LMFDB - Embedded newform 8041.2.a.f.1.14

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			1.14
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)

$f(q)$	$=$	$q-1.74128 q^{2} -2.85862 q^{3} +1.03206 q^{4} -1.07282 q^{5} +4.97766 q^{6} +2.85165 q^{7} +1.68545 q^{8} +5.17170 q^{9} +O(q^{10})$	\(q-1.74128 q^{2} -2.85862 q^{3} +1.03206 q^{4} -1.07282 q^{5} +4.97766 q^{6} +2.85165 q^{7} +1.68545 q^{8} +5.17170 q^{9} +1.86807 q^{10} -1.00000 q^{11} -2.95027 q^{12} +0.0989502 q^{13} -4.96552 q^{14} +3.06677 q^{15} -4.99897 q^{16} +1.00000 q^{17} -9.00539 q^{18} +0.192411 q^{19} -1.10721 q^{20} -8.15178 q^{21} +1.74128 q^{22} +5.90206 q^{23} -4.81806 q^{24} -3.84907 q^{25} -0.172300 q^{26} -6.20806 q^{27} +2.94308 q^{28} -7.37727 q^{29} -5.34011 q^{30} -3.51212 q^{31} +5.33372 q^{32} +2.85862 q^{33} -1.74128 q^{34} -3.05929 q^{35} +5.33752 q^{36} +1.29992 q^{37} -0.335041 q^{38} -0.282861 q^{39} -1.80818 q^{40} +4.87024 q^{41} +14.1945 q^{42} -1.00000 q^{43} -1.03206 q^{44} -5.54828 q^{45} -10.2771 q^{46} +1.86674 q^{47} +14.2902 q^{48} +1.13190 q^{49} +6.70231 q^{50} -2.85862 q^{51} +0.102123 q^{52} +8.96278 q^{53} +10.8100 q^{54} +1.07282 q^{55} +4.80632 q^{56} -0.550029 q^{57} +12.8459 q^{58} -9.22587 q^{59} +3.16510 q^{60} +4.82341 q^{61} +6.11560 q^{62} +14.7479 q^{63} +0.710441 q^{64} -0.106155 q^{65} -4.97766 q^{66} -3.54536 q^{67} +1.03206 q^{68} -16.8717 q^{69} +5.32709 q^{70} +0.305056 q^{71} +8.71665 q^{72} +14.3122 q^{73} -2.26353 q^{74} +11.0030 q^{75} +0.198580 q^{76} -2.85165 q^{77} +0.492540 q^{78} +9.96205 q^{79} +5.36297 q^{80} +2.23138 q^{81} -8.48046 q^{82} -1.72375 q^{83} -8.41314 q^{84} -1.07282 q^{85} +1.74128 q^{86} +21.0888 q^{87} -1.68545 q^{88} +3.99409 q^{89} +9.66111 q^{90} +0.282171 q^{91} +6.09129 q^{92} +10.0398 q^{93} -3.25052 q^{94} -0.206421 q^{95} -15.2471 q^{96} +5.64852 q^{97} -1.97096 q^{98} -5.17170 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.74128	−1.23127	−0.615636	−	0.788031i	$-0.711101\pi$
$2$	−1.74128	−1.23127	−0.615636	+	0.788031i	$0.711101\pi$
$3$	−2.85862	−1.65042	−0.825212	−	0.564823i	$-0.808944\pi$
$3$	−2.85862	−1.65042	−0.825212	+	0.564823i	$0.808944\pi$
$4$	1.03206	0.516031
$5$	−1.07282	−0.479777	−0.239889	−	0.970800i	$-0.577111\pi$
$5$	−1.07282	−0.479777	−0.239889	+	0.970800i	$0.577111\pi$
$6$	4.97766	2.03212
$7$	2.85165	1.07782	0.538911	−	0.842363i	$-0.318836\pi$
$7$	2.85165	1.07782	0.538911	+	0.842363i	$0.318836\pi$
$8$	1.68545	0.595897
$9$	5.17170	1.72390
$10$	1.86807	0.590737
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.95027	−0.851671
$13$	0.0989502	0.0274438	0.0137219	−	0.999906i	$-0.495632\pi$
$13$	0.0989502	0.0274438	0.0137219	+	0.999906i	$0.495632\pi$
$14$	−4.96552	−1.32709
$15$	3.06677	0.791836
$16$	−4.99897	−1.24974
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−9.00539	−2.12259
$19$	0.192411	0.0441420	0.0220710	−	0.999756i	$-0.492974\pi$
$19$	0.192411	0.0441420	0.0220710	+	0.999756i	$0.492974\pi$
$20$	−1.10721	−0.247580
$21$	−8.15178	−1.77886
$22$	1.74128	0.371243
$23$	5.90206	1.23066	0.615332	−	0.788268i	$-0.289022\pi$
$23$	5.90206	1.23066	0.615332	+	0.788268i	$0.289022\pi$
$24$	−4.81806	−0.983483
$25$	−3.84907	−0.769814
$26$	−0.172300	−0.0337908
$27$	−6.20806	−1.19474
$28$	2.94308	0.556190
$29$	−7.37727	−1.36992	−0.684962	−	0.728578i	$-0.740181\pi$
$29$	−7.37727	−1.36992	−0.684962	+	0.728578i	$0.740181\pi$
$30$	−5.34011	−0.974966
$31$	−3.51212	−0.630796	−0.315398	−	0.948959i	$-0.602138\pi$
$31$	−3.51212	−0.630796	−0.315398	+	0.948959i	$0.602138\pi$
$32$	5.33372	0.942877
$33$	2.85862	0.497622
$34$	−1.74128	−0.298627
$35$	−3.05929	−0.517115
$36$	5.33752	0.889586
$37$	1.29992	0.213705	0.106853	−	0.994275i	$-0.465923\pi$
$37$	1.29992	0.213705	0.106853	+	0.994275i	$0.465923\pi$
$38$	−0.335041	−0.0543508
$39$	−0.282861	−0.0452940
$40$	−1.80818	−0.285898
$41$	4.87024	0.760604	0.380302	−	0.924862i	$-0.375820\pi$
$41$	4.87024	0.760604	0.380302	+	0.924862i	$0.375820\pi$
$42$	14.1945	2.19026
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−1.03206	−0.155589
$45$	−5.54828	−0.827088
$46$	−10.2771	−1.51528
$47$	1.86674	0.272292	0.136146	−	0.990689i	$-0.456528\pi$
$47$	1.86674	0.272292	0.136146	+	0.990689i	$0.456528\pi$
$48$	14.2902	2.06261
$49$	1.13190	0.161700
$50$	6.70231	0.947850
$51$	−2.85862	−0.400287
$52$	0.102123	0.0141619
$53$	8.96278	1.23113	0.615566	−	0.788085i	$-0.288927\pi$
$53$	8.96278	1.23113	0.615566	+	0.788085i	$0.288927\pi$
$54$	10.8100	1.47105
$55$	1.07282	0.144658
$56$	4.80632	0.642271
$57$	−0.550029	−0.0728531
$58$	12.8459	1.68675
$59$	−9.22587	−1.20111	−0.600553	−	0.799585i	$-0.705053\pi$
$59$	−9.22587	−1.20111	−0.600553	+	0.799585i	$0.705053\pi$
$60$	3.16510	0.408612
$61$	4.82341	0.617575	0.308787	−	0.951131i	$-0.400077\pi$
$61$	4.82341	0.617575	0.308787	+	0.951131i	$0.400077\pi$
$62$	6.11560	0.776682
$63$	14.7479	1.85806
$64$	0.710441	0.0888051
$65$	−0.106155	−0.0131669
$66$	−4.97766	−0.612708
$67$	−3.54536	−0.433135	−0.216568	−	0.976268i	$-0.569486\pi$
$67$	−3.54536	−0.433135	−0.216568	+	0.976268i	$0.569486\pi$
$68$	1.03206	0.125156
$69$	−16.8717	−2.03112
$70$	5.32709	0.636709
$71$	0.305056	0.0362035	0.0181018	−	0.999836i	$-0.494238\pi$
$71$	0.305056	0.0362035	0.0181018	+	0.999836i	$0.494238\pi$
$72$	8.71665	1.02727
$73$	14.3122	1.67512	0.837560	−	0.546345i	$-0.183981\pi$
$73$	14.3122	1.67512	0.837560	+	0.546345i	$0.183981\pi$
$74$	−2.26353	−0.263129
$75$	11.0030	1.27052
$76$	0.198580	0.0227787
$77$	−2.85165	−0.324976
$78$	0.492540	0.0557692
$79$	9.96205	1.12082	0.560409	−	0.828216i	$-0.310644\pi$
$79$	9.96205	1.12082	0.560409	+	0.828216i	$0.310644\pi$
$80$	5.36297	0.599599
$81$	2.23138	0.247931
$82$	−8.48046	−0.936510
$83$	−1.72375	−0.189206	−0.0946029	−	0.995515i	$-0.530158\pi$
$83$	−1.72375	−0.189206	−0.0946029	+	0.995515i	$0.530158\pi$
$84$	−8.41314	−0.917949
$85$	−1.07282	−0.116363
$86$	1.74128	0.187767
$87$	21.0888	2.26096
$88$	−1.68545	−0.179670
$89$	3.99409	0.423373	0.211686	−	0.977338i	$-0.432104\pi$
$89$	3.99409	0.423373	0.211686	+	0.977338i	$0.432104\pi$
$90$	9.66111	1.01837
$91$	0.282171	0.0295796
$92$	6.09129	0.635061
$93$	10.0398	1.04108
$94$	−3.25052	−0.335266
$95$	−0.206421	−0.0211783
$96$	−15.2471	−1.55615
$97$	5.64852	0.573521	0.286760	−	0.958002i	$-0.407422\pi$
$97$	5.64852	0.573521	0.286760	+	0.958002i	$0.407422\pi$
$98$	−1.97096	−0.199097
$99$	−5.17170	−0.519775
$100$	−3.97248	−0.397248
$101$	−5.64898	−0.562094	−0.281047	−	0.959694i	$-0.590682\pi$
$101$	−5.64898	−0.562094	−0.281047	+	0.959694i	$0.590682\pi$
$102$	4.97766	0.492862
$103$	−0.653404	−0.0643818	−0.0321909	−	0.999482i	$-0.510248\pi$
$103$	−0.653404	−0.0643818	−0.0321909	+	0.999482i	$0.510248\pi$
$104$	0.166776	0.0163537
$105$	8.74535	0.853459
$106$	−15.6067	−1.51586
$107$	11.5790	1.11938	0.559692	−	0.828701i	$-0.310919\pi$
$107$	11.5790	1.11938	0.559692	+	0.828701i	$0.310919\pi$
$108$	−6.40711	−0.616524
$109$	1.82662	0.174959	0.0874794	−	0.996166i	$-0.472119\pi$
$109$	1.82662	0.174959	0.0874794	+	0.996166i	$0.472119\pi$
$110$	−1.86807	−0.178114
$111$	−3.71597	−0.352704
$112$	−14.2553	−1.34700
$113$	−4.50214	−0.423526	−0.211763	−	0.977321i	$-0.567920\pi$
$113$	−4.50214	−0.423526	−0.211763	+	0.977321i	$0.567920\pi$
$114$	0.957755	0.0897019
$115$	−6.33181	−0.590445
$116$	−7.61381	−0.706924
$117$	0.511741	0.0473104
$118$	16.0648	1.47889
$119$	2.85165	0.261410
$120$	5.16889	0.471853
$121$	1.00000	0.0909091
$122$	−8.39892	−0.760403
$123$	−13.9222	−1.25532
$124$	−3.62473	−0.325511
$125$	9.49341	0.849117
$126$	−25.6802	−2.28777
$127$	4.00985	0.355817	0.177908	−	0.984047i	$-0.443067\pi$
$127$	4.00985	0.355817	0.177908	+	0.984047i	$0.443067\pi$
$128$	−11.9045	−1.05222
$129$	2.85862	0.251687
$130$	0.184846	0.0162121
$131$	2.94640	0.257428	0.128714	−	0.991682i	$-0.458915\pi$
$131$	2.94640	0.257428	0.128714	+	0.991682i	$0.458915\pi$
$132$	2.95027	0.256788
$133$	0.548687	0.0475772
$134$	6.17348	0.533307
$135$	6.66010	0.573210
$136$	1.68545	0.144526
$137$	−4.49579	−0.384101	−0.192051	−	0.981385i	$-0.561514\pi$
$137$	−4.49579	−0.384101	−0.192051	+	0.981385i	$0.561514\pi$
$138$	29.3784	2.50086
$139$	−11.0676	−0.938740	−0.469370	−	0.883002i	$-0.655519\pi$
$139$	−11.0676	−0.938740	−0.469370	+	0.883002i	$0.655519\pi$
$140$	−3.15738	−0.266847
$141$	−5.33630	−0.449398
$142$	−0.531189	−0.0445764
$143$	−0.0989502	−0.00827463
$144$	−25.8532	−2.15443
$145$	7.91445	0.657259
$146$	−24.9216	−2.06253
$147$	−3.23567	−0.266874
$148$	1.34160	0.110279
$149$	0.934562	0.0765623	0.0382811	−	0.999267i	$-0.487812\pi$
$149$	0.934562	0.0765623	0.0382811	+	0.999267i	$0.487812\pi$
$150$	−19.1594	−1.56435
$151$	6.20815	0.505212	0.252606	−	0.967569i	$-0.418712\pi$
$151$	6.20815	0.505212	0.252606	+	0.967569i	$0.418712\pi$
$152$	0.324299	0.0263041
$153$	5.17170	0.418107
$154$	4.96552	0.400133
$155$	3.76786	0.302642
$156$	−0.291930	−0.0233731
$157$	−11.9700	−0.955308	−0.477654	−	0.878548i	$-0.658513\pi$
$157$	−11.9700	−0.955308	−0.477654	+	0.878548i	$0.658513\pi$
$158$	−17.3467	−1.38003
$159$	−25.6212	−2.03189
$160$	−5.72209	−0.452371
$161$	16.8306	1.32644
$162$	−3.88546	−0.305270
$163$	−4.34878	−0.340623	−0.170311	−	0.985390i	$-0.554477\pi$
$163$	−4.34878	−0.340623	−0.170311	+	0.985390i	$0.554477\pi$
$164$	5.02639	0.392495
$165$	−3.06677	−0.238748
$166$	3.00153	0.232964
$167$	0.205017	0.0158647	0.00793236	−	0.999969i	$-0.497475\pi$
$167$	0.205017	0.0158647	0.00793236	+	0.999969i	$0.497475\pi$
$168$	−13.7394	−1.06002
$169$	−12.9902	−0.999247
$170$	1.86807	0.143275
$171$	0.995090	0.0760964
$172$	−1.03206	−0.0786940
$173$	−19.6220	−1.49184	−0.745918	−	0.666038i	$-0.767989\pi$
$173$	−19.6220	−1.49184	−0.745918	+	0.666038i	$0.767989\pi$
$174$	−36.7216	−2.78385
$175$	−10.9762	−0.829722
$176$	4.99897	0.376812
$177$	26.3732	1.98233
$178$	−6.95483	−0.521287
$179$	20.5996	1.53969	0.769843	−	0.638233i	$-0.220335\pi$
$179$	20.5996	1.53969	0.769843	+	0.638233i	$0.220335\pi$
$180$	−5.72617	−0.426803
$181$	17.0663	1.26853	0.634263	−	0.773117i	$-0.281304\pi$
$181$	17.0663	1.26853	0.634263	+	0.773117i	$0.281304\pi$
$182$	−0.491339	−0.0364205
$183$	−13.7883	−1.01926
$184$	9.94763	0.733349
$185$	−1.39457	−0.102531
$186$	−17.4822	−1.28185
$187$	−1.00000	−0.0731272
$188$	1.92660	0.140511
$189$	−17.7032	−1.28772
$190$	0.359437	0.0260763
$191$	−0.258175	−0.0186809	−0.00934043	−	0.999956i	$-0.502973\pi$
$191$	−0.258175	−0.0186809	−0.00934043	+	0.999956i	$0.502973\pi$
$192$	−2.03088	−0.146566
$193$	4.14429	0.298313	0.149156	−	0.988814i	$-0.452344\pi$
$193$	4.14429	0.298313	0.149156	+	0.988814i	$0.452344\pi$
$194$	−9.83567	−0.706160
$195$	0.303457	0.0217310
$196$	1.16819	0.0834423
$197$	−2.96789	−0.211453	−0.105727	−	0.994395i	$-0.533717\pi$
$197$	−2.96789	−0.211453	−0.105727	+	0.994395i	$0.533717\pi$
$198$	9.00539	0.639985
$199$	−5.38684	−0.381863	−0.190932	−	0.981603i	$-0.561151\pi$
$199$	−5.38684	−0.381863	−0.190932	+	0.981603i	$0.561151\pi$
$200$	−6.48742	−0.458730
$201$	10.1348	0.714856
$202$	9.83647	0.692091
$203$	−21.0374	−1.47654
$204$	−2.95027	−0.206560
$205$	−5.22487	−0.364921
$206$	1.13776	0.0792716
$207$	30.5237	2.12154
$208$	−0.494649	−0.0342977
$209$	−0.192411	−0.0133093
$210$	−15.2281	−1.05084
$211$	−26.4225	−1.81900	−0.909499	−	0.415706i	$-0.863535\pi$
$211$	−26.4225	−1.81900	−0.909499	+	0.415706i	$0.863535\pi$
$212$	9.25015	0.635303
$213$	−0.872040	−0.0597512
$214$	−20.1623	−1.37827
$215$	1.07282	0.0731654
$216$	−10.4634	−0.711943
$217$	−10.0153	−0.679886
$218$	−3.18066	−0.215422
$219$	−40.9132	−2.76466
$220$	1.10721	0.0746482
$221$	0.0989502	0.00665611
$222$	6.47055	0.434275
$223$	−8.77087	−0.587341	−0.293670	−	0.955907i	$-0.594877\pi$
$223$	−8.77087	−0.587341	−0.293670	+	0.955907i	$0.594877\pi$
$224$	15.2099	1.01625
$225$	−19.9062	−1.32708
$226$	7.83950	0.521476
$227$	−14.2159	−0.943540	−0.471770	−	0.881722i	$-0.656385\pi$
$227$	−14.2159	−0.943540	−0.471770	+	0.881722i	$0.656385\pi$
$228$	−0.567664	−0.0375945
$229$	−0.731710	−0.0483528	−0.0241764	−	0.999708i	$-0.507696\pi$
$229$	−0.731710	−0.0483528	−0.0241764	+	0.999708i	$0.507696\pi$
$230$	11.0255	0.726998
$231$	8.15178	0.536347
$232$	−12.4340	−0.816334
$233$	23.4137	1.53388	0.766940	−	0.641718i	$-0.221778\pi$
$233$	23.4137	1.53388	0.766940	+	0.641718i	$0.221778\pi$
$234$	−0.891085	−0.0582520
$235$	−2.00267	−0.130640
$236$	−9.52168	−0.619808
$237$	−28.4777	−1.84983
$238$	−4.96552	−0.321867
$239$	12.6273	0.816792	0.408396	−	0.912805i	$-0.366088\pi$
$239$	12.6273	0.816792	0.408396	+	0.912805i	$0.366088\pi$
$240$	−15.3307	−0.989592
$241$	−4.31071	−0.277677	−0.138839	−	0.990315i	$-0.544337\pi$
$241$	−4.31071	−0.277677	−0.138839	+	0.990315i	$0.544337\pi$
$242$	−1.74128	−0.111934
$243$	12.2455	0.785551
$244$	4.97806	0.318688
$245$	−1.21432	−0.0775800
$246$	24.2424	1.54564
$247$	0.0190391	0.00121143
$248$	−5.91952	−0.375890
$249$	4.92754	0.312270
$250$	−16.5307	−1.04549
$251$	10.1293	0.639353	0.319676	−	0.947527i	$-0.396426\pi$
$251$	10.1293	0.639353	0.319676	+	0.947527i	$0.396426\pi$
$252$	15.2207	0.958816
$253$	−5.90206	−0.371059
$254$	−6.98228	−0.438107
$255$	3.06677	0.192049
$256$	19.3082	1.20676
$257$	3.78362	0.236016	0.118008	−	0.993013i	$-0.462349\pi$
$257$	3.78362	0.236016	0.118008	+	0.993013i	$0.462349\pi$
$258$	−4.97766	−0.309896
$259$	3.70691	0.230336
$260$	−0.109559	−0.00679455
$261$	−38.1530	−2.36161
$262$	−5.13052	−0.316964
$263$	17.2490	1.06362	0.531810	−	0.846864i	$-0.321512\pi$
$263$	17.2490	1.06362	0.531810	+	0.846864i	$0.321512\pi$
$264$	4.81806	0.296531
$265$	−9.61541	−0.590670
$266$	−0.955420	−0.0585805
$267$	−11.4176	−0.698744
$268$	−3.65904	−0.223511
$269$	10.7137	0.653227	0.326613	−	0.945158i	$-0.394093\pi$
$269$	10.7137	0.653227	0.326613	+	0.945158i	$0.394093\pi$
$270$	−11.5971	−0.705778
$271$	−18.9241	−1.14956	−0.574779	−	0.818309i	$-0.694912\pi$
$271$	−18.9241	−1.14956	−0.574779	+	0.818309i	$0.694912\pi$
$272$	−4.99897	−0.303107
$273$	−0.806620	−0.0488188
$274$	7.82844	0.472933
$275$	3.84907	0.232108
$276$	−17.4127	−1.04812
$277$	9.56727	0.574842	0.287421	−	0.957804i	$-0.407202\pi$
$277$	9.56727	0.574842	0.287421	+	0.957804i	$0.407202\pi$
$278$	19.2718	1.15584
$279$	−18.1637	−1.08743
$280$	−5.15629	−0.308147
$281$	17.4093	1.03855	0.519275	−	0.854607i	$-0.326202\pi$
$281$	17.4093	1.03855	0.519275	+	0.854607i	$0.326202\pi$
$282$	9.29201	0.553331
$283$	−27.0338	−1.60699	−0.803495	−	0.595311i	$-0.797029\pi$
$283$	−27.0338	−1.60699	−0.803495	+	0.595311i	$0.797029\pi$
$284$	0.314837	0.0186822
$285$	0.590079	0.0349533
$286$	0.172300	0.0101883
$287$	13.8882	0.819795
$288$	27.5844	1.62542
$289$	1.00000	0.0588235
$290$	−13.7813	−0.809265
$291$	−16.1470	−0.946553
$292$	14.7711	0.864415
$293$	−16.5696	−0.968009	−0.484004	−	0.875066i	$-0.660818\pi$
$293$	−16.5696	−0.968009	−0.484004	+	0.875066i	$0.660818\pi$
$294$	5.63422	0.328594
$295$	9.89765	0.576264
$296$	2.19095	0.127346
$297$	6.20806	0.360228
$298$	−1.62734	−0.0942690
$299$	0.584009	0.0337741
$300$	11.3558	0.655628
$301$	−2.85165	−0.164366
$302$	−10.8101	−0.622054
$303$	16.1483	0.927694
$304$	−0.961855	−0.0551662
$305$	−5.17463	−0.296298
$306$	−9.00539	−0.514804
$307$	−18.9431	−1.08114	−0.540571	−	0.841298i	$-0.681792\pi$
$307$	−18.9431	−1.08114	−0.540571	+	0.841298i	$0.681792\pi$
$308$	−2.94308	−0.167698
$309$	1.86783	0.106257
$310$	−6.56091	−0.372634
$311$	2.95531	0.167580	0.0837902	−	0.996483i	$-0.473297\pi$
$311$	2.95531	0.167580	0.0837902	+	0.996483i	$0.473297\pi$
$312$	−0.476748	−0.0269906
$313$	−15.5166	−0.877049	−0.438524	−	0.898719i	$-0.644499\pi$
$313$	−15.5166	−0.877049	−0.438524	+	0.898719i	$0.644499\pi$
$314$	20.8431	1.17624
$315$	−15.8217	−0.891454
$316$	10.2815	0.578377
$317$	−17.9062	−1.00571	−0.502856	−	0.864370i	$-0.667717\pi$
$317$	−17.9062	−1.00571	−0.502856	+	0.864370i	$0.667717\pi$
$318$	44.6137	2.50181
$319$	7.37727	0.413048
$320$	−0.762172	−0.0426067
$321$	−33.1000	−1.84746
$322$	−29.3068	−1.63320
$323$	0.192411	0.0107060
$324$	2.30292	0.127940
$325$	−0.380866	−0.0211266
$326$	7.57245	0.419399
$327$	−5.22162	−0.288756
$328$	8.20855	0.453242
$329$	5.32329	0.293483
$330$	5.34011	0.293963
$331$	31.9551	1.75641	0.878204	−	0.478285i	$-0.158742\pi$
$331$	31.9551	1.75641	0.878204	+	0.478285i	$0.158742\pi$
$332$	−1.77902	−0.0976361
$333$	6.72279	0.368407
$334$	−0.356993	−0.0195338
$335$	3.80352	0.207808
$336$	40.7505	2.22312
$337$	−31.3104	−1.70558	−0.852792	−	0.522250i	$-0.825093\pi$
$337$	−31.3104	−1.70558	−0.852792	+	0.522250i	$0.825093\pi$
$338$	22.6196	1.23034
$339$	12.8699	0.698997
$340$	−1.10721	−0.0600470
$341$	3.51212	0.190192
$342$	−1.73273	−0.0936954
$343$	−16.7338	−0.903538
$344$	−1.68545	−0.0908735
$345$	18.1002	0.974484
$346$	34.1675	1.83686
$347$	−13.0979	−0.703134	−0.351567	−	0.936163i	$-0.614351\pi$
$347$	−13.0979	−0.703134	−0.351567	+	0.936163i	$0.614351\pi$
$348$	21.7650	1.16672
$349$	−0.270242	−0.0144657	−0.00723285	−	0.999974i	$-0.502302\pi$
$349$	−0.270242	−0.0144657	−0.00723285	+	0.999974i	$0.502302\pi$
$350$	19.1126	1.02161
$351$	−0.614289	−0.0327883
$352$	−5.33372	−0.284288
$353$	22.9929	1.22379	0.611894	−	0.790940i	$-0.290408\pi$
$353$	22.9929	1.22379	0.611894	+	0.790940i	$0.290408\pi$
$354$	−45.9233	−2.44079
$355$	−0.327269	−0.0173696
$356$	4.12215	0.218474
$357$	−8.15178	−0.431438
$358$	−35.8697	−1.89577
$359$	−7.63343	−0.402877	−0.201438	−	0.979501i	$-0.564562\pi$
$359$	−7.63343	−0.402877	−0.201438	+	0.979501i	$0.564562\pi$
$360$	−9.35135	−0.492860
$361$	−18.9630	−0.998051
$362$	−29.7172	−1.56190
$363$	−2.85862	−0.150039
$364$	0.291218	0.0152640
$365$	−15.3544	−0.803685
$366$	24.0093	1.25499
$367$	−9.71756	−0.507252	−0.253626	−	0.967302i	$-0.581623\pi$
$367$	−9.71756	−0.507252	−0.253626	+	0.967302i	$0.581623\pi$
$368$	−29.5042	−1.53801
$369$	25.1874	1.31120
$370$	2.42834	0.126244
$371$	25.5587	1.32694
$372$	10.3617	0.537231
$373$	−31.5659	−1.63442	−0.817209	−	0.576341i	$-0.804480\pi$
$373$	−31.5659	−1.63442	−0.817209	+	0.576341i	$0.804480\pi$
$374$	1.74128	0.0900395
$375$	−27.1380	−1.40140
$376$	3.14630	0.162258
$377$	−0.729982	−0.0375960
$378$	30.8263	1.58553
$379$	−17.5942	−0.903752	−0.451876	−	0.892081i	$-0.649245\pi$
$379$	−17.5942	−0.903752	−0.451876	+	0.892081i	$0.649245\pi$
$380$	−0.213039	−0.0109287
$381$	−11.4626	−0.587248
$382$	0.449555	0.0230012
$383$	31.8074	1.62528	0.812642	−	0.582764i	$-0.198029\pi$
$383$	31.8074	1.62528	0.812642	+	0.582764i	$0.198029\pi$
$384$	34.0305	1.73661
$385$	3.05929	0.155916
$386$	−7.21638	−0.367304
$387$	−5.17170	−0.262892
$388$	5.82963	0.295955
$389$	−7.40010	−0.375200	−0.187600	−	0.982246i	$-0.560071\pi$
$389$	−7.40010	−0.375200	−0.187600	+	0.982246i	$0.560071\pi$
$390$	−0.528405	−0.0267568
$391$	5.90206	0.298480
$392$	1.90776	0.0963566
$393$	−8.42264	−0.424866
$394$	5.16793	0.260356
$395$	−10.6874	−0.537743
$396$	−5.33752	−0.268220
$397$	1.84747	0.0927219	0.0463610	−	0.998925i	$-0.485238\pi$
$397$	1.84747	0.0927219	0.0463610	+	0.998925i	$0.485238\pi$
$398$	9.38001	0.470177
$399$	−1.56849	−0.0785226
$400$	19.2414	0.962069
$401$	−8.43615	−0.421281	−0.210641	−	0.977564i	$-0.567555\pi$
$401$	−8.43615	−0.421281	−0.210641	+	0.977564i	$0.567555\pi$
$402$	−17.6476	−0.880183
$403$	−0.347525	−0.0173115
$404$	−5.83010	−0.290058
$405$	−2.39386	−0.118952
$406$	36.6320	1.81802
$407$	−1.29992	−0.0644346
$408$	−4.81806	−0.238530
$409$	11.6564	0.576372	0.288186	−	0.957574i	$-0.406948\pi$
$409$	11.6564	0.576372	0.288186	+	0.957574i	$0.406948\pi$
$410$	9.09797	0.449317
$411$	12.8518	0.633930
$412$	−0.674354	−0.0332231
$413$	−26.3089	−1.29458
$414$	−53.1503	−2.61219
$415$	1.84926	0.0907767
$416$	0.527772	0.0258762
$417$	31.6380	1.54932
$418$	0.335041	0.0163874
$419$	39.6875	1.93886	0.969430	−	0.245369i	$-0.0789092\pi$
$419$	39.6875	1.93886	0.969430	+	0.245369i	$0.0789092\pi$
$420$	9.02575	0.440411
$421$	27.5429	1.34236	0.671180	−	0.741294i	$-0.265788\pi$
$421$	27.5429	1.34236	0.671180	+	0.741294i	$0.265788\pi$
$422$	46.0090	2.23968
$423$	9.65423	0.469405
$424$	15.1063	0.733629
$425$	−3.84907	−0.186707
$426$	1.51847	0.0735700
$427$	13.7547	0.665635
$428$	11.9503	0.577638
$429$	0.282861	0.0136566
$430$	−1.86807	−0.0900865
$431$	2.11930	0.102083	0.0510416	−	0.998697i	$-0.483746\pi$
$431$	2.11930	0.102083	0.0510416	+	0.998697i	$0.483746\pi$
$432$	31.0339	1.49312
$433$	1.25190	0.0601623	0.0300812	−	0.999547i	$-0.490423\pi$
$433$	1.25190	0.0601623	0.0300812	+	0.999547i	$0.490423\pi$
$434$	17.4395	0.837125
$435$	−22.6244	−1.08476
$436$	1.88519	0.0902842
$437$	1.13562	0.0543240
$438$	71.2415	3.40405
$439$	11.3633	0.542339	0.271169	−	0.962532i	$-0.412590\pi$
$439$	11.3633	0.542339	0.271169	+	0.962532i	$0.412590\pi$
$440$	1.80818	0.0862015
$441$	5.85385	0.278755
$442$	−0.172300	−0.00819548
$443$	13.8377	0.657450	0.328725	−	0.944426i	$-0.393381\pi$
$443$	13.8377	0.657450	0.328725	+	0.944426i	$0.393381\pi$
$444$	−3.83512	−0.182007
$445$	−4.28492	−0.203125
$446$	15.2726	0.723176
$447$	−2.67156	−0.126360
$448$	2.02593	0.0957161
$449$	7.36503	0.347577	0.173789	−	0.984783i	$-0.444399\pi$
$449$	7.36503	0.347577	0.173789	+	0.984783i	$0.444399\pi$
$450$	34.6623	1.63400
$451$	−4.87024	−0.229331
$452$	−4.64649	−0.218553
$453$	−17.7467	−0.833814
$454$	24.7538	1.16175
$455$	−0.302717	−0.0141916
$456$	−0.927047	−0.0434129
$457$	9.29209	0.434666	0.217333	−	0.976098i	$-0.430264\pi$
$457$	9.29209	0.434666	0.217333	+	0.976098i	$0.430264\pi$
$458$	1.27411	0.0595354
$459$	−6.20806	−0.289767
$460$	−6.53483	−0.304688
$461$	4.86321	0.226502	0.113251	−	0.993566i	$-0.463874\pi$
$461$	4.86321	0.226502	0.113251	+	0.993566i	$0.463874\pi$
$462$	−14.1945	−0.660390
$463$	4.01896	0.186777	0.0933884	−	0.995630i	$-0.470230\pi$
$463$	4.01896	0.186777	0.0933884	+	0.995630i	$0.470230\pi$
$464$	36.8788	1.71205
$465$	−10.7709	−0.499487
$466$	−40.7698	−1.88863
$467$	7.63358	0.353240	0.176620	−	0.984279i	$-0.443484\pi$
$467$	7.63358	0.353240	0.176620	+	0.984279i	$0.443484\pi$
$468$	0.528148	0.0244137
$469$	−10.1101	−0.466842
$470$	3.48721	0.160853
$471$	34.2176	1.57666
$472$	−15.5498	−0.715736
$473$	1.00000	0.0459800
$474$	49.5877	2.27764
$475$	−0.740601	−0.0339811
$476$	2.94308	0.134896
$477$	46.3528	2.12235
$478$	−21.9877	−1.00569
$479$	−6.14421	−0.280736	−0.140368	−	0.990099i	$-0.544829\pi$
$479$	−6.14421	−0.280736	−0.140368	+	0.990099i	$0.544829\pi$
$480$	16.3573	0.746604
$481$	0.128627	0.00586490
$482$	7.50616	0.341896
$483$	−48.1122	−2.18918
$484$	1.03206	0.0469119
$485$	−6.05982	−0.275162
$486$	−21.3229	−0.967227
$487$	22.7752	1.03204	0.516022	−	0.856575i	$-0.327412\pi$
$487$	22.7752	1.03204	0.516022	+	0.856575i	$0.327412\pi$
$488$	8.12963	0.368011
$489$	12.4315	0.562172
$490$	2.11447	0.0955222
$491$	7.07603	0.319337	0.159668	−	0.987171i	$-0.448957\pi$
$491$	7.07603	0.319337	0.159668	+	0.987171i	$0.448957\pi$
$492$	−14.3685	−0.647784
$493$	−7.37727	−0.332256
$494$	−0.0331524	−0.00149160
$495$	5.54828	0.249376
$496$	17.5570	0.788333
$497$	0.869914	0.0390210
$498$	−8.58023	−0.384489
$499$	−29.3144	−1.31229	−0.656146	−	0.754634i	$-0.727815\pi$
$499$	−29.3144	−1.31229	−0.656146	+	0.754634i	$0.727815\pi$
$500$	9.79780	0.438171
$501$	−0.586067	−0.0261835
$502$	−17.6379	−0.787217
$503$	−11.1205	−0.495837	−0.247919	−	0.968781i	$-0.579747\pi$
$503$	−11.1205	−0.495837	−0.247919	+	0.968781i	$0.579747\pi$
$504$	24.8568	1.10721
$505$	6.06031	0.269680
$506$	10.2771	0.456875
$507$	37.1341	1.64918
$508$	4.13842	0.183612
$509$	29.9189	1.32613	0.663067	−	0.748560i	$-0.269255\pi$
$509$	29.9189	1.32613	0.663067	+	0.748560i	$0.269255\pi$
$510$	−5.34011	−0.236464
$511$	40.8135	1.80548
$512$	−9.81204	−0.433635
$513$	−1.19450	−0.0527383
$514$	−6.58835	−0.290600
$515$	0.700982	0.0308890
$516$	2.95027	0.129879
$517$	−1.86674	−0.0820992
$518$	−6.45478	−0.283607
$519$	56.0919	2.46216
$520$	−0.178920	−0.00784614
$521$	−26.0988	−1.14341	−0.571705	−	0.820459i	$-0.693718\pi$
$521$	−26.0988	−1.14341	−0.571705	+	0.820459i	$0.693718\pi$
$522$	66.4352	2.90779
$523$	23.2173	1.01522	0.507612	−	0.861586i	$-0.330528\pi$
$523$	23.2173	1.01522	0.507612	+	0.861586i	$0.330528\pi$
$524$	3.04087	0.132841
$525$	31.3767	1.36939
$526$	−30.0354	−1.30961
$527$	−3.51212	−0.152991
$528$	−14.2902	−0.621899
$529$	11.8343	0.514533
$530$	16.7431	0.727275
$531$	−47.7134	−2.07059
$532$	0.566280	0.0245513
$533$	0.481911	0.0208739
$534$	19.8812	0.860344
$535$	−12.4221	−0.537055
$536$	−5.97554	−0.258104
$537$	−58.8864	−2.54113
$538$	−18.6556	−0.804300
$539$	−1.13190	−0.0487544
$540$	6.87364	0.295794
$541$	−38.4658	−1.65378	−0.826888	−	0.562367i	$-0.809891\pi$
$541$	−38.4658	−1.65378	−0.826888	+	0.562367i	$0.809891\pi$
$542$	32.9522	1.41542
$543$	−48.7860	−2.09361
$544$	5.33372	0.228681
$545$	−1.95963	−0.0839412
$546$	1.40455	0.0601093
$547$	31.3365	1.33985	0.669925	−	0.742428i	$-0.266326\pi$
$547$	31.3365	1.33985	0.669925	+	0.742428i	$0.266326\pi$
$548$	−4.63994	−0.198208
$549$	24.9452	1.06464
$550$	−6.70231	−0.285788
$551$	−1.41947	−0.0604712
$552$	−28.4365	−1.21034
$553$	28.4083	1.20804
$554$	−16.6593	−0.707786
$555$	3.98655	0.169220
$556$	−11.4224	−0.484419
$557$	39.9874	1.69432	0.847160	−	0.531338i	$-0.178311\pi$
$557$	39.9874	1.69432	0.847160	+	0.531338i	$0.178311\pi$
$558$	31.6280	1.33892
$559$	−0.0989502	−0.00418515
$560$	15.2933	0.646260
$561$	2.85862	0.120691
$562$	−30.3145	−1.27874
$563$	46.9055	1.97683	0.988415	−	0.151777i	$-0.0484996\pi$
$563$	46.9055	1.97683	0.988415	+	0.151777i	$0.0484996\pi$
$564$	−5.50740	−0.231903
$565$	4.82997	0.203198
$566$	47.0734	1.97864
$567$	6.36310	0.267225
$568$	0.514158	0.0215736
$569$	36.0424	1.51097	0.755487	−	0.655164i	$-0.227400\pi$
$569$	36.0424	1.51097	0.755487	+	0.655164i	$0.227400\pi$
$570$	−1.02749	−0.0430370
$571$	18.7031	0.782701	0.391351	−	0.920242i	$-0.372008\pi$
$571$	18.7031	0.782701	0.391351	+	0.920242i	$0.372008\pi$
$572$	−0.102123	−0.00426997
$573$	0.738023	0.0308313
$574$	−24.1833	−1.00939
$575$	−22.7174	−0.947382
$576$	3.67419	0.153091
$577$	−3.50546	−0.145934	−0.0729670	−	0.997334i	$-0.523247\pi$
$577$	−3.50546	−0.145934	−0.0729670	+	0.997334i	$0.523247\pi$
$578$	−1.74128	−0.0724278
$579$	−11.8470	−0.492342
$580$	8.16821	0.339166
$581$	−4.91552	−0.203930
$582$	28.1164	1.16546
$583$	−8.96278	−0.371201
$584$	24.1226	0.998200
$585$	−0.549003	−0.0226985
$586$	28.8524	1.19188
$587$	26.6184	1.09866	0.549330	−	0.835605i	$-0.314883\pi$
$587$	26.6184	1.09866	0.549330	+	0.835605i	$0.314883\pi$
$588$	−3.33942	−0.137715
$589$	−0.675770	−0.0278446
$590$	−17.2346	−0.709537
$591$	8.48405	0.348987
$592$	−6.49826	−0.267077
$593$	9.59520	0.394028	0.197014	−	0.980401i	$-0.436876\pi$
$593$	9.59520	0.394028	0.197014	+	0.980401i	$0.436876\pi$
$594$	−10.8100	−0.443539
$595$	−3.05929	−0.125419
$596$	0.964526	0.0395085
$597$	15.3989	0.630236
$598$	−1.01693	−0.0415852
$599$	0.777548	0.0317697	0.0158849	−	0.999874i	$-0.494943\pi$
$599$	0.777548	0.0317697	0.0158849	+	0.999874i	$0.494943\pi$
$600$	18.5451	0.757099
$601$	−31.8536	−1.29934	−0.649668	−	0.760218i	$-0.725092\pi$
$601$	−31.8536	−1.29934	−0.649668	+	0.760218i	$0.725092\pi$
$602$	4.96552	0.202380
$603$	−18.3356	−0.746681
$604$	6.40720	0.260705
$605$	−1.07282	−0.0436161
$606$	−28.1187	−1.14224
$607$	13.8156	0.560758	0.280379	−	0.959889i	$-0.409540\pi$
$607$	13.8156	0.560758	0.280379	+	0.959889i	$0.409540\pi$
$608$	1.02626	0.0416205
$609$	60.1379	2.43691
$610$	9.01049	0.364824
$611$	0.184714	0.00747275
$612$	5.33752	0.215756
$613$	13.5708	0.548121	0.274060	−	0.961713i	$-0.411633\pi$
$613$	13.5708	0.548121	0.274060	+	0.961713i	$0.411633\pi$
$614$	32.9854	1.33118
$615$	14.9359	0.602274
$616$	−4.80632	−0.193652
$617$	−26.6209	−1.07172	−0.535859	−	0.844307i	$-0.680012\pi$
$617$	−26.6209	−1.07172	−0.535859	+	0.844307i	$0.680012\pi$
$618$	−3.25243	−0.130832
$619$	14.2525	0.572854	0.286427	−	0.958102i	$-0.407532\pi$
$619$	14.2525	0.572854	0.286427	+	0.958102i	$0.407532\pi$
$620$	3.88867	0.156173
$621$	−36.6403	−1.47033
$622$	−5.14604	−0.206337
$623$	11.3897	0.456320
$624$	1.41401	0.0566058
$625$	9.06066	0.362427
$626$	27.0187	1.07989
$627$	0.550029	0.0219660
$628$	−12.3538	−0.492969
$629$	1.29992	0.0518312
$630$	27.5501	1.09762
$631$	−22.6345	−0.901067	−0.450533	−	0.892760i	$-0.648766\pi$
$631$	−22.6345	−0.901067	−0.450533	+	0.892760i	$0.648766\pi$
$632$	16.7906	0.667892
$633$	75.5318	3.00212
$634$	31.1797	1.23831
$635$	−4.30183	−0.170713
$636$	−26.4427	−1.04852
$637$	0.112002	0.00443767
$638$	−12.8459	−0.508574
$639$	1.57766	0.0624113
$640$	12.7713	0.504831
$641$	−4.24359	−0.167612	−0.0838059	−	0.996482i	$-0.526708\pi$
$641$	−4.24359	−0.167612	−0.0838059	+	0.996482i	$0.526708\pi$
$642$	57.6364	2.27473
$643$	−8.57151	−0.338027	−0.169014	−	0.985614i	$-0.554058\pi$
$643$	−8.57151	−0.338027	−0.169014	+	0.985614i	$0.554058\pi$
$644$	17.3702	0.684483
$645$	−3.06677	−0.120754
$646$	−0.335041	−0.0131820
$647$	5.03843	0.198081	0.0990405	−	0.995083i	$-0.468423\pi$
$647$	5.03843	0.198081	0.0990405	+	0.995083i	$0.468423\pi$
$648$	3.76088	0.147741
$649$	9.22587	0.362147
$650$	0.663195	0.0260126
$651$	28.6301	1.12210
$652$	−4.48821	−0.175772
$653$	−35.4240	−1.38625	−0.693124	−	0.720818i	$-0.743766\pi$
$653$	−35.4240	−1.38625	−0.693124	+	0.720818i	$0.743766\pi$
$654$	9.09231	0.355537
$655$	−3.16094	−0.123508
$656$	−24.3462	−0.950559
$657$	74.0186	2.88774
$658$	−9.26935	−0.361357
$659$	17.5976	0.685506	0.342753	−	0.939426i	$-0.388641\pi$
$659$	17.5976	0.685506	0.342753	+	0.939426i	$0.388641\pi$
$660$	−3.16510	−0.123201
$661$	−9.23188	−0.359078	−0.179539	−	0.983751i	$-0.557461\pi$
$661$	−9.23188	−0.359078	−0.179539	+	0.983751i	$0.557461\pi$
$662$	−55.6428	−2.16262
$663$	−0.282861	−0.0109854
$664$	−2.90529	−0.112747
$665$	−0.588640	−0.0228265
$666$	−11.7063	−0.453609
$667$	−43.5411	−1.68592
$668$	0.211591	0.00818670
$669$	25.0726	0.969361
$670$	−6.62300	−0.255869
$671$	−4.82341	−0.186206
$672$	−43.4793	−1.67725
$673$	−14.7695	−0.569321	−0.284661	−	0.958628i	$-0.591881\pi$
$673$	−14.7695	−0.569321	−0.284661	+	0.958628i	$0.591881\pi$
$674$	54.5202	2.10004
$675$	23.8952	0.919728
$676$	−13.4067	−0.515643
$677$	−7.90107	−0.303663	−0.151831	−	0.988406i	$-0.548517\pi$
$677$	−7.90107	−0.303663	−0.151831	+	0.988406i	$0.548517\pi$
$678$	−22.4101	−0.860656
$679$	16.1076	0.618153
$680$	−1.80818	−0.0693405
$681$	40.6377	1.55724
$682$	−6.11560	−0.234178
$683$	21.8560	0.836296	0.418148	−	0.908379i	$-0.362679\pi$
$683$	21.8560	0.836296	0.418148	+	0.908379i	$0.362679\pi$
$684$	1.02700	0.0392681
$685$	4.82315	0.184283
$686$	29.1382	1.11250
$687$	2.09168	0.0798026
$688$	4.99897	0.190584
$689$	0.886869	0.0337870
$690$	−31.5176	−1.19986
$691$	48.8286	1.85753	0.928764	−	0.370672i	$-0.120872\pi$
$691$	48.8286	1.85753	0.928764	+	0.370672i	$0.120872\pi$
$692$	−20.2512	−0.769834
$693$	−14.7479	−0.560225
$694$	22.8072	0.865749
$695$	11.8735	0.450386
$696$	35.5442	1.34730
$697$	4.87024	0.184474
$698$	0.470567	0.0178112
$699$	−66.9308	−2.53155
$700$	−11.3281	−0.428163
$701$	−30.1504	−1.13876	−0.569382	−	0.822073i	$-0.692818\pi$
$701$	−30.1504	−1.13876	−0.569382	+	0.822073i	$0.692818\pi$
$702$	1.06965	0.0403713
$703$	0.250118	0.00943339
$704$	−0.710441	−0.0267757
$705$	5.72487	0.215611
$706$	−40.0371	−1.50682
$707$	−16.1089	−0.605838
$708$	27.2188	1.02295
$709$	−10.6697	−0.400708	−0.200354	−	0.979724i	$-0.564209\pi$
$709$	−10.6697	−0.400708	−0.200354	+	0.979724i	$0.564209\pi$
$710$	0.569868	0.0213868
$711$	51.5207	1.93218
$712$	6.73184	0.252287
$713$	−20.7288	−0.776298
$714$	14.1945	0.531217
$715$	0.106155	0.00396998
$716$	21.2601	0.794526
$717$	−36.0966	−1.34805
$718$	13.2919	0.496051
$719$	26.1143	0.973898	0.486949	−	0.873430i	$-0.338110\pi$
$719$	26.1143	0.973898	0.486949	+	0.873430i	$0.338110\pi$
$720$	27.7357	1.03365
$721$	−1.86328	−0.0693922
$722$	33.0199	1.22887
$723$	12.3227	0.458285
$724$	17.6135	0.654599
$725$	28.3956	1.05459
$726$	4.97766	0.184738
$727$	−29.9941	−1.11242	−0.556211	−	0.831041i	$-0.687745\pi$
$727$	−29.9941	−1.11242	−0.556211	+	0.831041i	$0.687745\pi$
$728$	0.475586	0.0176264
$729$	−41.6994	−1.54442
$730$	26.7363	0.989555
$731$	−1.00000	−0.0369863
$732$	−14.2304	−0.525970
$733$	−15.5911	−0.575872	−0.287936	−	0.957650i	$-0.592969\pi$
$733$	−15.5911	−0.575872	−0.287936	+	0.957650i	$0.592969\pi$
$734$	16.9210	0.624566
$735$	3.47128	0.128040
$736$	31.4799	1.16036
$737$	3.54536	0.130595
$738$	−43.8584	−1.61445
$739$	8.00156	0.294342	0.147171	−	0.989111i	$-0.452983\pi$
$739$	8.00156	0.294342	0.147171	+	0.989111i	$0.452983\pi$
$740$	−1.43929	−0.0529092
$741$	−0.0544254	−0.00199937
$742$	−44.5049	−1.63383
$743$	−32.3488	−1.18676	−0.593381	−	0.804922i	$-0.702207\pi$
$743$	−32.3488	−1.18676	−0.593381	+	0.804922i	$0.702207\pi$
$744$	16.9216	0.620377
$745$	−1.00261	−0.0367329
$746$	54.9651	2.01241
$747$	−8.91470	−0.326172
$748$	−1.03206	−0.0377359
$749$	33.0193	1.20650
$750$	47.2550	1.72551
$751$	30.2211	1.10278	0.551391	−	0.834247i	$-0.314097\pi$
$751$	30.2211	1.10278	0.551391	+	0.834247i	$0.314097\pi$
$752$	−9.33179	−0.340295
$753$	−28.9557	−1.05520
$754$	1.27110	0.0462909
$755$	−6.66020	−0.242389
$756$	−18.2708	−0.664503
$757$	10.6631	0.387557	0.193779	−	0.981045i	$-0.437926\pi$
$757$	10.6631	0.387557	0.193779	+	0.981045i	$0.437926\pi$
$758$	30.6364	1.11276
$759$	16.8717	0.612405
$760$	−0.347913	−0.0126201
$761$	46.3278	1.67938	0.839690	−	0.543065i	$-0.182736\pi$
$761$	46.3278	1.67938	0.839690	+	0.543065i	$0.182736\pi$
$762$	19.9597	0.723062
$763$	5.20889	0.188574
$764$	−0.266452	−0.00963991
$765$	−5.54828	−0.200598
$766$	−55.3857	−2.00117
$767$	−0.912902	−0.0329630
$768$	−55.1949	−1.99167
$769$	−45.1175	−1.62698	−0.813489	−	0.581581i	$-0.802434\pi$
$769$	−45.1175	−1.62698	−0.813489	+	0.581581i	$0.802434\pi$
$770$	−5.32709	−0.191975
$771$	−10.8159	−0.389526
$772$	4.27717	0.153939
$773$	−24.5595	−0.883345	−0.441672	−	0.897176i	$-0.645615\pi$
$773$	−24.5595	−0.883345	−0.441672	+	0.897176i	$0.645615\pi$
$774$	9.00539	0.323692
$775$	13.5184	0.485596
$776$	9.52032	0.341759
$777$	−10.5966	−0.380153
$778$	12.8857	0.461973
$779$	0.937086	0.0335746
$780$	0.313187	0.0112139
$781$	−0.305056	−0.0109158
$782$	−10.2771	−0.367510
$783$	45.7985	1.63671
$784$	−5.65834	−0.202084
$785$	12.8416	0.458335
$786$	14.6662	0.523126
$787$	−40.9680	−1.46035	−0.730176	−	0.683260i	$-0.760562\pi$
$787$	−40.9680	−1.46035	−0.730176	+	0.683260i	$0.760562\pi$
$788$	−3.06304	−0.109116
$789$	−49.3084	−1.75543
$790$	18.6098	0.662108
$791$	−12.8385	−0.456485
$792$	−8.71665	−0.309733
$793$	0.477277	0.0169486
$794$	−3.21697	−0.114166
$795$	27.4868	0.974856
$796$	−5.55956	−0.197053
$797$	10.9623	0.388305	0.194153	−	0.980971i	$-0.437804\pi$
$797$	10.9623	0.388305	0.194153	+	0.980971i	$0.437804\pi$
$798$	2.73118	0.0966827
$799$	1.86674	0.0660406
$800$	−20.5298	−0.725839
$801$	20.6562	0.729852
$802$	14.6897	0.518712
$803$	−14.3122	−0.505068
$804$	10.4598	0.368888
$805$	−18.0561	−0.636394
$806$	0.605140	0.0213151
$807$	−30.6264	−1.07810
$808$	−9.52108	−0.334951
$809$	−41.4681	−1.45794	−0.728970	−	0.684546i	$-0.760001\pi$
$809$	−41.4681	−1.45794	−0.728970	+	0.684546i	$0.760001\pi$
$810$	4.16838	0.146462
$811$	−41.0769	−1.44241	−0.721203	−	0.692724i	$-0.756410\pi$
$811$	−41.0769	−1.44241	−0.721203	+	0.692724i	$0.756410\pi$
$812$	−21.7119	−0.761938
$813$	54.0968	1.89726
$814$	2.26353	0.0793365
$815$	4.66544	0.163423
$816$	14.2902	0.500255
$817$	−0.192411	−0.00673159
$818$	−20.2971	−0.709671
$819$	1.45930	0.0509922
$820$	−5.39239	−0.188310
$821$	−34.0541	−1.18850	−0.594249	−	0.804281i	$-0.702550\pi$
$821$	−34.0541	−1.18850	−0.594249	+	0.804281i	$0.702550\pi$
$822$	−22.3785	−0.780541
$823$	25.9226	0.903606	0.451803	−	0.892118i	$-0.350781\pi$
$823$	25.9226	0.903606	0.451803	+	0.892118i	$0.350781\pi$
$824$	−1.10128	−0.0383650
$825$	−11.0030	−0.383076
$826$	45.8113	1.59398
$827$	19.9918	0.695182	0.347591	−	0.937646i	$-0.387000\pi$
$827$	19.9918	0.695182	0.347591	+	0.937646i	$0.387000\pi$
$828$	31.5023	1.09478
$829$	39.7036	1.37896	0.689482	−	0.724303i	$-0.257838\pi$
$829$	39.7036	1.37896	0.689482	+	0.724303i	$0.257838\pi$
$830$	−3.22009	−0.111771
$831$	−27.3492	−0.948732
$832$	0.0702982	0.00243715
$833$	1.13190	0.0392180
$834$	−55.0906	−1.90763
$835$	−0.219946	−0.00761154
$836$	−0.198580	−0.00686803
$837$	21.8035	0.753639
$838$	−69.1071	−2.38726
$839$	53.1315	1.83430	0.917152	−	0.398539i	$-0.130483\pi$
$839$	53.1315	1.83430	0.917152	+	0.398539i	$0.130483\pi$
$840$	14.7399	0.508574
$841$	25.4241	0.876694
$842$	−47.9600	−1.65281
$843$	−49.7665	−1.71405
$844$	−27.2697	−0.938660
$845$	13.9361	0.479416
$846$	−16.8107	−0.577965
$847$	2.85165	0.0979838
$848$	−44.8047	−1.53860
$849$	77.2792	2.65222
$850$	6.70231	0.229887
$851$	7.67219	0.262999
$852$	−0.900000	−0.0308335
$853$	−14.8624	−0.508879	−0.254440	−	0.967089i	$-0.581891\pi$
$853$	−14.8624	−0.508879	−0.254440	+	0.967089i	$0.581891\pi$
$854$	−23.9508	−0.819579
$855$	−1.06755	−0.0365093
$856$	19.5159	0.667038
$857$	18.3093	0.625434	0.312717	−	0.949846i	$-0.398761\pi$
$857$	18.3093	0.625434	0.312717	+	0.949846i	$0.398761\pi$
$858$	−0.492540	−0.0168151
$859$	−40.1468	−1.36979	−0.684896	−	0.728641i	$-0.740153\pi$
$859$	−40.1468	−1.36979	−0.684896	+	0.728641i	$0.740153\pi$
$860$	1.10721	0.0377556
$861$	−39.7011	−1.35301
$862$	−3.69030	−0.125692
$863$	−34.1614	−1.16287	−0.581434	−	0.813593i	$-0.697508\pi$
$863$	−34.1614	−1.16287	−0.581434	+	0.813593i	$0.697508\pi$
$864$	−33.1120	−1.12649
$865$	21.0508	0.715749
$866$	−2.17991	−0.0740762
$867$	−2.85862	−0.0970838
$868$	−10.3365	−0.350842
$869$	−9.96205	−0.337939
$870$	39.3954	1.33563
$871$	−0.350814	−0.0118869
$872$	3.07868	0.104257
$873$	29.2125	0.988692
$874$	−1.97743	−0.0668876
$875$	27.0719	0.915197
$876$	−42.2250	−1.42665
$877$	18.9286	0.639173	0.319587	−	0.947557i	$-0.396456\pi$
$877$	18.9286	0.639173	0.319587	+	0.947557i	$0.396456\pi$
$878$	−19.7866	−0.667766
$879$	47.3663	1.59762
$880$	−5.36297	−0.180786
$881$	−14.6685	−0.494196	−0.247098	−	0.968991i	$-0.579477\pi$
$881$	−14.6685	−0.494196	−0.247098	+	0.968991i	$0.579477\pi$
$882$	−10.1932	−0.343223
$883$	−14.1226	−0.475264	−0.237632	−	0.971355i	$-0.576371\pi$
$883$	−14.1226	−0.475264	−0.237632	+	0.971355i	$0.576371\pi$
$884$	0.102123	0.00343476
$885$	−28.2936	−0.951079
$886$	−24.0954	−0.809500
$887$	−11.7784	−0.395479	−0.197739	−	0.980255i	$-0.563360\pi$
$887$	−11.7784	−0.395479	−0.197739	+	0.980255i	$0.563360\pi$
$888$	−6.26309	−0.210176
$889$	11.4347	0.383507
$890$	7.46125	0.250102
$891$	−2.23138	−0.0747540
$892$	−9.05208	−0.303086
$893$	0.359181	0.0120195
$894$	4.65193	0.155584
$895$	−22.0996	−0.738707
$896$	−33.9475	−1.13411
$897$	−1.66946	−0.0557417
$898$	−12.8246	−0.427962
$899$	25.9099	0.864143
$900$	−20.5445	−0.684816
$901$	8.96278	0.298594
$902$	8.48046	0.282368
$903$	8.15178	0.271274
$904$	−7.58814	−0.252378
$905$	−18.3090	−0.608610
$906$	30.9021	1.02665
$907$	6.36453	0.211331	0.105665	−	0.994402i	$-0.466303\pi$
$907$	6.36453	0.211331	0.105665	+	0.994402i	$0.466303\pi$
$908$	−14.6717	−0.486896
$909$	−29.2148	−0.968995
$910$	0.527116	0.0174737
$911$	−4.29111	−0.142171	−0.0710855	−	0.997470i	$-0.522646\pi$
$911$	−4.29111	−0.142171	−0.0710855	+	0.997470i	$0.522646\pi$
$912$	2.74958	0.0910476
$913$	1.72375	0.0570477
$914$	−16.1802	−0.535192
$915$	14.7923	0.489018
$916$	−0.755171	−0.0249516
$917$	8.40210	0.277462
$918$	10.8100	0.356783
$919$	2.62357	0.0865437	0.0432718	−	0.999063i	$-0.486222\pi$
$919$	2.62357	0.0865437	0.0432718	+	0.999063i	$0.486222\pi$
$920$	−10.6720	−0.351844
$921$	54.1512	1.78434
$922$	−8.46822	−0.278886
$923$	0.0301854	0.000993564 0
$924$	8.41314	0.276772
$925$	−5.00348	−0.164513
$926$	−6.99814	−0.229973
$927$	−3.37921	−0.110988
$928$	−39.3483	−1.29167
$929$	37.1505	1.21887	0.609435	−	0.792836i	$-0.291396\pi$
$929$	37.1505	1.21887	0.609435	+	0.792836i	$0.291396\pi$
$930$	18.7551	0.615005
$931$	0.217790	0.00713777
$932$	24.1644	0.791531
$933$	−8.44812	−0.276579
$934$	−13.2922	−0.434934
$935$	1.07282	0.0350848
$936$	0.862514	0.0281922
$937$	−24.3401	−0.795155	−0.397577	−	0.917569i	$-0.630149\pi$
$937$	−24.3401	−0.795155	−0.397577	+	0.917569i	$0.630149\pi$
$938$	17.6046	0.574810
$939$	44.3560	1.44750
$940$	−2.06688	−0.0674142
$941$	−22.0549	−0.718968	−0.359484	−	0.933151i	$-0.617047\pi$
$941$	−22.0549	−0.718968	−0.359484	+	0.933151i	$0.617047\pi$
$942$	−59.5825	−1.94130
$943$	28.7444	0.936047
$944$	46.1199	1.50107
$945$	18.9923	0.617818
$946$	−1.74128	−0.0566140
$947$	18.3359	0.595837	0.297919	−	0.954591i	$-0.403708\pi$
$947$	18.3359	0.595837	0.297919	+	0.954591i	$0.403708\pi$
$948$	−29.3908	−0.954568
$949$	1.41620	0.0459717
$950$	1.28960	0.0418400
$951$	51.1870	1.65985
$952$	4.80632	0.155774
$953$	32.3465	1.04781	0.523903	−	0.851778i	$-0.324475\pi$
$953$	32.3465	1.04781	0.523903	+	0.851778i	$0.324475\pi$
$954$	−80.7133	−2.61319
$955$	0.276974	0.00896266
$956$	13.0322	0.421491
$957$	−21.0888	−0.681704
$958$	10.6988	0.345662
$959$	−12.8204	−0.413993
$960$	2.17876	0.0703191
$961$	−18.6650	−0.602096
$962$	−0.223976	−0.00722128
$963$	59.8831	1.92971
$964$	−4.44892	−0.143290
$965$	−4.44606	−0.143124
$966$	83.7770	2.69548
$967$	−36.7587	−1.18208	−0.591040	−	0.806643i	$-0.701282\pi$
$967$	−36.7587	−1.18208	−0.591040	+	0.806643i	$0.701282\pi$
$968$	1.68545	0.0541725
$969$	−0.550029	−0.0176695
$970$	10.5519	0.338800
$971$	−49.3234	−1.58286	−0.791432	−	0.611258i	$-0.790664\pi$
$971$	−49.3234	−1.58286	−0.791432	+	0.611258i	$0.790664\pi$
$972$	12.6381	0.405369
$973$	−31.5608	−1.01179
$974$	−39.6581	−1.27073
$975$	1.08875	0.0348679
$976$	−24.1121	−0.771810
$977$	−17.1452	−0.548525	−0.274263	−	0.961655i	$-0.588434\pi$
$977$	−17.1452	−0.548525	−0.274263	+	0.961655i	$0.588434\pi$
$978$	−21.6468	−0.692187
$979$	−3.99409	−0.127652
$980$	−1.25325	−0.0400337
$981$	9.44674	0.301611
$982$	−12.3214	−0.393191
$983$	−14.7940	−0.471854	−0.235927	−	0.971771i	$-0.575813\pi$
$983$	−14.7940	−0.471854	−0.235927	+	0.971771i	$0.575813\pi$
$984$	−23.4651	−0.748041
$985$	3.18399	0.101450
$986$	12.8459	0.409097
$987$	−15.2173	−0.484371
$988$	0.0196495	0.000625134 0
$989$	−5.90206	−0.187674
$990$	−9.66111	−0.307050
$991$	34.8884	1.10827	0.554134	−	0.832427i	$-0.313049\pi$
$991$	34.8884	1.10827	0.554134	+	0.832427i	$0.313049\pi$
$992$	−18.7327	−0.594763
$993$	−91.3473	−2.89882
$994$	−1.51477	−0.0480454
$995$	5.77908	0.183209
$996$	5.08553	0.161141
$997$	15.1318	0.479230	0.239615	−	0.970868i	$-0.422979\pi$
$997$	15.1318	0.479230	0.239615	+	0.970868i	$0.422979\pi$
$998$	51.0446	1.61579
$999$	−8.06997	−0.255323

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.f.1.14	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.f.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-1.74128 q^{2} -2.85862 q^{3} +1.03206 q^{4} -1.07282 q^{5} +4.97766 q^{6} +2.85165 q^{7} +1.68545 q^{8} +5.17170 q^{9} +O(q^{10})\)	\(q-1.74128 q^{2} -2.85862 q^{3} +1.03206 q^{4} -1.07282 q^{5} +4.97766 q^{6} +2.85165 q^{7} +1.68545 q^{8} +5.17170 q^{9} +1.86807 q^{10} -1.00000 q^{11} -2.95027 q^{12} +0.0989502 q^{13} -4.96552 q^{14} +3.06677 q^{15} -4.99897 q^{16} +1.00000 q^{17} -9.00539 q^{18} +0.192411 q^{19} -1.10721 q^{20} -8.15178 q^{21} +1.74128 q^{22} +5.90206 q^{23} -4.81806 q^{24} -3.84907 q^{25} -0.172300 q^{26} -6.20806 q^{27} +2.94308 q^{28} -7.37727 q^{29} -5.34011 q^{30} -3.51212 q^{31} +5.33372 q^{32} +2.85862 q^{33} -1.74128 q^{34} -3.05929 q^{35} +5.33752 q^{36} +1.29992 q^{37} -0.335041 q^{38} -0.282861 q^{39} -1.80818 q^{40} +4.87024 q^{41} +14.1945 q^{42} -1.00000 q^{43} -1.03206 q^{44} -5.54828 q^{45} -10.2771 q^{46} +1.86674 q^{47} +14.2902 q^{48} +1.13190 q^{49} +6.70231 q^{50} -2.85862 q^{51} +0.102123 q^{52} +8.96278 q^{53} +10.8100 q^{54} +1.07282 q^{55} +4.80632 q^{56} -0.550029 q^{57} +12.8459 q^{58} -9.22587 q^{59} +3.16510 q^{60} +4.82341 q^{61} +6.11560 q^{62} +14.7479 q^{63} +0.710441 q^{64} -0.106155 q^{65} -4.97766 q^{66} -3.54536 q^{67} +1.03206 q^{68} -16.8717 q^{69} +5.32709 q^{70} +0.305056 q^{71} +8.71665 q^{72} +14.3122 q^{73} -2.26353 q^{74} +11.0030 q^{75} +0.198580 q^{76} -2.85165 q^{77} +0.492540 q^{78} +9.96205 q^{79} +5.36297 q^{80} +2.23138 q^{81} -8.48046 q^{82} -1.72375 q^{83} -8.41314 q^{84} -1.07282 q^{85} +1.74128 q^{86} +21.0888 q^{87} -1.68545 q^{88} +3.99409 q^{89} +9.66111 q^{90} +0.282171 q^{91} +6.09129 q^{92} +10.0398 q^{93} -3.25052 q^{94} -0.206421 q^{95} -15.2471 q^{96} +5.64852 q^{97} -1.97096 q^{98} -5.17170 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) \) 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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