LMFDB - Embedded newform 8026.2.a.b.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.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:	$64.0879326623$
Analytic rank:	$1$
Dimension:	$81$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.92493 q^{3} +1.00000 q^{4} -0.857375 q^{5} +1.92493 q^{6} +1.26508 q^{7} -1.00000 q^{8} +0.705338 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.92493 q^{3} +1.00000 q^{4} -0.857375 q^{5} +1.92493 q^{6} +1.26508 q^{7} -1.00000 q^{8} +0.705338 q^{9} +0.857375 q^{10} -5.34689 q^{11} -1.92493 q^{12} +1.44087 q^{13} -1.26508 q^{14} +1.65038 q^{15} +1.00000 q^{16} -6.73687 q^{17} -0.705338 q^{18} +2.05737 q^{19} -0.857375 q^{20} -2.43518 q^{21} +5.34689 q^{22} -5.75526 q^{23} +1.92493 q^{24} -4.26491 q^{25} -1.44087 q^{26} +4.41705 q^{27} +1.26508 q^{28} +9.09168 q^{29} -1.65038 q^{30} -0.350682 q^{31} -1.00000 q^{32} +10.2924 q^{33} +6.73687 q^{34} -1.08465 q^{35} +0.705338 q^{36} +7.96580 q^{37} -2.05737 q^{38} -2.77356 q^{39} +0.857375 q^{40} +6.04283 q^{41} +2.43518 q^{42} +0.822568 q^{43} -5.34689 q^{44} -0.604740 q^{45} +5.75526 q^{46} +6.79953 q^{47} -1.92493 q^{48} -5.39957 q^{49} +4.26491 q^{50} +12.9680 q^{51} +1.44087 q^{52} +11.6367 q^{53} -4.41705 q^{54} +4.58429 q^{55} -1.26508 q^{56} -3.96028 q^{57} -9.09168 q^{58} -4.54798 q^{59} +1.65038 q^{60} +6.81691 q^{61} +0.350682 q^{62} +0.892310 q^{63} +1.00000 q^{64} -1.23536 q^{65} -10.2924 q^{66} -2.31293 q^{67} -6.73687 q^{68} +11.0784 q^{69} +1.08465 q^{70} -4.25432 q^{71} -0.705338 q^{72} +4.26181 q^{73} -7.96580 q^{74} +8.20963 q^{75} +2.05737 q^{76} -6.76425 q^{77} +2.77356 q^{78} -2.54309 q^{79} -0.857375 q^{80} -10.6185 q^{81} -6.04283 q^{82} -5.24868 q^{83} -2.43518 q^{84} +5.77602 q^{85} -0.822568 q^{86} -17.5008 q^{87} +5.34689 q^{88} +2.47301 q^{89} +0.604740 q^{90} +1.82281 q^{91} -5.75526 q^{92} +0.675037 q^{93} -6.79953 q^{94} -1.76393 q^{95} +1.92493 q^{96} -11.8228 q^{97} +5.39957 q^{98} -3.77137 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9}+O(q^{10}) $ 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9} + 26 q^{10} - 41 q^{11} - 10 q^{12} + 33 q^{13} - 3 q^{14} - 7 q^{15} + 81 q^{16} - 9 q^{17} - 59 q^{18} - 32 q^{19} - 26 q^{20} - 23 q^{21} + 41 q^{22} - 28 q^{23} + 10 q^{24} + 81 q^{25} - 33 q^{26} - 37 q^{27} + 3 q^{28} - 35 q^{29} + 7 q^{30} - 29 q^{31} - 81 q^{32} - 7 q^{33} + 9 q^{34} - 67 q^{35} + 59 q^{36} + 13 q^{37} + 32 q^{38} - 42 q^{39} + 26 q^{40} - 66 q^{41} + 23 q^{42} - 22 q^{43} - 41 q^{44} - 65 q^{45} + 28 q^{46} - 71 q^{47} - 10 q^{48} + 64 q^{49} - 81 q^{50} - 43 q^{51} + 33 q^{52} - 37 q^{53} + 37 q^{54} + 12 q^{55} - 3 q^{56} - q^{57} + 35 q^{58} - 162 q^{59} - 7 q^{60} + 19 q^{61} + 29 q^{62} - 16 q^{63} + 81 q^{64} - 45 q^{65} + 7 q^{66} - 43 q^{67} - 9 q^{68} - 21 q^{69} + 67 q^{70} - 99 q^{71} - 59 q^{72} + 53 q^{73} - 13 q^{74} - 61 q^{75} - 32 q^{76} - 31 q^{77} + 42 q^{78} + 4 q^{79} - 26 q^{80} + q^{81} + 66 q^{82} - 112 q^{83} - 23 q^{84} + 17 q^{85} + 22 q^{86} - 15 q^{87} + 41 q^{88} - 111 q^{89} + 65 q^{90} - 49 q^{91} - 28 q^{92} - 19 q^{93} + 71 q^{94} - 53 q^{95} + 10 q^{96} + 50 q^{97} - 64 q^{98} - 97 q^{99}+O(q^{100}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9 + 26 * q^10 - 41 * q^11 - 10 * q^12 + 33 * q^13 - 3 * q^14 - 7 * q^15 + 81 * q^16 - 9 * q^17 - 59 * q^18 - 32 * q^19 - 26 * q^20 - 23 * q^21 + 41 * q^22 - 28 * q^23 + 10 * q^24 + 81 * q^25 - 33 * q^26 - 37 * q^27 + 3 * q^28 - 35 * q^29 + 7 * q^30 - 29 * q^31 - 81 * q^32 - 7 * q^33 + 9 * q^34 - 67 * q^35 + 59 * q^36 + 13 * q^37 + 32 * q^38 - 42 * q^39 + 26 * q^40 - 66 * q^41 + 23 * q^42 - 22 * q^43 - 41 * q^44 - 65 * q^45 + 28 * q^46 - 71 * q^47 - 10 * q^48 + 64 * q^49 - 81 * q^50 - 43 * q^51 + 33 * q^52 - 37 * q^53 + 37 * q^54 + 12 * q^55 - 3 * q^56 - q^57 + 35 * q^58 - 162 * q^59 - 7 * q^60 + 19 * q^61 + 29 * q^62 - 16 * q^63 + 81 * q^64 - 45 * q^65 + 7 * q^66 - 43 * q^67 - 9 * q^68 - 21 * q^69 + 67 * q^70 - 99 * q^71 - 59 * q^72 + 53 * q^73 - 13 * q^74 - 61 * q^75 - 32 * q^76 - 31 * q^77 + 42 * q^78 + 4 * q^79 - 26 * q^80 + q^81 + 66 * q^82 - 112 * q^83 - 23 * q^84 + 17 * q^85 + 22 * q^86 - 15 * q^87 + 41 * q^88 - 111 * q^89 + 65 * q^90 - 49 * q^91 - 28 * q^92 - 19 * q^93 + 71 * q^94 - 53 * q^95 + 10 * q^96 + 50 * q^97 - 64 * q^98 - 97 * 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
$3$	−1.92493	−1.11136	−0.555678	−	0.831397i	$-0.687541\pi$
$3$	−1.92493	−1.11136	−0.555678	+	0.831397i	$0.687541\pi$
$4$	1.00000	0.500000
$5$	−0.857375	−0.383430	−0.191715	−	0.981451i	$-0.561405\pi$
$5$	−0.857375	−0.383430	−0.191715	+	0.981451i	$0.561405\pi$
$6$	1.92493	0.785848
$7$	1.26508	0.478155	0.239078	−	0.971000i	$-0.423155\pi$
$7$	1.26508	0.478155	0.239078	+	0.971000i	$0.423155\pi$
$8$	−1.00000	−0.353553
$9$	0.705338	0.235113
$10$	0.857375	0.271126
$11$	−5.34689	−1.61215	−0.806075	−	0.591814i	$-0.798412\pi$
$11$	−5.34689	−1.61215	−0.806075	+	0.591814i	$0.798412\pi$
$12$	−1.92493	−0.555678
$13$	1.44087	0.399625	0.199812	−	0.979834i	$-0.435967\pi$
$13$	1.44087	0.399625	0.199812	+	0.979834i	$0.435967\pi$
$14$	−1.26508	−0.338107
$15$	1.65038	0.426127
$16$	1.00000	0.250000
$17$	−6.73687	−1.63393	−0.816965	−	0.576687i	$-0.804345\pi$
$17$	−6.73687	−1.63393	−0.816965	+	0.576687i	$0.804345\pi$
$18$	−0.705338	−0.166250
$19$	2.05737	0.471992	0.235996	−	0.971754i	$-0.424165\pi$
$19$	2.05737	0.471992	0.235996	+	0.971754i	$0.424165\pi$
$20$	−0.857375	−0.191715
$21$	−2.43518	−0.531401
$22$	5.34689	1.13996
$23$	−5.75526	−1.20005	−0.600027	−	0.799980i	$-0.704844\pi$
$23$	−5.75526	−1.20005	−0.600027	+	0.799980i	$0.704844\pi$
$24$	1.92493	0.392924
$25$	−4.26491	−0.852982
$26$	−1.44087	−0.282577
$27$	4.41705	0.850062
$28$	1.26508	0.239078
$29$	9.09168	1.68828	0.844141	−	0.536121i	$-0.180111\pi$
$29$	9.09168	1.68828	0.844141	+	0.536121i	$0.180111\pi$
$30$	−1.65038	−0.301317
$31$	−0.350682	−0.0629843	−0.0314922	−	0.999504i	$-0.510026\pi$
$31$	−0.350682	−0.0629843	−0.0314922	+	0.999504i	$0.510026\pi$
$32$	−1.00000	−0.176777
$33$	10.2924	1.79167
$34$	6.73687	1.15536
$35$	−1.08465	−0.183339
$36$	0.705338	0.117556
$37$	7.96580	1.30957	0.654785	−	0.755815i	$-0.272759\pi$
$37$	7.96580	1.30957	0.654785	+	0.755815i	$0.272759\pi$
$38$	−2.05737	−0.333749
$39$	−2.77356	−0.444126
$40$	0.857375	0.135563
$41$	6.04283	0.943732	0.471866	−	0.881670i	$-0.343581\pi$
$41$	6.04283	0.943732	0.471866	+	0.881670i	$0.343581\pi$
$42$	2.43518	0.375757
$43$	0.822568	0.125440	0.0627202	−	0.998031i	$-0.480022\pi$
$43$	0.822568	0.125440	0.0627202	+	0.998031i	$0.480022\pi$
$44$	−5.34689	−0.806075
$45$	−0.604740	−0.0901493
$46$	5.75526	0.848566
$47$	6.79953	0.991814	0.495907	−	0.868376i	$-0.334836\pi$
$47$	6.79953	0.991814	0.495907	+	0.868376i	$0.334836\pi$
$48$	−1.92493	−0.277839
$49$	−5.39957	−0.771367
$50$	4.26491	0.603149
$51$	12.9680	1.81588
$52$	1.44087	0.199812
$53$	11.6367	1.59842	0.799210	−	0.601052i	$-0.205251\pi$
$53$	11.6367	1.59842	0.799210	+	0.601052i	$0.205251\pi$
$54$	−4.41705	−0.601085
$55$	4.58429	0.618146
$56$	−1.26508	−0.169053
$57$	−3.96028	−0.524551
$58$	−9.09168	−1.19380
$59$	−4.54798	−0.592097	−0.296049	−	0.955173i	$-0.595669\pi$
$59$	−4.54798	−0.592097	−0.296049	+	0.955173i	$0.595669\pi$
$60$	1.65038	0.213064
$61$	6.81691	0.872816	0.436408	−	0.899749i	$-0.356250\pi$
$61$	6.81691	0.872816	0.436408	+	0.899749i	$0.356250\pi$
$62$	0.350682	0.0445367
$63$	0.892310	0.112420
$64$	1.00000	0.125000
$65$	−1.23536	−0.153228
$66$	−10.2924	−1.26690
$67$	−2.31293	−0.282570	−0.141285	−	0.989969i	$-0.545123\pi$
$67$	−2.31293	−0.282570	−0.141285	+	0.989969i	$0.545123\pi$
$68$	−6.73687	−0.816965
$69$	11.0784	1.33369
$70$	1.08465	0.129640
$71$	−4.25432	−0.504895	−0.252447	−	0.967611i	$-0.581235\pi$
$71$	−4.25432	−0.504895	−0.252447	+	0.967611i	$0.581235\pi$
$72$	−0.705338	−0.0831249
$73$	4.26181	0.498808	0.249404	−	0.968400i	$-0.419765\pi$
$73$	4.26181	0.498808	0.249404	+	0.968400i	$0.419765\pi$
$74$	−7.96580	−0.926006
$75$	8.20963	0.947966
$76$	2.05737	0.235996
$77$	−6.76425	−0.770858
$78$	2.77356	0.314044
$79$	−2.54309	−0.286120	−0.143060	−	0.989714i	$-0.545694\pi$
$79$	−2.54309	−0.286120	−0.143060	+	0.989714i	$0.545694\pi$
$80$	−0.857375	−0.0958575
$81$	−10.6185	−1.17983
$82$	−6.04283	−0.667319
$83$	−5.24868	−0.576118	−0.288059	−	0.957613i	$-0.593010\pi$
$83$	−5.24868	−0.576118	−0.288059	+	0.957613i	$0.593010\pi$
$84$	−2.43518	−0.265700
$85$	5.77602	0.626497
$86$	−0.822568	−0.0886997
$87$	−17.5008	−1.87628
$88$	5.34689	0.569981
$89$	2.47301	0.262139	0.131069	−	0.991373i	$-0.458159\pi$
$89$	2.47301	0.262139	0.131069	+	0.991373i	$0.458159\pi$
$90$	0.604740	0.0637452
$91$	1.82281	0.191083
$92$	−5.75526	−0.600027
$93$	0.675037	0.0699980
$94$	−6.79953	−0.701318
$95$	−1.76393	−0.180976
$96$	1.92493	0.196462
$97$	−11.8228	−1.20043	−0.600214	−	0.799840i	$-0.704918\pi$
$97$	−11.8228	−1.20043	−0.600214	+	0.799840i	$0.704918\pi$
$98$	5.39957	0.545439
$99$	−3.77137	−0.379037
$100$	−4.26491	−0.426491
$101$	4.19486	0.417404	0.208702	−	0.977979i	$-0.433076\pi$
$101$	4.19486	0.417404	0.208702	+	0.977979i	$0.433076\pi$
$102$	−12.9680	−1.28402
$103$	4.09226	0.403222	0.201611	−	0.979466i	$-0.435382\pi$
$103$	4.09226	0.403222	0.201611	+	0.979466i	$0.435382\pi$
$104$	−1.44087	−0.141289
$105$	2.08787	0.203755
$106$	−11.6367	−1.13025
$107$	2.59092	0.250473	0.125237	−	0.992127i	$-0.460031\pi$
$107$	2.59092	0.250473	0.125237	+	0.992127i	$0.460031\pi$
$108$	4.41705	0.425031
$109$	0.0240516	0.00230373	0.00115186	−	0.999999i	$-0.499633\pi$
$109$	0.0240516	0.00230373	0.00115186	+	0.999999i	$0.499633\pi$
$110$	−4.58429	−0.437095
$111$	−15.3336	−1.45540
$112$	1.26508	0.119539
$113$	−10.3101	−0.969895	−0.484948	−	0.874543i	$-0.661161\pi$
$113$	−10.3101	−0.969895	−0.484948	+	0.874543i	$0.661161\pi$
$114$	3.96028	0.370914
$115$	4.93441	0.460136
$116$	9.09168	0.844141
$117$	1.01630	0.0939569
$118$	4.54798	0.418676
$119$	−8.52267	−0.781272
$120$	−1.65038	−0.150659
$121$	17.5893	1.59902
$122$	−6.81691	−0.617174
$123$	−11.6320	−1.04882
$124$	−0.350682	−0.0314922
$125$	7.94350	0.710488
$126$	−0.892310	−0.0794933
$127$	7.12920	0.632614	0.316307	−	0.948657i	$-0.397557\pi$
$127$	7.12920	0.632614	0.316307	+	0.948657i	$0.397557\pi$
$128$	−1.00000	−0.0883883
$129$	−1.58338	−0.139409
$130$	1.23536	0.108349
$131$	−15.0959	−1.31894	−0.659469	−	0.751731i	$-0.729219\pi$
$131$	−15.0959	−1.31894	−0.659469	+	0.751731i	$0.729219\pi$
$132$	10.2924	0.895836
$133$	2.60273	0.225686
$134$	2.31293	0.199807
$135$	−3.78707	−0.325939
$136$	6.73687	0.577681
$137$	10.6644	0.911123	0.455562	−	0.890204i	$-0.349438\pi$
$137$	10.6644	0.911123	0.455562	+	0.890204i	$0.349438\pi$
$138$	−11.0784	−0.943060
$139$	20.1241	1.70690	0.853451	−	0.521174i	$-0.174506\pi$
$139$	20.1241	1.70690	0.853451	+	0.521174i	$0.174506\pi$
$140$	−1.08465	−0.0916695
$141$	−13.0886	−1.10226
$142$	4.25432	0.357014
$143$	−7.70417	−0.644255
$144$	0.705338	0.0587782
$145$	−7.79498	−0.647338
$146$	−4.26181	−0.352710
$147$	10.3938	0.857264
$148$	7.96580	0.654785
$149$	−7.87452	−0.645106	−0.322553	−	0.946551i	$-0.604541\pi$
$149$	−7.87452	−0.645106	−0.322553	+	0.946551i	$0.604541\pi$
$150$	−8.20963	−0.670314
$151$	9.37233	0.762709	0.381355	−	0.924429i	$-0.375458\pi$
$151$	9.37233	0.762709	0.381355	+	0.924429i	$0.375458\pi$
$152$	−2.05737	−0.166874
$153$	−4.75177	−0.384158
$154$	6.76425	0.545079
$155$	0.300666	0.0241501
$156$	−2.77356	−0.222063
$157$	4.89179	0.390408	0.195204	−	0.980763i	$-0.437463\pi$
$157$	4.89179	0.390408	0.195204	+	0.980763i	$0.437463\pi$
$158$	2.54309	0.202317
$159$	−22.3997	−1.77641
$160$	0.857375	0.0677815
$161$	−7.28086	−0.573812
$162$	10.6185	0.834269
$163$	8.00736	0.627185	0.313592	−	0.949558i	$-0.398467\pi$
$163$	8.00736	0.627185	0.313592	+	0.949558i	$0.398467\pi$
$164$	6.04283	0.471866
$165$	−8.82442	−0.686980
$166$	5.24868	0.407377
$167$	10.9129	0.844469	0.422234	−	0.906487i	$-0.361246\pi$
$167$	10.9129	0.844469	0.422234	+	0.906487i	$0.361246\pi$
$168$	2.43518	0.187879
$169$	−10.9239	−0.840300
$170$	−5.77602	−0.443001
$171$	1.45114	0.110971
$172$	0.822568	0.0627202
$173$	−3.70204	−0.281461	−0.140730	−	0.990048i	$-0.544945\pi$
$173$	−3.70204	−0.281461	−0.140730	+	0.990048i	$0.544945\pi$
$174$	17.5008	1.32673
$175$	−5.39545	−0.407858
$176$	−5.34689	−0.403037
$177$	8.75453	0.658031
$178$	−2.47301	−0.185360
$179$	8.22004	0.614395	0.307197	−	0.951646i	$-0.400609\pi$
$179$	8.22004	0.614395	0.307197	+	0.951646i	$0.400609\pi$
$180$	−0.604740	−0.0450746
$181$	−11.3533	−0.843883	−0.421941	−	0.906623i	$-0.638651\pi$
$181$	−11.3533	−0.843883	−0.421941	+	0.906623i	$0.638651\pi$
$182$	−1.82281	−0.135116
$183$	−13.1221	−0.970010
$184$	5.75526	0.424283
$185$	−6.82968	−0.502128
$186$	−0.675037	−0.0494961
$187$	36.0213	2.63414
$188$	6.79953	0.495907
$189$	5.58793	0.406462
$190$	1.76393	0.127969
$191$	−11.0488	−0.799462	−0.399731	−	0.916632i	$-0.630897\pi$
$191$	−11.0488	−0.799462	−0.399731	+	0.916632i	$0.630897\pi$
$192$	−1.92493	−0.138920
$193$	−0.470778	−0.0338874	−0.0169437	−	0.999856i	$-0.505394\pi$
$193$	−0.470778	−0.0338874	−0.0169437	+	0.999856i	$0.505394\pi$
$194$	11.8228	0.848831
$195$	2.37798	0.170291
$196$	−5.39957	−0.385684
$197$	−18.9685	−1.35145	−0.675724	−	0.737155i	$-0.736169\pi$
$197$	−18.9685	−1.35145	−0.675724	+	0.737155i	$0.736169\pi$
$198$	3.77137	0.268020
$199$	12.5451	0.889296	0.444648	−	0.895706i	$-0.353329\pi$
$199$	12.5451	0.889296	0.444648	+	0.895706i	$0.353329\pi$
$200$	4.26491	0.301575
$201$	4.45222	0.314036
$202$	−4.19486	−0.295149
$203$	11.5017	0.807261
$204$	12.9680	0.907939
$205$	−5.18098	−0.361855
$206$	−4.09226	−0.285121
$207$	−4.05940	−0.282148
$208$	1.44087	0.0999062
$209$	−11.0005	−0.760922
$210$	−2.08787	−0.144077
$211$	−4.38632	−0.301967	−0.150983	−	0.988536i	$-0.548244\pi$
$211$	−4.38632	−0.301967	−0.150983	+	0.988536i	$0.548244\pi$
$212$	11.6367	0.799210
$213$	8.18924	0.561118
$214$	−2.59092	−0.177111
$215$	−0.705249	−0.0480976
$216$	−4.41705	−0.300542
$217$	−0.443641	−0.0301163
$218$	−0.0240516	−0.00162898
$219$	−8.20368	−0.554353
$220$	4.58429	0.309073
$221$	−9.70694	−0.652959
$222$	15.3336	1.02912
$223$	−4.89384	−0.327716	−0.163858	−	0.986484i	$-0.552394\pi$
$223$	−4.89384	−0.327716	−0.163858	+	0.986484i	$0.552394\pi$
$224$	−1.26508	−0.0845267
$225$	−3.00820	−0.200547
$226$	10.3101	0.685819
$227$	−19.5473	−1.29740	−0.648701	−	0.761043i	$-0.724688\pi$
$227$	−19.5473	−1.29740	−0.648701	+	0.761043i	$0.724688\pi$
$228$	−3.96028	−0.262276
$229$	−7.70850	−0.509392	−0.254696	−	0.967021i	$-0.581975\pi$
$229$	−7.70850	−0.509392	−0.254696	+	0.967021i	$0.581975\pi$
$230$	−4.93441	−0.325366
$231$	13.0207	0.856698
$232$	−9.09168	−0.596898
$233$	18.7374	1.22753	0.613763	−	0.789490i	$-0.289655\pi$
$233$	18.7374	1.22753	0.613763	+	0.789490i	$0.289655\pi$
$234$	−1.01630	−0.0664376
$235$	−5.82975	−0.380291
$236$	−4.54798	−0.296049
$237$	4.89526	0.317981
$238$	8.52267	0.552443
$239$	−4.77641	−0.308961	−0.154480	−	0.987996i	$-0.549370\pi$
$239$	−4.77641	−0.308961	−0.154480	+	0.987996i	$0.549370\pi$
$240$	1.65038	0.106532
$241$	28.2429	1.81929	0.909644	−	0.415389i	$-0.136354\pi$
$241$	28.2429	1.81929	0.909644	+	0.415389i	$0.136354\pi$
$242$	−17.5893	−1.13068
$243$	7.18869	0.461155
$244$	6.81691	0.436408
$245$	4.62946	0.295765
$246$	11.6320	0.741630
$247$	2.96439	0.188620
$248$	0.350682	0.0222683
$249$	10.1033	0.640272
$250$	−7.94350	−0.502391
$251$	−20.5495	−1.29707	−0.648537	−	0.761183i	$-0.724619\pi$
$251$	−20.5495	−1.29707	−0.648537	+	0.761183i	$0.724619\pi$
$252$	0.892310	0.0562102
$253$	30.7727	1.93467
$254$	−7.12920	−0.447326
$255$	−11.1184	−0.696262
$256$	1.00000	0.0625000
$257$	18.7293	1.16830	0.584152	−	0.811644i	$-0.301427\pi$
$257$	18.7293	1.16830	0.584152	+	0.811644i	$0.301427\pi$
$258$	1.58338	0.0985770
$259$	10.0774	0.626178
$260$	−1.23536	−0.0766141
$261$	6.41271	0.396937
$262$	15.0959	0.932631
$263$	0.946191	0.0583446	0.0291723	−	0.999574i	$-0.490713\pi$
$263$	0.946191	0.0583446	0.0291723	+	0.999574i	$0.490713\pi$
$264$	−10.2924	−0.633452
$265$	−9.97700	−0.612882
$266$	−2.60273	−0.159584
$267$	−4.76036	−0.291330
$268$	−2.31293	−0.141285
$269$	−8.44382	−0.514829	−0.257414	−	0.966301i	$-0.582871\pi$
$269$	−8.44382	−0.514829	−0.257414	+	0.966301i	$0.582871\pi$
$270$	3.78707	0.230474
$271$	4.92559	0.299208	0.149604	−	0.988746i	$-0.452200\pi$
$271$	4.92559	0.299208	0.149604	+	0.988746i	$0.452200\pi$
$272$	−6.73687	−0.408482
$273$	−3.50878	−0.212361
$274$	−10.6644	−0.644262
$275$	22.8040	1.37513
$276$	11.0784	0.666844
$277$	−10.3007	−0.618907	−0.309453	−	0.950915i	$-0.600146\pi$
$277$	−10.3007	−0.618907	−0.309453	+	0.950915i	$0.600146\pi$
$278$	−20.1241	−1.20696
$279$	−0.247349	−0.0148084
$280$	1.08465	0.0648201
$281$	−8.63849	−0.515329	−0.257665	−	0.966234i	$-0.582953\pi$
$281$	−8.63849	−0.515329	−0.257665	+	0.966234i	$0.582953\pi$
$282$	13.0886	0.779415
$283$	−8.74582	−0.519885	−0.259943	−	0.965624i	$-0.583704\pi$
$283$	−8.74582	−0.519885	−0.259943	+	0.965624i	$0.583704\pi$
$284$	−4.25432	−0.252447
$285$	3.39544	0.201129
$286$	7.70417	0.455557
$287$	7.64467	0.451251
$288$	−0.705338	−0.0415625
$289$	28.3854	1.66973
$290$	7.79498	0.457737
$291$	22.7581	1.33410
$292$	4.26181	0.249404
$293$	−15.4203	−0.900864	−0.450432	−	0.892811i	$-0.648730\pi$
$293$	−15.4203	−0.900864	−0.450432	+	0.892811i	$0.648730\pi$
$294$	−10.3938	−0.606177
$295$	3.89933	0.227028
$296$	−7.96580	−0.463003
$297$	−23.6175	−1.37043
$298$	7.87452	0.456159
$299$	−8.29257	−0.479572
$300$	8.20963	0.473983
$301$	1.04061	0.0599800
$302$	−9.37233	−0.539317
$303$	−8.07479	−0.463885
$304$	2.05737	0.117998
$305$	−5.84465	−0.334664
$306$	4.75177	0.271641
$307$	0.609670	0.0347957	0.0173978	−	0.999849i	$-0.494462\pi$
$307$	0.609670	0.0347957	0.0173978	+	0.999849i	$0.494462\pi$
$308$	−6.76425	−0.385429
$309$	−7.87729	−0.448123
$310$	−0.300666	−0.0170767
$311$	−16.9392	−0.960536	−0.480268	−	0.877122i	$-0.659461\pi$
$311$	−16.9392	−0.960536	−0.480268	+	0.877122i	$0.659461\pi$
$312$	2.77356	0.157022
$313$	19.9210	1.12600	0.563001	−	0.826456i	$-0.309647\pi$
$313$	19.9210	1.12600	0.563001	+	0.826456i	$0.309647\pi$
$314$	−4.89179	−0.276060
$315$	−0.765044	−0.0431053
$316$	−2.54309	−0.143060
$317$	−3.87266	−0.217511	−0.108755	−	0.994069i	$-0.534686\pi$
$317$	−3.87266	−0.217511	−0.108755	+	0.994069i	$0.534686\pi$
$318$	22.3997	1.25611
$319$	−48.6122	−2.72176
$320$	−0.857375	−0.0479287
$321$	−4.98732	−0.278365
$322$	7.28086	0.405747
$323$	−13.8602	−0.771202
$324$	−10.6185	−0.589917
$325$	−6.14517	−0.340873
$326$	−8.00736	−0.443487
$327$	−0.0462976	−0.00256026
$328$	−6.04283	−0.333660
$329$	8.60195	0.474241
$330$	8.82442	0.485769
$331$	23.3875	1.28549	0.642747	−	0.766079i	$-0.277795\pi$
$331$	23.3875	1.28549	0.642747	+	0.766079i	$0.277795\pi$
$332$	−5.24868	−0.288059
$333$	5.61859	0.307897
$334$	−10.9129	−0.597129
$335$	1.98305	0.108346
$336$	−2.43518	−0.132850
$337$	−24.3200	−1.32480	−0.662399	−	0.749152i	$-0.730461\pi$
$337$	−24.3200	−1.32480	−0.662399	+	0.749152i	$0.730461\pi$
$338$	10.9239	0.594182
$339$	19.8462	1.07790
$340$	5.77602	0.313249
$341$	1.87506	0.101540
$342$	−1.45114	−0.0784686
$343$	−15.6865	−0.846989
$344$	−0.822568	−0.0443499
$345$	−9.49838	−0.511376
$346$	3.70204	0.199023
$347$	−12.9918	−0.697437	−0.348719	−	0.937228i	$-0.613383\pi$
$347$	−12.9918	−0.697437	−0.348719	+	0.937228i	$0.613383\pi$
$348$	−17.5008	−0.938141
$349$	17.0332	0.911769	0.455884	−	0.890039i	$-0.349323\pi$
$349$	17.0332	0.911769	0.455884	+	0.890039i	$0.349323\pi$
$350$	5.39545	0.288399
$351$	6.36439	0.339706
$352$	5.34689	0.284990
$353$	18.2088	0.969156	0.484578	−	0.874748i	$-0.338973\pi$
$353$	18.2088	0.969156	0.484578	+	0.874748i	$0.338973\pi$
$354$	−8.75453	−0.465298
$355$	3.64755	0.193592
$356$	2.47301	0.131069
$357$	16.4055	0.868272
$358$	−8.22004	−0.434443
$359$	5.07398	0.267794	0.133897	−	0.990995i	$-0.457251\pi$
$359$	5.07398	0.267794	0.133897	+	0.990995i	$0.457251\pi$
$360$	0.604740	0.0318726
$361$	−14.7672	−0.777223
$362$	11.3533	0.596715
$363$	−33.8580	−1.77709
$364$	1.82281	0.0955414
$365$	−3.65397	−0.191258
$366$	13.1221	0.685901
$367$	1.19922	0.0625990	0.0312995	−	0.999510i	$-0.490035\pi$
$367$	1.19922	0.0625990	0.0312995	+	0.999510i	$0.490035\pi$
$368$	−5.75526	−0.300014
$369$	4.26224	0.221884
$370$	6.82968	0.355058
$371$	14.7213	0.764293
$372$	0.675037	0.0349990
$373$	12.8146	0.663517	0.331758	−	0.943364i	$-0.392358\pi$
$373$	12.8146	0.663517	0.331758	+	0.943364i	$0.392358\pi$
$374$	−36.0213	−1.86262
$375$	−15.2906	−0.789606
$376$	−6.79953	−0.350659
$377$	13.0999	0.674680
$378$	−5.58793	−0.287412
$379$	18.6508	0.958026	0.479013	−	0.877808i	$-0.340995\pi$
$379$	18.6508	0.958026	0.479013	+	0.877808i	$0.340995\pi$
$380$	−1.76393	−0.0904879
$381$	−13.7232	−0.703060
$382$	11.0488	0.565305
$383$	−6.37743	−0.325871	−0.162936	−	0.986637i	$-0.552096\pi$
$383$	−6.37743	−0.325871	−0.162936	+	0.986637i	$0.552096\pi$
$384$	1.92493	0.0982309
$385$	5.79950	0.295570
$386$	0.470778	0.0239620
$387$	0.580189	0.0294926
$388$	−11.8228	−0.600214
$389$	−32.6593	−1.65589	−0.827945	−	0.560809i	$-0.810490\pi$
$389$	−32.6593	−1.65589	−0.827945	+	0.560809i	$0.810490\pi$
$390$	−2.37798	−0.120414
$391$	38.7724	1.96080
$392$	5.39957	0.272720
$393$	29.0586	1.46581
$394$	18.9685	0.955618
$395$	2.18038	0.109707
$396$	−3.77137	−0.189518
$397$	22.4077	1.12461	0.562305	−	0.826930i	$-0.309915\pi$
$397$	22.4077	1.12461	0.562305	+	0.826930i	$0.309915\pi$
$398$	−12.5451	−0.628827
$399$	−5.01007	−0.250817
$400$	−4.26491	−0.213245
$401$	0.929509	0.0464175	0.0232087	−	0.999731i	$-0.492612\pi$
$401$	0.929509	0.0464175	0.0232087	+	0.999731i	$0.492612\pi$
$402$	−4.45222	−0.222057
$403$	−0.505286	−0.0251701
$404$	4.19486	0.208702
$405$	9.10405	0.452384
$406$	−11.5017	−0.570820
$407$	−42.5923	−2.11122
$408$	−12.9680	−0.642010
$409$	−35.5056	−1.75564	−0.877820	−	0.478991i	$-0.841003\pi$
$409$	−35.5056	−1.75564	−0.877820	+	0.478991i	$0.841003\pi$
$410$	5.18098	0.255870
$411$	−20.5282	−1.01258
$412$	4.09226	0.201611
$413$	−5.75356	−0.283114
$414$	4.05940	0.199509
$415$	4.50009	0.220901
$416$	−1.44087	−0.0706444
$417$	−38.7373	−1.89698
$418$	11.0005	0.538053
$419$	−5.67166	−0.277079	−0.138539	−	0.990357i	$-0.544241\pi$
$419$	−5.67166	−0.277079	−0.138539	+	0.990357i	$0.544241\pi$
$420$	2.08787	0.101877
$421$	−12.5299	−0.610669	−0.305335	−	0.952245i	$-0.598768\pi$
$421$	−12.5299	−0.610669	−0.305335	+	0.952245i	$0.598768\pi$
$422$	4.38632	0.213523
$423$	4.79597	0.233188
$424$	−11.6367	−0.565127
$425$	28.7321	1.39371
$426$	−8.18924	−0.396770
$427$	8.62394	0.417342
$428$	2.59092	0.125237
$429$	14.8300	0.715997
$430$	0.705249	0.0340101
$431$	−31.5956	−1.52191	−0.760953	−	0.648807i	$-0.775268\pi$
$431$	−31.5956	−1.52191	−0.760953	+	0.648807i	$0.775268\pi$
$432$	4.41705	0.212516
$433$	−6.09451	−0.292884	−0.146442	−	0.989219i	$-0.546782\pi$
$433$	−6.09451	−0.292884	−0.146442	+	0.989219i	$0.546782\pi$
$434$	0.443641	0.0212954
$435$	15.0047	0.719423
$436$	0.0240516	0.00115186
$437$	−11.8407	−0.566416
$438$	8.20368	0.391987
$439$	−27.4998	−1.31249	−0.656247	−	0.754546i	$-0.727857\pi$
$439$	−27.4998	−1.31249	−0.656247	+	0.754546i	$0.727857\pi$
$440$	−4.58429	−0.218548
$441$	−3.80853	−0.181358
$442$	9.70694	0.461712
$443$	−3.01688	−0.143336	−0.0716682	−	0.997429i	$-0.522832\pi$
$443$	−3.01688	−0.143336	−0.0716682	+	0.997429i	$0.522832\pi$
$444$	−15.3336	−0.727700
$445$	−2.12030	−0.100512
$446$	4.89384	0.231730
$447$	15.1579	0.716942
$448$	1.26508	0.0597694
$449$	25.9367	1.22403	0.612014	−	0.790847i	$-0.290360\pi$
$449$	25.9367	1.22403	0.612014	+	0.790847i	$0.290360\pi$
$450$	3.00820	0.141808
$451$	−32.3104	−1.52144
$452$	−10.3101	−0.484948
$453$	−18.0410	−0.847642
$454$	19.5473	0.917402
$455$	−1.56284	−0.0732668
$456$	3.96028	0.185457
$457$	27.6609	1.29392	0.646960	−	0.762524i	$-0.276040\pi$
$457$	27.6609	1.29392	0.646960	+	0.762524i	$0.276040\pi$
$458$	7.70850	0.360194
$459$	−29.7571	−1.38894
$460$	4.93441	0.230068
$461$	17.0673	0.794905	0.397452	−	0.917623i	$-0.369894\pi$
$461$	17.0673	0.794905	0.397452	+	0.917623i	$0.369894\pi$
$462$	−13.0207	−0.605777
$463$	33.7953	1.57060	0.785301	−	0.619115i	$-0.212508\pi$
$463$	33.7953	1.57060	0.785301	+	0.619115i	$0.212508\pi$
$464$	9.09168	0.422070
$465$	−0.578760	−0.0268393
$466$	−18.7374	−0.867992
$467$	−26.1961	−1.21221	−0.606105	−	0.795385i	$-0.707269\pi$
$467$	−26.1961	−1.21221	−0.606105	+	0.795385i	$0.707269\pi$
$468$	1.01630	0.0469785
$469$	−2.92604	−0.135112
$470$	5.82975	0.268906
$471$	−9.41634	−0.433882
$472$	4.54798	0.209338
$473$	−4.39818	−0.202229
$474$	−4.89526	−0.224847
$475$	−8.77448	−0.402601
$476$	−8.52267	−0.390636
$477$	8.20780	0.375809
$478$	4.77641	0.218468
$479$	−17.4545	−0.797518	−0.398759	−	0.917056i	$-0.630559\pi$
$479$	−17.4545	−0.797518	−0.398759	+	0.917056i	$0.630559\pi$
$480$	−1.65038	−0.0753293
$481$	11.4777	0.523337
$482$	−28.2429	−1.28643
$483$	14.0151	0.637710
$484$	17.5893	0.799512
$485$	10.1366	0.460280
$486$	−7.18869	−0.326086
$487$	−20.9462	−0.949162	−0.474581	−	0.880212i	$-0.657400\pi$
$487$	−20.9462	−0.949162	−0.474581	+	0.880212i	$0.657400\pi$
$488$	−6.81691	−0.308587
$489$	−15.4136	−0.697026
$490$	−4.62946	−0.209138
$491$	−13.2505	−0.597985	−0.298992	−	0.954255i	$-0.596651\pi$
$491$	−13.2505	−0.597985	−0.298992	+	0.954255i	$0.596651\pi$
$492$	−11.6320	−0.524411
$493$	−61.2494	−2.75853
$494$	−2.96439	−0.133374
$495$	3.23348	0.145334
$496$	−0.350682	−0.0157461
$497$	−5.38205	−0.241418
$498$	−10.1033	−0.452741
$499$	−16.3282	−0.730952	−0.365476	−	0.930821i	$-0.619094\pi$
$499$	−16.3282	−0.730952	−0.365476	+	0.930821i	$0.619094\pi$
$500$	7.94350	0.355244
$501$	−21.0066	−0.938505
$502$	20.5495	0.917170
$503$	37.1792	1.65774	0.828869	−	0.559442i	$-0.188985\pi$
$503$	37.1792	1.65774	0.828869	+	0.559442i	$0.188985\pi$
$504$	−0.892310	−0.0397466
$505$	−3.59657	−0.160045
$506$	−30.7727	−1.36802
$507$	21.0277	0.933873
$508$	7.12920	0.316307
$509$	30.8052	1.36542	0.682709	−	0.730691i	$-0.260802\pi$
$509$	30.8052	1.36542	0.682709	+	0.730691i	$0.260802\pi$
$510$	11.1184	0.492331
$511$	5.39154	0.238508
$512$	−1.00000	−0.0441942
$513$	9.08749	0.401223
$514$	−18.7293	−0.826116
$515$	−3.50860	−0.154607
$516$	−1.58338	−0.0697045
$517$	−36.3564	−1.59895
$518$	−10.0774	−0.442775
$519$	7.12615	0.312803
$520$	1.23536	0.0541743
$521$	16.3856	0.717866	0.358933	−	0.933363i	$-0.383141\pi$
$521$	16.3856	0.717866	0.358933	+	0.933363i	$0.383141\pi$
$522$	−6.41271	−0.280677
$523$	32.8604	1.43688	0.718442	−	0.695587i	$-0.244856\pi$
$523$	32.8604	1.43688	0.718442	+	0.695587i	$0.244856\pi$
$524$	−15.0959	−0.659469
$525$	10.3858	0.453275
$526$	−0.946191	−0.0412559
$527$	2.36250	0.102912
$528$	10.2924	0.447918
$529$	10.1230	0.440130
$530$	9.97700	0.433373
$531$	−3.20787	−0.139210
$532$	2.60273	0.112843
$533$	8.70693	0.377139
$534$	4.76036	0.206001
$535$	−2.22139	−0.0960389
$536$	2.31293	0.0999035
$537$	−15.8230	−0.682812
$538$	8.44382	0.364039
$539$	28.8709	1.24356
$540$	−3.78707	−0.162970
$541$	−15.8950	−0.683380	−0.341690	−	0.939813i	$-0.610999\pi$
$541$	−15.8950	−0.683380	−0.341690	+	0.939813i	$0.610999\pi$
$542$	−4.92559	−0.211572
$543$	21.8542	0.937854
$544$	6.73687	0.288841
$545$	−0.0206213	−0.000883317 0
$546$	3.50878	0.150162
$547$	−1.98404	−0.0848316	−0.0424158	−	0.999100i	$-0.513505\pi$
$547$	−1.98404	−0.0848316	−0.0424158	+	0.999100i	$0.513505\pi$
$548$	10.6644	0.455562
$549$	4.80823	0.205210
$550$	−22.8040	−0.972366
$551$	18.7049	0.796856
$552$	−11.0784	−0.471530
$553$	−3.21721	−0.136810
$554$	10.3007	0.437633
$555$	13.1466	0.558043
$556$	20.1241	0.853451
$557$	−39.8074	−1.68669	−0.843346	−	0.537371i	$-0.819417\pi$
$557$	−39.8074	−1.68669	−0.843346	+	0.537371i	$0.819417\pi$
$558$	0.247349	0.0104711
$559$	1.18521	0.0501291
$560$	−1.08465	−0.0458348
$561$	−69.3383	−2.92747
$562$	8.63849	0.364393
$563$	−8.30812	−0.350146	−0.175073	−	0.984555i	$-0.556016\pi$
$563$	−8.30812	−0.350146	−0.175073	+	0.984555i	$0.556016\pi$
$564$	−13.0886	−0.551129
$565$	8.83965	0.371887
$566$	8.74582	0.367614
$567$	−13.4333	−0.564144
$568$	4.25432	0.178507
$569$	−15.3546	−0.643697	−0.321848	−	0.946791i	$-0.604304\pi$
$569$	−15.3546	−0.643697	−0.321848	+	0.946791i	$0.604304\pi$
$570$	−3.39544	−0.142219
$571$	6.69151	0.280031	0.140015	−	0.990149i	$-0.455285\pi$
$571$	6.69151	0.280031	0.140015	+	0.990149i	$0.455285\pi$
$572$	−7.70417	−0.322127
$573$	21.2681	0.888488
$574$	−7.64467	−0.319082
$575$	24.5456	1.02362
$576$	0.705338	0.0293891
$577$	−9.59003	−0.399238	−0.199619	−	0.979874i	$-0.563971\pi$
$577$	−9.59003	−0.399238	−0.199619	+	0.979874i	$0.563971\pi$
$578$	−28.3854	−1.18068
$579$	0.906213	0.0376609
$580$	−7.79498	−0.323669
$581$	−6.64000	−0.275474
$582$	−22.7581	−0.943353
$583$	−62.2201	−2.57689
$584$	−4.26181	−0.176355
$585$	−0.871350	−0.0360259
$586$	15.4203	0.637007
$587$	−37.3586	−1.54196	−0.770978	−	0.636862i	$-0.780232\pi$
$587$	−37.3586	−1.54196	−0.770978	+	0.636862i	$0.780232\pi$
$588$	10.3938	0.428632
$589$	−0.721481	−0.0297281
$590$	−3.89933	−0.160533
$591$	36.5129	1.50194
$592$	7.96580	0.327393
$593$	13.7741	0.565635	0.282818	−	0.959174i	$-0.408731\pi$
$593$	13.7741	0.565635	0.282818	+	0.959174i	$0.408731\pi$
$594$	23.6175	0.969038
$595$	7.30713	0.299563
$596$	−7.87452	−0.322553
$597$	−24.1483	−0.988324
$598$	8.29257	0.339108
$599$	0.0186608	0.000762458 0	0.000381229	−	1.00000i	$-0.499879\pi$
$599$	0.0186608	0.000762458 0	0.000381229		1.00000i	$0.499879\pi$
$600$	−8.20963	−0.335157
$601$	24.1248	0.984072	0.492036	−	0.870575i	$-0.336253\pi$
$601$	24.1248	0.984072	0.492036	+	0.870575i	$0.336253\pi$
$602$	−1.04061	−0.0424123
$603$	−1.63140	−0.0664358
$604$	9.37233	0.381355
$605$	−15.0806	−0.613114
$606$	8.07479	0.328016
$607$	−30.3456	−1.23169	−0.615844	−	0.787868i	$-0.711185\pi$
$607$	−30.3456	−1.23169	−0.615844	+	0.787868i	$0.711185\pi$
$608$	−2.05737	−0.0834372
$609$	−22.1399	−0.897155
$610$	5.84465	0.236643
$611$	9.79723	0.396354
$612$	−4.75177	−0.192079
$613$	26.1677	1.05690	0.528451	−	0.848964i	$-0.322773\pi$
$613$	26.1677	1.05690	0.528451	+	0.848964i	$0.322773\pi$
$614$	−0.609670	−0.0246043
$615$	9.97299	0.402150
$616$	6.76425	0.272539
$617$	−18.0105	−0.725077	−0.362539	−	0.931969i	$-0.618090\pi$
$617$	−18.0105	−0.725077	−0.362539	+	0.931969i	$0.618090\pi$
$618$	7.87729	0.316871
$619$	−31.1665	−1.25269	−0.626343	−	0.779547i	$-0.715449\pi$
$619$	−31.1665	−1.25269	−0.626343	+	0.779547i	$0.715449\pi$
$620$	0.300666	0.0120750
$621$	−25.4213	−1.02012
$622$	16.9392	0.679202
$623$	3.12856	0.125343
$624$	−2.77356	−0.111031
$625$	14.5140	0.580559
$626$	−19.9210	−0.796204
$627$	21.1752	0.845655
$628$	4.89179	0.195204
$629$	−53.6646	−2.13975
$630$	0.765044	0.0304801
$631$	4.83739	0.192573	0.0962867	−	0.995354i	$-0.469303\pi$
$631$	4.83739	0.192573	0.0962867	+	0.995354i	$0.469303\pi$
$632$	2.54309	0.101159
$633$	8.44333	0.335592
$634$	3.87266	0.153803
$635$	−6.11240	−0.242563
$636$	−22.3997	−0.888207
$637$	−7.78007	−0.308258
$638$	48.6122	1.92458
$639$	−3.00073	−0.118707
$640$	0.857375	0.0338907
$641$	22.5805	0.891877	0.445938	−	0.895064i	$-0.352870\pi$
$641$	22.5805	0.891877	0.445938	+	0.895064i	$0.352870\pi$
$642$	4.98732	0.196834
$643$	−2.05857	−0.0811820	−0.0405910	−	0.999176i	$-0.512924\pi$
$643$	−2.05857	−0.0811820	−0.0405910	+	0.999176i	$0.512924\pi$
$644$	−7.28086	−0.286906
$645$	1.35755	0.0534535
$646$	13.8602	0.545322
$647$	−25.5947	−1.00623	−0.503115	−	0.864219i	$-0.667813\pi$
$647$	−25.5947	−1.00623	−0.503115	+	0.864219i	$0.667813\pi$
$648$	10.6185	0.417135
$649$	24.3176	0.954549
$650$	6.14517	0.241033
$651$	0.853975	0.0334699
$652$	8.00736	0.313592
$653$	38.0683	1.48973	0.744863	−	0.667217i	$-0.232515\pi$
$653$	38.0683	1.48973	0.744863	+	0.667217i	$0.232515\pi$
$654$	0.0462976	0.00181038
$655$	12.9429	0.505720
$656$	6.04283	0.235933
$657$	3.00602	0.117276
$658$	−8.60195	−0.335339
$659$	−27.3953	−1.06717	−0.533586	−	0.845746i	$-0.679156\pi$
$659$	−27.3953	−1.06717	−0.533586	+	0.845746i	$0.679156\pi$
$660$	−8.82442	−0.343490
$661$	−37.5944	−1.46225	−0.731126	−	0.682243i	$-0.761005\pi$
$661$	−37.5944	−1.46225	−0.731126	+	0.682243i	$0.761005\pi$
$662$	−23.3875	−0.908981
$663$	18.6851	0.725670
$664$	5.24868	0.203688
$665$	−2.23152	−0.0865346
$666$	−5.61859	−0.217716
$667$	−52.3249	−2.02603
$668$	10.9129	0.422234
$669$	9.42028	0.364209
$670$	−1.98305	−0.0766119
$671$	−36.4493	−1.40711
$672$	2.43518	0.0939393
$673$	−41.6134	−1.60408	−0.802039	−	0.597272i	$-0.796251\pi$
$673$	−41.6134	−1.60408	−0.802039	+	0.597272i	$0.796251\pi$
$674$	24.3200	0.936773
$675$	−18.8383	−0.725087
$676$	−10.9239	−0.420150
$677$	1.07675	0.0413829	0.0206914	−	0.999786i	$-0.493413\pi$
$677$	1.07675	0.0413829	0.0206914	+	0.999786i	$0.493413\pi$
$678$	−19.8462	−0.762190
$679$	−14.9568	−0.573991
$680$	−5.77602	−0.221500
$681$	37.6272	1.44188
$682$	−1.87506	−0.0717997
$683$	−31.6071	−1.20941	−0.604706	−	0.796449i	$-0.706709\pi$
$683$	−31.6071	−1.20941	−0.604706	+	0.796449i	$0.706709\pi$
$684$	1.45114	0.0554857
$685$	−9.14341	−0.349352
$686$	15.6865	0.598912
$687$	14.8383	0.566116
$688$	0.822568	0.0313601
$689$	16.7669	0.638769
$690$	9.49838	0.361597
$691$	−34.2270	−1.30206	−0.651028	−	0.759054i	$-0.725662\pi$
$691$	−34.2270	−1.30206	−0.651028	+	0.759054i	$0.725662\pi$
$692$	−3.70204	−0.140730
$693$	−4.77108	−0.181239
$694$	12.9918	0.493162
$695$	−17.2539	−0.654477
$696$	17.5008	0.663366
$697$	−40.7098	−1.54199
$698$	−17.0332	−0.644718
$699$	−36.0681	−1.36422
$700$	−5.39545	−0.203929
$701$	13.3514	0.504274	0.252137	−	0.967692i	$-0.418867\pi$
$701$	13.3514	0.504274	0.252137	+	0.967692i	$0.418867\pi$
$702$	−6.36439	−0.240208
$703$	16.3886	0.618107
$704$	−5.34689	−0.201519
$705$	11.2218	0.422639
$706$	−18.2088	−0.685297
$707$	5.30683	0.199584
$708$	8.75453	0.329015
$709$	18.4736	0.693790	0.346895	−	0.937904i	$-0.387236\pi$
$709$	18.4736	0.693790	0.346895	+	0.937904i	$0.387236\pi$
$710$	−3.64755	−0.136890
$711$	−1.79374	−0.0672705
$712$	−2.47301	−0.0926801
$713$	2.01826	0.0755846
$714$	−16.4055	−0.613961
$715$	6.60536	0.247027
$716$	8.22004	0.307197
$717$	9.19424	0.343365
$718$	−5.07398	−0.189359
$719$	32.4474	1.21008	0.605041	−	0.796194i	$-0.293157\pi$
$719$	32.4474	1.21008	0.605041	+	0.796194i	$0.293157\pi$
$720$	−0.604740	−0.0225373
$721$	5.17703	0.192803
$722$	14.7672	0.549580
$723$	−54.3656	−2.02188
$724$	−11.3533	−0.421941
$725$	−38.7752	−1.44007
$726$	33.8580	1.25659
$727$	−12.3490	−0.457999	−0.229000	−	0.973427i	$-0.573545\pi$
$727$	−12.3490	−0.457999	−0.229000	+	0.973427i	$0.573545\pi$
$728$	−1.82281	−0.0675580
$729$	18.0178	0.667328
$730$	3.65397	0.135240
$731$	−5.54153	−0.204961
$732$	−13.1221	−0.485005
$733$	−8.94888	−0.330534	−0.165267	−	0.986249i	$-0.552849\pi$
$733$	−8.94888	−0.330534	−0.165267	+	0.986249i	$0.552849\pi$
$734$	−1.19922	−0.0442642
$735$	−8.91136	−0.328701
$736$	5.75526	0.212142
$737$	12.3670	0.455544
$738$	−4.26224	−0.156895
$739$	7.66165	0.281838	0.140919	−	0.990021i	$-0.454994\pi$
$739$	7.66165	0.281838	0.140919	+	0.990021i	$0.454994\pi$
$740$	−6.82968	−0.251064
$741$	−5.70624	−0.209624
$742$	−14.7213	−0.540437
$743$	−48.9416	−1.79549	−0.897747	−	0.440511i	$-0.854797\pi$
$743$	−48.9416	−1.79549	−0.897747	+	0.440511i	$0.854797\pi$
$744$	−0.675037	−0.0247480
$745$	6.75142	0.247353
$746$	−12.8146	−0.469177
$747$	−3.70210	−0.135453
$748$	36.0213	1.31707
$749$	3.27772	0.119765
$750$	15.2906	0.558336
$751$	−13.0372	−0.475733	−0.237867	−	0.971298i	$-0.576448\pi$
$751$	−13.0372	−0.475733	−0.237867	+	0.971298i	$0.576448\pi$
$752$	6.79953	0.247953
$753$	39.5563	1.44151
$754$	−13.0999	−0.477070
$755$	−8.03560	−0.292446
$756$	5.58793	0.203231
$757$	−33.2831	−1.20970	−0.604848	−	0.796341i	$-0.706766\pi$
$757$	−33.2831	−1.20970	−0.604848	+	0.796341i	$0.706766\pi$
$758$	−18.6508	−0.677427
$759$	−59.2352	−2.15010
$760$	1.76393	0.0639846
$761$	−4.48847	−0.162707	−0.0813535	−	0.996685i	$-0.525924\pi$
$761$	−4.48847	−0.162707	−0.0813535	+	0.996685i	$0.525924\pi$
$762$	13.7232	0.497138
$763$	0.0304272	0.00110154
$764$	−11.0488	−0.399731
$765$	4.07405	0.147298
$766$	6.37743	0.230426
$767$	−6.55305	−0.236617
$768$	−1.92493	−0.0694598
$769$	−44.0733	−1.58933	−0.794663	−	0.607051i	$-0.792352\pi$
$769$	−44.0733	−1.58933	−0.794663	+	0.607051i	$0.792352\pi$
$770$	−5.79950	−0.208999
$771$	−36.0526	−1.29840
$772$	−0.470778	−0.0169437
$773$	41.4453	1.49069	0.745343	−	0.666682i	$-0.232286\pi$
$773$	41.4453	1.49069	0.745343	+	0.666682i	$0.232286\pi$
$774$	−0.580189	−0.0208544
$775$	1.49563	0.0537245
$776$	11.8228	0.424415
$777$	−19.3982	−0.695907
$778$	32.6593	1.17089
$779$	12.4323	0.445434
$780$	2.37798	0.0851455
$781$	22.7474	0.813965
$782$	−38.7724	−1.38650
$783$	40.1584	1.43514
$784$	−5.39957	−0.192842
$785$	−4.19410	−0.149694
$786$	−29.0586	−1.03648
$787$	−32.5279	−1.15949	−0.579747	−	0.814796i	$-0.696849\pi$
$787$	−32.5279	−1.15949	−0.579747	+	0.814796i	$0.696849\pi$
$788$	−18.9685	−0.675724
$789$	−1.82135	−0.0648417
$790$	−2.18038	−0.0775745
$791$	−13.0431	−0.463760
$792$	3.77137	0.134010
$793$	9.82227	0.348799
$794$	−22.4077	−0.795220
$795$	19.2050	0.681130
$796$	12.5451	0.444648
$797$	18.2792	0.647484	0.323742	−	0.946145i	$-0.395059\pi$
$797$	18.2792	0.647484	0.323742	+	0.946145i	$0.395059\pi$
$798$	5.01007	0.177354
$799$	−45.8075	−1.62055
$800$	4.26491	0.150787
$801$	1.74431	0.0616322
$802$	−0.929509	−0.0328221
$803$	−22.7875	−0.804152
$804$	4.45222	0.157018
$805$	6.24243	0.220017
$806$	0.505286	0.0177980
$807$	16.2537	0.572158
$808$	−4.19486	−0.147575
$809$	−46.0635	−1.61951	−0.809754	−	0.586770i	$-0.800399\pi$
$809$	−46.0635	−1.61951	−0.809754	+	0.586770i	$0.800399\pi$
$810$	−9.10405	−0.319884
$811$	−13.7702	−0.483537	−0.241768	−	0.970334i	$-0.577727\pi$
$811$	−13.7702	−0.483537	−0.241768	+	0.970334i	$0.577727\pi$
$812$	11.5017	0.403630
$813$	−9.48140	−0.332527
$814$	42.5923	1.49286
$815$	−6.86531	−0.240481
$816$	12.9680	0.453970
$817$	1.69232	0.0592069
$818$	35.5056	1.24142
$819$	1.28570	0.0449260
$820$	−5.18098	−0.180928
$821$	−28.5847	−0.997612	−0.498806	−	0.866714i	$-0.666228\pi$
$821$	−28.5847	−0.997612	−0.498806	+	0.866714i	$0.666228\pi$
$822$	20.5282	0.716004
$823$	−22.7546	−0.793176	−0.396588	−	0.917997i	$-0.629806\pi$
$823$	−22.7546	−0.793176	−0.396588	+	0.917997i	$0.629806\pi$
$824$	−4.09226	−0.142560
$825$	−43.8960	−1.52826
$826$	5.75356	0.200192
$827$	−5.71087	−0.198586	−0.0992932	−	0.995058i	$-0.531658\pi$
$827$	−5.71087	−0.198586	−0.0992932	+	0.995058i	$0.531658\pi$
$828$	−4.05940	−0.141074
$829$	−7.39400	−0.256804	−0.128402	−	0.991722i	$-0.540985\pi$
$829$	−7.39400	−0.256804	−0.128402	+	0.991722i	$0.540985\pi$
$830$	−4.50009	−0.156200
$831$	19.8280	0.687826
$832$	1.44087	0.0499531
$833$	36.3762	1.26036
$834$	38.7373	1.34136
$835$	−9.35648	−0.323794
$836$	−11.0005	−0.380461
$837$	−1.54898	−0.0535406
$838$	5.67166	0.195924
$839$	−46.6056	−1.60900	−0.804501	−	0.593951i	$-0.797567\pi$
$839$	−46.6056	−1.60900	−0.804501	+	0.593951i	$0.797567\pi$
$840$	−2.08787	−0.0720383
$841$	53.6586	1.85030
$842$	12.5299	0.431808
$843$	16.6285	0.572714
$844$	−4.38632	−0.150983
$845$	9.36588	0.322196
$846$	−4.79597	−0.164889
$847$	22.2518	0.764582
$848$	11.6367	0.399605
$849$	16.8351	0.577778
$850$	−28.7321	−0.985503
$851$	−45.8453	−1.57156
$852$	8.18924	0.280559
$853$	37.6694	1.28977	0.644887	−	0.764278i	$-0.276904\pi$
$853$	37.6694	1.28977	0.644887	+	0.764278i	$0.276904\pi$
$854$	−8.62394	−0.295105
$855$	−1.24417	−0.0425497
$856$	−2.59092	−0.0885557
$857$	6.76183	0.230980	0.115490	−	0.993309i	$-0.463156\pi$
$857$	6.76183	0.230980	0.115490	+	0.993309i	$0.463156\pi$
$858$	−14.8300	−0.506286
$859$	10.1591	0.346625	0.173313	−	0.984867i	$-0.444553\pi$
$859$	10.1591	0.346625	0.173313	+	0.984867i	$0.444553\pi$
$860$	−0.705249	−0.0240488
$861$	−14.7154	−0.501500
$862$	31.5956	1.07615
$863$	−52.2564	−1.77883	−0.889414	−	0.457102i	$-0.848887\pi$
$863$	−52.2564	−1.77883	−0.889414	+	0.457102i	$0.848887\pi$
$864$	−4.41705	−0.150271
$865$	3.17404	0.107920
$866$	6.09451	0.207100
$867$	−54.6397	−1.85566
$868$	−0.443641	−0.0150581
$869$	13.5976	0.461268
$870$	−15.0047	−0.508709
$871$	−3.33263	−0.112922
$872$	−0.0240516	−0.000814490 0
$873$	−8.33910	−0.282236
$874$	11.8407	0.400517
$875$	10.0492	0.339724
$876$	−8.20368	−0.277176
$877$	−23.9908	−0.810111	−0.405055	−	0.914292i	$-0.632748\pi$
$877$	−23.9908	−0.810111	−0.405055	+	0.914292i	$0.632748\pi$
$878$	27.4998	0.928073
$879$	29.6829	1.00118
$880$	4.58429	0.154537
$881$	−13.0531	−0.439770	−0.219885	−	0.975526i	$-0.570568\pi$
$881$	−13.0531	−0.439770	−0.219885	+	0.975526i	$0.570568\pi$
$882$	3.80853	0.128240
$883$	−34.4353	−1.15884	−0.579420	−	0.815029i	$-0.696721\pi$
$883$	−34.4353	−1.15884	−0.579420	+	0.815029i	$0.696721\pi$
$884$	−9.70694	−0.326480
$885$	−7.50592	−0.252309
$886$	3.01688	0.101354
$887$	21.1058	0.708665	0.354332	−	0.935120i	$-0.384708\pi$
$887$	21.1058	0.708665	0.354332	+	0.935120i	$0.384708\pi$
$888$	15.3336	0.514561
$889$	9.01901	0.302488
$890$	2.12030	0.0710726
$891$	56.7761	1.90207
$892$	−4.89384	−0.163858
$893$	13.9891	0.468128
$894$	−15.1579	−0.506955
$895$	−7.04766	−0.235577
$896$	−1.26508	−0.0422634
$897$	15.9626	0.532975
$898$	−25.9367	−0.865518
$899$	−3.18829	−0.106335
$900$	−3.00820	−0.100273
$901$	−78.3947	−2.61171
$902$	32.3104	1.07582
$903$	−2.00310	−0.0666591
$904$	10.3101	0.342910
$905$	9.73402	0.323570
$906$	18.0410	0.599373
$907$	18.4580	0.612888	0.306444	−	0.951889i	$-0.400861\pi$
$907$	18.4580	0.612888	0.306444	+	0.951889i	$0.400861\pi$
$908$	−19.5473	−0.648701
$909$	2.95879	0.0981370
$910$	1.56284	0.0518075
$911$	11.6721	0.386713	0.193356	−	0.981129i	$-0.438063\pi$
$911$	11.6721	0.386713	0.193356	+	0.981129i	$0.438063\pi$
$912$	−3.96028	−0.131138
$913$	28.0641	0.928788
$914$	−27.6609	−0.914940
$915$	11.2505	0.371931
$916$	−7.70850	−0.254696
$917$	−19.0976	−0.630658
$918$	29.7571	0.982130
$919$	5.18811	0.171140	0.0855700	−	0.996332i	$-0.472729\pi$
$919$	5.18811	0.171140	0.0855700	+	0.996332i	$0.472729\pi$
$920$	−4.93441	−0.162683
$921$	−1.17357	−0.0386704
$922$	−17.0673	−0.562082
$923$	−6.12991	−0.201768
$924$	13.0207	0.428349
$925$	−33.9734	−1.11704
$926$	−33.7953	−1.11058
$927$	2.88642	0.0948026
$928$	−9.09168	−0.298449
$929$	−35.9631	−1.17991	−0.589956	−	0.807436i	$-0.700855\pi$
$929$	−35.9631	−1.17991	−0.589956	+	0.807436i	$0.700855\pi$
$930$	0.578760	0.0189783
$931$	−11.1089	−0.364079
$932$	18.7374	0.613763
$933$	32.6068	1.06750
$934$	26.1961	0.857162
$935$	−30.8838	−1.01001
$936$	−1.01630	−0.0332188
$937$	15.5026	0.506448	0.253224	−	0.967408i	$-0.418509\pi$
$937$	15.5026	0.506448	0.253224	+	0.967408i	$0.418509\pi$
$938$	2.92604	0.0955388
$939$	−38.3465	−1.25139
$940$	−5.82975	−0.190146
$941$	55.8993	1.82227	0.911133	−	0.412113i	$-0.135209\pi$
$941$	55.8993	1.82227	0.911133	+	0.412113i	$0.135209\pi$
$942$	9.41634	0.306801
$943$	−34.7781	−1.13253
$944$	−4.54798	−0.148024
$945$	−4.79095	−0.155850
$946$	4.39818	0.142997
$947$	48.6589	1.58120	0.790601	−	0.612332i	$-0.209768\pi$
$947$	48.6589	1.58120	0.790601	+	0.612332i	$0.209768\pi$
$948$	4.89526	0.158991
$949$	6.14071	0.199336
$950$	8.77448	0.284682
$951$	7.45459	0.241732
$952$	8.52267	0.276221
$953$	1.32236	0.0428354	0.0214177	−	0.999771i	$-0.493182\pi$
$953$	1.32236	0.0428354	0.0214177	+	0.999771i	$0.493182\pi$
$954$	−8.20780	−0.265737
$955$	9.47296	0.306538
$956$	−4.77641	−0.154480
$957$	93.5749	3.02485
$958$	17.4545	0.563931
$959$	13.4914	0.435659
$960$	1.65038	0.0532659
$961$	−30.8770	−0.996033
$962$	−11.4777	−0.370055
$963$	1.82747	0.0588895
$964$	28.2429	0.909644
$965$	0.403634	0.0129934
$966$	−14.0151	−0.450929
$967$	1.86060	0.0598330	0.0299165	−	0.999552i	$-0.490476\pi$
$967$	1.86060	0.0598330	0.0299165	+	0.999552i	$0.490476\pi$
$968$	−17.5893	−0.565341
$969$	26.6799	0.857080
$970$	−10.1366	−0.325467
$971$	−47.1113	−1.51187	−0.755937	−	0.654645i	$-0.772818\pi$
$971$	−47.1113	−1.51187	−0.755937	+	0.654645i	$0.772818\pi$
$972$	7.18869	0.230577
$973$	25.4586	0.816164
$974$	20.9462	0.671159
$975$	11.8290	0.378831
$976$	6.81691	0.218204
$977$	56.5483	1.80914	0.904571	−	0.426324i	$-0.140192\pi$
$977$	56.5483	1.80914	0.904571	+	0.426324i	$0.140192\pi$
$978$	15.4136	0.492872
$979$	−13.2229	−0.422607
$980$	4.62946	0.147883
$981$	0.0169645	0.000541636 0
$982$	13.2505	0.422839
$983$	52.9672	1.68939	0.844695	−	0.535248i	$-0.179782\pi$
$983$	52.9672	1.68939	0.844695	+	0.535248i	$0.179782\pi$
$984$	11.6320	0.370815
$985$	16.2631	0.518185
$986$	61.2494	1.95058
$987$	−16.5581	−0.527051
$988$	2.96439	0.0943099
$989$	−4.73409	−0.150535
$990$	−3.23348	−0.102767
$991$	−14.2874	−0.453855	−0.226928	−	0.973912i	$-0.572868\pi$
$991$	−14.2874	−0.453855	−0.226928	+	0.973912i	$0.572868\pi$
$992$	0.350682	0.0111342
$993$	−45.0192	−1.42864
$994$	5.38205	0.170708
$995$	−10.7558	−0.340982
$996$	10.1033	0.320136
$997$	45.5006	1.44102	0.720509	−	0.693446i	$-0.243908\pi$
$997$	45.5006	1.44102	0.720509	+	0.693446i	$0.243908\pi$
$998$	16.3282	0.516861
$999$	35.1854	1.11322

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.b.1.20	✓	81

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.b.1.20	✓	81	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.92493 q^{3} +1.00000 q^{4} -0.857375 q^{5} +1.92493 q^{6} +1.26508 q^{7} -1.00000 q^{8} +0.705338 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.92493 q^{3} +1.00000 q^{4} -0.857375 q^{5} +1.92493 q^{6} +1.26508 q^{7} -1.00000 q^{8} +0.705338 q^{9} +0.857375 q^{10} -5.34689 q^{11} -1.92493 q^{12} +1.44087 q^{13} -1.26508 q^{14} +1.65038 q^{15} +1.00000 q^{16} -6.73687 q^{17} -0.705338 q^{18} +2.05737 q^{19} -0.857375 q^{20} -2.43518 q^{21} +5.34689 q^{22} -5.75526 q^{23} +1.92493 q^{24} -4.26491 q^{25} -1.44087 q^{26} +4.41705 q^{27} +1.26508 q^{28} +9.09168 q^{29} -1.65038 q^{30} -0.350682 q^{31} -1.00000 q^{32} +10.2924 q^{33} +6.73687 q^{34} -1.08465 q^{35} +0.705338 q^{36} +7.96580 q^{37} -2.05737 q^{38} -2.77356 q^{39} +0.857375 q^{40} +6.04283 q^{41} +2.43518 q^{42} +0.822568 q^{43} -5.34689 q^{44} -0.604740 q^{45} +5.75526 q^{46} +6.79953 q^{47} -1.92493 q^{48} -5.39957 q^{49} +4.26491 q^{50} +12.9680 q^{51} +1.44087 q^{52} +11.6367 q^{53} -4.41705 q^{54} +4.58429 q^{55} -1.26508 q^{56} -3.96028 q^{57} -9.09168 q^{58} -4.54798 q^{59} +1.65038 q^{60} +6.81691 q^{61} +0.350682 q^{62} +0.892310 q^{63} +1.00000 q^{64} -1.23536 q^{65} -10.2924 q^{66} -2.31293 q^{67} -6.73687 q^{68} +11.0784 q^{69} +1.08465 q^{70} -4.25432 q^{71} -0.705338 q^{72} +4.26181 q^{73} -7.96580 q^{74} +8.20963 q^{75} +2.05737 q^{76} -6.76425 q^{77} +2.77356 q^{78} -2.54309 q^{79} -0.857375 q^{80} -10.6185 q^{81} -6.04283 q^{82} -5.24868 q^{83} -2.43518 q^{84} +5.77602 q^{85} -0.822568 q^{86} -17.5008 q^{87} +5.34689 q^{88} +2.47301 q^{89} +0.604740 q^{90} +1.82281 q^{91} -5.75526 q^{92} +0.675037 q^{93} -6.79953 q^{94} -1.76393 q^{95} +1.92493 q^{96} -11.8228 q^{97} +5.39957 q^{98} -3.77137 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9}+O(q^{10}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9} + 26 q^{10} - 41 q^{11} - 10 q^{12} + 33 q^{13} - 3 q^{14} - 7 q^{15} + 81 q^{16} - 9 q^{17} - 59 q^{18} - 32 q^{19} - 26 q^{20} - 23 q^{21} + 41 q^{22} - 28 q^{23} + 10 q^{24} + 81 q^{25} - 33 q^{26} - 37 q^{27} + 3 q^{28} - 35 q^{29} + 7 q^{30} - 29 q^{31} - 81 q^{32} - 7 q^{33} + 9 q^{34} - 67 q^{35} + 59 q^{36} + 13 q^{37} + 32 q^{38} - 42 q^{39} + 26 q^{40} - 66 q^{41} + 23 q^{42} - 22 q^{43} - 41 q^{44} - 65 q^{45} + 28 q^{46} - 71 q^{47} - 10 q^{48} + 64 q^{49} - 81 q^{50} - 43 q^{51} + 33 q^{52} - 37 q^{53} + 37 q^{54} + 12 q^{55} - 3 q^{56} - q^{57} + 35 q^{58} - 162 q^{59} - 7 q^{60} + 19 q^{61} + 29 q^{62} - 16 q^{63} + 81 q^{64} - 45 q^{65} + 7 q^{66} - 43 q^{67} - 9 q^{68} - 21 q^{69} + 67 q^{70} - 99 q^{71} - 59 q^{72} + 53 q^{73} - 13 q^{74} - 61 q^{75} - 32 q^{76} - 31 q^{77} + 42 q^{78} + 4 q^{79} - 26 q^{80} + q^{81} + 66 q^{82} - 112 q^{83} - 23 q^{84} + 17 q^{85} + 22 q^{86} - 15 q^{87} + 41 q^{88} - 111 q^{89} + 65 q^{90} - 49 q^{91} - 28 q^{92} - 19 q^{93} + 71 q^{94} - 53 q^{95} + 10 q^{96} + 50 q^{97} - 64 q^{98} - 97 q^{99}+O(q^{100}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9 + 26 * q^10 - 41 * q^11 - 10 * q^12 + 33 * q^13 - 3 * q^14 - 7 * q^15 + 81 * q^16 - 9 * q^17 - 59 * q^18 - 32 * q^19 - 26 * q^20 - 23 * q^21 + 41 * q^22 - 28 * q^23 + 10 * q^24 + 81 * q^25 - 33 * q^26 - 37 * q^27 + 3 * q^28 - 35 * q^29 + 7 * q^30 - 29 * q^31 - 81 * q^32 - 7 * q^33 + 9 * q^34 - 67 * q^35 + 59 * q^36 + 13 * q^37 + 32 * q^38 - 42 * q^39 + 26 * q^40 - 66 * q^41 + 23 * q^42 - 22 * q^43 - 41 * q^44 - 65 * q^45 + 28 * q^46 - 71 * q^47 - 10 * q^48 + 64 * q^49 - 81 * q^50 - 43 * q^51 + 33 * q^52 - 37 * q^53 + 37 * q^54 + 12 * q^55 - 3 * q^56 - q^57 + 35 * q^58 - 162 * q^59 - 7 * q^60 + 19 * q^61 + 29 * q^62 - 16 * q^63 + 81 * q^64 - 45 * q^65 + 7 * q^66 - 43 * q^67 - 9 * q^68 - 21 * q^69 + 67 * q^70 - 99 * q^71 - 59 * q^72 + 53 * q^73 - 13 * q^74 - 61 * q^75 - 32 * q^76 - 31 * q^77 + 42 * q^78 + 4 * q^79 - 26 * q^80 + q^81 + 66 * q^82 - 112 * q^83 - 23 * q^84 + 17 * q^85 + 22 * q^86 - 15 * q^87 + 41 * q^88 - 111 * q^89 + 65 * q^90 - 49 * q^91 - 28 * q^92 - 19 * q^93 + 71 * q^94 - 53 * q^95 + 10 * q^96 + 50 * q^97 - 64 * q^98 - 97 * q^99

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