LMFDB - Embedded newform 8041.2.a.f.1.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.38
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.723284 q^{2} -0.489043 q^{3} -1.47686 q^{4} -2.47276 q^{5} -0.353717 q^{6} +1.15367 q^{7} -2.51476 q^{8} -2.76084 q^{9} +O(q^{10})$	\(q+0.723284 q^{2} -0.489043 q^{3} -1.47686 q^{4} -2.47276 q^{5} -0.353717 q^{6} +1.15367 q^{7} -2.51476 q^{8} -2.76084 q^{9} -1.78850 q^{10} -1.00000 q^{11} +0.722248 q^{12} -2.87171 q^{13} +0.834433 q^{14} +1.20928 q^{15} +1.13484 q^{16} +1.00000 q^{17} -1.99687 q^{18} -0.684876 q^{19} +3.65192 q^{20} -0.564195 q^{21} -0.723284 q^{22} -6.52871 q^{23} +1.22982 q^{24} +1.11452 q^{25} -2.07706 q^{26} +2.81729 q^{27} -1.70381 q^{28} +0.102928 q^{29} +0.874655 q^{30} -5.40296 q^{31} +5.85032 q^{32} +0.489043 q^{33} +0.723284 q^{34} -2.85275 q^{35} +4.07737 q^{36} -8.58715 q^{37} -0.495360 q^{38} +1.40439 q^{39} +6.21838 q^{40} -5.75036 q^{41} -0.408073 q^{42} -1.00000 q^{43} +1.47686 q^{44} +6.82688 q^{45} -4.72211 q^{46} -8.93028 q^{47} -0.554984 q^{48} -5.66904 q^{49} +0.806117 q^{50} -0.489043 q^{51} +4.24112 q^{52} -5.36568 q^{53} +2.03770 q^{54} +2.47276 q^{55} -2.90121 q^{56} +0.334933 q^{57} +0.0744461 q^{58} +5.09105 q^{59} -1.78594 q^{60} +1.42613 q^{61} -3.90787 q^{62} -3.18510 q^{63} +1.96177 q^{64} +7.10105 q^{65} +0.353717 q^{66} -1.01188 q^{67} -1.47686 q^{68} +3.19282 q^{69} -2.06335 q^{70} -15.4778 q^{71} +6.94284 q^{72} -15.5408 q^{73} -6.21095 q^{74} -0.545049 q^{75} +1.01147 q^{76} -1.15367 q^{77} +1.01577 q^{78} -4.14871 q^{79} -2.80618 q^{80} +6.90474 q^{81} -4.15914 q^{82} -13.3106 q^{83} +0.833238 q^{84} -2.47276 q^{85} -0.723284 q^{86} -0.0503361 q^{87} +2.51476 q^{88} +16.6142 q^{89} +4.93777 q^{90} -3.31302 q^{91} +9.64200 q^{92} +2.64228 q^{93} -6.45913 q^{94} +1.69353 q^{95} -2.86106 q^{96} +4.43058 q^{97} -4.10032 q^{98} +2.76084 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) $ 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * 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 $

$2$	0.723284	0.511439	0.255719	−	0.966751i	$-0.417688\pi$
$2$	0.723284	0.511439	0.255719	+	0.966751i	$0.417688\pi$
$3$	−0.489043	−0.282349	−0.141174	−	0.989985i	$-0.545088\pi$
$3$	−0.489043	−0.282349	−0.141174	+	0.989985i	$0.545088\pi$
$4$	−1.47686	−0.738430
$5$	−2.47276	−1.10585	−0.552925	−	0.833231i	$-0.686488\pi$
$5$	−2.47276	−1.10585	−0.552925	+	0.833231i	$0.686488\pi$
$6$	−0.353717	−0.144404
$7$	1.15367	0.436048	0.218024	−	0.975943i	$-0.430039\pi$
$7$	1.15367	0.436048	0.218024	+	0.975943i	$0.430039\pi$
$8$	−2.51476	−0.889101
$9$	−2.76084	−0.920279
$10$	−1.78850	−0.565575
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.722248	0.208495
$13$	−2.87171	−0.796470	−0.398235	−	0.917283i	$-0.630377\pi$
$13$	−2.87171	−0.796470	−0.398235	+	0.917283i	$0.630377\pi$
$14$	0.834433	0.223012
$15$	1.20928	0.312236
$16$	1.13484	0.283709
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.99687	−0.470667
$19$	−0.684876	−0.157121	−0.0785607	−	0.996909i	$-0.525032\pi$
$19$	−0.684876	−0.157121	−0.0785607	+	0.996909i	$0.525032\pi$
$20$	3.65192	0.816593
$21$	−0.564195	−0.123118
$22$	−0.723284	−0.154205
$23$	−6.52871	−1.36133	−0.680666	−	0.732594i	$-0.738309\pi$
$23$	−6.52871	−1.36133	−0.680666	+	0.732594i	$0.738309\pi$
$24$	1.22982	0.251037
$25$	1.11452	0.222905
$26$	−2.07706	−0.407346
$27$	2.81729	0.542189
$28$	−1.70381	−0.321991
$29$	0.102928	0.0191132	0.00955662	−	0.999954i	$-0.496958\pi$
$29$	0.102928	0.0191132	0.00955662	+	0.999954i	$0.496958\pi$
$30$	0.874655	0.159689
$31$	−5.40296	−0.970399	−0.485200	−	0.874403i	$-0.661253\pi$
$31$	−5.40296	−0.970399	−0.485200	+	0.874403i	$0.661253\pi$
$32$	5.85032	1.03420
$33$	0.489043	0.0851314
$34$	0.723284	0.124042
$35$	−2.85275	−0.482203
$36$	4.07737	0.679562
$37$	−8.58715	−1.41172	−0.705860	−	0.708352i	$-0.749439\pi$
$37$	−8.58715	−1.41172	−0.705860	+	0.708352i	$0.749439\pi$
$38$	−0.495360	−0.0803580
$39$	1.40439	0.224882
$40$	6.21838	0.983212
$41$	−5.75036	−0.898055	−0.449028	−	0.893518i	$-0.648230\pi$
$41$	−5.75036	−0.898055	−0.449028	+	0.893518i	$0.648230\pi$
$42$	−0.408073	−0.0629671
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.47686	0.222645
$45$	6.82688	1.01769
$46$	−4.72211	−0.696238
$47$	−8.93028	−1.30261	−0.651307	−	0.758814i	$-0.725779\pi$
$47$	−8.93028	−1.30261	−0.651307	+	0.758814i	$0.725779\pi$
$48$	−0.554984	−0.0801050
$49$	−5.66904	−0.809863
$50$	0.806117	0.114002
$51$	−0.489043	−0.0684797
$52$	4.24112	0.588137
$53$	−5.36568	−0.737033	−0.368516	−	0.929621i	$-0.620134\pi$
$53$	−5.36568	−0.737033	−0.368516	+	0.929621i	$0.620134\pi$
$54$	2.03770	0.277296
$55$	2.47276	0.333426
$56$	−2.90121	−0.387690
$57$	0.334933	0.0443630
$58$	0.0744461	0.00977525
$59$	5.09105	0.662798	0.331399	−	0.943491i	$-0.392479\pi$
$59$	5.09105	0.662798	0.331399	+	0.943491i	$0.392479\pi$
$60$	−1.78594	−0.230564
$61$	1.42613	0.182597	0.0912986	−	0.995824i	$-0.470898\pi$
$61$	1.42613	0.182597	0.0912986	+	0.995824i	$0.470898\pi$
$62$	−3.90787	−0.496300
$63$	−3.18510	−0.401285
$64$	1.96177	0.245221
$65$	7.10105	0.880776
$66$	0.353717	0.0435395
$67$	−1.01188	−0.123621	−0.0618104	−	0.998088i	$-0.519687\pi$
$67$	−1.01188	−0.123621	−0.0618104	+	0.998088i	$0.519687\pi$
$68$	−1.47686	−0.179096
$69$	3.19282	0.384370
$70$	−2.06335	−0.246617
$71$	−15.4778	−1.83688	−0.918439	−	0.395563i	$-0.870549\pi$
$71$	−15.4778	−1.83688	−0.918439	+	0.395563i	$0.870549\pi$
$72$	6.94284	0.818221
$73$	−15.5408	−1.81891	−0.909455	−	0.415801i	$-0.863501\pi$
$73$	−15.5408	−1.81891	−0.909455	+	0.415801i	$0.863501\pi$
$74$	−6.21095	−0.722008
$75$	−0.545049	−0.0629369
$76$	1.01147	0.116023
$77$	−1.15367	−0.131473
$78$	1.01577	0.115014
$79$	−4.14871	−0.466766	−0.233383	−	0.972385i	$-0.574980\pi$
$79$	−4.14871	−0.466766	−0.233383	+	0.972385i	$0.574980\pi$
$80$	−2.80618	−0.313740
$81$	6.90474	0.767193
$82$	−4.15914	−0.459300
$83$	−13.3106	−1.46103	−0.730516	−	0.682896i	$-0.760720\pi$
$83$	−13.3106	−1.46103	−0.730516	+	0.682896i	$0.760720\pi$
$84$	0.833238	0.0909137
$85$	−2.47276	−0.268208
$86$	−0.723284	−0.0779937
$87$	−0.0503361	−0.00539660
$88$	2.51476	0.268074
$89$	16.6142	1.76110	0.880548	−	0.473956i	$-0.157175\pi$
$89$	16.6142	1.76110	0.880548	+	0.473956i	$0.157175\pi$
$90$	4.93777	0.520487
$91$	−3.31302	−0.347299
$92$	9.64200	1.00525
$93$	2.64228	0.273991
$94$	−6.45913	−0.666208
$95$	1.69353	0.173753
$96$	−2.86106	−0.292005
$97$	4.43058	0.449857	0.224928	−	0.974375i	$-0.427785\pi$
$97$	4.43058	0.449857	0.224928	+	0.974375i	$0.427785\pi$
$98$	−4.10032	−0.414195
$99$	2.76084	0.277475
$100$	−1.64600	−0.164600
$101$	2.91351	0.289905	0.144952	−	0.989439i	$-0.453697\pi$
$101$	2.91351	0.289905	0.144952	+	0.989439i	$0.453697\pi$
$102$	−0.353717	−0.0350232
$103$	6.97938	0.687699	0.343849	−	0.939025i	$-0.388269\pi$
$103$	6.97938	0.687699	0.343849	+	0.939025i	$0.388269\pi$
$104$	7.22166	0.708142
$105$	1.39512	0.136150
$106$	−3.88091	−0.376947
$107$	17.0001	1.64346	0.821729	−	0.569878i	$-0.193010\pi$
$107$	17.0001	1.64346	0.821729	+	0.569878i	$0.193010\pi$
$108$	−4.16075	−0.400368
$109$	−9.33382	−0.894018	−0.447009	−	0.894530i	$-0.647511\pi$
$109$	−9.33382	−0.894018	−0.447009	+	0.894530i	$0.647511\pi$
$110$	1.78850	0.170527
$111$	4.19948	0.398597
$112$	1.30923	0.123711
$113$	−16.1168	−1.51614	−0.758069	−	0.652175i	$-0.773857\pi$
$113$	−16.1168	−1.51614	−0.758069	+	0.652175i	$0.773857\pi$
$114$	0.242252	0.0226890
$115$	16.1439	1.50543
$116$	−0.152010	−0.0141138
$117$	7.92833	0.732975
$118$	3.68227	0.338981
$119$	1.15367	0.105757
$120$	−3.04105	−0.277609
$121$	1.00000	0.0909091
$122$	1.03150	0.0933873
$123$	2.81217	0.253565
$124$	7.97941	0.716572
$125$	9.60784	0.859351
$126$	−2.30373	−0.205233
$127$	1.20419	0.106854	0.0534272	−	0.998572i	$-0.482985\pi$
$127$	1.20419	0.106854	0.0534272	+	0.998572i	$0.482985\pi$
$128$	−10.2817	−0.908785
$129$	0.489043	0.0430578
$130$	5.13607	0.450463
$131$	−2.36529	−0.206656	−0.103328	−	0.994647i	$-0.532949\pi$
$131$	−2.36529	−0.206656	−0.103328	+	0.994647i	$0.532949\pi$
$132$	−0.722248	−0.0628636
$133$	−0.790123	−0.0685124
$134$	−0.731876	−0.0632245
$135$	−6.96648	−0.599579
$136$	−2.51476	−0.215639
$137$	7.03175	0.600763	0.300382	−	0.953819i	$-0.402886\pi$
$137$	7.03175	0.600763	0.300382	+	0.953819i	$0.402886\pi$
$138$	2.30931	0.196582
$139$	14.7903	1.25450	0.627248	−	0.778820i	$-0.284181\pi$
$139$	14.7903	1.25450	0.627248	+	0.778820i	$0.284181\pi$
$140$	4.21312	0.356073
$141$	4.36729	0.367792
$142$	−11.1948	−0.939451
$143$	2.87171	0.240145
$144$	−3.13310	−0.261092
$145$	−0.254516	−0.0211364
$146$	−11.2404	−0.930262
$147$	2.77240	0.228664
$148$	12.6820	1.04246
$149$	−9.93534	−0.813935	−0.406967	−	0.913443i	$-0.633414\pi$
$149$	−9.93534	−0.813935	−0.406967	+	0.913443i	$0.633414\pi$
$150$	−0.394225	−0.0321884
$151$	8.88831	0.723320	0.361660	−	0.932310i	$-0.382210\pi$
$151$	8.88831	0.723320	0.361660	+	0.932310i	$0.382210\pi$
$152$	1.72230	0.139697
$153$	−2.76084	−0.223200
$154$	−0.834433	−0.0672405
$155$	13.3602	1.07312
$156$	−2.07409	−0.166060
$157$	−6.22921	−0.497145	−0.248573	−	0.968613i	$-0.579961\pi$
$157$	−6.22921	−0.497145	−0.248573	+	0.968613i	$0.579961\pi$
$158$	−3.00070	−0.238723
$159$	2.62405	0.208100
$160$	−14.4664	−1.14367
$161$	−7.53200	−0.593605
$162$	4.99408	0.392372
$163$	−21.8761	−1.71347	−0.856735	−	0.515758i	$-0.827510\pi$
$163$	−21.8761	−1.71347	−0.856735	+	0.515758i	$0.827510\pi$
$164$	8.49248	0.663151
$165$	−1.20928	−0.0941426
$166$	−9.62737	−0.747228
$167$	7.50583	0.580818	0.290409	−	0.956903i	$-0.406209\pi$
$167$	7.50583	0.580818	0.290409	+	0.956903i	$0.406209\pi$
$168$	1.41881	0.109464
$169$	−4.75326	−0.365636
$170$	−1.78850	−0.137172
$171$	1.89083	0.144595
$172$	1.47686	0.112610
$173$	3.41157	0.259377	0.129688	−	0.991555i	$-0.458602\pi$
$173$	3.41157	0.259377	0.129688	+	0.991555i	$0.458602\pi$
$174$	−0.0364073	−0.00276003
$175$	1.28580	0.0971970
$176$	−1.13484	−0.0855416
$177$	−2.48974	−0.187140
$178$	12.0167	0.900693
$179$	−4.73916	−0.354221	−0.177111	−	0.984191i	$-0.556675\pi$
$179$	−4.73916	−0.354221	−0.177111	+	0.984191i	$0.556675\pi$
$180$	−10.0823	−0.751494
$181$	−2.53812	−0.188657	−0.0943284	−	0.995541i	$-0.530070\pi$
$181$	−2.53812	−0.188657	−0.0943284	+	0.995541i	$0.530070\pi$
$182$	−2.39625	−0.177622
$183$	−0.697438	−0.0515561
$184$	16.4181	1.21036
$185$	21.2339	1.56115
$186$	1.91111	0.140130
$187$	−1.00000	−0.0731272
$188$	13.1888	0.961890
$189$	3.25024	0.236420
$190$	1.22490	0.0888639
$191$	8.45591	0.611849	0.305924	−	0.952056i	$-0.401035\pi$
$191$	8.45591	0.611849	0.305924	+	0.952056i	$0.401035\pi$
$192$	−0.959389	−0.0692379
$193$	−0.157021	−0.0113026	−0.00565132	−	0.999984i	$-0.501799\pi$
$193$	−0.157021	−0.0113026	−0.00565132	+	0.999984i	$0.501799\pi$
$194$	3.20456	0.230074
$195$	−3.47271	−0.248686
$196$	8.37238	0.598027
$197$	7.26032	0.517277	0.258638	−	0.965974i	$-0.416726\pi$
$197$	7.26032	0.517277	0.258638	+	0.965974i	$0.416726\pi$
$198$	1.99687	0.141911
$199$	26.1553	1.85410	0.927050	−	0.374937i	$-0.122336\pi$
$199$	26.1553	1.85410	0.927050	+	0.374937i	$0.122336\pi$
$200$	−2.80276	−0.198185
$201$	0.494852	0.0349042
$202$	2.10729	0.148269
$203$	0.118745	0.00833428
$204$	0.722248	0.0505674
$205$	14.2192	0.993115
$206$	5.04807	0.351716
$207$	18.0247	1.25280
$208$	−3.25893	−0.225966
$209$	0.684876	0.0473739
$210$	1.00907	0.0696322
$211$	13.4568	0.926406	0.463203	−	0.886252i	$-0.346700\pi$
$211$	13.4568	0.926406	0.463203	+	0.886252i	$0.346700\pi$
$212$	7.92436	0.544247
$213$	7.56931	0.518640
$214$	12.2959	0.840528
$215$	2.47276	0.168641
$216$	−7.08481	−0.482060
$217$	−6.23325	−0.423140
$218$	−6.75100	−0.457235
$219$	7.60010	0.513567
$220$	−3.65192	−0.246212
$221$	−2.87171	−0.193172
$222$	3.03742	0.203858
$223$	13.4652	0.901699	0.450850	−	0.892600i	$-0.351121\pi$
$223$	13.4652	0.901699	0.450850	+	0.892600i	$0.351121\pi$
$224$	6.74936	0.450961
$225$	−3.07702	−0.205135
$226$	−11.6570	−0.775412
$227$	−7.98584	−0.530039	−0.265019	−	0.964243i	$-0.585378\pi$
$227$	−7.98584	−0.530039	−0.265019	+	0.964243i	$0.585378\pi$
$228$	−0.494650	−0.0327590
$229$	−24.2727	−1.60399	−0.801994	−	0.597332i	$-0.796227\pi$
$229$	−24.2727	−1.60399	−0.801994	+	0.597332i	$0.796227\pi$
$230$	11.6766	0.769935
$231$	0.564195	0.0371213
$232$	−0.258839	−0.0169936
$233$	3.15930	0.206972	0.103486	−	0.994631i	$-0.467000\pi$
$233$	3.15930	0.206972	0.103486	+	0.994631i	$0.467000\pi$
$234$	5.73443	0.374872
$235$	22.0824	1.44050
$236$	−7.51877	−0.489430
$237$	2.02890	0.131791
$238$	0.834433	0.0540883
$239$	−11.6926	−0.756331	−0.378165	−	0.925738i	$-0.623445\pi$
$239$	−11.6926	−0.756331	−0.378165	+	0.925738i	$0.623445\pi$
$240$	1.37234	0.0885842
$241$	4.81877	0.310404	0.155202	−	0.987883i	$-0.450397\pi$
$241$	4.81877	0.310404	0.155202	+	0.987883i	$0.450397\pi$
$242$	0.723284	0.0464944
$243$	−11.8286	−0.758805
$244$	−2.10620	−0.134835
$245$	14.0181	0.895587
$246$	2.03400	0.129683
$247$	1.96677	0.125142
$248$	13.5871	0.862783
$249$	6.50947	0.412521
$250$	6.94919	0.439506
$251$	−10.5667	−0.666965	−0.333483	−	0.942756i	$-0.608224\pi$
$251$	−10.5667	−0.666965	−0.333483	+	0.942756i	$0.608224\pi$
$252$	4.70395	0.296321
$253$	6.52871	0.410457
$254$	0.870970	0.0546495
$255$	1.20928	0.0757282
$256$	−11.3601	−0.710009
$257$	−15.8333	−0.987652	−0.493826	−	0.869561i	$-0.664402\pi$
$257$	−15.8333	−0.987652	−0.493826	+	0.869561i	$0.664402\pi$
$258$	0.353717	0.0220214
$259$	−9.90677	−0.615577
$260$	−10.4873	−0.650392
$261$	−0.284167	−0.0175895
$262$	−1.71077	−0.105692
$263$	−9.65354	−0.595263	−0.297631	−	0.954681i	$-0.596197\pi$
$263$	−9.65354	−0.595263	−0.297631	+	0.954681i	$0.596197\pi$
$264$	−1.22982	−0.0756904
$265$	13.2680	0.815048
$266$	−0.571483	−0.0350399
$267$	−8.12503	−0.497244
$268$	1.49441	0.0912853
$269$	23.2699	1.41879	0.709395	−	0.704812i	$-0.248968\pi$
$269$	23.2699	1.41879	0.709395	+	0.704812i	$0.248968\pi$
$270$	−5.03874	−0.306648
$271$	19.4849	1.18362	0.591810	−	0.806077i	$-0.298413\pi$
$271$	19.4849	1.18362	0.591810	+	0.806077i	$0.298413\pi$
$272$	1.13484	0.0688097
$273$	1.62021	0.0980594
$274$	5.08595	0.307254
$275$	−1.11452	−0.0672083
$276$	−4.71535	−0.283831
$277$	9.39466	0.564470	0.282235	−	0.959345i	$-0.408924\pi$
$277$	9.39466	0.564470	0.282235	+	0.959345i	$0.408924\pi$
$278$	10.6976	0.641598
$279$	14.9167	0.893038
$280$	7.17398	0.428727
$281$	12.2397	0.730161	0.365080	−	0.930976i	$-0.381041\pi$
$281$	12.2397	0.730161	0.365080	+	0.930976i	$0.381041\pi$
$282$	3.15879	0.188103
$283$	−23.2159	−1.38004	−0.690022	−	0.723788i	$-0.742399\pi$
$283$	−23.2159	−1.38004	−0.690022	+	0.723788i	$0.742399\pi$
$284$	22.8586	1.35641
$285$	−0.828209	−0.0490589
$286$	2.07706	0.122819
$287$	−6.63404	−0.391595
$288$	−16.1518	−0.951754
$289$	1.00000	0.0588235
$290$	−0.184087	−0.0108100
$291$	−2.16674	−0.127017
$292$	22.9516	1.34314
$293$	7.33899	0.428749	0.214374	−	0.976752i	$-0.431229\pi$
$293$	7.33899	0.428749	0.214374	+	0.976752i	$0.431229\pi$
$294$	2.00523	0.116948
$295$	−12.5889	−0.732955
$296$	21.5946	1.25516
$297$	−2.81729	−0.163476
$298$	−7.18607	−0.416278
$299$	18.7486	1.08426
$300$	0.804962	0.0464745
$301$	−1.15367	−0.0664966
$302$	6.42877	0.369934
$303$	−1.42483	−0.0818543
$304$	−0.777223	−0.0445768
$305$	−3.52647	−0.201925
$306$	−1.99687	−0.114153
$307$	−28.7958	−1.64346	−0.821732	−	0.569874i	$-0.806992\pi$
$307$	−28.7958	−1.64346	−0.821732	+	0.569874i	$0.806992\pi$
$308$	1.70381	0.0970838
$309$	−3.41321	−0.194171
$310$	9.66321	0.548833
$311$	14.1958	0.804970	0.402485	−	0.915427i	$-0.368147\pi$
$311$	14.1958	0.804970	0.402485	+	0.915427i	$0.368147\pi$
$312$	−3.53170	−0.199943
$313$	21.6662	1.22464	0.612322	−	0.790609i	$-0.290236\pi$
$313$	21.6662	1.22464	0.612322	+	0.790609i	$0.290236\pi$
$314$	−4.50549	−0.254259
$315$	7.87599	0.443762
$316$	6.12707	0.344674
$317$	5.84969	0.328551	0.164276	−	0.986414i	$-0.447471\pi$
$317$	5.84969	0.328551	0.164276	+	0.986414i	$0.447471\pi$
$318$	1.89793	0.106431
$319$	−0.102928	−0.00576286
$320$	−4.85098	−0.271178
$321$	−8.31375	−0.464029
$322$	−5.44778	−0.303593
$323$	−0.684876	−0.0381075
$324$	−10.1973	−0.566518
$325$	−3.20059	−0.177537
$326$	−15.8226	−0.876335
$327$	4.56463	0.252425
$328$	14.4608	0.798462
$329$	−10.3026	−0.568002
$330$	−0.874655	−0.0481482
$331$	−11.6286	−0.639166	−0.319583	−	0.947558i	$-0.603543\pi$
$331$	−11.6286	−0.639166	−0.319583	+	0.947558i	$0.603543\pi$
$332$	19.6579	1.07887
$333$	23.7077	1.29918
$334$	5.42884	0.297053
$335$	2.50213	0.136706
$336$	−0.640270	−0.0349296
$337$	−9.20096	−0.501208	−0.250604	−	0.968090i	$-0.580629\pi$
$337$	−9.20096	−0.501208	−0.250604	+	0.968090i	$0.580629\pi$
$338$	−3.43796	−0.187000
$339$	7.88178	0.428080
$340$	3.65192	0.198053
$341$	5.40296	0.292586
$342$	1.36761	0.0739517
$343$	−14.6159	−0.789186
$344$	2.51476	0.135587
$345$	−7.89506	−0.425056
$346$	2.46753	0.132655
$347$	−13.8811	−0.745175	−0.372588	−	0.927997i	$-0.621529\pi$
$347$	−13.8811	−0.745175	−0.372588	+	0.927997i	$0.621529\pi$
$348$	0.0743395	0.00398501
$349$	11.8280	0.633138	0.316569	−	0.948569i	$-0.397469\pi$
$349$	11.8280	0.633138	0.316569	+	0.948569i	$0.397469\pi$
$350$	0.929996	0.0497104
$351$	−8.09046	−0.431837
$352$	−5.85032	−0.311823
$353$	−18.9781	−1.01010	−0.505050	−	0.863090i	$-0.668526\pi$
$353$	−18.9781	−1.01010	−0.505050	+	0.863090i	$0.668526\pi$
$354$	−1.80079	−0.0957108
$355$	38.2728	2.03131
$356$	−24.5368	−1.30045
$357$	−0.564195	−0.0298604
$358$	−3.42776	−0.181163
$359$	−13.9860	−0.738154	−0.369077	−	0.929399i	$-0.620326\pi$
$359$	−13.9860	−0.738154	−0.369077	+	0.929399i	$0.620326\pi$
$360$	−17.1679	−0.904830
$361$	−18.5309	−0.975313
$362$	−1.83578	−0.0964865
$363$	−0.489043	−0.0256681
$364$	4.89287	0.256456
$365$	38.4286	2.01144
$366$	−0.504446	−0.0263678
$367$	−4.64014	−0.242213	−0.121107	−	0.992640i	$-0.538644\pi$
$367$	−4.64014	−0.242213	−0.121107	+	0.992640i	$0.538644\pi$
$368$	−7.40903	−0.386222
$369$	15.8758	0.826462
$370$	15.3582	0.798433
$371$	−6.19024	−0.321381
$372$	−3.90227	−0.202323
$373$	26.6262	1.37865	0.689326	−	0.724451i	$-0.257907\pi$
$373$	26.6262	1.37865	0.689326	+	0.724451i	$0.257907\pi$
$374$	−0.723284	−0.0374001
$375$	−4.69864	−0.242637
$376$	22.4575	1.15816
$377$	−0.295579	−0.0152231
$378$	2.35084	0.120914
$379$	−18.0347	−0.926383	−0.463191	−	0.886258i	$-0.653296\pi$
$379$	−18.0347	−0.926383	−0.463191	+	0.886258i	$0.653296\pi$
$380$	−2.50111	−0.128304
$381$	−0.588899	−0.0301702
$382$	6.11603	0.312923
$383$	−5.52418	−0.282272	−0.141136	−	0.989990i	$-0.545076\pi$
$383$	−5.52418	−0.282272	−0.141136	+	0.989990i	$0.545076\pi$
$384$	5.02820	0.256594
$385$	2.85275	0.145390
$386$	−0.113571	−0.00578061
$387$	2.76084	0.140341
$388$	−6.54334	−0.332188
$389$	18.9687	0.961754	0.480877	−	0.876788i	$-0.340318\pi$
$389$	18.9687	0.961754	0.480877	+	0.876788i	$0.340318\pi$
$390$	−2.51176	−0.127188
$391$	−6.52871	−0.330171
$392$	14.2563	0.720050
$393$	1.15673	0.0583491
$394$	5.25127	0.264555
$395$	10.2588	0.516174
$396$	−4.07737	−0.204896
$397$	11.3779	0.571041	0.285520	−	0.958373i	$-0.407834\pi$
$397$	11.3779	0.571041	0.285520	+	0.958373i	$0.407834\pi$
$398$	18.9177	0.948259
$399$	0.386404	0.0193444
$400$	1.26480	0.0632402
$401$	30.6242	1.52930	0.764649	−	0.644447i	$-0.222912\pi$
$401$	30.6242	1.52930	0.764649	+	0.644447i	$0.222912\pi$
$402$	0.357919	0.0178514
$403$	15.5157	0.772894
$404$	−4.30284	−0.214074
$405$	−17.0737	−0.848400
$406$	0.0858865	0.00426247
$407$	8.58715	0.425649
$408$	1.22982	0.0608853
$409$	−29.6743	−1.46730	−0.733651	−	0.679527i	$-0.762185\pi$
$409$	−29.6743	−1.46730	−0.733651	+	0.679527i	$0.762185\pi$
$410$	10.2845	0.507918
$411$	−3.43883	−0.169625
$412$	−10.3076	−0.507817
$413$	5.87341	0.289011
$414$	13.0370	0.640733
$415$	32.9139	1.61568
$416$	−16.8005	−0.823710
$417$	−7.23308	−0.354205
$418$	0.495360	0.0242288
$419$	−25.6557	−1.25336	−0.626681	−	0.779276i	$-0.715587\pi$
$419$	−25.6557	−1.25336	−0.626681	+	0.779276i	$0.715587\pi$
$420$	−2.06039	−0.100537
$421$	27.3980	1.33530	0.667649	−	0.744476i	$-0.267301\pi$
$421$	27.3980	1.33530	0.667649	+	0.744476i	$0.267301\pi$
$422$	9.73310	0.473800
$423$	24.6550	1.19877
$424$	13.4934	0.655296
$425$	1.11452	0.0540623
$426$	5.47476	0.265253
$427$	1.64529	0.0796211
$428$	−25.1067	−1.21358
$429$	−1.40439	−0.0678046
$430$	1.78850	0.0862494
$431$	11.9502	0.575620	0.287810	−	0.957688i	$-0.407073\pi$
$431$	11.9502	0.575620	0.287810	+	0.957688i	$0.407073\pi$
$432$	3.19717	0.153824
$433$	−38.2793	−1.83959	−0.919793	−	0.392404i	$-0.871643\pi$
$433$	−38.2793	−1.83959	−0.919793	+	0.392404i	$0.871643\pi$
$434$	−4.50841	−0.216410
$435$	0.124469	0.00596783
$436$	13.7847	0.660170
$437$	4.47136	0.213894
$438$	5.49703	0.262658
$439$	−23.0343	−1.09937	−0.549684	−	0.835373i	$-0.685252\pi$
$439$	−23.0343	−1.09937	−0.549684	+	0.835373i	$0.685252\pi$
$440$	−6.21838	−0.296450
$441$	15.6513	0.745300
$442$	−2.07706	−0.0987958
$443$	−9.94700	−0.472596	−0.236298	−	0.971681i	$-0.575934\pi$
$443$	−9.94700	−0.472596	−0.236298	+	0.971681i	$0.575934\pi$
$444$	−6.20205	−0.294336
$445$	−41.0827	−1.94751
$446$	9.73919	0.461164
$447$	4.85880	0.229814
$448$	2.26324	0.106928
$449$	11.6643	0.550474	0.275237	−	0.961376i	$-0.411244\pi$
$449$	11.6643	0.550474	0.275237	+	0.961376i	$0.411244\pi$
$450$	−2.22556	−0.104914
$451$	5.75036	0.270774
$452$	23.8022	1.11956
$453$	−4.34676	−0.204229
$454$	−5.77603	−0.271082
$455$	8.19229	0.384060
$456$	−0.842276	−0.0394432
$457$	20.1783	0.943903	0.471952	−	0.881624i	$-0.343550\pi$
$457$	20.1783	0.943903	0.471952	+	0.881624i	$0.343550\pi$
$458$	−17.5561	−0.820342
$459$	2.81729	0.131500
$460$	−23.8423	−1.11165
$461$	37.7724	1.75924	0.879619	−	0.475679i	$-0.157798\pi$
$461$	37.7724	1.75924	0.879619	+	0.475679i	$0.157798\pi$
$462$	0.408073	0.0189853
$463$	16.6420	0.773418	0.386709	−	0.922202i	$-0.373612\pi$
$463$	16.6420	0.773418	0.386709	+	0.922202i	$0.373612\pi$
$464$	0.116807	0.00542261
$465$	−6.53370	−0.302993
$466$	2.28507	0.105854
$467$	−18.2162	−0.842945	−0.421473	−	0.906841i	$-0.638487\pi$
$467$	−18.2162	−0.842945	−0.421473	+	0.906841i	$0.638487\pi$
$468$	−11.7090	−0.541251
$469$	−1.16738	−0.0539045
$470$	15.9718	0.736726
$471$	3.04635	0.140368
$472$	−12.8027	−0.589294
$473$	1.00000	0.0459800
$474$	1.46747	0.0674030
$475$	−0.763310	−0.0350231
$476$	−1.70381	−0.0780942
$477$	14.8138	0.678276
$478$	−8.45706	−0.386817
$479$	11.4894	0.524964	0.262482	−	0.964937i	$-0.415459\pi$
$479$	11.4894	0.524964	0.262482	+	0.964937i	$0.415459\pi$
$480$	7.07470	0.322914
$481$	24.6598	1.12439
$482$	3.48534	0.158753
$483$	3.68347	0.167604
$484$	−1.47686	−0.0671300
$485$	−10.9557	−0.497474
$486$	−8.55543	−0.388082
$487$	−21.2281	−0.961937	−0.480968	−	0.876738i	$-0.659715\pi$
$487$	−21.2281	−0.961937	−0.480968	+	0.876738i	$0.659715\pi$
$488$	−3.58637	−0.162347
$489$	10.6983	0.483796
$490$	10.1391	0.458038
$491$	−40.4382	−1.82495	−0.912475	−	0.409133i	$-0.865831\pi$
$491$	−40.4382	−1.82495	−0.912475	+	0.409133i	$0.865831\pi$
$492$	−4.15318	−0.187240
$493$	0.102928	0.00463564
$494$	1.42253	0.0640027
$495$	−6.82688	−0.306845
$496$	−6.13148	−0.275311
$497$	−17.8563	−0.800966
$498$	4.70819	0.210979
$499$	−25.7710	−1.15367	−0.576835	−	0.816861i	$-0.695712\pi$
$499$	−25.7710	−1.15367	−0.576835	+	0.816861i	$0.695712\pi$
$500$	−14.1894	−0.634571
$501$	−3.67067	−0.163993
$502$	−7.64273	−0.341112
$503$	−33.0393	−1.47315	−0.736575	−	0.676356i	$-0.763558\pi$
$503$	−33.0393	−1.47315	−0.736575	+	0.676356i	$0.763558\pi$
$504$	8.00976	0.356783
$505$	−7.20439	−0.320591
$506$	4.72211	0.209924
$507$	2.32455	0.103237
$508$	−1.77842	−0.0789045
$509$	9.56659	0.424032	0.212016	−	0.977266i	$-0.431997\pi$
$509$	9.56659	0.424032	0.212016	+	0.977266i	$0.431997\pi$
$510$	0.874655	0.0387304
$511$	−17.9290	−0.793132
$512$	12.3469	0.545659
$513$	−1.92950	−0.0851894
$514$	−11.4519	−0.505124
$515$	−17.2583	−0.760492
$516$	−0.722248	−0.0317952
$517$	8.93028	0.392753
$518$	−7.16540	−0.314830
$519$	−1.66840	−0.0732347
$520$	−17.8574	−0.783099
$521$	−36.8591	−1.61482	−0.807412	−	0.589988i	$-0.799133\pi$
$521$	−36.8591	−1.61482	−0.807412	+	0.589988i	$0.799133\pi$
$522$	−0.205534	−0.00899596
$523$	31.3681	1.37163	0.685815	−	0.727776i	$-0.259446\pi$
$523$	31.3681	1.37163	0.685815	+	0.727776i	$0.259446\pi$
$524$	3.49320	0.152601
$525$	−0.628809	−0.0274435
$526$	−6.98225	−0.304441
$527$	−5.40296	−0.235356
$528$	0.554984	0.0241526
$529$	19.6241	0.853222
$530$	9.59654	0.416847
$531$	−14.0556	−0.609959
$532$	1.16690	0.0505916
$533$	16.5134	0.715274
$534$	−5.87670	−0.254310
$535$	−42.0370	−1.81742
$536$	2.54463	0.109911
$537$	2.31765	0.100014
$538$	16.8307	0.725624
$539$	5.66904	0.244183
$540$	10.2885	0.442748
$541$	−4.25256	−0.182832	−0.0914160	−	0.995813i	$-0.529139\pi$
$541$	−4.25256	−0.182832	−0.0914160	+	0.995813i	$0.529139\pi$
$542$	14.0931	0.605350
$543$	1.24125	0.0532670
$544$	5.85032	0.250831
$545$	23.0803	0.988650
$546$	1.17187	0.0501514
$547$	−27.5775	−1.17913	−0.589564	−	0.807722i	$-0.700701\pi$
$547$	−27.5775	−1.17913	−0.589564	+	0.807722i	$0.700701\pi$
$548$	−10.3849	−0.443622
$549$	−3.93731	−0.168040
$550$	−0.806117	−0.0343729
$551$	−0.0704929	−0.00300310
$552$	−8.02916	−0.341744
$553$	−4.78626	−0.203532
$554$	6.79501	0.288692
$555$	−10.3843	−0.440789
$556$	−21.8432	−0.926357
$557$	0.644016	0.0272878	0.0136439	−	0.999907i	$-0.495657\pi$
$557$	0.644016	0.0272878	0.0136439	+	0.999907i	$0.495657\pi$
$558$	10.7890	0.456735
$559$	2.87171	0.121461
$560$	−3.23741	−0.136806
$561$	0.489043	0.0206474
$562$	8.85280	0.373433
$563$	16.3380	0.688566	0.344283	−	0.938866i	$-0.388122\pi$
$563$	16.3380	0.688566	0.344283	+	0.938866i	$0.388122\pi$
$564$	−6.44987	−0.271589
$565$	39.8528	1.67662
$566$	−16.7917	−0.705808
$567$	7.96581	0.334533
$568$	38.9229	1.63317
$569$	32.1052	1.34592	0.672961	−	0.739678i	$-0.265022\pi$
$569$	32.1052	1.34592	0.672961	+	0.739678i	$0.265022\pi$
$570$	−0.599030	−0.0250906
$571$	9.09350	0.380551	0.190276	−	0.981731i	$-0.439062\pi$
$571$	9.09350	0.380551	0.190276	+	0.981731i	$0.439062\pi$
$572$	−4.24112	−0.177330
$573$	−4.13530	−0.172755
$574$	−4.79829	−0.200277
$575$	−7.27641	−0.303447
$576$	−5.41613	−0.225672
$577$	−18.0973	−0.753400	−0.376700	−	0.926335i	$-0.622941\pi$
$577$	−18.0973	−0.753400	−0.376700	+	0.926335i	$0.622941\pi$
$578$	0.723284	0.0300846
$579$	0.0767901	0.00319129
$580$	0.375884	0.0156077
$581$	−15.3561	−0.637079
$582$	−1.56717	−0.0649612
$583$	5.36568	0.222224
$584$	39.0813	1.61720
$585$	−19.6048	−0.810560
$586$	5.30817	0.219279
$587$	35.2995	1.45697	0.728483	−	0.685064i	$-0.240226\pi$
$587$	35.2995	1.45697	0.728483	+	0.685064i	$0.240226\pi$
$588$	−4.09445	−0.168852
$589$	3.70035	0.152470
$590$	−9.10536	−0.374862
$591$	−3.55061	−0.146052
$592$	−9.74502	−0.400518
$593$	21.6826	0.890397	0.445199	−	0.895432i	$-0.353133\pi$
$593$	21.6826	0.890397	0.445199	+	0.895432i	$0.353133\pi$
$594$	−2.03770	−0.0836080
$595$	−2.85275	−0.116951
$596$	14.6731	0.601034
$597$	−12.7911	−0.523503
$598$	13.5606	0.554532
$599$	7.53345	0.307808	0.153904	−	0.988086i	$-0.450815\pi$
$599$	7.53345	0.307808	0.153904	+	0.988086i	$0.450815\pi$
$600$	1.37067	0.0559572
$601$	−38.2220	−1.55911	−0.779553	−	0.626336i	$-0.784554\pi$
$601$	−38.2220	−1.55911	−0.779553	+	0.626336i	$0.784554\pi$
$602$	−0.834433	−0.0340090
$603$	2.79364	0.113766
$604$	−13.1268	−0.534121
$605$	−2.47276	−0.100532
$606$	−1.03056	−0.0418635
$607$	−21.3855	−0.868012	−0.434006	−	0.900910i	$-0.642900\pi$
$607$	−21.3855	−0.868012	−0.434006	+	0.900910i	$0.642900\pi$
$608$	−4.00675	−0.162495
$609$	−0.0580715	−0.00235317
$610$	−2.55064	−0.103272
$611$	25.6452	1.03749
$612$	4.07737	0.164818
$613$	−35.2945	−1.42553	−0.712766	−	0.701401i	$-0.752558\pi$
$613$	−35.2945	−1.42553	−0.712766	+	0.701401i	$0.752558\pi$
$614$	−20.8275	−0.840531
$615$	−6.95381	−0.280405
$616$	2.90121	0.116893
$617$	14.7867	0.595291	0.297645	−	0.954676i	$-0.403799\pi$
$617$	14.7867	0.595291	0.297645	+	0.954676i	$0.403799\pi$
$618$	−2.46872	−0.0993066
$619$	9.08157	0.365019	0.182509	−	0.983204i	$-0.441578\pi$
$619$	9.08157	0.365019	0.182509	+	0.983204i	$0.441578\pi$
$620$	−19.7311	−0.792422
$621$	−18.3933	−0.738098
$622$	10.2676	0.411693
$623$	19.1673	0.767922
$624$	1.59375	0.0638013
$625$	−29.3305	−1.17322
$626$	15.6708	0.626331
$627$	−0.334933	−0.0133760
$628$	9.19968	0.367107
$629$	−8.58715	−0.342392
$630$	5.69657	0.226957
$631$	8.70268	0.346448	0.173224	−	0.984882i	$-0.444582\pi$
$631$	8.70268	0.346448	0.173224	+	0.984882i	$0.444582\pi$
$632$	10.4330	0.415002
$633$	−6.58096	−0.261570
$634$	4.23099	0.168034
$635$	−2.97766	−0.118165
$636$	−3.87535	−0.153668
$637$	16.2798	0.645031
$638$	−0.0744461	−0.00294735
$639$	42.7317	1.69044
$640$	25.4242	1.00498
$641$	3.45857	0.136605	0.0683027	−	0.997665i	$-0.478242\pi$
$641$	3.45857	0.136605	0.0683027	+	0.997665i	$0.478242\pi$
$642$	−6.01320	−0.237322
$643$	25.1690	0.992570	0.496285	−	0.868160i	$-0.334697\pi$
$643$	25.1690	0.992570	0.496285	+	0.868160i	$0.334697\pi$
$644$	11.1237	0.438336
$645$	−1.20928	−0.0476155
$646$	−0.495360	−0.0194897
$647$	−15.5230	−0.610271	−0.305135	−	0.952309i	$-0.598702\pi$
$647$	−15.5230	−0.610271	−0.305135	+	0.952309i	$0.598702\pi$
$648$	−17.3637	−0.682112
$649$	−5.09105	−0.199841
$650$	−2.31494	−0.0907993
$651$	3.04832	0.119473
$652$	32.3080	1.26528
$653$	11.6532	0.456025	0.228013	−	0.973658i	$-0.426777\pi$
$653$	11.6532	0.456025	0.228013	+	0.973658i	$0.426777\pi$
$654$	3.30153	0.129100
$655$	5.84878	0.228531
$656$	−6.52573	−0.254787
$657$	42.9056	1.67391
$658$	−7.45172	−0.290498
$659$	−28.8853	−1.12521	−0.562607	−	0.826725i	$-0.690201\pi$
$659$	−28.8853	−1.12521	−0.562607	+	0.826725i	$0.690201\pi$
$660$	1.78594	0.0695177
$661$	29.6783	1.15435	0.577176	−	0.816619i	$-0.304154\pi$
$661$	29.6783	1.15435	0.577176	+	0.816619i	$0.304154\pi$
$662$	−8.41079	−0.326895
$663$	1.40439	0.0545420
$664$	33.4730	1.29900
$665$	1.95378	0.0757644
$666$	17.1474	0.664449
$667$	−0.671987	−0.0260194
$668$	−11.0851	−0.428894
$669$	−6.58508	−0.254594
$670$	1.80975	0.0699168
$671$	−1.42613	−0.0550551
$672$	−3.30073	−0.127328
$673$	−26.3293	−1.01492	−0.507460	−	0.861675i	$-0.669416\pi$
$673$	−26.3293	−1.01492	−0.507460	+	0.861675i	$0.669416\pi$
$674$	−6.65491	−0.256337
$675$	3.13994	0.120856
$676$	7.01991	0.269997
$677$	−0.220841	−0.00848760	−0.00424380	−	0.999991i	$-0.501351\pi$
$677$	−0.220841	−0.00848760	−0.00424380	+	0.999991i	$0.501351\pi$
$678$	5.70077	0.218937
$679$	5.11144	0.196159
$680$	6.21838	0.238464
$681$	3.90542	0.149656
$682$	3.90787	0.149640
$683$	37.1091	1.41994	0.709970	−	0.704232i	$-0.248709\pi$
$683$	37.1091	1.41994	0.709970	+	0.704232i	$0.248709\pi$
$684$	−2.79249	−0.106774
$685$	−17.3878	−0.664354
$686$	−10.5715	−0.403620
$687$	11.8704	0.452884
$688$	−1.13484	−0.0432653
$689$	15.4087	0.587024
$690$	−5.71037	−0.217390
$691$	−41.8310	−1.59132	−0.795662	−	0.605740i	$-0.792877\pi$
$691$	−41.8310	−1.59132	−0.795662	+	0.605740i	$0.792877\pi$
$692$	−5.03841	−0.191531
$693$	3.18510	0.120992
$694$	−10.0400	−0.381112
$695$	−36.5728	−1.38728
$696$	0.126583	0.00479812
$697$	−5.75036	−0.217810
$698$	8.55500	0.323812
$699$	−1.54503	−0.0584384
$700$	−1.89894	−0.0717732
$701$	−17.7358	−0.669873	−0.334937	−	0.942241i	$-0.608715\pi$
$701$	−17.7358	−0.669873	−0.334937	+	0.942241i	$0.608715\pi$
$702$	−5.85170	−0.220858
$703$	5.88113	0.221811
$704$	−1.96177	−0.0739370
$705$	−10.7992	−0.406723
$706$	−13.7265	−0.516605
$707$	3.36123	0.126412
$708$	3.67700	0.138190
$709$	16.5342	0.620955	0.310477	−	0.950581i	$-0.399511\pi$
$709$	16.5342	0.620955	0.310477	+	0.950581i	$0.399511\pi$
$710$	27.6821	1.03889
$711$	11.4539	0.429555
$712$	−41.7806	−1.56579
$713$	35.2744	1.32103
$714$	−0.408073	−0.0152718
$715$	−7.10105	−0.265564
$716$	6.99908	0.261568
$717$	5.71817	0.213549
$718$	−10.1159	−0.377521
$719$	34.1997	1.27543	0.637717	−	0.770271i	$-0.279879\pi$
$719$	34.1997	1.27543	0.637717	+	0.770271i	$0.279879\pi$
$720$	7.74740	0.288729
$721$	8.05192	0.299869
$722$	−13.4031	−0.498813
$723$	−2.35658	−0.0876422
$724$	3.74845	0.139310
$725$	0.114716	0.00426043
$726$	−0.353717	−0.0131277
$727$	−11.8777	−0.440519	−0.220260	−	0.975441i	$-0.570690\pi$
$727$	−11.8777	−0.440519	−0.220260	+	0.975441i	$0.570690\pi$
$728$	8.33144	0.308784
$729$	−14.9295	−0.552945
$730$	27.7948	1.02873
$731$	−1.00000	−0.0369863
$732$	1.03002	0.0380706
$733$	−2.38877	−0.0882313	−0.0441156	−	0.999026i	$-0.514047\pi$
$733$	−2.38877	−0.0882313	−0.0441156	+	0.999026i	$0.514047\pi$
$734$	−3.35614	−0.123877
$735$	−6.85547	−0.252868
$736$	−38.1951	−1.40789
$737$	1.01188	0.0372731
$738$	11.4827	0.422685
$739$	40.8437	1.50246	0.751229	−	0.660042i	$-0.229461\pi$
$739$	40.8437	1.50246	0.751229	+	0.660042i	$0.229461\pi$
$740$	−31.3596	−1.15280
$741$	−0.961833	−0.0353338
$742$	−4.47730	−0.164367
$743$	17.5651	0.644399	0.322200	−	0.946672i	$-0.395578\pi$
$743$	17.5651	0.644399	0.322200	+	0.946672i	$0.395578\pi$
$744$	−6.64468	−0.243606
$745$	24.5677	0.900090
$746$	19.2583	0.705096
$747$	36.7485	1.34456
$748$	1.47686	0.0539994
$749$	19.6125	0.716626
$750$	−3.39845	−0.124094
$751$	4.48815	0.163775	0.0818874	−	0.996642i	$-0.473905\pi$
$751$	4.48815	0.163775	0.0818874	+	0.996642i	$0.473905\pi$
$752$	−10.1344	−0.369564
$753$	5.16757	0.188317
$754$	−0.213788	−0.00778569
$755$	−21.9786	−0.799884
$756$	−4.80015	−0.174580
$757$	−33.8655	−1.23086	−0.615432	−	0.788190i	$-0.711018\pi$
$757$	−33.8655	−1.23086	−0.615432	+	0.788190i	$0.711018\pi$
$758$	−13.0442	−0.473788
$759$	−3.19282	−0.115892
$760$	−4.25882	−0.154484
$761$	−16.6461	−0.603422	−0.301711	−	0.953399i	$-0.597558\pi$
$761$	−16.6461	−0.603422	−0.301711	+	0.953399i	$0.597558\pi$
$762$	−0.425941	−0.0154302
$763$	−10.7682	−0.389834
$764$	−12.4882	−0.451807
$765$	6.82688	0.246826
$766$	−3.99555	−0.144365
$767$	−14.6200	−0.527899
$768$	5.55560	0.200470
$769$	11.3241	0.408357	0.204178	−	0.978934i	$-0.434548\pi$
$769$	11.3241	0.408357	0.204178	+	0.978934i	$0.434548\pi$
$770$	2.06335	0.0743580
$771$	7.74314	0.278862
$772$	0.231899	0.00834621
$773$	−16.9102	−0.608218	−0.304109	−	0.952637i	$-0.598359\pi$
$773$	−16.9102	−0.608218	−0.304109	+	0.952637i	$0.598359\pi$
$774$	1.99687	0.0717760
$775$	−6.02172	−0.216307
$776$	−11.1418	−0.399968
$777$	4.84483	0.173807
$778$	13.7198	0.491878
$779$	3.93828	0.141104
$780$	5.12871	0.183637
$781$	15.4778	0.553839
$782$	−4.72211	−0.168862
$783$	0.289978	0.0103630
$784$	−6.43344	−0.229766
$785$	15.4033	0.549768
$786$	0.836641	0.0298420
$787$	8.66508	0.308877	0.154438	−	0.988002i	$-0.450643\pi$
$787$	8.66508	0.308877	0.154438	+	0.988002i	$0.450643\pi$
$788$	−10.7225	−0.381973
$789$	4.72099	0.168072
$790$	7.41999	0.263991
$791$	−18.5935	−0.661108
$792$	−6.94284	−0.246703
$793$	−4.09544	−0.145433
$794$	8.22946	0.292053
$795$	−6.48862	−0.230128
$796$	−38.6277	−1.36912
$797$	43.1338	1.52788	0.763939	−	0.645289i	$-0.223263\pi$
$797$	43.1338	1.52788	0.763939	+	0.645289i	$0.223263\pi$
$798$	0.279480	0.00989347
$799$	−8.93028	−0.315931
$800$	6.52032	0.230528
$801$	−45.8690	−1.62070
$802$	22.1500	0.782143
$803$	15.5408	0.548422
$804$	−0.730828	−0.0257743
$805$	18.6248	0.656438
$806$	11.2223	0.395288
$807$	−11.3800	−0.400594
$808$	−7.32676	−0.257755
$809$	−8.92623	−0.313830	−0.156915	−	0.987612i	$-0.550155\pi$
$809$	−8.92623	−0.313830	−0.156915	+	0.987612i	$0.550155\pi$
$810$	−12.3492	−0.433905
$811$	−49.9993	−1.75571	−0.877856	−	0.478925i	$-0.841027\pi$
$811$	−49.9993	−1.75571	−0.877856	+	0.478925i	$0.841027\pi$
$812$	−0.175370	−0.00615428
$813$	−9.52892	−0.334194
$814$	6.21095	0.217694
$815$	54.0943	1.89484
$816$	−0.554984	−0.0194283
$817$	0.684876	0.0239608
$818$	−21.4630	−0.750435
$819$	9.14671	0.319612
$820$	−20.9998	−0.733346
$821$	−18.0943	−0.631497	−0.315748	−	0.948843i	$-0.602256\pi$
$821$	−18.0943	−0.631497	−0.315748	+	0.948843i	$0.602256\pi$
$822$	−2.48725	−0.0867527
$823$	29.5238	1.02914	0.514568	−	0.857450i	$-0.327952\pi$
$823$	29.5238	1.02914	0.514568	+	0.857450i	$0.327952\pi$
$824$	−17.5514	−0.611433
$825$	0.545049	0.0189762
$826$	4.24814	0.147812
$827$	−44.0151	−1.53056	−0.765278	−	0.643700i	$-0.777399\pi$
$827$	−44.0151	−1.53056	−0.765278	+	0.643700i	$0.777399\pi$
$828$	−26.6200	−0.925109
$829$	17.2344	0.598575	0.299288	−	0.954163i	$-0.403251\pi$
$829$	17.2344	0.598575	0.299288	+	0.954163i	$0.403251\pi$
$830$	23.8061	0.826323
$831$	−4.59439	−0.159378
$832$	−5.63364	−0.195311
$833$	−5.66904	−0.196421
$834$	−5.23157	−0.181154
$835$	−18.5601	−0.642298
$836$	−1.01147	−0.0349823
$837$	−15.2217	−0.526140
$838$	−18.5563	−0.641018
$839$	−9.81348	−0.338799	−0.169399	−	0.985547i	$-0.554183\pi$
$839$	−9.81348	−0.338799	−0.169399	+	0.985547i	$0.554183\pi$
$840$	−3.50838	−0.121051
$841$	−28.9894	−0.999635
$842$	19.8166	0.682924
$843$	−5.98575	−0.206160
$844$	−19.8738	−0.684086
$845$	11.7537	0.404338
$846$	17.8326	0.613097
$847$	1.15367	0.0396407
$848$	−6.08918	−0.209103
$849$	11.3536	0.389654
$850$	0.806117	0.0276496
$851$	56.0631	1.92182
$852$	−11.1788	−0.382980
$853$	−24.2916	−0.831727	−0.415864	−	0.909427i	$-0.636521\pi$
$853$	−24.2916	−0.831727	−0.415864	+	0.909427i	$0.636521\pi$
$854$	1.19001	0.0407213
$855$	−4.67556	−0.159901
$856$	−42.7510	−1.46120
$857$	41.5516	1.41937	0.709687	−	0.704517i	$-0.248836\pi$
$857$	41.5516	1.41937	0.709687	+	0.704517i	$0.248836\pi$
$858$	−1.01577	−0.0346779
$859$	1.85878	0.0634209	0.0317104	−	0.999497i	$-0.489905\pi$
$859$	1.85878	0.0634209	0.0317104	+	0.999497i	$0.489905\pi$
$860$	−3.65192	−0.124529
$861$	3.24433	0.110566
$862$	8.64337	0.294394
$863$	5.24384	0.178502	0.0892511	−	0.996009i	$-0.471553\pi$
$863$	5.24384	0.178502	0.0892511	+	0.996009i	$0.471553\pi$
$864$	16.4821	0.560732
$865$	−8.43597	−0.286832
$866$	−27.6868	−0.940836
$867$	−0.489043	−0.0166088
$868$	9.20563	0.312460
$869$	4.14871	0.140735
$870$	0.0900264	0.00305218
$871$	2.90583	0.0984602
$872$	23.4723	0.794872
$873$	−12.2321	−0.413994
$874$	3.23406	0.109394
$875$	11.0843	0.374718
$876$	−11.2243	−0.379234
$877$	−42.3961	−1.43161	−0.715807	−	0.698298i	$-0.753941\pi$
$877$	−42.3961	−1.43161	−0.715807	+	0.698298i	$0.753941\pi$
$878$	−16.6603	−0.562260
$879$	−3.58908	−0.121057
$880$	2.80618	0.0945962
$881$	−19.2638	−0.649015	−0.324507	−	0.945883i	$-0.605199\pi$
$881$	−19.2638	−0.649015	−0.324507	+	0.945883i	$0.605199\pi$
$882$	11.3203	0.381175
$883$	42.0945	1.41659	0.708296	−	0.705916i	$-0.249464\pi$
$883$	42.0945	1.41659	0.708296	+	0.705916i	$0.249464\pi$
$884$	4.24112	0.142644
$885$	6.15652	0.206949
$886$	−7.19451	−0.241704
$887$	−49.4468	−1.66026	−0.830131	−	0.557568i	$-0.811735\pi$
$887$	−49.4468	−1.66026	−0.830131	+	0.557568i	$0.811735\pi$
$888$	−10.5607	−0.354393
$889$	1.38924	0.0465936
$890$	−29.7145	−0.996032
$891$	−6.90474	−0.231317
$892$	−19.8863	−0.665842
$893$	6.11613	0.204669
$894$	3.51429	0.117536
$895$	11.7188	0.391716
$896$	−11.8618	−0.396274
$897$	−9.16886	−0.306139
$898$	8.43663	0.281534
$899$	−0.556115	−0.0185475
$900$	4.54433	0.151478
$901$	−5.36568	−0.178757
$902$	4.15914	0.138484
$903$	0.564195	0.0187752
$904$	40.5297	1.34800
$905$	6.27615	0.208626
$906$	−3.14394	−0.104450
$907$	2.16323	0.0718290	0.0359145	−	0.999355i	$-0.488566\pi$
$907$	2.16323	0.0718290	0.0359145	+	0.999355i	$0.488566\pi$
$908$	11.7940	0.391397
$909$	−8.04372	−0.266793
$910$	5.92535	0.196423
$911$	21.9337	0.726695	0.363348	−	0.931654i	$-0.381634\pi$
$911$	21.9337	0.726695	0.363348	+	0.931654i	$0.381634\pi$
$912$	0.380095	0.0125862
$913$	13.3106	0.440518
$914$	14.5947	0.482749
$915$	1.72460	0.0570134
$916$	35.8475	1.18443
$917$	−2.72877	−0.0901119
$918$	2.03770	0.0672542
$919$	−35.7374	−1.17887	−0.589433	−	0.807817i	$-0.700649\pi$
$919$	−35.7374	−1.17887	−0.589433	+	0.807817i	$0.700649\pi$
$920$	−40.5980	−1.33848
$921$	14.0824	0.464030
$922$	27.3202	0.899743
$923$	44.4478	1.46302
$924$	−0.833238	−0.0274115
$925$	−9.57058	−0.314679
$926$	12.0369	0.395556
$927$	−19.2689	−0.632875
$928$	0.602162	0.0197669
$929$	27.8655	0.914237	0.457118	−	0.889406i	$-0.348882\pi$
$929$	27.8655	0.914237	0.457118	+	0.889406i	$0.348882\pi$
$930$	−4.72572	−0.154963
$931$	3.88259	0.127247
$932$	−4.66584	−0.152835
$933$	−6.94235	−0.227282
$934$	−13.1755	−0.431115
$935$	2.47276	0.0808678
$936$	−19.9378	−0.651688
$937$	−22.1625	−0.724018	−0.362009	−	0.932175i	$-0.617909\pi$
$937$	−22.1625	−0.724018	−0.362009	+	0.932175i	$0.617909\pi$
$938$	−0.844346	−0.0275689
$939$	−10.5957	−0.345777
$940$	−32.6126	−1.06371
$941$	−12.5767	−0.409987	−0.204994	−	0.978763i	$-0.565717\pi$
$941$	−12.5767	−0.409987	−0.204994	+	0.978763i	$0.565717\pi$
$942$	2.20338	0.0717899
$943$	37.5425	1.22255
$944$	5.77751	0.188042
$945$	−8.03705	−0.261445
$946$	0.723284	0.0235160
$947$	48.9355	1.59019	0.795095	−	0.606485i	$-0.207421\pi$
$947$	48.9355	1.59019	0.795095	+	0.606485i	$0.207421\pi$
$948$	−2.99640	−0.0973184
$949$	44.6287	1.44871
$950$	−0.552090	−0.0179122
$951$	−2.86075	−0.0927661
$952$	−2.90121	−0.0940287
$953$	−38.2289	−1.23836	−0.619178	−	0.785251i	$-0.712534\pi$
$953$	−38.2289	−1.23836	−0.619178	+	0.785251i	$0.712534\pi$
$954$	10.7146	0.346897
$955$	−20.9094	−0.676613
$956$	17.2683	0.558497
$957$	0.0503361	0.00162714
$958$	8.31009	0.268487
$959$	8.11235	0.261961
$960$	2.37233	0.0765668
$961$	−1.80807	−0.0583250
$962$	17.8361	0.575058
$963$	−46.9344	−1.51244
$964$	−7.11665	−0.229212
$965$	0.388275	0.0124990
$966$	2.66419	0.0857191
$967$	21.2701	0.684002	0.342001	−	0.939700i	$-0.388895\pi$
$967$	21.2701	0.684002	0.342001	+	0.939700i	$0.388895\pi$
$968$	−2.51476	−0.0808274
$969$	0.334933	0.0107596
$970$	−7.92411	−0.254428
$971$	−9.06190	−0.290810	−0.145405	−	0.989372i	$-0.546449\pi$
$971$	−9.06190	−0.290810	−0.145405	+	0.989372i	$0.546449\pi$
$972$	17.4692	0.560324
$973$	17.0631	0.547019
$974$	−15.3539	−0.491972
$975$	1.56523	0.0501273
$976$	1.61843	0.0518046
$977$	19.7048	0.630413	0.315206	−	0.949023i	$-0.397926\pi$
$977$	19.7048	0.630413	0.315206	+	0.949023i	$0.397926\pi$
$978$	7.73794	0.247432
$979$	−16.6142	−0.530991
$980$	−20.7029	−0.661328
$981$	25.7692	0.822746
$982$	−29.2483	−0.933350
$983$	35.1150	1.11999	0.559997	−	0.828495i	$-0.310802\pi$
$983$	35.1150	1.11999	0.559997	+	0.828495i	$0.310802\pi$
$984$	−7.07193	−0.225445
$985$	−17.9530	−0.572030
$986$	0.0744461	0.00237085
$987$	5.03842	0.160375
$988$	−2.90464	−0.0924089
$989$	6.52871	0.207601
$990$	−4.93777	−0.156933
$991$	−7.89992	−0.250949	−0.125475	−	0.992097i	$-0.540045\pi$
$991$	−7.89992	−0.250949	−0.125475	+	0.992097i	$0.540045\pi$
$992$	−31.6090	−1.00359
$993$	5.68689	0.180468
$994$	−12.9152	−0.409645
$995$	−64.6757	−2.05036
$996$	−9.61357	−0.304618
$997$	9.10362	0.288315	0.144157	−	0.989555i	$-0.453953\pi$
$997$	9.10362	0.288315	0.144157	+	0.989555i	$0.453953\pi$
$998$	−18.6398	−0.590031
$999$	−24.1925	−0.765418

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.f.1.38	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.f.1.38	✓	66	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q+0.723284 q^{2} -0.489043 q^{3} -1.47686 q^{4} -2.47276 q^{5} -0.353717 q^{6} +1.15367 q^{7} -2.51476 q^{8} -2.76084 q^{9} +O(q^{10})\)	\(q+0.723284 q^{2} -0.489043 q^{3} -1.47686 q^{4} -2.47276 q^{5} -0.353717 q^{6} +1.15367 q^{7} -2.51476 q^{8} -2.76084 q^{9} -1.78850 q^{10} -1.00000 q^{11} +0.722248 q^{12} -2.87171 q^{13} +0.834433 q^{14} +1.20928 q^{15} +1.13484 q^{16} +1.00000 q^{17} -1.99687 q^{18} -0.684876 q^{19} +3.65192 q^{20} -0.564195 q^{21} -0.723284 q^{22} -6.52871 q^{23} +1.22982 q^{24} +1.11452 q^{25} -2.07706 q^{26} +2.81729 q^{27} -1.70381 q^{28} +0.102928 q^{29} +0.874655 q^{30} -5.40296 q^{31} +5.85032 q^{32} +0.489043 q^{33} +0.723284 q^{34} -2.85275 q^{35} +4.07737 q^{36} -8.58715 q^{37} -0.495360 q^{38} +1.40439 q^{39} +6.21838 q^{40} -5.75036 q^{41} -0.408073 q^{42} -1.00000 q^{43} +1.47686 q^{44} +6.82688 q^{45} -4.72211 q^{46} -8.93028 q^{47} -0.554984 q^{48} -5.66904 q^{49} +0.806117 q^{50} -0.489043 q^{51} +4.24112 q^{52} -5.36568 q^{53} +2.03770 q^{54} +2.47276 q^{55} -2.90121 q^{56} +0.334933 q^{57} +0.0744461 q^{58} +5.09105 q^{59} -1.78594 q^{60} +1.42613 q^{61} -3.90787 q^{62} -3.18510 q^{63} +1.96177 q^{64} +7.10105 q^{65} +0.353717 q^{66} -1.01188 q^{67} -1.47686 q^{68} +3.19282 q^{69} -2.06335 q^{70} -15.4778 q^{71} +6.94284 q^{72} -15.5408 q^{73} -6.21095 q^{74} -0.545049 q^{75} +1.01147 q^{76} -1.15367 q^{77} +1.01577 q^{78} -4.14871 q^{79} -2.80618 q^{80} +6.90474 q^{81} -4.15914 q^{82} -13.3106 q^{83} +0.833238 q^{84} -2.47276 q^{85} -0.723284 q^{86} -0.0503361 q^{87} +2.51476 q^{88} +16.6142 q^{89} +4.93777 q^{90} -3.31302 q^{91} +9.64200 q^{92} +2.64228 q^{93} -6.45913 q^{94} +1.69353 q^{95} -2.86106 q^{96} +4.43058 q^{97} -4.10032 q^{98} +2.76084 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * q^99

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