LMFDB - Embedded newform 8041.2.a.f.1.20

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			1.20
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)

$f(q)$	$=$	$q-1.16270 q^{2} -2.59083 q^{3} -0.648140 q^{4} -0.596152 q^{5} +3.01234 q^{6} -2.62369 q^{7} +3.07898 q^{8} +3.71239 q^{9} +O(q^{10})$	\(q-1.16270 q^{2} -2.59083 q^{3} -0.648140 q^{4} -0.596152 q^{5} +3.01234 q^{6} -2.62369 q^{7} +3.07898 q^{8} +3.71239 q^{9} +0.693143 q^{10} -1.00000 q^{11} +1.67922 q^{12} -0.231454 q^{13} +3.05056 q^{14} +1.54453 q^{15} -2.28363 q^{16} +1.00000 q^{17} -4.31638 q^{18} +5.45220 q^{19} +0.386390 q^{20} +6.79754 q^{21} +1.16270 q^{22} -0.801064 q^{23} -7.97711 q^{24} -4.64460 q^{25} +0.269110 q^{26} -1.84569 q^{27} +1.70052 q^{28} +7.41982 q^{29} -1.79581 q^{30} +7.39994 q^{31} -3.50279 q^{32} +2.59083 q^{33} -1.16270 q^{34} +1.56412 q^{35} -2.40615 q^{36} +7.80833 q^{37} -6.33925 q^{38} +0.599657 q^{39} -1.83554 q^{40} +8.33371 q^{41} -7.90347 q^{42} -1.00000 q^{43} +0.648140 q^{44} -2.21315 q^{45} +0.931393 q^{46} +6.73420 q^{47} +5.91651 q^{48} -0.116229 q^{49} +5.40026 q^{50} -2.59083 q^{51} +0.150014 q^{52} -5.75237 q^{53} +2.14597 q^{54} +0.596152 q^{55} -8.07830 q^{56} -14.1257 q^{57} -8.62699 q^{58} +2.56023 q^{59} -1.00107 q^{60} +1.46840 q^{61} -8.60388 q^{62} -9.74018 q^{63} +8.63994 q^{64} +0.137982 q^{65} -3.01234 q^{66} +6.54304 q^{67} -0.648140 q^{68} +2.07542 q^{69} -1.81859 q^{70} -8.44269 q^{71} +11.4304 q^{72} -5.18414 q^{73} -9.07871 q^{74} +12.0334 q^{75} -3.53379 q^{76} +2.62369 q^{77} -0.697218 q^{78} +10.3185 q^{79} +1.36139 q^{80} -6.35532 q^{81} -9.68956 q^{82} +9.24085 q^{83} -4.40576 q^{84} -0.596152 q^{85} +1.16270 q^{86} -19.2235 q^{87} -3.07898 q^{88} +14.9516 q^{89} +2.57322 q^{90} +0.607264 q^{91} +0.519202 q^{92} -19.1720 q^{93} -7.82983 q^{94} -3.25034 q^{95} +9.07512 q^{96} -1.30429 q^{97} +0.135139 q^{98} -3.71239 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.16270	−0.822150	−0.411075	−	0.911602i	$-0.634847\pi$
$2$	−1.16270	−0.822150	−0.411075	+	0.911602i	$0.634847\pi$
$3$	−2.59083	−1.49582	−0.747908	−	0.663803i	$-0.768941\pi$
$3$	−2.59083	−1.49582	−0.747908	+	0.663803i	$0.768941\pi$
$4$	−0.648140	−0.324070
$5$	−0.596152	−0.266607	−0.133304	−	0.991075i	$-0.542559\pi$
$5$	−0.596152	−0.266607	−0.133304	+	0.991075i	$0.542559\pi$
$6$	3.01234	1.22978
$7$	−2.62369	−0.991663	−0.495832	−	0.868419i	$-0.665137\pi$
$7$	−2.62369	−0.991663	−0.495832	+	0.868419i	$0.665137\pi$
$8$	3.07898	1.08858
$9$	3.71239	1.23746
$10$	0.693143	0.219191
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.67922	0.484749
$13$	−0.231454	−0.0641937	−0.0320969	−	0.999485i	$-0.510219\pi$
$13$	−0.231454	−0.0641937	−0.0320969	+	0.999485i	$0.510219\pi$
$14$	3.05056	0.815295
$15$	1.54453	0.398795
$16$	−2.28363	−0.570909
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−4.31638	−1.01738
$19$	5.45220	1.25082	0.625411	−	0.780296i	$-0.284931\pi$
$19$	5.45220	1.25082	0.625411	+	0.780296i	$0.284931\pi$
$20$	0.386390	0.0863994
$21$	6.79754	1.48335
$22$	1.16270	0.247887
$23$	−0.801064	−0.167033	−0.0835167	−	0.996506i	$-0.526615\pi$
$23$	−0.801064	−0.167033	−0.0835167	+	0.996506i	$0.526615\pi$
$24$	−7.97711	−1.62832
$25$	−4.64460	−0.928921
$26$	0.269110	0.0527769
$27$	−1.84569	−0.355202
$28$	1.70052	0.321368
$29$	7.41982	1.37783	0.688913	−	0.724844i	$-0.258088\pi$
$29$	7.41982	1.37783	0.688913	+	0.724844i	$0.258088\pi$
$30$	−1.79581	−0.327869
$31$	7.39994	1.32907	0.664534	−	0.747258i	$-0.268630\pi$
$31$	7.39994	1.32907	0.664534	+	0.747258i	$0.268630\pi$
$32$	−3.50279	−0.619211
$33$	2.59083	0.451005
$34$	−1.16270	−0.199401
$35$	1.56412	0.264385
$36$	−2.40615	−0.401025
$37$	7.80833	1.28368	0.641841	−	0.766838i	$-0.278171\pi$
$37$	7.80833	1.28368	0.641841	+	0.766838i	$0.278171\pi$
$38$	−6.33925	−1.02836
$39$	0.599657	0.0960220
$40$	−1.83554	−0.290224
$41$	8.33371	1.30151	0.650753	−	0.759289i	$-0.274453\pi$
$41$	8.33371	1.30151	0.650753	+	0.759289i	$0.274453\pi$
$42$	−7.90347	−1.21953
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	0.648140	0.0977108
$45$	−2.21315	−0.329917
$46$	0.931393	0.137326
$47$	6.73420	0.982285	0.491142	−	0.871079i	$-0.336579\pi$
$47$	6.73420	0.982285	0.491142	+	0.871079i	$0.336579\pi$
$48$	5.91651	0.853974
$49$	−0.116229	−0.0166042
$50$	5.40026	0.763712
$51$	−2.59083	−0.362789
$52$	0.150014	0.0208033
$53$	−5.75237	−0.790149	−0.395074	−	0.918649i	$-0.629281\pi$
$53$	−5.75237	−0.790149	−0.395074	+	0.918649i	$0.629281\pi$
$54$	2.14597	0.292029
$55$	0.596152	0.0803851
$56$	−8.07830	−1.07951
$57$	−14.1257	−1.87100
$58$	−8.62699	−1.13278
$59$	2.56023	0.333314	0.166657	−	0.986015i	$-0.446703\pi$
$59$	2.56023	0.333314	0.166657	+	0.986015i	$0.446703\pi$
$60$	−1.00107	−0.129238
$61$	1.46840	0.188009	0.0940045	−	0.995572i	$-0.470033\pi$
$61$	1.46840	0.188009	0.0940045	+	0.995572i	$0.470033\pi$
$62$	−8.60388	−1.09269
$63$	−9.74018	−1.22715
$64$	8.63994	1.07999
$65$	0.137982	0.0171145
$66$	−3.01234	−0.370794
$67$	6.54304	0.799359	0.399680	−	0.916655i	$-0.369121\pi$
$67$	6.54304	0.799359	0.399680	+	0.916655i	$0.369121\pi$
$68$	−0.648140	−0.0785985
$69$	2.07542	0.249851
$70$	−1.81859	−0.217364
$71$	−8.44269	−1.00196	−0.500981	−	0.865458i	$-0.667027\pi$
$71$	−8.44269	−1.00196	−0.500981	+	0.865458i	$0.667027\pi$
$72$	11.4304	1.34708
$73$	−5.18414	−0.606758	−0.303379	−	0.952870i	$-0.598115\pi$
$73$	−5.18414	−0.606758	−0.303379	+	0.952870i	$0.598115\pi$
$74$	−9.07871	−1.05538
$75$	12.0334	1.38949
$76$	−3.53379	−0.405354
$77$	2.62369	0.298998
$78$	−0.697218	−0.0789444
$79$	10.3185	1.16092	0.580459	−	0.814289i	$-0.302873\pi$
$79$	10.3185	1.16092	0.580459	+	0.814289i	$0.302873\pi$
$80$	1.36139	0.152208
$81$	−6.35532	−0.706147
$82$	−9.68956	−1.07003
$83$	9.24085	1.01432	0.507158	−	0.861853i	$-0.330696\pi$
$83$	9.24085	1.01432	0.507158	+	0.861853i	$0.330696\pi$
$84$	−4.40576	−0.480708
$85$	−0.596152	−0.0646617
$86$	1.16270	0.125377
$87$	−19.2235	−2.06097
$88$	−3.07898	−0.328220
$89$	14.9516	1.58486	0.792432	−	0.609960i	$-0.208815\pi$
$89$	14.9516	1.58486	0.792432	+	0.609960i	$0.208815\pi$
$90$	2.57322	0.271241
$91$	0.607264	0.0636586
$92$	0.519202	0.0541305
$93$	−19.1720	−1.98804
$94$	−7.82983	−0.807585
$95$	−3.25034	−0.333478
$96$	9.07512	0.926226
$97$	−1.30429	−0.132431	−0.0662153	−	0.997805i	$-0.521092\pi$
$97$	−1.30429	−0.132431	−0.0662153	+	0.997805i	$0.521092\pi$
$98$	0.135139	0.0136511
$99$	−3.71239	−0.373109
$100$	3.01035	0.301035
$101$	6.17300	0.614237	0.307118	−	0.951671i	$-0.400635\pi$
$101$	6.17300	0.614237	0.307118	+	0.951671i	$0.400635\pi$
$102$	3.01234	0.298266
$103$	11.3842	1.12171	0.560857	−	0.827912i	$-0.310472\pi$
$103$	11.3842	1.12171	0.560857	+	0.827912i	$0.310472\pi$
$104$	−0.712642	−0.0698803
$105$	−4.05237	−0.395470
$106$	6.68825	0.649621
$107$	−6.42568	−0.621194	−0.310597	−	0.950542i	$-0.600529\pi$
$107$	−6.42568	−0.621194	−0.310597	+	0.950542i	$0.600529\pi$
$108$	1.19626	0.115110
$109$	−3.56662	−0.341620	−0.170810	−	0.985304i	$-0.554639\pi$
$109$	−3.56662	−0.341620	−0.170810	+	0.985304i	$0.554639\pi$
$110$	−0.693143	−0.0660886
$111$	−20.2300	−1.92015
$112$	5.99156	0.566149
$113$	−5.15928	−0.485344	−0.242672	−	0.970108i	$-0.578024\pi$
$113$	−5.15928	−0.485344	−0.242672	+	0.970108i	$0.578024\pi$
$114$	16.4239	1.53824
$115$	0.477556	0.0445323
$116$	−4.80908	−0.446512
$117$	−0.859247	−0.0794374
$118$	−2.97677	−0.274034
$119$	−2.62369	−0.240514
$120$	4.75557	0.434122
$121$	1.00000	0.0909091
$122$	−1.70730	−0.154572
$123$	−21.5912	−1.94681
$124$	−4.79620	−0.430711
$125$	5.74965	0.514264
$126$	11.3249	1.00890
$127$	17.7167	1.57210	0.786052	−	0.618160i	$-0.212122\pi$
$127$	17.7167	1.57210	0.786052	+	0.618160i	$0.212122\pi$
$128$	−3.04004	−0.268704
$129$	2.59083	0.228110
$130$	−0.160431	−0.0140707
$131$	9.68042	0.845782	0.422891	−	0.906181i	$-0.361015\pi$
$131$	9.68042	0.845782	0.422891	+	0.906181i	$0.361015\pi$
$132$	−1.67922	−0.146157
$133$	−14.3049	−1.24039
$134$	−7.60756	−0.657193
$135$	1.10031	0.0946995
$136$	3.07898	0.264020
$137$	7.21073	0.616054	0.308027	−	0.951378i	$-0.400331\pi$
$137$	7.21073	0.616054	0.308027	+	0.951378i	$0.400331\pi$
$138$	−2.41308	−0.205415
$139$	0.707368	0.0599982	0.0299991	−	0.999550i	$-0.490450\pi$
$139$	0.707368	0.0599982	0.0299991	+	0.999550i	$0.490450\pi$
$140$	−1.01377	−0.0856791
$141$	−17.4472	−1.46932
$142$	9.81627	0.823763
$143$	0.231454	0.0193551
$144$	−8.47775	−0.706479
$145$	−4.42334	−0.367338
$146$	6.02757	0.498846
$147$	0.301130	0.0248368
$148$	−5.06089	−0.416003
$149$	−3.89037	−0.318711	−0.159356	−	0.987221i	$-0.550942\pi$
$149$	−3.89037	−0.318711	−0.159356	+	0.987221i	$0.550942\pi$
$150$	−13.9911	−1.14237
$151$	−17.8526	−1.45283	−0.726414	−	0.687258i	$-0.758814\pi$
$151$	−17.8526	−1.45283	−0.726414	+	0.687258i	$0.758814\pi$
$152$	16.7872	1.36162
$153$	3.71239	0.300129
$154$	−3.05056	−0.245821
$155$	−4.41149	−0.354339
$156$	−0.388662	−0.0311178
$157$	−15.7217	−1.25473	−0.627366	−	0.778725i	$-0.715867\pi$
$157$	−15.7217	−1.25473	−0.627366	+	0.778725i	$0.715867\pi$
$158$	−11.9972	−0.954449
$159$	14.9034	1.18192
$160$	2.08819	0.165086
$161$	2.10175	0.165641
$162$	7.38930	0.580558
$163$	−11.9884	−0.939004	−0.469502	−	0.882931i	$-0.655567\pi$
$163$	−11.9884	−0.939004	−0.469502	+	0.882931i	$0.655567\pi$
$164$	−5.40141	−0.421779
$165$	−1.54453	−0.120241
$166$	−10.7443	−0.833919
$167$	−21.9593	−1.69926	−0.849629	−	0.527380i	$-0.823174\pi$
$167$	−21.9593	−1.69926	−0.849629	+	0.527380i	$0.823174\pi$
$168$	20.9295	1.61475
$169$	−12.9464	−0.995879
$170$	0.693143	0.0531616
$171$	20.2407	1.54785
$172$	0.648140	0.0494202
$173$	−10.4161	−0.791925	−0.395962	−	0.918267i	$-0.629589\pi$
$173$	−10.4161	−0.791925	−0.395962	+	0.918267i	$0.629589\pi$
$174$	22.3510	1.69443
$175$	12.1860	0.921176
$176$	2.28363	0.172135
$177$	−6.63313	−0.498576
$178$	−17.3841	−1.30300
$179$	5.38191	0.402263	0.201132	−	0.979564i	$-0.435538\pi$
$179$	5.38191	0.402263	0.201132	+	0.979564i	$0.435538\pi$
$180$	1.43443	0.106916
$181$	6.95655	0.517077	0.258538	−	0.966001i	$-0.416759\pi$
$181$	6.95655	0.517077	0.258538	+	0.966001i	$0.416759\pi$
$182$	−0.706063	−0.0523369
$183$	−3.80436	−0.281227
$184$	−2.46646	−0.181830
$185$	−4.65495	−0.342239
$186$	22.2912	1.63447
$187$	−1.00000	−0.0731272
$188$	−4.36471	−0.318329
$189$	4.84251	0.352241
$190$	3.77916	0.274169
$191$	−5.85664	−0.423772	−0.211886	−	0.977294i	$-0.567961\pi$
$191$	−5.85664	−0.423772	−0.211886	+	0.977294i	$0.567961\pi$
$192$	−22.3846	−1.61547
$193$	−24.1982	−1.74183	−0.870914	−	0.491436i	$-0.836472\pi$
$193$	−24.1982	−1.74183	−0.870914	+	0.491436i	$0.836472\pi$
$194$	1.51649	0.108878
$195$	−0.357487	−0.0256002
$196$	0.0753329	0.00538092
$197$	−15.2843	−1.08896	−0.544479	−	0.838774i	$-0.683273\pi$
$197$	−15.2843	−1.08896	−0.544479	+	0.838774i	$0.683273\pi$
$198$	4.31638	0.306752
$199$	24.1498	1.71194	0.855968	−	0.517029i	$-0.172962\pi$
$199$	24.1498	1.71194	0.855968	+	0.517029i	$0.172962\pi$
$200$	−14.3006	−1.01121
$201$	−16.9519	−1.19569
$202$	−7.17732	−0.504994
$203$	−19.4673	−1.36634
$204$	1.67922	0.117569
$205$	−4.96816	−0.346991
$206$	−13.2363	−0.922217
$207$	−2.97386	−0.206698
$208$	0.528556	0.0366488
$209$	−5.45220	−0.377137
$210$	4.71167	0.325136
$211$	−9.66396	−0.665294	−0.332647	−	0.943051i	$-0.607942\pi$
$211$	−9.66396	−0.665294	−0.332647	+	0.943051i	$0.607942\pi$
$212$	3.72834	0.256064
$213$	21.8736	1.49875
$214$	7.47110	0.510714
$215$	0.596152	0.0406572
$216$	−5.68283	−0.386667
$217$	−19.4152	−1.31799
$218$	4.14689	0.280863
$219$	13.4312	0.907598
$220$	−0.386390	−0.0260504
$221$	−0.231454	−0.0155693
$222$	23.5214	1.57865
$223$	−4.50010	−0.301349	−0.150675	−	0.988583i	$-0.548145\pi$
$223$	−4.50010	−0.301349	−0.150675	+	0.988583i	$0.548145\pi$
$224$	9.19024	0.614049
$225$	−17.2426	−1.14951
$226$	5.99867	0.399026
$227$	6.06314	0.402424	0.201212	−	0.979548i	$-0.435512\pi$
$227$	6.06314	0.402424	0.201212	+	0.979548i	$0.435512\pi$
$228$	9.15545	0.606334
$229$	23.1604	1.53048	0.765241	−	0.643744i	$-0.222620\pi$
$229$	23.1604	1.53048	0.765241	+	0.643744i	$0.222620\pi$
$230$	−0.555252	−0.0366122
$231$	−6.79754	−0.447245
$232$	22.8455	1.49988
$233$	−24.8303	−1.62669	−0.813343	−	0.581785i	$-0.802355\pi$
$233$	−24.8303	−1.62669	−0.813343	+	0.581785i	$0.802355\pi$
$234$	0.999043	0.0653095
$235$	−4.01461	−0.261884
$236$	−1.65939	−0.108017
$237$	−26.7334	−1.73652
$238$	3.05056	0.197738
$239$	−29.5738	−1.91297	−0.956486	−	0.291777i	$-0.905753\pi$
$239$	−29.5738	−1.91297	−0.956486	+	0.291777i	$0.905753\pi$
$240$	−3.52713	−0.227676
$241$	14.0523	0.905189	0.452595	−	0.891716i	$-0.350498\pi$
$241$	14.0523	0.905189	0.452595	+	0.891716i	$0.350498\pi$
$242$	−1.16270	−0.0747409
$243$	22.0026	1.41147
$244$	−0.951727	−0.0609281
$245$	0.0692903	0.00442680
$246$	25.1040	1.60057
$247$	−1.26193	−0.0802949
$248$	22.7843	1.44680
$249$	−23.9415	−1.51723
$250$	−6.68509	−0.422802
$251$	8.94204	0.564417	0.282208	−	0.959353i	$-0.408933\pi$
$251$	8.94204	0.564417	0.282208	+	0.959353i	$0.408933\pi$
$252$	6.31300	0.397682
$253$	0.801064	0.0503625
$254$	−20.5991	−1.29250
$255$	1.54453	0.0967220
$256$	−13.7452	−0.859078
$257$	−7.82535	−0.488132	−0.244066	−	0.969759i	$-0.578481\pi$
$257$	−7.82535	−0.488132	−0.244066	+	0.969759i	$0.578481\pi$
$258$	−3.01234	−0.187540
$259$	−20.4867	−1.27298
$260$	−0.0894314	−0.00554630
$261$	27.5453	1.70501
$262$	−11.2554	−0.695359
$263$	18.6926	1.15264	0.576318	−	0.817226i	$-0.304489\pi$
$263$	18.6926	1.15264	0.576318	+	0.817226i	$0.304489\pi$
$264$	7.97711	0.490957
$265$	3.42929	0.210659
$266$	16.6323	1.01979
$267$	−38.7370	−2.37066
$268$	−4.24080	−0.259048
$269$	−16.3814	−0.998795	−0.499397	−	0.866373i	$-0.666445\pi$
$269$	−16.3814	−0.998795	−0.499397	+	0.866373i	$0.666445\pi$
$270$	−1.27932	−0.0778572
$271$	14.6648	0.890825	0.445413	−	0.895325i	$-0.353057\pi$
$271$	14.6648	0.890825	0.445413	+	0.895325i	$0.353057\pi$
$272$	−2.28363	−0.138466
$273$	−1.57332	−0.0952215
$274$	−8.38388	−0.506488
$275$	4.64460	0.280080
$276$	−1.34516	−0.0809693
$277$	14.5051	0.871528	0.435764	−	0.900061i	$-0.356478\pi$
$277$	14.5051	0.871528	0.435764	+	0.900061i	$0.356478\pi$
$278$	−0.822453	−0.0493275
$279$	27.4715	1.64467
$280$	4.81589	0.287805
$281$	0.386840	0.0230770	0.0115385	−	0.999933i	$-0.496327\pi$
$281$	0.386840	0.0230770	0.0115385	+	0.999933i	$0.496327\pi$
$282$	20.2857	1.20800
$283$	20.0354	1.19098	0.595490	−	0.803363i	$-0.296958\pi$
$283$	20.0354	1.19098	0.595490	+	0.803363i	$0.296958\pi$
$284$	5.47204	0.324706
$285$	8.42108	0.498821
$286$	−0.269110	−0.0159128
$287$	−21.8651	−1.29066
$288$	−13.0037	−0.766252
$289$	1.00000	0.0588235
$290$	5.14299	0.302007
$291$	3.37919	0.198092
$292$	3.36005	0.196632
$293$	8.52708	0.498158	0.249079	−	0.968483i	$-0.419872\pi$
$293$	8.52708	0.498158	0.249079	+	0.968483i	$0.419872\pi$
$294$	−0.350123	−0.0204196
$295$	−1.52629	−0.0888639
$296$	24.0417	1.39739
$297$	1.84569	0.107098
$298$	4.52331	0.262029
$299$	0.185409	0.0107225
$300$	−7.79931	−0.450293
$301$	2.62369	0.151227
$302$	20.7572	1.19444
$303$	−15.9932	−0.918785
$304$	−12.4508	−0.714105
$305$	−0.875387	−0.0501245
$306$	−4.31638	−0.246751
$307$	27.5770	1.57390	0.786951	−	0.617015i	$-0.211658\pi$
$307$	27.5770	1.57390	0.786951	+	0.617015i	$0.211658\pi$
$308$	−1.70052	−0.0968962
$309$	−29.4944	−1.67788
$310$	5.12922	0.291320
$311$	−25.5940	−1.45130	−0.725650	−	0.688064i	$-0.758461\pi$
$311$	−25.5940	−1.45130	−0.725650	+	0.688064i	$0.758461\pi$
$312$	1.84633	0.104528
$313$	7.95278	0.449518	0.224759	−	0.974414i	$-0.427841\pi$
$313$	7.95278	0.449518	0.224759	+	0.974414i	$0.427841\pi$
$314$	18.2796	1.03158
$315$	5.80663	0.327166
$316$	−6.68781	−0.376219
$317$	22.0380	1.23778	0.618889	−	0.785479i	$-0.287583\pi$
$317$	22.0380	1.23778	0.618889	+	0.785479i	$0.287583\pi$
$318$	−17.3281	−0.971712
$319$	−7.41982	−0.415430
$320$	−5.15072	−0.287934
$321$	16.6478	0.929191
$322$	−2.44369	−0.136182
$323$	5.45220	0.303369
$324$	4.11914	0.228841
$325$	1.07501	0.0596309
$326$	13.9389	0.772002
$327$	9.24051	0.511001
$328$	25.6593	1.41680
$329$	−17.6685	−0.974096
$330$	1.79581	0.0988563
$331$	−0.325818	−0.0179086	−0.00895428	−	0.999960i	$-0.502850\pi$
$331$	−0.325818	−0.0179086	−0.00895428	+	0.999960i	$0.502850\pi$
$332$	−5.98937	−0.328709
$333$	28.9876	1.58851
$334$	25.5319	1.39704
$335$	−3.90064	−0.213115
$336$	−15.5231	−0.846855
$337$	3.77432	0.205600	0.102800	−	0.994702i	$-0.467220\pi$
$337$	3.77432	0.205600	0.102800	+	0.994702i	$0.467220\pi$
$338$	15.0528	0.818762
$339$	13.3668	0.725986
$340$	0.386390	0.0209549
$341$	−7.39994	−0.400729
$342$	−23.5338	−1.27256
$343$	18.6708	1.00813
$344$	−3.07898	−0.166007
$345$	−1.23726	−0.0666121
$346$	12.1108	0.651081
$347$	6.15554	0.330447	0.165223	−	0.986256i	$-0.447165\pi$
$347$	6.15554	0.330447	0.165223	+	0.986256i	$0.447165\pi$
$348$	12.4595	0.667899
$349$	−15.1045	−0.808528	−0.404264	−	0.914642i	$-0.632472\pi$
$349$	−15.1045	−0.808528	−0.404264	+	0.914642i	$0.632472\pi$
$350$	−14.1686	−0.757345
$351$	0.427191	0.0228018
$352$	3.50279	0.186699
$353$	26.2773	1.39860	0.699298	−	0.714830i	$-0.253496\pi$
$353$	26.2773	1.39860	0.699298	+	0.714830i	$0.253496\pi$
$354$	7.71230	0.409904
$355$	5.03312	0.267130
$356$	−9.69071	−0.513607
$357$	6.79754	0.359764
$358$	−6.25752	−0.330720
$359$	6.13711	0.323904	0.161952	−	0.986799i	$-0.448221\pi$
$359$	6.13711	0.323904	0.161952	+	0.986799i	$0.448221\pi$
$360$	−6.81424	−0.359142
$361$	10.7265	0.564554
$362$	−8.08835	−0.425114
$363$	−2.59083	−0.135983
$364$	−0.393592	−0.0206298
$365$	3.09053	0.161766
$366$	4.42332	0.231210
$367$	−31.9199	−1.66621	−0.833103	−	0.553118i	$-0.813438\pi$
$367$	−31.9199	−1.66621	−0.833103	+	0.553118i	$0.813438\pi$
$368$	1.82934	0.0953608
$369$	30.9380	1.61057
$370$	5.41229	0.281371
$371$	15.0925	0.783561
$372$	12.4261	0.644265
$373$	−13.7577	−0.712346	−0.356173	−	0.934420i	$-0.615919\pi$
$373$	−13.7577	−0.712346	−0.356173	+	0.934420i	$0.615919\pi$
$374$	1.16270	0.0601215
$375$	−14.8963	−0.769244
$376$	20.7345	1.06930
$377$	−1.71734	−0.0884478
$378$	−5.63037	−0.289595
$379$	17.1714	0.882037	0.441018	−	0.897498i	$-0.354617\pi$
$379$	17.1714	0.882037	0.441018	+	0.897498i	$0.354617\pi$
$380$	2.10668	0.108070
$381$	−45.9010	−2.35158
$382$	6.80949	0.348404
$383$	18.4497	0.942734	0.471367	−	0.881937i	$-0.343761\pi$
$383$	18.4497	0.942734	0.471367	+	0.881937i	$0.343761\pi$
$384$	7.87623	0.401932
$385$	−1.56412	−0.0797149
$386$	28.1352	1.43204
$387$	−3.71239	−0.188711
$388$	0.845362	0.0429168
$389$	4.01546	0.203592	0.101796	−	0.994805i	$-0.467541\pi$
$389$	4.01546	0.203592	0.101796	+	0.994805i	$0.467541\pi$
$390$	0.415648	0.0210472
$391$	−0.801064	−0.0405115
$392$	−0.357868	−0.0180751
$393$	−25.0803	−1.26513
$394$	17.7709	0.895287
$395$	−6.15137	−0.309509
$396$	2.40615	0.120914
$397$	−25.8232	−1.29603	−0.648015	−	0.761627i	$-0.724401\pi$
$397$	−25.8232	−1.29603	−0.648015	+	0.761627i	$0.724401\pi$
$398$	−28.0789	−1.40747
$399$	37.0616	1.85540
$400$	10.6066	0.530329
$401$	−23.2777	−1.16243	−0.581215	−	0.813750i	$-0.697423\pi$
$401$	−23.2777	−1.16243	−0.581215	+	0.813750i	$0.697423\pi$
$402$	19.7099	0.983039
$403$	−1.71274	−0.0853179
$404$	−4.00097	−0.199056
$405$	3.78874	0.188264
$406$	22.6346	1.12333
$407$	−7.80833	−0.387045
$408$	−7.97711	−0.394926
$409$	−29.0382	−1.43585	−0.717924	−	0.696121i	$-0.754908\pi$
$409$	−29.0382	−1.43585	−0.717924	+	0.696121i	$0.754908\pi$
$410$	5.77645	0.285279
$411$	−18.6818	−0.921503
$412$	−7.37853	−0.363514
$413$	−6.71727	−0.330535
$414$	3.45770	0.169937
$415$	−5.50895	−0.270424
$416$	0.810734	0.0397495
$417$	−1.83267	−0.0897462
$418$	6.33925	0.310063
$419$	−15.6625	−0.765162	−0.382581	−	0.923922i	$-0.624965\pi$
$419$	−15.6625	−0.765162	−0.382581	+	0.923922i	$0.624965\pi$
$420$	2.62650	0.128160
$421$	20.0236	0.975889	0.487944	−	0.872875i	$-0.337747\pi$
$421$	20.0236	0.975889	0.487944	+	0.872875i	$0.337747\pi$
$422$	11.2362	0.546971
$423$	25.0000	1.21554
$424$	−17.7114	−0.860143
$425$	−4.64460	−0.225296
$426$	−25.4323	−1.23220
$427$	−3.85262	−0.186442
$428$	4.16474	0.201310
$429$	−0.599657	−0.0289517
$430$	−0.693143	−0.0334263
$431$	21.7868	1.04943	0.524717	−	0.851277i	$-0.324171\pi$
$431$	21.7868	1.04943	0.524717	+	0.851277i	$0.324171\pi$
$432$	4.21487	0.202788
$433$	−24.4849	−1.17667	−0.588334	−	0.808618i	$-0.700216\pi$
$433$	−24.4849	−1.17667	−0.588334	+	0.808618i	$0.700216\pi$
$434$	22.5739	1.08358
$435$	11.4601	0.549470
$436$	2.31167	0.110709
$437$	−4.36756	−0.208929
$438$	−15.6164	−0.746181
$439$	6.06515	0.289474	0.144737	−	0.989470i	$-0.453766\pi$
$439$	6.06515	0.289474	0.144737	+	0.989470i	$0.453766\pi$
$440$	1.83554	0.0875059
$441$	−0.431489	−0.0205471
$442$	0.269110	0.0128003
$443$	3.08168	0.146415	0.0732075	−	0.997317i	$-0.476676\pi$
$443$	3.08168	0.146415	0.0732075	+	0.997317i	$0.476676\pi$
$444$	13.1119	0.622263
$445$	−8.91341	−0.422536
$446$	5.23225	0.247754
$447$	10.0793	0.476734
$448$	−22.6686	−1.07099
$449$	25.8737	1.22105	0.610527	−	0.791996i	$-0.290958\pi$
$449$	25.8737	1.22105	0.610527	+	0.791996i	$0.290958\pi$
$450$	20.0479	0.945066
$451$	−8.33371	−0.392419
$452$	3.34394	0.157286
$453$	46.2531	2.17316
$454$	−7.04958	−0.330853
$455$	−0.362022	−0.0169718
$456$	−43.4928	−2.03674
$457$	34.2937	1.60419	0.802097	−	0.597194i	$-0.203718\pi$
$457$	34.2937	1.60419	0.802097	+	0.597194i	$0.203718\pi$
$458$	−26.9285	−1.25828
$459$	−1.84569	−0.0861492
$460$	−0.309523	−0.0144316
$461$	−6.78055	−0.315801	−0.157901	−	0.987455i	$-0.550473\pi$
$461$	−6.78055	−0.315801	−0.157901	+	0.987455i	$0.550473\pi$
$462$	7.90347	0.367703
$463$	34.7493	1.61494	0.807468	−	0.589912i	$-0.200838\pi$
$463$	34.7493	1.61494	0.807468	+	0.589912i	$0.200838\pi$
$464$	−16.9442	−0.786612
$465$	11.4294	0.530026
$466$	28.8700	1.33738
$467$	−33.4550	−1.54811	−0.774056	−	0.633117i	$-0.781775\pi$
$467$	−33.4550	−1.54811	−0.774056	+	0.633117i	$0.781775\pi$
$468$	0.556913	0.0257433
$469$	−17.1669	−0.792695
$470$	4.66777	0.215308
$471$	40.7323	1.87685
$472$	7.88291	0.362840
$473$	1.00000	0.0459800
$474$	31.0828	1.42768
$475$	−25.3233	−1.16191
$476$	1.70052	0.0779433
$477$	−21.3551	−0.977781
$478$	34.3854	1.57275
$479$	−19.7808	−0.903809	−0.451905	−	0.892066i	$-0.649255\pi$
$479$	−19.7808	−0.903809	−0.451905	+	0.892066i	$0.649255\pi$
$480$	−5.41015	−0.246938
$481$	−1.80727	−0.0824043
$482$	−16.3386	−0.744201
$483$	−5.44527	−0.247768
$484$	−0.648140	−0.0294609
$485$	0.777555	0.0353069
$486$	−25.5823	−1.16044
$487$	5.41960	0.245586	0.122793	−	0.992432i	$-0.460815\pi$
$487$	5.41960	0.245586	0.122793	+	0.992432i	$0.460815\pi$
$488$	4.52116	0.204663
$489$	31.0599	1.40458
$490$	−0.0805635	−0.00363949
$491$	38.9240	1.75662	0.878308	−	0.478095i	$-0.158673\pi$
$491$	38.9240	1.75662	0.878308	+	0.478095i	$0.158673\pi$
$492$	13.9941	0.630904
$493$	7.41982	0.334172
$494$	1.46724	0.0660144
$495$	2.21315	0.0994736
$496$	−16.8988	−0.758777
$497$	22.1510	0.993610
$498$	27.8366	1.24739
$499$	3.52197	0.157665	0.0788324	−	0.996888i	$-0.474881\pi$
$499$	3.52197	0.157665	0.0788324	+	0.996888i	$0.474881\pi$
$500$	−3.72658	−0.166658
$501$	56.8927	2.54178
$502$	−10.3969	−0.464035
$503$	22.1953	0.989639	0.494820	−	0.868996i	$-0.335234\pi$
$503$	22.1953	0.989639	0.494820	+	0.868996i	$0.335234\pi$
$504$	−29.9898	−1.33585
$505$	−3.68005	−0.163760
$506$	−0.931393	−0.0414055
$507$	33.5420	1.48965
$508$	−11.4829	−0.509472
$509$	26.2041	1.16148	0.580738	−	0.814091i	$-0.302764\pi$
$509$	26.2041	1.16148	0.580738	+	0.814091i	$0.302764\pi$
$510$	−1.79581	−0.0795200
$511$	13.6016	0.601699
$512$	22.0616	0.974995
$513$	−10.0631	−0.444295
$514$	9.09850	0.401317
$515$	−6.78669	−0.299057
$516$	−1.67922	−0.0739235
$517$	−6.73420	−0.296170
$518$	23.8197	1.04658
$519$	26.9864	1.18457
$520$	0.424843	0.0186306
$521$	43.7123	1.91507	0.957536	−	0.288314i	$-0.0930948\pi$
$521$	43.7123	1.91507	0.957536	+	0.288314i	$0.0930948\pi$
$522$	−32.0268	−1.40177
$523$	11.0083	0.481358	0.240679	−	0.970605i	$-0.422630\pi$
$523$	11.0083	0.481358	0.240679	+	0.970605i	$0.422630\pi$
$524$	−6.27426	−0.274093
$525$	−31.5719	−1.37791
$526$	−21.7338	−0.947639
$527$	7.39994	0.322347
$528$	−5.91651	−0.257483
$529$	−22.3583	−0.972100
$530$	−3.98721	−0.173193
$531$	9.50459	0.412464
$532$	9.27159	0.401974
$533$	−1.92887	−0.0835486
$534$	45.0393	1.94904
$535$	3.83068	0.165615
$536$	20.1459	0.870169
$537$	−13.9436	−0.601711
$538$	19.0466	0.821159
$539$	0.116229	0.00500635
$540$	−0.713154	−0.0306893
$541$	26.8980	1.15644	0.578218	−	0.815882i	$-0.303748\pi$
$541$	26.8980	1.15644	0.578218	+	0.815882i	$0.303748\pi$
$542$	−17.0507	−0.732392
$543$	−18.0232	−0.773451
$544$	−3.50279	−0.150181
$545$	2.12625	0.0910785
$546$	1.82929	0.0782863
$547$	−34.5903	−1.47898	−0.739488	−	0.673170i	$-0.764932\pi$
$547$	−34.5903	−1.47898	−0.739488	+	0.673170i	$0.764932\pi$
$548$	−4.67356	−0.199645
$549$	5.45127	0.232654
$550$	−5.40026	−0.230268
$551$	40.4544	1.72341
$552$	6.39017	0.271984
$553$	−27.0725	−1.15124
$554$	−16.8650	−0.716526
$555$	12.0602	0.511926
$556$	−0.458473	−0.0194436
$557$	−24.9950	−1.05907	−0.529536	−	0.848287i	$-0.677634\pi$
$557$	−24.9950	−1.05907	−0.529536	+	0.848287i	$0.677634\pi$
$558$	−31.9410	−1.35217
$559$	0.231454	0.00978945
$560$	−3.57188	−0.150939
$561$	2.59083	0.109385
$562$	−0.449777	−0.0189727
$563$	−12.3009	−0.518421	−0.259210	−	0.965821i	$-0.583462\pi$
$563$	−12.3009	−0.518421	−0.259210	+	0.965821i	$0.583462\pi$
$564$	11.3082	0.476161
$565$	3.07571	0.129396
$566$	−23.2950	−0.979164
$567$	16.6744	0.700260
$568$	−25.9949	−1.09072
$569$	−9.10135	−0.381548	−0.190774	−	0.981634i	$-0.561100\pi$
$569$	−9.10135	−0.381548	−0.190774	+	0.981634i	$0.561100\pi$
$570$	−9.79114	−0.410106
$571$	19.7276	0.825573	0.412787	−	0.910828i	$-0.364556\pi$
$571$	19.7276	0.825573	0.412787	+	0.910828i	$0.364556\pi$
$572$	−0.150014	−0.00627242
$573$	15.1736	0.633884
$574$	25.4224	1.06111
$575$	3.72062	0.155161
$576$	32.0749	1.33645
$577$	−31.5955	−1.31534	−0.657669	−	0.753307i	$-0.728458\pi$
$577$	−31.5955	−1.31534	−0.657669	+	0.753307i	$0.728458\pi$
$578$	−1.16270	−0.0483617
$579$	62.6935	2.60545
$580$	2.86694	0.119043
$581$	−24.2452	−1.00586
$582$	−3.92897	−0.162861
$583$	5.75237	0.238239
$584$	−15.9619	−0.660507
$585$	0.512242	0.0211786
$586$	−9.91440	−0.409560
$587$	−15.0937	−0.622983	−0.311492	−	0.950249i	$-0.600829\pi$
$587$	−15.0937	−0.622983	−0.311492	+	0.950249i	$0.600829\pi$
$588$	−0.195175	−0.00804886
$589$	40.3460	1.66243
$590$	1.77461	0.0730594
$591$	39.5989	1.62888
$592$	−17.8314	−0.732865
$593$	29.7512	1.22173	0.610867	−	0.791733i	$-0.290821\pi$
$593$	29.7512	1.22173	0.610867	+	0.791733i	$0.290821\pi$
$594$	−2.14597	−0.0880502
$595$	1.56412	0.0641227
$596$	2.52150	0.103285
$597$	−62.5681	−2.56074
$598$	−0.215575	−0.00881550
$599$	37.1485	1.51785	0.758924	−	0.651180i	$-0.225726\pi$
$599$	37.1485	1.51785	0.758924	+	0.651180i	$0.225726\pi$
$600$	37.0505	1.51258
$601$	−25.5044	−1.04035	−0.520173	−	0.854061i	$-0.674133\pi$
$601$	−25.5044	−1.04035	−0.520173	+	0.854061i	$0.674133\pi$
$602$	−3.05056	−0.124331
$603$	24.2903	0.989178
$604$	11.5710	0.470818
$605$	−0.596152	−0.0242370
$606$	18.5952	0.755379
$607$	0.600697	0.0243815	0.0121908	−	0.999926i	$-0.496119\pi$
$607$	0.600697	0.0243815	0.0121908	+	0.999926i	$0.496119\pi$
$608$	−19.0979	−0.774523
$609$	50.4365	2.04379
$610$	1.01781	0.0412099
$611$	−1.55866	−0.0630565
$612$	−2.40615	−0.0972628
$613$	−35.1364	−1.41914	−0.709572	−	0.704633i	$-0.751112\pi$
$613$	−35.1364	−1.41914	−0.709572	+	0.704633i	$0.751112\pi$
$614$	−32.0636	−1.29398
$615$	12.8716	0.519035
$616$	8.07830	0.325484
$617$	23.5064	0.946333	0.473166	−	0.880973i	$-0.343111\pi$
$617$	23.5064	0.946333	0.473166	+	0.880973i	$0.343111\pi$
$618$	34.2930	1.37947
$619$	−27.1244	−1.09022	−0.545110	−	0.838364i	$-0.683512\pi$
$619$	−27.1244	−1.09022	−0.545110	+	0.838364i	$0.683512\pi$
$620$	2.85926	0.114831
$621$	1.47851	0.0593307
$622$	29.7580	1.19319
$623$	−39.2284	−1.57165
$624$	−1.36940	−0.0548198
$625$	19.7954	0.791814
$626$	−9.24666	−0.369571
$627$	14.1257	0.564127
$628$	10.1899	0.406621
$629$	7.80833	0.311338
$630$	−6.75134	−0.268980
$631$	26.5249	1.05594	0.527969	−	0.849264i	$-0.322954\pi$
$631$	26.5249	1.05594	0.527969	+	0.849264i	$0.322954\pi$
$632$	31.7704	1.26376
$633$	25.0377	0.995157
$634$	−25.6235	−1.01764
$635$	−10.5619	−0.419134
$636$	−9.65949	−0.383024
$637$	0.0269017	0.00106589
$638$	8.62699	0.341546
$639$	−31.3426	−1.23989
$640$	1.81233	0.0716385
$641$	44.3646	1.75230	0.876148	−	0.482042i	$-0.160105\pi$
$641$	44.3646	1.75230	0.876148	+	0.482042i	$0.160105\pi$
$642$	−19.3563	−0.763934
$643$	28.8158	1.13639	0.568193	−	0.822895i	$-0.307643\pi$
$643$	28.8158	1.13639	0.568193	+	0.822895i	$0.307643\pi$
$644$	−1.36223	−0.0536792
$645$	−1.54453	−0.0608157
$646$	−6.33925	−0.249414
$647$	33.7673	1.32753	0.663764	−	0.747942i	$-0.268958\pi$
$647$	33.7673	1.32753	0.663764	+	0.747942i	$0.268958\pi$
$648$	−19.5679	−0.768700
$649$	−2.56023	−0.100498
$650$	−1.24991	−0.0490255
$651$	50.3014	1.97147
$652$	7.77016	0.304303
$653$	−43.7379	−1.71160	−0.855798	−	0.517310i	$-0.826933\pi$
$653$	−43.7379	−1.71160	−0.855798	+	0.517310i	$0.826933\pi$
$654$	−10.7439	−0.420119
$655$	−5.77100	−0.225491
$656$	−19.0311	−0.743041
$657$	−19.2456	−0.750841
$658$	20.5431	0.800852
$659$	23.6729	0.922166	0.461083	−	0.887357i	$-0.347461\pi$
$659$	23.6729	0.922166	0.461083	+	0.887357i	$0.347461\pi$
$660$	1.00107	0.0389666
$661$	−23.7498	−0.923759	−0.461879	−	0.886943i	$-0.652825\pi$
$661$	−23.7498	−0.923759	−0.461879	+	0.886943i	$0.652825\pi$
$662$	0.378827	0.0147235
$663$	0.599657	0.0232888
$664$	28.4524	1.10417
$665$	8.52790	0.330698
$666$	−33.7037	−1.30599
$667$	−5.94375	−0.230143
$668$	14.2327	0.550679
$669$	11.6590	0.450763
$670$	4.53526	0.175212
$671$	−1.46840	−0.0566868
$672$	−23.8103	−0.918504
$673$	1.07058	0.0412680	0.0206340	−	0.999787i	$-0.493432\pi$
$673$	1.07058	0.0412680	0.0206340	+	0.999787i	$0.493432\pi$
$674$	−4.38839	−0.169034
$675$	8.57248	0.329955
$676$	8.39110	0.322735
$677$	22.2830	0.856407	0.428204	−	0.903682i	$-0.359147\pi$
$677$	22.2830	0.856407	0.428204	+	0.903682i	$0.359147\pi$
$678$	−15.5415	−0.596869
$679$	3.42206	0.131327
$680$	−1.83554	−0.0703897
$681$	−15.7085	−0.601953
$682$	8.60388	0.329459
$683$	9.93446	0.380132	0.190066	−	0.981771i	$-0.439130\pi$
$683$	9.93446	0.380132	0.190066	+	0.981771i	$0.439130\pi$
$684$	−13.1188	−0.501611
$685$	−4.29869	−0.164244
$686$	−21.7085	−0.828833
$687$	−60.0046	−2.28932
$688$	2.28363	0.0870628
$689$	1.33141	0.0507226
$690$	1.43856	0.0547651
$691$	−23.6231	−0.898666	−0.449333	−	0.893364i	$-0.648338\pi$
$691$	−23.6231	−0.898666	−0.449333	+	0.893364i	$0.648338\pi$
$692$	6.75112	0.256639
$693$	9.74018	0.369999
$694$	−7.15702	−0.271677
$695$	−0.421699	−0.0159959
$696$	−59.1887	−2.24354
$697$	8.33371	0.315662
$698$	17.5620	0.664731
$699$	64.3310	2.43322
$700$	−7.89825	−0.298526
$701$	−18.1618	−0.685962	−0.342981	−	0.939342i	$-0.611437\pi$
$701$	−18.1618	−0.685962	−0.342981	+	0.939342i	$0.611437\pi$
$702$	−0.496693	−0.0187465
$703$	42.5726	1.60566
$704$	−8.63994	−0.325630
$705$	10.4012	0.391730
$706$	−30.5524	−1.14986
$707$	−16.1961	−0.609116
$708$	4.29919	0.161574
$709$	−13.9237	−0.522916	−0.261458	−	0.965215i	$-0.584203\pi$
$709$	−13.9237	−0.522916	−0.261458	+	0.965215i	$0.584203\pi$
$710$	−5.85199	−0.219621
$711$	38.3062	1.43659
$712$	46.0356	1.72526
$713$	−5.92783	−0.221999
$714$	−7.90347	−0.295780
$715$	−0.137982	−0.00516022
$716$	−3.48823	−0.130361
$717$	76.6207	2.86145
$718$	−7.13559	−0.266298
$719$	−27.8121	−1.03722	−0.518609	−	0.855012i	$-0.673550\pi$
$719$	−27.8121	−1.03722	−0.518609	+	0.855012i	$0.673550\pi$
$720$	5.05402	0.188352
$721$	−29.8686	−1.11236
$722$	−12.4717	−0.464148
$723$	−36.4071	−1.35400
$724$	−4.50882	−0.167569
$725$	−34.4621	−1.27989
$726$	3.01234	0.111799
$727$	39.5237	1.46585	0.732927	−	0.680307i	$-0.238154\pi$
$727$	39.5237	1.46585	0.732927	+	0.680307i	$0.238154\pi$
$728$	1.86975	0.0692977
$729$	−37.9390	−1.40515
$730$	−3.59335	−0.132996
$731$	−1.00000	−0.0369863
$732$	2.46576	0.0911371
$733$	−32.7661	−1.21024	−0.605121	−	0.796133i	$-0.706875\pi$
$733$	−32.7661	−1.21024	−0.605121	+	0.796133i	$0.706875\pi$
$734$	37.1131	1.36987
$735$	−0.179519	−0.00662167
$736$	2.80596	0.103429
$737$	−6.54304	−0.241016
$738$	−35.9715	−1.32413
$739$	49.3193	1.81424	0.907119	−	0.420874i	$-0.138277\pi$
$739$	49.3193	1.81424	0.907119	+	0.420874i	$0.138277\pi$
$740$	3.01706	0.110909
$741$	3.26945	0.120106
$742$	−17.5479	−0.644205
$743$	−52.1237	−1.91223	−0.956117	−	0.292985i	$-0.905351\pi$
$743$	−52.1237	−1.91223	−0.956117	+	0.292985i	$0.905351\pi$
$744$	−59.0301	−2.16415
$745$	2.31925	0.0849708
$746$	15.9960	0.585655
$747$	34.3057	1.25518
$748$	0.648140	0.0236983
$749$	16.8590	0.616015
$750$	17.3199	0.632434
$751$	−28.6005	−1.04365	−0.521824	−	0.853053i	$-0.674748\pi$
$751$	−28.6005	−1.04365	−0.521824	+	0.853053i	$0.674748\pi$
$752$	−15.3785	−0.560795
$753$	−23.1673	−0.844263
$754$	1.99675	0.0727173
$755$	10.6429	0.387334
$756$	−3.13863	−0.114151
$757$	19.3980	0.705032	0.352516	−	0.935806i	$-0.385326\pi$
$757$	19.3980	0.705032	0.352516	+	0.935806i	$0.385326\pi$
$758$	−19.9651	−0.725166
$759$	−2.07542	−0.0753330
$760$	−10.0077	−0.363019
$761$	11.8835	0.430776	0.215388	−	0.976529i	$-0.430898\pi$
$761$	11.8835	0.430776	0.215388	+	0.976529i	$0.430898\pi$
$762$	53.3688	1.93335
$763$	9.35773	0.338772
$764$	3.79592	0.137332
$765$	−2.21315	−0.0800166
$766$	−21.4513	−0.775068
$767$	−0.592576	−0.0213967
$768$	35.6116	1.28502
$769$	−0.679268	−0.0244950	−0.0122475	−	0.999925i	$-0.503899\pi$
$769$	−0.679268	−0.0244950	−0.0122475	+	0.999925i	$0.503899\pi$
$770$	1.81859	0.0655376
$771$	20.2741	0.730155
$772$	15.6838	0.564474
$773$	50.9902	1.83399	0.916995	−	0.398898i	$-0.130607\pi$
$773$	50.9902	1.83399	0.916995	+	0.398898i	$0.130607\pi$
$774$	4.31638	0.155149
$775$	−34.3698	−1.23460
$776$	−4.01588	−0.144162
$777$	53.0774	1.90414
$778$	−4.66875	−0.167383
$779$	45.4371	1.62795
$780$	0.231701	0.00829624
$781$	8.44269	0.302103
$782$	0.931393	0.0333066
$783$	−13.6946	−0.489407
$784$	0.265425	0.00947948
$785$	9.37254	0.334520
$786$	29.1607	1.04013
$787$	−12.3225	−0.439250	−0.219625	−	0.975584i	$-0.570483\pi$
$787$	−12.3225	−0.439250	−0.219625	+	0.975584i	$0.570483\pi$
$788$	9.90634	0.352899
$789$	−48.4293	−1.72413
$790$	7.15217	0.254463
$791$	13.5364	0.481298
$792$	−11.4304	−0.406161
$793$	−0.339866	−0.0120690
$794$	30.0245	1.06553
$795$	−8.88469	−0.315107
$796$	−15.6525	−0.554787
$797$	−52.7088	−1.86704	−0.933521	−	0.358522i	$-0.883281\pi$
$797$	−52.7088	−1.86704	−0.933521	+	0.358522i	$0.883281\pi$
$798$	−43.0913	−1.52542
$799$	6.73420	0.238239
$800$	16.2691	0.575198
$801$	55.5061	1.96121
$802$	27.0648	0.955692
$803$	5.18414	0.182944
$804$	10.9872	0.387489
$805$	−1.25296	−0.0441610
$806$	1.99140	0.0701441
$807$	42.4415	1.49401
$808$	19.0065	0.668648
$809$	25.7570	0.905567	0.452784	−	0.891620i	$-0.350431\pi$
$809$	25.7570	0.905567	0.452784	+	0.891620i	$0.350431\pi$
$810$	−4.40514	−0.154781
$811$	22.0913	0.775731	0.387865	−	0.921716i	$-0.373213\pi$
$811$	22.0913	0.775731	0.387865	+	0.921716i	$0.373213\pi$
$812$	12.6176	0.442789
$813$	−37.9941	−1.33251
$814$	9.07871	0.318209
$815$	7.14691	0.250345
$816$	5.91651	0.207119
$817$	−5.45220	−0.190748
$818$	33.7626	1.18048
$819$	2.25440	0.0787752
$820$	3.22006	0.112449
$821$	46.8725	1.63586	0.817931	−	0.575316i	$-0.195121\pi$
$821$	46.8725	1.63586	0.817931	+	0.575316i	$0.195121\pi$
$822$	21.7212	0.757613
$823$	−19.2999	−0.672753	−0.336376	−	0.941728i	$-0.609201\pi$
$823$	−19.2999	−0.672753	−0.336376	+	0.941728i	$0.609201\pi$
$824$	35.0516	1.22108
$825$	−12.0334	−0.418948
$826$	7.81014	0.271749
$827$	−40.7983	−1.41869	−0.709347	−	0.704859i	$-0.751010\pi$
$827$	−40.7983	−1.41869	−0.709347	+	0.704859i	$0.751010\pi$
$828$	1.92748	0.0669846
$829$	51.3742	1.78430	0.892149	−	0.451741i	$-0.149197\pi$
$829$	51.3742	1.78430	0.892149	+	0.451741i	$0.149197\pi$
$830$	6.40523	0.222329
$831$	−37.5803	−1.30365
$832$	−1.99975	−0.0693288
$833$	−0.116229	−0.00402711
$834$	2.13084	0.0737848
$835$	13.0911	0.453035
$836$	3.53379	0.122219
$837$	−13.6580	−0.472088
$838$	18.2107	0.629078
$839$	−5.34428	−0.184505	−0.0922524	−	0.995736i	$-0.529407\pi$
$839$	−5.34428	−0.184505	−0.0922524	+	0.995736i	$0.529407\pi$
$840$	−12.4772	−0.430503
$841$	26.0537	0.898403
$842$	−23.2813	−0.802327
$843$	−1.00224	−0.0345189
$844$	6.26360	0.215602
$845$	7.71804	0.265509
$846$	−29.0674	−0.999357
$847$	−2.62369	−0.0901512
$848$	13.1363	0.451103
$849$	−51.9082	−1.78149
$850$	5.40026	0.185227
$851$	−6.25497	−0.214418
$852$	−14.1771	−0.485700
$853$	−12.3481	−0.422790	−0.211395	−	0.977401i	$-0.567801\pi$
$853$	−12.3481	−0.422790	−0.211395	+	0.977401i	$0.567801\pi$
$854$	4.47943	0.153283
$855$	−12.0665	−0.412667
$856$	−19.7845	−0.676221
$857$	9.74502	0.332883	0.166442	−	0.986051i	$-0.446772\pi$
$857$	9.74502	0.332883	0.166442	+	0.986051i	$0.446772\pi$
$858$	0.697218	0.0238026
$859$	40.8621	1.39420	0.697099	−	0.716975i	$-0.254474\pi$
$859$	40.8621	1.39420	0.697099	+	0.716975i	$0.254474\pi$
$860$	−0.386390	−0.0131758
$861$	56.6487	1.93058
$862$	−25.3314	−0.862792
$863$	0.271981	0.00925834	0.00462917	−	0.999989i	$-0.498526\pi$
$863$	0.271981	0.00925834	0.00462917	+	0.999989i	$0.498526\pi$
$864$	6.46505	0.219945
$865$	6.20960	0.211133
$866$	28.4685	0.967398
$867$	−2.59083	−0.0879891
$868$	12.5838	0.427121
$869$	−10.3185	−0.350030
$870$	−13.3246	−0.451747
$871$	−1.51441	−0.0513139
$872$	−10.9816	−0.371882
$873$	−4.84204	−0.163878
$874$	5.07815	0.171771
$875$	−15.0853	−0.509977
$876$	−8.70531	−0.294125
$877$	−48.8420	−1.64928	−0.824639	−	0.565659i	$-0.808622\pi$
$877$	−48.8420	−1.64928	−0.824639	+	0.565659i	$0.808622\pi$
$878$	−7.05192	−0.237991
$879$	−22.0922	−0.745152
$880$	−1.36139	−0.0458925
$881$	−50.0620	−1.68663	−0.843315	−	0.537419i	$-0.819399\pi$
$881$	−50.0620	−1.68663	−0.843315	+	0.537419i	$0.819399\pi$
$882$	0.501690	0.0168928
$883$	25.2906	0.851097	0.425549	−	0.904936i	$-0.360081\pi$
$883$	25.2906	0.851097	0.425549	+	0.904936i	$0.360081\pi$
$884$	0.150014	0.00504553
$885$	3.95435	0.132924
$886$	−3.58305	−0.120375
$887$	−14.3618	−0.482222	−0.241111	−	0.970498i	$-0.577512\pi$
$887$	−14.3618	−0.482222	−0.241111	+	0.970498i	$0.577512\pi$
$888$	−62.2879	−2.09024
$889$	−46.4832	−1.55900
$890$	10.3636	0.347388
$891$	6.35532	0.212911
$892$	2.91670	0.0976582
$893$	36.7163	1.22866
$894$	−11.7191	−0.391946
$895$	−3.20844	−0.107246
$896$	7.97615	0.266464
$897$	−0.480364	−0.0160389
$898$	−30.0832	−1.00389
$899$	54.9062	1.83122
$900$	11.1756	0.372520
$901$	−5.75237	−0.191639
$902$	9.68956	0.322627
$903$	−6.79754	−0.226208
$904$	−15.8853	−0.528338
$905$	−4.14716	−0.137856
$906$	−53.7783	−1.78666
$907$	−9.37018	−0.311132	−0.155566	−	0.987826i	$-0.549720\pi$
$907$	−9.37018	−0.311132	−0.155566	+	0.987826i	$0.549720\pi$
$908$	−3.92976	−0.130414
$909$	22.9166	0.760096
$910$	0.420921	0.0139534
$911$	34.1438	1.13124	0.565618	−	0.824667i	$-0.308638\pi$
$911$	34.1438	1.13124	0.565618	+	0.824667i	$0.308638\pi$
$912$	32.2580	1.06817
$913$	−9.24085	−0.305828
$914$	−39.8732	−1.31889
$915$	2.26798	0.0749771
$916$	−15.0112	−0.495983
$917$	−25.3984	−0.838731
$918$	2.14597	0.0708276
$919$	29.3795	0.969139	0.484569	−	0.874753i	$-0.338976\pi$
$919$	29.3795	0.969139	0.484569	+	0.874753i	$0.338976\pi$
$920$	1.47038	0.0484771
$921$	−71.4473	−2.35427
$922$	7.88371	0.259636
$923$	1.95409	0.0643197
$924$	4.40576	0.144939
$925$	−36.2666	−1.19244
$926$	−40.4028	−1.32772
$927$	42.2625	1.38808
$928$	−25.9900	−0.853165
$929$	−19.0871	−0.626227	−0.313114	−	0.949716i	$-0.601372\pi$
$929$	−19.0871	−0.626227	−0.313114	+	0.949716i	$0.601372\pi$
$930$	−13.2889	−0.435761
$931$	−0.633706	−0.0207689
$932$	16.0935	0.527160
$933$	66.3096	2.17088
$934$	38.8980	1.27278
$935$	0.596152	0.0194962
$936$	−2.64560	−0.0864743
$937$	−52.9461	−1.72968	−0.864838	−	0.502052i	$-0.832579\pi$
$937$	−52.9461	−1.72968	−0.864838	+	0.502052i	$0.832579\pi$
$938$	19.9599	0.651714
$939$	−20.6043	−0.672396
$940$	2.60203	0.0848688
$941$	−46.8683	−1.52786	−0.763931	−	0.645298i	$-0.776733\pi$
$941$	−46.8683	−1.52786	−0.763931	+	0.645298i	$0.776733\pi$
$942$	−47.3593	−1.54305
$943$	−6.67583	−0.217395
$944$	−5.84664	−0.190292
$945$	−2.88687	−0.0939100
$946$	−1.16270	−0.0378025
$947$	39.4690	1.28257	0.641285	−	0.767303i	$-0.278402\pi$
$947$	39.4690	1.28257	0.641285	+	0.767303i	$0.278402\pi$
$948$	17.3270	0.562754
$949$	1.19989	0.0389500
$950$	29.4433	0.955267
$951$	−57.0967	−1.85149
$952$	−8.07830	−0.261819
$953$	9.22359	0.298781	0.149391	−	0.988778i	$-0.452269\pi$
$953$	9.22359	0.298781	0.149391	+	0.988778i	$0.452269\pi$
$954$	24.8294	0.803882
$955$	3.49145	0.112981
$956$	19.1680	0.619937
$957$	19.2235	0.621407
$958$	22.9991	0.743066
$959$	−18.9187	−0.610918
$960$	13.3446	0.430696
$961$	23.7591	0.766424
$962$	2.10130	0.0677487
$963$	−23.8546	−0.768705
$964$	−9.10787	−0.293345
$965$	14.4258	0.464384
$966$	6.33118	0.203703
$967$	−40.7009	−1.30885	−0.654426	−	0.756126i	$-0.727090\pi$
$967$	−40.7009	−1.30885	−0.654426	+	0.756126i	$0.727090\pi$
$968$	3.07898	0.0989621
$969$	−14.1257	−0.453784
$970$	−0.904059	−0.0290276
$971$	6.48630	0.208155	0.104078	−	0.994569i	$-0.466811\pi$
$971$	6.48630	0.208155	0.104078	+	0.994569i	$0.466811\pi$
$972$	−14.2608	−0.457414
$973$	−1.85592	−0.0594980
$974$	−6.30134	−0.201908
$975$	−2.78517	−0.0891968
$976$	−3.35328	−0.107336
$977$	49.6822	1.58947	0.794737	−	0.606954i	$-0.207609\pi$
$977$	49.6822	1.58947	0.794737	+	0.606954i	$0.207609\pi$
$978$	−36.1132	−1.15477
$979$	−14.9516	−0.477854
$980$	−0.0449098	−0.00143459
$981$	−13.2407	−0.422743
$982$	−45.2568	−1.44420
$983$	−49.9529	−1.59325	−0.796625	−	0.604473i	$-0.793384\pi$
$983$	−49.9529	−1.59325	−0.796625	+	0.604473i	$0.793384\pi$
$984$	−66.4789	−2.11927
$985$	9.11174	0.290324
$986$	−8.62699	−0.274739
$987$	45.7760	1.45707
$988$	0.817910	0.0260212
$989$	0.801064	0.0254724
$990$	−2.57322	−0.0817822
$991$	−14.0325	−0.445757	−0.222879	−	0.974846i	$-0.571545\pi$
$991$	−14.0325	−0.445757	−0.222879	+	0.974846i	$0.571545\pi$
$992$	−25.9204	−0.822975
$993$	0.844138	0.0267879
$994$	−25.7549	−0.816896
$995$	−14.3970	−0.456414
$996$	15.5174	0.491688
$997$	41.7100	1.32097	0.660485	−	0.750840i	$-0.270351\pi$
$997$	41.7100	1.32097	0.660485	+	0.750840i	$0.270351\pi$
$998$	−4.09497	−0.129624
$999$	−14.4117	−0.455967

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.f.1.20	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.f.1.20	✓	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)

\(f(q)\)	\(=\)	\(q-1.16270 q^{2} -2.59083 q^{3} -0.648140 q^{4} -0.596152 q^{5} +3.01234 q^{6} -2.62369 q^{7} +3.07898 q^{8} +3.71239 q^{9} +O(q^{10})\)	\(q-1.16270 q^{2} -2.59083 q^{3} -0.648140 q^{4} -0.596152 q^{5} +3.01234 q^{6} -2.62369 q^{7} +3.07898 q^{8} +3.71239 q^{9} +0.693143 q^{10} -1.00000 q^{11} +1.67922 q^{12} -0.231454 q^{13} +3.05056 q^{14} +1.54453 q^{15} -2.28363 q^{16} +1.00000 q^{17} -4.31638 q^{18} +5.45220 q^{19} +0.386390 q^{20} +6.79754 q^{21} +1.16270 q^{22} -0.801064 q^{23} -7.97711 q^{24} -4.64460 q^{25} +0.269110 q^{26} -1.84569 q^{27} +1.70052 q^{28} +7.41982 q^{29} -1.79581 q^{30} +7.39994 q^{31} -3.50279 q^{32} +2.59083 q^{33} -1.16270 q^{34} +1.56412 q^{35} -2.40615 q^{36} +7.80833 q^{37} -6.33925 q^{38} +0.599657 q^{39} -1.83554 q^{40} +8.33371 q^{41} -7.90347 q^{42} -1.00000 q^{43} +0.648140 q^{44} -2.21315 q^{45} +0.931393 q^{46} +6.73420 q^{47} +5.91651 q^{48} -0.116229 q^{49} +5.40026 q^{50} -2.59083 q^{51} +0.150014 q^{52} -5.75237 q^{53} +2.14597 q^{54} +0.596152 q^{55} -8.07830 q^{56} -14.1257 q^{57} -8.62699 q^{58} +2.56023 q^{59} -1.00107 q^{60} +1.46840 q^{61} -8.60388 q^{62} -9.74018 q^{63} +8.63994 q^{64} +0.137982 q^{65} -3.01234 q^{66} +6.54304 q^{67} -0.648140 q^{68} +2.07542 q^{69} -1.81859 q^{70} -8.44269 q^{71} +11.4304 q^{72} -5.18414 q^{73} -9.07871 q^{74} +12.0334 q^{75} -3.53379 q^{76} +2.62369 q^{77} -0.697218 q^{78} +10.3185 q^{79} +1.36139 q^{80} -6.35532 q^{81} -9.68956 q^{82} +9.24085 q^{83} -4.40576 q^{84} -0.596152 q^{85} +1.16270 q^{86} -19.2235 q^{87} -3.07898 q^{88} +14.9516 q^{89} +2.57322 q^{90} +0.607264 q^{91} +0.519202 q^{92} -19.1720 q^{93} -7.82983 q^{94} -3.25034 q^{95} +9.07512 q^{96} -1.30429 q^{97} +0.135139 q^{98} -3.71239 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) \) 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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