LMFDB - Embedded newform 8018.2.a.k.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.460040 q^{3} +1.00000 q^{4} -0.746209 q^{5} -0.460040 q^{6} -4.50236 q^{7} +1.00000 q^{8} -2.78836 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.460040 q^{3} +1.00000 q^{4} -0.746209 q^{5} -0.460040 q^{6} -4.50236 q^{7} +1.00000 q^{8} -2.78836 q^{9} -0.746209 q^{10} -0.256350 q^{11} -0.460040 q^{12} +2.84000 q^{13} -4.50236 q^{14} +0.343286 q^{15} +1.00000 q^{16} -2.44196 q^{17} -2.78836 q^{18} +1.00000 q^{19} -0.746209 q^{20} +2.07126 q^{21} -0.256350 q^{22} -4.38723 q^{23} -0.460040 q^{24} -4.44317 q^{25} +2.84000 q^{26} +2.66288 q^{27} -4.50236 q^{28} -6.48624 q^{29} +0.343286 q^{30} +3.86450 q^{31} +1.00000 q^{32} +0.117931 q^{33} -2.44196 q^{34} +3.35970 q^{35} -2.78836 q^{36} -4.11156 q^{37} +1.00000 q^{38} -1.30651 q^{39} -0.746209 q^{40} -3.55157 q^{41} +2.07126 q^{42} +7.52143 q^{43} -0.256350 q^{44} +2.08070 q^{45} -4.38723 q^{46} -12.5980 q^{47} -0.460040 q^{48} +13.2712 q^{49} -4.44317 q^{50} +1.12340 q^{51} +2.84000 q^{52} +2.21292 q^{53} +2.66288 q^{54} +0.191291 q^{55} -4.50236 q^{56} -0.460040 q^{57} -6.48624 q^{58} +1.94036 q^{59} +0.343286 q^{60} +7.65724 q^{61} +3.86450 q^{62} +12.5542 q^{63} +1.00000 q^{64} -2.11923 q^{65} +0.117931 q^{66} +5.07022 q^{67} -2.44196 q^{68} +2.01830 q^{69} +3.35970 q^{70} -2.65720 q^{71} -2.78836 q^{72} +10.5873 q^{73} -4.11156 q^{74} +2.04404 q^{75} +1.00000 q^{76} +1.15418 q^{77} -1.30651 q^{78} +10.3761 q^{79} -0.746209 q^{80} +7.14006 q^{81} -3.55157 q^{82} +9.13287 q^{83} +2.07126 q^{84} +1.82221 q^{85} +7.52143 q^{86} +2.98393 q^{87} -0.256350 q^{88} +3.48874 q^{89} +2.08070 q^{90} -12.7867 q^{91} -4.38723 q^{92} -1.77782 q^{93} -12.5980 q^{94} -0.746209 q^{95} -0.460040 q^{96} +13.0307 q^{97} +13.2712 q^{98} +0.714798 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9}+O(q^{10}) $ 49 * q + 49 * q^2 + 13 * q^3 + 49 * q^4 + 17 * q^5 + 13 * q^6 + 22 * q^7 + 49 * q^8 + 66 * q^9	\( 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9} + 17 q^{10} + 21 q^{11} + 13 q^{12} + 13 q^{13} + 22 q^{14} + 8 q^{15} + 49 q^{16} + 24 q^{17} + 66 q^{18} + 49 q^{19} + 17 q^{20} + 6 q^{21} + 21 q^{22} + 22 q^{23} + 13 q^{24} + 96 q^{25} + 13 q^{26} + 31 q^{27} + 22 q^{28} + 33 q^{29} + 8 q^{30} + 21 q^{31} + 49 q^{32} + 20 q^{33} + 24 q^{34} + 18 q^{35} + 66 q^{36} + 48 q^{37} + 49 q^{38} + 4 q^{39} + 17 q^{40} + 37 q^{41} + 6 q^{42} + 43 q^{43} + 21 q^{44} + 47 q^{45} + 22 q^{46} + 7 q^{47} + 13 q^{48} + 87 q^{49} + 96 q^{50} + 12 q^{51} + 13 q^{52} + 23 q^{53} + 31 q^{54} + 31 q^{55} + 22 q^{56} + 13 q^{57} + 33 q^{58} + 37 q^{59} + 8 q^{60} + 61 q^{61} + 21 q^{62} + 45 q^{63} + 49 q^{64} + 36 q^{65} + 20 q^{66} + 43 q^{67} + 24 q^{68} + 18 q^{69} + 18 q^{70} + 14 q^{71} + 66 q^{72} + 90 q^{73} + 48 q^{74} + 53 q^{75} + 49 q^{76} + 46 q^{77} + 4 q^{78} + 16 q^{79} + 17 q^{80} + 97 q^{81} + 37 q^{82} + 11 q^{83} + 6 q^{84} + 88 q^{85} + 43 q^{86} - 35 q^{87} + 21 q^{88} + 46 q^{89} + 47 q^{90} + 27 q^{91} + 22 q^{92} + 9 q^{93} + 7 q^{94} + 17 q^{95} + 13 q^{96} + 34 q^{97} + 87 q^{98} + 84 q^{99}+O(q^{100}) \) 49 * q + 49 * q^2 + 13 * q^3 + 49 * q^4 + 17 * q^5 + 13 * q^6 + 22 * q^7 + 49 * q^8 + 66 * q^9 + 17 * q^10 + 21 * q^11 + 13 * q^12 + 13 * q^13 + 22 * q^14 + 8 * q^15 + 49 * q^16 + 24 * q^17 + 66 * q^18 + 49 * q^19 + 17 * q^20 + 6 * q^21 + 21 * q^22 + 22 * q^23 + 13 * q^24 + 96 * q^25 + 13 * q^26 + 31 * q^27 + 22 * q^28 + 33 * q^29 + 8 * q^30 + 21 * q^31 + 49 * q^32 + 20 * q^33 + 24 * q^34 + 18 * q^35 + 66 * q^36 + 48 * q^37 + 49 * q^38 + 4 * q^39 + 17 * q^40 + 37 * q^41 + 6 * q^42 + 43 * q^43 + 21 * q^44 + 47 * q^45 + 22 * q^46 + 7 * q^47 + 13 * q^48 + 87 * q^49 + 96 * q^50 + 12 * q^51 + 13 * q^52 + 23 * q^53 + 31 * q^54 + 31 * q^55 + 22 * q^56 + 13 * q^57 + 33 * q^58 + 37 * q^59 + 8 * q^60 + 61 * q^61 + 21 * q^62 + 45 * q^63 + 49 * q^64 + 36 * q^65 + 20 * q^66 + 43 * q^67 + 24 * q^68 + 18 * q^69 + 18 * q^70 + 14 * q^71 + 66 * q^72 + 90 * q^73 + 48 * q^74 + 53 * q^75 + 49 * q^76 + 46 * q^77 + 4 * q^78 + 16 * q^79 + 17 * q^80 + 97 * q^81 + 37 * q^82 + 11 * q^83 + 6 * q^84 + 88 * q^85 + 43 * q^86 - 35 * q^87 + 21 * q^88 + 46 * q^89 + 47 * q^90 + 27 * q^91 + 22 * q^92 + 9 * q^93 + 7 * q^94 + 17 * q^95 + 13 * q^96 + 34 * q^97 + 87 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.460040	−0.265604	−0.132802	−	0.991143i	$-0.542397\pi$
$3$	−0.460040	−0.265604	−0.132802	+	0.991143i	$0.542397\pi$
$4$	1.00000	0.500000
$5$	−0.746209	−0.333715	−0.166857	−	0.985981i	$-0.553362\pi$
$5$	−0.746209	−0.333715	−0.166857	+	0.985981i	$0.553362\pi$
$6$	−0.460040	−0.187810
$7$	−4.50236	−1.70173	−0.850865	−	0.525384i	$-0.823922\pi$
$7$	−4.50236	−1.70173	−0.850865	+	0.525384i	$0.823922\pi$
$8$	1.00000	0.353553
$9$	−2.78836	−0.929455
$10$	−0.746209	−0.235972
$11$	−0.256350	−0.0772925	−0.0386463	−	0.999253i	$-0.512305\pi$
$11$	−0.256350	−0.0772925	−0.0386463	+	0.999253i	$0.512305\pi$
$12$	−0.460040	−0.132802
$13$	2.84000	0.787675	0.393838	−	0.919180i	$-0.371147\pi$
$13$	2.84000	0.787675	0.393838	+	0.919180i	$0.371147\pi$
$14$	−4.50236	−1.20331
$15$	0.343286	0.0886359
$16$	1.00000	0.250000
$17$	−2.44196	−0.592263	−0.296131	−	0.955147i	$-0.595697\pi$
$17$	−2.44196	−0.592263	−0.296131	+	0.955147i	$0.595697\pi$
$18$	−2.78836	−0.657224
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−0.746209	−0.166857
$21$	2.07126	0.451986
$22$	−0.256350	−0.0546541
$23$	−4.38723	−0.914801	−0.457401	−	0.889261i	$-0.651219\pi$
$23$	−4.38723	−0.914801	−0.457401	+	0.889261i	$0.651219\pi$
$24$	−0.460040	−0.0939052
$25$	−4.44317	−0.888635
$26$	2.84000	0.556970
$27$	2.66288	0.512471
$28$	−4.50236	−0.850865
$29$	−6.48624	−1.20447	−0.602233	−	0.798321i	$-0.705722\pi$
$29$	−6.48624	−1.20447	−0.602233	+	0.798321i	$0.705722\pi$
$30$	0.343286	0.0626751
$31$	3.86450	0.694085	0.347043	−	0.937849i	$-0.387186\pi$
$31$	3.86450	0.694085	0.347043	+	0.937849i	$0.387186\pi$
$32$	1.00000	0.176777
$33$	0.117931	0.0205292
$34$	−2.44196	−0.418793
$35$	3.35970	0.567892
$36$	−2.78836	−0.464727
$37$	−4.11156	−0.675937	−0.337969	−	0.941157i	$-0.609740\pi$
$37$	−4.11156	−0.675937	−0.337969	+	0.941157i	$0.609740\pi$
$38$	1.00000	0.162221
$39$	−1.30651	−0.209210
$40$	−0.746209	−0.117986
$41$	−3.55157	−0.554663	−0.277331	−	0.960774i	$-0.589450\pi$
$41$	−3.55157	−0.554663	−0.277331	+	0.960774i	$0.589450\pi$
$42$	2.07126	0.319603
$43$	7.52143	1.14701	0.573503	−	0.819203i	$-0.305584\pi$
$43$	7.52143	1.14701	0.573503	+	0.819203i	$0.305584\pi$
$44$	−0.256350	−0.0386463
$45$	2.08070	0.310173
$46$	−4.38723	−0.646862
$47$	−12.5980	−1.83761	−0.918805	−	0.394711i	$-0.870845\pi$
$47$	−12.5980	−1.83761	−0.918805	+	0.394711i	$0.870845\pi$
$48$	−0.460040	−0.0664010
$49$	13.2712	1.89589
$50$	−4.44317	−0.628359
$51$	1.12340	0.157307
$52$	2.84000	0.393838
$53$	2.21292	0.303968	0.151984	−	0.988383i	$-0.451434\pi$
$53$	2.21292	0.303968	0.151984	+	0.988383i	$0.451434\pi$
$54$	2.66288	0.362372
$55$	0.191291	0.0257937
$56$	−4.50236	−0.601653
$57$	−0.460040	−0.0609337
$58$	−6.48624	−0.851685
$59$	1.94036	0.252614	0.126307	−	0.991991i	$-0.459688\pi$
$59$	1.94036	0.252614	0.126307	+	0.991991i	$0.459688\pi$
$60$	0.343286	0.0443180
$61$	7.65724	0.980409	0.490205	−	0.871607i	$-0.336922\pi$
$61$	7.65724	0.980409	0.490205	+	0.871607i	$0.336922\pi$
$62$	3.86450	0.490792
$63$	12.5542	1.58168
$64$	1.00000	0.125000
$65$	−2.11923	−0.262859
$66$	0.117931	0.0145163
$67$	5.07022	0.619426	0.309713	−	0.950830i	$-0.399767\pi$
$67$	5.07022	0.619426	0.309713	+	0.950830i	$0.399767\pi$
$68$	−2.44196	−0.296131
$69$	2.01830	0.242975
$70$	3.35970	0.401561
$71$	−2.65720	−0.315351	−0.157676	−	0.987491i	$-0.550400\pi$
$71$	−2.65720	−0.315351	−0.157676	+	0.987491i	$0.550400\pi$
$72$	−2.78836	−0.328612
$73$	10.5873	1.23914	0.619572	−	0.784940i	$-0.287306\pi$
$73$	10.5873	1.23914	0.619572	+	0.784940i	$0.287306\pi$
$74$	−4.11156	−0.477960
$75$	2.04404	0.236025
$76$	1.00000	0.114708
$77$	1.15418	0.131531
$78$	−1.30651	−0.147934
$79$	10.3761	1.16741	0.583703	−	0.811968i	$-0.301603\pi$
$79$	10.3761	1.16741	0.583703	+	0.811968i	$0.301603\pi$
$80$	−0.746209	−0.0834287
$81$	7.14006	0.793340
$82$	−3.55157	−0.392206
$83$	9.13287	1.00246	0.501232	−	0.865313i	$-0.332880\pi$
$83$	9.13287	1.00246	0.501232	+	0.865313i	$0.332880\pi$
$84$	2.07126	0.225993
$85$	1.82221	0.197647
$86$	7.52143	0.811056
$87$	2.98393	0.319911
$88$	−0.256350	−0.0273270
$89$	3.48874	0.369805	0.184903	−	0.982757i	$-0.440803\pi$
$89$	3.48874	0.369805	0.184903	+	0.982757i	$0.440803\pi$
$90$	2.08070	0.219325
$91$	−12.7867	−1.34041
$92$	−4.38723	−0.457401
$93$	−1.77782	−0.184352
$94$	−12.5980	−1.29939
$95$	−0.746209	−0.0765594
$96$	−0.460040	−0.0469526
$97$	13.0307	1.32307	0.661534	−	0.749915i	$-0.269906\pi$
$97$	13.0307	1.32307	0.661534	+	0.749915i	$0.269906\pi$
$98$	13.2712	1.34059
$99$	0.714798	0.0718399
$100$	−4.44317	−0.444317
$101$	−14.3183	−1.42472	−0.712361	−	0.701813i	$-0.752374\pi$
$101$	−14.3183	−1.42472	−0.712361	+	0.701813i	$0.752374\pi$
$102$	1.12340	0.111233
$103$	−12.3865	−1.22048	−0.610241	−	0.792216i	$-0.708928\pi$
$103$	−12.3865	−1.22048	−0.610241	+	0.792216i	$0.708928\pi$
$104$	2.84000	0.278485
$105$	−1.54559	−0.150834
$106$	2.21292	0.214938
$107$	−14.6991	−1.42101	−0.710506	−	0.703691i	$-0.751534\pi$
$107$	−14.6991	−1.42101	−0.710506	+	0.703691i	$0.751534\pi$
$108$	2.66288	0.256235
$109$	−1.21159	−0.116049	−0.0580247	−	0.998315i	$-0.518480\pi$
$109$	−1.21159	−0.116049	−0.0580247	+	0.998315i	$0.518480\pi$
$110$	0.191291	0.0182389
$111$	1.89148	0.179532
$112$	−4.50236	−0.425433
$113$	−10.4094	−0.979236	−0.489618	−	0.871937i	$-0.662864\pi$
$113$	−10.4094	−0.979236	−0.489618	+	0.871937i	$0.662864\pi$
$114$	−0.460040	−0.0430867
$115$	3.27379	0.305283
$116$	−6.48624	−0.602233
$117$	−7.91896	−0.732108
$118$	1.94036	0.178625
$119$	10.9946	1.00787
$120$	0.343286	0.0313375
$121$	−10.9343	−0.994026
$122$	7.65724	0.693254
$123$	1.63386	0.147321
$124$	3.86450	0.347043
$125$	7.04658	0.630265
$126$	12.5542	1.11842
$127$	3.47751	0.308579	0.154290	−	0.988026i	$-0.450691\pi$
$127$	3.47751	0.308579	0.154290	+	0.988026i	$0.450691\pi$
$128$	1.00000	0.0883883
$129$	−3.46015	−0.304650
$130$	−2.11923	−0.185869
$131$	−12.1726	−1.06352	−0.531761	−	0.846895i	$-0.678469\pi$
$131$	−12.1726	−1.06352	−0.531761	+	0.846895i	$0.678469\pi$
$132$	0.117931	0.0102646
$133$	−4.50236	−0.390404
$134$	5.07022	0.438000
$135$	−1.98706	−0.171019
$136$	−2.44196	−0.209396
$137$	3.53355	0.301892	0.150946	−	0.988542i	$-0.451768\pi$
$137$	3.53355	0.301892	0.150946	+	0.988542i	$0.451768\pi$
$138$	2.01830	0.171809
$139$	21.8983	1.85739	0.928696	−	0.370842i	$-0.120931\pi$
$139$	21.8983	1.85739	0.928696	+	0.370842i	$0.120931\pi$
$140$	3.35970	0.283946
$141$	5.79559	0.488077
$142$	−2.65720	−0.222987
$143$	−0.728036	−0.0608814
$144$	−2.78836	−0.232364
$145$	4.84009	0.401948
$146$	10.5873	0.876208
$147$	−6.10528	−0.503555
$148$	−4.11156	−0.337969
$149$	11.3366	0.928727	0.464364	−	0.885645i	$-0.346283\pi$
$149$	11.3366	0.928727	0.464364	+	0.885645i	$0.346283\pi$
$150$	2.04404	0.166895
$151$	2.74090	0.223051	0.111526	−	0.993762i	$-0.464426\pi$
$151$	2.74090	0.223051	0.111526	+	0.993762i	$0.464426\pi$
$152$	1.00000	0.0811107
$153$	6.80908	0.550481
$154$	1.15418	0.0930065
$155$	−2.88373	−0.231626
$156$	−1.30651	−0.104605
$157$	14.1586	1.12998	0.564991	−	0.825097i	$-0.308880\pi$
$157$	14.1586	1.12998	0.564991	+	0.825097i	$0.308880\pi$
$158$	10.3761	0.825480
$159$	−1.01803	−0.0807351
$160$	−0.746209	−0.0589930
$161$	19.7529	1.55674
$162$	7.14006	0.560976
$163$	6.42281	0.503074	0.251537	−	0.967848i	$-0.419064\pi$
$163$	6.42281	0.503074	0.251537	+	0.967848i	$0.419064\pi$
$164$	−3.55157	−0.277331
$165$	−0.0880014	−0.00685090
$166$	9.13287	0.708848
$167$	19.8961	1.53961	0.769803	−	0.638281i	$-0.220354\pi$
$167$	19.8961	1.53961	0.769803	+	0.638281i	$0.220354\pi$
$168$	2.07126	0.159801
$169$	−4.93438	−0.379568
$170$	1.82221	0.139757
$171$	−2.78836	−0.213231
$172$	7.52143	0.573503
$173$	−12.3515	−0.939071	−0.469535	−	0.882914i	$-0.655579\pi$
$173$	−12.3515	−0.939071	−0.469535	+	0.882914i	$0.655579\pi$
$174$	2.98393	0.226211
$175$	20.0047	1.51222
$176$	−0.256350	−0.0193231
$177$	−0.892644	−0.0670952
$178$	3.48874	0.261492
$179$	−4.09041	−0.305731	−0.152866	−	0.988247i	$-0.548850\pi$
$179$	−4.09041	−0.305731	−0.152866	+	0.988247i	$0.548850\pi$
$180$	2.08070	0.155086
$181$	9.13756	0.679189	0.339595	−	0.940572i	$-0.389710\pi$
$181$	9.13756	0.679189	0.339595	+	0.940572i	$0.389710\pi$
$182$	−12.7867	−0.947814
$183$	−3.52263	−0.260401
$184$	−4.38723	−0.323431
$185$	3.06809	0.225570
$186$	−1.77782	−0.130356
$187$	0.625998	0.0457775
$188$	−12.5980	−0.918805
$189$	−11.9892	−0.872087
$190$	−0.746209	−0.0541357
$191$	−9.46268	−0.684696	−0.342348	−	0.939573i	$-0.611222\pi$
$191$	−9.46268	−0.684696	−0.342348	+	0.939573i	$0.611222\pi$
$192$	−0.460040	−0.0332005
$193$	21.7174	1.56325	0.781625	−	0.623748i	$-0.214391\pi$
$193$	21.7174	1.56325	0.781625	+	0.623748i	$0.214391\pi$
$194$	13.0307	0.935550
$195$	0.974932	0.0698163
$196$	13.2712	0.947943
$197$	−7.77774	−0.554141	−0.277071	−	0.960850i	$-0.589364\pi$
$197$	−7.77774	−0.554141	−0.277071	+	0.960850i	$0.589364\pi$
$198$	0.714798	0.0507985
$199$	−5.16989	−0.366484	−0.183242	−	0.983068i	$-0.558659\pi$
$199$	−5.16989	−0.366484	−0.183242	+	0.983068i	$0.558659\pi$
$200$	−4.44317	−0.314180
$201$	−2.33250	−0.164522
$202$	−14.3183	−1.00743
$203$	29.2034	2.04967
$204$	1.12340	0.0786537
$205$	2.65021	0.185099
$206$	−12.3865	−0.863012
$207$	12.2332	0.850266
$208$	2.84000	0.196919
$209$	−0.256350	−0.0177321
$210$	−1.54559	−0.106656
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	2.21292	0.151984
$213$	1.22242	0.0837585
$214$	−14.6991	−1.00481
$215$	−5.61255	−0.382773
$216$	2.66288	0.181186
$217$	−17.3994	−1.18115
$218$	−1.21159	−0.0820593
$219$	−4.87056	−0.329122
$220$	0.191291	0.0128968
$221$	−6.93518	−0.466511
$222$	1.89148	0.126948
$223$	22.5538	1.51031	0.755157	−	0.655544i	$-0.227561\pi$
$223$	22.5538	1.51031	0.755157	+	0.655544i	$0.227561\pi$
$224$	−4.50236	−0.300826
$225$	12.3892	0.825945
$226$	−10.4094	−0.692425
$227$	23.4512	1.55651	0.778256	−	0.627947i	$-0.216104\pi$
$227$	23.4512	1.55651	0.778256	+	0.627947i	$0.216104\pi$
$228$	−0.460040	−0.0304669
$229$	2.68431	0.177384	0.0886920	−	0.996059i	$-0.471731\pi$
$229$	2.68431	0.177384	0.0886920	+	0.996059i	$0.471731\pi$
$230$	3.27379	0.215867
$231$	−0.530969	−0.0349352
$232$	−6.48624	−0.425843
$233$	1.44592	0.0947251	0.0473626	−	0.998878i	$-0.484918\pi$
$233$	1.44592	0.0947251	0.0473626	+	0.998878i	$0.484918\pi$
$234$	−7.91896	−0.517679
$235$	9.40076	0.613238
$236$	1.94036	0.126307
$237$	−4.77343	−0.310067
$238$	10.9946	0.712673
$239$	−4.79113	−0.309912	−0.154956	−	0.987921i	$-0.549524\pi$
$239$	−4.79113	−0.309912	−0.154956	+	0.987921i	$0.549524\pi$
$240$	0.343286	0.0221590
$241$	16.1347	1.03932	0.519662	−	0.854372i	$-0.326058\pi$
$241$	16.1347	1.03932	0.519662	+	0.854372i	$0.326058\pi$
$242$	−10.9343	−0.702882
$243$	−11.2733	−0.723185
$244$	7.65724	0.490205
$245$	−9.90309	−0.632685
$246$	1.63386	0.104171
$247$	2.84000	0.180705
$248$	3.86450	0.245396
$249$	−4.20148	−0.266258
$250$	7.04658	0.445665
$251$	−1.41837	−0.0895266	−0.0447633	−	0.998998i	$-0.514253\pi$
$251$	−1.41837	−0.0895266	−0.0447633	+	0.998998i	$0.514253\pi$
$252$	12.5542	0.790840
$253$	1.12467	0.0707073
$254$	3.47751	0.218199
$255$	−0.838290	−0.0524958
$256$	1.00000	0.0625000
$257$	27.4894	1.71474	0.857371	−	0.514699i	$-0.172096\pi$
$257$	27.4894	1.71474	0.857371	+	0.514699i	$0.172096\pi$
$258$	−3.46015	−0.215420
$259$	18.5117	1.15026
$260$	−2.11923	−0.131429
$261$	18.0860	1.11950
$262$	−12.1726	−0.752023
$263$	5.89902	0.363749	0.181874	−	0.983322i	$-0.441784\pi$
$263$	5.89902	0.363749	0.181874	+	0.983322i	$0.441784\pi$
$264$	0.117931	0.00725817
$265$	−1.65130	−0.101439
$266$	−4.50236	−0.276057
$267$	−1.60496	−0.0982217
$268$	5.07022	0.309713
$269$	29.7420	1.81340	0.906702	−	0.421772i	$-0.138592\pi$
$269$	29.7420	1.81340	0.906702	+	0.421772i	$0.138592\pi$
$270$	−1.98706	−0.120929
$271$	−26.2214	−1.59284	−0.796418	−	0.604746i	$-0.793275\pi$
$271$	−26.2214	−1.59284	−0.796418	+	0.604746i	$0.793275\pi$
$272$	−2.44196	−0.148066
$273$	5.88239	0.356018
$274$	3.53355	0.213470
$275$	1.13901	0.0686848
$276$	2.01830	0.121487
$277$	9.33671	0.560988	0.280494	−	0.959856i	$-0.409502\pi$
$277$	9.33671	0.560988	0.280494	+	0.959856i	$0.409502\pi$
$278$	21.8983	1.31337
$279$	−10.7756	−0.645121
$280$	3.35970	0.200780
$281$	14.5287	0.866710	0.433355	−	0.901223i	$-0.357330\pi$
$281$	14.5287	0.866710	0.433355	+	0.901223i	$0.357330\pi$
$282$	5.79559	0.345122
$283$	−20.6480	−1.22740	−0.613698	−	0.789541i	$-0.710319\pi$
$283$	−20.6480	−1.22740	−0.613698	+	0.789541i	$0.710319\pi$
$284$	−2.65720	−0.157676
$285$	0.343286	0.0203345
$286$	−0.728036	−0.0430497
$287$	15.9904	0.943886
$288$	−2.78836	−0.164306
$289$	−11.0368	−0.649225
$290$	4.84009	0.284220
$291$	−5.99464	−0.351412
$292$	10.5873	0.619572
$293$	3.85705	0.225331	0.112666	−	0.993633i	$-0.464061\pi$
$293$	3.85705	0.225331	0.112666	+	0.993633i	$0.464061\pi$
$294$	−6.10528	−0.356067
$295$	−1.44792	−0.0843009
$296$	−4.11156	−0.238980
$297$	−0.682629	−0.0396102
$298$	11.3366	0.656709
$299$	−12.4598	−0.720566
$300$	2.04404	0.118012
$301$	−33.8641	−1.95190
$302$	2.74090	0.157721
$303$	6.58698	0.378412
$304$	1.00000	0.0573539
$305$	−5.71390	−0.327177
$306$	6.80908	0.389249
$307$	0.183585	0.0104777	0.00523887	−	0.999986i	$-0.498332\pi$
$307$	0.183585	0.0104777	0.00523887	+	0.999986i	$0.498332\pi$
$308$	1.15418	0.0657655
$309$	5.69830	0.324165
$310$	−2.88373	−0.163785
$311$	−17.1556	−0.972806	−0.486403	−	0.873735i	$-0.661691\pi$
$311$	−17.1556	−0.972806	−0.486403	+	0.873735i	$0.661691\pi$
$312$	−1.30651	−0.0739668
$313$	−7.35295	−0.415613	−0.207807	−	0.978170i	$-0.566632\pi$
$313$	−7.35295	−0.415613	−0.207807	+	0.978170i	$0.566632\pi$
$314$	14.1586	0.799018
$315$	−9.36806	−0.527830
$316$	10.3761	0.583703
$317$	17.0186	0.955858	0.477929	−	0.878398i	$-0.341388\pi$
$317$	17.0186	0.955858	0.477929	+	0.878398i	$0.341388\pi$
$318$	−1.01803	−0.0570883
$319$	1.66275	0.0930962
$320$	−0.746209	−0.0417143
$321$	6.76215	0.377427
$322$	19.7529	1.10078
$323$	−2.44196	−0.135874
$324$	7.14006	0.396670
$325$	−12.6186	−0.699955
$326$	6.42281	0.355727
$327$	0.557380	0.0308232
$328$	−3.55157	−0.196103
$329$	56.7208	3.12712
$330$	−0.0880014	−0.00484432
$331$	−10.0824	−0.554179	−0.277089	−	0.960844i	$-0.589370\pi$
$331$	−10.0824	−0.554179	−0.277089	+	0.960844i	$0.589370\pi$
$332$	9.13287	0.501232
$333$	11.4645	0.628253
$334$	19.8961	1.08867
$335$	−3.78344	−0.206712
$336$	2.07126	0.112997
$337$	11.1820	0.609121	0.304561	−	0.952493i	$-0.401490\pi$
$337$	11.1820	0.609121	0.304561	+	0.952493i	$0.401490\pi$
$338$	−4.93438	−0.268395
$339$	4.78875	0.260089
$340$	1.82221	0.0988234
$341$	−0.990667	−0.0536476
$342$	−2.78836	−0.150777
$343$	−28.2352	−1.52456
$344$	7.52143	0.405528
$345$	−1.50607	−0.0810843
$346$	−12.3515	−0.664023
$347$	7.85053	0.421439	0.210719	−	0.977547i	$-0.432419\pi$
$347$	7.85053	0.421439	0.210719	+	0.977547i	$0.432419\pi$
$348$	2.98393	0.159955
$349$	2.96368	0.158642	0.0793212	−	0.996849i	$-0.474725\pi$
$349$	2.96368	0.158642	0.0793212	+	0.996849i	$0.474725\pi$
$350$	20.0047	1.06930
$351$	7.56258	0.403661
$352$	−0.256350	−0.0136635
$353$	−10.9160	−0.581000	−0.290500	−	0.956875i	$-0.593822\pi$
$353$	−10.9160	−0.581000	−0.290500	+	0.956875i	$0.593822\pi$
$354$	−0.892644	−0.0474435
$355$	1.98282	0.105237
$356$	3.48874	0.184903
$357$	−5.05794	−0.267695
$358$	−4.09041	−0.216185
$359$	−11.1098	−0.586355	−0.293177	−	0.956058i	$-0.594713\pi$
$359$	−11.1098	−0.586355	−0.293177	+	0.956058i	$0.594713\pi$
$360$	2.08070	0.109663
$361$	1.00000	0.0526316
$362$	9.13756	0.480259
$363$	5.03020	0.264017
$364$	−12.7867	−0.670205
$365$	−7.90030	−0.413521
$366$	−3.52263	−0.184131
$367$	−2.48972	−0.129962	−0.0649811	−	0.997886i	$-0.520699\pi$
$367$	−2.48972	−0.129962	−0.0649811	+	0.997886i	$0.520699\pi$
$368$	−4.38723	−0.228700
$369$	9.90308	0.515534
$370$	3.06809	0.159502
$371$	−9.96335	−0.517271
$372$	−1.77782	−0.0921759
$373$	−24.5744	−1.27242	−0.636208	−	0.771517i	$-0.719498\pi$
$373$	−24.5744	−1.27242	−0.636208	+	0.771517i	$0.719498\pi$
$374$	0.625998	0.0323696
$375$	−3.24170	−0.167401
$376$	−12.5980	−0.649694
$377$	−18.4209	−0.948727
$378$	−11.9892	−0.616659
$379$	2.96763	0.152437	0.0762184	−	0.997091i	$-0.475715\pi$
$379$	2.96763	0.152437	0.0762184	+	0.997091i	$0.475715\pi$
$380$	−0.746209	−0.0382797
$381$	−1.59979	−0.0819599
$382$	−9.46268	−0.484153
$383$	3.08027	0.157395	0.0786973	−	0.996899i	$-0.474924\pi$
$383$	3.08027	0.157395	0.0786973	+	0.996899i	$0.474924\pi$
$384$	−0.460040	−0.0234763
$385$	−0.861259	−0.0438938
$386$	21.7174	1.10539
$387$	−20.9725	−1.06609
$388$	13.0307	0.661534
$389$	2.35489	0.119398	0.0596989	−	0.998216i	$-0.480986\pi$
$389$	2.35489	0.119398	0.0596989	+	0.998216i	$0.480986\pi$
$390$	0.974932	0.0493676
$391$	10.7135	0.541803
$392$	13.2712	0.670297
$393$	5.59986	0.282476
$394$	−7.77774	−0.391837
$395$	−7.74275	−0.389580
$396$	0.714798	0.0359200
$397$	24.1824	1.21368	0.606839	−	0.794825i	$-0.292437\pi$
$397$	24.1824	1.21368	0.606839	+	0.794825i	$0.292437\pi$
$398$	−5.16989	−0.259143
$399$	2.07126	0.103693
$400$	−4.44317	−0.222159
$401$	2.98952	0.149289	0.0746446	−	0.997210i	$-0.476218\pi$
$401$	2.98952	0.149289	0.0746446	+	0.997210i	$0.476218\pi$
$402$	−2.33250	−0.116335
$403$	10.9752	0.546714
$404$	−14.3183	−0.712361
$405$	−5.32798	−0.264749
$406$	29.2034	1.44934
$407$	1.05400	0.0522449
$408$	1.12340	0.0556165
$409$	4.33779	0.214490	0.107245	−	0.994233i	$-0.465797\pi$
$409$	4.33779	0.214490	0.107245	+	0.994233i	$0.465797\pi$
$410$	2.65021	0.130885
$411$	−1.62557	−0.0801836
$412$	−12.3865	−0.610241
$413$	−8.73621	−0.429881
$414$	12.2332	0.601229
$415$	−6.81503	−0.334537
$416$	2.84000	0.139243
$417$	−10.0741	−0.493331
$418$	−0.256350	−0.0125385
$419$	11.5444	0.563982	0.281991	−	0.959417i	$-0.409005\pi$
$419$	11.5444	0.563982	0.281991	+	0.959417i	$0.409005\pi$
$420$	−1.54559	−0.0754172
$421$	−0.720995	−0.0351392	−0.0175696	−	0.999846i	$-0.505593\pi$
$421$	−0.720995	−0.0351392	−0.0175696	+	0.999846i	$0.505593\pi$
$422$	1.00000	0.0486792
$423$	35.1279	1.70798
$424$	2.21292	0.107469
$425$	10.8501	0.526305
$426$	1.22242	0.0592262
$427$	−34.4756	−1.66839
$428$	−14.6991	−0.710506
$429$	0.334925	0.0161703
$430$	−5.61255	−0.270661
$431$	−5.20100	−0.250523	−0.125262	−	0.992124i	$-0.539977\pi$
$431$	−5.20100	−0.250523	−0.125262	+	0.992124i	$0.539977\pi$
$432$	2.66288	0.128118
$433$	4.97408	0.239039	0.119520	−	0.992832i	$-0.461865\pi$
$433$	4.97408	0.239039	0.119520	+	0.992832i	$0.461865\pi$
$434$	−17.3994	−0.835196
$435$	−2.22663	−0.106759
$436$	−1.21159	−0.0580247
$437$	−4.38723	−0.209870
$438$	−4.87056	−0.232724
$439$	31.9558	1.52517	0.762584	−	0.646889i	$-0.223930\pi$
$439$	31.9558	1.52517	0.762584	+	0.646889i	$0.223930\pi$
$440$	0.191291	0.00911943
$441$	−37.0049	−1.76214
$442$	−6.93518	−0.329873
$443$	−20.1812	−0.958839	−0.479420	−	0.877586i	$-0.659153\pi$
$443$	−20.1812	−0.958839	−0.479420	+	0.877586i	$0.659153\pi$
$444$	1.89148	0.0897658
$445$	−2.60332	−0.123409
$446$	22.5538	1.06795
$447$	−5.21527	−0.246674
$448$	−4.50236	−0.212716
$449$	34.1665	1.61242	0.806209	−	0.591631i	$-0.201516\pi$
$449$	34.1665	1.61242	0.806209	+	0.591631i	$0.201516\pi$
$450$	12.3892	0.584032
$451$	0.910447	0.0428713
$452$	−10.4094	−0.489618
$453$	−1.26092	−0.0592434
$454$	23.4512	1.10062
$455$	9.54155	0.447315
$456$	−0.460040	−0.0215433
$457$	41.7679	1.95382	0.976909	−	0.213655i	$-0.0685369\pi$
$457$	41.7679	1.95382	0.976909	+	0.213655i	$0.0685369\pi$
$458$	2.68431	0.125429
$459$	−6.50264	−0.303517
$460$	3.27379	0.152641
$461$	5.00415	0.233067	0.116533	−	0.993187i	$-0.462822\pi$
$461$	5.00415	0.233067	0.116533	+	0.993187i	$0.462822\pi$
$462$	−0.530969	−0.0247029
$463$	−12.9335	−0.601070	−0.300535	−	0.953771i	$-0.597165\pi$
$463$	−12.9335	−0.601070	−0.300535	+	0.953771i	$0.597165\pi$
$464$	−6.48624	−0.301116
$465$	1.32663	0.0615209
$466$	1.44592	0.0669808
$467$	−37.9576	−1.75647	−0.878235	−	0.478230i	$-0.841279\pi$
$467$	−37.9576	−1.75647	−0.878235	+	0.478230i	$0.841279\pi$
$468$	−7.91896	−0.366054
$469$	−22.8279	−1.05410
$470$	9.40076	0.433625
$471$	−6.51353	−0.300128
$472$	1.94036	0.0893125
$473$	−1.92812	−0.0886551
$474$	−4.77343	−0.219251
$475$	−4.44317	−0.203867
$476$	10.9946	0.503936
$477$	−6.17042	−0.282524
$478$	−4.79113	−0.219141
$479$	14.0415	0.641571	0.320786	−	0.947152i	$-0.396053\pi$
$479$	14.0415	0.641571	0.320786	+	0.947152i	$0.396053\pi$
$480$	0.343286	0.0156688
$481$	−11.6769	−0.532419
$482$	16.1347	0.734914
$483$	−9.08711	−0.413478
$484$	−10.9343	−0.497013
$485$	−9.72362	−0.441527
$486$	−11.2733	−0.511369
$487$	−10.4745	−0.474645	−0.237323	−	0.971431i	$-0.576270\pi$
$487$	−10.4745	−0.474645	−0.237323	+	0.971431i	$0.576270\pi$
$488$	7.65724	0.346627
$489$	−2.95475	−0.133618
$490$	−9.90309	−0.447376
$491$	−30.5611	−1.37921	−0.689603	−	0.724188i	$-0.742215\pi$
$491$	−30.5611	−1.37921	−0.689603	+	0.724188i	$0.742215\pi$
$492$	1.63386	0.0736603
$493$	15.8392	0.713360
$494$	2.84000	0.127778
$495$	−0.533388	−0.0239740
$496$	3.86450	0.173521
$497$	11.9636	0.536643
$498$	−4.20148	−0.188273
$499$	20.9497	0.937838	0.468919	−	0.883241i	$-0.344644\pi$
$499$	20.9497	0.937838	0.468919	+	0.883241i	$0.344644\pi$
$500$	7.04658	0.315133
$501$	−9.15299	−0.408926
$502$	−1.41837	−0.0633049
$503$	−19.7576	−0.880946	−0.440473	−	0.897766i	$-0.645189\pi$
$503$	−19.7576	−0.880946	−0.440473	+	0.897766i	$0.645189\pi$
$504$	12.5542	0.559209
$505$	10.6844	0.475451
$506$	1.12467	0.0499976
$507$	2.27001	0.100815
$508$	3.47751	0.154290
$509$	−35.9779	−1.59469	−0.797346	−	0.603522i	$-0.793763\pi$
$509$	−35.9779	−1.59469	−0.797346	+	0.603522i	$0.793763\pi$
$510$	−0.838290	−0.0371201
$511$	−47.6676	−2.10869
$512$	1.00000	0.0441942
$513$	2.66288	0.117569
$514$	27.4894	1.21251
$515$	9.24295	0.407293
$516$	−3.46015	−0.152325
$517$	3.22951	0.142034
$518$	18.5117	0.813359
$519$	5.68220	0.249421
$520$	−2.11923	−0.0929346
$521$	24.9316	1.09227	0.546137	−	0.837696i	$-0.316098\pi$
$521$	24.9316	1.09227	0.546137	+	0.837696i	$0.316098\pi$
$522$	18.0860	0.791603
$523$	29.7263	1.29984	0.649919	−	0.760003i	$-0.274803\pi$
$523$	29.7263	1.29984	0.649919	+	0.760003i	$0.274803\pi$
$524$	−12.1726	−0.531761
$525$	−9.20297	−0.401651
$526$	5.89902	0.257209
$527$	−9.43697	−0.411081
$528$	0.117931	0.00513230
$529$	−3.75219	−0.163139
$530$	−1.65130	−0.0717279
$531$	−5.41044	−0.234793
$532$	−4.50236	−0.195202
$533$	−10.0865	−0.436894
$534$	−1.60496	−0.0694533
$535$	10.9686	0.474213
$536$	5.07022	0.219000
$537$	1.88175	0.0812035
$538$	29.7420	1.28227
$539$	−3.40208	−0.146538
$540$	−1.98706	−0.0855095
$541$	−13.2061	−0.567777	−0.283888	−	0.958857i	$-0.591624\pi$
$541$	−13.2061	−0.567777	−0.283888	+	0.958857i	$0.591624\pi$
$542$	−26.2214	−1.12631
$543$	−4.20364	−0.180395
$544$	−2.44196	−0.104698
$545$	0.904099	0.0387274
$546$	5.88239	0.251743
$547$	15.9516	0.682039	0.341020	−	0.940056i	$-0.389228\pi$
$547$	15.9516	0.682039	0.341020	+	0.940056i	$0.389228\pi$
$548$	3.53355	0.150946
$549$	−21.3512	−0.911246
$550$	1.13901	0.0485675
$551$	−6.48624	−0.276323
$552$	2.01830	0.0859046
$553$	−46.7170	−1.98661
$554$	9.33671	0.396679
$555$	−1.41144	−0.0599123
$556$	21.8983	0.928696
$557$	5.00532	0.212082	0.106041	−	0.994362i	$-0.466183\pi$
$557$	5.00532	0.212082	0.106041	+	0.994362i	$0.466183\pi$
$558$	−10.7756	−0.456169
$559$	21.3609	0.903469
$560$	3.35970	0.141973
$561$	−0.287984	−0.0121587
$562$	14.5287	0.612857
$563$	−35.2134	−1.48407	−0.742034	−	0.670363i	$-0.766139\pi$
$563$	−35.2134	−1.48407	−0.742034	+	0.670363i	$0.766139\pi$
$564$	5.79559	0.244038
$565$	7.76760	0.326786
$566$	−20.6480	−0.867900
$567$	−32.1471	−1.35005
$568$	−2.65720	−0.111493
$569$	32.6119	1.36716	0.683582	−	0.729874i	$-0.260421\pi$
$569$	32.6119	1.36716	0.683582	+	0.729874i	$0.260421\pi$
$570$	0.343286	0.0143786
$571$	−33.1336	−1.38660	−0.693298	−	0.720651i	$-0.743843\pi$
$571$	−33.1336	−1.38660	−0.693298	+	0.720651i	$0.743843\pi$
$572$	−0.728036	−0.0304407
$573$	4.35321	0.181858
$574$	15.9904	0.667428
$575$	19.4932	0.812924
$576$	−2.78836	−0.116182
$577$	44.5722	1.85556	0.927782	−	0.373122i	$-0.121713\pi$
$577$	44.5722	1.85556	0.927782	+	0.373122i	$0.121713\pi$
$578$	−11.0368	−0.459071
$579$	−9.99085	−0.415206
$580$	4.84009	0.200974
$581$	−41.1194	−1.70592
$582$	−5.99464	−0.248486
$583$	−0.567283	−0.0234944
$584$	10.5873	0.438104
$585$	5.90920	0.244315
$586$	3.85705	0.159333
$587$	−29.2334	−1.20659	−0.603296	−	0.797517i	$-0.706146\pi$
$587$	−29.2334	−1.20659	−0.603296	+	0.797517i	$0.706146\pi$
$588$	−6.10528	−0.251777
$589$	3.86450	0.159234
$590$	−1.44792	−0.0596098
$591$	3.57807	0.147182
$592$	−4.11156	−0.168984
$593$	4.10003	0.168368	0.0841841	−	0.996450i	$-0.473172\pi$
$593$	4.10003	0.168368	0.0841841	+	0.996450i	$0.473172\pi$
$594$	−0.682629	−0.0280086
$595$	−8.20425	−0.336341
$596$	11.3366	0.464364
$597$	2.37835	0.0973395
$598$	−12.4598	−0.509517
$599$	−23.3244	−0.953009	−0.476505	−	0.879172i	$-0.658096\pi$
$599$	−23.3244	−0.953009	−0.476505	+	0.879172i	$0.658096\pi$
$600$	2.04404	0.0834474
$601$	−15.1673	−0.618689	−0.309344	−	0.950950i	$-0.600110\pi$
$601$	−15.1673	−0.618689	−0.309344	+	0.950950i	$0.600110\pi$
$602$	−33.8641	−1.38020
$603$	−14.1376	−0.575728
$604$	2.74090	0.111526
$605$	8.15926	0.331721
$606$	6.58698	0.267578
$607$	14.3471	0.582330	0.291165	−	0.956673i	$-0.405957\pi$
$607$	14.3471	0.582330	0.291165	+	0.956673i	$0.405957\pi$
$608$	1.00000	0.0405554
$609$	−13.4347	−0.544402
$610$	−5.71390	−0.231349
$611$	−35.7784	−1.44744
$612$	6.80908	0.275241
$613$	−35.5083	−1.43417	−0.717083	−	0.696987i	$-0.754523\pi$
$613$	−35.5083	−1.43417	−0.717083	+	0.696987i	$0.754523\pi$
$614$	0.183585	0.00740888
$615$	−1.21920	−0.0491630
$616$	1.15418	0.0465033
$617$	14.2075	0.571973	0.285986	−	0.958234i	$-0.407679\pi$
$617$	14.2075	0.571973	0.285986	+	0.958234i	$0.407679\pi$
$618$	5.69830	0.229219
$619$	−39.4807	−1.58686	−0.793431	−	0.608660i	$-0.791708\pi$
$619$	−39.4807	−1.58686	−0.793431	+	0.608660i	$0.791708\pi$
$620$	−2.88373	−0.115813
$621$	−11.6827	−0.468809
$622$	−17.1556	−0.687877
$623$	−15.7075	−0.629309
$624$	−1.30651	−0.0523024
$625$	16.9576	0.678306
$626$	−7.35295	−0.293883
$627$	0.117931	0.00470972
$628$	14.1586	0.564991
$629$	10.0403	0.400332
$630$	−9.36806	−0.373232
$631$	−34.8467	−1.38722	−0.693612	−	0.720349i	$-0.743982\pi$
$631$	−34.8467	−1.38722	−0.693612	+	0.720349i	$0.743982\pi$
$632$	10.3761	0.412740
$633$	−0.460040	−0.0182849
$634$	17.0186	0.675894
$635$	−2.59495	−0.102977
$636$	−1.01803	−0.0403675
$637$	37.6903	1.49334
$638$	1.66275	0.0658289
$639$	7.40923	0.293105
$640$	−0.746209	−0.0294965
$641$	19.6637	0.776669	0.388335	−	0.921518i	$-0.373050\pi$
$641$	19.6637	0.776669	0.388335	+	0.921518i	$0.373050\pi$
$642$	6.76215	0.266881
$643$	−20.9889	−0.827722	−0.413861	−	0.910340i	$-0.635820\pi$
$643$	−20.9889	−0.827722	−0.413861	+	0.910340i	$0.635820\pi$
$644$	19.7529	0.778372
$645$	2.58200	0.101666
$646$	−2.44196	−0.0960777
$647$	35.5783	1.39873	0.699364	−	0.714766i	$-0.253467\pi$
$647$	35.5783	1.39873	0.699364	+	0.714766i	$0.253467\pi$
$648$	7.14006	0.280488
$649$	−0.497413	−0.0195252
$650$	−12.6186	−0.494943
$651$	8.00440	0.313717
$652$	6.42281	0.251537
$653$	21.8849	0.856422	0.428211	−	0.903679i	$-0.359144\pi$
$653$	21.8849	0.856422	0.428211	+	0.903679i	$0.359144\pi$
$654$	0.557380	0.0217953
$655$	9.08327	0.354913
$656$	−3.55157	−0.138666
$657$	−29.5211	−1.15173
$658$	56.7208	2.21121
$659$	14.5870	0.568227	0.284114	−	0.958791i	$-0.408301\pi$
$659$	14.5870	0.568227	0.284114	+	0.958791i	$0.408301\pi$
$660$	−0.0880014	−0.00342545
$661$	8.69416	0.338164	0.169082	−	0.985602i	$-0.445920\pi$
$661$	8.69416	0.338164	0.169082	+	0.985602i	$0.445920\pi$
$662$	−10.0824	−0.391864
$663$	3.19046	0.123907
$664$	9.13287	0.354424
$665$	3.35970	0.130283
$666$	11.4645	0.444242
$667$	28.4567	1.10185
$668$	19.8961	0.769803
$669$	−10.3756	−0.401145
$670$	−3.78344	−0.146167
$671$	−1.96294	−0.0757783
$672$	2.07126	0.0799007
$673$	11.3150	0.436163	0.218081	−	0.975931i	$-0.430020\pi$
$673$	11.3150	0.436163	0.218081	+	0.975931i	$0.430020\pi$
$674$	11.1820	0.430714
$675$	−11.8316	−0.455399
$676$	−4.93438	−0.189784
$677$	13.8902	0.533845	0.266923	−	0.963718i	$-0.413993\pi$
$677$	13.8902	0.533845	0.266923	+	0.963718i	$0.413993\pi$
$678$	4.78875	0.183911
$679$	−58.6689	−2.25150
$680$	1.82221	0.0698787
$681$	−10.7885	−0.413416
$682$	−0.990667	−0.0379346
$683$	−3.68415	−0.140970	−0.0704850	−	0.997513i	$-0.522455\pi$
$683$	−3.68415	−0.140970	−0.0704850	+	0.997513i	$0.522455\pi$
$684$	−2.78836	−0.106616
$685$	−2.63677	−0.100746
$686$	−28.2352	−1.07802
$687$	−1.23489	−0.0471139
$688$	7.52143	0.286752
$689$	6.28470	0.239428
$690$	−1.50607	−0.0573352
$691$	5.27232	0.200569	0.100284	−	0.994959i	$-0.468025\pi$
$691$	5.27232	0.200569	0.100284	+	0.994959i	$0.468025\pi$
$692$	−12.3515	−0.469535
$693$	−3.21827	−0.122252
$694$	7.85053	0.298002
$695$	−16.3407	−0.619839
$696$	2.98393	0.113106
$697$	8.67280	0.328506
$698$	2.96368	0.112177
$699$	−0.665179	−0.0251594
$700$	20.0047	0.756108
$701$	−40.3206	−1.52289	−0.761444	−	0.648230i	$-0.775509\pi$
$701$	−40.3206	−1.52289	−0.761444	+	0.648230i	$0.775509\pi$
$702$	7.56258	0.285431
$703$	−4.11156	−0.155071
$704$	−0.256350	−0.00966157
$705$	−4.32472	−0.162878
$706$	−10.9160	−0.410829
$707$	64.4660	2.42449
$708$	−0.892644	−0.0335476
$709$	−7.72549	−0.290137	−0.145068	−	0.989422i	$-0.546340\pi$
$709$	−7.72549	−0.290137	−0.145068	+	0.989422i	$0.546340\pi$
$710$	1.98282	0.0744140
$711$	−28.9324	−1.08505
$712$	3.48874	0.130746
$713$	−16.9545	−0.634950
$714$	−5.05794	−0.189289
$715$	0.543267	0.0203170
$716$	−4.09041	−0.152866
$717$	2.20411	0.0823139
$718$	−11.1098	−0.414616
$719$	−5.17976	−0.193173	−0.0965863	−	0.995325i	$-0.530792\pi$
$719$	−5.17976	−0.193173	−0.0965863	+	0.995325i	$0.530792\pi$
$720$	2.08070	0.0775431
$721$	55.7686	2.07693
$722$	1.00000	0.0372161
$723$	−7.42258	−0.276049
$724$	9.13756	0.339595
$725$	28.8195	1.07033
$726$	5.03020	0.186688
$727$	−10.5398	−0.390899	−0.195449	−	0.980714i	$-0.562617\pi$
$727$	−10.5398	−0.390899	−0.195449	+	0.980714i	$0.562617\pi$
$728$	−12.7867	−0.473907
$729$	−16.2340	−0.601259
$730$	−7.90030	−0.292403
$731$	−18.3670	−0.679329
$732$	−3.52263	−0.130200
$733$	−1.87765	−0.0693528	−0.0346764	−	0.999399i	$-0.511040\pi$
$733$	−1.87765	−0.0693528	−0.0346764	+	0.999399i	$0.511040\pi$
$734$	−2.48972	−0.0918972
$735$	4.55581	0.168044
$736$	−4.38723	−0.161716
$737$	−1.29975	−0.0478770
$738$	9.90308	0.364537
$739$	17.0868	0.628549	0.314275	−	0.949332i	$-0.398239\pi$
$739$	17.0868	0.628549	0.314275	+	0.949332i	$0.398239\pi$
$740$	3.06809	0.112785
$741$	−1.30651	−0.0479960
$742$	−9.96335	−0.365766
$743$	35.9454	1.31871	0.659355	−	0.751832i	$-0.270829\pi$
$743$	35.9454	1.31871	0.659355	+	0.751832i	$0.270829\pi$
$744$	−1.77782	−0.0651782
$745$	−8.45944	−0.309930
$746$	−24.5744	−0.899734
$747$	−25.4658	−0.931744
$748$	0.625998	0.0228887
$749$	66.1804	2.41818
$750$	−3.24170	−0.118370
$751$	−23.9014	−0.872176	−0.436088	−	0.899904i	$-0.643636\pi$
$751$	−23.9014	−0.872176	−0.436088	+	0.899904i	$0.643636\pi$
$752$	−12.5980	−0.459403
$753$	0.652506	0.0237786
$754$	−18.4209	−0.670851
$755$	−2.04528	−0.0744355
$756$	−11.9892	−0.436044
$757$	−27.2233	−0.989447	−0.494724	−	0.869050i	$-0.664731\pi$
$757$	−27.2233	−0.989447	−0.494724	+	0.869050i	$0.664731\pi$
$758$	2.96763	0.107789
$759$	−0.517392	−0.0187801
$760$	−0.746209	−0.0270678
$761$	−5.54569	−0.201031	−0.100516	−	0.994935i	$-0.532049\pi$
$761$	−5.54569	−0.201031	−0.100516	+	0.994935i	$0.532049\pi$
$762$	−1.59979	−0.0579544
$763$	5.45501	0.197485
$764$	−9.46268	−0.342348
$765$	−5.08099	−0.183704
$766$	3.08027	0.111295
$767$	5.51064	0.198978
$768$	−0.460040	−0.0166002
$769$	−22.2214	−0.801326	−0.400663	−	0.916226i	$-0.631220\pi$
$769$	−22.2214	−0.801326	−0.400663	+	0.916226i	$0.631220\pi$
$770$	−0.861259	−0.0310376
$771$	−12.6462	−0.455442
$772$	21.7174	0.781625
$773$	15.4379	0.555263	0.277632	−	0.960688i	$-0.410451\pi$
$773$	15.4379	0.555263	0.277632	+	0.960688i	$0.410451\pi$
$774$	−20.9725	−0.753840
$775$	−17.1707	−0.616788
$776$	13.0307	0.467775
$777$	−8.51613	−0.305514
$778$	2.35489	0.0844270
$779$	−3.55157	−0.127248
$780$	0.974932	0.0349082
$781$	0.681173	0.0243743
$782$	10.7135	0.383112
$783$	−17.2721	−0.617253
$784$	13.2712	0.473972
$785$	−10.5653	−0.377092
$786$	5.59986	0.199740
$787$	−34.2973	−1.22257	−0.611283	−	0.791412i	$-0.709346\pi$
$787$	−34.2973	−1.22257	−0.611283	+	0.791412i	$0.709346\pi$
$788$	−7.77774	−0.277071
$789$	−2.71378	−0.0966132
$790$	−7.74275	−0.275475
$791$	46.8669	1.66640
$792$	0.714798	0.0253992
$793$	21.7466	0.772244
$794$	24.1824	0.858200
$795$	0.759663	0.0269425
$796$	−5.16989	−0.183242
$797$	−33.9062	−1.20102	−0.600509	−	0.799618i	$-0.705035\pi$
$797$	−33.9062	−1.20102	−0.600509	+	0.799618i	$0.705035\pi$
$798$	2.07126	0.0733219
$799$	30.7639	1.08835
$800$	−4.44317	−0.157090
$801$	−9.72786	−0.343717
$802$	2.98952	0.105563
$803$	−2.71405	−0.0957766
$804$	−2.33250	−0.0822610
$805$	−14.7398	−0.519509
$806$	10.9752	0.386585
$807$	−13.6825	−0.481647
$808$	−14.3183	−0.503715
$809$	−41.2684	−1.45092	−0.725460	−	0.688264i	$-0.758373\pi$
$809$	−41.2684	−1.45092	−0.725460	+	0.688264i	$0.758373\pi$
$810$	−5.32798	−0.187206
$811$	2.93642	0.103112	0.0515558	−	0.998670i	$-0.483582\pi$
$811$	2.93642	0.103112	0.0515558	+	0.998670i	$0.483582\pi$
$812$	29.2034	1.02484
$813$	12.0629	0.423064
$814$	1.05400	0.0369427
$815$	−4.79276	−0.167883
$816$	1.12340	0.0393268
$817$	7.52143	0.263141
$818$	4.33779	0.151667
$819$	35.6540	1.24585
$820$	2.65021	0.0925495
$821$	−3.58482	−0.125111	−0.0625555	−	0.998041i	$-0.519925\pi$
$821$	−3.58482	−0.125111	−0.0625555	+	0.998041i	$0.519925\pi$
$822$	−1.62557	−0.0566984
$823$	15.6237	0.544609	0.272305	−	0.962211i	$-0.412214\pi$
$823$	15.6237	0.544609	0.272305	+	0.962211i	$0.412214\pi$
$824$	−12.3865	−0.431506
$825$	−0.523989	−0.0182430
$826$	−8.73621	−0.303972
$827$	35.7591	1.24346	0.621732	−	0.783230i	$-0.286429\pi$
$827$	35.7591	1.24346	0.621732	+	0.783230i	$0.286429\pi$
$828$	12.2332	0.425133
$829$	−27.0777	−0.940447	−0.470224	−	0.882547i	$-0.655827\pi$
$829$	−27.0777	−0.940447	−0.470224	+	0.882547i	$0.655827\pi$
$830$	−6.81503	−0.236553
$831$	−4.29526	−0.149001
$832$	2.84000	0.0984594
$833$	−32.4078	−1.12286
$834$	−10.0741	−0.348837
$835$	−14.8466	−0.513789
$836$	−0.256350	−0.00886606
$837$	10.2907	0.355698
$838$	11.5444	0.398796
$839$	−34.4317	−1.18871	−0.594357	−	0.804201i	$-0.702594\pi$
$839$	−34.4317	−1.18871	−0.594357	+	0.804201i	$0.702594\pi$
$840$	−1.54559	−0.0533280
$841$	13.0713	0.450736
$842$	−0.720995	−0.0248471
$843$	−6.68378	−0.230202
$844$	1.00000	0.0344214
$845$	3.68208	0.126667
$846$	35.1279	1.20772
$847$	49.2300	1.69156
$848$	2.21292	0.0759920
$849$	9.49889	0.326001
$850$	10.8501	0.372154
$851$	18.0384	0.618348
$852$	1.22242	0.0418793
$853$	4.33264	0.148347	0.0741734	−	0.997245i	$-0.476368\pi$
$853$	4.33264	0.148347	0.0741734	+	0.997245i	$0.476368\pi$
$854$	−34.4756	−1.17973
$855$	2.08070	0.0711585
$856$	−14.6991	−0.502404
$857$	11.2164	0.383145	0.191573	−	0.981478i	$-0.438641\pi$
$857$	11.2164	0.383145	0.191573	+	0.981478i	$0.438641\pi$
$858$	0.334925	0.0114342
$859$	−17.5959	−0.600363	−0.300181	−	0.953882i	$-0.597047\pi$
$859$	−17.5959	−0.600363	−0.300181	+	0.953882i	$0.597047\pi$
$860$	−5.61255	−0.191386
$861$	−7.35624	−0.250700
$862$	−5.20100	−0.177147
$863$	−18.6210	−0.633865	−0.316932	−	0.948448i	$-0.602653\pi$
$863$	−18.6210	−0.633865	−0.316932	+	0.948448i	$0.602653\pi$
$864$	2.66288	0.0905929
$865$	9.21683	0.313382
$866$	4.97408	0.169026
$867$	5.07738	0.172437
$868$	−17.3994	−0.590573
$869$	−2.65992	−0.0902317
$870$	−2.22663	−0.0754899
$871$	14.3994	0.487907
$872$	−1.21159	−0.0410296
$873$	−36.3343	−1.22973
$874$	−4.38723	−0.148400
$875$	−31.7262	−1.07254
$876$	−4.87056	−0.164561
$877$	−20.9708	−0.708134	−0.354067	−	0.935220i	$-0.615201\pi$
$877$	−20.9708	−0.708134	−0.354067	+	0.935220i	$0.615201\pi$
$878$	31.9558	1.07846
$879$	−1.77440	−0.0598489
$880$	0.191291	0.00644841
$881$	−9.75349	−0.328604	−0.164302	−	0.986410i	$-0.552537\pi$
$881$	−9.75349	−0.328604	−0.164302	+	0.986410i	$0.552537\pi$
$882$	−37.0049	−1.24602
$883$	−37.4119	−1.25901	−0.629506	−	0.776996i	$-0.716743\pi$
$883$	−37.4119	−1.25901	−0.629506	+	0.776996i	$0.716743\pi$
$884$	−6.93518	−0.233255
$885$	0.666099	0.0223907
$886$	−20.1812	−0.678002
$887$	21.7466	0.730178	0.365089	−	0.930973i	$-0.381039\pi$
$887$	21.7466	0.730178	0.365089	+	0.930973i	$0.381039\pi$
$888$	1.89148	0.0634740
$889$	−15.6570	−0.525119
$890$	−2.60332	−0.0872636
$891$	−1.83036	−0.0613193
$892$	22.5538	0.755157
$893$	−12.5980	−0.421577
$894$	−5.21527	−0.174425
$895$	3.05230	0.102027
$896$	−4.50236	−0.150413
$897$	5.73198	0.191385
$898$	34.1665	1.14015
$899$	−25.0661	−0.836001
$900$	12.3892	0.412973
$901$	−5.40386	−0.180029
$902$	0.910447	0.0303146
$903$	15.5788	0.518431
$904$	−10.4094	−0.346212
$905$	−6.81852	−0.226655
$906$	−1.26092	−0.0418914
$907$	−5.22188	−0.173390	−0.0866948	−	0.996235i	$-0.527630\pi$
$907$	−5.22188	−0.173390	−0.0866948	+	0.996235i	$0.527630\pi$
$908$	23.4512	0.778256
$909$	39.9246	1.32421
$910$	9.54155	0.316299
$911$	54.3509	1.80073	0.900363	−	0.435139i	$-0.143301\pi$
$911$	54.3509	1.80073	0.900363	+	0.435139i	$0.143301\pi$
$912$	−0.460040	−0.0152334
$913$	−2.34122	−0.0774829
$914$	41.7679	1.38156
$915$	2.62862	0.0868995
$916$	2.68431	0.0886920
$917$	54.8052	1.80983
$918$	−6.50264	−0.214619
$919$	37.4418	1.23509	0.617546	−	0.786535i	$-0.288127\pi$
$919$	37.4418	1.23509	0.617546	+	0.786535i	$0.288127\pi$
$920$	3.27379	0.107934
$921$	−0.0844563	−0.00278293
$922$	5.00415	0.164803
$923$	−7.54644	−0.248394
$924$	−0.530969	−0.0174676
$925$	18.2684	0.600661
$926$	−12.9335	−0.425021
$927$	34.5382	1.13438
$928$	−6.48624	−0.212921
$929$	19.2829	0.632652	0.316326	−	0.948650i	$-0.397551\pi$
$929$	19.2829	0.632652	0.316326	+	0.948650i	$0.397551\pi$
$930$	1.32663	0.0435018
$931$	13.2712	0.434946
$932$	1.44592	0.0473626
$933$	7.89226	0.258381
$934$	−37.9576	−1.24201
$935$	−0.467125	−0.0152766
$936$	−7.91896	−0.258839
$937$	−27.1090	−0.885612	−0.442806	−	0.896617i	$-0.646017\pi$
$937$	−27.1090	−0.885612	−0.442806	+	0.896617i	$0.646017\pi$
$938$	−22.8279	−0.745359
$939$	3.38265	0.110389
$940$	9.40076	0.306619
$941$	10.9052	0.355499	0.177749	−	0.984076i	$-0.443118\pi$
$941$	10.9052	0.355499	0.177749	+	0.984076i	$0.443118\pi$
$942$	−6.51353	−0.212222
$943$	15.5816	0.507406
$944$	1.94036	0.0631535
$945$	8.94646	0.291028
$946$	−1.92812	−0.0626886
$947$	−1.10143	−0.0357918	−0.0178959	−	0.999840i	$-0.505697\pi$
$947$	−1.10143	−0.0357918	−0.0178959	+	0.999840i	$0.505697\pi$
$948$	−4.77343	−0.155034
$949$	30.0678	0.976044
$950$	−4.44317	−0.144156
$951$	−7.82922	−0.253880
$952$	10.9946	0.356336
$953$	−5.42014	−0.175576	−0.0877879	−	0.996139i	$-0.527980\pi$
$953$	−5.42014	−0.175576	−0.0877879	+	0.996139i	$0.527980\pi$
$954$	−6.17042	−0.199775
$955$	7.06114	0.228493
$956$	−4.79113	−0.154956
$957$	−0.764931	−0.0247267
$958$	14.0415	0.453659
$959$	−15.9093	−0.513738
$960$	0.343286	0.0110795
$961$	−16.0656	−0.518246
$962$	−11.6769	−0.376477
$963$	40.9863	1.32077
$964$	16.1347	0.519662
$965$	−16.2057	−0.521680
$966$	−9.08711	−0.292373
$967$	−14.5172	−0.466841	−0.233420	−	0.972376i	$-0.574992\pi$
$967$	−14.5172	−0.466841	−0.233420	+	0.972376i	$0.574992\pi$
$968$	−10.9343	−0.351441
$969$	1.12340	0.0360888
$970$	−9.72362	−0.312207
$971$	50.8301	1.63122	0.815609	−	0.578604i	$-0.196402\pi$
$971$	50.8301	1.63122	0.815609	+	0.578604i	$0.196402\pi$
$972$	−11.2733	−0.361593
$973$	−98.5940	−3.16078
$974$	−10.4745	−0.335625
$975$	5.80507	0.185911
$976$	7.65724	0.245102
$977$	−29.7415	−0.951516	−0.475758	−	0.879576i	$-0.657826\pi$
$977$	−29.7415	−0.951516	−0.475758	+	0.879576i	$0.657826\pi$
$978$	−2.95475	−0.0944824
$979$	−0.894339	−0.0285832
$980$	−9.90309	−0.316342
$981$	3.37835	0.107863
$982$	−30.5611	−0.975245
$983$	−45.7363	−1.45876	−0.729381	−	0.684107i	$-0.760192\pi$
$983$	−45.7363	−1.45876	−0.729381	+	0.684107i	$0.760192\pi$
$984$	1.63386	0.0520857
$985$	5.80382	0.184925
$986$	15.8392	0.504421
$987$	−26.0938	−0.830575
$988$	2.84000	0.0903525
$989$	−32.9982	−1.04928
$990$	−0.533388	−0.0169522
$991$	16.6340	0.528396	0.264198	−	0.964468i	$-0.414893\pi$
$991$	16.6340	0.528396	0.264198	+	0.964468i	$0.414893\pi$
$992$	3.86450	0.122698
$993$	4.63830	0.147192
$994$	11.9636	0.379464
$995$	3.85781	0.122301
$996$	−4.20148	−0.133129
$997$	10.6200	0.336338	0.168169	−	0.985758i	$-0.446215\pi$
$997$	10.6200	0.336338	0.168169	+	0.985758i	$0.446215\pi$
$998$	20.9497	0.663152
$999$	−10.9486	−0.346398

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.k.1.19	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.k.1.19	✓	49	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.460040 q^{3} +1.00000 q^{4} -0.746209 q^{5} -0.460040 q^{6} -4.50236 q^{7} +1.00000 q^{8} -2.78836 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.460040 q^{3} +1.00000 q^{4} -0.746209 q^{5} -0.460040 q^{6} -4.50236 q^{7} +1.00000 q^{8} -2.78836 q^{9} -0.746209 q^{10} -0.256350 q^{11} -0.460040 q^{12} +2.84000 q^{13} -4.50236 q^{14} +0.343286 q^{15} +1.00000 q^{16} -2.44196 q^{17} -2.78836 q^{18} +1.00000 q^{19} -0.746209 q^{20} +2.07126 q^{21} -0.256350 q^{22} -4.38723 q^{23} -0.460040 q^{24} -4.44317 q^{25} +2.84000 q^{26} +2.66288 q^{27} -4.50236 q^{28} -6.48624 q^{29} +0.343286 q^{30} +3.86450 q^{31} +1.00000 q^{32} +0.117931 q^{33} -2.44196 q^{34} +3.35970 q^{35} -2.78836 q^{36} -4.11156 q^{37} +1.00000 q^{38} -1.30651 q^{39} -0.746209 q^{40} -3.55157 q^{41} +2.07126 q^{42} +7.52143 q^{43} -0.256350 q^{44} +2.08070 q^{45} -4.38723 q^{46} -12.5980 q^{47} -0.460040 q^{48} +13.2712 q^{49} -4.44317 q^{50} +1.12340 q^{51} +2.84000 q^{52} +2.21292 q^{53} +2.66288 q^{54} +0.191291 q^{55} -4.50236 q^{56} -0.460040 q^{57} -6.48624 q^{58} +1.94036 q^{59} +0.343286 q^{60} +7.65724 q^{61} +3.86450 q^{62} +12.5542 q^{63} +1.00000 q^{64} -2.11923 q^{65} +0.117931 q^{66} +5.07022 q^{67} -2.44196 q^{68} +2.01830 q^{69} +3.35970 q^{70} -2.65720 q^{71} -2.78836 q^{72} +10.5873 q^{73} -4.11156 q^{74} +2.04404 q^{75} +1.00000 q^{76} +1.15418 q^{77} -1.30651 q^{78} +10.3761 q^{79} -0.746209 q^{80} +7.14006 q^{81} -3.55157 q^{82} +9.13287 q^{83} +2.07126 q^{84} +1.82221 q^{85} +7.52143 q^{86} +2.98393 q^{87} -0.256350 q^{88} +3.48874 q^{89} +2.08070 q^{90} -12.7867 q^{91} -4.38723 q^{92} -1.77782 q^{93} -12.5980 q^{94} -0.746209 q^{95} -0.460040 q^{96} +13.0307 q^{97} +13.2712 q^{98} +0.714798 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9}+O(q^{10}) \) 49 * q + 49 * q^2 + 13 * q^3 + 49 * q^4 + 17 * q^5 + 13 * q^6 + 22 * q^7 + 49 * q^8 + 66 * q^9	\( 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9} + 17 q^{10} + 21 q^{11} + 13 q^{12} + 13 q^{13} + 22 q^{14} + 8 q^{15} + 49 q^{16} + 24 q^{17} + 66 q^{18} + 49 q^{19} + 17 q^{20} + 6 q^{21} + 21 q^{22} + 22 q^{23} + 13 q^{24} + 96 q^{25} + 13 q^{26} + 31 q^{27} + 22 q^{28} + 33 q^{29} + 8 q^{30} + 21 q^{31} + 49 q^{32} + 20 q^{33} + 24 q^{34} + 18 q^{35} + 66 q^{36} + 48 q^{37} + 49 q^{38} + 4 q^{39} + 17 q^{40} + 37 q^{41} + 6 q^{42} + 43 q^{43} + 21 q^{44} + 47 q^{45} + 22 q^{46} + 7 q^{47} + 13 q^{48} + 87 q^{49} + 96 q^{50} + 12 q^{51} + 13 q^{52} + 23 q^{53} + 31 q^{54} + 31 q^{55} + 22 q^{56} + 13 q^{57} + 33 q^{58} + 37 q^{59} + 8 q^{60} + 61 q^{61} + 21 q^{62} + 45 q^{63} + 49 q^{64} + 36 q^{65} + 20 q^{66} + 43 q^{67} + 24 q^{68} + 18 q^{69} + 18 q^{70} + 14 q^{71} + 66 q^{72} + 90 q^{73} + 48 q^{74} + 53 q^{75} + 49 q^{76} + 46 q^{77} + 4 q^{78} + 16 q^{79} + 17 q^{80} + 97 q^{81} + 37 q^{82} + 11 q^{83} + 6 q^{84} + 88 q^{85} + 43 q^{86} - 35 q^{87} + 21 q^{88} + 46 q^{89} + 47 q^{90} + 27 q^{91} + 22 q^{92} + 9 q^{93} + 7 q^{94} + 17 q^{95} + 13 q^{96} + 34 q^{97} + 87 q^{98} + 84 q^{99}+O(q^{100}) \) 49 * q + 49 * q^2 + 13 * q^3 + 49 * q^4 + 17 * q^5 + 13 * q^6 + 22 * q^7 + 49 * q^8 + 66 * q^9 + 17 * q^10 + 21 * q^11 + 13 * q^12 + 13 * q^13 + 22 * q^14 + 8 * q^15 + 49 * q^16 + 24 * q^17 + 66 * q^18 + 49 * q^19 + 17 * q^20 + 6 * q^21 + 21 * q^22 + 22 * q^23 + 13 * q^24 + 96 * q^25 + 13 * q^26 + 31 * q^27 + 22 * q^28 + 33 * q^29 + 8 * q^30 + 21 * q^31 + 49 * q^32 + 20 * q^33 + 24 * q^34 + 18 * q^35 + 66 * q^36 + 48 * q^37 + 49 * q^38 + 4 * q^39 + 17 * q^40 + 37 * q^41 + 6 * q^42 + 43 * q^43 + 21 * q^44 + 47 * q^45 + 22 * q^46 + 7 * q^47 + 13 * q^48 + 87 * q^49 + 96 * q^50 + 12 * q^51 + 13 * q^52 + 23 * q^53 + 31 * q^54 + 31 * q^55 + 22 * q^56 + 13 * q^57 + 33 * q^58 + 37 * q^59 + 8 * q^60 + 61 * q^61 + 21 * q^62 + 45 * q^63 + 49 * q^64 + 36 * q^65 + 20 * q^66 + 43 * q^67 + 24 * q^68 + 18 * q^69 + 18 * q^70 + 14 * q^71 + 66 * q^72 + 90 * q^73 + 48 * q^74 + 53 * q^75 + 49 * q^76 + 46 * q^77 + 4 * q^78 + 16 * q^79 + 17 * q^80 + 97 * q^81 + 37 * q^82 + 11 * q^83 + 6 * q^84 + 88 * q^85 + 43 * q^86 - 35 * q^87 + 21 * q^88 + 46 * q^89 + 47 * q^90 + 27 * q^91 + 22 * q^92 + 9 * q^93 + 7 * q^94 + 17 * q^95 + 13 * q^96 + 34 * q^97 + 87 * q^98 + 84 * q^99

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