LMFDB - Embedded newform 8041.2.a.f.1.12

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			1.12
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)

$f(q)$	$=$	$q-1.88001 q^{2} -1.81223 q^{3} +1.53444 q^{4} +2.13867 q^{5} +3.40702 q^{6} +1.99941 q^{7} +0.875255 q^{8} +0.284183 q^{9} +O(q^{10})$	\(q-1.88001 q^{2} -1.81223 q^{3} +1.53444 q^{4} +2.13867 q^{5} +3.40702 q^{6} +1.99941 q^{7} +0.875255 q^{8} +0.284183 q^{9} -4.02072 q^{10} -1.00000 q^{11} -2.78076 q^{12} +4.25393 q^{13} -3.75891 q^{14} -3.87576 q^{15} -4.71437 q^{16} +1.00000 q^{17} -0.534267 q^{18} -0.707473 q^{19} +3.28166 q^{20} -3.62339 q^{21} +1.88001 q^{22} -3.06526 q^{23} -1.58616 q^{24} -0.426098 q^{25} -7.99743 q^{26} +4.92169 q^{27} +3.06798 q^{28} -5.23837 q^{29} +7.28648 q^{30} -5.06928 q^{31} +7.11256 q^{32} +1.81223 q^{33} -1.88001 q^{34} +4.27607 q^{35} +0.436062 q^{36} +0.886799 q^{37} +1.33006 q^{38} -7.70910 q^{39} +1.87188 q^{40} -11.8879 q^{41} +6.81202 q^{42} -1.00000 q^{43} -1.53444 q^{44} +0.607772 q^{45} +5.76272 q^{46} -0.190411 q^{47} +8.54353 q^{48} -3.00236 q^{49} +0.801069 q^{50} -1.81223 q^{51} +6.52740 q^{52} +0.911927 q^{53} -9.25283 q^{54} -2.13867 q^{55} +1.74999 q^{56} +1.28211 q^{57} +9.84818 q^{58} +14.1241 q^{59} -5.94713 q^{60} -3.89447 q^{61} +9.53030 q^{62} +0.568198 q^{63} -3.94295 q^{64} +9.09774 q^{65} -3.40702 q^{66} +0.454713 q^{67} +1.53444 q^{68} +5.55496 q^{69} -8.03907 q^{70} -7.59083 q^{71} +0.248732 q^{72} -1.67046 q^{73} -1.66719 q^{74} +0.772188 q^{75} -1.08558 q^{76} -1.99941 q^{77} +14.4932 q^{78} -11.5452 q^{79} -10.0825 q^{80} -9.77179 q^{81} +22.3494 q^{82} +12.0546 q^{83} -5.55989 q^{84} +2.13867 q^{85} +1.88001 q^{86} +9.49313 q^{87} -0.875255 q^{88} +2.13778 q^{89} -1.14262 q^{90} +8.50534 q^{91} -4.70346 q^{92} +9.18671 q^{93} +0.357975 q^{94} -1.51305 q^{95} -12.8896 q^{96} +13.1998 q^{97} +5.64447 q^{98} -0.284183 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.88001	−1.32937	−0.664684	−	0.747124i	$-0.731434\pi$
$2$	−1.88001	−1.32937	−0.664684	+	0.747124i	$0.731434\pi$
$3$	−1.81223	−1.04629	−0.523146	−	0.852243i	$-0.675242\pi$
$3$	−1.81223	−1.04629	−0.523146	+	0.852243i	$0.675242\pi$
$4$	1.53444	0.767221
$5$	2.13867	0.956442	0.478221	−	0.878240i	$-0.341282\pi$
$5$	2.13867	0.956442	0.478221	+	0.878240i	$0.341282\pi$
$6$	3.40702	1.39091
$7$	1.99941	0.755706	0.377853	−	0.925866i	$-0.376662\pi$
$7$	1.99941	0.755706	0.377853	+	0.925866i	$0.376662\pi$
$8$	0.875255	0.309449
$9$	0.284183	0.0947275
$10$	−4.02072	−1.27146
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.78076	−0.802737
$13$	4.25393	1.17983	0.589914	−	0.807466i	$-0.299162\pi$
$13$	4.25393	1.17983	0.589914	+	0.807466i	$0.299162\pi$
$14$	−3.75891	−1.00461
$15$	−3.87576	−1.00072
$16$	−4.71437	−1.17859
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.534267	−0.125928
$19$	−0.707473	−0.162306	−0.0811528	−	0.996702i	$-0.525860\pi$
$19$	−0.707473	−0.162306	−0.0811528	+	0.996702i	$0.525860\pi$
$20$	3.28166	0.733802
$21$	−3.62339	−0.790689
$22$	1.88001	0.400820
$23$	−3.06526	−0.639151	−0.319575	−	0.947561i	$-0.603540\pi$
$23$	−3.06526	−0.639151	−0.319575	+	0.947561i	$0.603540\pi$
$24$	−1.58616	−0.323774
$25$	−0.426098	−0.0852196
$26$	−7.99743	−1.56843
$27$	4.92169	0.947180
$28$	3.06798	0.579793
$29$	−5.23837	−0.972740	−0.486370	−	0.873753i	$-0.661679\pi$
$29$	−5.23837	−0.972740	−0.486370	+	0.873753i	$0.661679\pi$
$30$	7.28648	1.33032
$31$	−5.06928	−0.910470	−0.455235	−	0.890371i	$-0.650445\pi$
$31$	−5.06928	−0.910470	−0.455235	+	0.890371i	$0.650445\pi$
$32$	7.11256	1.25734
$33$	1.81223	0.315469
$34$	−1.88001	−0.322419
$35$	4.27607	0.722788
$36$	0.436062	0.0726770
$37$	0.886799	0.145789	0.0728944	−	0.997340i	$-0.476776\pi$
$37$	0.886799	0.145789	0.0728944	+	0.997340i	$0.476776\pi$
$38$	1.33006	0.215764
$39$	−7.70910	−1.23444
$40$	1.87188	0.295970
$41$	−11.8879	−1.85658	−0.928292	−	0.371853i	$-0.878722\pi$
$41$	−11.8879	−1.85658	−0.928292	+	0.371853i	$0.878722\pi$
$42$	6.81202	1.05112
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−1.53444	−0.231326
$45$	0.607772	0.0906014
$46$	5.76272	0.849667
$47$	−0.190411	−0.0277743	−0.0138871	−	0.999904i	$-0.504421\pi$
$47$	−0.190411	−0.0277743	−0.0138871	+	0.999904i	$0.504421\pi$
$48$	8.54353	1.23315
$49$	−3.00236	−0.428909
$50$	0.801069	0.113288
$51$	−1.81223	−0.253763
$52$	6.52740	0.905188
$53$	0.911927	0.125263	0.0626314	−	0.998037i	$-0.480051\pi$
$53$	0.911927	0.125263	0.0626314	+	0.998037i	$0.480051\pi$
$54$	−9.25283	−1.25915
$55$	−2.13867	−0.288378
$56$	1.74999	0.233853
$57$	1.28211	0.169819
$58$	9.84818	1.29313
$59$	14.1241	1.83880	0.919399	−	0.393326i	$-0.128676\pi$
$59$	14.1241	1.83880	0.919399	+	0.393326i	$0.128676\pi$
$60$	−5.94713	−0.767771
$61$	−3.89447	−0.498636	−0.249318	−	0.968422i	$-0.580206\pi$
$61$	−3.89447	−0.498636	−0.249318	+	0.968422i	$0.580206\pi$
$62$	9.53030	1.21035
$63$	0.568198	0.0715862
$64$	−3.94295	−0.492869
$65$	9.09774	1.12844
$66$	−3.40702	−0.419375
$67$	0.454713	0.0555520	0.0277760	−	0.999614i	$-0.491157\pi$
$67$	0.454713	0.0555520	0.0277760	+	0.999614i	$0.491157\pi$
$68$	1.53444	0.186078
$69$	5.55496	0.668739
$70$	−8.03907	−0.960852
$71$	−7.59083	−0.900866	−0.450433	−	0.892810i	$-0.648730\pi$
$71$	−7.59083	−0.900866	−0.450433	+	0.892810i	$0.648730\pi$
$72$	0.248732	0.0293134
$73$	−1.67046	−0.195512	−0.0977561	−	0.995210i	$-0.531166\pi$
$73$	−1.67046	−0.195512	−0.0977561	+	0.995210i	$0.531166\pi$
$74$	−1.66719	−0.193807
$75$	0.772188	0.0891646
$76$	−1.08558	−0.124524
$77$	−1.99941	−0.227854
$78$	14.4932	1.64103
$79$	−11.5452	−1.29894	−0.649470	−	0.760387i	$-0.725009\pi$
$79$	−11.5452	−1.29894	−0.649470	+	0.760387i	$0.725009\pi$
$80$	−10.0825	−1.12726
$81$	−9.77179	−1.08575
$82$	22.3494	2.46808
$83$	12.0546	1.32316	0.661580	−	0.749874i	$-0.269886\pi$
$83$	12.0546	1.32316	0.661580	+	0.749874i	$0.269886\pi$
$84$	−5.55989	−0.606633
$85$	2.13867	0.231971
$86$	1.88001	0.202727
$87$	9.49313	1.01777
$88$	−0.875255	−0.0933025
$89$	2.13778	0.226604	0.113302	−	0.993561i	$-0.463857\pi$
$89$	2.13778	0.226604	0.113302	+	0.993561i	$0.463857\pi$
$90$	−1.14262	−0.120443
$91$	8.50534	0.891602
$92$	−4.70346	−0.490370
$93$	9.18671	0.952617
$94$	0.357975	0.0369223
$95$	−1.51305	−0.155236
$96$	−12.8896	−1.31554
$97$	13.1998	1.34023	0.670117	−	0.742255i	$-0.266244\pi$
$97$	13.1998	1.34023	0.670117	+	0.742255i	$0.266244\pi$
$98$	5.64447	0.570178
$99$	−0.284183	−0.0285614
$100$	−0.653823	−0.0653823
$101$	10.8530	1.07992	0.539959	−	0.841691i	$-0.318440\pi$
$101$	10.8530	1.07992	0.539959	+	0.841691i	$0.318440\pi$
$102$	3.40702	0.337345
$103$	3.80038	0.374462	0.187231	−	0.982316i	$-0.440049\pi$
$103$	3.80038	0.374462	0.187231	+	0.982316i	$0.440049\pi$
$104$	3.72327	0.365097
$105$	−7.74924	−0.756248
$106$	−1.71443	−0.166520
$107$	16.1824	1.56441	0.782204	−	0.623023i	$-0.214096\pi$
$107$	16.1824	1.56441	0.782204	+	0.623023i	$0.214096\pi$
$108$	7.55205	0.726696
$109$	6.45509	0.618285	0.309143	−	0.951016i	$-0.399958\pi$
$109$	6.45509	0.618285	0.309143	+	0.951016i	$0.399958\pi$
$110$	4.02072	0.383361
$111$	−1.60708	−0.152538
$112$	−9.42596	−0.890670
$113$	−3.33175	−0.313425	−0.156712	−	0.987644i	$-0.550090\pi$
$113$	−3.33175	−0.313425	−0.156712	+	0.987644i	$0.550090\pi$
$114$	−2.41037	−0.225752
$115$	−6.55557	−0.611310
$116$	−8.03797	−0.746306
$117$	1.20889	0.111762
$118$	−26.5534	−2.44444
$119$	1.99941	0.183286
$120$	−3.39228	−0.309671
$121$	1.00000	0.0909091
$122$	7.32164	0.662871
$123$	21.5437	1.94253
$124$	−7.77852	−0.698531
$125$	−11.6046	−1.03795
$126$	−1.06822	−0.0951644
$127$	9.83546	0.872756	0.436378	−	0.899764i	$-0.356261\pi$
$127$	9.83546	0.872756	0.436378	+	0.899764i	$0.356261\pi$
$128$	−6.81233	−0.602131
$129$	1.81223	0.159558
$130$	−17.1039	−1.50011
$131$	−5.04454	−0.440744	−0.220372	−	0.975416i	$-0.570727\pi$
$131$	−5.04454	−0.440744	−0.220372	+	0.975416i	$0.570727\pi$
$132$	2.78076	0.242034
$133$	−1.41453	−0.122655
$134$	−0.854865	−0.0738491
$135$	10.5259	0.905922
$136$	0.875255	0.0750525
$137$	21.0364	1.79726	0.898629	−	0.438709i	$-0.144564\pi$
$137$	21.0364	1.79726	0.898629	+	0.438709i	$0.144564\pi$
$138$	−10.4434	−0.889000
$139$	−5.97666	−0.506934	−0.253467	−	0.967344i	$-0.581571\pi$
$139$	−5.97666	−0.506934	−0.253467	+	0.967344i	$0.581571\pi$
$140$	6.56139	0.554538
$141$	0.345069	0.0290600
$142$	14.2708	1.19758
$143$	−4.25393	−0.355731
$144$	−1.33974	−0.111645
$145$	−11.2031	−0.930369
$146$	3.14048	0.259908
$147$	5.44097	0.448764
$148$	1.36074	0.111852
$149$	14.1709	1.16092	0.580462	−	0.814288i	$-0.302872\pi$
$149$	14.1709	1.16092	0.580462	+	0.814288i	$0.302872\pi$
$150$	−1.45172	−0.118533
$151$	−5.94204	−0.483557	−0.241778	−	0.970332i	$-0.577731\pi$
$151$	−5.94204	−0.483557	−0.241778	+	0.970332i	$0.577731\pi$
$152$	−0.619219	−0.0502253
$153$	0.284183	0.0229748
$154$	3.75891	0.302902
$155$	−10.8415	−0.870811
$156$	−11.8292	−0.947091
$157$	14.5051	1.15763	0.578817	−	0.815457i	$-0.303515\pi$
$157$	14.5051	1.15763	0.578817	+	0.815457i	$0.303515\pi$
$158$	21.7052	1.72677
$159$	−1.65262	−0.131062
$160$	15.2114	1.20257
$161$	−6.12871	−0.483010
$162$	18.3711	1.44337
$163$	11.6991	0.916347	0.458174	−	0.888863i	$-0.348504\pi$
$163$	11.6991	0.916347	0.458174	+	0.888863i	$0.348504\pi$
$164$	−18.2413	−1.42441
$165$	3.87576	0.301728
$166$	−22.6627	−1.75897
$167$	7.55035	0.584263	0.292132	−	0.956378i	$-0.405635\pi$
$167$	7.55035	0.584263	0.292132	+	0.956378i	$0.405635\pi$
$168$	−3.17139	−0.244678
$169$	5.09590	0.391992
$170$	−4.02072	−0.308375
$171$	−0.201052	−0.0153748
$172$	−1.53444	−0.117000
$173$	19.1551	1.45633	0.728166	−	0.685400i	$-0.240373\pi$
$173$	19.1551	1.45633	0.728166	+	0.685400i	$0.240373\pi$
$174$	−17.8472	−1.35299
$175$	−0.851944	−0.0644009
$176$	4.71437	0.355359
$177$	−25.5961	−1.92392
$178$	−4.01905	−0.301240
$179$	13.1573	0.983425	0.491713	−	0.870758i	$-0.336371\pi$
$179$	13.1573	0.983425	0.491713	+	0.870758i	$0.336371\pi$
$180$	0.932591	0.0695113
$181$	−17.9342	−1.33304	−0.666521	−	0.745487i	$-0.732217\pi$
$181$	−17.9342	−1.33304	−0.666521	+	0.745487i	$0.732217\pi$
$182$	−15.9901	−1.18527
$183$	7.05768	0.521719
$184$	−2.68288	−0.197785
$185$	1.89657	0.139439
$186$	−17.2711	−1.26638
$187$	−1.00000	−0.0731272
$188$	−0.292174	−0.0213090
$189$	9.84047	0.715789
$190$	2.84455	0.206366
$191$	10.1029	0.731019	0.365509	−	0.930808i	$-0.380895\pi$
$191$	10.1029	0.731019	0.365509	+	0.930808i	$0.380895\pi$
$192$	7.14554	0.515685
$193$	2.37117	0.170681	0.0853405	−	0.996352i	$-0.472802\pi$
$193$	2.37117	0.170681	0.0853405	+	0.996352i	$0.472802\pi$
$194$	−24.8157	−1.78167
$195$	−16.4872	−1.18067
$196$	−4.60695	−0.329068
$197$	−19.3249	−1.37684	−0.688422	−	0.725310i	$-0.741696\pi$
$197$	−19.3249	−1.37684	−0.688422	+	0.725310i	$0.741696\pi$
$198$	0.534267	0.0379687
$199$	5.73344	0.406433	0.203216	−	0.979134i	$-0.434860\pi$
$199$	5.73344	0.406433	0.203216	+	0.979134i	$0.434860\pi$
$200$	−0.372944	−0.0263711
$201$	−0.824045	−0.0581236
$202$	−20.4038	−1.43561
$203$	−10.4736	−0.735105
$204$	−2.78076	−0.194692
$205$	−25.4243	−1.77571
$206$	−7.14475	−0.497798
$207$	−0.871094	−0.0605452
$208$	−20.0546	−1.39054
$209$	0.707473	0.0489370
$210$	14.5687	1.00533
$211$	7.32341	0.504165	0.252082	−	0.967706i	$-0.418885\pi$
$211$	7.32341	0.504165	0.252082	+	0.967706i	$0.418885\pi$
$212$	1.39930	0.0961042
$213$	13.7563	0.942569
$214$	−30.4230	−2.07967
$215$	−2.13867	−0.145856
$216$	4.30773	0.293104
$217$	−10.1356	−0.688047
$218$	−12.1356	−0.821929
$219$	3.02725	0.204563
$220$	−3.28166	−0.221250
$221$	4.25393	0.286150
$222$	3.02134	0.202779
$223$	14.5664	0.975436	0.487718	−	0.873001i	$-0.337829\pi$
$223$	14.5664	0.975436	0.487718	+	0.873001i	$0.337829\pi$
$224$	14.2209	0.950176
$225$	−0.121090	−0.00807264
$226$	6.26373	0.416657
$227$	−4.50646	−0.299104	−0.149552	−	0.988754i	$-0.547783\pi$
$227$	−4.50646	−0.299104	−0.149552	+	0.988754i	$0.547783\pi$
$228$	1.96732	0.130289
$229$	17.9103	1.18354	0.591772	−	0.806105i	$-0.298429\pi$
$229$	17.9103	1.18354	0.591772	+	0.806105i	$0.298429\pi$
$230$	12.3246	0.812657
$231$	3.62339	0.238402
$232$	−4.58490	−0.301014
$233$	−1.39299	−0.0912578	−0.0456289	−	0.998958i	$-0.514529\pi$
$233$	−1.39299	−0.0912578	−0.0456289	+	0.998958i	$0.514529\pi$
$234$	−2.27273	−0.148573
$235$	−0.407226	−0.0265645
$236$	21.6726	1.41076
$237$	20.9226	1.35907
$238$	−3.75891	−0.243654
$239$	−19.8049	−1.28107	−0.640537	−	0.767927i	$-0.721288\pi$
$239$	−19.8049	−1.28107	−0.640537	+	0.767927i	$0.721288\pi$
$240$	18.2718	1.17944
$241$	−8.42924	−0.542975	−0.271487	−	0.962442i	$-0.587516\pi$
$241$	−8.42924	−0.542975	−0.271487	+	0.962442i	$0.587516\pi$
$242$	−1.88001	−0.120852
$243$	2.94367	0.188837
$244$	−5.97584	−0.382564
$245$	−6.42105	−0.410226
$246$	−40.5024	−2.58234
$247$	−3.00954	−0.191493
$248$	−4.43691	−0.281744
$249$	−21.8457	−1.38441
$250$	21.8168	1.37982
$251$	24.3191	1.53501	0.767503	−	0.641046i	$-0.221499\pi$
$251$	24.3191	1.53501	0.767503	+	0.641046i	$0.221499\pi$
$252$	0.871866	0.0549224
$253$	3.06526	0.192711
$254$	−18.4908	−1.16021
$255$	−3.87576	−0.242710
$256$	20.6932	1.29332
$257$	−13.4581	−0.839495	−0.419748	−	0.907641i	$-0.637881\pi$
$257$	−13.4581	−0.839495	−0.419748	+	0.907641i	$0.637881\pi$
$258$	−3.40702	−0.212111
$259$	1.77307	0.110173
$260$	13.9600	0.865759
$261$	−1.48865	−0.0921453
$262$	9.48380	0.585911
$263$	−13.6757	−0.843280	−0.421640	−	0.906763i	$-0.638545\pi$
$263$	−13.6757	−0.843280	−0.421640	+	0.906763i	$0.638545\pi$
$264$	1.58616	0.0976216
$265$	1.95031	0.119807
$266$	2.65933	0.163054
$267$	−3.87415	−0.237094
$268$	0.697730	0.0426207
$269$	−10.1954	−0.621624	−0.310812	−	0.950471i	$-0.600601\pi$
$269$	−10.1954	−0.621624	−0.310812	+	0.950471i	$0.600601\pi$
$270$	−19.7887	−1.20430
$271$	17.5673	1.06714	0.533568	−	0.845757i	$-0.320851\pi$
$271$	17.5673	1.06714	0.533568	+	0.845757i	$0.320851\pi$
$272$	−4.71437	−0.285851
$273$	−15.4137	−0.932877
$274$	−39.5486	−2.38922
$275$	0.426098	0.0256947
$276$	8.52376	0.513070
$277$	5.88237	0.353438	0.176719	−	0.984261i	$-0.443452\pi$
$277$	5.88237	0.353438	0.176719	+	0.984261i	$0.443452\pi$
$278$	11.2362	0.673902
$279$	−1.44060	−0.0862466
$280$	3.74265	0.223666
$281$	3.17331	0.189304	0.0946519	−	0.995510i	$-0.469826\pi$
$281$	3.17331	0.189304	0.0946519	+	0.995510i	$0.469826\pi$
$282$	−0.648733	−0.0386315
$283$	15.2523	0.906656	0.453328	−	0.891344i	$-0.350237\pi$
$283$	15.2523	0.906656	0.453328	+	0.891344i	$0.350237\pi$
$284$	−11.6477	−0.691163
$285$	2.74200	0.162422
$286$	7.99743	0.472898
$287$	−23.7688	−1.40303
$288$	2.02127	0.119104
$289$	1.00000	0.0588235
$290$	21.0620	1.23680
$291$	−23.9211	−1.40228
$292$	−2.56322	−0.150001
$293$	−16.2711	−0.950566	−0.475283	−	0.879833i	$-0.657654\pi$
$293$	−16.2711	−0.950566	−0.475283	+	0.879833i	$0.657654\pi$
$294$	−10.2291	−0.596572
$295$	30.2067	1.75870
$296$	0.776175	0.0451142
$297$	−4.92169	−0.285585
$298$	−26.6414	−1.54329
$299$	−13.0394	−0.754088
$300$	1.18488	0.0684089
$301$	−1.99941	−0.115244
$302$	11.1711	0.642825
$303$	−19.6682	−1.12991
$304$	3.33529	0.191292
$305$	−8.32898	−0.476916
$306$	−0.534267	−0.0305420
$307$	0.340661	0.0194426	0.00972128	−	0.999953i	$-0.496906\pi$
$307$	0.340661	0.0194426	0.00972128	+	0.999953i	$0.496906\pi$
$308$	−3.06798	−0.174814
$309$	−6.88716	−0.391797
$310$	20.3822	1.15763
$311$	−8.90724	−0.505083	−0.252542	−	0.967586i	$-0.581266\pi$
$311$	−8.90724	−0.505083	−0.252542	+	0.967586i	$0.581266\pi$
$312$	−6.74743	−0.381998
$313$	−22.6051	−1.27771	−0.638857	−	0.769326i	$-0.720592\pi$
$313$	−22.6051	−1.27771	−0.638857	+	0.769326i	$0.720592\pi$
$314$	−27.2698	−1.53892
$315$	1.21519	0.0684680
$316$	−17.7155	−0.996575
$317$	14.9356	0.838864	0.419432	−	0.907787i	$-0.362229\pi$
$317$	14.9356	0.838864	0.419432	+	0.907787i	$0.362229\pi$
$318$	3.10695	0.174229
$319$	5.23837	0.293292
$320$	−8.43267	−0.471400
$321$	−29.3262	−1.63683
$322$	11.5220	0.642098
$323$	−0.707473	−0.0393649
$324$	−14.9942	−0.833013
$325$	−1.81259	−0.100544
$326$	−21.9945	−1.21816
$327$	−11.6981	−0.646907
$328$	−10.4050	−0.574518
$329$	−0.380709	−0.0209892
$330$	−7.28648	−0.401107
$331$	−10.1486	−0.557816	−0.278908	−	0.960318i	$-0.589972\pi$
$331$	−10.1486	−0.557816	−0.278908	+	0.960318i	$0.589972\pi$
$332$	18.4970	1.01516
$333$	0.252013	0.0138102
$334$	−14.1947	−0.776701
$335$	0.972480	0.0531323
$336$	17.0820	0.931901
$337$	−16.9001	−0.920607	−0.460304	−	0.887762i	$-0.652259\pi$
$337$	−16.9001	−0.920607	−0.460304	+	0.887762i	$0.652259\pi$
$338$	−9.58035	−0.521102
$339$	6.03791	0.327934
$340$	3.28166	0.177973
$341$	5.06928	0.274517
$342$	0.377979	0.0204388
$343$	−19.9988	−1.07983
$344$	−0.875255	−0.0471906
$345$	11.8802	0.639609
$346$	−36.0117	−1.93600
$347$	−22.0887	−1.18578	−0.592892	−	0.805282i	$-0.702014\pi$
$347$	−22.0887	−1.18578	−0.592892	+	0.805282i	$0.702014\pi$
$348$	14.5667	0.780855
$349$	3.52856	0.188879	0.0944396	−	0.995531i	$-0.469894\pi$
$349$	3.52856	0.188879	0.0944396	+	0.995531i	$0.469894\pi$
$350$	1.60167	0.0856126
$351$	20.9365	1.11751
$352$	−7.11256	−0.379101
$353$	32.6969	1.74028	0.870140	−	0.492804i	$-0.164028\pi$
$353$	32.6969	1.74028	0.870140	+	0.492804i	$0.164028\pi$
$354$	48.1209	2.55760
$355$	−16.2343	−0.861626
$356$	3.28030	0.173855
$357$	−3.62339	−0.191770
$358$	−24.7359	−1.30733
$359$	11.8340	0.624573	0.312286	−	0.949988i	$-0.398905\pi$
$359$	11.8340	0.624573	0.312286	+	0.949988i	$0.398905\pi$
$360$	0.531956	0.0280365
$361$	−18.4995	−0.973657
$362$	33.7166	1.77210
$363$	−1.81223	−0.0951175
$364$	13.0510	0.684056
$365$	−3.57255	−0.186996
$366$	−13.2685	−0.693556
$367$	29.0175	1.51470	0.757351	−	0.653008i	$-0.226493\pi$
$367$	29.0175	1.51470	0.757351	+	0.653008i	$0.226493\pi$
$368$	14.4508	0.753299
$369$	−3.37834	−0.175870
$370$	−3.56557	−0.185365
$371$	1.82332	0.0946618
$372$	14.0965	0.730868
$373$	19.6652	1.01823	0.509113	−	0.860699i	$-0.329973\pi$
$373$	19.6652	1.01823	0.509113	+	0.860699i	$0.329973\pi$
$374$	1.88001	0.0972131
$375$	21.0303	1.08600
$376$	−0.166658	−0.00859473
$377$	−22.2836	−1.14767
$378$	−18.5002	−0.951548
$379$	13.8566	0.711765	0.355883	−	0.934531i	$-0.384180\pi$
$379$	13.8566	0.711765	0.355883	+	0.934531i	$0.384180\pi$
$380$	−2.32169	−0.119100
$381$	−17.8241	−0.913157
$382$	−18.9935	−0.971793
$383$	6.98091	0.356708	0.178354	−	0.983966i	$-0.442923\pi$
$383$	6.98091	0.356708	0.178354	+	0.983966i	$0.442923\pi$
$384$	12.3455	0.630005
$385$	−4.27607	−0.217929
$386$	−4.45784	−0.226898
$387$	−0.284183	−0.0144458
$388$	20.2543	1.02826
$389$	11.5799	0.587123	0.293561	−	0.955940i	$-0.405159\pi$
$389$	11.5799	0.587123	0.293561	+	0.955940i	$0.405159\pi$
$390$	30.9961	1.56955
$391$	−3.06526	−0.155017
$392$	−2.62783	−0.132725
$393$	9.14188	0.461147
$394$	36.3311	1.83033
$395$	−24.6914	−1.24236
$396$	−0.436062	−0.0219129
$397$	7.69569	0.386235	0.193118	−	0.981176i	$-0.438140\pi$
$397$	7.69569	0.386235	0.193118	+	0.981176i	$0.438140\pi$
$398$	−10.7789	−0.540299
$399$	2.56345	0.128333
$400$	2.00878	0.100439
$401$	−24.5314	−1.22504	−0.612521	−	0.790455i	$-0.709844\pi$
$401$	−24.5314	−1.22504	−0.612521	+	0.790455i	$0.709844\pi$
$402$	1.54921	0.0772678
$403$	−21.5644	−1.07420
$404$	16.6534	0.828536
$405$	−20.8986	−1.03846
$406$	19.6906	0.977226
$407$	−0.886799	−0.0439570
$408$	−1.58616	−0.0785268
$409$	−11.7216	−0.579596	−0.289798	−	0.957088i	$-0.593588\pi$
$409$	−11.7216	−0.579596	−0.289798	+	0.957088i	$0.593588\pi$
$410$	47.7980	2.36058
$411$	−38.1228	−1.88046
$412$	5.83146	0.287295
$413$	28.2398	1.38959
$414$	1.63767	0.0804869
$415$	25.7807	1.26553
$416$	30.2563	1.48344
$417$	10.8311	0.530401
$418$	−1.33006	−0.0650553
$419$	4.18945	0.204668	0.102334	−	0.994750i	$-0.467369\pi$
$419$	4.18945	0.204668	0.102334	+	0.994750i	$0.467369\pi$
$420$	−11.8908	−0.580209
$421$	−5.87141	−0.286155	−0.143077	−	0.989711i	$-0.545700\pi$
$421$	−5.87141	−0.286155	−0.143077	+	0.989711i	$0.545700\pi$
$422$	−13.7681	−0.670220
$423$	−0.0541115	−0.00263099
$424$	0.798168	0.0387625
$425$	−0.426098	−0.0206688
$426$	−25.8621	−1.25302
$427$	−7.78664	−0.376822
$428$	24.8309	1.20025
$429$	7.70910	0.372199
$430$	4.02072	0.193896
$431$	39.7637	1.91535	0.957675	−	0.287853i	$-0.0929413\pi$
$431$	39.7637	1.91535	0.957675	+	0.287853i	$0.0929413\pi$
$432$	−23.2027	−1.11634
$433$	−1.83223	−0.0880513	−0.0440257	−	0.999030i	$-0.514018\pi$
$433$	−1.83223	−0.0880513	−0.0440257	+	0.999030i	$0.514018\pi$
$434$	19.0550	0.914668
$435$	20.3027	0.973438
$436$	9.90496	0.474361
$437$	2.16859	0.103738
$438$	−5.69127	−0.271939
$439$	−13.5113	−0.644859	−0.322429	−	0.946593i	$-0.604500\pi$
$439$	−13.5113	−0.644859	−0.322429	+	0.946593i	$0.604500\pi$
$440$	−1.87188	−0.0892383
$441$	−0.853219	−0.0406295
$442$	−7.99743	−0.380399
$443$	33.6845	1.60040	0.800200	−	0.599733i	$-0.204727\pi$
$443$	33.6845	1.60040	0.800200	+	0.599733i	$0.204727\pi$
$444$	−2.46598	−0.117030
$445$	4.57200	0.216733
$446$	−27.3849	−1.29671
$447$	−25.6809	−1.21466
$448$	−7.88358	−0.372464
$449$	−15.9188	−0.751253	−0.375627	−	0.926771i	$-0.622572\pi$
$449$	−15.9188	−0.751253	−0.375627	+	0.926771i	$0.622572\pi$
$450$	0.227650	0.0107315
$451$	11.8879	0.559781
$452$	−5.11238	−0.240466
$453$	10.7684	0.505941
$454$	8.47220	0.397620
$455$	18.1901	0.852766
$456$	1.12217	0.0525504
$457$	−32.2446	−1.50834	−0.754170	−	0.656679i	$-0.771961\pi$
$457$	−32.2446	−1.50834	−0.754170	+	0.656679i	$0.771961\pi$
$458$	−33.6715	−1.57337
$459$	4.92169	0.229725
$460$	−10.0591	−0.469010
$461$	15.7293	0.732589	0.366294	−	0.930499i	$-0.380626\pi$
$461$	15.7293	0.732589	0.366294	+	0.930499i	$0.380626\pi$
$462$	−6.81202	−0.316924
$463$	−25.7686	−1.19757	−0.598783	−	0.800911i	$-0.704349\pi$
$463$	−25.7686	−1.19757	−0.598783	+	0.800911i	$0.704349\pi$
$464$	24.6956	1.14646
$465$	19.6473	0.911123
$466$	2.61884	0.121315
$467$	29.8072	1.37931	0.689656	−	0.724137i	$-0.257762\pi$
$467$	29.8072	1.37931	0.689656	+	0.724137i	$0.257762\pi$
$468$	1.85497	0.0857462
$469$	0.909157	0.0419810
$470$	0.765589	0.0353140
$471$	−26.2866	−1.21122
$472$	12.3622	0.569015
$473$	1.00000	0.0459800
$474$	−39.3348	−1.80671
$475$	0.301453	0.0138316
$476$	3.06798	0.140621
$477$	0.259154	0.0118658
$478$	37.2335	1.70302
$479$	27.8238	1.27130	0.635650	−	0.771977i	$-0.280732\pi$
$479$	27.8238	1.27130	0.635650	+	0.771977i	$0.280732\pi$
$480$	−27.5666	−1.25824
$481$	3.77238	0.172006
$482$	15.8471	0.721814
$483$	11.1066	0.505370
$484$	1.53444	0.0697474
$485$	28.2299	1.28186
$486$	−5.53414	−0.251034
$487$	−7.84419	−0.355454	−0.177727	−	0.984080i	$-0.556874\pi$
$487$	−7.84419	−0.355454	−0.177727	+	0.984080i	$0.556874\pi$
$488$	−3.40865	−0.154302
$489$	−21.2015	−0.958767
$490$	12.0717	0.545342
$491$	36.6271	1.65296	0.826479	−	0.562968i	$-0.190340\pi$
$491$	36.6271	1.65296	0.826479	+	0.562968i	$0.190340\pi$
$492$	33.0575	1.49035
$493$	−5.23837	−0.235924
$494$	5.65797	0.254564
$495$	−0.607772	−0.0273173
$496$	23.8985	1.07307
$497$	−15.1772	−0.680790
$498$	41.0701	1.84039
$499$	16.6339	0.744637	0.372318	−	0.928105i	$-0.378563\pi$
$499$	16.6339	0.744637	0.372318	+	0.928105i	$0.378563\pi$
$500$	−17.8066	−0.796336
$501$	−13.6830	−0.611310
$502$	−45.7201	−2.04059
$503$	−25.3762	−1.13147	−0.565735	−	0.824587i	$-0.691407\pi$
$503$	−25.3762	−1.13147	−0.565735	+	0.824587i	$0.691407\pi$
$504$	0.497318	0.0221523
$505$	23.2111	1.03288
$506$	−5.76272	−0.256184
$507$	−9.23495	−0.410139
$508$	15.0919	0.669596
$509$	−14.8618	−0.658736	−0.329368	−	0.944202i	$-0.606836\pi$
$509$	−14.8618	−0.658736	−0.329368	+	0.944202i	$0.606836\pi$
$510$	7.28648	0.322651
$511$	−3.33993	−0.147750
$512$	−25.2787	−1.11717
$513$	−3.48196	−0.153733
$514$	25.3014	1.11600
$515$	8.12775	0.358151
$516$	2.78076	0.122416
$517$	0.190411	0.00837426
$518$	−3.33340	−0.146461
$519$	−34.7134	−1.52375
$520$	7.96284	0.349194
$521$	7.47851	0.327639	0.163820	−	0.986490i	$-0.447618\pi$
$521$	7.47851	0.327639	0.163820	+	0.986490i	$0.447618\pi$
$522$	2.79868	0.122495
$523$	34.2799	1.49896	0.749478	−	0.662029i	$-0.230304\pi$
$523$	34.2799	1.49896	0.749478	+	0.662029i	$0.230304\pi$
$524$	−7.74056	−0.338148
$525$	1.54392	0.0673822
$526$	25.7105	1.12103
$527$	−5.06928	−0.220821
$528$	−8.54353	−0.371810
$529$	−13.6042	−0.591486
$530$	−3.66660	−0.159267
$531$	4.01382	0.174185
$532$	−2.17051	−0.0941037
$533$	−50.5704	−2.19045
$534$	7.28344	0.315185
$535$	34.6087	1.49626
$536$	0.397990	0.0171905
$537$	−23.8441	−1.02895
$538$	19.1674	0.826367
$539$	3.00236	0.129321
$540$	16.1513	0.695042
$541$	43.3922	1.86558	0.932788	−	0.360426i	$-0.117369\pi$
$541$	43.3922	1.86558	0.932788	+	0.360426i	$0.117369\pi$
$542$	−33.0267	−1.41862
$543$	32.5010	1.39475
$544$	7.11256	0.304949
$545$	13.8053	0.591354
$546$	28.9778	1.24014
$547$	−28.5082	−1.21892	−0.609461	−	0.792816i	$-0.708614\pi$
$547$	−28.5082	−1.21892	−0.609461	+	0.792816i	$0.708614\pi$
$548$	32.2791	1.37889
$549$	−1.10674	−0.0472345
$550$	−0.801069	−0.0341577
$551$	3.70600	0.157881
$552$	4.86200	0.206941
$553$	−23.0837	−0.981617
$554$	−11.0589	−0.469849
$555$	−3.43702	−0.145893
$556$	−9.17084	−0.388930
$557$	−15.7623	−0.667871	−0.333936	−	0.942596i	$-0.608377\pi$
$557$	−15.7623	−0.667871	−0.333936	+	0.942596i	$0.608377\pi$
$558$	2.70835	0.114653
$559$	−4.25393	−0.179922
$560$	−20.1590	−0.851873
$561$	1.81223	0.0765125
$562$	−5.96586	−0.251655
$563$	42.5440	1.79302	0.896508	−	0.443029i	$-0.146096\pi$
$563$	42.5440	1.79302	0.896508	+	0.443029i	$0.146096\pi$
$564$	0.529488	0.0222955
$565$	−7.12551	−0.299773
$566$	−28.6745	−1.20528
$567$	−19.5378	−0.820511
$568$	−6.64391	−0.278772
$569$	−38.0140	−1.59363	−0.796814	−	0.604224i	$-0.793483\pi$
$569$	−38.0140	−1.59363	−0.796814	+	0.604224i	$0.793483\pi$
$570$	−5.15499	−0.215919
$571$	−28.7771	−1.20428	−0.602142	−	0.798389i	$-0.705686\pi$
$571$	−28.7771	−1.20428	−0.602142	+	0.798389i	$0.705686\pi$
$572$	−6.52740	−0.272924
$573$	−18.3088	−0.764859
$574$	44.6857	1.86515
$575$	1.30610	0.0544682
$576$	−1.12052	−0.0466883
$577$	−29.2051	−1.21582	−0.607912	−	0.794004i	$-0.707993\pi$
$577$	−29.2051	−1.21582	−0.607912	+	0.794004i	$0.707993\pi$
$578$	−1.88001	−0.0781982
$579$	−4.29712	−0.178582
$580$	−17.1905	−0.713798
$581$	24.1020	0.999920
$582$	44.9718	1.86414
$583$	−0.911927	−0.0377682
$584$	−1.46207	−0.0605011
$585$	2.58542	0.106894
$586$	30.5898	1.26365
$587$	38.7591	1.59976	0.799881	−	0.600159i	$-0.204896\pi$
$587$	38.7591	1.59976	0.799881	+	0.600159i	$0.204896\pi$
$588$	8.34885	0.344301
$589$	3.58638	0.147774
$590$	−56.7890	−2.33796
$591$	35.0213	1.44058
$592$	−4.18070	−0.171826
$593$	30.9686	1.27173	0.635863	−	0.771802i	$-0.280644\pi$
$593$	30.9686	1.27173	0.635863	+	0.771802i	$0.280644\pi$
$594$	9.25283	0.379648
$595$	4.27607	0.175302
$596$	21.7444	0.890684
$597$	−10.3903	−0.425248
$598$	24.5142	1.00246
$599$	−7.43052	−0.303603	−0.151801	−	0.988411i	$-0.548507\pi$
$599$	−7.43052	−0.303603	−0.151801	+	0.988411i	$0.548507\pi$
$600$	0.675861	0.0275919
$601$	46.7269	1.90603	0.953016	−	0.302921i	$-0.0979619\pi$
$601$	46.7269	1.90603	0.953016	+	0.302921i	$0.0979619\pi$
$602$	3.75891	0.153202
$603$	0.129221	0.00526231
$604$	−9.11772	−0.370995
$605$	2.13867	0.0869492
$606$	36.9765	1.50207
$607$	36.7112	1.49006	0.745032	−	0.667029i	$-0.232434\pi$
$607$	36.7112	1.49006	0.745032	+	0.667029i	$0.232434\pi$
$608$	−5.03195	−0.204072
$609$	18.9807	0.769135
$610$	15.6586	0.633997
$611$	−0.809994	−0.0327689
$612$	0.436062	0.0176267
$613$	42.4964	1.71641	0.858207	−	0.513303i	$-0.171578\pi$
$613$	42.4964	1.71641	0.858207	+	0.513303i	$0.171578\pi$
$614$	−0.640447	−0.0258463
$615$	46.0748	1.85792
$616$	−1.74999	−0.0705092
$617$	17.0326	0.685708	0.342854	−	0.939389i	$-0.388606\pi$
$617$	17.0326	0.685708	0.342854	+	0.939389i	$0.388606\pi$
$618$	12.9479	0.520843
$619$	−24.6400	−0.990365	−0.495183	−	0.868789i	$-0.664899\pi$
$619$	−24.6400	−0.990365	−0.495183	+	0.868789i	$0.664899\pi$
$620$	−16.6357	−0.668104
$621$	−15.0863	−0.605391
$622$	16.7457	0.671442
$623$	4.27429	0.171246
$624$	36.3436	1.45491
$625$	−22.6880	−0.907518
$626$	42.4978	1.69855
$627$	−1.28211	−0.0512024
$628$	22.2573	0.888161
$629$	0.886799	0.0353590
$630$	−2.28456	−0.0910192
$631$	−39.4416	−1.57015	−0.785073	−	0.619404i	$-0.787374\pi$
$631$	−39.4416	−1.57015	−0.785073	+	0.619404i	$0.787374\pi$
$632$	−10.1050	−0.401956
$633$	−13.2717	−0.527503
$634$	−28.0790	−1.11516
$635$	21.0348	0.834740
$636$	−2.53585	−0.100553
$637$	−12.7718	−0.506038
$638$	−9.84818	−0.389893
$639$	−2.15718	−0.0853368
$640$	−14.5693	−0.575903
$641$	41.7534	1.64916	0.824581	−	0.565744i	$-0.191411\pi$
$641$	41.7534	1.64916	0.824581	+	0.565744i	$0.191411\pi$
$642$	55.1335	2.17595
$643$	−41.9037	−1.65252	−0.826259	−	0.563290i	$-0.809535\pi$
$643$	−41.9037	−1.65252	−0.826259	+	0.563290i	$0.809535\pi$
$644$	−9.40415	−0.370575
$645$	3.87576	0.152608
$646$	1.33006	0.0523304
$647$	37.8310	1.48729	0.743644	−	0.668576i	$-0.233096\pi$
$647$	37.8310	1.48729	0.743644	+	0.668576i	$0.233096\pi$
$648$	−8.55280	−0.335986
$649$	−14.1241	−0.554419
$650$	3.40769	0.133661
$651$	18.3680	0.719899
$652$	17.9516	0.703041
$653$	−8.95335	−0.350372	−0.175186	−	0.984535i	$-0.556053\pi$
$653$	−8.95335	−0.350372	−0.175186	+	0.984535i	$0.556053\pi$
$654$	21.9926	0.859978
$655$	−10.7886	−0.421546
$656$	56.0441	2.18816
$657$	−0.474715	−0.0185204
$658$	0.715738	0.0279024
$659$	16.7723	0.653357	0.326679	−	0.945135i	$-0.394070\pi$
$659$	16.7723	0.653357	0.326679	+	0.945135i	$0.394070\pi$
$660$	5.94713	0.231492
$661$	−8.57000	−0.333335	−0.166667	−	0.986013i	$-0.553301\pi$
$661$	−8.57000	−0.333335	−0.166667	+	0.986013i	$0.553301\pi$
$662$	19.0794	0.741542
$663$	−7.70910	−0.299397
$664$	10.5508	0.409451
$665$	−3.02521	−0.117313
$666$	−0.473787	−0.0183589
$667$	16.0569	0.621728
$668$	11.5856	0.448259
$669$	−26.3976	−1.02059
$670$	−1.82827	−0.0706324
$671$	3.89447	0.150344
$672$	−25.7716	−0.994161
$673$	−37.0850	−1.42952	−0.714762	−	0.699368i	$-0.753465\pi$
$673$	−37.0850	−1.42952	−0.714762	+	0.699368i	$0.753465\pi$
$674$	31.7724	1.22383
$675$	−2.09712	−0.0807183
$676$	7.81936	0.300745
$677$	17.2615	0.663413	0.331707	−	0.943383i	$-0.392376\pi$
$677$	17.2615	0.663413	0.331707	+	0.943383i	$0.392376\pi$
$678$	−11.3513	−0.435945
$679$	26.3918	1.01282
$680$	1.87188	0.0717833
$681$	8.16675	0.312951
$682$	−9.53030	−0.364934
$683$	−13.5834	−0.519753	−0.259877	−	0.965642i	$-0.583682\pi$
$683$	−13.5834	−0.519753	−0.259877	+	0.965642i	$0.583682\pi$
$684$	−0.308502	−0.0117959
$685$	44.9898	1.71897
$686$	37.5980	1.43550
$687$	−32.4575	−1.23833
$688$	4.71437	0.179734
$689$	3.87927	0.147788
$690$	−22.3349	−0.850277
$691$	14.9297	0.567952	0.283976	−	0.958831i	$-0.408346\pi$
$691$	14.9297	0.567952	0.283976	+	0.958831i	$0.408346\pi$
$692$	29.3923	1.11733
$693$	−0.568198	−0.0215840
$694$	41.5270	1.57634
$695$	−12.7821	−0.484852
$696$	8.30891	0.314948
$697$	−11.8879	−0.450288
$698$	−6.63372	−0.251090
$699$	2.52442	0.0954824
$700$	−1.30726	−0.0494098
$701$	−45.3083	−1.71127	−0.855636	−	0.517579i	$-0.826833\pi$
$701$	−45.3083	−1.71127	−0.855636	+	0.517579i	$0.826833\pi$
$702$	−39.3609	−1.48558
$703$	−0.627387	−0.0236623
$704$	3.94295	0.148606
$705$	0.737987	0.0277942
$706$	−61.4705	−2.31347
$707$	21.6997	0.816100
$708$	−39.2757	−1.47607
$709$	24.9600	0.937391	0.468696	−	0.883360i	$-0.344724\pi$
$709$	24.9600	0.937391	0.468696	+	0.883360i	$0.344724\pi$
$710$	30.5206	1.14542
$711$	−3.28096	−0.123045
$712$	1.87110	0.0701224
$713$	15.5387	0.581927
$714$	6.81202	0.254933
$715$	−9.09774	−0.340236
$716$	20.1892	0.754504
$717$	35.8911	1.34038
$718$	−22.2480	−0.830287
$719$	29.3000	1.09271	0.546354	−	0.837555i	$-0.316016\pi$
$719$	29.3000	1.09271	0.546354	+	0.837555i	$0.316016\pi$
$720$	−2.86527	−0.106782
$721$	7.59851	0.282983
$722$	34.7792	1.29435
$723$	15.2757	0.568110
$724$	−27.5190	−1.02274
$725$	2.23206	0.0828965
$726$	3.40702	0.126446
$727$	28.1274	1.04319	0.521593	−	0.853194i	$-0.325338\pi$
$727$	28.1274	1.04319	0.521593	+	0.853194i	$0.325338\pi$
$728$	7.44434	0.275906
$729$	23.9807	0.888176
$730$	6.71644	0.248587
$731$	−1.00000	−0.0369863
$732$	10.8296	0.400273
$733$	44.9386	1.65985	0.829923	−	0.557878i	$-0.188384\pi$
$733$	44.9386	1.65985	0.829923	+	0.557878i	$0.188384\pi$
$734$	−54.5533	−2.01360
$735$	11.6364	0.429216
$736$	−21.8019	−0.803627
$737$	−0.454713	−0.0167496
$738$	6.35132	0.233795
$739$	−7.32228	−0.269354	−0.134677	−	0.990890i	$-0.543000\pi$
$739$	−7.32228	−0.269354	−0.134677	+	0.990890i	$0.543000\pi$
$740$	2.91017	0.106980
$741$	5.45398	0.200357
$742$	−3.42785	−0.125840
$743$	52.6372	1.93107	0.965536	−	0.260271i	$-0.0838119\pi$
$743$	52.6372	1.93107	0.965536	+	0.260271i	$0.0838119\pi$
$744$	8.04071	0.294787
$745$	30.3068	1.11036
$746$	−36.9708	−1.35360
$747$	3.42570	0.125340
$748$	−1.53444	−0.0561047
$749$	32.3552	1.18223
$750$	−39.5371	−1.44369
$751$	20.9875	0.765846	0.382923	−	0.923780i	$-0.374917\pi$
$751$	20.9875	0.765846	0.382923	+	0.923780i	$0.374917\pi$
$752$	0.897668	0.0327346
$753$	−44.0718	−1.60606
$754$	41.8935	1.52567
$755$	−12.7081	−0.462494
$756$	15.0996	0.549168
$757$	1.85701	0.0674941	0.0337471	−	0.999430i	$-0.489256\pi$
$757$	1.85701	0.0674941	0.0337471	+	0.999430i	$0.489256\pi$
$758$	−26.0505	−0.946198
$759$	−5.55496	−0.201632
$760$	−1.32430	−0.0480376
$761$	−10.5079	−0.380910	−0.190455	−	0.981696i	$-0.560996\pi$
$761$	−10.5079	−0.380910	−0.190455	+	0.981696i	$0.560996\pi$
$762$	33.5095	1.21392
$763$	12.9064	0.467242
$764$	15.5023	0.560853
$765$	0.607772	0.0219741
$766$	−13.1242	−0.474196
$767$	60.0828	2.16946
$768$	−37.5008	−1.35319
$769$	28.7584	1.03705	0.518527	−	0.855061i	$-0.326481\pi$
$769$	28.7584	1.03705	0.518527	+	0.855061i	$0.326481\pi$
$770$	8.03907	0.289708
$771$	24.3893	0.878358
$772$	3.63843	0.130950
$773$	21.8254	0.785005	0.392502	−	0.919751i	$-0.371609\pi$
$773$	21.8254	0.785005	0.392502	+	0.919751i	$0.371609\pi$
$774$	0.534267	0.0192038
$775$	2.16001	0.0775899
$776$	11.5532	0.414735
$777$	−3.21322	−0.115274
$778$	−21.7703	−0.780503
$779$	8.41040	0.301334
$780$	−25.2987	−0.905837
$781$	7.59083	0.271621
$782$	5.76272	0.206075
$783$	−25.7816	−0.921359
$784$	14.1542	0.505509
$785$	31.0216	1.10721
$786$	−17.1868	−0.613034
$787$	18.9920	0.676991	0.338495	−	0.940968i	$-0.390082\pi$
$787$	18.9920	0.676991	0.338495	+	0.940968i	$0.390082\pi$
$788$	−29.6530	−1.05634
$789$	24.7835	0.882317
$790$	46.4202	1.65156
$791$	−6.66154	−0.236857
$792$	−0.248732	−0.00883831
$793$	−16.5668	−0.588304
$794$	−14.4680	−0.513449
$795$	−3.53441	−0.125353
$796$	8.79763	0.311824
$797$	−40.6278	−1.43911	−0.719555	−	0.694435i	$-0.755654\pi$
$797$	−40.6278	−1.43911	−0.719555	+	0.694435i	$0.755654\pi$
$798$	−4.81932	−0.170602
$799$	−0.190411	−0.00673625
$800$	−3.03065	−0.107150
$801$	0.607519	0.0214656
$802$	46.1194	1.62853
$803$	1.67046	0.0589491
$804$	−1.26445	−0.0445937
$805$	−13.1073	−0.461971
$806$	40.5412	1.42800
$807$	18.4764	0.650400
$808$	9.49917	0.334180
$809$	−22.6179	−0.795204	−0.397602	−	0.917558i	$-0.630157\pi$
$809$	−22.6179	−0.795204	−0.397602	+	0.917558i	$0.630157\pi$
$810$	39.2896	1.38050
$811$	49.9534	1.75410	0.877050	−	0.480399i	$-0.159508\pi$
$811$	49.9534	1.75410	0.877050	+	0.480399i	$0.159508\pi$
$812$	−16.0712	−0.563988
$813$	−31.8360	−1.11654
$814$	1.66719	0.0584350
$815$	25.0206	0.876433
$816$	8.54353	0.299083
$817$	0.707473	0.0247514
$818$	22.0367	0.770497
$819$	2.41707	0.0844593
$820$	−39.0122	−1.36236
$821$	−16.2155	−0.565923	−0.282962	−	0.959131i	$-0.591317\pi$
$821$	−16.2155	−0.565923	−0.282962	+	0.959131i	$0.591317\pi$
$822$	71.6712	2.49982
$823$	4.49896	0.156824	0.0784120	−	0.996921i	$-0.475015\pi$
$823$	4.49896	0.156824	0.0784120	+	0.996921i	$0.475015\pi$
$824$	3.32630	0.115877
$825$	−0.772188	−0.0268841
$826$	−53.0912	−1.84728
$827$	−12.4709	−0.433655	−0.216827	−	0.976210i	$-0.569571\pi$
$827$	−12.4709	−0.433655	−0.216827	+	0.976210i	$0.569571\pi$
$828$	−1.33664	−0.0464515
$829$	12.7023	0.441170	0.220585	−	0.975368i	$-0.429203\pi$
$829$	12.7023	0.441170	0.220585	+	0.975368i	$0.429203\pi$
$830$	−48.4680	−1.68235
$831$	−10.6602	−0.369799
$832$	−16.7730	−0.581500
$833$	−3.00236	−0.104026
$834$	−20.3626	−0.705098
$835$	16.1477	0.558814
$836$	1.08558	0.0375455
$837$	−24.9494	−0.862378
$838$	−7.87622	−0.272080
$839$	−45.2975	−1.56384	−0.781922	−	0.623376i	$-0.785761\pi$
$839$	−45.2975	−1.56384	−0.781922	+	0.623376i	$0.785761\pi$
$840$	−6.78256	−0.234020
$841$	−1.55953	−0.0537770
$842$	11.0383	0.380405
$843$	−5.75077	−0.198067
$844$	11.2374	0.386806
$845$	10.8984	0.374918
$846$	0.101730	0.00349756
$847$	1.99941	0.0687005
$848$	−4.29916	−0.147634
$849$	−27.6407	−0.948627
$850$	0.801069	0.0274764
$851$	−2.71827	−0.0931811
$852$	21.1083	0.723159
$853$	10.9791	0.375918	0.187959	−	0.982177i	$-0.439813\pi$
$853$	10.9791	0.375918	0.187959	+	0.982177i	$0.439813\pi$
$854$	14.6390	0.500935
$855$	−0.429983	−0.0147051
$856$	14.1637	0.484105
$857$	45.6343	1.55884	0.779419	−	0.626503i	$-0.215515\pi$
$857$	45.6343	1.55884	0.779419	+	0.626503i	$0.215515\pi$
$858$	−14.4932	−0.494790
$859$	−16.2717	−0.555182	−0.277591	−	0.960699i	$-0.589536\pi$
$859$	−16.2717	−0.555182	−0.277591	+	0.960699i	$0.589536\pi$
$860$	−3.28166	−0.111904
$861$	43.0747	1.46798
$862$	−74.7562	−2.54621
$863$	−6.39173	−0.217577	−0.108788	−	0.994065i	$-0.534697\pi$
$863$	−6.39173	−0.217577	−0.108788	+	0.994065i	$0.534697\pi$
$864$	35.0058	1.19092
$865$	40.9663	1.39290
$866$	3.44461	0.117053
$867$	−1.81223	−0.0615466
$868$	−15.5524	−0.527884
$869$	11.5452	0.391645
$870$	−38.1692	−1.29406
$871$	1.93432	0.0655418
$872$	5.64985	0.191328
$873$	3.75115	0.126957
$874$	−4.07697	−0.137906
$875$	−23.2024	−0.784384
$876$	4.64514	0.156945
$877$	28.9058	0.976078	0.488039	−	0.872822i	$-0.337712\pi$
$877$	28.9058	0.976078	0.488039	+	0.872822i	$0.337712\pi$
$878$	25.4014	0.857255
$879$	29.4869	0.994570
$880$	10.0825	0.339880
$881$	−20.7403	−0.698757	−0.349379	−	0.936982i	$-0.613607\pi$
$881$	−20.7403	−0.698757	−0.349379	+	0.936982i	$0.613607\pi$
$882$	1.60406	0.0540115
$883$	−12.1813	−0.409934	−0.204967	−	0.978769i	$-0.565709\pi$
$883$	−12.1813	−0.409934	−0.204967	+	0.978769i	$0.565709\pi$
$884$	6.52740	0.219540
$885$	−54.7416	−1.84012
$886$	−63.3273	−2.12752
$887$	11.2595	0.378057	0.189028	−	0.981972i	$-0.439466\pi$
$887$	11.2595	0.378057	0.189028	+	0.981972i	$0.439466\pi$
$888$	−1.40661	−0.0472027
$889$	19.6651	0.659547
$890$	−8.59541	−0.288119
$891$	9.77179	0.327367
$892$	22.3512	0.748375
$893$	0.134711	0.00450792
$894$	48.2804	1.61474
$895$	28.1392	0.940589
$896$	−13.6206	−0.455034
$897$	23.6304	0.788996
$898$	29.9275	0.998693
$899$	26.5547	0.885650
$900$	−0.185805	−0.00619350
$901$	0.911927	0.0303807
$902$	−22.3494	−0.744155
$903$	3.62339	0.120579
$904$	−2.91613	−0.0969891
$905$	−38.3554	−1.27498
$906$	−20.2446	−0.672583
$907$	−19.1794	−0.636841	−0.318421	−	0.947950i	$-0.603152\pi$
$907$	−19.1794	−0.636841	−0.318421	+	0.947950i	$0.603152\pi$
$908$	−6.91490	−0.229479
$909$	3.08425	0.102298
$910$	−34.1976	−1.13364
$911$	7.03875	0.233204	0.116602	−	0.993179i	$-0.462800\pi$
$911$	7.03875	0.233204	0.116602	+	0.993179i	$0.462800\pi$
$912$	−6.04432	−0.200148
$913$	−12.0546	−0.398948
$914$	60.6203	2.00514
$915$	15.0940	0.498993
$916$	27.4823	0.908040
$917$	−10.0861	−0.333073
$918$	−9.25283	−0.305389
$919$	−47.6378	−1.57143	−0.785713	−	0.618591i	$-0.787704\pi$
$919$	−47.6378	−1.57143	−0.785713	+	0.618591i	$0.787704\pi$
$920$	−5.73780	−0.189170
$921$	−0.617357	−0.0203426
$922$	−29.5713	−0.973880
$923$	−32.2909	−1.06287
$924$	5.55989	0.182907
$925$	−0.377863	−0.0124241
$926$	48.4452	1.59201
$927$	1.08000	0.0354719
$928$	−37.2582	−1.22306
$929$	−30.4836	−1.00014	−0.500068	−	0.865986i	$-0.666692\pi$
$929$	−30.4836	−1.00014	−0.500068	+	0.865986i	$0.666692\pi$
$930$	−36.9372	−1.21122
$931$	2.12409	0.0696142
$932$	−2.13746	−0.0700149
$933$	16.1420	0.528465
$934$	−56.0378	−1.83361
$935$	−2.13867	−0.0699419
$936$	1.05809	0.0345847
$937$	−51.5350	−1.68357	−0.841787	−	0.539810i	$-0.818496\pi$
$937$	−51.5350	−1.68357	−0.841787	+	0.539810i	$0.818496\pi$
$938$	−1.70923	−0.0558082
$939$	40.9656	1.33686
$940$	−0.624864	−0.0203808
$941$	27.1236	0.884203	0.442101	−	0.896965i	$-0.354233\pi$
$941$	27.1236	0.884203	0.442101	+	0.896965i	$0.354233\pi$
$942$	49.4191	1.61016
$943$	36.4396	1.18664
$944$	−66.5862	−2.16719
$945$	21.0455	0.684611
$946$	−1.88001	−0.0611244
$947$	54.1326	1.75907	0.879536	−	0.475832i	$-0.157853\pi$
$947$	54.1326	1.75907	0.879536	+	0.475832i	$0.157853\pi$
$948$	32.1046	1.04271
$949$	−7.10600	−0.230671
$950$	−0.566735	−0.0183873
$951$	−27.0667	−0.877697
$952$	1.74999	0.0567176
$953$	5.77919	0.187206	0.0936031	−	0.995610i	$-0.470162\pi$
$953$	5.77919	0.187206	0.0936031	+	0.995610i	$0.470162\pi$
$954$	−0.487212	−0.0157741
$955$	21.6067	0.699176
$956$	−30.3895	−0.982867
$957$	−9.49313	−0.306869
$958$	−52.3090	−1.69003
$959$	42.0603	1.35820
$960$	15.2819	0.493223
$961$	−5.30239	−0.171045
$962$	−7.09211	−0.228659
$963$	4.59874	0.148192
$964$	−12.9342	−0.416582
$965$	5.07116	0.163246
$966$	−20.8806	−0.671823
$967$	−24.6408	−0.792395	−0.396197	−	0.918165i	$-0.629670\pi$
$967$	−24.6408	−0.792395	−0.396197	+	0.918165i	$0.629670\pi$
$968$	0.875255	0.0281317
$969$	1.28211	0.0411872
$970$	−53.0726	−1.70406
$971$	57.9207	1.85876	0.929382	−	0.369119i	$-0.120340\pi$
$971$	57.9207	1.85876	0.929382	+	0.369119i	$0.120340\pi$
$972$	4.51689	0.144879
$973$	−11.9498	−0.383093
$974$	14.7472	0.472530
$975$	3.28483	0.105199
$976$	18.3600	0.587688
$977$	−1.03680	−0.0331703	−0.0165851	−	0.999862i	$-0.505279\pi$
$977$	−1.03680	−0.0331703	−0.0165851	+	0.999862i	$0.505279\pi$
$978$	39.8591	1.27455
$979$	−2.13778	−0.0683237
$980$	−9.85273	−0.314734
$981$	1.83442	0.0585686
$982$	−68.8593	−2.19739
$983$	16.0469	0.511818	0.255909	−	0.966701i	$-0.417625\pi$
$983$	16.0469	0.511818	0.255909	+	0.966701i	$0.417625\pi$
$984$	18.8562	0.601114
$985$	−41.3296	−1.31687
$986$	9.84818	0.313630
$987$	0.689934	0.0219608
$988$	−4.61797	−0.146917
$989$	3.06526	0.0974696
$990$	1.14262	0.0363148
$991$	−14.6016	−0.463835	−0.231918	−	0.972735i	$-0.574500\pi$
$991$	−14.6016	−0.463835	−0.231918	+	0.972735i	$0.574500\pi$
$992$	−36.0556	−1.14477
$993$	18.3915	0.583638
$994$	28.5333	0.905021
$995$	12.2619	0.388729
$996$	−33.5209	−1.06215
$997$	10.4509	0.330983	0.165492	−	0.986211i	$-0.447079\pi$
$997$	10.4509	0.330983	0.165492	+	0.986211i	$0.447079\pi$
$998$	−31.2720	−0.989896
$999$	4.36455	0.138088

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.f.1.12	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.f.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-1.88001 q^{2} -1.81223 q^{3} +1.53444 q^{4} +2.13867 q^{5} +3.40702 q^{6} +1.99941 q^{7} +0.875255 q^{8} +0.284183 q^{9} +O(q^{10})\)	\(q-1.88001 q^{2} -1.81223 q^{3} +1.53444 q^{4} +2.13867 q^{5} +3.40702 q^{6} +1.99941 q^{7} +0.875255 q^{8} +0.284183 q^{9} -4.02072 q^{10} -1.00000 q^{11} -2.78076 q^{12} +4.25393 q^{13} -3.75891 q^{14} -3.87576 q^{15} -4.71437 q^{16} +1.00000 q^{17} -0.534267 q^{18} -0.707473 q^{19} +3.28166 q^{20} -3.62339 q^{21} +1.88001 q^{22} -3.06526 q^{23} -1.58616 q^{24} -0.426098 q^{25} -7.99743 q^{26} +4.92169 q^{27} +3.06798 q^{28} -5.23837 q^{29} +7.28648 q^{30} -5.06928 q^{31} +7.11256 q^{32} +1.81223 q^{33} -1.88001 q^{34} +4.27607 q^{35} +0.436062 q^{36} +0.886799 q^{37} +1.33006 q^{38} -7.70910 q^{39} +1.87188 q^{40} -11.8879 q^{41} +6.81202 q^{42} -1.00000 q^{43} -1.53444 q^{44} +0.607772 q^{45} +5.76272 q^{46} -0.190411 q^{47} +8.54353 q^{48} -3.00236 q^{49} +0.801069 q^{50} -1.81223 q^{51} +6.52740 q^{52} +0.911927 q^{53} -9.25283 q^{54} -2.13867 q^{55} +1.74999 q^{56} +1.28211 q^{57} +9.84818 q^{58} +14.1241 q^{59} -5.94713 q^{60} -3.89447 q^{61} +9.53030 q^{62} +0.568198 q^{63} -3.94295 q^{64} +9.09774 q^{65} -3.40702 q^{66} +0.454713 q^{67} +1.53444 q^{68} +5.55496 q^{69} -8.03907 q^{70} -7.59083 q^{71} +0.248732 q^{72} -1.67046 q^{73} -1.66719 q^{74} +0.772188 q^{75} -1.08558 q^{76} -1.99941 q^{77} +14.4932 q^{78} -11.5452 q^{79} -10.0825 q^{80} -9.77179 q^{81} +22.3494 q^{82} +12.0546 q^{83} -5.55989 q^{84} +2.13867 q^{85} +1.88001 q^{86} +9.49313 q^{87} -0.875255 q^{88} +2.13778 q^{89} -1.14262 q^{90} +8.50534 q^{91} -4.70346 q^{92} +9.18671 q^{93} +0.357975 q^{94} -1.51305 q^{95} -12.8896 q^{96} +13.1998 q^{97} +5.64447 q^{98} -0.284183 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) \) 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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