LMFDB - Embedded newform 8043.2.a.t.1.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.29
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.423981 q^{2} -1.00000 q^{3} -1.82024 q^{4} -4.28511 q^{5} -0.423981 q^{6} +1.00000 q^{7} -1.61971 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.423981 q^{2} -1.00000 q^{3} -1.82024 q^{4} -4.28511 q^{5} -0.423981 q^{6} +1.00000 q^{7} -1.61971 q^{8} +1.00000 q^{9} -1.81680 q^{10} +2.86093 q^{11} +1.82024 q^{12} +6.37475 q^{13} +0.423981 q^{14} +4.28511 q^{15} +2.95375 q^{16} +4.28543 q^{17} +0.423981 q^{18} -3.49808 q^{19} +7.79993 q^{20} -1.00000 q^{21} +1.21298 q^{22} -5.36862 q^{23} +1.61971 q^{24} +13.3621 q^{25} +2.70277 q^{26} -1.00000 q^{27} -1.82024 q^{28} -3.99217 q^{29} +1.81680 q^{30} +7.42174 q^{31} +4.49175 q^{32} -2.86093 q^{33} +1.81694 q^{34} -4.28511 q^{35} -1.82024 q^{36} +6.39970 q^{37} -1.48312 q^{38} -6.37475 q^{39} +6.94063 q^{40} -1.97035 q^{41} -0.423981 q^{42} +7.26726 q^{43} -5.20759 q^{44} -4.28511 q^{45} -2.27619 q^{46} +0.539922 q^{47} -2.95375 q^{48} +1.00000 q^{49} +5.66530 q^{50} -4.28543 q^{51} -11.6036 q^{52} -3.79424 q^{53} -0.423981 q^{54} -12.2594 q^{55} -1.61971 q^{56} +3.49808 q^{57} -1.69261 q^{58} -10.7719 q^{59} -7.79993 q^{60} -4.58270 q^{61} +3.14668 q^{62} +1.00000 q^{63} -4.00309 q^{64} -27.3165 q^{65} -1.21298 q^{66} +9.99054 q^{67} -7.80051 q^{68} +5.36862 q^{69} -1.81680 q^{70} -10.9198 q^{71} -1.61971 q^{72} -0.0742538 q^{73} +2.71335 q^{74} -13.3621 q^{75} +6.36734 q^{76} +2.86093 q^{77} -2.70277 q^{78} -2.91590 q^{79} -12.6572 q^{80} +1.00000 q^{81} -0.835390 q^{82} -12.1091 q^{83} +1.82024 q^{84} -18.3635 q^{85} +3.08118 q^{86} +3.99217 q^{87} -4.63388 q^{88} +7.42795 q^{89} -1.81680 q^{90} +6.37475 q^{91} +9.77218 q^{92} -7.42174 q^{93} +0.228917 q^{94} +14.9896 q^{95} -4.49175 q^{96} -11.4286 q^{97} +0.423981 q^{98} +2.86093 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) $ 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9} - 2 q^{10} + 9 q^{11} - 61 q^{12} + 44 q^{13} + 3 q^{14} + 7 q^{15} + 95 q^{16} - 6 q^{17} + 3 q^{18} + 7 q^{19} - 21 q^{20} - 52 q^{21} + 19 q^{22} - 4 q^{23} - 24 q^{24} + 83 q^{25} - 5 q^{26} - 52 q^{27} + 61 q^{28} + 31 q^{29} + 2 q^{30} + 11 q^{31} + 71 q^{32} - 9 q^{33} + 17 q^{34} - 7 q^{35} + 61 q^{36} + 71 q^{37} - 8 q^{38} - 44 q^{39} + 20 q^{40} - 25 q^{41} - 3 q^{42} + 75 q^{43} + 14 q^{44} - 7 q^{45} + 36 q^{46} - 20 q^{47} - 95 q^{48} + 52 q^{49} + 26 q^{50} + 6 q^{51} + 88 q^{52} + 70 q^{53} - 3 q^{54} + 12 q^{55} + 24 q^{56} - 7 q^{57} + 48 q^{58} - 27 q^{59} + 21 q^{60} + 59 q^{61} - 23 q^{62} + 52 q^{63} + 138 q^{64} + 44 q^{65} - 19 q^{66} + 65 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{70} - 11 q^{71} + 24 q^{72} + 34 q^{73} + 38 q^{74} - 83 q^{75} + 31 q^{76} + 9 q^{77} + 5 q^{78} + 74 q^{79} - 5 q^{80} + 52 q^{81} + 51 q^{82} - 30 q^{83} - 61 q^{84} + 70 q^{85} + 29 q^{86} - 31 q^{87} + 90 q^{88} - q^{89} - 2 q^{90} + 44 q^{91} + 34 q^{92} - 11 q^{93} + 27 q^{94} + 9 q^{95} - 71 q^{96} + 73 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9 - 2 * q^10 + 9 * q^11 - 61 * q^12 + 44 * q^13 + 3 * q^14 + 7 * q^15 + 95 * q^16 - 6 * q^17 + 3 * q^18 + 7 * q^19 - 21 * q^20 - 52 * q^21 + 19 * q^22 - 4 * q^23 - 24 * q^24 + 83 * q^25 - 5 * q^26 - 52 * q^27 + 61 * q^28 + 31 * q^29 + 2 * q^30 + 11 * q^31 + 71 * q^32 - 9 * q^33 + 17 * q^34 - 7 * q^35 + 61 * q^36 + 71 * q^37 - 8 * q^38 - 44 * q^39 + 20 * q^40 - 25 * q^41 - 3 * q^42 + 75 * q^43 + 14 * q^44 - 7 * q^45 + 36 * q^46 - 20 * q^47 - 95 * q^48 + 52 * q^49 + 26 * q^50 + 6 * q^51 + 88 * q^52 + 70 * q^53 - 3 * q^54 + 12 * q^55 + 24 * q^56 - 7 * q^57 + 48 * q^58 - 27 * q^59 + 21 * q^60 + 59 * q^61 - 23 * q^62 + 52 * q^63 + 138 * q^64 + 44 * q^65 - 19 * q^66 + 65 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^70 - 11 * q^71 + 24 * q^72 + 34 * q^73 + 38 * q^74 - 83 * q^75 + 31 * q^76 + 9 * q^77 + 5 * q^78 + 74 * q^79 - 5 * q^80 + 52 * q^81 + 51 * q^82 - 30 * q^83 - 61 * q^84 + 70 * q^85 + 29 * q^86 - 31 * q^87 + 90 * q^88 - q^89 - 2 * q^90 + 44 * q^91 + 34 * q^92 - 11 * q^93 + 27 * q^94 + 9 * q^95 - 71 * q^96 + 73 * q^97 + 3 * q^98 + 9 * 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 $

$2$	0.423981	0.299800	0.149900	−	0.988701i	$-0.452105\pi$
$2$	0.423981	0.299800	0.149900	+	0.988701i	$0.452105\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.82024	−0.910120
$5$	−4.28511	−1.91636	−0.958179	−	0.286169i	$-0.907618\pi$
$5$	−4.28511	−1.91636	−0.958179	+	0.286169i	$0.907618\pi$
$6$	−0.423981	−0.173090
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.61971	−0.572654
$9$	1.00000	0.333333
$10$	−1.81680	−0.574524
$11$	2.86093	0.862604	0.431302	−	0.902208i	$-0.358054\pi$
$11$	2.86093	0.862604	0.431302	+	0.902208i	$0.358054\pi$
$12$	1.82024	0.525458
$13$	6.37475	1.76804	0.884019	−	0.467451i	$-0.154828\pi$
$13$	6.37475	1.76804	0.884019	+	0.467451i	$0.154828\pi$
$14$	0.423981	0.113314
$15$	4.28511	1.10641
$16$	2.95375	0.738439
$17$	4.28543	1.03937	0.519684	−	0.854358i	$-0.326050\pi$
$17$	4.28543	1.03937	0.519684	+	0.854358i	$0.326050\pi$
$18$	0.423981	0.0999333
$19$	−3.49808	−0.802514	−0.401257	−	0.915966i	$-0.631426\pi$
$19$	−3.49808	−0.802514	−0.401257	+	0.915966i	$0.631426\pi$
$20$	7.79993	1.74412
$21$	−1.00000	−0.218218
$22$	1.21298	0.258609
$23$	−5.36862	−1.11943	−0.559717	−	0.828684i	$-0.689090\pi$
$23$	−5.36862	−1.11943	−0.559717	+	0.828684i	$0.689090\pi$
$24$	1.61971	0.330622
$25$	13.3621	2.67243
$26$	2.70277	0.530057
$27$	−1.00000	−0.192450
$28$	−1.82024	−0.343993
$29$	−3.99217	−0.741328	−0.370664	−	0.928767i	$-0.620870\pi$
$29$	−3.99217	−0.741328	−0.370664	+	0.928767i	$0.620870\pi$
$30$	1.81680	0.331702
$31$	7.42174	1.33298	0.666492	−	0.745513i	$-0.267795\pi$
$31$	7.42174	1.33298	0.666492	+	0.745513i	$0.267795\pi$
$32$	4.49175	0.794037
$33$	−2.86093	−0.498025
$34$	1.81694	0.311603
$35$	−4.28511	−0.724315
$36$	−1.82024	−0.303373
$37$	6.39970	1.05210	0.526052	−	0.850452i	$-0.323672\pi$
$37$	6.39970	1.05210	0.526052	+	0.850452i	$0.323672\pi$
$38$	−1.48312	−0.240593
$39$	−6.37475	−1.02078
$40$	6.94063	1.09741
$41$	−1.97035	−0.307717	−0.153858	−	0.988093i	$-0.549170\pi$
$41$	−1.97035	−0.307717	−0.153858	+	0.988093i	$0.549170\pi$
$42$	−0.423981	−0.0654217
$43$	7.26726	1.10825	0.554123	−	0.832435i	$-0.313054\pi$
$43$	7.26726	1.10825	0.554123	+	0.832435i	$0.313054\pi$
$44$	−5.20759	−0.785073
$45$	−4.28511	−0.638786
$46$	−2.27619	−0.335606
$47$	0.539922	0.0787557	0.0393779	−	0.999224i	$-0.487462\pi$
$47$	0.539922	0.0787557	0.0393779	+	0.999224i	$0.487462\pi$
$48$	−2.95375	−0.426338
$49$	1.00000	0.142857
$50$	5.66530	0.801194
$51$	−4.28543	−0.600080
$52$	−11.6036	−1.60913
$53$	−3.79424	−0.521179	−0.260589	−	0.965450i	$-0.583917\pi$
$53$	−3.79424	−0.521179	−0.260589	+	0.965450i	$0.583917\pi$
$54$	−0.423981	−0.0576965
$55$	−12.2594	−1.65306
$56$	−1.61971	−0.216443
$57$	3.49808	0.463331
$58$	−1.69261	−0.222250
$59$	−10.7719	−1.40238	−0.701189	−	0.712975i	$-0.747347\pi$
$59$	−10.7719	−1.40238	−0.701189	+	0.712975i	$0.747347\pi$
$60$	−7.79993	−1.00697
$61$	−4.58270	−0.586755	−0.293377	−	0.955997i	$-0.594779\pi$
$61$	−4.58270	−0.586755	−0.293377	+	0.955997i	$0.594779\pi$
$62$	3.14668	0.399628
$63$	1.00000	0.125988
$64$	−4.00309	−0.500386
$65$	−27.3165	−3.38819
$66$	−1.21298	−0.149308
$67$	9.99054	1.22054	0.610270	−	0.792194i	$-0.291061\pi$
$67$	9.99054	1.22054	0.610270	+	0.792194i	$0.291061\pi$
$68$	−7.80051	−0.945950
$69$	5.36862	0.646306
$70$	−1.81680	−0.217150
$71$	−10.9198	−1.29594	−0.647972	−	0.761664i	$-0.724383\pi$
$71$	−10.9198	−1.29594	−0.647972	+	0.761664i	$0.724383\pi$
$72$	−1.61971	−0.190885
$73$	−0.0742538	−0.00869076	−0.00434538	−	0.999991i	$-0.501383\pi$
$73$	−0.0742538	−0.00869076	−0.00434538	+	0.999991i	$0.501383\pi$
$74$	2.71335	0.315421
$75$	−13.3621	−1.54293
$76$	6.36734	0.730384
$77$	2.86093	0.326034
$78$	−2.70277	−0.306029
$79$	−2.91590	−0.328064	−0.164032	−	0.986455i	$-0.552450\pi$
$79$	−2.91590	−0.328064	−0.164032	+	0.986455i	$0.552450\pi$
$80$	−12.6572	−1.41511
$81$	1.00000	0.111111
$82$	−0.835390	−0.0922534
$83$	−12.1091	−1.32915	−0.664573	−	0.747223i	$-0.731386\pi$
$83$	−12.1091	−1.32915	−0.664573	+	0.747223i	$0.731386\pi$
$84$	1.82024	0.198604
$85$	−18.3635	−1.99180
$86$	3.08118	0.332252
$87$	3.99217	0.428006
$88$	−4.63388	−0.493974
$89$	7.42795	0.787361	0.393681	−	0.919247i	$-0.371202\pi$
$89$	7.42795	0.787361	0.393681	+	0.919247i	$0.371202\pi$
$90$	−1.81680	−0.191508
$91$	6.37475	0.668255
$92$	9.77218	1.01882
$93$	−7.42174	−0.769598
$94$	0.228917	0.0236109
$95$	14.9896	1.53790
$96$	−4.49175	−0.458438
$97$	−11.4286	−1.16040	−0.580198	−	0.814475i	$-0.697025\pi$
$97$	−11.4286	−1.16040	−0.580198	+	0.814475i	$0.697025\pi$
$98$	0.423981	0.0428285
$99$	2.86093	0.287535
$100$	−24.3223	−2.43223
$101$	17.9798	1.78906	0.894529	−	0.447010i	$-0.147511\pi$
$101$	17.9798	1.78906	0.894529	+	0.447010i	$0.147511\pi$
$102$	−1.81694	−0.179904
$103$	−8.70259	−0.857492	−0.428746	−	0.903425i	$-0.641044\pi$
$103$	−8.70259	−0.857492	−0.428746	+	0.903425i	$0.641044\pi$
$104$	−10.3252	−1.01247
$105$	4.28511	0.418184
$106$	−1.60869	−0.156249
$107$	6.60403	0.638436	0.319218	−	0.947681i	$-0.396580\pi$
$107$	6.60403	0.638436	0.319218	+	0.947681i	$0.396580\pi$
$108$	1.82024	0.175153
$109$	5.59469	0.535875	0.267937	−	0.963436i	$-0.413658\pi$
$109$	5.59469	0.535875	0.267937	+	0.963436i	$0.413658\pi$
$110$	−5.19776	−0.495587
$111$	−6.39970	−0.607432
$112$	2.95375	0.279104
$113$	9.20778	0.866195	0.433098	−	0.901347i	$-0.357421\pi$
$113$	9.20778	0.866195	0.433098	+	0.901347i	$0.357421\pi$
$114$	1.48312	0.138907
$115$	23.0051	2.14524
$116$	7.26672	0.674698
$117$	6.37475	0.589346
$118$	−4.56707	−0.420433
$119$	4.28543	0.392844
$120$	−6.94063	−0.633590
$121$	−2.81505	−0.255914
$122$	−1.94298	−0.175909
$123$	1.97035	0.177660
$124$	−13.5093	−1.21317
$125$	−35.8327	−3.20498
$126$	0.423981	0.0377712
$127$	18.5404	1.64519	0.822597	−	0.568624i	$-0.192524\pi$
$127$	18.5404	1.64519	0.822597	+	0.568624i	$0.192524\pi$
$128$	−10.6807	−0.944053
$129$	−7.26726	−0.639847
$130$	−11.5817	−1.01578
$131$	20.6405	1.80337	0.901686	−	0.432391i	$-0.142330\pi$
$131$	20.6405	1.80337	0.901686	+	0.432391i	$0.142330\pi$
$132$	5.20759	0.453262
$133$	−3.49808	−0.303322
$134$	4.23580	0.365917
$135$	4.28511	0.368803
$136$	−6.94114	−0.595198
$137$	12.3870	1.05830	0.529148	−	0.848529i	$-0.322512\pi$
$137$	12.3870	1.05830	0.529148	+	0.848529i	$0.322512\pi$
$138$	2.27619	0.193762
$139$	−3.26805	−0.277192	−0.138596	−	0.990349i	$-0.544259\pi$
$139$	−3.26805	−0.277192	−0.138596	+	0.990349i	$0.544259\pi$
$140$	7.79993	0.659214
$141$	−0.539922	−0.0454696
$142$	−4.62980	−0.388524
$143$	18.2377	1.52512
$144$	2.95375	0.246146
$145$	17.1069	1.42065
$146$	−0.0314822	−0.00260549
$147$	−1.00000	−0.0824786
$148$	−11.6490	−0.957541
$149$	21.0515	1.72460	0.862302	−	0.506394i	$-0.169022\pi$
$149$	21.0515	1.72460	0.862302	+	0.506394i	$0.169022\pi$
$150$	−5.66530	−0.462570
$151$	−21.6380	−1.76087	−0.880437	−	0.474164i	$-0.842751\pi$
$151$	−21.6380	−1.76087	−0.880437	+	0.474164i	$0.842751\pi$
$152$	5.66586	0.459562
$153$	4.28543	0.346456
$154$	1.21298	0.0977449
$155$	−31.8029	−2.55447
$156$	11.6036	0.929030
$157$	1.82706	0.145815	0.0729076	−	0.997339i	$-0.476772\pi$
$157$	1.82706	0.145815	0.0729076	+	0.997339i	$0.476772\pi$
$158$	−1.23629	−0.0983536
$159$	3.79424	0.300903
$160$	−19.2477	−1.52166
$161$	−5.36862	−0.423107
$162$	0.423981	0.0333111
$163$	−16.6408	−1.30341	−0.651706	−	0.758472i	$-0.725946\pi$
$163$	−16.6408	−1.30341	−0.651706	+	0.758472i	$0.725946\pi$
$164$	3.58650	0.280059
$165$	12.2594	0.954394
$166$	−5.13403	−0.398478
$167$	−17.7272	−1.37177	−0.685886	−	0.727709i	$-0.740585\pi$
$167$	−17.7272	−1.37177	−0.685886	+	0.727709i	$0.740585\pi$
$168$	1.61971	0.124963
$169$	27.6375	2.12596
$170$	−7.78578	−0.597142
$171$	−3.49808	−0.267505
$172$	−13.2282	−1.00864
$173$	−4.48355	−0.340878	−0.170439	−	0.985368i	$-0.554519\pi$
$173$	−4.48355	−0.340878	−0.170439	+	0.985368i	$0.554519\pi$
$174$	1.69261	0.128316
$175$	13.3621	1.01008
$176$	8.45050	0.636980
$177$	10.7719	0.809663
$178$	3.14931	0.236051
$179$	−2.54617	−0.190310	−0.0951548	−	0.995462i	$-0.530335\pi$
$179$	−2.54617	−0.190310	−0.0951548	+	0.995462i	$0.530335\pi$
$180$	7.79993	0.581372
$181$	22.6323	1.68224	0.841121	−	0.540847i	$-0.181896\pi$
$181$	22.6323	1.68224	0.841121	+	0.540847i	$0.181896\pi$
$182$	2.70277	0.200343
$183$	4.58270	0.338763
$184$	8.69560	0.641048
$185$	−27.4234	−2.01621
$186$	−3.14668	−0.230725
$187$	12.2603	0.896564
$188$	−0.982788	−0.0716772
$189$	−1.00000	−0.0727393
$190$	6.35532	0.461063
$191$	−14.8768	−1.07645	−0.538225	−	0.842801i	$-0.680905\pi$
$191$	−14.8768	−1.07645	−0.538225	+	0.842801i	$0.680905\pi$
$192$	4.00309	0.288898
$193$	−9.86771	−0.710294	−0.355147	−	0.934811i	$-0.615569\pi$
$193$	−9.86771	−0.710294	−0.355147	+	0.934811i	$0.615569\pi$
$194$	−4.84550	−0.347887
$195$	27.3165	1.95617
$196$	−1.82024	−0.130017
$197$	−18.4583	−1.31510	−0.657548	−	0.753413i	$-0.728406\pi$
$197$	−18.4583	−1.31510	−0.657548	+	0.753413i	$0.728406\pi$
$198$	1.21298	0.0862029
$199$	24.0396	1.70412	0.852060	−	0.523444i	$-0.175353\pi$
$199$	24.0396	1.70412	0.852060	+	0.523444i	$0.175353\pi$
$200$	−21.6428	−1.53038
$201$	−9.99054	−0.704679
$202$	7.62310	0.536359
$203$	−3.99217	−0.280196
$204$	7.80051	0.546145
$205$	8.44315	0.589695
$206$	−3.68973	−0.257076
$207$	−5.36862	−0.373145
$208$	18.8294	1.30559
$209$	−10.0078	−0.692252
$210$	1.81680	0.125371
$211$	−5.38105	−0.370447	−0.185224	−	0.982696i	$-0.559301\pi$
$211$	−5.38105	−0.370447	−0.185224	+	0.982696i	$0.559301\pi$
$212$	6.90643	0.474335
$213$	10.9198	0.748214
$214$	2.79998	0.191403
$215$	−31.1410	−2.12380
$216$	1.61971	0.110207
$217$	7.42174	0.503820
$218$	2.37204	0.160655
$219$	0.0742538	0.00501761
$220$	22.3151	1.50448
$221$	27.3185	1.83764
$222$	−2.71335	−0.182108
$223$	−12.8459	−0.860227	−0.430113	−	0.902775i	$-0.641526\pi$
$223$	−12.8459	−0.860227	−0.430113	+	0.902775i	$0.641526\pi$
$224$	4.49175	0.300118
$225$	13.3621	0.890810
$226$	3.90393	0.259685
$227$	−5.41190	−0.359201	−0.179600	−	0.983740i	$-0.557480\pi$
$227$	−5.41190	−0.359201	−0.179600	+	0.983740i	$0.557480\pi$
$228$	−6.36734	−0.421687
$229$	7.01390	0.463491	0.231746	−	0.972776i	$-0.425556\pi$
$229$	7.01390	0.463491	0.231746	+	0.972776i	$0.425556\pi$
$230$	9.75373	0.643142
$231$	−2.86093	−0.188236
$232$	6.46616	0.424524
$233$	12.3359	0.808154	0.404077	−	0.914725i	$-0.367593\pi$
$233$	12.3359	0.808154	0.404077	+	0.914725i	$0.367593\pi$
$234$	2.70277	0.176686
$235$	−2.31362	−0.150924
$236$	19.6074	1.27633
$237$	2.91590	0.189408
$238$	1.81694	0.117775
$239$	28.3785	1.83565	0.917826	−	0.396983i	$-0.129943\pi$
$239$	28.3785	1.83565	0.917826	+	0.396983i	$0.129943\pi$
$240$	12.6572	0.817016
$241$	−27.7510	−1.78760	−0.893800	−	0.448465i	$-0.851971\pi$
$241$	−27.7510	−1.78760	−0.893800	+	0.448465i	$0.851971\pi$
$242$	−1.19353	−0.0767229
$243$	−1.00000	−0.0641500
$244$	8.34162	0.534017
$245$	−4.28511	−0.273766
$246$	0.835390	0.0532625
$247$	−22.2994	−1.41887
$248$	−12.0211	−0.763338
$249$	12.1091	0.767383
$250$	−15.1924	−0.960851
$251$	−17.0166	−1.07408	−0.537040	−	0.843557i	$-0.680458\pi$
$251$	−17.0166	−1.07408	−0.537040	+	0.843557i	$0.680458\pi$
$252$	−1.82024	−0.114664
$253$	−15.3593	−0.965629
$254$	7.86078	0.493229
$255$	18.3635	1.14997
$256$	3.47775	0.217359
$257$	4.35360	0.271570	0.135785	−	0.990738i	$-0.456644\pi$
$257$	4.35360	0.271570	0.135785	+	0.990738i	$0.456644\pi$
$258$	−3.08118	−0.191826
$259$	6.39970	0.397658
$260$	49.7226	3.08366
$261$	−3.99217	−0.247109
$262$	8.75120	0.540651
$263$	−25.8851	−1.59614	−0.798070	−	0.602564i	$-0.794146\pi$
$263$	−25.8851	−1.59614	−0.798070	+	0.602564i	$0.794146\pi$
$264$	4.63388	0.285196
$265$	16.2587	0.998765
$266$	−1.48312	−0.0909358
$267$	−7.42795	−0.454583
$268$	−18.1852	−1.11084
$269$	15.9730	0.973892	0.486946	−	0.873432i	$-0.338111\pi$
$269$	15.9730	0.973892	0.486946	+	0.873432i	$0.338111\pi$
$270$	1.81680	0.110567
$271$	9.43949	0.573408	0.286704	−	0.958019i	$-0.407440\pi$
$271$	9.43949	0.573408	0.286704	+	0.958019i	$0.407440\pi$
$272$	12.6581	0.767510
$273$	−6.37475	−0.385817
$274$	5.25187	0.317277
$275$	38.2282	2.30525
$276$	−9.77218	−0.588216
$277$	29.3846	1.76555	0.882776	−	0.469794i	$-0.155672\pi$
$277$	29.3846	1.76555	0.882776	+	0.469794i	$0.155672\pi$
$278$	−1.38559	−0.0831022
$279$	7.42174	0.444328
$280$	6.94063	0.414782
$281$	26.8495	1.60171	0.800853	−	0.598860i	$-0.204380\pi$
$281$	26.8495	1.60171	0.800853	+	0.598860i	$0.204380\pi$
$282$	−0.228917	−0.0136318
$283$	−12.4652	−0.740981	−0.370491	−	0.928836i	$-0.620810\pi$
$283$	−12.4652	−0.740981	−0.370491	+	0.928836i	$0.620810\pi$
$284$	19.8767	1.17947
$285$	−14.9896	−0.887909
$286$	7.73246	0.457230
$287$	−1.97035	−0.116306
$288$	4.49175	0.264679
$289$	1.36488	0.0802871
$290$	7.25300	0.425911
$291$	11.4286	0.669955
$292$	0.135160	0.00790963
$293$	9.73554	0.568756	0.284378	−	0.958712i	$-0.408213\pi$
$293$	9.73554	0.568756	0.284378	+	0.958712i	$0.408213\pi$
$294$	−0.423981	−0.0247271
$295$	46.1586	2.68746
$296$	−10.3656	−0.602491
$297$	−2.86093	−0.166008
$298$	8.92543	0.517036
$299$	−34.2236	−1.97920
$300$	24.3223	1.40425
$301$	7.26726	0.418878
$302$	−9.17409	−0.527910
$303$	−17.9798	−1.03291
$304$	−10.3325	−0.592607
$305$	19.6374	1.12443
$306$	1.81694	0.103868
$307$	−7.54036	−0.430351	−0.215175	−	0.976575i	$-0.569032\pi$
$307$	−7.54036	−0.430351	−0.215175	+	0.976575i	$0.569032\pi$
$308$	−5.20759	−0.296730
$309$	8.70259	0.495073
$310$	−13.4838	−0.765831
$311$	9.69970	0.550019	0.275010	−	0.961441i	$-0.411319\pi$
$311$	9.69970	0.550019	0.275010	+	0.961441i	$0.411319\pi$
$312$	10.3252	0.584552
$313$	−14.3066	−0.808657	−0.404329	−	0.914614i	$-0.632495\pi$
$313$	−14.3066	−0.808657	−0.404329	+	0.914614i	$0.632495\pi$
$314$	0.774638	0.0437154
$315$	−4.28511	−0.241438
$316$	5.30764	0.298578
$317$	6.49820	0.364975	0.182488	−	0.983208i	$-0.441585\pi$
$317$	6.49820	0.364975	0.182488	+	0.983208i	$0.441585\pi$
$318$	1.60869	0.0902106
$319$	−11.4213	−0.639473
$320$	17.1537	0.958920
$321$	−6.60403	−0.368601
$322$	−2.27619	−0.126847
$323$	−14.9907	−0.834107
$324$	−1.82024	−0.101124
$325$	85.1804	4.72496
$326$	−7.05540	−0.390763
$327$	−5.59469	−0.309387
$328$	3.19139	0.176215
$329$	0.539922	0.0297669
$330$	5.19776	0.286127
$331$	9.78226	0.537682	0.268841	−	0.963185i	$-0.413359\pi$
$331$	9.78226	0.537682	0.268841	+	0.963185i	$0.413359\pi$
$332$	22.0415	1.20968
$333$	6.39970	0.350701
$334$	−7.51600	−0.411257
$335$	−42.8106	−2.33899
$336$	−2.95375	−0.161141
$337$	8.45557	0.460604	0.230302	−	0.973119i	$-0.426029\pi$
$337$	8.45557	0.460604	0.230302	+	0.973119i	$0.426029\pi$
$338$	11.7178	0.637362
$339$	−9.20778	−0.500098
$340$	33.4260	1.81278
$341$	21.2331	1.14984
$342$	−1.48312	−0.0801978
$343$	1.00000	0.0539949
$344$	−11.7708	−0.634642
$345$	−23.0051	−1.23855
$346$	−1.90094	−0.102195
$347$	18.0419	0.968540	0.484270	−	0.874919i	$-0.339085\pi$
$347$	18.0419	0.968540	0.484270	+	0.874919i	$0.339085\pi$
$348$	−7.26672	−0.389537
$349$	14.7868	0.791521	0.395760	−	0.918354i	$-0.370481\pi$
$349$	14.7868	0.791521	0.395760	+	0.918354i	$0.370481\pi$
$350$	5.66530	0.302823
$351$	−6.37475	−0.340259
$352$	12.8506	0.684940
$353$	7.64588	0.406949	0.203475	−	0.979080i	$-0.434777\pi$
$353$	7.64588	0.406949	0.203475	+	0.979080i	$0.434777\pi$
$354$	4.56707	0.242737
$355$	46.7926	2.48349
$356$	−13.5207	−0.716593
$357$	−4.28543	−0.226809
$358$	−1.07953	−0.0570548
$359$	20.4636	1.08003	0.540013	−	0.841657i	$-0.318419\pi$
$359$	20.4636	1.08003	0.540013	+	0.841657i	$0.318419\pi$
$360$	6.94063	0.365803
$361$	−6.76347	−0.355972
$362$	9.59565	0.504336
$363$	2.81505	0.147752
$364$	−11.6036	−0.608193
$365$	0.318186	0.0166546
$366$	1.94298	0.101561
$367$	−13.6615	−0.713124	−0.356562	−	0.934272i	$-0.616051\pi$
$367$	−13.6615	−0.713124	−0.356562	+	0.934272i	$0.616051\pi$
$368$	−15.8576	−0.826634
$369$	−1.97035	−0.102572
$370$	−11.6270	−0.604459
$371$	−3.79424	−0.196987
$372$	13.5093	0.700427
$373$	22.2363	1.15135	0.575676	−	0.817678i	$-0.304739\pi$
$373$	22.2363	1.15135	0.575676	+	0.817678i	$0.304739\pi$
$374$	5.19815	0.268790
$375$	35.8327	1.85039
$376$	−0.874517	−0.0450997
$377$	−25.4491	−1.31070
$378$	−0.423981	−0.0218072
$379$	−5.42406	−0.278615	−0.139308	−	0.990249i	$-0.544488\pi$
$379$	−5.42406	−0.278615	−0.139308	+	0.990249i	$0.544488\pi$
$380$	−27.2847	−1.39968
$381$	−18.5404	−0.949853
$382$	−6.30750	−0.322720
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	10.6807	0.545049
$385$	−12.2594	−0.624798
$386$	−4.18372	−0.212946
$387$	7.26726	0.369416
$388$	20.8028	1.05610
$389$	−5.61709	−0.284798	−0.142399	−	0.989809i	$-0.545482\pi$
$389$	−5.61709	−0.284798	−0.142399	+	0.989809i	$0.545482\pi$
$390$	11.5817	0.586461
$391$	−23.0068	−1.16351
$392$	−1.61971	−0.0818077
$393$	−20.6405	−1.04118
$394$	−7.82595	−0.394266
$395$	12.4949	0.628689
$396$	−5.20759	−0.261691
$397$	8.35931	0.419542	0.209771	−	0.977751i	$-0.432728\pi$
$397$	8.35931	0.419542	0.209771	+	0.977751i	$0.432728\pi$
$398$	10.1923	0.510895
$399$	3.49808	0.175123
$400$	39.4685	1.97343
$401$	−8.36366	−0.417661	−0.208831	−	0.977952i	$-0.566966\pi$
$401$	−8.36366	−0.417661	−0.208831	+	0.977952i	$0.566966\pi$
$402$	−4.23580	−0.211263
$403$	47.3117	2.35676
$404$	−32.7276	−1.62826
$405$	−4.28511	−0.212929
$406$	−1.69261	−0.0840026
$407$	18.3091	0.907549
$408$	6.94114	0.343638
$409$	−10.4779	−0.518101	−0.259050	−	0.965864i	$-0.583410\pi$
$409$	−10.4779	−0.518101	−0.259050	+	0.965864i	$0.583410\pi$
$410$	3.57974	0.176791
$411$	−12.3870	−0.611008
$412$	15.8408	0.780421
$413$	−10.7719	−0.530049
$414$	−2.27619	−0.111869
$415$	51.8888	2.54712
$416$	28.6338	1.40389
$417$	3.26805	0.160037
$418$	−4.24310	−0.207537
$419$	−5.34291	−0.261018	−0.130509	−	0.991447i	$-0.541661\pi$
$419$	−5.34291	−0.261018	−0.130509	+	0.991447i	$0.541661\pi$
$420$	−7.79993	−0.380597
$421$	−10.3935	−0.506548	−0.253274	−	0.967395i	$-0.581507\pi$
$421$	−10.3935	−0.506548	−0.253274	+	0.967395i	$0.581507\pi$
$422$	−2.28146	−0.111060
$423$	0.539922	0.0262519
$424$	6.14556	0.298455
$425$	57.2625	2.77764
$426$	4.62980	0.224314
$427$	−4.58270	−0.221772
$428$	−12.0209	−0.581053
$429$	−18.2377	−0.880527
$430$	−13.2032	−0.636714
$431$	24.0682	1.15932	0.579662	−	0.814857i	$-0.303184\pi$
$431$	24.0682	1.15932	0.579662	+	0.814857i	$0.303184\pi$
$432$	−2.95375	−0.142113
$433$	3.41370	0.164052	0.0820259	−	0.996630i	$-0.473861\pi$
$433$	3.41370	0.164052	0.0820259	+	0.996630i	$0.473861\pi$
$434$	3.14668	0.151045
$435$	−17.1069	−0.820213
$436$	−10.1837	−0.487710
$437$	18.7798	0.898361
$438$	0.0314822	0.00150428
$439$	38.1989	1.82313	0.911567	−	0.411152i	$-0.134874\pi$
$439$	38.1989	1.82313	0.911567	+	0.411152i	$0.134874\pi$
$440$	19.8567	0.946630
$441$	1.00000	0.0476190
$442$	11.5825	0.550925
$443$	−10.6037	−0.503798	−0.251899	−	0.967754i	$-0.581055\pi$
$443$	−10.6037	−0.503798	−0.251899	+	0.967754i	$0.581055\pi$
$444$	11.6490	0.552836
$445$	−31.8296	−1.50887
$446$	−5.44643	−0.257896
$447$	−21.0515	−0.995701
$448$	−4.00309	−0.189128
$449$	−5.04621	−0.238145	−0.119073	−	0.992886i	$-0.537992\pi$
$449$	−5.04621	−0.238145	−0.119073	+	0.992886i	$0.537992\pi$
$450$	5.66530	0.267065
$451$	−5.63703	−0.265438
$452$	−16.7604	−0.788342
$453$	21.6380	1.01664
$454$	−2.29454	−0.107688
$455$	−27.3165	−1.28062
$456$	−5.66586	−0.265328
$457$	−9.88060	−0.462195	−0.231097	−	0.972931i	$-0.574232\pi$
$457$	−9.88060	−0.462195	−0.231097	+	0.972931i	$0.574232\pi$
$458$	2.97376	0.138955
$459$	−4.28543	−0.200027
$460$	−41.8748	−1.95242
$461$	−39.3913	−1.83463	−0.917317	−	0.398158i	$-0.869649\pi$
$461$	−39.3913	−1.83463	−0.917317	+	0.398158i	$0.869649\pi$
$462$	−1.21298	−0.0564330
$463$	−4.08016	−0.189621	−0.0948106	−	0.995495i	$-0.530225\pi$
$463$	−4.08016	−0.189621	−0.0948106	+	0.995495i	$0.530225\pi$
$464$	−11.7919	−0.547425
$465$	31.8029	1.47483
$466$	5.23020	0.242284
$467$	−14.1986	−0.657032	−0.328516	−	0.944498i	$-0.606549\pi$
$467$	−14.1986	−0.657032	−0.328516	+	0.944498i	$0.606549\pi$
$468$	−11.6036	−0.536376
$469$	9.99054	0.461320
$470$	−0.980932	−0.0452470
$471$	−1.82706	−0.0841865
$472$	17.4473	0.803077
$473$	20.7912	0.955978
$474$	1.23629	0.0567845
$475$	−46.7418	−2.14466
$476$	−7.80051	−0.357536
$477$	−3.79424	−0.173726
$478$	12.0319	0.550328
$479$	−8.66585	−0.395953	−0.197976	−	0.980207i	$-0.563437\pi$
$479$	−8.66585	−0.395953	−0.197976	+	0.980207i	$0.563437\pi$
$480$	19.2477	0.878531
$481$	40.7965	1.86016
$482$	−11.7659	−0.535922
$483$	5.36862	0.244281
$484$	5.12407	0.232912
$485$	48.9727	2.22374
$486$	−0.423981	−0.0192322
$487$	−3.44999	−0.156334	−0.0781669	−	0.996940i	$-0.524907\pi$
$487$	−3.44999	−0.156334	−0.0781669	+	0.996940i	$0.524907\pi$
$488$	7.42264	0.336007
$489$	16.6408	0.752525
$490$	−1.81680	−0.0820749
$491$	27.8143	1.25524	0.627622	−	0.778518i	$-0.284028\pi$
$491$	27.8143	1.25524	0.627622	+	0.778518i	$0.284028\pi$
$492$	−3.58650	−0.161692
$493$	−17.1082	−0.770513
$494$	−9.45450	−0.425378
$495$	−12.2594	−0.551020
$496$	21.9220	0.984326
$497$	−10.9198	−0.489821
$498$	5.13403	0.230061
$499$	−6.26258	−0.280352	−0.140176	−	0.990127i	$-0.544767\pi$
$499$	−6.26258	−0.280352	−0.140176	+	0.990127i	$0.544767\pi$
$500$	65.2241	2.91691
$501$	17.7272	0.791993
$502$	−7.21473	−0.322009
$503$	5.95413	0.265482	0.132741	−	0.991151i	$-0.457622\pi$
$503$	5.95413	0.265482	0.132741	+	0.991151i	$0.457622\pi$
$504$	−1.61971	−0.0721476
$505$	−77.0454	−3.42848
$506$	−6.51204	−0.289495
$507$	−27.6375	−1.22742
$508$	−33.7480	−1.49732
$509$	−19.9005	−0.882075	−0.441037	−	0.897489i	$-0.645389\pi$
$509$	−19.9005	−0.882075	−0.441037	+	0.897489i	$0.645389\pi$
$510$	7.78578	0.344760
$511$	−0.0742538	−0.00328480
$512$	22.8360	1.00922
$513$	3.49808	0.154444
$514$	1.84584	0.0814167
$515$	37.2916	1.64326
$516$	13.2282	0.582337
$517$	1.54468	0.0679350
$518$	2.71335	0.119218
$519$	4.48355	0.196806
$520$	44.2448	1.94026
$521$	−43.5345	−1.90728	−0.953641	−	0.300946i	$-0.902698\pi$
$521$	−43.5345	−1.90728	−0.953641	+	0.300946i	$0.902698\pi$
$522$	−1.69261	−0.0740833
$523$	21.9223	0.958596	0.479298	−	0.877652i	$-0.340891\pi$
$523$	21.9223	0.958596	0.479298	+	0.877652i	$0.340891\pi$
$524$	−37.5707	−1.64129
$525$	−13.3621	−0.583172
$526$	−10.9748	−0.478523
$527$	31.8053	1.38546
$528$	−8.45050	−0.367761
$529$	5.82208	0.253134
$530$	6.89339	0.299430
$531$	−10.7719	−0.467459
$532$	6.36734	0.276059
$533$	−12.5605	−0.544054
$534$	−3.14931	−0.136284
$535$	−28.2990	−1.22347
$536$	−16.1818	−0.698946
$537$	2.54617	0.109875
$538$	6.77226	0.291973
$539$	2.86093	0.123229
$540$	−7.79993	−0.335655
$541$	34.1083	1.46643	0.733216	−	0.679996i	$-0.238018\pi$
$541$	34.1083	1.46643	0.733216	+	0.679996i	$0.238018\pi$
$542$	4.00217	0.171908
$543$	−22.6323	−0.971243
$544$	19.2491	0.825298
$545$	−23.9739	−1.02693
$546$	−2.70277	−0.115668
$547$	17.7915	0.760707	0.380354	−	0.924841i	$-0.375802\pi$
$547$	17.7915	0.760707	0.380354	+	0.924841i	$0.375802\pi$
$548$	−22.5474	−0.963177
$549$	−4.58270	−0.195585
$550$	16.2080	0.691113
$551$	13.9649	0.594926
$552$	−8.69560	−0.370109
$553$	−2.91590	−0.123997
$554$	12.4585	0.529312
$555$	27.4234	1.16406
$556$	5.94863	0.252278
$557$	−2.89145	−0.122515	−0.0612574	−	0.998122i	$-0.519511\pi$
$557$	−2.89145	−0.122515	−0.0612574	+	0.998122i	$0.519511\pi$
$558$	3.14668	0.133209
$559$	46.3270	1.95942
$560$	−12.6572	−0.534862
$561$	−12.2603	−0.517631
$562$	11.3837	0.480191
$563$	42.4979	1.79107	0.895537	−	0.444988i	$-0.146792\pi$
$563$	42.4979	1.79107	0.895537	+	0.444988i	$0.146792\pi$
$564$	0.982788	0.0413828
$565$	−39.4563	−1.65994
$566$	−5.28502	−0.222146
$567$	1.00000	0.0419961
$568$	17.6869	0.742127
$569$	−14.7820	−0.619692	−0.309846	−	0.950787i	$-0.600277\pi$
$569$	−14.7820	−0.619692	−0.309846	+	0.950787i	$0.600277\pi$
$570$	−6.35532	−0.266195
$571$	26.8275	1.12270	0.561348	−	0.827580i	$-0.310283\pi$
$571$	26.8275	1.12270	0.561348	+	0.827580i	$0.310283\pi$
$572$	−33.1971	−1.38804
$573$	14.8768	0.621489
$574$	−0.835390	−0.0348685
$575$	−71.7363	−2.99161
$576$	−4.00309	−0.166795
$577$	−14.6210	−0.608679	−0.304339	−	0.952564i	$-0.598436\pi$
$577$	−14.6210	−0.608679	−0.304339	+	0.952564i	$0.598436\pi$
$578$	0.578684	0.0240701
$579$	9.86771	0.410088
$580$	−31.1387	−1.29296
$581$	−12.1091	−0.502370
$582$	4.84550	0.200852
$583$	−10.8551	−0.449571
$584$	0.120270	0.00497679
$585$	−27.3165	−1.12940
$586$	4.12768	0.170513
$587$	−16.7517	−0.691418	−0.345709	−	0.938342i	$-0.612362\pi$
$587$	−16.7517	−0.691418	−0.345709	+	0.938342i	$0.612362\pi$
$588$	1.82024	0.0750654
$589$	−25.9618	−1.06974
$590$	19.5704	0.805700
$591$	18.4583	0.759271
$592$	18.9031	0.776914
$593$	−2.52161	−0.103550	−0.0517750	−	0.998659i	$-0.516488\pi$
$593$	−2.52161	−0.103550	−0.0517750	+	0.998659i	$0.516488\pi$
$594$	−1.21298	−0.0497693
$595$	−18.3635	−0.752831
$596$	−38.3187	−1.56960
$597$	−24.0396	−0.983874
$598$	−14.5102	−0.593365
$599$	4.08212	0.166791	0.0833954	−	0.996517i	$-0.473424\pi$
$599$	4.08212	0.166791	0.0833954	+	0.996517i	$0.473424\pi$
$600$	21.6428	0.883563
$601$	−28.0653	−1.14481	−0.572405	−	0.819971i	$-0.693989\pi$
$601$	−28.0653	−1.14481	−0.572405	+	0.819971i	$0.693989\pi$
$602$	3.08118	0.125580
$603$	9.99054	0.406846
$604$	39.3863	1.60261
$605$	12.0628	0.490423
$606$	−7.62310	−0.309667
$607$	23.2616	0.944158	0.472079	−	0.881556i	$-0.343504\pi$
$607$	23.2616	0.944158	0.472079	+	0.881556i	$0.343504\pi$
$608$	−15.7125	−0.637226
$609$	3.99217	0.161771
$610$	8.32587	0.337105
$611$	3.44187	0.139243
$612$	−7.80051	−0.315317
$613$	8.14155	0.328834	0.164417	−	0.986391i	$-0.447426\pi$
$613$	8.14155	0.328834	0.164417	+	0.986391i	$0.447426\pi$
$614$	−3.19697	−0.129019
$615$	−8.44315	−0.340461
$616$	−4.63388	−0.186704
$617$	−17.5691	−0.707306	−0.353653	−	0.935377i	$-0.615061\pi$
$617$	−17.5691	−0.707306	−0.353653	+	0.935377i	$0.615061\pi$
$618$	3.68973	0.148423
$619$	5.41343	0.217584	0.108792	−	0.994065i	$-0.465302\pi$
$619$	5.41343	0.217584	0.108792	+	0.994065i	$0.465302\pi$
$620$	57.8890	2.32488
$621$	5.36862	0.215435
$622$	4.11249	0.164896
$623$	7.42795	0.297595
$624$	−18.8294	−0.753781
$625$	86.7363	3.46945
$626$	−6.06573	−0.242435
$627$	10.0078	0.399672
$628$	−3.32569	−0.132709
$629$	27.4254	1.09352
$630$	−1.81680	−0.0723832
$631$	11.4719	0.456688	0.228344	−	0.973581i	$-0.426669\pi$
$631$	11.4719	0.456688	0.228344	+	0.973581i	$0.426669\pi$
$632$	4.72291	0.187867
$633$	5.38105	0.213878
$634$	2.75511	0.109420
$635$	−79.4476	−3.15278
$636$	−6.90643	−0.273858
$637$	6.37475	0.252577
$638$	−4.84244	−0.191714
$639$	−10.9198	−0.431982
$640$	45.7681	1.80914
$641$	39.5053	1.56037	0.780183	−	0.625552i	$-0.215126\pi$
$641$	39.5053	1.56037	0.780183	+	0.625552i	$0.215126\pi$
$642$	−2.79998	−0.110507
$643$	−38.6819	−1.52547	−0.762733	−	0.646713i	$-0.776143\pi$
$643$	−38.6819	−1.52547	−0.762733	+	0.646713i	$0.776143\pi$
$644$	9.77218	0.385078
$645$	31.1410	1.22618
$646$	−6.35579	−0.250065
$647$	−8.98778	−0.353346	−0.176673	−	0.984270i	$-0.556534\pi$
$647$	−8.98778	−0.353346	−0.176673	+	0.984270i	$0.556534\pi$
$648$	−1.61971	−0.0636282
$649$	−30.8176	−1.20970
$650$	36.1149	1.41654
$651$	−7.42174	−0.290881
$652$	30.2903	1.18626
$653$	37.0396	1.44947	0.724735	−	0.689027i	$-0.241962\pi$
$653$	37.0396	1.44947	0.724735	+	0.689027i	$0.241962\pi$
$654$	−2.37204	−0.0927543
$655$	−88.4469	−3.45591
$656$	−5.81992	−0.227230
$657$	−0.0742538	−0.00289692
$658$	0.228917	0.00892410
$659$	−4.16250	−0.162148	−0.0810740	−	0.996708i	$-0.525835\pi$
$659$	−4.16250	−0.162148	−0.0810740	+	0.996708i	$0.525835\pi$
$660$	−22.3151	−0.868613
$661$	−20.1438	−0.783501	−0.391751	−	0.920071i	$-0.628130\pi$
$661$	−20.1438	−0.783501	−0.391751	+	0.920071i	$0.628130\pi$
$662$	4.14749	0.161197
$663$	−27.3185	−1.06096
$664$	19.6132	0.761140
$665$	14.9896	0.581273
$666$	2.71335	0.105140
$667$	21.4325	0.829868
$668$	32.2678	1.24848
$669$	12.8459	0.496652
$670$	−18.1509	−0.701229
$671$	−13.1108	−0.506137
$672$	−4.49175	−0.173273
$673$	−40.7921	−1.57242	−0.786211	−	0.617958i	$-0.787960\pi$
$673$	−40.7921	−1.57242	−0.786211	+	0.617958i	$0.787960\pi$
$674$	3.58500	0.138089
$675$	−13.3621	−0.514309
$676$	−50.3068	−1.93488
$677$	−43.2052	−1.66051	−0.830255	−	0.557384i	$-0.811805\pi$
$677$	−43.2052	−1.66051	−0.830255	+	0.557384i	$0.811805\pi$
$678$	−3.90393	−0.149929
$679$	−11.4286	−0.438589
$680$	29.7436	1.14061
$681$	5.41190	0.207385
$682$	9.00243	0.344721
$683$	−5.11872	−0.195862	−0.0979312	−	0.995193i	$-0.531223\pi$
$683$	−5.11872	−0.195862	−0.0979312	+	0.995193i	$0.531223\pi$
$684$	6.36734	0.243461
$685$	−53.0798	−2.02808
$686$	0.423981	0.0161877
$687$	−7.01390	−0.267597
$688$	21.4657	0.818372
$689$	−24.1873	−0.921464
$690$	−9.75373	−0.371318
$691$	−37.0490	−1.40941	−0.704705	−	0.709500i	$-0.748921\pi$
$691$	−37.0490	−1.40941	−0.704705	+	0.709500i	$0.748921\pi$
$692$	8.16114	0.310240
$693$	2.86093	0.108678
$694$	7.64942	0.290368
$695$	14.0039	0.531200
$696$	−6.46616	−0.245099
$697$	−8.44378	−0.319831
$698$	6.26933	0.237298
$699$	−12.3359	−0.466588
$700$	−24.3223	−0.919297
$701$	32.3787	1.22293	0.611464	−	0.791273i	$-0.290581\pi$
$701$	32.3787	1.22293	0.611464	+	0.791273i	$0.290581\pi$
$702$	−2.70277	−0.102010
$703$	−22.3866	−0.844328
$704$	−11.4526	−0.431635
$705$	2.31362	0.0871361
$706$	3.24171	0.122003
$707$	17.9798	0.676201
$708$	−19.6074	−0.736891
$709$	−10.2172	−0.383715	−0.191857	−	0.981423i	$-0.561451\pi$
$709$	−10.2172	−0.383715	−0.191857	+	0.981423i	$0.561451\pi$
$710$	19.8392	0.744551
$711$	−2.91590	−0.109355
$712$	−12.0311	−0.450885
$713$	−39.8445	−1.49219
$714$	−1.81694	−0.0679972
$715$	−78.1507	−2.92267
$716$	4.63464	0.173205
$717$	−28.3785	−1.05981
$718$	8.67616	0.323791
$719$	−19.5816	−0.730271	−0.365136	−	0.930954i	$-0.618977\pi$
$719$	−19.5816	−0.730271	−0.365136	+	0.930954i	$0.618977\pi$
$720$	−12.6572	−0.471704
$721$	−8.70259	−0.324102
$722$	−2.86758	−0.106720
$723$	27.7510	1.03207
$724$	−41.1961	−1.53104
$725$	−53.3440	−1.98115
$726$	1.19353	0.0442960
$727$	44.7063	1.65807	0.829033	−	0.559200i	$-0.188892\pi$
$727$	44.7063	1.65807	0.829033	+	0.559200i	$0.188892\pi$
$728$	−10.3252	−0.382679
$729$	1.00000	0.0370370
$730$	0.134905	0.00499305
$731$	31.1433	1.15188
$732$	−8.34162	−0.308315
$733$	1.70203	0.0628660	0.0314330	−	0.999506i	$-0.489993\pi$
$733$	1.70203	0.0628660	0.0314330	+	0.999506i	$0.489993\pi$
$734$	−5.79221	−0.213794
$735$	4.28511	0.158059
$736$	−24.1145	−0.888873
$737$	28.5823	1.05284
$738$	−0.835390	−0.0307511
$739$	50.0503	1.84113	0.920566	−	0.390587i	$-0.127728\pi$
$739$	50.0503	1.84113	0.920566	+	0.390587i	$0.127728\pi$
$740$	49.9172	1.83499
$741$	22.2994	0.819187
$742$	−1.60869	−0.0590567
$743$	33.1952	1.21781	0.608907	−	0.793242i	$-0.291608\pi$
$743$	33.1952	1.21781	0.608907	+	0.793242i	$0.291608\pi$
$744$	12.0211	0.440713
$745$	−90.2079	−3.30496
$746$	9.42776	0.345175
$747$	−12.1091	−0.443049
$748$	−22.3167	−0.815981
$749$	6.60403	0.241306
$750$	15.1924	0.554748
$751$	17.1239	0.624859	0.312429	−	0.949941i	$-0.398857\pi$
$751$	17.1239	0.624859	0.312429	+	0.949941i	$0.398857\pi$
$752$	1.59480	0.0581563
$753$	17.0166	0.620121
$754$	−10.7899	−0.392946
$755$	92.7211	3.37446
$756$	1.82024	0.0662015
$757$	38.7567	1.40864	0.704318	−	0.709884i	$-0.251253\pi$
$757$	38.7567	1.40864	0.704318	+	0.709884i	$0.251253\pi$
$758$	−2.29970	−0.0835289
$759$	15.3593	0.557506
$760$	−24.2788	−0.880686
$761$	29.9354	1.08516	0.542579	−	0.840005i	$-0.317448\pi$
$761$	29.9354	1.08516	0.542579	+	0.840005i	$0.317448\pi$
$762$	−7.86078	−0.284766
$763$	5.59469	0.202542
$764$	27.0794	0.979700
$765$	−18.3635	−0.663934
$766$	−0.423981	−0.0153191
$767$	−68.6680	−2.47946
$768$	−3.47775	−0.125492
$769$	2.46401	0.0888546	0.0444273	−	0.999013i	$-0.485854\pi$
$769$	2.46401	0.0888546	0.0444273	+	0.999013i	$0.485854\pi$
$770$	−5.19776	−0.187314
$771$	−4.35360	−0.156791
$772$	17.9616	0.646452
$773$	36.3389	1.30702	0.653510	−	0.756918i	$-0.273296\pi$
$773$	36.3389	1.30702	0.653510	+	0.756918i	$0.273296\pi$
$774$	3.08118	0.110751
$775$	99.1704	3.56230
$776$	18.5110	0.664505
$777$	−6.39970	−0.229588
$778$	−2.38154	−0.0853823
$779$	6.89242	0.246947
$780$	−49.7226	−1.78035
$781$	−31.2409	−1.11789
$782$	−9.75446	−0.348819
$783$	3.99217	0.142669
$784$	2.95375	0.105491
$785$	−7.82915	−0.279434
$786$	−8.75120	−0.312145
$787$	22.9792	0.819119	0.409559	−	0.912283i	$-0.365682\pi$
$787$	22.9792	0.819119	0.409559	+	0.912283i	$0.365682\pi$
$788$	33.5985	1.19690
$789$	25.8851	0.921532
$790$	5.29762	0.188481
$791$	9.20778	0.327391
$792$	−4.63388	−0.164658
$793$	−29.2136	−1.03740
$794$	3.54419	0.125779
$795$	−16.2587	−0.576637
$796$	−43.7578	−1.55095
$797$	−23.5252	−0.833306	−0.416653	−	0.909066i	$-0.636797\pi$
$797$	−23.5252	−0.833306	−0.416653	+	0.909066i	$0.636797\pi$
$798$	1.48312	0.0525018
$799$	2.31380	0.0818562
$800$	60.0195	2.12201
$801$	7.42795	0.262454
$802$	−3.54603	−0.125215
$803$	−0.212435	−0.00749668
$804$	18.1852	0.641342
$805$	23.0051	0.810824
$806$	20.0593	0.706558
$807$	−15.9730	−0.562277
$808$	−29.1221	−1.02451
$809$	29.8181	1.04835	0.524174	−	0.851611i	$-0.324374\pi$
$809$	29.8181	1.04835	0.524174	+	0.851611i	$0.324374\pi$
$810$	−1.81680	−0.0638360
$811$	−31.1411	−1.09351	−0.546755	−	0.837292i	$-0.684137\pi$
$811$	−31.1411	−1.09351	−0.546755	+	0.837292i	$0.684137\pi$
$812$	7.26672	0.255012
$813$	−9.43949	−0.331057
$814$	7.76272	0.272083
$815$	71.3078	2.49780
$816$	−12.6581	−0.443122
$817$	−25.4214	−0.889383
$818$	−4.44245	−0.155327
$819$	6.37475	0.222752
$820$	−15.3686	−0.536693
$821$	−14.2169	−0.496174	−0.248087	−	0.968738i	$-0.579802\pi$
$821$	−14.2169	−0.496174	−0.248087	+	0.968738i	$0.579802\pi$
$822$	−5.25187	−0.183180
$823$	−21.2804	−0.741788	−0.370894	−	0.928675i	$-0.620949\pi$
$823$	−21.2804	−0.741788	−0.370894	+	0.928675i	$0.620949\pi$
$824$	14.0957	0.491046
$825$	−38.2282	−1.33094
$826$	−4.56707	−0.158909
$827$	−5.22326	−0.181630	−0.0908152	−	0.995868i	$-0.528947\pi$
$827$	−5.22326	−0.181630	−0.0908152	+	0.995868i	$0.528947\pi$
$828$	9.77218	0.339607
$829$	22.2251	0.771908	0.385954	−	0.922518i	$-0.373872\pi$
$829$	22.2251	0.771908	0.385954	+	0.922518i	$0.373872\pi$
$830$	21.9999	0.763626
$831$	−29.3846	−1.01934
$832$	−25.5187	−0.884702
$833$	4.28543	0.148481
$834$	1.38559	0.0479791
$835$	75.9630	2.62881
$836$	18.2165	0.630032
$837$	−7.42174	−0.256533
$838$	−2.26529	−0.0782532
$839$	−1.18068	−0.0407616	−0.0203808	−	0.999792i	$-0.506488\pi$
$839$	−1.18068	−0.0407616	−0.0203808	+	0.999792i	$0.506488\pi$
$840$	−6.94063	−0.239474
$841$	−13.0625	−0.450433
$842$	−4.40664	−0.151863
$843$	−26.8495	−0.924746
$844$	9.79481	0.337151
$845$	−118.429	−4.07410
$846$	0.228917	0.00787032
$847$	−2.81505	−0.0967263
$848$	−11.2072	−0.384859
$849$	12.4652	0.427806
$850$	24.2782	0.832736
$851$	−34.3575	−1.17776
$852$	−19.8767	−0.680965
$853$	−37.0265	−1.26776	−0.633882	−	0.773430i	$-0.718540\pi$
$853$	−37.0265	−1.26776	−0.633882	+	0.773430i	$0.718540\pi$
$854$	−1.94298	−0.0664873
$855$	14.9896	0.512635
$856$	−10.6966	−0.365603
$857$	28.0542	0.958313	0.479157	−	0.877729i	$-0.340943\pi$
$857$	28.0542	0.958313	0.479157	+	0.877729i	$0.340943\pi$
$858$	−7.73246	−0.263982
$859$	26.8377	0.915691	0.457846	−	0.889032i	$-0.348621\pi$
$859$	26.8377	0.915691	0.457846	+	0.889032i	$0.348621\pi$
$860$	56.6841	1.93291
$861$	1.97035	0.0671492
$862$	10.2045	0.347565
$863$	−8.22038	−0.279825	−0.139913	−	0.990164i	$-0.544682\pi$
$863$	−8.22038	−0.279825	−0.139913	+	0.990164i	$0.544682\pi$
$864$	−4.49175	−0.152813
$865$	19.2125	0.653245
$866$	1.44734	0.0491827
$867$	−1.36488	−0.0463538
$868$	−13.5093	−0.458537
$869$	−8.34220	−0.282990
$870$	−7.25300	−0.245900
$871$	63.6872	2.15796
$872$	−9.06178	−0.306871
$873$	−11.4286	−0.386799
$874$	7.96229	0.269329
$875$	−35.8327	−1.21137
$876$	−0.135160	−0.00456663
$877$	22.7121	0.766935	0.383467	−	0.923554i	$-0.374730\pi$
$877$	22.7121	0.766935	0.383467	+	0.923554i	$0.374730\pi$
$878$	16.1956	0.546575
$879$	−9.73554	−0.328372
$880$	−36.2113	−1.22068
$881$	48.1457	1.62207	0.811035	−	0.584997i	$-0.198905\pi$
$881$	48.1457	1.62207	0.811035	+	0.584997i	$0.198905\pi$
$882$	0.423981	0.0142762
$883$	49.6376	1.67044	0.835219	−	0.549918i	$-0.185341\pi$
$883$	49.6376	1.67044	0.835219	+	0.549918i	$0.185341\pi$
$884$	−49.7263	−1.67248
$885$	−46.1586	−1.55161
$886$	−4.49577	−0.151038
$887$	7.42430	0.249284	0.124642	−	0.992202i	$-0.460222\pi$
$887$	7.42430	0.249284	0.124642	+	0.992202i	$0.460222\pi$
$888$	10.3656	0.347848
$889$	18.5404	0.621825
$890$	−13.4951	−0.452358
$891$	2.86093	0.0958449
$892$	23.3827	0.782909
$893$	−1.88869	−0.0632025
$894$	−8.92543	−0.298511
$895$	10.9106	0.364701
$896$	−10.6807	−0.356819
$897$	34.2236	1.14269
$898$	−2.13950	−0.0713959
$899$	−29.6289	−0.988178
$900$	−24.3223	−0.810744
$901$	−16.2599	−0.541697
$902$	−2.39000	−0.0795781
$903$	−7.26726	−0.241839
$904$	−14.9139	−0.496030
$905$	−96.9816	−3.22378
$906$	9.17409	0.304789
$907$	10.2075	0.338934	0.169467	−	0.985536i	$-0.445795\pi$
$907$	10.2075	0.338934	0.169467	+	0.985536i	$0.445795\pi$
$908$	9.85096	0.326916
$909$	17.9798	0.596353
$910$	−11.5817	−0.383929
$911$	35.4903	1.17585	0.587923	−	0.808917i	$-0.299946\pi$
$911$	35.4903	1.17585	0.587923	+	0.808917i	$0.299946\pi$
$912$	10.3325	0.342142
$913$	−34.6433	−1.14653
$914$	−4.18919	−0.138566
$915$	−19.6374	−0.649191
$916$	−12.7670	−0.421833
$917$	20.6405	0.681611
$918$	−1.81694	−0.0599679
$919$	−43.6977	−1.44145	−0.720726	−	0.693220i	$-0.756192\pi$
$919$	−43.6977	−1.44145	−0.720726	+	0.693220i	$0.756192\pi$
$920$	−37.2616	−1.22848
$921$	7.54036	0.248463
$922$	−16.7011	−0.550023
$923$	−69.6112	−2.29128
$924$	5.20759	0.171317
$925$	85.5137	2.81167
$926$	−1.72991	−0.0568484
$927$	−8.70259	−0.285831
$928$	−17.9319	−0.588642
$929$	−15.6630	−0.513886	−0.256943	−	0.966427i	$-0.582715\pi$
$929$	−15.6630	−0.513886	−0.256943	+	0.966427i	$0.582715\pi$
$930$	13.4838	0.442153
$931$	−3.49808	−0.114645
$932$	−22.4544	−0.735517
$933$	−9.69970	−0.317554
$934$	−6.01993	−0.196978
$935$	−52.5368	−1.71814
$936$	−10.3252	−0.337491
$937$	10.3033	0.336596	0.168298	−	0.985736i	$-0.446173\pi$
$937$	10.3033	0.336596	0.168298	+	0.985736i	$0.446173\pi$
$938$	4.23580	0.138304
$939$	14.3066	0.466878
$940$	4.21135	0.137359
$941$	20.3609	0.663745	0.331872	−	0.943324i	$-0.392320\pi$
$941$	20.3609	0.663745	0.331872	+	0.943324i	$0.392320\pi$
$942$	−0.774638	−0.0252391
$943$	10.5780	0.344469
$944$	−31.8175	−1.03557
$945$	4.28511	0.139395
$946$	8.81506	0.286602
$947$	53.6514	1.74344	0.871718	−	0.490007i	$-0.163006\pi$
$947$	53.6514	1.74344	0.871718	+	0.490007i	$0.163006\pi$
$948$	−5.30764	−0.172384
$949$	−0.473350	−0.0153656
$950$	−19.8176	−0.642969
$951$	−6.49820	−0.210719
$952$	−6.94114	−0.224964
$953$	14.4027	0.466549	0.233274	−	0.972411i	$-0.425056\pi$
$953$	14.4027	0.466549	0.233274	+	0.972411i	$0.425056\pi$
$954$	−1.60869	−0.0520831
$955$	63.7489	2.06287
$956$	−51.6557	−1.67066
$957$	11.4213	0.369200
$958$	−3.67416	−0.118707
$959$	12.3870	0.399999
$960$	−17.1537	−0.553632
$961$	24.0822	0.776844
$962$	17.2969	0.557675
$963$	6.60403	0.212812
$964$	50.5135	1.62693
$965$	42.2842	1.36118
$966$	2.27619	0.0732353
$967$	50.6335	1.62826	0.814131	−	0.580681i	$-0.197214\pi$
$967$	50.6335	1.62826	0.814131	+	0.580681i	$0.197214\pi$
$968$	4.55957	0.146550
$969$	14.9907	0.481572
$970$	20.7635	0.666675
$971$	24.3944	0.782855	0.391427	−	0.920209i	$-0.371981\pi$
$971$	24.3944	0.782855	0.391427	+	0.920209i	$0.371981\pi$
$972$	1.82024	0.0583842
$973$	−3.26805	−0.104769
$974$	−1.46273	−0.0468688
$975$	−85.1804	−2.72796
$976$	−13.5362	−0.433282
$977$	29.4481	0.942127	0.471064	−	0.882099i	$-0.343870\pi$
$977$	29.4481	0.942127	0.471064	+	0.882099i	$0.343870\pi$
$978$	7.05540	0.225607
$979$	21.2509	0.679181
$980$	7.79993	0.249159
$981$	5.59469	0.178625
$982$	11.7928	0.376322
$983$	−44.9851	−1.43480	−0.717401	−	0.696660i	$-0.754669\pi$
$983$	−44.9851	−1.43480	−0.717401	+	0.696660i	$0.754669\pi$
$984$	−3.19139	−0.101738
$985$	79.0956	2.52020
$986$	−7.25354	−0.231000
$987$	−0.539922	−0.0171859
$988$	40.5902	1.29135
$989$	−39.0152	−1.24061
$990$	−5.19776	−0.165196
$991$	41.8636	1.32984	0.664920	−	0.746914i	$-0.268466\pi$
$991$	41.8636	1.32984	0.664920	+	0.746914i	$0.268466\pi$
$992$	33.3366	1.05844
$993$	−9.78226	−0.310431
$994$	−4.62980	−0.146848
$995$	−103.012	−3.26570
$996$	−22.0415	−0.698410
$997$	−27.5172	−0.871478	−0.435739	−	0.900073i	$-0.643513\pi$
$997$	−27.5172	−0.871478	−0.435739	+	0.900073i	$0.643513\pi$
$998$	−2.65522	−0.0840494
$999$	−6.39970	−0.202477

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.t.1.29	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.t.1.29	✓	52	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q+0.423981 q^{2} -1.00000 q^{3} -1.82024 q^{4} -4.28511 q^{5} -0.423981 q^{6} +1.00000 q^{7} -1.61971 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.423981 q^{2} -1.00000 q^{3} -1.82024 q^{4} -4.28511 q^{5} -0.423981 q^{6} +1.00000 q^{7} -1.61971 q^{8} +1.00000 q^{9} -1.81680 q^{10} +2.86093 q^{11} +1.82024 q^{12} +6.37475 q^{13} +0.423981 q^{14} +4.28511 q^{15} +2.95375 q^{16} +4.28543 q^{17} +0.423981 q^{18} -3.49808 q^{19} +7.79993 q^{20} -1.00000 q^{21} +1.21298 q^{22} -5.36862 q^{23} +1.61971 q^{24} +13.3621 q^{25} +2.70277 q^{26} -1.00000 q^{27} -1.82024 q^{28} -3.99217 q^{29} +1.81680 q^{30} +7.42174 q^{31} +4.49175 q^{32} -2.86093 q^{33} +1.81694 q^{34} -4.28511 q^{35} -1.82024 q^{36} +6.39970 q^{37} -1.48312 q^{38} -6.37475 q^{39} +6.94063 q^{40} -1.97035 q^{41} -0.423981 q^{42} +7.26726 q^{43} -5.20759 q^{44} -4.28511 q^{45} -2.27619 q^{46} +0.539922 q^{47} -2.95375 q^{48} +1.00000 q^{49} +5.66530 q^{50} -4.28543 q^{51} -11.6036 q^{52} -3.79424 q^{53} -0.423981 q^{54} -12.2594 q^{55} -1.61971 q^{56} +3.49808 q^{57} -1.69261 q^{58} -10.7719 q^{59} -7.79993 q^{60} -4.58270 q^{61} +3.14668 q^{62} +1.00000 q^{63} -4.00309 q^{64} -27.3165 q^{65} -1.21298 q^{66} +9.99054 q^{67} -7.80051 q^{68} +5.36862 q^{69} -1.81680 q^{70} -10.9198 q^{71} -1.61971 q^{72} -0.0742538 q^{73} +2.71335 q^{74} -13.3621 q^{75} +6.36734 q^{76} +2.86093 q^{77} -2.70277 q^{78} -2.91590 q^{79} -12.6572 q^{80} +1.00000 q^{81} -0.835390 q^{82} -12.1091 q^{83} +1.82024 q^{84} -18.3635 q^{85} +3.08118 q^{86} +3.99217 q^{87} -4.63388 q^{88} +7.42795 q^{89} -1.81680 q^{90} +6.37475 q^{91} +9.77218 q^{92} -7.42174 q^{93} +0.228917 q^{94} +14.9896 q^{95} -4.49175 q^{96} -11.4286 q^{97} +0.423981 q^{98} +2.86093 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9} - 2 q^{10} + 9 q^{11} - 61 q^{12} + 44 q^{13} + 3 q^{14} + 7 q^{15} + 95 q^{16} - 6 q^{17} + 3 q^{18} + 7 q^{19} - 21 q^{20} - 52 q^{21} + 19 q^{22} - 4 q^{23} - 24 q^{24} + 83 q^{25} - 5 q^{26} - 52 q^{27} + 61 q^{28} + 31 q^{29} + 2 q^{30} + 11 q^{31} + 71 q^{32} - 9 q^{33} + 17 q^{34} - 7 q^{35} + 61 q^{36} + 71 q^{37} - 8 q^{38} - 44 q^{39} + 20 q^{40} - 25 q^{41} - 3 q^{42} + 75 q^{43} + 14 q^{44} - 7 q^{45} + 36 q^{46} - 20 q^{47} - 95 q^{48} + 52 q^{49} + 26 q^{50} + 6 q^{51} + 88 q^{52} + 70 q^{53} - 3 q^{54} + 12 q^{55} + 24 q^{56} - 7 q^{57} + 48 q^{58} - 27 q^{59} + 21 q^{60} + 59 q^{61} - 23 q^{62} + 52 q^{63} + 138 q^{64} + 44 q^{65} - 19 q^{66} + 65 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{70} - 11 q^{71} + 24 q^{72} + 34 q^{73} + 38 q^{74} - 83 q^{75} + 31 q^{76} + 9 q^{77} + 5 q^{78} + 74 q^{79} - 5 q^{80} + 52 q^{81} + 51 q^{82} - 30 q^{83} - 61 q^{84} + 70 q^{85} + 29 q^{86} - 31 q^{87} + 90 q^{88} - q^{89} - 2 q^{90} + 44 q^{91} + 34 q^{92} - 11 q^{93} + 27 q^{94} + 9 q^{95} - 71 q^{96} + 73 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9 - 2 * q^10 + 9 * q^11 - 61 * q^12 + 44 * q^13 + 3 * q^14 + 7 * q^15 + 95 * q^16 - 6 * q^17 + 3 * q^18 + 7 * q^19 - 21 * q^20 - 52 * q^21 + 19 * q^22 - 4 * q^23 - 24 * q^24 + 83 * q^25 - 5 * q^26 - 52 * q^27 + 61 * q^28 + 31 * q^29 + 2 * q^30 + 11 * q^31 + 71 * q^32 - 9 * q^33 + 17 * q^34 - 7 * q^35 + 61 * q^36 + 71 * q^37 - 8 * q^38 - 44 * q^39 + 20 * q^40 - 25 * q^41 - 3 * q^42 + 75 * q^43 + 14 * q^44 - 7 * q^45 + 36 * q^46 - 20 * q^47 - 95 * q^48 + 52 * q^49 + 26 * q^50 + 6 * q^51 + 88 * q^52 + 70 * q^53 - 3 * q^54 + 12 * q^55 + 24 * q^56 - 7 * q^57 + 48 * q^58 - 27 * q^59 + 21 * q^60 + 59 * q^61 - 23 * q^62 + 52 * q^63 + 138 * q^64 + 44 * q^65 - 19 * q^66 + 65 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^70 - 11 * q^71 + 24 * q^72 + 34 * q^73 + 38 * q^74 - 83 * q^75 + 31 * q^76 + 9 * q^77 + 5 * q^78 + 74 * q^79 - 5 * q^80 + 52 * q^81 + 51 * q^82 - 30 * q^83 - 61 * q^84 + 70 * q^85 + 29 * q^86 - 31 * q^87 + 90 * q^88 - q^89 - 2 * q^90 + 44 * q^91 + 34 * q^92 - 11 * q^93 + 27 * q^94 + 9 * q^95 - 71 * q^96 + 73 * q^97 + 3 * q^98 + 9 * q^99

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