−	0.913133i	$-0.633656\pi$
$829$	−23.4750	−0.815322	−0.407661	+	0.913133i	$0.633656\pi$
$830$	30.9444	1.07409
$831$	67.3905	2.33775
$832$	−1.92598	−0.0667713
$833$	−0.0937988	−0.00324993
$834$	24.0793	0.833799
$835$	−12.2618	−0.424337
$836$	0.677923	0.0234465
$837$	−77.6865	−2.68524
$838$	6.67006	0.230413
$839$	−49.5773	−1.71160	−0.855800	−	0.517307i	$-0.826934\pi$
$839$	−49.5773	−1.71160	−0.855800	+	0.517307i	$0.826934\pi$
$840$	−20.0892	−0.693145
$841$	−15.1296	−0.521710
$842$	31.9362	1.10059
$843$	21.5562	0.742435
$844$	−1.00000	−0.0344214
$845$	−20.2231	−0.695696
$846$	−64.0888	−2.20342
$847$	−30.9989	−1.06514
$848$	9.62968	0.330684
$849$	74.3465	2.55157
$850$	0.0148934	0.000510840 0
$851$	−23.0469	−0.790038
$852$	13.0877	0.448376
$853$	42.7692	1.46439	0.732195	−	0.681095i	$-0.238496\pi$
$853$	42.7692	1.46439	0.732195	+	0.681095i	$0.238496\pi$
$854$	22.2893	0.762723
$855$	−14.9059	−0.509772
$856$	6.18607	0.211436
$857$	−6.49610	−0.221903	−0.110951	−	0.993826i	$-0.535390\pi$
$857$	−6.49610	−0.221903	−0.110951	+	0.993826i	$0.535390\pi$
$858$	−4.09735	−0.139881
$859$	−25.4880	−0.869640	−0.434820	−	0.900517i	$-0.643188\pi$
$859$	−25.4880	−0.869640	−0.434820	+	0.900517i	$0.643188\pi$
$860$	0.196117	0.00668752
$861$	−39.2301	−1.33696
$862$	3.40300	0.115907
$863$	−6.89141	−0.234586	−0.117293	−	0.993097i	$-0.537422\pi$
$863$	−6.89141	−0.234586	−0.117293	+	0.993097i	$0.537422\pi$
$864$	−12.0751	−0.410804
$865$	40.2828	1.36966
$866$	32.9384	1.11929
$867$	53.3381	1.81146
$868$	18.9209	0.642218
$869$	−8.30524	−0.281736
$870$	−25.4401	−0.862502
$871$	−14.4468	−0.489512
$872$	6.65064	0.225219
$873$	11.6236	0.393401
$874$	7.41334	0.250760
$875$	−33.6847	−1.13875
$876$	−46.4919	−1.57082
$877$	−28.0141	−0.945968	−0.472984	−	0.881071i	$-0.656823\pi$
$877$	−28.0141	−0.945968	−0.472984	+	0.881071i	$0.656823\pi$
$878$	−36.8895	−1.24496
$879$	−57.2227	−1.93007
$880$	−1.47565	−0.0497442
$881$	2.18960	0.0737696	0.0368848	−	0.999320i	$-0.488257\pi$
$881$	2.18960	0.0737696	0.0368848	+	0.999320i	$0.488257\pi$
$882$	11.2937	0.380280
$883$	25.2565	0.849948	0.424974	−	0.905206i	$-0.360283\pi$
$883$	25.2565	0.849948	0.424974	+	0.905206i	$0.360283\pi$
$884$	0.109538	0.00368418
$885$	19.9149	0.669432
$886$	5.25207	0.176447
$887$	−14.1888	−0.476414	−0.238207	−	0.971214i	$-0.576560\pi$
$887$	−14.1888	−0.476414	−0.238207	+	0.971214i	$0.576560\pi$
$888$	−9.75595	−0.327388
$889$	−0.107823	−0.00361628
$890$	−6.48847	−0.217494
$891$	−11.7618	−0.394035
$892$	22.6646	0.758868
$893$	9.35894	0.313185
$894$	−56.0086	−1.87321
$895$	22.0056	0.735568
$896$	2.94096	0.0982505
$897$	−44.8060	−1.49603
$898$	−16.5954	−0.553794
$899$	23.9606	0.799131
$900$	−1.79322	−0.0597741
$901$	−0.547680	−0.0182459
$902$	−2.88164	−0.0959482
$903$	−0.831516	−0.0276711
$904$	−0.172612	−0.00574100
$905$	−30.7948	−1.02365
$906$	−6.16682	−0.204879
$907$	25.5966	0.849920	0.424960	−	0.905212i	$-0.360288\pi$
$907$	25.5966	0.849920	0.424960	+	0.905212i	$0.360288\pi$
$908$	−27.0609	−0.898047
$909$	−95.9996	−3.18411
$910$	−12.3295	−0.408717
$911$	18.9005	0.626203	0.313102	−	0.949720i	$-0.398632\pi$
$911$	18.9005	0.626203	0.313102	+	0.949720i	$0.398632\pi$
$912$	3.13813	0.103914
$913$	−9.63737	−0.318950
$914$	21.1449	0.699412
$915$	−51.7705	−1.71148
$916$	−17.9654	−0.593592
$917$	−45.6486	−1.50745
$918$	0.686764	0.0226666
$919$	−20.7549	−0.684640	−0.342320	−	0.939583i	$-0.611213\pi$
$919$	−20.7549	−0.684640	−0.342320	+	0.939583i	$0.611213\pi$
$920$	−16.1368	−0.532015
$921$	−61.9118	−2.04006
$922$	3.07268	0.101193
$923$	8.03235	0.264388
$924$	6.25663	0.205828
$925$	−0.814099	−0.0267674
$926$	27.7827	0.912998
$927$	45.0429	1.47940
$928$	3.72430	0.122256
$929$	−33.7447	−1.10713	−0.553564	−	0.832807i	$-0.686732\pi$
$929$	−33.7447	−1.10713	−0.553564	+	0.832807i	$0.686732\pi$
$930$	−43.9469	−1.44108
$931$	−1.64923	−0.0540514
$932$	12.5585	0.411368
$933$	51.5970	1.68921
$934$	−4.37619	−0.143193
$935$	0.0839265	0.00274469
$936$	−13.1889	−0.431091
$937$	25.1692	0.822241	0.411121	−	0.911581i	$-0.365138\pi$
$937$	25.1692	0.822241	0.411121	+	0.911581i	$0.365138\pi$
$938$	22.0602	0.720292
$939$	−94.5855	−3.08668
$940$	−20.3718	−0.664456
$941$	−3.23958	−0.105607	−0.0528036	−	0.998605i	$-0.516816\pi$
$941$	−3.23958	−0.105607	−0.0528036	+	0.998605i	$0.516816\pi$
$942$	−64.1836	−2.09121
$943$	−31.5118	−1.02617
$944$	−2.91543	−0.0948893
$945$	−77.3009	−2.51460
$946$	−0.0610789	−0.00198585
$947$	34.0316	1.10588	0.552939	−	0.833222i	$-0.313506\pi$
$947$	34.0316	1.10588	0.552939	+	0.833222i	$0.313506\pi$
$948$	−38.4453	−1.24864
$949$	−28.5337	−0.926242
$950$	0.261866	0.00849605
$951$	−8.16734	−0.264844
$952$	−0.167265	−0.00542108
$953$	−47.5069	−1.53890	−0.769450	−	0.638707i	$-0.779469\pi$
$953$	−47.5069	−1.53890	−0.769450	+	0.638707i	$0.779469\pi$
$954$	65.9428	2.13498
$955$	−15.2819	−0.494512
$956$	1.08193	0.0349920
$957$	7.92312	0.256118
$958$	−12.2778	−0.396679
$959$	−1.77554	−0.0573351
$960$	−6.83085	−0.220465
$961$	10.3911	0.335196
$962$	−5.98756	−0.193047
$963$	42.3614	1.36508
$964$	7.91764	0.255010
$965$	17.8574	0.574849
$966$	68.4186	2.20133
$967$	−41.1823	−1.32433	−0.662167	−	0.749356i	$-0.730363\pi$
$967$	−41.1823	−1.32433	−0.662167	+	0.749356i	$0.730363\pi$
$968$	−10.5404	−0.338782
$969$	−0.178479	−0.00573356
$970$	3.69480	0.118633
$971$	34.8476	1.11831	0.559156	−	0.829063i	$-0.311125\pi$
$971$	34.8476	1.11831	0.559156	+	0.829063i	$0.311125\pi$
$972$	−18.2204	−0.584419
$973$	−22.5664	−0.723445
$974$	−18.3877	−0.589180
$975$	−1.58271	−0.0506873
$976$	7.57892	0.242595
$977$	−45.8194	−1.46589	−0.732947	−	0.680286i	$-0.761856\pi$
$977$	−45.8194	−1.46589	−0.732947	+	0.680286i	$0.761856\pi$
$978$	5.75635	0.184068
$979$	2.02078	0.0645844
$980$	3.58993	0.114676
$981$	45.5427	1.45407
$982$	29.5824	0.944012
$983$	9.81624	0.313090	0.156545	−	0.987671i	$-0.449964\pi$
$983$	9.81624	0.313090	0.156545	+	0.987671i	$0.449964\pi$
$984$	−13.3392	−0.425239
$985$	38.5833	1.22937
$986$	−0.211817	−0.00674561
$987$	86.3747	2.74934
$988$	1.92598	0.0612735
$989$	−0.667921	−0.0212386
$990$	−10.1051	−0.321160
$991$	18.0515	0.573425	0.286713	−	0.958017i	$-0.407437\pi$
$991$	18.0515	0.573425	0.286713	+	0.958017i	$0.407437\pi$
$992$	6.43359	0.204267
$993$	−49.2760	−1.56373
$994$	−12.2654	−0.389033
$995$	30.3346	0.961673
$996$	−44.6117	−1.41358
$997$	−2.53260	−0.0802082	−0.0401041	−	0.999196i	$-0.512769\pi$
$997$	−2.53260	−0.0802082	−0.0401041	+	0.999196i	$0.512769\pi$
$998$	10.7603	0.340611
$999$	−37.5397	−1.18770

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.2	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.2	✓	47	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.13813 q^{3} +1.00000 q^{4} +2.17673 q^{5} -3.13813 q^{6} +2.94096 q^{7} +1.00000 q^{8} +6.84787 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.13813 q^{3} +1.00000 q^{4} +2.17673 q^{5} -3.13813 q^{6} +2.94096 q^{7} +1.00000 q^{8} +6.84787 q^{9} +2.17673 q^{10} -0.677923 q^{11} -3.13813 q^{12} -1.92598 q^{13} +2.94096 q^{14} -6.83085 q^{15} +1.00000 q^{16} -0.0568742 q^{17} +6.84787 q^{18} -1.00000 q^{19} +2.17673 q^{20} -9.22911 q^{21} -0.677923 q^{22} -7.41334 q^{23} -3.13813 q^{24} -0.261866 q^{25} -1.92598 q^{26} -12.0751 q^{27} +2.94096 q^{28} +3.72430 q^{29} -6.83085 q^{30} +6.43359 q^{31} +1.00000 q^{32} +2.12741 q^{33} -0.0568742 q^{34} +6.40166 q^{35} +6.84787 q^{36} +3.10884 q^{37} -1.00000 q^{38} +6.04397 q^{39} +2.17673 q^{40} +4.25069 q^{41} -9.22911 q^{42} +0.0900971 q^{43} -0.677923 q^{44} +14.9059 q^{45} -7.41334 q^{46} -9.35894 q^{47} -3.13813 q^{48} +1.64923 q^{49} -0.261866 q^{50} +0.178479 q^{51} -1.92598 q^{52} +9.62968 q^{53} -12.0751 q^{54} -1.47565 q^{55} +2.94096 q^{56} +3.13813 q^{57} +3.72430 q^{58} -2.91543 q^{59} -6.83085 q^{60} +7.57892 q^{61} +6.43359 q^{62} +20.1393 q^{63} +1.00000 q^{64} -4.19232 q^{65} +2.12741 q^{66} +7.50104 q^{67} -0.0568742 q^{68} +23.2640 q^{69} +6.40166 q^{70} -4.17053 q^{71} +6.84787 q^{72} +14.8152 q^{73} +3.10884 q^{74} +0.821770 q^{75} -1.00000 q^{76} -1.99374 q^{77} +6.04397 q^{78} +12.2510 q^{79} +2.17673 q^{80} +17.3497 q^{81} +4.25069 q^{82} +14.2160 q^{83} -9.22911 q^{84} -0.123800 q^{85} +0.0900971 q^{86} -11.6873 q^{87} -0.677923 q^{88} -2.98084 q^{89} +14.9059 q^{90} -5.66422 q^{91} -7.41334 q^{92} -20.1895 q^{93} -9.35894 q^{94} -2.17673 q^{95} -3.13813 q^{96} +1.69741 q^{97} +1.64923 q^{98} -4.64233 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * q^99

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