LMFDB - Embedded newform 6010.2.a.j.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$0$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.649976 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.649976 q^{6} +1.95740 q^{7} +1.00000 q^{8} -2.57753 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.649976 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.649976 q^{6} +1.95740 q^{7} +1.00000 q^{8} -2.57753 q^{9} +1.00000 q^{10} -0.533483 q^{11} +0.649976 q^{12} +3.04079 q^{13} +1.95740 q^{14} +0.649976 q^{15} +1.00000 q^{16} +3.79249 q^{17} -2.57753 q^{18} +2.82801 q^{19} +1.00000 q^{20} +1.27226 q^{21} -0.533483 q^{22} -6.17157 q^{23} +0.649976 q^{24} +1.00000 q^{25} +3.04079 q^{26} -3.62526 q^{27} +1.95740 q^{28} +8.32598 q^{29} +0.649976 q^{30} -2.76750 q^{31} +1.00000 q^{32} -0.346751 q^{33} +3.79249 q^{34} +1.95740 q^{35} -2.57753 q^{36} +11.1647 q^{37} +2.82801 q^{38} +1.97644 q^{39} +1.00000 q^{40} +7.15290 q^{41} +1.27226 q^{42} -3.28082 q^{43} -0.533483 q^{44} -2.57753 q^{45} -6.17157 q^{46} -8.22028 q^{47} +0.649976 q^{48} -3.16858 q^{49} +1.00000 q^{50} +2.46503 q^{51} +3.04079 q^{52} +0.727663 q^{53} -3.62526 q^{54} -0.533483 q^{55} +1.95740 q^{56} +1.83814 q^{57} +8.32598 q^{58} -8.03359 q^{59} +0.649976 q^{60} +11.1116 q^{61} -2.76750 q^{62} -5.04526 q^{63} +1.00000 q^{64} +3.04079 q^{65} -0.346751 q^{66} -5.92445 q^{67} +3.79249 q^{68} -4.01137 q^{69} +1.95740 q^{70} +6.25458 q^{71} -2.57753 q^{72} +3.20419 q^{73} +11.1647 q^{74} +0.649976 q^{75} +2.82801 q^{76} -1.04424 q^{77} +1.97644 q^{78} -13.7769 q^{79} +1.00000 q^{80} +5.37626 q^{81} +7.15290 q^{82} +3.03085 q^{83} +1.27226 q^{84} +3.79249 q^{85} -3.28082 q^{86} +5.41169 q^{87} -0.533483 q^{88} +4.92922 q^{89} -2.57753 q^{90} +5.95205 q^{91} -6.17157 q^{92} -1.79881 q^{93} -8.22028 q^{94} +2.82801 q^{95} +0.649976 q^{96} +10.3625 q^{97} -3.16858 q^{98} +1.37507 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9}+O(q^{10}) $ 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9	\( 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9} + 33 q^{10} + 12 q^{11} + 6 q^{12} + 20 q^{13} + 4 q^{14} + 6 q^{15} + 33 q^{16} + 33 q^{17} + 49 q^{18} + 17 q^{19} + 33 q^{20} + 26 q^{21} + 12 q^{22} + 7 q^{23} + 6 q^{24} + 33 q^{25} + 20 q^{26} + 21 q^{27} + 4 q^{28} + 33 q^{29} + 6 q^{30} + 35 q^{31} + 33 q^{32} + 25 q^{33} + 33 q^{34} + 4 q^{35} + 49 q^{36} + 16 q^{37} + 17 q^{38} + 22 q^{39} + 33 q^{40} + 39 q^{41} + 26 q^{42} - 3 q^{43} + 12 q^{44} + 49 q^{45} + 7 q^{46} + 19 q^{47} + 6 q^{48} + 69 q^{49} + 33 q^{50} + 21 q^{51} + 20 q^{52} + 41 q^{53} + 21 q^{54} + 12 q^{55} + 4 q^{56} + 33 q^{58} + 18 q^{59} + 6 q^{60} + 30 q^{61} + 35 q^{62} - 15 q^{63} + 33 q^{64} + 20 q^{65} + 25 q^{66} - 9 q^{67} + 33 q^{68} + 23 q^{69} + 4 q^{70} + 36 q^{71} + 49 q^{72} + 35 q^{73} + 16 q^{74} + 6 q^{75} + 17 q^{76} + 26 q^{77} + 22 q^{78} + 32 q^{79} + 33 q^{80} + 53 q^{81} + 39 q^{82} + 24 q^{83} + 26 q^{84} + 33 q^{85} - 3 q^{86} + 12 q^{87} + 12 q^{88} + 40 q^{89} + 49 q^{90} + 5 q^{91} + 7 q^{92} + 18 q^{93} + 19 q^{94} + 17 q^{95} + 6 q^{96} + 39 q^{97} + 69 q^{98} + 3 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9 + 33 * q^10 + 12 * q^11 + 6 * q^12 + 20 * q^13 + 4 * q^14 + 6 * q^15 + 33 * q^16 + 33 * q^17 + 49 * q^18 + 17 * q^19 + 33 * q^20 + 26 * q^21 + 12 * q^22 + 7 * q^23 + 6 * q^24 + 33 * q^25 + 20 * q^26 + 21 * q^27 + 4 * q^28 + 33 * q^29 + 6 * q^30 + 35 * q^31 + 33 * q^32 + 25 * q^33 + 33 * q^34 + 4 * q^35 + 49 * q^36 + 16 * q^37 + 17 * q^38 + 22 * q^39 + 33 * q^40 + 39 * q^41 + 26 * q^42 - 3 * q^43 + 12 * q^44 + 49 * q^45 + 7 * q^46 + 19 * q^47 + 6 * q^48 + 69 * q^49 + 33 * q^50 + 21 * q^51 + 20 * q^52 + 41 * q^53 + 21 * q^54 + 12 * q^55 + 4 * q^56 + 33 * q^58 + 18 * q^59 + 6 * q^60 + 30 * q^61 + 35 * q^62 - 15 * q^63 + 33 * q^64 + 20 * q^65 + 25 * q^66 - 9 * q^67 + 33 * q^68 + 23 * q^69 + 4 * q^70 + 36 * q^71 + 49 * q^72 + 35 * q^73 + 16 * q^74 + 6 * q^75 + 17 * q^76 + 26 * q^77 + 22 * q^78 + 32 * q^79 + 33 * q^80 + 53 * q^81 + 39 * q^82 + 24 * q^83 + 26 * q^84 + 33 * q^85 - 3 * q^86 + 12 * q^87 + 12 * q^88 + 40 * q^89 + 49 * q^90 + 5 * q^91 + 7 * q^92 + 18 * q^93 + 19 * q^94 + 17 * q^95 + 6 * q^96 + 39 * q^97 + 69 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.649976	0.375264	0.187632	−	0.982239i	$-0.439919\pi$
$3$	0.649976	0.375264	0.187632	+	0.982239i	$0.439919\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.649976	0.265351
$7$	1.95740	0.739828	0.369914	−	0.929066i	$-0.379387\pi$
$7$	1.95740	0.739828	0.369914	+	0.929066i	$0.379387\pi$
$8$	1.00000	0.353553
$9$	−2.57753	−0.859177
$10$	1.00000	0.316228
$11$	−0.533483	−0.160851	−0.0804256	−	0.996761i	$-0.525628\pi$
$11$	−0.533483	−0.160851	−0.0804256	+	0.996761i	$0.525628\pi$
$12$	0.649976	0.187632
$13$	3.04079	0.843364	0.421682	−	0.906744i	$-0.361440\pi$
$13$	3.04079	0.843364	0.421682	+	0.906744i	$0.361440\pi$
$14$	1.95740	0.523137
$15$	0.649976	0.167823
$16$	1.00000	0.250000
$17$	3.79249	0.919814	0.459907	−	0.887967i	$-0.347883\pi$
$17$	3.79249	0.919814	0.459907	+	0.887967i	$0.347883\pi$
$18$	−2.57753	−0.607530
$19$	2.82801	0.648789	0.324395	−	0.945922i	$-0.394839\pi$
$19$	2.82801	0.648789	0.324395	+	0.945922i	$0.394839\pi$
$20$	1.00000	0.223607
$21$	1.27226	0.277631
$22$	−0.533483	−0.113739
$23$	−6.17157	−1.28686	−0.643431	−	0.765504i	$-0.722490\pi$
$23$	−6.17157	−1.28686	−0.643431	+	0.765504i	$0.722490\pi$
$24$	0.649976	0.132676
$25$	1.00000	0.200000
$26$	3.04079	0.596349
$27$	−3.62526	−0.697682
$28$	1.95740	0.369914
$29$	8.32598	1.54610	0.773048	−	0.634347i	$-0.218731\pi$
$29$	8.32598	1.54610	0.773048	+	0.634347i	$0.218731\pi$
$30$	0.649976	0.118669
$31$	−2.76750	−0.497058	−0.248529	−	0.968624i	$-0.579947\pi$
$31$	−2.76750	−0.497058	−0.248529	+	0.968624i	$0.579947\pi$
$32$	1.00000	0.176777
$33$	−0.346751	−0.0603616
$34$	3.79249	0.650407
$35$	1.95740	0.330861
$36$	−2.57753	−0.429589
$37$	11.1647	1.83546	0.917732	−	0.397201i	$-0.130018\pi$
$37$	11.1647	1.83546	0.917732	+	0.397201i	$0.130018\pi$
$38$	2.82801	0.458763
$39$	1.97644	0.316484
$40$	1.00000	0.158114
$41$	7.15290	1.11710	0.558548	−	0.829472i	$-0.311359\pi$
$41$	7.15290	1.11710	0.558548	+	0.829472i	$0.311359\pi$
$42$	1.27226	0.196314
$43$	−3.28082	−0.500321	−0.250160	−	0.968204i	$-0.580483\pi$
$43$	−3.28082	−0.500321	−0.250160	+	0.968204i	$0.580483\pi$
$44$	−0.533483	−0.0804256
$45$	−2.57753	−0.384236
$46$	−6.17157	−0.909948
$47$	−8.22028	−1.19905	−0.599526	−	0.800355i	$-0.704644\pi$
$47$	−8.22028	−1.19905	−0.599526	+	0.800355i	$0.704644\pi$
$48$	0.649976	0.0938159
$49$	−3.16858	−0.452655
$50$	1.00000	0.141421
$51$	2.46503	0.345173
$52$	3.04079	0.421682
$53$	0.727663	0.0999522	0.0499761	−	0.998750i	$-0.484085\pi$
$53$	0.727663	0.0999522	0.0499761	+	0.998750i	$0.484085\pi$
$54$	−3.62526	−0.493335
$55$	−0.533483	−0.0719349
$56$	1.95740	0.261569
$57$	1.83814	0.243467
$58$	8.32598	1.09326
$59$	−8.03359	−1.04588	−0.522942	−	0.852368i	$-0.675166\pi$
$59$	−8.03359	−1.04588	−0.522942	+	0.852368i	$0.675166\pi$
$60$	0.649976	0.0839115
$61$	11.1116	1.42270	0.711349	−	0.702839i	$-0.248085\pi$
$61$	11.1116	1.42270	0.711349	+	0.702839i	$0.248085\pi$
$62$	−2.76750	−0.351473
$63$	−5.04526	−0.635643
$64$	1.00000	0.125000
$65$	3.04079	0.377164
$66$	−0.346751	−0.0426821
$67$	−5.92445	−0.723787	−0.361893	−	0.932220i	$-0.617870\pi$
$67$	−5.92445	−0.723787	−0.361893	+	0.932220i	$0.617870\pi$
$68$	3.79249	0.459907
$69$	−4.01137	−0.482912
$70$	1.95740	0.233954
$71$	6.25458	0.742282	0.371141	−	0.928577i	$-0.378967\pi$
$71$	6.25458	0.742282	0.371141	+	0.928577i	$0.378967\pi$
$72$	−2.57753	−0.303765
$73$	3.20419	0.375022	0.187511	−	0.982263i	$-0.439958\pi$
$73$	3.20419	0.375022	0.187511	+	0.982263i	$0.439958\pi$
$74$	11.1647	1.29787
$75$	0.649976	0.0750527
$76$	2.82801	0.324395
$77$	−1.04424	−0.119002
$78$	1.97644	0.223788
$79$	−13.7769	−1.55002	−0.775008	−	0.631951i	$-0.782254\pi$
$79$	−13.7769	−1.55002	−0.775008	+	0.631951i	$0.782254\pi$
$80$	1.00000	0.111803
$81$	5.37626	0.597363
$82$	7.15290	0.789906
$83$	3.03085	0.332679	0.166340	−	0.986069i	$-0.446805\pi$
$83$	3.03085	0.332679	0.166340	+	0.986069i	$0.446805\pi$
$84$	1.27226	0.138815
$85$	3.79249	0.411353
$86$	−3.28082	−0.353780
$87$	5.41169	0.580194
$88$	−0.533483	−0.0568695
$89$	4.92922	0.522497	0.261248	−	0.965272i	$-0.415866\pi$
$89$	4.92922	0.522497	0.261248	+	0.965272i	$0.415866\pi$
$90$	−2.57753	−0.271696
$91$	5.95205	0.623945
$92$	−6.17157	−0.643431
$93$	−1.79881	−0.186528
$94$	−8.22028	−0.847857
$95$	2.82801	0.290147
$96$	0.649976	0.0663379
$97$	10.3625	1.05215	0.526075	−	0.850438i	$-0.323663\pi$
$97$	10.3625	1.05215	0.526075	+	0.850438i	$0.323663\pi$
$98$	−3.16858	−0.320075
$99$	1.37507	0.138200
$100$	1.00000	0.100000
$101$	6.90140	0.686715	0.343357	−	0.939205i	$-0.388436\pi$
$101$	6.90140	0.686715	0.343357	+	0.939205i	$0.388436\pi$
$102$	2.46503	0.244074
$103$	2.34728	0.231285	0.115642	−	0.993291i	$-0.463107\pi$
$103$	2.34728	0.231285	0.115642	+	0.993291i	$0.463107\pi$
$104$	3.04079	0.298174
$105$	1.27226	0.124160
$106$	0.727663	0.0706768
$107$	18.2485	1.76415	0.882075	−	0.471109i	$-0.156146\pi$
$107$	18.2485	1.76415	0.882075	+	0.471109i	$0.156146\pi$
$108$	−3.62526	−0.348841
$109$	−5.85635	−0.560936	−0.280468	−	0.959863i	$-0.590490\pi$
$109$	−5.85635	−0.560936	−0.280468	+	0.959863i	$0.590490\pi$
$110$	−0.533483	−0.0508656
$111$	7.25677	0.688783
$112$	1.95740	0.184957
$113$	6.00108	0.564534	0.282267	−	0.959336i	$-0.408914\pi$
$113$	6.00108	0.564534	0.282267	+	0.959336i	$0.408914\pi$
$114$	1.83814	0.172157
$115$	−6.17157	−0.575502
$116$	8.32598	0.773048
$117$	−7.83774	−0.724600
$118$	−8.03359	−0.739552
$119$	7.42342	0.680504
$120$	0.649976	0.0593344
$121$	−10.7154	−0.974127
$122$	11.1116	1.00600
$123$	4.64921	0.419205
$124$	−2.76750	−0.248529
$125$	1.00000	0.0894427
$126$	−5.04526	−0.449468
$127$	−1.70824	−0.151582	−0.0757911	−	0.997124i	$-0.524148\pi$
$127$	−1.70824	−0.151582	−0.0757911	+	0.997124i	$0.524148\pi$
$128$	1.00000	0.0883883
$129$	−2.13245	−0.187752
$130$	3.04079	0.266695
$131$	−7.71695	−0.674233	−0.337117	−	0.941463i	$-0.609452\pi$
$131$	−7.71695	−0.674233	−0.337117	+	0.941463i	$0.609452\pi$
$132$	−0.346751	−0.0301808
$133$	5.53554	0.479993
$134$	−5.92445	−0.511794
$135$	−3.62526	−0.312013
$136$	3.79249	0.325203
$137$	−1.94093	−0.165825	−0.0829125	−	0.996557i	$-0.526422\pi$
$137$	−1.94093	−0.165825	−0.0829125	+	0.996557i	$0.526422\pi$
$138$	−4.01137	−0.341471
$139$	2.95142	0.250336	0.125168	−	0.992136i	$-0.460053\pi$
$139$	2.95142	0.250336	0.125168	+	0.992136i	$0.460053\pi$
$140$	1.95740	0.165431
$141$	−5.34298	−0.449960
$142$	6.25458	0.524873
$143$	−1.62221	−0.135656
$144$	−2.57753	−0.214794
$145$	8.32598	0.691435
$146$	3.20419	0.265181
$147$	−2.05950	−0.169865
$148$	11.1647	0.917732
$149$	16.3805	1.34195	0.670973	−	0.741482i	$-0.265877\pi$
$149$	16.3805	1.34195	0.670973	+	0.741482i	$0.265877\pi$
$150$	0.649976	0.0530703
$151$	−3.67784	−0.299298	−0.149649	−	0.988739i	$-0.547814\pi$
$151$	−3.67784	−0.299298	−0.149649	+	0.988739i	$0.547814\pi$
$152$	2.82801	0.229382
$153$	−9.77526	−0.790283
$154$	−1.04424	−0.0841473
$155$	−2.76750	−0.222291
$156$	1.97644	0.158242
$157$	1.31550	0.104988	0.0524940	−	0.998621i	$-0.483283\pi$
$157$	1.31550	0.104988	0.0524940	+	0.998621i	$0.483283\pi$
$158$	−13.7769	−1.09603
$159$	0.472963	0.0375084
$160$	1.00000	0.0790569
$161$	−12.0802	−0.952056
$162$	5.37626	0.422399
$163$	0.868038	0.0679900	0.0339950	−	0.999422i	$-0.489177\pi$
$163$	0.868038	0.0679900	0.0339950	+	0.999422i	$0.489177\pi$
$164$	7.15290	0.558548
$165$	−0.346751	−0.0269945
$166$	3.03085	0.235240
$167$	5.57096	0.431094	0.215547	−	0.976493i	$-0.430847\pi$
$167$	5.57096	0.431094	0.215547	+	0.976493i	$0.430847\pi$
$168$	1.27226	0.0981572
$169$	−3.75357	−0.288736
$170$	3.79249	0.290871
$171$	−7.28928	−0.557425
$172$	−3.28082	−0.250160
$173$	−7.18962	−0.546616	−0.273308	−	0.961927i	$-0.588118\pi$
$173$	−7.18962	−0.546616	−0.273308	+	0.961927i	$0.588118\pi$
$174$	5.41169	0.410259
$175$	1.95740	0.147966
$176$	−0.533483	−0.0402128
$177$	−5.22164	−0.392482
$178$	4.92922	0.369461
$179$	8.17763	0.611224	0.305612	−	0.952156i	$-0.401139\pi$
$179$	8.17763	0.611224	0.305612	+	0.952156i	$0.401139\pi$
$180$	−2.57753	−0.192118
$181$	−11.3639	−0.844675	−0.422338	−	0.906439i	$-0.638790\pi$
$181$	−11.3639	−0.844675	−0.422338	+	0.906439i	$0.638790\pi$
$182$	5.95205	0.441195
$183$	7.22229	0.533887
$184$	−6.17157	−0.454974
$185$	11.1647	0.820844
$186$	−1.79881	−0.131895
$187$	−2.02323	−0.147953
$188$	−8.22028	−0.599526
$189$	−7.09609	−0.516164
$190$	2.82801	0.205165
$191$	−13.5008	−0.976881	−0.488440	−	0.872597i	$-0.662434\pi$
$191$	−13.5008	−0.976881	−0.488440	+	0.872597i	$0.662434\pi$
$192$	0.649976	0.0469080
$193$	9.13530	0.657573	0.328787	−	0.944404i	$-0.393360\pi$
$193$	9.13530	0.657573	0.328787	+	0.944404i	$0.393360\pi$
$194$	10.3625	0.743982
$195$	1.97644	0.141536
$196$	−3.16858	−0.226327
$197$	−10.4267	−0.742872	−0.371436	−	0.928459i	$-0.621135\pi$
$197$	−10.4267	−0.742872	−0.371436	+	0.928459i	$0.621135\pi$
$198$	1.37507	0.0977220
$199$	−10.8529	−0.769345	−0.384672	−	0.923053i	$-0.625686\pi$
$199$	−10.8529	−0.769345	−0.384672	+	0.923053i	$0.625686\pi$
$200$	1.00000	0.0707107
$201$	−3.85075	−0.271611
$202$	6.90140	0.485580
$203$	16.2973	1.14385
$204$	2.46503	0.172586
$205$	7.15290	0.499581
$206$	2.34728	0.163543
$207$	15.9074	1.10564
$208$	3.04079	0.210841
$209$	−1.50869	−0.104359
$210$	1.27226	0.0877945
$211$	−11.5080	−0.792246	−0.396123	−	0.918197i	$-0.629645\pi$
$211$	−11.5080	−0.792246	−0.396123	+	0.918197i	$0.629645\pi$
$212$	0.727663	0.0499761
$213$	4.06532	0.278551
$214$	18.2485	1.24744
$215$	−3.28082	−0.223750
$216$	−3.62526	−0.246668
$217$	−5.41712	−0.367738
$218$	−5.85635	−0.396642
$219$	2.08264	0.140732
$220$	−0.533483	−0.0359674
$221$	11.5322	0.775739
$222$	7.25677	0.487043
$223$	0.836834	0.0560385	0.0280193	−	0.999607i	$-0.491080\pi$
$223$	0.836834	0.0560385	0.0280193	+	0.999607i	$0.491080\pi$
$224$	1.95740	0.130784
$225$	−2.57753	−0.171835
$226$	6.00108	0.399186
$227$	22.0674	1.46466	0.732332	−	0.680948i	$-0.238432\pi$
$227$	22.0674	1.46466	0.732332	+	0.680948i	$0.238432\pi$
$228$	1.83814	0.121734
$229$	12.2032	0.806412	0.403206	−	0.915109i	$-0.367896\pi$
$229$	12.2032	0.806412	0.403206	+	0.915109i	$0.367896\pi$
$230$	−6.17157	−0.406941
$231$	−0.678731	−0.0446572
$232$	8.32598	0.546628
$233$	−21.6445	−1.41798	−0.708989	−	0.705220i	$-0.750848\pi$
$233$	−21.6445	−1.41798	−0.708989	+	0.705220i	$0.750848\pi$
$234$	−7.83774	−0.512369
$235$	−8.22028	−0.536232
$236$	−8.03359	−0.522942
$237$	−8.95462	−0.581665
$238$	7.42342	0.481189
$239$	3.38189	0.218756	0.109378	−	0.994000i	$-0.465114\pi$
$239$	3.38189	0.218756	0.109378	+	0.994000i	$0.465114\pi$
$240$	0.649976	0.0419557
$241$	2.21558	0.142718	0.0713592	−	0.997451i	$-0.477266\pi$
$241$	2.21558	0.142718	0.0713592	+	0.997451i	$0.477266\pi$
$242$	−10.7154	−0.688812
$243$	14.3702	0.921850
$244$	11.1116	0.711349
$245$	−3.16858	−0.202433
$246$	4.64921	0.296423
$247$	8.59939	0.547166
$248$	−2.76750	−0.175737
$249$	1.96998	0.124842
$250$	1.00000	0.0632456
$251$	−6.27207	−0.395890	−0.197945	−	0.980213i	$-0.563427\pi$
$251$	−6.27207	−0.395890	−0.197945	+	0.980213i	$0.563427\pi$
$252$	−5.04526	−0.317822
$253$	3.29243	0.206993
$254$	−1.70824	−0.107185
$255$	2.46503	0.154366
$256$	1.00000	0.0625000
$257$	−16.7715	−1.04618	−0.523090	−	0.852277i	$-0.675221\pi$
$257$	−16.7715	−1.04618	−0.523090	+	0.852277i	$0.675221\pi$
$258$	−2.13245	−0.132761
$259$	21.8538	1.35793
$260$	3.04079	0.188582
$261$	−21.4605	−1.32837
$262$	−7.71695	−0.476755
$263$	29.8899	1.84309	0.921546	−	0.388268i	$-0.126927\pi$
$263$	29.8899	1.84309	0.921546	+	0.388268i	$0.126927\pi$
$264$	−0.346751	−0.0213411
$265$	0.727663	0.0447000
$266$	5.53554	0.339406
$267$	3.20388	0.196074
$268$	−5.92445	−0.361893
$269$	7.69031	0.468887	0.234443	−	0.972130i	$-0.424673\pi$
$269$	7.69031	0.468887	0.234443	+	0.972130i	$0.424673\pi$
$270$	−3.62526	−0.220626
$271$	−16.0547	−0.975252	−0.487626	−	0.873053i	$-0.662137\pi$
$271$	−16.0547	−0.975252	−0.487626	+	0.873053i	$0.662137\pi$
$272$	3.79249	0.229954
$273$	3.86869	0.234144
$274$	−1.94093	−0.117256
$275$	−0.533483	−0.0321703
$276$	−4.01137	−0.241456
$277$	30.5226	1.83392	0.916962	−	0.398974i	$-0.130634\pi$
$277$	30.5226	1.83392	0.916962	+	0.398974i	$0.130634\pi$
$278$	2.95142	0.177014
$279$	7.13333	0.427061
$280$	1.95740	0.116977
$281$	4.11589	0.245533	0.122767	−	0.992436i	$-0.460823\pi$
$281$	4.11589	0.245533	0.122767	+	0.992436i	$0.460823\pi$
$282$	−5.34298	−0.318170
$283$	17.1430	1.01905	0.509523	−	0.860457i	$-0.329822\pi$
$283$	17.1430	1.01905	0.509523	+	0.860457i	$0.329822\pi$
$284$	6.25458	0.371141
$285$	1.83814	0.108882
$286$	−1.62221	−0.0959235
$287$	14.0011	0.826459
$288$	−2.57753	−0.151883
$289$	−2.61701	−0.153942
$290$	8.32598	0.488919
$291$	6.73535	0.394833
$292$	3.20419	0.187511
$293$	−11.4235	−0.667367	−0.333684	−	0.942685i	$-0.608292\pi$
$293$	−11.4235	−0.667367	−0.333684	+	0.942685i	$0.608292\pi$
$294$	−2.05950	−0.120113
$295$	−8.03359	−0.467734
$296$	11.1647	0.648934
$297$	1.93402	0.112223
$298$	16.3805	0.948899
$299$	−18.7665	−1.08529
$300$	0.649976	0.0375264
$301$	−6.42189	−0.370151
$302$	−3.67784	−0.211636
$303$	4.48574	0.257699
$304$	2.82801	0.162197
$305$	11.1116	0.636250
$306$	−9.77526	−0.558815
$307$	−4.50166	−0.256923	−0.128462	−	0.991714i	$-0.541004\pi$
$307$	−4.50166	−0.256923	−0.128462	+	0.991714i	$0.541004\pi$
$308$	−1.04424	−0.0595011
$309$	1.52568	0.0867927
$310$	−2.76750	−0.157184
$311$	−16.8293	−0.954302	−0.477151	−	0.878821i	$-0.658331\pi$
$311$	−16.8293	−0.954302	−0.477151	+	0.878821i	$0.658331\pi$
$312$	1.97644	0.111894
$313$	−27.3428	−1.54551	−0.772754	−	0.634705i	$-0.781122\pi$
$313$	−27.3428	−1.54551	−0.772754	+	0.634705i	$0.781122\pi$
$314$	1.31550	0.0742378
$315$	−5.04526	−0.284268
$316$	−13.7769	−0.775008
$317$	18.1971	1.02205	0.511026	−	0.859565i	$-0.329266\pi$
$317$	18.1971	1.02205	0.511026	+	0.859565i	$0.329266\pi$
$318$	0.472963	0.0265224
$319$	−4.44177	−0.248692
$320$	1.00000	0.0559017
$321$	11.8611	0.662021
$322$	−12.0802	−0.673205
$323$	10.7252	0.596766
$324$	5.37626	0.298681
$325$	3.04079	0.168673
$326$	0.868038	0.0480762
$327$	−3.80648	−0.210499
$328$	7.15290	0.394953
$329$	−16.0904	−0.887092
$330$	−0.346751	−0.0190880
$331$	13.2356	0.727492	0.363746	−	0.931498i	$-0.381498\pi$
$331$	13.2356	0.727492	0.363746	+	0.931498i	$0.381498\pi$
$332$	3.03085	0.166340
$333$	−28.7773	−1.57699
$334$	5.57096	0.304830
$335$	−5.92445	−0.323687
$336$	1.27226	0.0694076
$337$	−28.5466	−1.55503	−0.777516	−	0.628864i	$-0.783520\pi$
$337$	−28.5466	−1.55503	−0.777516	+	0.628864i	$0.783520\pi$
$338$	−3.75357	−0.204167
$339$	3.90056	0.211849
$340$	3.79249	0.205677
$341$	1.47642	0.0799525
$342$	−7.28928	−0.394159
$343$	−19.9040	−1.07471
$344$	−3.28082	−0.176890
$345$	−4.01137	−0.215965
$346$	−7.18962	−0.386516
$347$	−5.31861	−0.285518	−0.142759	−	0.989757i	$-0.545597\pi$
$347$	−5.31861	−0.285518	−0.142759	+	0.989757i	$0.545597\pi$
$348$	5.41169	0.290097
$349$	−27.6806	−1.48171	−0.740854	−	0.671666i	$-0.765579\pi$
$349$	−27.6806	−1.48171	−0.740854	+	0.671666i	$0.765579\pi$
$350$	1.95740	0.104627
$351$	−11.0237	−0.588400
$352$	−0.533483	−0.0284348
$353$	18.0916	0.962921	0.481460	−	0.876468i	$-0.340107\pi$
$353$	18.0916	0.962921	0.481460	+	0.876468i	$0.340107\pi$
$354$	−5.22164	−0.277527
$355$	6.25458	0.331959
$356$	4.92922	0.261248
$357$	4.82505	0.255368
$358$	8.17763	0.432201
$359$	−29.1432	−1.53812	−0.769059	−	0.639178i	$-0.779275\pi$
$359$	−29.1432	−1.53812	−0.769059	+	0.639178i	$0.779275\pi$
$360$	−2.57753	−0.135848
$361$	−11.0024	−0.579072
$362$	−11.3639	−0.597276
$363$	−6.96475	−0.365554
$364$	5.95205	0.311972
$365$	3.20419	0.167715
$366$	7.22229	0.377515
$367$	−7.22004	−0.376883	−0.188442	−	0.982084i	$-0.560344\pi$
$367$	−7.22004	−0.376883	−0.188442	+	0.982084i	$0.560344\pi$
$368$	−6.17157	−0.321715
$369$	−18.4368	−0.959783
$370$	11.1647	0.580424
$371$	1.42433	0.0739474
$372$	−1.79881	−0.0932640
$373$	−4.18781	−0.216837	−0.108418	−	0.994105i	$-0.534579\pi$
$373$	−4.18781	−0.216837	−0.108418	+	0.994105i	$0.534579\pi$
$374$	−2.02323	−0.104619
$375$	0.649976	0.0335646
$376$	−8.22028	−0.423929
$377$	25.3176	1.30392
$378$	−7.09609	−0.364983
$379$	16.8593	0.866002	0.433001	−	0.901393i	$-0.357455\pi$
$379$	16.8593	0.866002	0.433001	+	0.901393i	$0.357455\pi$
$380$	2.82801	0.145074
$381$	−1.11032	−0.0568832
$382$	−13.5008	−0.690759
$383$	−9.93958	−0.507889	−0.253944	−	0.967219i	$-0.581728\pi$
$383$	−9.93958	−0.507889	−0.253944	+	0.967219i	$0.581728\pi$
$384$	0.649976	0.0331689
$385$	−1.04424	−0.0532194
$386$	9.13530	0.464975
$387$	8.45642	0.429864
$388$	10.3625	0.526075
$389$	7.26070	0.368132	0.184066	−	0.982914i	$-0.441074\pi$
$389$	7.26070	0.368132	0.184066	+	0.982914i	$0.441074\pi$
$390$	1.97644	0.100081
$391$	−23.4056	−1.18367
$392$	−3.16858	−0.160038
$393$	−5.01583	−0.253015
$394$	−10.4267	−0.525290
$395$	−13.7769	−0.693189
$396$	1.37507	0.0690999
$397$	11.8917	0.596825	0.298413	−	0.954437i	$-0.403543\pi$
$397$	11.8917	0.596825	0.298413	+	0.954437i	$0.403543\pi$
$398$	−10.8529	−0.544009
$399$	3.59797	0.180124
$400$	1.00000	0.0500000
$401$	17.3892	0.868374	0.434187	−	0.900823i	$-0.357036\pi$
$401$	17.3892	0.868374	0.434187	+	0.900823i	$0.357036\pi$
$402$	−3.85075	−0.192058
$403$	−8.41541	−0.419201
$404$	6.90140	0.343357
$405$	5.37626	0.267149
$406$	16.2973	0.808821
$407$	−5.95617	−0.295237
$408$	2.46503	0.122037
$409$	−26.1268	−1.29189	−0.645944	−	0.763384i	$-0.723536\pi$
$409$	−26.1268	−1.29189	−0.645944	+	0.763384i	$0.723536\pi$
$410$	7.15290	0.353257
$411$	−1.26156	−0.0622281
$412$	2.34728	0.115642
$413$	−15.7250	−0.773775
$414$	15.9074	0.781807
$415$	3.03085	0.148779
$416$	3.04079	0.149087
$417$	1.91835	0.0939421
$418$	−1.50869	−0.0737927
$419$	0.616616	0.0301237	0.0150618	−	0.999887i	$-0.495205\pi$
$419$	0.616616	0.0301237	0.0150618	+	0.999887i	$0.495205\pi$
$420$	1.27226	0.0620801
$421$	−29.1244	−1.41944	−0.709718	−	0.704486i	$-0.751178\pi$
$421$	−29.1244	−1.41944	−0.709718	+	0.704486i	$0.751178\pi$
$422$	−11.5080	−0.560203
$423$	21.1880	1.03020
$424$	0.727663	0.0353384
$425$	3.79249	0.183963
$426$	4.06532	0.196966
$427$	21.7499	1.05255
$428$	18.2485	0.882075
$429$	−1.05440	−0.0509069
$430$	−3.28082	−0.158215
$431$	−6.91704	−0.333182	−0.166591	−	0.986026i	$-0.553276\pi$
$431$	−6.91704	−0.333182	−0.166591	+	0.986026i	$0.553276\pi$
$432$	−3.62526	−0.174420
$433$	−22.5163	−1.08206	−0.541031	−	0.841003i	$-0.681966\pi$
$433$	−22.5163	−1.08206	−0.541031	+	0.841003i	$0.681966\pi$
$434$	−5.41712	−0.260030
$435$	5.41169	0.259470
$436$	−5.85635	−0.280468
$437$	−17.4532	−0.834902
$438$	2.08264	0.0995126
$439$	6.89601	0.329128	0.164564	−	0.986366i	$-0.447378\pi$
$439$	6.89601	0.329128	0.164564	+	0.986366i	$0.447378\pi$
$440$	−0.533483	−0.0254328
$441$	8.16712	0.388910
$442$	11.5322	0.548530
$443$	−18.2237	−0.865835	−0.432917	−	0.901434i	$-0.642516\pi$
$443$	−18.2237	−0.865835	−0.432917	+	0.901434i	$0.642516\pi$
$444$	7.25677	0.344391
$445$	4.92922	0.233668
$446$	0.836834	0.0396252
$447$	10.6470	0.503584
$448$	1.95740	0.0924785
$449$	−1.31646	−0.0621276	−0.0310638	−	0.999517i	$-0.509890\pi$
$449$	−1.31646	−0.0621276	−0.0310638	+	0.999517i	$0.509890\pi$
$450$	−2.57753	−0.121506
$451$	−3.81596	−0.179686
$452$	6.00108	0.282267
$453$	−2.39051	−0.112316
$454$	22.0674	1.03567
$455$	5.95205	0.279037
$456$	1.83814	0.0860786
$457$	22.1429	1.03580	0.517900	−	0.855441i	$-0.326714\pi$
$457$	22.1429	1.03580	0.517900	+	0.855441i	$0.326714\pi$
$458$	12.2032	0.570219
$459$	−13.7488	−0.641737
$460$	−6.17157	−0.287751
$461$	22.8879	1.06600	0.532998	−	0.846117i	$-0.321065\pi$
$461$	22.8879	1.06600	0.532998	+	0.846117i	$0.321065\pi$
$462$	−0.678731	−0.0315774
$463$	−39.7770	−1.84859	−0.924297	−	0.381675i	$-0.875347\pi$
$463$	−39.7770	−1.84859	−0.924297	+	0.381675i	$0.875347\pi$
$464$	8.32598	0.386524
$465$	−1.79881	−0.0834178
$466$	−21.6445	−1.00266
$467$	−2.23979	−0.103645	−0.0518227	−	0.998656i	$-0.516503\pi$
$467$	−2.23979	−0.103645	−0.0518227	+	0.998656i	$0.516503\pi$
$468$	−7.83774	−0.362300
$469$	−11.5965	−0.535478
$470$	−8.22028	−0.379173
$471$	0.855041	0.0393982
$472$	−8.03359	−0.369776
$473$	1.75026	0.0804772
$474$	−8.95462	−0.411299
$475$	2.82801	0.129758
$476$	7.42342	0.340252
$477$	−1.87557	−0.0858766
$478$	3.38189	0.154684
$479$	1.11594	0.0509886	0.0254943	−	0.999675i	$-0.491884\pi$
$479$	1.11594	0.0509886	0.0254943	+	0.999675i	$0.491884\pi$
$480$	0.649976	0.0296672
$481$	33.9495	1.54796
$482$	2.21558	0.100917
$483$	−7.85186	−0.357272
$484$	−10.7154	−0.487063
$485$	10.3625	0.470536
$486$	14.3702	0.651846
$487$	7.43155	0.336756	0.168378	−	0.985723i	$-0.446147\pi$
$487$	7.43155	0.336756	0.168378	+	0.985723i	$0.446147\pi$
$488$	11.1116	0.503000
$489$	0.564203	0.0255142
$490$	−3.16858	−0.143142
$491$	8.10904	0.365956	0.182978	−	0.983117i	$-0.441426\pi$
$491$	8.10904	0.365956	0.182978	+	0.983117i	$0.441426\pi$
$492$	4.64921	0.209603
$493$	31.5762	1.42212
$494$	8.59939	0.386905
$495$	1.37507	0.0618048
$496$	−2.76750	−0.124265
$497$	12.2427	0.549161
$498$	1.96998	0.0882769
$499$	21.5473	0.964590	0.482295	−	0.876009i	$-0.339803\pi$
$499$	21.5473	0.964590	0.482295	+	0.876009i	$0.339803\pi$
$500$	1.00000	0.0447214
$501$	3.62099	0.161774
$502$	−6.27207	−0.279936
$503$	−14.0736	−0.627513	−0.313756	−	0.949504i	$-0.601588\pi$
$503$	−14.0736	−0.627513	−0.313756	+	0.949504i	$0.601588\pi$
$504$	−5.04526	−0.224734
$505$	6.90140	0.307108
$506$	3.29243	0.146366
$507$	−2.43973	−0.108352
$508$	−1.70824	−0.0757911
$509$	−9.58511	−0.424853	−0.212426	−	0.977177i	$-0.568137\pi$
$509$	−9.58511	−0.424853	−0.212426	+	0.977177i	$0.568137\pi$
$510$	2.46503	0.109153
$511$	6.27188	0.277452
$512$	1.00000	0.0441942
$513$	−10.2523	−0.452648
$514$	−16.7715	−0.739761
$515$	2.34728	0.103434
$516$	−2.13245	−0.0938761
$517$	4.38538	0.192869
$518$	21.8538	0.960199
$519$	−4.67308	−0.205125
$520$	3.04079	0.133348
$521$	−8.80545	−0.385774	−0.192887	−	0.981221i	$-0.561785\pi$
$521$	−8.80545	−0.385774	−0.192887	+	0.981221i	$0.561785\pi$
$522$	−21.4605	−0.939300
$523$	−28.6729	−1.25378	−0.626889	−	0.779109i	$-0.715672\pi$
$523$	−28.6729	−1.25378	−0.626889	+	0.779109i	$0.715672\pi$
$524$	−7.71695	−0.337117
$525$	1.27226	0.0555261
$526$	29.8899	1.30326
$527$	−10.4957	−0.457201
$528$	−0.346751	−0.0150904
$529$	15.0883	0.656012
$530$	0.727663	0.0316076
$531$	20.7068	0.898600
$532$	5.53554	0.239996
$533$	21.7505	0.942119
$534$	3.20388	0.138645
$535$	18.2485	0.788952
$536$	−5.92445	−0.255897
$537$	5.31526	0.229370
$538$	7.69031	0.331553
$539$	1.69039	0.0728101
$540$	−3.62526	−0.156006
$541$	−8.13238	−0.349638	−0.174819	−	0.984601i	$-0.555934\pi$
$541$	−8.13238	−0.349638	−0.174819	+	0.984601i	$0.555934\pi$
$542$	−16.0547	−0.689607
$543$	−7.38629	−0.316976
$544$	3.79249	0.162602
$545$	−5.85635	−0.250858
$546$	3.86869	0.165565
$547$	−4.39940	−0.188105	−0.0940524	−	0.995567i	$-0.529982\pi$
$547$	−4.39940	−0.188105	−0.0940524	+	0.995567i	$0.529982\pi$
$548$	−1.94093	−0.0829125
$549$	−28.6406	−1.22235
$550$	−0.533483	−0.0227478
$551$	23.5459	1.00309
$552$	−4.01137	−0.170735
$553$	−26.9668	−1.14675
$554$	30.5226	1.29678
$555$	7.25677	0.308033
$556$	2.95142	0.125168
$557$	4.86500	0.206137	0.103068	−	0.994674i	$-0.467134\pi$
$557$	4.86500	0.206137	0.103068	+	0.994674i	$0.467134\pi$
$558$	7.13333	0.301978
$559$	−9.97631	−0.421953
$560$	1.95740	0.0827153
$561$	−1.31505	−0.0555215
$562$	4.11589	0.173618
$563$	21.5721	0.909156	0.454578	−	0.890707i	$-0.349790\pi$
$563$	21.5721	0.909156	0.454578	+	0.890707i	$0.349790\pi$
$564$	−5.34298	−0.224980
$565$	6.00108	0.252467
$566$	17.1430	0.720574
$567$	10.5235	0.441946
$568$	6.25458	0.262436
$569$	27.0681	1.13475	0.567377	−	0.823458i	$-0.307958\pi$
$569$	27.0681	1.13475	0.567377	+	0.823458i	$0.307958\pi$
$570$	1.83814	0.0769910
$571$	32.9780	1.38009	0.690043	−	0.723768i	$-0.257592\pi$
$571$	32.9780	1.38009	0.690043	+	0.723768i	$0.257592\pi$
$572$	−1.62221	−0.0678281
$573$	−8.77517	−0.366588
$574$	14.0011	0.584395
$575$	−6.17157	−0.257372
$576$	−2.57753	−0.107397
$577$	−28.6503	−1.19273	−0.596364	−	0.802714i	$-0.703388\pi$
$577$	−28.6503	−1.19273	−0.596364	+	0.802714i	$0.703388\pi$
$578$	−2.61701	−0.108853
$579$	5.93772	0.246763
$580$	8.32598	0.345718
$581$	5.93259	0.246125
$582$	6.73535	0.279189
$583$	−0.388196	−0.0160774
$584$	3.20419	0.132590
$585$	−7.83774	−0.324051
$586$	−11.4235	−0.471900
$587$	−1.42245	−0.0587109	−0.0293555	−	0.999569i	$-0.509345\pi$
$587$	−1.42245	−0.0587109	−0.0293555	+	0.999569i	$0.509345\pi$
$588$	−2.05950	−0.0849324
$589$	−7.82652	−0.322486
$590$	−8.03359	−0.330738
$591$	−6.77711	−0.278773
$592$	11.1647	0.458866
$593$	−29.7128	−1.22016	−0.610079	−	0.792340i	$-0.708862\pi$
$593$	−29.7128	−1.22016	−0.610079	+	0.792340i	$0.708862\pi$
$594$	1.93402	0.0793536
$595$	7.42342	0.304331
$596$	16.3805	0.670973
$597$	−7.05415	−0.288707
$598$	−18.7665	−0.767418
$599$	7.05178	0.288128	0.144064	−	0.989568i	$-0.453983\pi$
$599$	7.05178	0.288128	0.144064	+	0.989568i	$0.453983\pi$
$600$	0.649976	0.0265351
$601$	1.00000	0.0407909
$601$	1.00000	0.0407909
$602$	−6.42189	−0.261737
$603$	15.2705	0.621861
$604$	−3.67784	−0.149649
$605$	−10.7154	−0.435643
$606$	4.48574	0.182221
$607$	−12.8823	−0.522878	−0.261439	−	0.965220i	$-0.584197\pi$
$607$	−12.8823	−0.522878	−0.261439	+	0.965220i	$0.584197\pi$
$608$	2.82801	0.114691
$609$	10.5928	0.429243
$610$	11.1116	0.449897
$611$	−24.9962	−1.01124
$612$	−9.77526	−0.395142
$613$	−30.0028	−1.21180	−0.605900	−	0.795541i	$-0.707187\pi$
$613$	−30.0028	−1.21180	−0.605900	+	0.795541i	$0.707187\pi$
$614$	−4.50166	−0.181672
$615$	4.64921	0.187474
$616$	−1.04424	−0.0420737
$617$	21.6326	0.870897	0.435448	−	0.900214i	$-0.356590\pi$
$617$	21.6326	0.870897	0.435448	+	0.900214i	$0.356590\pi$
$618$	1.52568	0.0613717
$619$	40.4628	1.62634	0.813168	−	0.582029i	$-0.197741\pi$
$619$	40.4628	1.62634	0.813168	+	0.582029i	$0.197741\pi$
$620$	−2.76750	−0.111146
$621$	22.3735	0.897819
$622$	−16.8293	−0.674793
$623$	9.64847	0.386558
$624$	1.97644	0.0791210
$625$	1.00000	0.0400000
$626$	−27.3428	−1.09284
$627$	−0.980615	−0.0391620
$628$	1.31550	0.0524940
$629$	42.3420	1.68828
$630$	−5.04526	−0.201008
$631$	−21.6863	−0.863316	−0.431658	−	0.902037i	$-0.642071\pi$
$631$	−21.6863	−0.863316	−0.431658	+	0.902037i	$0.642071\pi$
$632$	−13.7769	−0.548014
$633$	−7.47995	−0.297301
$634$	18.1971	0.722699
$635$	−1.70824	−0.0677896
$636$	0.472963	0.0187542
$637$	−9.63500	−0.381753
$638$	−4.44177	−0.175851
$639$	−16.1214	−0.637752
$640$	1.00000	0.0395285
$641$	19.2155	0.758966	0.379483	−	0.925199i	$-0.376102\pi$
$641$	19.2155	0.758966	0.379483	+	0.925199i	$0.376102\pi$
$642$	11.8611	0.468120
$643$	−4.79521	−0.189104	−0.0945522	−	0.995520i	$-0.530142\pi$
$643$	−4.79521	−0.189104	−0.0945522	+	0.995520i	$0.530142\pi$
$644$	−12.0802	−0.476028
$645$	−2.13245	−0.0839653
$646$	10.7252	0.421977
$647$	−26.7742	−1.05260	−0.526301	−	0.850298i	$-0.676422\pi$
$647$	−26.7742	−1.05260	−0.526301	+	0.850298i	$0.676422\pi$
$648$	5.37626	0.211200
$649$	4.28579	0.168232
$650$	3.04079	0.119270
$651$	−3.52099	−0.137999
$652$	0.868038	0.0339950
$653$	9.75020	0.381555	0.190777	−	0.981633i	$-0.438899\pi$
$653$	9.75020	0.381555	0.190777	+	0.981633i	$0.438899\pi$
$654$	−3.80648	−0.148845
$655$	−7.71695	−0.301526
$656$	7.15290	0.279274
$657$	−8.25890	−0.322210
$658$	−16.0904	−0.627269
$659$	4.62555	0.180186	0.0900929	−	0.995933i	$-0.471284\pi$
$659$	4.62555	0.180186	0.0900929	+	0.995933i	$0.471284\pi$
$660$	−0.346751	−0.0134973
$661$	−26.3177	−1.02364	−0.511821	−	0.859092i	$-0.671029\pi$
$661$	−26.3177	−1.02364	−0.511821	+	0.859092i	$0.671029\pi$
$662$	13.2356	0.514414
$663$	7.49564	0.291106
$664$	3.03085	0.117620
$665$	5.53554	0.214659
$666$	−28.7773	−1.11510
$667$	−51.3844	−1.98961
$668$	5.57096	0.215547
$669$	0.543921	0.0210292
$670$	−5.92445	−0.228881
$671$	−5.92787	−0.228843
$672$	1.27226	0.0490786
$673$	−33.5789	−1.29437	−0.647186	−	0.762332i	$-0.724054\pi$
$673$	−33.5789	−1.29437	−0.647186	+	0.762332i	$0.724054\pi$
$674$	−28.5466	−1.09957
$675$	−3.62526	−0.139536
$676$	−3.75357	−0.144368
$677$	−16.2599	−0.624918	−0.312459	−	0.949931i	$-0.601153\pi$
$677$	−16.2599	−0.624918	−0.312459	+	0.949931i	$0.601153\pi$
$678$	3.90056	0.149800
$679$	20.2835	0.778410
$680$	3.79249	0.145435
$681$	14.3433	0.549635
$682$	1.47642	0.0565349
$683$	−46.4873	−1.77879	−0.889393	−	0.457144i	$-0.848873\pi$
$683$	−46.4873	−1.77879	−0.889393	+	0.457144i	$0.848873\pi$
$684$	−7.28928	−0.278713
$685$	−1.94093	−0.0741592
$686$	−19.9040	−0.759938
$687$	7.93180	0.302617
$688$	−3.28082	−0.125080
$689$	2.21267	0.0842961
$690$	−4.01137	−0.152710
$691$	41.5913	1.58221	0.791104	−	0.611682i	$-0.209507\pi$
$691$	41.5913	1.58221	0.791104	+	0.611682i	$0.209507\pi$
$692$	−7.18962	−0.273308
$693$	2.69156	0.102244
$694$	−5.31861	−0.201892
$695$	2.95142	0.111954
$696$	5.41169	0.205129
$697$	27.1273	1.02752
$698$	−27.6806	−1.04773
$699$	−14.0684	−0.532116
$700$	1.95740	0.0739828
$701$	−11.1137	−0.419759	−0.209879	−	0.977727i	$-0.567307\pi$
$701$	−11.1137	−0.419759	−0.209879	+	0.977727i	$0.567307\pi$
$702$	−11.0237	−0.416062
$703$	31.5738	1.19083
$704$	−0.533483	−0.0201064
$705$	−5.34298	−0.201228
$706$	18.0916	0.680888
$707$	13.5088	0.508051
$708$	−5.22164	−0.196241
$709$	20.6950	0.777218	0.388609	−	0.921403i	$-0.372956\pi$
$709$	20.6950	0.777218	0.388609	+	0.921403i	$0.372956\pi$
$710$	6.25458	0.234730
$711$	35.5103	1.33174
$712$	4.92922	0.184731
$713$	17.0798	0.639645
$714$	4.82505	0.180573
$715$	−1.62221	−0.0606673
$716$	8.17763	0.305612
$717$	2.19814	0.0820912
$718$	−29.1432	−1.08761
$719$	−5.88793	−0.219583	−0.109791	−	0.993955i	$-0.535018\pi$
$719$	−5.88793	−0.219583	−0.109791	+	0.993955i	$0.535018\pi$
$720$	−2.57753	−0.0960589
$721$	4.59457	0.171111
$722$	−11.0024	−0.409466
$723$	1.44008	0.0535570
$724$	−11.3639	−0.422338
$725$	8.32598	0.309219
$726$	−6.96475	−0.258486
$727$	1.84768	0.0685266	0.0342633	−	0.999413i	$-0.489092\pi$
$727$	1.84768	0.0685266	0.0342633	+	0.999413i	$0.489092\pi$
$728$	5.95205	0.220598
$729$	−6.78850	−0.251426
$730$	3.20419	0.118592
$731$	−12.4425	−0.460202
$732$	7.22229	0.266943
$733$	−11.9579	−0.441674	−0.220837	−	0.975311i	$-0.570879\pi$
$733$	−11.9579	−0.441674	−0.220837	+	0.975311i	$0.570879\pi$
$734$	−7.22004	−0.266497
$735$	−2.05950	−0.0759658
$736$	−6.17157	−0.227487
$737$	3.16060	0.116422
$738$	−18.4368	−0.678669
$739$	0.112391	0.00413436	0.00206718	−	0.999998i	$-0.499342\pi$
$739$	0.112391	0.00413436	0.00206718	+	0.999998i	$0.499342\pi$
$740$	11.1647	0.410422
$741$	5.58939	0.205331
$742$	1.42433	0.0522887
$743$	27.6059	1.01276	0.506381	−	0.862310i	$-0.330983\pi$
$743$	27.6059	1.01276	0.506381	+	0.862310i	$0.330983\pi$
$744$	−1.79881	−0.0659476
$745$	16.3805	0.600137
$746$	−4.18781	−0.153327
$747$	−7.81212	−0.285830
$748$	−2.02323	−0.0739766
$749$	35.7197	1.30517
$750$	0.649976	0.0237338
$751$	−11.7560	−0.428981	−0.214490	−	0.976726i	$-0.568809\pi$
$751$	−11.7560	−0.428981	−0.214490	+	0.976726i	$0.568809\pi$
$752$	−8.22028	−0.299763
$753$	−4.07669	−0.148563
$754$	25.3176	0.922012
$755$	−3.67784	−0.133850
$756$	−7.09609	−0.258082
$757$	32.4947	1.18104	0.590520	−	0.807023i	$-0.298922\pi$
$757$	32.4947	1.18104	0.590520	+	0.807023i	$0.298922\pi$
$758$	16.8593	0.612356
$759$	2.14000	0.0776770
$760$	2.82801	0.102583
$761$	−52.0633	−1.88729	−0.943647	−	0.330954i	$-0.892629\pi$
$761$	−52.0633	−1.88729	−0.943647	+	0.330954i	$0.892629\pi$
$762$	−1.11032	−0.0402225
$763$	−11.4632	−0.414996
$764$	−13.5008	−0.488440
$765$	−9.77526	−0.353425
$766$	−9.93958	−0.359132
$767$	−24.4285	−0.882062
$768$	0.649976	0.0234540
$769$	42.8907	1.54668	0.773338	−	0.633993i	$-0.218585\pi$
$769$	42.8907	1.54668	0.773338	+	0.633993i	$0.218585\pi$
$770$	−1.04424	−0.0376318
$771$	−10.9011	−0.392593
$772$	9.13530	0.328787
$773$	−11.4094	−0.410368	−0.205184	−	0.978723i	$-0.565779\pi$
$773$	−11.4094	−0.410368	−0.205184	+	0.978723i	$0.565779\pi$
$774$	8.45642	0.303960
$775$	−2.76750	−0.0994117
$776$	10.3625	0.371991
$777$	14.2044	0.509581
$778$	7.26070	0.260309
$779$	20.2285	0.724760
$780$	1.97644	0.0707680
$781$	−3.33671	−0.119397
$782$	−23.4056	−0.836983
$783$	−30.1838	−1.07868
$784$	−3.16858	−0.113164
$785$	1.31550	0.0469521
$786$	−5.01583	−0.178909
$787$	−5.92655	−0.211259	−0.105629	−	0.994406i	$-0.533686\pi$
$787$	−5.92655	−0.211259	−0.105629	+	0.994406i	$0.533686\pi$
$788$	−10.4267	−0.371436
$789$	19.4277	0.691646
$790$	−13.7769	−0.490158
$791$	11.7465	0.417658
$792$	1.37507	0.0488610
$793$	33.7882	1.19985
$794$	11.8917	0.422019
$795$	0.472963	0.0167743
$796$	−10.8529	−0.384672
$797$	10.7271	0.379974	0.189987	−	0.981787i	$-0.439155\pi$
$797$	10.7271	0.379974	0.189987	+	0.981787i	$0.439155\pi$
$798$	3.59797	0.127367
$799$	−31.1753	−1.10290
$800$	1.00000	0.0353553
$801$	−12.7052	−0.448917
$802$	17.3892	0.614033
$803$	−1.70938	−0.0603227
$804$	−3.85075	−0.135805
$805$	−12.0802	−0.425772
$806$	−8.41541	−0.296420
$807$	4.99852	0.175956
$808$	6.90140	0.242790
$809$	10.7012	0.376233	0.188117	−	0.982147i	$-0.439762\pi$
$809$	10.7012	0.376233	0.188117	+	0.982147i	$0.439762\pi$
$810$	5.37626	0.188903
$811$	−1.78941	−0.0628348	−0.0314174	−	0.999506i	$-0.510002\pi$
$811$	−1.78941	−0.0628348	−0.0314174	+	0.999506i	$0.510002\pi$
$812$	16.2973	0.571923
$813$	−10.4351	−0.365976
$814$	−5.95617	−0.208764
$815$	0.868038	0.0304060
$816$	2.46503	0.0862932
$817$	−9.27819	−0.324603
$818$	−26.1268	−0.913503
$819$	−15.3416	−0.536079
$820$	7.15290	0.249790
$821$	13.3897	0.467302	0.233651	−	0.972321i	$-0.424933\pi$
$821$	13.3897	0.467302	0.233651	+	0.972321i	$0.424933\pi$
$822$	−1.26156	−0.0440019
$823$	48.7215	1.69833	0.849163	−	0.528131i	$-0.177107\pi$
$823$	48.7215	1.69833	0.849163	+	0.528131i	$0.177107\pi$
$824$	2.34728	0.0817715
$825$	−0.346751	−0.0120723
$826$	−15.7250	−0.547141
$827$	23.7028	0.824229	0.412114	−	0.911132i	$-0.364790\pi$
$827$	23.7028	0.824229	0.412114	+	0.911132i	$0.364790\pi$
$828$	15.9074	0.552821
$829$	−19.6309	−0.681810	−0.340905	−	0.940098i	$-0.610733\pi$
$829$	−19.6309	−0.681810	−0.340905	+	0.940098i	$0.610733\pi$
$830$	3.03085	0.105202
$831$	19.8389	0.688205
$832$	3.04079	0.105421
$833$	−12.0168	−0.416358
$834$	1.91835	0.0664271
$835$	5.57096	0.192791
$836$	−1.50869	−0.0521793
$837$	10.0329	0.346789
$838$	0.616616	0.0213006
$839$	−11.5444	−0.398558	−0.199279	−	0.979943i	$-0.563860\pi$
$839$	−11.5444	−0.398558	−0.199279	+	0.979943i	$0.563860\pi$
$840$	1.27226	0.0438972
$841$	40.3220	1.39041
$842$	−29.1244	−1.00369
$843$	2.67523	0.0921398
$844$	−11.5080	−0.396123
$845$	−3.75357	−0.129127
$846$	21.1880	0.728460
$847$	−20.9743	−0.720686
$848$	0.727663	0.0249880
$849$	11.1425	0.382411
$850$	3.79249	0.130081
$851$	−68.9036	−2.36199
$852$	4.06532	0.139276
$853$	−53.4957	−1.83166	−0.915829	−	0.401568i	$-0.868465\pi$
$853$	−53.4957	−1.83166	−0.915829	+	0.401568i	$0.868465\pi$
$854$	21.7499	0.744267
$855$	−7.28928	−0.249288
$856$	18.2485	0.623721
$857$	−18.7406	−0.640166	−0.320083	−	0.947390i	$-0.603711\pi$
$857$	−18.7406	−0.640166	−0.320083	+	0.947390i	$0.603711\pi$
$858$	−1.05440	−0.0359966
$859$	−17.7654	−0.606149	−0.303074	−	0.952967i	$-0.598013\pi$
$859$	−17.7654	−0.606149	−0.303074	+	0.952967i	$0.598013\pi$
$860$	−3.28082	−0.111875
$861$	9.10038	0.310140
$862$	−6.91704	−0.235595
$863$	−49.0615	−1.67007	−0.835037	−	0.550194i	$-0.814554\pi$
$863$	−49.0615	−1.67007	−0.835037	+	0.550194i	$0.814554\pi$
$864$	−3.62526	−0.123334
$865$	−7.18962	−0.244454
$866$	−22.5163	−0.765133
$867$	−1.70100	−0.0577688
$868$	−5.41712	−0.183869
$869$	7.34972	0.249322
$870$	5.41169	0.183473
$871$	−18.0150	−0.610416
$872$	−5.85635	−0.198321
$873$	−26.7096	−0.903983
$874$	−17.4532	−0.590365
$875$	1.95740	0.0661722
$876$	2.08264	0.0703660
$877$	1.64531	0.0555581	0.0277791	−	0.999614i	$-0.491157\pi$
$877$	1.64531	0.0555581	0.0277791	+	0.999614i	$0.491157\pi$
$878$	6.89601	0.232729
$879$	−7.42499	−0.250439
$880$	−0.533483	−0.0179837
$881$	−3.14834	−0.106070	−0.0530351	−	0.998593i	$-0.516890\pi$
$881$	−3.14834	−0.106070	−0.0530351	+	0.998593i	$0.516890\pi$
$882$	8.16712	0.275001
$883$	−18.3046	−0.615998	−0.307999	−	0.951387i	$-0.599659\pi$
$883$	−18.3046	−0.615998	−0.307999	+	0.951387i	$0.599659\pi$
$884$	11.5322	0.387869
$885$	−5.22164	−0.175523
$886$	−18.2237	−0.612238
$887$	−28.9953	−0.973568	−0.486784	−	0.873522i	$-0.661830\pi$
$887$	−28.9953	−0.973568	−0.486784	+	0.873522i	$0.661830\pi$
$888$	7.25677	0.243521
$889$	−3.34372	−0.112145
$890$	4.92922	0.165228
$891$	−2.86815	−0.0960866
$892$	0.836834	0.0280193
$893$	−23.2470	−0.777932
$894$	10.6470	0.356087
$895$	8.17763	0.273348
$896$	1.95740	0.0653922
$897$	−12.1977	−0.407271
$898$	−1.31646	−0.0439309
$899$	−23.0422	−0.768500
$900$	−2.57753	−0.0859177
$901$	2.75965	0.0919374
$902$	−3.81596	−0.127057
$903$	−4.17407	−0.138904
$904$	6.00108	0.199593
$905$	−11.3639	−0.377750
$906$	−2.39051	−0.0794193
$907$	31.8803	1.05857	0.529284	−	0.848445i	$-0.322461\pi$
$907$	31.8803	1.05857	0.529284	+	0.848445i	$0.322461\pi$
$908$	22.0674	0.732332
$909$	−17.7886	−0.590009
$910$	5.95205	0.197309
$911$	16.0141	0.530570	0.265285	−	0.964170i	$-0.414534\pi$
$911$	16.0141	0.530570	0.265285	+	0.964170i	$0.414534\pi$
$912$	1.83814	0.0608668
$913$	−1.61691	−0.0535119
$914$	22.1429	0.732421
$915$	7.22229	0.238761
$916$	12.2032	0.403206
$917$	−15.1052	−0.498816
$918$	−13.7488	−0.453777
$919$	12.7588	0.420875	0.210438	−	0.977607i	$-0.432511\pi$
$919$	12.7588	0.420875	0.210438	+	0.977607i	$0.432511\pi$
$920$	−6.17157	−0.203471
$921$	−2.92597	−0.0964139
$922$	22.8879	0.753773
$923$	19.0189	0.626014
$924$	−0.678731	−0.0223286
$925$	11.1647	0.367093
$926$	−39.7770	−1.30715
$927$	−6.05020	−0.198715
$928$	8.32598	0.273314
$929$	4.57721	0.150173	0.0750866	−	0.997177i	$-0.476077\pi$
$929$	4.57721	0.150173	0.0750866	+	0.997177i	$0.476077\pi$
$930$	−1.79881	−0.0589853
$931$	−8.96077	−0.293677
$932$	−21.6445	−0.708989
$933$	−10.9386	−0.358115
$934$	−2.23979	−0.0732883
$935$	−2.02323	−0.0661667
$936$	−7.83774	−0.256185
$937$	12.4693	0.407353	0.203677	−	0.979038i	$-0.434711\pi$
$937$	12.4693	0.407353	0.203677	+	0.979038i	$0.434711\pi$
$938$	−11.5965	−0.378640
$939$	−17.7722	−0.579973
$940$	−8.22028	−0.268116
$941$	5.52996	0.180271	0.0901357	−	0.995929i	$-0.471270\pi$
$941$	5.52996	0.180271	0.0901357	+	0.995929i	$0.471270\pi$
$942$	0.855041	0.0278587
$943$	−44.1447	−1.43755
$944$	−8.03359	−0.261471
$945$	−7.09609	−0.230836
$946$	1.75026	0.0569060
$947$	−6.60518	−0.214639	−0.107320	−	0.994225i	$-0.534227\pi$
$947$	−6.60518	−0.214639	−0.107320	+	0.994225i	$0.534227\pi$
$948$	−8.95462	−0.290832
$949$	9.74328	0.316280
$950$	2.82801	0.0917527
$951$	11.8277	0.383539
$952$	7.42342	0.240595
$953$	−44.2711	−1.43408	−0.717041	−	0.697031i	$-0.754504\pi$
$953$	−44.2711	−1.43408	−0.717041	+	0.697031i	$0.754504\pi$
$954$	−1.87557	−0.0607239
$955$	−13.5008	−0.436874
$956$	3.38189	0.109378
$957$	−2.88704	−0.0933249
$958$	1.11594	0.0360544
$959$	−3.79918	−0.122682
$960$	0.649976	0.0209779
$961$	−23.3409	−0.752933
$962$	33.9495	1.09458
$963$	−47.0361	−1.51572
$964$	2.21558	0.0713592
$965$	9.13530	0.294076
$966$	−7.85186	−0.252629
$967$	−28.2064	−0.907056	−0.453528	−	0.891242i	$-0.649835\pi$
$967$	−28.2064	−0.907056	−0.453528	+	0.891242i	$0.649835\pi$
$968$	−10.7154	−0.344406
$969$	6.97111	0.223944
$970$	10.3625	0.332719
$971$	−2.17007	−0.0696408	−0.0348204	−	0.999394i	$-0.511086\pi$
$971$	−2.17007	−0.0696408	−0.0348204	+	0.999394i	$0.511086\pi$
$972$	14.3702	0.460925
$973$	5.77711	0.185206
$974$	7.43155	0.238122
$975$	1.97644	0.0632968
$976$	11.1116	0.355675
$977$	3.60107	0.115208	0.0576042	−	0.998339i	$-0.481654\pi$
$977$	3.60107	0.115208	0.0576042	+	0.998339i	$0.481654\pi$
$978$	0.564203	0.0180412
$979$	−2.62966	−0.0840443
$980$	−3.16858	−0.101217
$981$	15.0949	0.481944
$982$	8.10904	0.258770
$983$	−27.9152	−0.890356	−0.445178	−	0.895442i	$-0.646860\pi$
$983$	−27.9152	−0.890356	−0.445178	+	0.895442i	$0.646860\pi$
$984$	4.64921	0.148212
$985$	−10.4267	−0.332223
$986$	31.5762	1.00559
$987$	−10.4584	−0.332893
$988$	8.59939	0.273583
$989$	20.2478	0.643843
$990$	1.37507	0.0437026
$991$	4.39947	0.139754	0.0698769	−	0.997556i	$-0.477739\pi$
$991$	4.39947	0.139754	0.0698769	+	0.997556i	$0.477739\pi$
$992$	−2.76750	−0.0878684
$993$	8.60279	0.273001
$994$	12.2427	0.388315
$995$	−10.8529	−0.344061
$996$	1.96998	0.0624212
$997$	32.3968	1.02602	0.513008	−	0.858384i	$-0.328531\pi$
$997$	32.3968	1.02602	0.513008	+	0.858384i	$0.328531\pi$
$998$	21.5473	0.682068
$999$	−40.4749	−1.28057

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.j.1.19	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.j.1.19	✓	33	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.649976 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.649976 q^{6} +1.95740 q^{7} +1.00000 q^{8} -2.57753 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.649976 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.649976 q^{6} +1.95740 q^{7} +1.00000 q^{8} -2.57753 q^{9} +1.00000 q^{10} -0.533483 q^{11} +0.649976 q^{12} +3.04079 q^{13} +1.95740 q^{14} +0.649976 q^{15} +1.00000 q^{16} +3.79249 q^{17} -2.57753 q^{18} +2.82801 q^{19} +1.00000 q^{20} +1.27226 q^{21} -0.533483 q^{22} -6.17157 q^{23} +0.649976 q^{24} +1.00000 q^{25} +3.04079 q^{26} -3.62526 q^{27} +1.95740 q^{28} +8.32598 q^{29} +0.649976 q^{30} -2.76750 q^{31} +1.00000 q^{32} -0.346751 q^{33} +3.79249 q^{34} +1.95740 q^{35} -2.57753 q^{36} +11.1647 q^{37} +2.82801 q^{38} +1.97644 q^{39} +1.00000 q^{40} +7.15290 q^{41} +1.27226 q^{42} -3.28082 q^{43} -0.533483 q^{44} -2.57753 q^{45} -6.17157 q^{46} -8.22028 q^{47} +0.649976 q^{48} -3.16858 q^{49} +1.00000 q^{50} +2.46503 q^{51} +3.04079 q^{52} +0.727663 q^{53} -3.62526 q^{54} -0.533483 q^{55} +1.95740 q^{56} +1.83814 q^{57} +8.32598 q^{58} -8.03359 q^{59} +0.649976 q^{60} +11.1116 q^{61} -2.76750 q^{62} -5.04526 q^{63} +1.00000 q^{64} +3.04079 q^{65} -0.346751 q^{66} -5.92445 q^{67} +3.79249 q^{68} -4.01137 q^{69} +1.95740 q^{70} +6.25458 q^{71} -2.57753 q^{72} +3.20419 q^{73} +11.1647 q^{74} +0.649976 q^{75} +2.82801 q^{76} -1.04424 q^{77} +1.97644 q^{78} -13.7769 q^{79} +1.00000 q^{80} +5.37626 q^{81} +7.15290 q^{82} +3.03085 q^{83} +1.27226 q^{84} +3.79249 q^{85} -3.28082 q^{86} +5.41169 q^{87} -0.533483 q^{88} +4.92922 q^{89} -2.57753 q^{90} +5.95205 q^{91} -6.17157 q^{92} -1.79881 q^{93} -8.22028 q^{94} +2.82801 q^{95} +0.649976 q^{96} +10.3625 q^{97} -3.16858 q^{98} +1.37507 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9}+O(q^{10}) \) 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9	\( 33 q + 33 q^{2} + 6 q^{3} + 33 q^{4} + 33 q^{5} + 6 q^{6} + 4 q^{7} + 33 q^{8} + 49 q^{9} + 33 q^{10} + 12 q^{11} + 6 q^{12} + 20 q^{13} + 4 q^{14} + 6 q^{15} + 33 q^{16} + 33 q^{17} + 49 q^{18} + 17 q^{19} + 33 q^{20} + 26 q^{21} + 12 q^{22} + 7 q^{23} + 6 q^{24} + 33 q^{25} + 20 q^{26} + 21 q^{27} + 4 q^{28} + 33 q^{29} + 6 q^{30} + 35 q^{31} + 33 q^{32} + 25 q^{33} + 33 q^{34} + 4 q^{35} + 49 q^{36} + 16 q^{37} + 17 q^{38} + 22 q^{39} + 33 q^{40} + 39 q^{41} + 26 q^{42} - 3 q^{43} + 12 q^{44} + 49 q^{45} + 7 q^{46} + 19 q^{47} + 6 q^{48} + 69 q^{49} + 33 q^{50} + 21 q^{51} + 20 q^{52} + 41 q^{53} + 21 q^{54} + 12 q^{55} + 4 q^{56} + 33 q^{58} + 18 q^{59} + 6 q^{60} + 30 q^{61} + 35 q^{62} - 15 q^{63} + 33 q^{64} + 20 q^{65} + 25 q^{66} - 9 q^{67} + 33 q^{68} + 23 q^{69} + 4 q^{70} + 36 q^{71} + 49 q^{72} + 35 q^{73} + 16 q^{74} + 6 q^{75} + 17 q^{76} + 26 q^{77} + 22 q^{78} + 32 q^{79} + 33 q^{80} + 53 q^{81} + 39 q^{82} + 24 q^{83} + 26 q^{84} + 33 q^{85} - 3 q^{86} + 12 q^{87} + 12 q^{88} + 40 q^{89} + 49 q^{90} + 5 q^{91} + 7 q^{92} + 18 q^{93} + 19 q^{94} + 17 q^{95} + 6 q^{96} + 39 q^{97} + 69 q^{98} + 3 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 + 6 * q^3 + 33 * q^4 + 33 * q^5 + 6 * q^6 + 4 * q^7 + 33 * q^8 + 49 * q^9 + 33 * q^10 + 12 * q^11 + 6 * q^12 + 20 * q^13 + 4 * q^14 + 6 * q^15 + 33 * q^16 + 33 * q^17 + 49 * q^18 + 17 * q^19 + 33 * q^20 + 26 * q^21 + 12 * q^22 + 7 * q^23 + 6 * q^24 + 33 * q^25 + 20 * q^26 + 21 * q^27 + 4 * q^28 + 33 * q^29 + 6 * q^30 + 35 * q^31 + 33 * q^32 + 25 * q^33 + 33 * q^34 + 4 * q^35 + 49 * q^36 + 16 * q^37 + 17 * q^38 + 22 * q^39 + 33 * q^40 + 39 * q^41 + 26 * q^42 - 3 * q^43 + 12 * q^44 + 49 * q^45 + 7 * q^46 + 19 * q^47 + 6 * q^48 + 69 * q^49 + 33 * q^50 + 21 * q^51 + 20 * q^52 + 41 * q^53 + 21 * q^54 + 12 * q^55 + 4 * q^56 + 33 * q^58 + 18 * q^59 + 6 * q^60 + 30 * q^61 + 35 * q^62 - 15 * q^63 + 33 * q^64 + 20 * q^65 + 25 * q^66 - 9 * q^67 + 33 * q^68 + 23 * q^69 + 4 * q^70 + 36 * q^71 + 49 * q^72 + 35 * q^73 + 16 * q^74 + 6 * q^75 + 17 * q^76 + 26 * q^77 + 22 * q^78 + 32 * q^79 + 33 * q^80 + 53 * q^81 + 39 * q^82 + 24 * q^83 + 26 * q^84 + 33 * q^85 - 3 * q^86 + 12 * q^87 + 12 * q^88 + 40 * q^89 + 49 * q^90 + 5 * q^91 + 7 * q^92 + 18 * q^93 + 19 * q^94 + 17 * q^95 + 6 * q^96 + 39 * q^97 + 69 * q^98 + 3 * q^99

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