LMFDB - Embedded newform 8041.2.a.c.1.15

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:	$1$
Dimension:	$60$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q-1.55010 q^{2} +2.25408 q^{3} +0.402812 q^{4} -2.41752 q^{5} -3.49405 q^{6} +2.04645 q^{7} +2.47580 q^{8} +2.08087 q^{9} +O(q^{10})$	\(q-1.55010 q^{2} +2.25408 q^{3} +0.402812 q^{4} -2.41752 q^{5} -3.49405 q^{6} +2.04645 q^{7} +2.47580 q^{8} +2.08087 q^{9} +3.74740 q^{10} +1.00000 q^{11} +0.907969 q^{12} -1.72594 q^{13} -3.17220 q^{14} -5.44928 q^{15} -4.64337 q^{16} +1.00000 q^{17} -3.22556 q^{18} -1.96990 q^{19} -0.973805 q^{20} +4.61286 q^{21} -1.55010 q^{22} -7.37478 q^{23} +5.58066 q^{24} +0.844399 q^{25} +2.67537 q^{26} -2.07178 q^{27} +0.824334 q^{28} +7.42634 q^{29} +8.44693 q^{30} +10.1471 q^{31} +2.24608 q^{32} +2.25408 q^{33} -1.55010 q^{34} -4.94733 q^{35} +0.838200 q^{36} +2.39587 q^{37} +3.05354 q^{38} -3.89040 q^{39} -5.98530 q^{40} -11.2249 q^{41} -7.15040 q^{42} -1.00000 q^{43} +0.402812 q^{44} -5.03055 q^{45} +11.4317 q^{46} +8.15297 q^{47} -10.4665 q^{48} -2.81204 q^{49} -1.30890 q^{50} +2.25408 q^{51} -0.695227 q^{52} -4.44172 q^{53} +3.21147 q^{54} -2.41752 q^{55} +5.06661 q^{56} -4.44031 q^{57} -11.5116 q^{58} +6.44436 q^{59} -2.19503 q^{60} -2.90887 q^{61} -15.7289 q^{62} +4.25840 q^{63} +5.80508 q^{64} +4.17248 q^{65} -3.49405 q^{66} +3.49168 q^{67} +0.402812 q^{68} -16.6233 q^{69} +7.66886 q^{70} +9.78766 q^{71} +5.15183 q^{72} +7.97619 q^{73} -3.71384 q^{74} +1.90334 q^{75} -0.793498 q^{76} +2.04645 q^{77} +6.03050 q^{78} -11.5260 q^{79} +11.2254 q^{80} -10.9126 q^{81} +17.3998 q^{82} -4.50980 q^{83} +1.85811 q^{84} -2.41752 q^{85} +1.55010 q^{86} +16.7396 q^{87} +2.47580 q^{88} -1.37304 q^{89} +7.79786 q^{90} -3.53204 q^{91} -2.97065 q^{92} +22.8723 q^{93} -12.6379 q^{94} +4.76227 q^{95} +5.06284 q^{96} -10.1474 q^{97} +4.35895 q^{98} +2.08087 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) $ 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * 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 $

$2$	−1.55010	−1.09609	−0.548043	−	0.836450i	$-0.684627\pi$
$2$	−1.55010	−1.09609	−0.548043	+	0.836450i	$0.684627\pi$
$3$	2.25408	1.30139	0.650697	−	0.759338i	$-0.274477\pi$
$3$	2.25408	1.30139	0.650697	+	0.759338i	$0.274477\pi$
$4$	0.402812	0.201406
$5$	−2.41752	−1.08115	−0.540574	−	0.841297i	$-0.681793\pi$
$5$	−2.41752	−1.08115	−0.540574	+	0.841297i	$0.681793\pi$
$6$	−3.49405	−1.42644
$7$	2.04645	0.773485	0.386743	−	0.922188i	$-0.373600\pi$
$7$	2.04645	0.773485	0.386743	+	0.922188i	$0.373600\pi$
$8$	2.47580	0.875328
$9$	2.08087	0.693624
$10$	3.74740	1.18503
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.907969	0.262108
$13$	−1.72594	−0.478688	−0.239344	−	0.970935i	$-0.576932\pi$
$13$	−1.72594	−0.478688	−0.239344	+	0.970935i	$0.576932\pi$
$14$	−3.17220	−0.847807
$15$	−5.44928	−1.40700
$16$	−4.64337	−1.16084
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−3.22556	−0.760272
$19$	−1.96990	−0.451926	−0.225963	−	0.974136i	$-0.572553\pi$
$19$	−1.96990	−0.451926	−0.225963	+	0.974136i	$0.572553\pi$
$20$	−0.973805	−0.217749
$21$	4.61286	1.00661
$22$	−1.55010	−0.330483
$23$	−7.37478	−1.53775	−0.768874	−	0.639400i	$-0.779183\pi$
$23$	−7.37478	−1.53775	−0.768874	+	0.639400i	$0.779183\pi$
$24$	5.58066	1.13915
$25$	0.844399	0.168880
$26$	2.67537	0.524684
$27$	−2.07178	−0.398715
$28$	0.824334	0.155784
$29$	7.42634	1.37904	0.689519	−	0.724268i	$-0.257822\pi$
$29$	7.42634	1.37904	0.689519	+	0.724268i	$0.257822\pi$
$30$	8.44693	1.54219
$31$	10.1471	1.82246	0.911232	−	0.411893i	$-0.135132\pi$
$31$	10.1471	1.82246	0.911232	+	0.411893i	$0.135132\pi$
$32$	2.24608	0.397054
$33$	2.25408	0.392385
$34$	−1.55010	−0.265840
$35$	−4.94733	−0.836252
$36$	0.838200	0.139700
$37$	2.39587	0.393878	0.196939	−	0.980416i	$-0.436900\pi$
$37$	2.39587	0.393878	0.196939	+	0.980416i	$0.436900\pi$
$38$	3.05354	0.495350
$39$	−3.89040	−0.622962
$40$	−5.98530	−0.946359
$41$	−11.2249	−1.75304	−0.876520	−	0.481365i	$-0.840141\pi$
$41$	−11.2249	−1.75304	−0.876520	+	0.481365i	$0.840141\pi$
$42$	−7.15040	−1.10333
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	0.402812	0.0607261
$45$	−5.03055	−0.749910
$46$	11.4317	1.68551
$47$	8.15297	1.18923	0.594617	−	0.804009i	$-0.297304\pi$
$47$	8.15297	1.18923	0.594617	+	0.804009i	$0.297304\pi$
$48$	−10.4665	−1.51071
$49$	−2.81204	−0.401720
$50$	−1.30890	−0.185107
$51$	2.25408	0.315634
$52$	−0.695227	−0.0964106
$53$	−4.44172	−0.610118	−0.305059	−	0.952334i	$-0.598676\pi$
$53$	−4.44172	−0.610118	−0.305059	+	0.952334i	$0.598676\pi$
$54$	3.21147	0.437026
$55$	−2.41752	−0.325978
$56$	5.06661	0.677054
$57$	−4.44031	−0.588133
$58$	−11.5116	−1.51154
$59$	6.44436	0.838984	0.419492	−	0.907759i	$-0.362208\pi$
$59$	6.44436	0.838984	0.419492	+	0.907759i	$0.362208\pi$
$60$	−2.19503	−0.283378
$61$	−2.90887	−0.372443	−0.186222	−	0.982508i	$-0.559624\pi$
$61$	−2.90887	−0.372443	−0.186222	+	0.982508i	$0.559624\pi$
$62$	−15.7289	−1.99758
$63$	4.25840	0.536508
$64$	5.80508	0.725636
$65$	4.17248	0.517533
$66$	−3.49405	−0.430088
$67$	3.49168	0.426577	0.213289	−	0.976989i	$-0.431583\pi$
$67$	3.49168	0.426577	0.213289	+	0.976989i	$0.431583\pi$
$68$	0.402812	0.0488481
$69$	−16.6233	−2.00122
$70$	7.66886	0.916604
$71$	9.78766	1.16158	0.580791	−	0.814053i	$-0.302743\pi$
$71$	9.78766	1.16158	0.580791	+	0.814053i	$0.302743\pi$
$72$	5.15183	0.607149
$73$	7.97619	0.933542	0.466771	−	0.884378i	$-0.345417\pi$
$73$	7.97619	0.933542	0.466771	+	0.884378i	$0.345417\pi$
$74$	−3.71384	−0.431725
$75$	1.90334	0.219779
$76$	−0.793498	−0.0910204
$77$	2.04645	0.233215
$78$	6.03050	0.682820
$79$	−11.5260	−1.29678	−0.648390	−	0.761308i	$-0.724558\pi$
$79$	−11.5260	−1.29678	−0.648390	+	0.761308i	$0.724558\pi$
$80$	11.2254	1.25504
$81$	−10.9126	−1.21251
$82$	17.3998	1.92148
$83$	−4.50980	−0.495015	−0.247507	−	0.968886i	$-0.579611\pi$
$83$	−4.50980	−0.495015	−0.247507	+	0.968886i	$0.579611\pi$
$84$	1.85811	0.202737
$85$	−2.41752	−0.262217
$86$	1.55010	0.167152
$87$	16.7396	1.79467
$88$	2.47580	0.263921
$89$	−1.37304	−0.145542	−0.0727712	−	0.997349i	$-0.523184\pi$
$89$	−1.37304	−0.145542	−0.0727712	+	0.997349i	$0.523184\pi$
$90$	7.79786	0.821967
$91$	−3.53204	−0.370258
$92$	−2.97065	−0.309711
$93$	22.8723	2.37174
$94$	−12.6379	−1.30350
$95$	4.76227	0.488598
$96$	5.06284	0.516724
$97$	−10.1474	−1.03031	−0.515154	−	0.857098i	$-0.672265\pi$
$97$	−10.1474	−1.03031	−0.515154	+	0.857098i	$0.672265\pi$
$98$	4.35895	0.440320
$99$	2.08087	0.209136
$100$	0.340134	0.0340134
$101$	−18.8401	−1.87466	−0.937330	−	0.348442i	$-0.886711\pi$
$101$	−18.8401	−1.87466	−0.937330	+	0.348442i	$0.886711\pi$
$102$	−3.49405	−0.345962
$103$	−9.48777	−0.934858	−0.467429	−	0.884031i	$-0.654820\pi$
$103$	−9.48777	−0.934858	−0.467429	+	0.884031i	$0.654820\pi$
$104$	−4.27308	−0.419010
$105$	−11.1517	−1.08829
$106$	6.88512	0.668742
$107$	−9.01057	−0.871084	−0.435542	−	0.900168i	$-0.643443\pi$
$107$	−9.01057	−0.871084	−0.435542	+	0.900168i	$0.643443\pi$
$108$	−0.834539	−0.0803035
$109$	−5.71656	−0.547547	−0.273774	−	0.961794i	$-0.588272\pi$
$109$	−5.71656	−0.547547	−0.273774	+	0.961794i	$0.588272\pi$
$110$	3.74740	0.357300
$111$	5.40048	0.512590
$112$	−9.50242	−0.897894
$113$	−18.8894	−1.77697	−0.888485	−	0.458906i	$-0.848242\pi$
$113$	−18.8894	−1.77697	−0.888485	+	0.458906i	$0.848242\pi$
$114$	6.88292	0.644645
$115$	17.8287	1.66253
$116$	2.99142	0.277746
$117$	−3.59145	−0.332030
$118$	−9.98940	−0.919599
$119$	2.04645	0.187598
$120$	−13.4913	−1.23159
$121$	1.00000	0.0909091
$122$	4.50905	0.408230
$123$	−25.3019	−2.28139
$124$	4.08735	0.367055
$125$	10.0462	0.898563
$126$	−6.60095	−0.588060
$127$	1.10197	0.0977839	0.0488919	−	0.998804i	$-0.484431\pi$
$127$	1.10197	0.0977839	0.0488919	+	0.998804i	$0.484431\pi$
$128$	−13.4906	−1.19241
$129$	−2.25408	−0.198461
$130$	−6.46777	−0.567261
$131$	−10.6143	−0.927372	−0.463686	−	0.886000i	$-0.653473\pi$
$131$	−10.6143	−0.927372	−0.463686	+	0.886000i	$0.653473\pi$
$132$	0.907969	0.0790286
$133$	−4.03130	−0.349558
$134$	−5.41246	−0.467565
$135$	5.00858	0.431070
$136$	2.47580	0.212298
$137$	6.52379	0.557365	0.278683	−	0.960383i	$-0.410102\pi$
$137$	6.52379	0.557365	0.278683	+	0.960383i	$0.410102\pi$
$138$	25.7679	2.19351
$139$	12.4397	1.05512	0.527562	−	0.849517i	$-0.323106\pi$
$139$	12.4397	1.05512	0.527562	+	0.849517i	$0.323106\pi$
$140$	−1.99284	−0.168426
$141$	18.3774	1.54766
$142$	−15.1719	−1.27319
$143$	−1.72594	−0.144330
$144$	−9.66226	−0.805188
$145$	−17.9533	−1.49094
$146$	−12.3639	−1.02324
$147$	−6.33857	−0.522796
$148$	0.965083	0.0793293
$149$	15.8848	1.30133	0.650665	−	0.759365i	$-0.274490\pi$
$149$	15.8848	1.30133	0.650665	+	0.759365i	$0.274490\pi$
$150$	−2.95037	−0.240897
$151$	3.36627	0.273943	0.136972	−	0.990575i	$-0.456263\pi$
$151$	3.36627	0.273943	0.136972	+	0.990575i	$0.456263\pi$
$152$	−4.87708	−0.395583
$153$	2.08087	0.168229
$154$	−3.17220	−0.255623
$155$	−24.5307	−1.97035
$156$	−1.56710	−0.125468
$157$	−3.65123	−0.291400	−0.145700	−	0.989329i	$-0.546543\pi$
$157$	−3.65123	−0.291400	−0.145700	+	0.989329i	$0.546543\pi$
$158$	17.8665	1.42138
$159$	−10.0120	−0.794003
$160$	−5.42994	−0.429274
$161$	−15.0921	−1.18943
$162$	16.9156	1.32902
$163$	10.7605	0.842828	0.421414	−	0.906868i	$-0.361534\pi$
$163$	10.7605	0.842828	0.421414	+	0.906868i	$0.361534\pi$
$164$	−4.52153	−0.353072
$165$	−5.44928	−0.424226
$166$	6.99064	0.542579
$167$	−1.42771	−0.110480	−0.0552398	−	0.998473i	$-0.517592\pi$
$167$	−1.42771	−0.110480	−0.0552398	+	0.998473i	$0.517592\pi$
$168$	11.4205	0.881113
$169$	−10.0211	−0.770857
$170$	3.74740	0.287412
$171$	−4.09911	−0.313467
$172$	−0.402812	−0.0307141
$173$	−10.6499	−0.809694	−0.404847	−	0.914384i	$-0.632675\pi$
$173$	−10.6499	−0.809694	−0.404847	+	0.914384i	$0.632675\pi$
$174$	−25.9480	−1.96711
$175$	1.72802	0.130626
$176$	−4.64337	−0.350007
$177$	14.5261	1.09185
$178$	2.12836	0.159527
$179$	−14.2762	−1.06706	−0.533528	−	0.845782i	$-0.679134\pi$
$179$	−14.2762	−1.06706	−0.533528	+	0.845782i	$0.679134\pi$
$180$	−2.02636	−0.151036
$181$	−6.00698	−0.446496	−0.223248	−	0.974762i	$-0.571666\pi$
$181$	−6.00698	−0.446496	−0.223248	+	0.974762i	$0.571666\pi$
$182$	5.47502	0.405835
$183$	−6.55683	−0.484695
$184$	−18.2585	−1.34603
$185$	−5.79206	−0.425840
$186$	−35.4543	−2.59964
$187$	1.00000	0.0731272
$188$	3.28411	0.239518
$189$	−4.23980	−0.308400
$190$	−7.38199	−0.535546
$191$	−7.74521	−0.560424	−0.280212	−	0.959938i	$-0.590405\pi$
$191$	−7.74521	−0.560424	−0.280212	+	0.959938i	$0.590405\pi$
$192$	13.0851	0.944337
$193$	22.4613	1.61680	0.808400	−	0.588634i	$-0.200334\pi$
$193$	22.4613	1.61680	0.808400	+	0.588634i	$0.200334\pi$
$194$	15.7294	1.12931
$195$	9.40511	0.673514
$196$	−1.13272	−0.0809088
$197$	−3.45199	−0.245944	−0.122972	−	0.992410i	$-0.539243\pi$
$197$	−3.45199	−0.245944	−0.122972	+	0.992410i	$0.539243\pi$
$198$	−3.22556	−0.229231
$199$	9.77171	0.692698	0.346349	−	0.938106i	$-0.387421\pi$
$199$	9.77171	0.692698	0.346349	+	0.938106i	$0.387421\pi$
$200$	2.09057	0.147825
$201$	7.87053	0.555145
$202$	29.2041	2.05479
$203$	15.1976	1.06666
$204$	0.907969	0.0635706
$205$	27.1365	1.89529
$206$	14.7070	1.02469
$207$	−15.3460	−1.06662
$208$	8.01415	0.555681
$209$	−1.96990	−0.136261
$210$	17.2862	1.19286
$211$	8.45264	0.581904	0.290952	−	0.956738i	$-0.406028\pi$
$211$	8.45264	0.581904	0.290952	+	0.956738i	$0.406028\pi$
$212$	−1.78918	−0.122881
$213$	22.0622	1.51167
$214$	13.9673	0.954784
$215$	2.41752	0.164873
$216$	−5.12933	−0.349007
$217$	20.7654	1.40965
$218$	8.86124	0.600159
$219$	17.9790	1.21491
$220$	−0.973805	−0.0656539
$221$	−1.72594	−0.116099
$222$	−8.37128	−0.561843
$223$	3.91986	0.262493	0.131247	−	0.991350i	$-0.458102\pi$
$223$	3.91986	0.262493	0.131247	+	0.991350i	$0.458102\pi$
$224$	4.59649	0.307116
$225$	1.75709	0.117139
$226$	29.2805	1.94771
$227$	−2.71198	−0.180001	−0.0900003	−	0.995942i	$-0.528687\pi$
$227$	−2.71198	−0.180001	−0.0900003	+	0.995942i	$0.528687\pi$
$228$	−1.78861	−0.118453
$229$	−2.25707	−0.149152	−0.0745758	−	0.997215i	$-0.523760\pi$
$229$	−2.25707	−0.149152	−0.0745758	+	0.997215i	$0.523760\pi$
$230$	−27.6362	−1.82228
$231$	4.61286	0.303504
$232$	18.3862	1.20711
$233$	−8.01855	−0.525313	−0.262656	−	0.964889i	$-0.584599\pi$
$233$	−8.01855	−0.525313	−0.262656	+	0.964889i	$0.584599\pi$
$234$	5.56711	0.363934
$235$	−19.7100	−1.28574
$236$	2.59586	0.168976
$237$	−25.9806	−1.68762
$238$	−3.17220	−0.205623
$239$	−3.33149	−0.215496	−0.107748	−	0.994178i	$-0.534364\pi$
$239$	−3.33149	−0.215496	−0.107748	+	0.994178i	$0.534364\pi$
$240$	25.3030	1.63330
$241$	15.4979	0.998311	0.499155	−	0.866513i	$-0.333644\pi$
$241$	15.4979	0.998311	0.499155	+	0.866513i	$0.333644\pi$
$242$	−1.55010	−0.0996442
$243$	−18.3825	−1.17924
$244$	−1.17173	−0.0750122
$245$	6.79817	0.434319
$246$	39.2205	2.50061
$247$	3.39992	0.216332
$248$	25.1221	1.59525
$249$	−10.1654	−0.644209
$250$	−15.5727	−0.984903
$251$	3.63692	0.229560	0.114780	−	0.993391i	$-0.463384\pi$
$251$	3.63692	0.229560	0.114780	+	0.993391i	$0.463384\pi$
$252$	1.71533	0.108056
$253$	−7.37478	−0.463649
$254$	−1.70816	−0.107180
$255$	−5.44928	−0.341247
$256$	9.30165	0.581353
$257$	13.9276	0.868777	0.434389	−	0.900726i	$-0.356964\pi$
$257$	13.9276	0.868777	0.434389	+	0.900726i	$0.356964\pi$
$258$	3.49405	0.217530
$259$	4.90302	0.304659
$260$	1.68072	0.104234
$261$	15.4533	0.956534
$262$	16.4532	1.01648
$263$	6.53093	0.402714	0.201357	−	0.979518i	$-0.435465\pi$
$263$	6.53093	0.402714	0.201357	+	0.979518i	$0.435465\pi$
$264$	5.58066	0.343466
$265$	10.7380	0.659627
$266$	6.24892	0.383146
$267$	−3.09495	−0.189408
$268$	1.40649	0.0859151
$269$	−20.8290	−1.26997	−0.634983	−	0.772526i	$-0.718993\pi$
$269$	−20.8290	−1.26997	−0.634983	+	0.772526i	$0.718993\pi$
$270$	−7.76380	−0.472490
$271$	−23.6069	−1.43402	−0.717009	−	0.697064i	$-0.754489\pi$
$271$	−23.6069	−1.43402	−0.717009	+	0.697064i	$0.754489\pi$
$272$	−4.64337	−0.281545
$273$	−7.96150	−0.481852
$274$	−10.1125	−0.610920
$275$	0.844399	0.0509192
$276$	−6.69608	−0.403056
$277$	−1.85144	−0.111242	−0.0556212	−	0.998452i	$-0.517714\pi$
$277$	−1.85144	−0.111242	−0.0556212	+	0.998452i	$0.517714\pi$
$278$	−19.2828	−1.15651
$279$	21.1147	1.26411
$280$	−12.2486	−0.731995
$281$	−0.348488	−0.0207891	−0.0103945	−	0.999946i	$-0.503309\pi$
$281$	−0.348488	−0.0207891	−0.0103945	+	0.999946i	$0.503309\pi$
$282$	−28.4869	−1.69637
$283$	−4.12602	−0.245266	−0.122633	−	0.992452i	$-0.539134\pi$
$283$	−4.12602	−0.245266	−0.122633	+	0.992452i	$0.539134\pi$
$284$	3.94258	0.233949
$285$	10.7345	0.635858
$286$	2.67537	0.158198
$287$	−22.9713	−1.35595
$288$	4.67380	0.275407
$289$	1.00000	0.0588235
$290$	27.8295	1.63420
$291$	−22.8729	−1.34084
$292$	3.21290	0.188021
$293$	14.4770	0.845758	0.422879	−	0.906186i	$-0.361020\pi$
$293$	14.4770	0.845758	0.422879	+	0.906186i	$0.361020\pi$
$294$	9.82542	0.573030
$295$	−15.5794	−0.907065
$296$	5.93169	0.344773
$297$	−2.07178	−0.120217
$298$	−24.6230	−1.42637
$299$	12.7284	0.736102
$300$	0.766688	0.0442648
$301$	−2.04645	−0.117955
$302$	−5.21805	−0.300265
$303$	−42.4671	−2.43967
$304$	9.14696	0.524614
$305$	7.03226	0.402666
$306$	−3.22556	−0.184393
$307$	−13.2879	−0.758379	−0.379190	−	0.925319i	$-0.623797\pi$
$307$	−13.2879	−0.758379	−0.379190	+	0.925319i	$0.623797\pi$
$308$	0.824334	0.0469708
$309$	−21.3862	−1.21662
$310$	38.0250	2.15968
$311$	−5.36978	−0.304492	−0.152246	−	0.988343i	$-0.548651\pi$
$311$	−5.36978	−0.304492	−0.152246	+	0.988343i	$0.548651\pi$
$312$	−9.63185	−0.545296
$313$	29.8276	1.68596	0.842979	−	0.537946i	$-0.180800\pi$
$313$	29.8276	1.68596	0.842979	+	0.537946i	$0.180800\pi$
$314$	5.65977	0.319400
$315$	−10.2948	−0.580045
$316$	−4.64282	−0.261179
$317$	23.1013	1.29750	0.648750	−	0.761001i	$-0.275292\pi$
$317$	23.1013	1.29750	0.648750	+	0.761001i	$0.275292\pi$
$318$	15.5196	0.870296
$319$	7.42634	0.415795
$320$	−14.0339	−0.784519
$321$	−20.3105	−1.13362
$322$	23.3943	1.30371
$323$	−1.96990	−0.109608
$324$	−4.39572	−0.244206
$325$	−1.45738	−0.0808408
$326$	−16.6799	−0.923813
$327$	−12.8856	−0.712574
$328$	−27.7907	−1.53449
$329$	16.6846	0.919854
$330$	8.44693	0.464988
$331$	21.9077	1.20416	0.602079	−	0.798437i	$-0.294339\pi$
$331$	21.9077	1.20416	0.602079	+	0.798437i	$0.294339\pi$
$332$	−1.81660	−0.0996988
$333$	4.98550	0.273204
$334$	2.21309	0.121095
$335$	−8.44121	−0.461193
$336$	−21.4192	−1.16851
$337$	−12.3043	−0.670257	−0.335129	−	0.942172i	$-0.608780\pi$
$337$	−12.3043	−0.670257	−0.335129	+	0.942172i	$0.608780\pi$
$338$	15.5338	0.844926
$339$	−42.5783	−2.31254
$340$	−0.973805	−0.0528120
$341$	10.1471	0.549494
$342$	6.35403	0.343587
$343$	−20.0799	−1.08421
$344$	−2.47580	−0.133486
$345$	40.1873	2.16361
$346$	16.5084	0.887495
$347$	−8.91292	−0.478470	−0.239235	−	0.970962i	$-0.576897\pi$
$347$	−8.91292	−0.478470	−0.239235	+	0.970962i	$0.576897\pi$
$348$	6.74289	0.361457
$349$	2.55455	0.136742	0.0683708	−	0.997660i	$-0.478220\pi$
$349$	2.55455	0.136742	0.0683708	+	0.997660i	$0.478220\pi$
$350$	−2.67860	−0.143177
$351$	3.57577	0.190860
$352$	2.24608	0.119716
$353$	2.67380	0.142312	0.0711560	−	0.997465i	$-0.477331\pi$
$353$	2.67380	0.142312	0.0711560	+	0.997465i	$0.477331\pi$
$354$	−22.5169	−1.19676
$355$	−23.6619	−1.25584
$356$	−0.553078	−0.0293131
$357$	4.61286	0.244138
$358$	22.1296	1.16959
$359$	22.8166	1.20421	0.602107	−	0.798416i	$-0.294328\pi$
$359$	22.8166	1.20421	0.602107	+	0.798416i	$0.294328\pi$
$360$	−12.4547	−0.656418
$361$	−15.1195	−0.795763
$362$	9.31143	0.489398
$363$	2.25408	0.118308
$364$	−1.42275	−0.0745722
$365$	−19.2826	−1.00930
$366$	10.1638	0.531268
$367$	−5.73027	−0.299118	−0.149559	−	0.988753i	$-0.547785\pi$
$367$	−5.73027	−0.299118	−0.149559	+	0.988753i	$0.547785\pi$
$368$	34.2438	1.78508
$369$	−23.3577	−1.21595
$370$	8.97827	0.466758
$371$	−9.08976	−0.471917
$372$	9.21321	0.477683
$373$	4.55867	0.236039	0.118020	−	0.993011i	$-0.462345\pi$
$373$	4.55867	0.236039	0.118020	+	0.993011i	$0.462345\pi$
$374$	−1.55010	−0.0801538
$375$	22.6450	1.16938
$376$	20.1851	1.04097
$377$	−12.8174	−0.660129
$378$	6.57212	0.338033
$379$	−27.2073	−1.39754	−0.698771	−	0.715345i	$-0.746270\pi$
$379$	−27.2073	−1.39754	−0.698771	+	0.715345i	$0.746270\pi$
$380$	1.91830	0.0984065
$381$	2.48392	0.127255
$382$	12.0059	0.614273
$383$	−30.2527	−1.54584	−0.772921	−	0.634502i	$-0.781205\pi$
$383$	−30.2527	−1.54584	−0.772921	+	0.634502i	$0.781205\pi$
$384$	−30.4089	−1.55180
$385$	−4.94733	−0.252139
$386$	−34.8173	−1.77215
$387$	−2.08087	−0.105777
$388$	−4.08747	−0.207510
$389$	−29.1348	−1.47719	−0.738595	−	0.674149i	$-0.764511\pi$
$389$	−29.1348	−1.47719	−0.738595	+	0.674149i	$0.764511\pi$
$390$	−14.5789	−0.738229
$391$	−7.37478	−0.372959
$392$	−6.96206	−0.351637
$393$	−23.9254	−1.20688
$394$	5.35093	0.269576
$395$	27.8644	1.40201
$396$	0.838200	0.0421211
$397$	−37.1053	−1.86226	−0.931131	−	0.364685i	$-0.881177\pi$
$397$	−37.1053	−1.86226	−0.931131	+	0.364685i	$0.881177\pi$
$398$	−15.1471	−0.759257
$399$	−9.08686	−0.454912
$400$	−3.92085	−0.196043
$401$	−32.2957	−1.61277	−0.806386	−	0.591390i	$-0.798579\pi$
$401$	−32.2957	−1.61277	−0.806386	+	0.591390i	$0.798579\pi$
$402$	−12.2001	−0.608487
$403$	−17.5132	−0.872392
$404$	−7.58901	−0.377567
$405$	26.3814	1.31090
$406$	−23.5579	−1.16916
$407$	2.39587	0.118759
$408$	5.58066	0.276284
$409$	−38.8019	−1.91863	−0.959316	−	0.282333i	$-0.908892\pi$
$409$	−38.8019	−1.91863	−0.959316	+	0.282333i	$0.908892\pi$
$410$	−42.0643	−2.07741
$411$	14.7051	0.725351
$412$	−3.82178	−0.188286
$413$	13.1881	0.648942
$414$	23.7878	1.16911
$415$	10.9025	0.535184
$416$	−3.87659	−0.190065
$417$	28.0401	1.37313
$418$	3.05354	0.149354
$419$	−10.8199	−0.528588	−0.264294	−	0.964442i	$-0.585139\pi$
$419$	−10.8199	−0.528588	−0.264294	+	0.964442i	$0.585139\pi$
$420$	−4.49202	−0.219188
$421$	−20.3194	−0.990309	−0.495155	−	0.868805i	$-0.664889\pi$
$421$	−20.3194	−0.990309	−0.495155	+	0.868805i	$0.664889\pi$
$422$	−13.1024	−0.637817
$423$	16.9653	0.824881
$424$	−10.9968	−0.534053
$425$	0.844399	0.0409594
$426$	−34.1986	−1.65693
$427$	−5.95287	−0.288079
$428$	−3.62956	−0.175441
$429$	−3.89040	−0.187830
$430$	−3.74740	−0.180716
$431$	−27.6268	−1.33074	−0.665369	−	0.746514i	$-0.731726\pi$
$431$	−27.6268	−1.33074	−0.665369	+	0.746514i	$0.731726\pi$
$432$	9.62006	0.462845
$433$	−25.8952	−1.24444	−0.622222	−	0.782841i	$-0.713770\pi$
$433$	−25.8952	−1.24444	−0.622222	+	0.782841i	$0.713770\pi$
$434$	−32.1885	−1.54510
$435$	−40.4682	−1.94030
$436$	−2.30270	−0.110279
$437$	14.5276	0.694948
$438$	−27.8692	−1.33164
$439$	35.7644	1.70694	0.853472	−	0.521139i	$-0.174493\pi$
$439$	35.7644	1.70694	0.853472	+	0.521139i	$0.174493\pi$
$440$	−5.98530	−0.285338
$441$	−5.85151	−0.278643
$442$	2.67537	0.127255
$443$	7.49459	0.356079	0.178039	−	0.984023i	$-0.443025\pi$
$443$	7.49459	0.356079	0.178039	+	0.984023i	$0.443025\pi$
$444$	2.17537	0.103239
$445$	3.31936	0.157353
$446$	−6.07618	−0.287715
$447$	35.8055	1.69354
$448$	11.8798	0.561268
$449$	−23.7795	−1.12222	−0.561112	−	0.827740i	$-0.689626\pi$
$449$	−23.7795	−1.12222	−0.561112	+	0.827740i	$0.689626\pi$
$450$	−2.72366	−0.128395
$451$	−11.2249	−0.528562
$452$	−7.60889	−0.357892
$453$	7.58784	0.356508
$454$	4.20384	0.197296
$455$	8.53878	0.400304
$456$	−10.9933	−0.514809
$457$	18.6701	0.873349	0.436674	−	0.899620i	$-0.356156\pi$
$457$	18.6701	0.873349	0.436674	+	0.899620i	$0.356156\pi$
$458$	3.49869	0.163483
$459$	−2.07178	−0.0967026
$460$	7.18160	0.334844
$461$	−31.2003	−1.45314	−0.726572	−	0.687090i	$-0.758888\pi$
$461$	−31.2003	−1.45314	−0.726572	+	0.687090i	$0.758888\pi$
$462$	−7.15040	−0.332667
$463$	−13.7218	−0.637708	−0.318854	−	0.947804i	$-0.603298\pi$
$463$	−13.7218	−0.637708	−0.318854	+	0.947804i	$0.603298\pi$
$464$	−34.4832	−1.60084
$465$	−55.2941	−2.56420
$466$	12.4296	0.575788
$467$	16.7882	0.776863	0.388432	−	0.921478i	$-0.373017\pi$
$467$	16.7882	0.776863	0.388432	+	0.921478i	$0.373017\pi$
$468$	−1.44668	−0.0668727
$469$	7.14556	0.329951
$470$	30.5524	1.40928
$471$	−8.23016	−0.379226
$472$	15.9550	0.734386
$473$	−1.00000	−0.0459800
$474$	40.2726	1.84978
$475$	−1.66338	−0.0763211
$476$	0.824334	0.0377833
$477$	−9.24266	−0.423192
$478$	5.16415	0.236203
$479$	9.97496	0.455768	0.227884	−	0.973688i	$-0.426819\pi$
$479$	9.97496	0.455768	0.227884	+	0.973688i	$0.426819\pi$
$480$	−12.2395	−0.558655
$481$	−4.13511	−0.188545
$482$	−24.0234	−1.09423
$483$	−34.0188	−1.54791
$484$	0.402812	0.0183096
$485$	24.5314	1.11391
$486$	28.4947	1.29255
$487$	−34.1782	−1.54876	−0.774381	−	0.632719i	$-0.781939\pi$
$487$	−34.1782	−1.54876	−0.774381	+	0.632719i	$0.781939\pi$
$488$	−7.20180	−0.326010
$489$	24.2550	1.09685
$490$	−10.5378	−0.476051
$491$	−32.9965	−1.48911	−0.744555	−	0.667561i	$-0.767338\pi$
$491$	−32.9965	−1.48911	−0.744555	+	0.667561i	$0.767338\pi$
$492$	−10.1919	−0.459486
$493$	7.42634	0.334466
$494$	−5.27021	−0.237118
$495$	−5.03055	−0.226106
$496$	−47.1165	−2.11559
$497$	20.0300	0.898467
$498$	15.7575	0.706109
$499$	−6.47198	−0.289726	−0.144863	−	0.989452i	$-0.546274\pi$
$499$	−6.47198	−0.289726	−0.144863	+	0.989452i	$0.546274\pi$
$500$	4.04674	0.180976
$501$	−3.21817	−0.143777
$502$	−5.63759	−0.251618
$503$	−17.0452	−0.760008	−0.380004	−	0.924985i	$-0.624077\pi$
$503$	−17.0452	−0.760008	−0.380004	+	0.924985i	$0.624077\pi$
$504$	10.5430	0.469621
$505$	45.5463	2.02678
$506$	11.4317	0.508199
$507$	−22.5885	−1.00319
$508$	0.443886	0.0196942
$509$	−33.1888	−1.47107	−0.735535	−	0.677487i	$-0.763069\pi$
$509$	−33.1888	−1.47107	−0.735535	+	0.677487i	$0.763069\pi$
$510$	8.44693	0.374036
$511$	16.3229	0.722081
$512$	12.5627	0.555200
$513$	4.08120	0.180190
$514$	−21.5891	−0.952255
$515$	22.9369	1.01072
$516$	−0.907969	−0.0399711
$517$	8.15297	0.358567
$518$	−7.60018	−0.333933
$519$	−24.0056	−1.05373
$520$	10.3302	0.453011
$521$	−22.2504	−0.974810	−0.487405	−	0.873176i	$-0.662056\pi$
$521$	−22.2504	−0.974810	−0.487405	+	0.873176i	$0.662056\pi$
$522$	−23.9541	−1.04844
$523$	4.56650	0.199679	0.0998395	−	0.995004i	$-0.468167\pi$
$523$	4.56650	0.199679	0.0998395	+	0.995004i	$0.468167\pi$
$524$	−4.27554	−0.186778
$525$	3.89509	0.169996
$526$	−10.1236	−0.441410
$527$	10.1471	0.442012
$528$	−10.4665	−0.455497
$529$	31.3874	1.36467
$530$	−16.6449	−0.723008
$531$	13.4099	0.581940
$532$	−1.62385	−0.0704030
$533$	19.3735	0.839160
$534$	4.79748	0.207607
$535$	21.7832	0.941771
$536$	8.64472	0.373395
$537$	−32.1798	−1.38866
$538$	32.2870	1.39199
$539$	−2.81204	−0.121123
$540$	2.01751	0.0868200
$541$	−12.4375	−0.534732	−0.267366	−	0.963595i	$-0.586153\pi$
$541$	−12.4375	−0.534732	−0.267366	+	0.963595i	$0.586153\pi$
$542$	36.5931	1.57181
$543$	−13.5402	−0.581066
$544$	2.24608	0.0962998
$545$	13.8199	0.591979
$546$	12.3411	0.528151
$547$	−17.0527	−0.729119	−0.364559	−	0.931180i	$-0.618780\pi$
$547$	−17.0527	−0.729119	−0.364559	+	0.931180i	$0.618780\pi$
$548$	2.62786	0.112257
$549$	−6.05300	−0.258336
$550$	−1.30890	−0.0558118
$551$	−14.6291	−0.623222
$552$	−41.1561	−1.75172
$553$	−23.5875	−1.00304
$554$	2.86992	0.121931
$555$	−13.0558	−0.554186
$556$	5.01087	0.212508
$557$	−39.5713	−1.67669	−0.838346	−	0.545139i	$-0.816477\pi$
$557$	−39.5713	−1.67669	−0.838346	+	0.545139i	$0.816477\pi$
$558$	−32.7299	−1.38557
$559$	1.72594	0.0729993
$560$	22.9723	0.970756
$561$	2.25408	0.0951673
$562$	0.540192	0.0227866
$563$	15.3506	0.646951	0.323475	−	0.946237i	$-0.395149\pi$
$563$	15.3506	0.646951	0.323475	+	0.946237i	$0.395149\pi$
$564$	7.40265	0.311708
$565$	45.6656	1.92117
$566$	6.39574	0.268833
$567$	−22.3321	−0.937858
$568$	24.2323	1.01677
$569$	−20.0992	−0.842602	−0.421301	−	0.906921i	$-0.638426\pi$
$569$	−20.0992	−0.842602	−0.421301	+	0.906921i	$0.638426\pi$
$570$	−16.6396	−0.696956
$571$	40.9003	1.71162	0.855812	−	0.517287i	$-0.173058\pi$
$571$	40.9003	1.71162	0.855812	+	0.517287i	$0.173058\pi$
$572$	−0.695227	−0.0290689
$573$	−17.4583	−0.729332
$574$	35.6078	1.48624
$575$	−6.22726	−0.259695
$576$	12.0796	0.503318
$577$	38.0187	1.58274	0.791369	−	0.611339i	$-0.209369\pi$
$577$	38.0187	1.58274	0.791369	+	0.611339i	$0.209369\pi$
$578$	−1.55010	−0.0644757
$579$	50.6296	2.10409
$580$	−7.23181	−0.300284
$581$	−9.22908	−0.382887
$582$	35.4554	1.46967
$583$	−4.44172	−0.183957
$584$	19.7475	0.817156
$585$	8.68241	0.358973
$586$	−22.4409	−0.927024
$587$	−13.4772	−0.556263	−0.278132	−	0.960543i	$-0.589715\pi$
$587$	−13.4772	−0.556263	−0.278132	+	0.960543i	$0.589715\pi$
$588$	−2.55325	−0.105294
$589$	−19.9887	−0.823618
$590$	24.1496	0.994222
$591$	−7.78106	−0.320070
$592$	−11.1249	−0.457230
$593$	29.0120	1.19138	0.595691	−	0.803214i	$-0.296878\pi$
$593$	29.0120	1.19138	0.595691	+	0.803214i	$0.296878\pi$
$594$	3.21147	0.131768
$595$	−4.94733	−0.202821
$596$	6.39857	0.262096
$597$	22.0262	0.901473
$598$	−19.7303	−0.806832
$599$	−47.1571	−1.92679	−0.963394	−	0.268089i	$-0.913608\pi$
$599$	−47.1571	−1.92679	−0.963394	+	0.268089i	$0.913608\pi$
$600$	4.71230	0.192379
$601$	1.09703	0.0447488	0.0223744	−	0.999750i	$-0.492877\pi$
$601$	1.09703	0.0447488	0.0223744	+	0.999750i	$0.492877\pi$
$602$	3.17220	0.129289
$603$	7.26575	0.295884
$604$	1.35597	0.0551737
$605$	−2.41752	−0.0982861
$606$	65.8283	2.67409
$607$	24.1375	0.979710	0.489855	−	0.871804i	$-0.337050\pi$
$607$	24.1375	0.979710	0.489855	+	0.871804i	$0.337050\pi$
$608$	−4.42455	−0.179439
$609$	34.2567	1.38815
$610$	−10.9007	−0.441357
$611$	−14.0715	−0.569272
$612$	0.838200	0.0338822
$613$	30.0553	1.21392	0.606961	−	0.794732i	$-0.292389\pi$
$613$	30.0553	1.21392	0.606961	+	0.794732i	$0.292389\pi$
$614$	20.5976	0.831250
$615$	61.1678	2.46652
$616$	5.06661	0.204139
$617$	−45.7451	−1.84163	−0.920815	−	0.390001i	$-0.872475\pi$
$617$	−45.7451	−1.84163	−0.920815	+	0.390001i	$0.872475\pi$
$618$	33.1507	1.33352
$619$	29.7281	1.19487	0.597436	−	0.801917i	$-0.296186\pi$
$619$	29.7281	1.19487	0.597436	+	0.801917i	$0.296186\pi$
$620$	−9.88125	−0.396840
$621$	15.2790	0.613124
$622$	8.32370	0.333750
$623$	−2.80987	−0.112575
$624$	18.0645	0.723160
$625$	−28.5090	−1.14036
$626$	−46.2358	−1.84796
$627$	−4.44031	−0.177329
$628$	−1.47076	−0.0586896
$629$	2.39587	0.0955295
$630$	15.9579	0.635779
$631$	15.9141	0.633531	0.316766	−	0.948504i	$-0.397403\pi$
$631$	15.9141	0.633531	0.316766	+	0.948504i	$0.397403\pi$
$632$	−28.5362	−1.13511
$633$	19.0529	0.757286
$634$	−35.8094	−1.42217
$635$	−2.66403	−0.105719
$636$	−4.03295	−0.159917
$637$	4.85341	0.192299
$638$	−11.5116	−0.455748
$639$	20.3669	0.805702
$640$	32.6138	1.28918
$641$	15.4859	0.611655	0.305827	−	0.952087i	$-0.401067\pi$
$641$	15.4859	0.611655	0.305827	+	0.952087i	$0.401067\pi$
$642$	31.4834	1.24255
$643$	−15.3431	−0.605071	−0.302536	−	0.953138i	$-0.597833\pi$
$643$	−15.3431	−0.605071	−0.302536	+	0.953138i	$0.597833\pi$
$644$	−6.07928	−0.239557
$645$	5.44928	0.214565
$646$	3.05354	0.120140
$647$	−1.23339	−0.0484894	−0.0242447	−	0.999706i	$-0.507718\pi$
$647$	−1.23339	−0.0484894	−0.0242447	+	0.999706i	$0.507718\pi$
$648$	−27.0174	−1.06134
$649$	6.44436	0.252963
$650$	2.25908	0.0886085
$651$	46.8069	1.83451
$652$	4.33446	0.169750
$653$	11.7027	0.457963	0.228981	−	0.973431i	$-0.426461\pi$
$653$	11.7027	0.457963	0.228981	+	0.973431i	$0.426461\pi$
$654$	19.9739	0.781043
$655$	25.6602	1.00263
$656$	52.1215	2.03500
$657$	16.5974	0.647528
$658$	−25.8629	−1.00824
$659$	35.2967	1.37496	0.687482	−	0.726201i	$-0.258716\pi$
$659$	35.2967	1.37496	0.687482	+	0.726201i	$0.258716\pi$
$660$	−2.19503	−0.0854415
$661$	25.4615	0.990339	0.495170	−	0.868796i	$-0.335106\pi$
$661$	25.4615	0.990339	0.495170	+	0.868796i	$0.335106\pi$
$662$	−33.9592	−1.31986
$663$	−3.89040	−0.151090
$664$	−11.1654	−0.433300
$665$	9.74574	0.377923
$666$	−7.72802	−0.299455
$667$	−54.7677	−2.12061
$668$	−0.575098	−0.0222512
$669$	8.83567	0.341607
$670$	13.0847	0.505507
$671$	−2.90887	−0.112296
$672$	10.3608	0.399678
$673$	−23.4215	−0.902832	−0.451416	−	0.892314i	$-0.649081\pi$
$673$	−23.4215	−0.902832	−0.451416	+	0.892314i	$0.649081\pi$
$674$	19.0729	0.734660
$675$	−1.74941	−0.0673349
$676$	−4.03663	−0.155255
$677$	−22.8492	−0.878165	−0.439083	−	0.898447i	$-0.644696\pi$
$677$	−22.8492	−0.878165	−0.439083	+	0.898447i	$0.644696\pi$
$678$	66.0007	2.53474
$679$	−20.7661	−0.796928
$680$	−5.98530	−0.229526
$681$	−6.11302	−0.234251
$682$	−15.7289	−0.602293
$683$	−4.05658	−0.155221	−0.0776104	−	0.996984i	$-0.524729\pi$
$683$	−4.05658	−0.155221	−0.0776104	+	0.996984i	$0.524729\pi$
$684$	−1.65117	−0.0631340
$685$	−15.7714	−0.602594
$686$	31.1258	1.18839
$687$	−5.08762	−0.194105
$688$	4.64337	0.177027
$689$	7.66613	0.292056
$690$	−62.2943	−2.37150
$691$	−3.15132	−0.119882	−0.0599410	−	0.998202i	$-0.519091\pi$
$691$	−3.15132	−0.119882	−0.0599410	+	0.998202i	$0.519091\pi$
$692$	−4.28989	−0.163077
$693$	4.25840	0.161763
$694$	13.8159	0.524445
$695$	−30.0733	−1.14074
$696$	41.4439	1.57093
$697$	−11.2249	−0.425175
$698$	−3.95980	−0.149881
$699$	−18.0745	−0.683639
$700$	0.696066	0.0263088
$701$	−1.26901	−0.0479300	−0.0239650	−	0.999713i	$-0.507629\pi$
$701$	−1.26901	−0.0479300	−0.0239650	+	0.999713i	$0.507629\pi$
$702$	−5.54280	−0.209199
$703$	−4.71961	−0.178004
$704$	5.80508	0.218787
$705$	−44.4278	−1.67325
$706$	−4.14466	−0.155986
$707$	−38.5553	−1.45002
$708$	5.85128	0.219904
$709$	22.4414	0.842803	0.421402	−	0.906874i	$-0.361538\pi$
$709$	22.4414	0.842803	0.421402	+	0.906874i	$0.361538\pi$
$710$	36.6783	1.37651
$711$	−23.9842	−0.899479
$712$	−3.39939	−0.127397
$713$	−74.8323	−2.80249
$714$	−7.15040	−0.267597
$715$	4.17248	0.156042
$716$	−5.75063	−0.214911
$717$	−7.50945	−0.280445
$718$	−35.3680	−1.31992
$719$	24.4291	0.911050	0.455525	−	0.890223i	$-0.349452\pi$
$719$	24.4291	0.911050	0.455525	+	0.890223i	$0.349452\pi$
$720$	23.3587	0.870527
$721$	−19.4162	−0.723099
$722$	23.4367	0.872225
$723$	34.9336	1.29919
$724$	−2.41968	−0.0899268
$725$	6.27080	0.232891
$726$	−3.49405	−0.129676
$727$	34.8601	1.29289	0.646445	−	0.762961i	$-0.276255\pi$
$727$	34.8601	1.29289	0.646445	+	0.762961i	$0.276255\pi$
$728$	−8.74463	−0.324098
$729$	−8.69781	−0.322141
$730$	29.8899	1.10628
$731$	−1.00000	−0.0369863
$732$	−2.64117	−0.0976204
$733$	−26.1482	−0.965805	−0.482902	−	0.875674i	$-0.660417\pi$
$733$	−26.1482	−0.965805	−0.482902	+	0.875674i	$0.660417\pi$
$734$	8.88250	0.327859
$735$	15.3236	0.565220
$736$	−16.5643	−0.610570
$737$	3.49168	0.128618
$738$	36.2067	1.33279
$739$	1.36509	0.0502158	0.0251079	−	0.999685i	$-0.492007\pi$
$739$	1.36509	0.0502158	0.0251079	+	0.999685i	$0.492007\pi$
$740$	−2.33311	−0.0857667
$741$	7.66368	0.281532
$742$	14.0900	0.517262
$743$	18.6713	0.684985	0.342492	−	0.939521i	$-0.388729\pi$
$743$	18.6713	0.684985	0.342492	+	0.939521i	$0.388729\pi$
$744$	56.6272	2.07605
$745$	−38.4017	−1.40693
$746$	−7.06640	−0.258719
$747$	−9.38432	−0.343354
$748$	0.402812	0.0147282
$749$	−18.4397	−0.673771
$750$	−35.1021	−1.28175
$751$	−21.5663	−0.786966	−0.393483	−	0.919332i	$-0.628730\pi$
$751$	−21.5663	−0.786966	−0.393483	+	0.919332i	$0.628730\pi$
$752$	−37.8572	−1.38051
$753$	8.19790	0.298748
$754$	19.8682	0.723559
$755$	−8.13802	−0.296173
$756$	−1.70784	−0.0621136
$757$	3.98216	0.144734	0.0723671	−	0.997378i	$-0.476945\pi$
$757$	3.98216	0.144734	0.0723671	+	0.997378i	$0.476945\pi$
$758$	42.1740	1.53183
$759$	−16.6233	−0.603389
$760$	11.7904	0.427684
$761$	24.1831	0.876635	0.438317	−	0.898820i	$-0.355575\pi$
$761$	24.1831	0.876635	0.438317	+	0.898820i	$0.355575\pi$
$762$	−3.85033	−0.139483
$763$	−11.6987	−0.423520
$764$	−3.11986	−0.112873
$765$	−5.03055	−0.181880
$766$	46.8948	1.69438
$767$	−11.1225	−0.401612
$768$	20.9667	0.756569
$769$	10.9561	0.395086	0.197543	−	0.980294i	$-0.436704\pi$
$769$	10.9561	0.395086	0.197543	+	0.980294i	$0.436704\pi$
$770$	7.66886	0.276367
$771$	31.3938	1.13062
$772$	9.04767	0.325633
$773$	−6.36004	−0.228755	−0.114377	−	0.993437i	$-0.536487\pi$
$773$	−6.36004	−0.228755	−0.114377	+	0.993437i	$0.536487\pi$
$774$	3.22556	0.115940
$775$	8.56816	0.307777
$776$	−25.1229	−0.901858
$777$	11.0518	0.396481
$778$	45.1618	1.61913
$779$	22.1120	0.792244
$780$	3.78849	0.135650
$781$	9.78766	0.350230
$782$	11.4317	0.408795
$783$	−15.3858	−0.549843
$784$	13.0573	0.466334
$785$	8.82692	0.315046
$786$	37.0867	1.32284
$787$	46.4819	1.65690	0.828451	−	0.560061i	$-0.189222\pi$
$787$	46.4819	1.65690	0.828451	+	0.560061i	$0.189222\pi$
$788$	−1.39050	−0.0495346
$789$	14.7212	0.524089
$790$	−43.1927	−1.53673
$791$	−38.6563	−1.37446
$792$	5.15183	0.183062
$793$	5.02053	0.178284
$794$	57.5170	2.04120
$795$	24.2042	0.858434
$796$	3.93616	0.139513
$797$	−43.4838	−1.54028	−0.770138	−	0.637877i	$-0.779813\pi$
$797$	−43.4838	−1.54028	−0.770138	+	0.637877i	$0.779813\pi$
$798$	14.0856	0.498623
$799$	8.15297	0.288431
$800$	1.89659	0.0670545
$801$	−2.85713	−0.100952
$802$	50.0616	1.76774
$803$	7.97619	0.281474
$804$	3.17034	0.111809
$805$	36.4855	1.28594
$806$	27.1471	0.956218
$807$	−46.9502	−1.65273
$808$	−46.6444	−1.64094
$809$	−9.56394	−0.336250	−0.168125	−	0.985766i	$-0.553771\pi$
$809$	−9.56394	−0.336250	−0.168125	+	0.985766i	$0.553771\pi$
$810$	−40.8938	−1.43686
$811$	−27.5169	−0.966251	−0.483125	−	0.875551i	$-0.660498\pi$
$811$	−27.5169	−0.966251	−0.483125	+	0.875551i	$0.660498\pi$
$812$	6.12178	0.214832
$813$	−53.2118	−1.86622
$814$	−3.71384	−0.130170
$815$	−26.0137	−0.911221
$816$	−10.4665	−0.366401
$817$	1.96990	0.0689180
$818$	60.1469	2.10299
$819$	−7.34973	−0.256820
$820$	10.9309	0.381723
$821$	0.696516	0.0243086	0.0121543	−	0.999926i	$-0.496131\pi$
$821$	0.696516	0.0243086	0.0121543	+	0.999926i	$0.496131\pi$
$822$	−22.7944	−0.795048
$823$	22.5414	0.785745	0.392872	−	0.919593i	$-0.371481\pi$
$823$	22.5414	0.785745	0.392872	+	0.919593i	$0.371481\pi$
$824$	−23.4899	−0.818308
$825$	1.90334	0.0662659
$826$	−20.4428	−0.711296
$827$	10.7832	0.374967	0.187483	−	0.982268i	$-0.439967\pi$
$827$	10.7832	0.374967	0.187483	+	0.982268i	$0.439967\pi$
$828$	−6.18154	−0.214823
$829$	10.6944	0.371434	0.185717	−	0.982603i	$-0.440539\pi$
$829$	10.6944	0.371434	0.185717	+	0.982603i	$0.440539\pi$
$830$	−16.9000	−0.586608
$831$	−4.17330	−0.144770
$832$	−10.0192	−0.347353
$833$	−2.81204	−0.0974315
$834$	−43.4650	−1.50507
$835$	3.45152	0.119445
$836$	−0.793498	−0.0274437
$837$	−21.0225	−0.726644
$838$	16.7720	0.579379
$839$	7.32734	0.252968	0.126484	−	0.991969i	$-0.459631\pi$
$839$	7.32734	0.252968	0.126484	+	0.991969i	$0.459631\pi$
$840$	−27.6094	−0.952613
$841$	26.1506	0.901743
$842$	31.4972	1.08546
$843$	−0.785520	−0.0270547
$844$	3.40482	0.117199
$845$	24.2263	0.833411
$846$	−26.2979	−0.904141
$847$	2.04645	0.0703168
$848$	20.6245	0.708250
$849$	−9.30036	−0.319188
$850$	−1.30890	−0.0448950
$851$	−17.6690	−0.605686
$852$	8.88690	0.304460
$853$	−28.7462	−0.984250	−0.492125	−	0.870525i	$-0.663780\pi$
$853$	−28.7462	−0.984250	−0.492125	+	0.870525i	$0.663780\pi$
$854$	9.22754	0.315760
$855$	9.90967	0.338904
$856$	−22.3084	−0.762485
$857$	−49.2823	−1.68345	−0.841725	−	0.539906i	$-0.818460\pi$
$857$	−49.2823	−1.68345	−0.841725	+	0.539906i	$0.818460\pi$
$858$	6.03050	0.205878
$859$	22.8387	0.779245	0.389623	−	0.920975i	$-0.372605\pi$
$859$	22.8387	0.779245	0.389623	+	0.920975i	$0.372605\pi$
$860$	0.973805	0.0332065
$861$	−51.7790	−1.76463
$862$	42.8244	1.45860
$863$	−42.9725	−1.46280	−0.731400	−	0.681948i	$-0.761133\pi$
$863$	−42.9725	−1.46280	−0.731400	+	0.681948i	$0.761133\pi$
$864$	−4.65339	−0.158312
$865$	25.7463	0.875399
$866$	40.1402	1.36402
$867$	2.25408	0.0765525
$868$	8.36455	0.283911
$869$	−11.5260	−0.390994
$870$	62.7298	2.12674
$871$	−6.02642	−0.204198
$872$	−14.1531	−0.479284
$873$	−21.1154	−0.714647
$874$	−22.5192	−0.761723
$875$	20.5591	0.695026
$876$	7.24213	0.244689
$877$	−50.7918	−1.71512	−0.857558	−	0.514387i	$-0.828019\pi$
$877$	−50.7918	−1.71512	−0.857558	+	0.514387i	$0.828019\pi$
$878$	−55.4385	−1.87096
$879$	32.6324	1.10066
$880$	11.2254	0.378409
$881$	−46.2107	−1.55688	−0.778439	−	0.627720i	$-0.783988\pi$
$881$	−46.2107	−1.55688	−0.778439	+	0.627720i	$0.783988\pi$
$882$	9.07042	0.305417
$883$	38.2589	1.28752	0.643758	−	0.765230i	$-0.277375\pi$
$883$	38.2589	1.28752	0.643758	+	0.765230i	$0.277375\pi$
$884$	−0.695227	−0.0233830
$885$	−35.1171	−1.18045
$886$	−11.6174	−0.390293
$887$	−32.8427	−1.10275	−0.551374	−	0.834258i	$-0.685896\pi$
$887$	−32.8427	−1.10275	−0.551374	+	0.834258i	$0.685896\pi$
$888$	13.3705	0.448685
$889$	2.25512	0.0756344
$890$	−5.14534	−0.172472
$891$	−10.9126	−0.365585
$892$	1.57896	0.0528676
$893$	−16.0605	−0.537445
$894$	−55.5021	−1.85627
$895$	34.5131	1.15365
$896$	−27.6079	−0.922315
$897$	28.6908	0.957959
$898$	36.8606	1.23005
$899$	75.3555	2.51325
$900$	0.707775	0.0235925
$901$	−4.44172	−0.147975
$902$	17.3998	0.579349
$903$	−4.61286	−0.153506
$904$	−46.7665	−1.55543
$905$	14.5220	0.482728
$906$	−11.7619	−0.390763
$907$	−0.610354	−0.0202665	−0.0101332	−	0.999949i	$-0.503226\pi$
$907$	−0.610354	−0.0202665	−0.0101332	+	0.999949i	$0.503226\pi$
$908$	−1.09242	−0.0362532
$909$	−39.2039	−1.30031
$910$	−13.2360	−0.438768
$911$	29.0072	0.961050	0.480525	−	0.876981i	$-0.340446\pi$
$911$	29.0072	0.961050	0.480525	+	0.876981i	$0.340446\pi$
$912$	20.6180	0.682729
$913$	−4.50980	−0.149253
$914$	−28.9405	−0.957266
$915$	15.8513	0.524027
$916$	−0.909175	−0.0300400
$917$	−21.7215	−0.717308
$918$	3.21147	0.105994
$919$	45.5420	1.50229	0.751146	−	0.660136i	$-0.229501\pi$
$919$	45.5420	1.50229	0.751146	+	0.660136i	$0.229501\pi$
$920$	44.1403	1.45526
$921$	−29.9519	−0.986950
$922$	48.3636	1.59277
$923$	−16.8929	−0.556036
$924$	1.85811	0.0611274
$925$	2.02307	0.0665181
$926$	21.2702	0.698983
$927$	−19.7428	−0.648440
$928$	16.6801	0.547553
$929$	55.2542	1.81283	0.906415	−	0.422388i	$-0.138808\pi$
$929$	55.2542	1.81283	0.906415	+	0.422388i	$0.138808\pi$
$930$	85.7114	2.81059
$931$	5.53944	0.181548
$932$	−3.22997	−0.105801
$933$	−12.1039	−0.396264
$934$	−26.0233	−0.851509
$935$	−2.41752	−0.0790613
$936$	−8.89173	−0.290635
$937$	−14.3783	−0.469719	−0.234859	−	0.972029i	$-0.575463\pi$
$937$	−14.3783	−0.469719	−0.234859	+	0.972029i	$0.575463\pi$
$938$	−11.0763	−0.361655
$939$	67.2339	2.19409
$940$	−7.93940	−0.258955
$941$	−17.6002	−0.573750	−0.286875	−	0.957968i	$-0.592616\pi$
$941$	−17.6002	−0.573750	−0.286875	+	0.957968i	$0.592616\pi$
$942$	12.7576	0.415664
$943$	82.7815	2.69574
$944$	−29.9235	−0.973927
$945$	10.2498	0.333426
$946$	1.55010	0.0503981
$947$	−34.1454	−1.10958	−0.554788	−	0.831992i	$-0.687200\pi$
$947$	−34.1454	−1.10958	−0.554788	+	0.831992i	$0.687200\pi$
$948$	−10.4653	−0.339897
$949$	−13.7664	−0.446876
$950$	2.57841	0.0836545
$951$	52.0722	1.68856
$952$	5.06661	0.164210
$953$	5.58983	0.181072	0.0905362	−	0.995893i	$-0.471142\pi$
$953$	5.58983	0.181072	0.0905362	+	0.995893i	$0.471142\pi$
$954$	14.3271	0.463856
$955$	18.7242	0.605901
$956$	−1.34196	−0.0434022
$957$	16.7396	0.541113
$958$	−15.4622	−0.499561
$959$	13.3506	0.431114
$960$	−31.6335	−1.02097
$961$	71.9626	2.32138
$962$	6.40984	0.206662
$963$	−18.7498	−0.604205
$964$	6.24275	0.201066
$965$	−54.3006	−1.74800
$966$	52.7326	1.69664
$967$	25.9605	0.834834	0.417417	−	0.908715i	$-0.362935\pi$
$967$	25.9605	0.834834	0.417417	+	0.908715i	$0.362935\pi$
$968$	2.47580	0.0795753
$969$	−4.44031	−0.142643
$970$	−38.0262	−1.22095
$971$	33.0099	1.05934	0.529669	−	0.848205i	$-0.322316\pi$
$971$	33.0099	1.05934	0.529669	+	0.848205i	$0.322316\pi$
$972$	−7.40468	−0.237505
$973$	25.4573	0.816123
$974$	52.9796	1.69758
$975$	−3.28505	−0.105206
$976$	13.5070	0.432348
$977$	−8.26544	−0.264435	−0.132217	−	0.991221i	$-0.542210\pi$
$977$	−8.26544	−0.264435	−0.132217	+	0.991221i	$0.542210\pi$
$978$	−37.5977	−1.20224
$979$	−1.37304	−0.0438827
$980$	2.73838	0.0874744
$981$	−11.8954	−0.379792
$982$	51.1478	1.63219
$983$	−51.0515	−1.62829	−0.814144	−	0.580663i	$-0.802794\pi$
$983$	−51.0515	−1.62829	−0.814144	+	0.580663i	$0.802794\pi$
$984$	−62.6425	−1.99697
$985$	8.34525	0.265902
$986$	−11.5116	−0.366603
$987$	37.6085	1.19709
$988$	1.36953	0.0435704
$989$	7.37478	0.234504
$990$	7.79786	0.247832
$991$	−30.3485	−0.964052	−0.482026	−	0.876157i	$-0.660099\pi$
$991$	−30.3485	−0.964052	−0.482026	+	0.876157i	$0.660099\pi$
$992$	22.7911	0.723617
$993$	49.3817	1.56708
$994$	−31.0485	−0.984797
$995$	−23.6233	−0.748909
$996$	−4.09476	−0.129747
$997$	28.6191	0.906377	0.453188	−	0.891415i	$-0.350286\pi$
$997$	28.6191	0.906377	0.453188	+	0.891415i	$0.350286\pi$
$998$	10.0322	0.317565
$999$	−4.96372	−0.157045

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.c.1.15	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.c.1.15	✓	60	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)

\(f(q)\)	\(=\)	\(q-1.55010 q^{2} +2.25408 q^{3} +0.402812 q^{4} -2.41752 q^{5} -3.49405 q^{6} +2.04645 q^{7} +2.47580 q^{8} +2.08087 q^{9} +O(q^{10})\)	\(q-1.55010 q^{2} +2.25408 q^{3} +0.402812 q^{4} -2.41752 q^{5} -3.49405 q^{6} +2.04645 q^{7} +2.47580 q^{8} +2.08087 q^{9} +3.74740 q^{10} +1.00000 q^{11} +0.907969 q^{12} -1.72594 q^{13} -3.17220 q^{14} -5.44928 q^{15} -4.64337 q^{16} +1.00000 q^{17} -3.22556 q^{18} -1.96990 q^{19} -0.973805 q^{20} +4.61286 q^{21} -1.55010 q^{22} -7.37478 q^{23} +5.58066 q^{24} +0.844399 q^{25} +2.67537 q^{26} -2.07178 q^{27} +0.824334 q^{28} +7.42634 q^{29} +8.44693 q^{30} +10.1471 q^{31} +2.24608 q^{32} +2.25408 q^{33} -1.55010 q^{34} -4.94733 q^{35} +0.838200 q^{36} +2.39587 q^{37} +3.05354 q^{38} -3.89040 q^{39} -5.98530 q^{40} -11.2249 q^{41} -7.15040 q^{42} -1.00000 q^{43} +0.402812 q^{44} -5.03055 q^{45} +11.4317 q^{46} +8.15297 q^{47} -10.4665 q^{48} -2.81204 q^{49} -1.30890 q^{50} +2.25408 q^{51} -0.695227 q^{52} -4.44172 q^{53} +3.21147 q^{54} -2.41752 q^{55} +5.06661 q^{56} -4.44031 q^{57} -11.5116 q^{58} +6.44436 q^{59} -2.19503 q^{60} -2.90887 q^{61} -15.7289 q^{62} +4.25840 q^{63} +5.80508 q^{64} +4.17248 q^{65} -3.49405 q^{66} +3.49168 q^{67} +0.402812 q^{68} -16.6233 q^{69} +7.66886 q^{70} +9.78766 q^{71} +5.15183 q^{72} +7.97619 q^{73} -3.71384 q^{74} +1.90334 q^{75} -0.793498 q^{76} +2.04645 q^{77} +6.03050 q^{78} -11.5260 q^{79} +11.2254 q^{80} -10.9126 q^{81} +17.3998 q^{82} -4.50980 q^{83} +1.85811 q^{84} -2.41752 q^{85} +1.55010 q^{86} +16.7396 q^{87} +2.47580 q^{88} -1.37304 q^{89} +7.79786 q^{90} -3.53204 q^{91} -2.97065 q^{92} +22.8723 q^{93} -12.6379 q^{94} +4.76227 q^{95} +5.06284 q^{96} -10.1474 q^{97} +4.35895 q^{98} +2.08087 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * q^99

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