LMFDB - Embedded newform 8018.2.a.e.1.8

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:	$1$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.92818 q^{3} +1.00000 q^{4} -0.990094 q^{5} -1.92818 q^{6} +2.57830 q^{7} +1.00000 q^{8} +0.717864 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.92818 q^{3} +1.00000 q^{4} -0.990094 q^{5} -1.92818 q^{6} +2.57830 q^{7} +1.00000 q^{8} +0.717864 q^{9} -0.990094 q^{10} +1.94413 q^{11} -1.92818 q^{12} +2.98889 q^{13} +2.57830 q^{14} +1.90907 q^{15} +1.00000 q^{16} +0.268732 q^{17} +0.717864 q^{18} -1.00000 q^{19} -0.990094 q^{20} -4.97141 q^{21} +1.94413 q^{22} -5.59119 q^{23} -1.92818 q^{24} -4.01971 q^{25} +2.98889 q^{26} +4.40036 q^{27} +2.57830 q^{28} -2.20661 q^{29} +1.90907 q^{30} -8.68104 q^{31} +1.00000 q^{32} -3.74862 q^{33} +0.268732 q^{34} -2.55275 q^{35} +0.717864 q^{36} +8.78817 q^{37} -1.00000 q^{38} -5.76310 q^{39} -0.990094 q^{40} -8.40839 q^{41} -4.97141 q^{42} -11.5413 q^{43} +1.94413 q^{44} -0.710752 q^{45} -5.59119 q^{46} +7.52236 q^{47} -1.92818 q^{48} -0.352387 q^{49} -4.01971 q^{50} -0.518162 q^{51} +2.98889 q^{52} -0.0668310 q^{53} +4.40036 q^{54} -1.92487 q^{55} +2.57830 q^{56} +1.92818 q^{57} -2.20661 q^{58} -9.06504 q^{59} +1.90907 q^{60} -14.9747 q^{61} -8.68104 q^{62} +1.85087 q^{63} +1.00000 q^{64} -2.95928 q^{65} -3.74862 q^{66} +13.5234 q^{67} +0.268732 q^{68} +10.7808 q^{69} -2.55275 q^{70} -5.59302 q^{71} +0.717864 q^{72} -1.45928 q^{73} +8.78817 q^{74} +7.75072 q^{75} -1.00000 q^{76} +5.01254 q^{77} -5.76310 q^{78} +10.9022 q^{79} -0.990094 q^{80} -10.6383 q^{81} -8.40839 q^{82} +13.7562 q^{83} -4.97141 q^{84} -0.266070 q^{85} -11.5413 q^{86} +4.25473 q^{87} +1.94413 q^{88} +11.5986 q^{89} -0.710752 q^{90} +7.70624 q^{91} -5.59119 q^{92} +16.7386 q^{93} +7.52236 q^{94} +0.990094 q^{95} -1.92818 q^{96} +5.98151 q^{97} -0.352387 q^{98} +1.39562 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9}+O(q^{10}) $ 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9} - 6 q^{10} - 21 q^{11} - 7 q^{12} - 19 q^{13} - 5 q^{14} - 14 q^{15} + 32 q^{16} - 14 q^{17} + 15 q^{18} - 32 q^{19} - 6 q^{20} - 26 q^{21} - 21 q^{22} - 13 q^{23} - 7 q^{24} - 10 q^{25} - 19 q^{26} - 25 q^{27} - 5 q^{28} - 42 q^{29} - 14 q^{30} - 15 q^{31} + 32 q^{32} - 32 q^{33} - 14 q^{34} - 22 q^{35} + 15 q^{36} - 54 q^{37} - 32 q^{38} - 32 q^{39} - 6 q^{40} - 16 q^{41} - 26 q^{42} - 37 q^{43} - 21 q^{44} - 46 q^{45} - 13 q^{46} - 9 q^{47} - 7 q^{48} - 7 q^{49} - 10 q^{50} - 32 q^{51} - 19 q^{52} - 53 q^{53} - 25 q^{54} - 17 q^{55} - 5 q^{56} + 7 q^{57} - 42 q^{58} - 34 q^{59} - 14 q^{60} - 33 q^{61} - 15 q^{62} + 18 q^{63} + 32 q^{64} - 50 q^{65} - 32 q^{66} - 53 q^{67} - 14 q^{68} - 40 q^{69} - 22 q^{70} - 27 q^{71} + 15 q^{72} - 43 q^{73} - 54 q^{74} + 5 q^{75} - 32 q^{76} - 56 q^{77} - 32 q^{78} - 11 q^{79} - 6 q^{80} - 8 q^{81} - 16 q^{82} - 17 q^{83} - 26 q^{84} - 30 q^{85} - 37 q^{86} + 3 q^{87} - 21 q^{88} - 21 q^{89} - 46 q^{90} - 67 q^{91} - 13 q^{92} - 31 q^{93} - 9 q^{94} + 6 q^{95} - 7 q^{96} - 51 q^{97} - 7 q^{98} - 32 q^{99}+O(q^{100}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9 - 6 * q^10 - 21 * q^11 - 7 * q^12 - 19 * q^13 - 5 * q^14 - 14 * q^15 + 32 * q^16 - 14 * q^17 + 15 * q^18 - 32 * q^19 - 6 * q^20 - 26 * q^21 - 21 * q^22 - 13 * q^23 - 7 * q^24 - 10 * q^25 - 19 * q^26 - 25 * q^27 - 5 * q^28 - 42 * q^29 - 14 * q^30 - 15 * q^31 + 32 * q^32 - 32 * q^33 - 14 * q^34 - 22 * q^35 + 15 * q^36 - 54 * q^37 - 32 * q^38 - 32 * q^39 - 6 * q^40 - 16 * q^41 - 26 * q^42 - 37 * q^43 - 21 * q^44 - 46 * q^45 - 13 * q^46 - 9 * q^47 - 7 * q^48 - 7 * q^49 - 10 * q^50 - 32 * q^51 - 19 * q^52 - 53 * q^53 - 25 * q^54 - 17 * q^55 - 5 * q^56 + 7 * q^57 - 42 * q^58 - 34 * q^59 - 14 * q^60 - 33 * q^61 - 15 * q^62 + 18 * q^63 + 32 * q^64 - 50 * q^65 - 32 * q^66 - 53 * q^67 - 14 * q^68 - 40 * q^69 - 22 * q^70 - 27 * q^71 + 15 * q^72 - 43 * q^73 - 54 * q^74 + 5 * q^75 - 32 * q^76 - 56 * q^77 - 32 * q^78 - 11 * q^79 - 6 * q^80 - 8 * q^81 - 16 * q^82 - 17 * q^83 - 26 * q^84 - 30 * q^85 - 37 * q^86 + 3 * q^87 - 21 * q^88 - 21 * q^89 - 46 * q^90 - 67 * q^91 - 13 * q^92 - 31 * q^93 - 9 * q^94 + 6 * q^95 - 7 * q^96 - 51 * q^97 - 7 * q^98 - 32 * 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
$3$	−1.92818	−1.11323	−0.556617	−	0.830770i	$-0.687901\pi$
$3$	−1.92818	−1.11323	−0.556617	+	0.830770i	$0.687901\pi$
$4$	1.00000	0.500000
$5$	−0.990094	−0.442783	−0.221392	−	0.975185i	$-0.571060\pi$
$5$	−0.990094	−0.442783	−0.221392	+	0.975185i	$0.571060\pi$
$6$	−1.92818	−0.787175
$7$	2.57830	0.974504	0.487252	−	0.873261i	$-0.337999\pi$
$7$	2.57830	0.974504	0.487252	+	0.873261i	$0.337999\pi$
$8$	1.00000	0.353553
$9$	0.717864	0.239288
$10$	−0.990094	−0.313095
$11$	1.94413	0.586177	0.293088	−	0.956085i	$-0.405317\pi$
$11$	1.94413	0.586177	0.293088	+	0.956085i	$0.405317\pi$
$12$	−1.92818	−0.556617
$13$	2.98889	0.828968	0.414484	−	0.910057i	$-0.363962\pi$
$13$	2.98889	0.828968	0.414484	+	0.910057i	$0.363962\pi$
$14$	2.57830	0.689079
$15$	1.90907	0.492921
$16$	1.00000	0.250000
$17$	0.268732	0.0651770	0.0325885	−	0.999469i	$-0.489625\pi$
$17$	0.268732	0.0651770	0.0325885	+	0.999469i	$0.489625\pi$
$18$	0.717864	0.169202
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−0.990094	−0.221392
$21$	−4.97141	−1.08485
$22$	1.94413	0.414490
$23$	−5.59119	−1.16584	−0.582922	−	0.812528i	$-0.698091\pi$
$23$	−5.59119	−1.16584	−0.582922	+	0.812528i	$0.698091\pi$
$24$	−1.92818	−0.393587
$25$	−4.01971	−0.803943
$26$	2.98889	0.586169
$27$	4.40036	0.846850
$28$	2.57830	0.487252
$29$	−2.20661	−0.409757	−0.204879	−	0.978787i	$-0.565680\pi$
$29$	−2.20661	−0.409757	−0.204879	+	0.978787i	$0.565680\pi$
$30$	1.90907	0.348548
$31$	−8.68104	−1.55916	−0.779580	−	0.626302i	$-0.784568\pi$
$31$	−8.68104	−1.55916	−0.779580	+	0.626302i	$0.784568\pi$
$32$	1.00000	0.176777
$33$	−3.74862	−0.652551
$34$	0.268732	0.0460871
$35$	−2.55275	−0.431494
$36$	0.717864	0.119644
$37$	8.78817	1.44477	0.722384	−	0.691493i	$-0.243047\pi$
$37$	8.78817	1.44477	0.722384	+	0.691493i	$0.243047\pi$
$38$	−1.00000	−0.162221
$39$	−5.76310	−0.922835
$40$	−0.990094	−0.156548
$41$	−8.40839	−1.31317	−0.656585	−	0.754252i	$-0.728000\pi$
$41$	−8.40839	−1.31317	−0.656585	+	0.754252i	$0.728000\pi$
$42$	−4.97141	−0.767105
$43$	−11.5413	−1.76002	−0.880012	−	0.474951i	$-0.842466\pi$
$43$	−11.5413	−1.76002	−0.880012	+	0.474951i	$0.842466\pi$
$44$	1.94413	0.293088
$45$	−0.710752	−0.105953
$46$	−5.59119	−0.824376
$47$	7.52236	1.09725	0.548624	−	0.836069i	$-0.315152\pi$
$47$	7.52236	1.09725	0.548624	+	0.836069i	$0.315152\pi$
$48$	−1.92818	−0.278308
$49$	−0.352387	−0.0503410
$50$	−4.01971	−0.568474
$51$	−0.518162	−0.0725572
$52$	2.98889	0.414484
$53$	−0.0668310	−0.00917994	−0.00458997	−	0.999989i	$-0.501461\pi$
$53$	−0.0668310	−0.00917994	−0.00458997	+	0.999989i	$0.501461\pi$
$54$	4.40036	0.598813
$55$	−1.92487	−0.259549
$56$	2.57830	0.344539
$57$	1.92818	0.255393
$58$	−2.20661	−0.289742
$59$	−9.06504	−1.18017	−0.590084	−	0.807342i	$-0.700905\pi$
$59$	−9.06504	−1.18017	−0.590084	+	0.807342i	$0.700905\pi$
$60$	1.90907	0.246461
$61$	−14.9747	−1.91732	−0.958660	−	0.284555i	$-0.908154\pi$
$61$	−14.9747	−1.91732	−0.958660	+	0.284555i	$0.908154\pi$
$62$	−8.68104	−1.10249
$63$	1.85087	0.233187
$64$	1.00000	0.125000
$65$	−2.95928	−0.367053
$66$	−3.74862	−0.461424
$67$	13.5234	1.65214	0.826071	−	0.563566i	$-0.190571\pi$
$67$	13.5234	1.65214	0.826071	+	0.563566i	$0.190571\pi$
$68$	0.268732	0.0325885
$69$	10.7808	1.29786
$70$	−2.55275	−0.305113
$71$	−5.59302	−0.663770	−0.331885	−	0.943320i	$-0.607685\pi$
$71$	−5.59302	−0.663770	−0.331885	+	0.943320i	$0.607685\pi$
$72$	0.717864	0.0846011
$73$	−1.45928	−0.170796	−0.0853978	−	0.996347i	$-0.527216\pi$
$73$	−1.45928	−0.170796	−0.0853978	+	0.996347i	$0.527216\pi$
$74$	8.78817	1.02160
$75$	7.75072	0.894976
$76$	−1.00000	−0.114708
$77$	5.01254	0.571232
$78$	−5.76310	−0.652543
$79$	10.9022	1.22659	0.613297	−	0.789853i	$-0.289843\pi$
$79$	10.9022	1.22659	0.613297	+	0.789853i	$0.289843\pi$
$80$	−0.990094	−0.110696
$81$	−10.6383	−1.18203
$82$	−8.40839	−0.928551
$83$	13.7562	1.50994	0.754971	−	0.655758i	$-0.227651\pi$
$83$	13.7562	1.50994	0.754971	+	0.655758i	$0.227651\pi$
$84$	−4.97141	−0.542425
$85$	−0.266070	−0.0288593
$86$	−11.5413	−1.24453
$87$	4.25473	0.456155
$88$	1.94413	0.207245
$89$	11.5986	1.22945	0.614724	−	0.788742i	$-0.289267\pi$
$89$	11.5986	1.22945	0.614724	+	0.788742i	$0.289267\pi$
$90$	−0.710752	−0.0749199
$91$	7.70624	0.807833
$92$	−5.59119	−0.582922
$93$	16.7386	1.73571
$94$	7.52236	0.775872
$95$	0.990094	0.101581
$96$	−1.92818	−0.196794
$97$	5.98151	0.607331	0.303665	−	0.952779i	$-0.401790\pi$
$97$	5.98151	0.607331	0.303665	+	0.952779i	$0.401790\pi$
$98$	−0.352387	−0.0355965
$99$	1.39562	0.140265
$100$	−4.01971	−0.401971
$101$	10.2239	1.01732	0.508659	−	0.860968i	$-0.330141\pi$
$101$	10.2239	1.01732	0.508659	+	0.860968i	$0.330141\pi$
$102$	−0.518162	−0.0513057
$103$	0.133709	0.0131747	0.00658735	−	0.999978i	$-0.497903\pi$
$103$	0.133709	0.0131747	0.00658735	+	0.999978i	$0.497903\pi$
$104$	2.98889	0.293085
$105$	4.92216	0.480354
$106$	−0.0668310	−0.00649120
$107$	3.30683	0.319683	0.159842	−	0.987143i	$-0.448902\pi$
$107$	3.30683	0.319683	0.159842	+	0.987143i	$0.448902\pi$
$108$	4.40036	0.423425
$109$	−6.45699	−0.618467	−0.309234	−	0.950986i	$-0.600073\pi$
$109$	−6.45699	−0.618467	−0.309234	+	0.950986i	$0.600073\pi$
$110$	−1.92487	−0.183529
$111$	−16.9452	−1.60836
$112$	2.57830	0.243626
$113$	−13.4151	−1.26199	−0.630993	−	0.775789i	$-0.717352\pi$
$113$	−13.4151	−1.26199	−0.630993	+	0.775789i	$0.717352\pi$
$114$	1.92818	0.180590
$115$	5.53580	0.516216
$116$	−2.20661	−0.204879
$117$	2.14561	0.198362
$118$	−9.06504	−0.834504
$119$	0.692870	0.0635153
$120$	1.90907	0.174274
$121$	−7.22036	−0.656397
$122$	−14.9747	−1.35575
$123$	16.2128	1.46186
$124$	−8.68104	−0.779580
$125$	8.93036	0.798756
$126$	1.85087	0.164888
$127$	−12.9915	−1.15281	−0.576406	−	0.817164i	$-0.695545\pi$
$127$	−12.9915	−1.15281	−0.576406	+	0.817164i	$0.695545\pi$
$128$	1.00000	0.0883883
$129$	22.2536	1.95932
$130$	−2.95928	−0.259546
$131$	−16.6541	−1.45508	−0.727538	−	0.686067i	$-0.759335\pi$
$131$	−16.6541	−1.45508	−0.727538	+	0.686067i	$0.759335\pi$
$132$	−3.74862	−0.326276
$133$	−2.57830	−0.223567
$134$	13.5234	1.16824
$135$	−4.35677	−0.374971
$136$	0.268732	0.0230436
$137$	20.2203	1.72754	0.863769	−	0.503887i	$-0.168097\pi$
$137$	20.2203	1.72754	0.863769	+	0.503887i	$0.168097\pi$
$138$	10.7808	0.917723
$139$	−13.2878	−1.12706	−0.563529	−	0.826096i	$-0.690557\pi$
$139$	−13.2878	−1.12706	−0.563529	+	0.826096i	$0.690557\pi$
$140$	−2.55275	−0.215747
$141$	−14.5044	−1.22149
$142$	−5.59302	−0.469356
$143$	5.81078	0.485922
$144$	0.717864	0.0598220
$145$	2.18475	0.181434
$146$	−1.45928	−0.120771
$147$	0.679464	0.0560413
$148$	8.78817	0.722384
$149$	−18.3444	−1.50284	−0.751418	−	0.659827i	$-0.770630\pi$
$149$	−18.3444	−1.50284	−0.751418	+	0.659827i	$0.770630\pi$
$150$	7.75072	0.632844
$151$	−2.50997	−0.204259	−0.102129	−	0.994771i	$-0.532566\pi$
$151$	−2.50997	−0.204259	−0.102129	+	0.994771i	$0.532566\pi$
$152$	−1.00000	−0.0811107
$153$	0.192913	0.0155961
$154$	5.01254	0.403922
$155$	8.59504	0.690370
$156$	−5.76310	−0.461418
$157$	4.20604	0.335679	0.167839	−	0.985814i	$-0.446321\pi$
$157$	4.20604	0.335679	0.167839	+	0.985814i	$0.446321\pi$
$158$	10.9022	0.867332
$159$	0.128862	0.0102194
$160$	−0.990094	−0.0782738
$161$	−14.4158	−1.13612
$162$	−10.6383	−0.835821
$163$	−4.07933	−0.319518	−0.159759	−	0.987156i	$-0.551072\pi$
$163$	−4.07933	−0.319518	−0.159759	+	0.987156i	$0.551072\pi$
$164$	−8.40839	−0.656585
$165$	3.71149	0.288939
$166$	13.7562	1.06769
$167$	1.93048	0.149385	0.0746924	−	0.997207i	$-0.476203\pi$
$167$	1.93048	0.149385	0.0746924	+	0.997207i	$0.476203\pi$
$168$	−4.97141	−0.383553
$169$	−4.06655	−0.312811
$170$	−0.266070	−0.0204066
$171$	−0.717864	−0.0548964
$172$	−11.5413	−0.880012
$173$	−10.9039	−0.829010	−0.414505	−	0.910047i	$-0.636045\pi$
$173$	−10.9039	−0.829010	−0.414505	+	0.910047i	$0.636045\pi$
$174$	4.25473	0.322550
$175$	−10.3640	−0.783446
$176$	1.94413	0.146544
$177$	17.4790	1.31380
$178$	11.5986	0.869351
$179$	−16.0460	−1.19933	−0.599666	−	0.800250i	$-0.704700\pi$
$179$	−16.0460	−1.19933	−0.599666	+	0.800250i	$0.704700\pi$
$180$	−0.710752	−0.0529764
$181$	−18.2159	−1.35398	−0.676988	−	0.735994i	$-0.736715\pi$
$181$	−18.2159	−1.35398	−0.676988	+	0.735994i	$0.736715\pi$
$182$	7.70624	0.571224
$183$	28.8739	2.13442
$184$	−5.59119	−0.412188
$185$	−8.70112	−0.639719
$186$	16.7386	1.22733
$187$	0.522449	0.0382053
$188$	7.52236	0.548624
$189$	11.3454	0.825259
$190$	0.990094	0.0718289
$191$	−15.0671	−1.09022	−0.545109	−	0.838365i	$-0.683512\pi$
$191$	−15.0671	−1.09022	−0.545109	+	0.838365i	$0.683512\pi$
$192$	−1.92818	−0.139154
$193$	−3.07910	−0.221638	−0.110819	−	0.993841i	$-0.535347\pi$
$193$	−3.07910	−0.221638	−0.110819	+	0.993841i	$0.535347\pi$
$194$	5.98151	0.429448
$195$	5.70601	0.408616
$196$	−0.352387	−0.0251705
$197$	22.8402	1.62730	0.813649	−	0.581357i	$-0.197478\pi$
$197$	22.8402	1.62730	0.813649	+	0.581357i	$0.197478\pi$
$198$	1.39562	0.0991824
$199$	−18.1633	−1.28757	−0.643783	−	0.765208i	$-0.722636\pi$
$199$	−18.1633	−1.28757	−0.643783	+	0.765208i	$0.722636\pi$
$200$	−4.01971	−0.284237
$201$	−26.0754	−1.83922
$202$	10.2239	0.719353
$203$	−5.68929	−0.399310
$204$	−0.518162	−0.0362786
$205$	8.32509	0.581449
$206$	0.133709	0.00931592
$207$	−4.01372	−0.278973
$208$	2.98889	0.207242
$209$	−1.94413	−0.134478
$210$	4.92216	0.339661
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−0.0668310	−0.00458997
$213$	10.7843	0.738930
$214$	3.30683	0.226050
$215$	11.4269	0.779310
$216$	4.40036	0.299407
$217$	−22.3823	−1.51941
$218$	−6.45699	−0.437323
$219$	2.81374	0.190135
$220$	−1.92487	−0.129775
$221$	0.803209	0.0540297
$222$	−16.9452	−1.13728
$223$	9.38745	0.628630	0.314315	−	0.949319i	$-0.398225\pi$
$223$	9.38745	0.628630	0.314315	+	0.949319i	$0.398225\pi$
$224$	2.57830	0.172270
$225$	−2.88561	−0.192374
$226$	−13.4151	−0.892358
$227$	3.02935	0.201065	0.100533	−	0.994934i	$-0.467945\pi$
$227$	3.02935	0.201065	0.100533	+	0.994934i	$0.467945\pi$
$228$	1.92818	0.127697
$229$	24.2534	1.60271	0.801355	−	0.598190i	$-0.204113\pi$
$229$	24.2534	1.60271	0.801355	+	0.598190i	$0.204113\pi$
$230$	5.53580	0.365020
$231$	−9.66506	−0.635914
$232$	−2.20661	−0.144871
$233$	−25.5496	−1.67381	−0.836906	−	0.547347i	$-0.815638\pi$
$233$	−25.5496	−1.67381	−0.836906	+	0.547347i	$0.815638\pi$
$234$	2.14561	0.140263
$235$	−7.44784	−0.485843
$236$	−9.06504	−0.590084
$237$	−21.0214	−1.36548
$238$	0.692870	0.0449121
$239$	25.8236	1.67039	0.835196	−	0.549952i	$-0.185354\pi$
$239$	25.8236	1.67039	0.835196	+	0.549952i	$0.185354\pi$
$240$	1.90907	0.123230
$241$	−3.12994	−0.201617	−0.100809	−	0.994906i	$-0.532143\pi$
$241$	−3.12994	−0.201617	−0.100809	+	0.994906i	$0.532143\pi$
$242$	−7.22036	−0.464143
$243$	7.31136	0.469024
$244$	−14.9747	−0.958660
$245$	0.348896	0.0222902
$246$	16.2128	1.03369
$247$	−2.98889	−0.190178
$248$	−8.68104	−0.551247
$249$	−26.5244	−1.68092
$250$	8.93036	0.564806
$251$	6.86046	0.433028	0.216514	−	0.976279i	$-0.430531\pi$
$251$	6.86046	0.433028	0.216514	+	0.976279i	$0.430531\pi$
$252$	1.85087	0.116594
$253$	−10.8700	−0.683391
$254$	−12.9915	−0.815161
$255$	0.513029	0.0321271
$256$	1.00000	0.0625000
$257$	−5.39222	−0.336358	−0.168179	−	0.985757i	$-0.553789\pi$
$257$	−5.39222	−0.336358	−0.168179	+	0.985757i	$0.553789\pi$
$258$	22.2536	1.38545
$259$	22.6585	1.40793
$260$	−2.95928	−0.183527
$261$	−1.58405	−0.0980500
$262$	−16.6541	−1.02889
$263$	−0.179009	−0.0110382	−0.00551908	−	0.999985i	$-0.501757\pi$
$263$	−0.179009	−0.0110382	−0.00551908	+	0.999985i	$0.501757\pi$
$264$	−3.74862	−0.230712
$265$	0.0661689	0.00406472
$266$	−2.57830	−0.158086
$267$	−22.3641	−1.36866
$268$	13.5234	0.826071
$269$	21.2789	1.29740	0.648699	−	0.761045i	$-0.275313\pi$
$269$	21.2789	1.29740	0.648699	+	0.761045i	$0.275313\pi$
$270$	−4.35677	−0.265145
$271$	0.000837891 0	5.08983e−5 0	2.54491e−5	−	1.00000i	$-0.499992\pi$
$271$	0.000837891 0	5.08983e−5 0	2.54491e−5		1.00000i	$0.499992\pi$
$272$	0.268732	0.0162943
$273$	−14.8590	−0.899307
$274$	20.2203	1.22155
$275$	−7.81484	−0.471253
$276$	10.7808	0.648928
$277$	−24.3494	−1.46301	−0.731507	−	0.681834i	$-0.761182\pi$
$277$	−24.3494	−1.46301	−0.731507	+	0.681834i	$0.761182\pi$
$278$	−13.2878	−0.796951
$279$	−6.23180	−0.373088
$280$	−2.55275	−0.152556
$281$	6.62031	0.394935	0.197467	−	0.980309i	$-0.436728\pi$
$281$	6.62031	0.394935	0.197467	+	0.980309i	$0.436728\pi$
$282$	−14.5044	−0.863726
$283$	26.5408	1.57769	0.788843	−	0.614595i	$-0.210681\pi$
$283$	26.5408	1.57769	0.788843	+	0.614595i	$0.210681\pi$
$284$	−5.59302	−0.331885
$285$	−1.90907	−0.113084
$286$	5.81078	0.343599
$287$	−21.6793	−1.27969
$288$	0.717864	0.0423005
$289$	−16.9278	−0.995752
$290$	2.18475	0.128293
$291$	−11.5334	−0.676101
$292$	−1.45928	−0.0853978
$293$	−21.4870	−1.25528	−0.627642	−	0.778502i	$-0.715980\pi$
$293$	−21.4870	−1.25528	−0.627642	+	0.778502i	$0.715980\pi$
$294$	0.679464	0.0396272
$295$	8.97523	0.522558
$296$	8.78817	0.510802
$297$	8.55487	0.496404
$298$	−18.3444	−1.06267
$299$	−16.7114	−0.966448
$300$	7.75072	0.447488
$301$	−29.7568	−1.71515
$302$	−2.50997	−0.144433
$303$	−19.7135	−1.13251
$304$	−1.00000	−0.0573539
$305$	14.8264	0.848957
$306$	0.192913	0.0110281
$307$	−25.8012	−1.47255	−0.736277	−	0.676681i	$-0.763418\pi$
$307$	−25.8012	−1.47255	−0.736277	+	0.676681i	$0.763418\pi$
$308$	5.01254	0.285616
$309$	−0.257814	−0.0146665
$310$	8.59504	0.488166
$311$	−3.23630	−0.183514	−0.0917569	−	0.995781i	$-0.529248\pi$
$311$	−3.23630	−0.183514	−0.0917569	+	0.995781i	$0.529248\pi$
$312$	−5.76310	−0.326271
$313$	31.0954	1.75761	0.878807	−	0.477177i	$-0.158340\pi$
$313$	31.0954	1.75761	0.878807	+	0.477177i	$0.158340\pi$
$314$	4.20604	0.237361
$315$	−1.83253	−0.103251
$316$	10.9022	0.613297
$317$	9.92367	0.557369	0.278684	−	0.960383i	$-0.410102\pi$
$317$	9.92367	0.557369	0.278684	+	0.960383i	$0.410102\pi$
$318$	0.128862	0.00722621
$319$	−4.28993	−0.240190
$320$	−0.990094	−0.0553479
$321$	−6.37615	−0.355882
$322$	−14.4158	−0.803359
$323$	−0.268732	−0.0149526
$324$	−10.6383	−0.591015
$325$	−12.0145	−0.666443
$326$	−4.07933	−0.225933
$327$	12.4502	0.688498
$328$	−8.40839	−0.464275
$329$	19.3949	1.06927
$330$	3.71149	0.204311
$331$	3.11309	0.171111	0.0855556	−	0.996333i	$-0.472733\pi$
$331$	3.11309	0.171111	0.0855556	+	0.996333i	$0.472733\pi$
$332$	13.7562	0.754971
$333$	6.30871	0.345715
$334$	1.93048	0.105631
$335$	−13.3894	−0.731541
$336$	−4.97141	−0.271213
$337$	24.1689	1.31657	0.658283	−	0.752771i	$-0.271283\pi$
$337$	24.1689	1.31657	0.658283	+	0.752771i	$0.271283\pi$
$338$	−4.06655	−0.221191
$339$	25.8667	1.40488
$340$	−0.266070	−0.0144297
$341$	−16.8771	−0.913944
$342$	−0.717864	−0.0388176
$343$	−18.9566	−1.02356
$344$	−11.5413	−0.622263
$345$	−10.6740	−0.574669
$346$	−10.9039	−0.586198
$347$	−22.9811	−1.23369	−0.616844	−	0.787086i	$-0.711589\pi$
$347$	−22.9811	−1.23369	−0.616844	+	0.787086i	$0.711589\pi$
$348$	4.25473	0.228078
$349$	−27.2264	−1.45740	−0.728699	−	0.684835i	$-0.759874\pi$
$349$	−27.2264	−1.45740	−0.728699	+	0.684835i	$0.759874\pi$
$350$	−10.3640	−0.553980
$351$	13.1522	0.702012
$352$	1.94413	0.103622
$353$	10.3747	0.552191	0.276095	−	0.961130i	$-0.410959\pi$
$353$	10.3747	0.552191	0.276095	+	0.961130i	$0.410959\pi$
$354$	17.4790	0.928998
$355$	5.53762	0.293906
$356$	11.5986	0.614724
$357$	−1.33598	−0.0707074
$358$	−16.0460	−0.848056
$359$	−23.6161	−1.24641	−0.623206	−	0.782058i	$-0.714170\pi$
$359$	−23.6161	−1.24641	−0.623206	+	0.782058i	$0.714170\pi$
$360$	−0.710752	−0.0374599
$361$	1.00000	0.0526316
$362$	−18.2159	−0.957406
$363$	13.9221	0.730723
$364$	7.70624	0.403917
$365$	1.44482	0.0756254
$366$	28.8739	1.50927
$367$	−29.7471	−1.55279	−0.776394	−	0.630248i	$-0.782953\pi$
$367$	−29.7471	−1.55279	−0.776394	+	0.630248i	$0.782953\pi$
$368$	−5.59119	−0.291461
$369$	−6.03608	−0.314226
$370$	−8.70112	−0.452349
$371$	−0.172310	−0.00894589
$372$	16.7386	0.867855
$373$	−29.2991	−1.51705	−0.758526	−	0.651643i	$-0.774080\pi$
$373$	−29.2991	−1.51705	−0.758526	+	0.651643i	$0.774080\pi$
$374$	0.522449	0.0270152
$375$	−17.2193	−0.889201
$376$	7.52236	0.387936
$377$	−6.59531	−0.339676
$378$	11.3454	0.583546
$379$	−1.92246	−0.0987499	−0.0493749	−	0.998780i	$-0.515723\pi$
$379$	−1.92246	−0.0987499	−0.0493749	+	0.998780i	$0.515723\pi$
$380$	0.990094	0.0507907
$381$	25.0500	1.28335
$382$	−15.0671	−0.770901
$383$	14.3126	0.731340	0.365670	−	0.930745i	$-0.380840\pi$
$383$	14.3126	0.731340	0.365670	+	0.930745i	$0.380840\pi$
$384$	−1.92818	−0.0983968
$385$	−4.96288	−0.252932
$386$	−3.07910	−0.156722
$387$	−8.28505	−0.421153
$388$	5.98151	0.303665
$389$	8.82759	0.447576	0.223788	−	0.974638i	$-0.428158\pi$
$389$	8.82759	0.447576	0.223788	+	0.974638i	$0.428158\pi$
$390$	5.70601	0.288935
$391$	−1.50253	−0.0759863
$392$	−0.352387	−0.0177982
$393$	32.1121	1.61984
$394$	22.8402	1.15067
$395$	−10.7942	−0.543115
$396$	1.39562	0.0701325
$397$	−11.1686	−0.560537	−0.280268	−	0.959922i	$-0.590423\pi$
$397$	−11.1686	−0.560537	−0.280268	+	0.959922i	$0.590423\pi$
$398$	−18.1633	−0.910446
$399$	4.97141	0.248882
$400$	−4.01971	−0.200986
$401$	−23.1985	−1.15848	−0.579238	−	0.815159i	$-0.696650\pi$
$401$	−23.1985	−1.15848	−0.579238	+	0.815159i	$0.696650\pi$
$402$	−26.0754	−1.30052
$403$	−25.9467	−1.29249
$404$	10.2239	0.508659
$405$	10.5329	0.523383
$406$	−5.68929	−0.282355
$407$	17.0853	0.846889
$408$	−0.518162	−0.0256529
$409$	−22.1636	−1.09592	−0.547960	−	0.836504i	$-0.684595\pi$
$409$	−22.1636	−1.09592	−0.547960	+	0.836504i	$0.684595\pi$
$410$	8.32509	0.411147
$411$	−38.9883	−1.92315
$412$	0.133709	0.00658735
$413$	−23.3724	−1.15008
$414$	−4.01372	−0.197263
$415$	−13.6200	−0.668577
$416$	2.98889	0.146542
$417$	25.6213	1.25468
$418$	−1.94413	−0.0950904
$419$	−6.45283	−0.315242	−0.157621	−	0.987500i	$-0.550382\pi$
$419$	−6.45283	−0.315242	−0.157621	+	0.987500i	$0.550382\pi$
$420$	4.92216	0.240177
$421$	−2.18675	−0.106575	−0.0532877	−	0.998579i	$-0.516970\pi$
$421$	−2.18675	−0.106575	−0.0532877	+	0.998579i	$0.516970\pi$
$422$	1.00000	0.0486792
$423$	5.40003	0.262558
$424$	−0.0668310	−0.00324560
$425$	−1.08023	−0.0523986
$426$	10.7843	0.522503
$427$	−38.6093	−1.86844
$428$	3.30683	0.159842
$429$	−11.2042	−0.540944
$430$	11.4269	0.551055
$431$	−9.17833	−0.442105	−0.221052	−	0.975262i	$-0.570949\pi$
$431$	−9.17833	−0.442105	−0.221052	+	0.975262i	$0.570949\pi$
$432$	4.40036	0.211712
$433$	−20.3563	−0.978263	−0.489132	−	0.872210i	$-0.662686\pi$
$433$	−20.3563	−0.978263	−0.489132	+	0.872210i	$0.662686\pi$
$434$	−22.3823	−1.07438
$435$	−4.21258	−0.201978
$436$	−6.45699	−0.309234
$437$	5.59119	0.267463
$438$	2.81374	0.134446
$439$	−15.0434	−0.717981	−0.358991	−	0.933341i	$-0.616879\pi$
$439$	−15.0434	−0.717981	−0.358991	+	0.933341i	$0.616879\pi$
$440$	−1.92487	−0.0917645
$441$	−0.252966	−0.0120460
$442$	0.803209	0.0382048
$443$	−22.3905	−1.06381	−0.531903	−	0.846805i	$-0.678523\pi$
$443$	−22.3905	−1.06381	−0.531903	+	0.846805i	$0.678523\pi$
$444$	−16.9452	−0.804181
$445$	−11.4837	−0.544379
$446$	9.38745	0.444509
$447$	35.3713	1.67301
$448$	2.57830	0.121813
$449$	4.11099	0.194010	0.0970048	−	0.995284i	$-0.469074\pi$
$449$	4.11099	0.194010	0.0970048	+	0.995284i	$0.469074\pi$
$450$	−2.88561	−0.136029
$451$	−16.3470	−0.769749
$452$	−13.4151	−0.630993
$453$	4.83967	0.227388
$454$	3.02935	0.142175
$455$	−7.62990	−0.357695
$456$	1.92818	0.0902951
$457$	27.8382	1.30222	0.651108	−	0.758985i	$-0.274304\pi$
$457$	27.8382	1.30222	0.651108	+	0.758985i	$0.274304\pi$
$458$	24.2534	1.13329
$459$	1.18252	0.0551952
$460$	5.53580	0.258108
$461$	20.3726	0.948846	0.474423	−	0.880297i	$-0.342657\pi$
$461$	20.3726	0.948846	0.474423	+	0.880297i	$0.342657\pi$
$462$	−9.66506	−0.449659
$463$	−10.7383	−0.499051	−0.249525	−	0.968368i	$-0.580275\pi$
$463$	−10.7383	−0.499051	−0.249525	+	0.968368i	$0.580275\pi$
$464$	−2.20661	−0.102439
$465$	−16.5728	−0.768543
$466$	−25.5496	−1.18356
$467$	12.6788	0.586706	0.293353	−	0.956004i	$-0.405229\pi$
$467$	12.6788	0.586706	0.293353	+	0.956004i	$0.405229\pi$
$468$	2.14561	0.0991811
$469$	34.8673	1.61002
$470$	−7.44784	−0.343543
$471$	−8.10999	−0.373689
$472$	−9.06504	−0.417252
$473$	−22.4377	−1.03169
$474$	−21.0214	−0.965543
$475$	4.01971	0.184437
$476$	0.692870	0.0317577
$477$	−0.0479755	−0.00219665
$478$	25.8236	1.18115
$479$	9.24974	0.422632	0.211316	−	0.977418i	$-0.432225\pi$
$479$	9.24974	0.422632	0.211316	+	0.977418i	$0.432225\pi$
$480$	1.90907	0.0871369
$481$	26.2669	1.19767
$482$	−3.12994	−0.142565
$483$	27.7961	1.26477
$484$	−7.22036	−0.328198
$485$	−5.92226	−0.268916
$486$	7.31136	0.331650
$487$	−27.8965	−1.26411	−0.632055	−	0.774924i	$-0.717788\pi$
$487$	−27.8965	−1.26411	−0.632055	+	0.774924i	$0.717788\pi$
$488$	−14.9747	−0.677875
$489$	7.86568	0.355698
$490$	0.348896	0.0157615
$491$	39.2733	1.77238	0.886190	−	0.463322i	$-0.153343\pi$
$491$	39.2733	1.77238	0.886190	+	0.463322i	$0.153343\pi$
$492$	16.2128	0.730932
$493$	−0.592986	−0.0267068
$494$	−2.98889	−0.134476
$495$	−1.38179	−0.0621070
$496$	−8.68104	−0.389790
$497$	−14.4205	−0.646847
$498$	−26.5244	−1.18859
$499$	13.4691	0.602959	0.301479	−	0.953473i	$-0.402520\pi$
$499$	13.4691	0.602959	0.301479	+	0.953473i	$0.402520\pi$
$500$	8.93036	0.399378
$501$	−3.72230	−0.166300
$502$	6.86046	0.306197
$503$	38.7085	1.72593	0.862963	−	0.505268i	$-0.168606\pi$
$503$	38.7085	1.72593	0.862963	+	0.505268i	$0.168606\pi$
$504$	1.85087	0.0824441
$505$	−10.1226	−0.450452
$506$	−10.8700	−0.483230
$507$	7.84102	0.348232
$508$	−12.9915	−0.576406
$509$	5.22170	0.231448	0.115724	−	0.993281i	$-0.463081\pi$
$509$	5.22170	0.231448	0.115724	+	0.993281i	$0.463081\pi$
$510$	0.513029	0.0227173
$511$	−3.76245	−0.166441
$512$	1.00000	0.0441942
$513$	−4.40036	−0.194281
$514$	−5.39222	−0.237841
$515$	−0.132384	−0.00583354
$516$	22.2536	0.979659
$517$	14.6244	0.643182
$518$	22.6585	0.995558
$519$	21.0247	0.922881
$520$	−2.95928	−0.129773
$521$	−6.65924	−0.291747	−0.145873	−	0.989303i	$-0.546599\pi$
$521$	−6.65924	−0.291747	−0.145873	+	0.989303i	$0.546599\pi$
$522$	−1.58405	−0.0693318
$523$	21.9829	0.961245	0.480623	−	0.876927i	$-0.340411\pi$
$523$	21.9829	0.961245	0.480623	+	0.876927i	$0.340411\pi$
$524$	−16.6541	−0.727538
$525$	19.9837	0.872158
$526$	−0.179009	−0.00780516
$527$	−2.33287	−0.101621
$528$	−3.74862	−0.163138
$529$	8.26144	0.359193
$530$	0.0661689	0.00287419
$531$	−6.50746	−0.282400
$532$	−2.57830	−0.111783
$533$	−25.1317	−1.08858
$534$	−22.3641	−0.967791
$535$	−3.27407	−0.141550
$536$	13.5234	0.584121
$537$	30.9394	1.33514
$538$	21.2789	0.917399
$539$	−0.685086	−0.0295087
$540$	−4.35677	−0.187485
$541$	−26.1425	−1.12396	−0.561978	−	0.827152i	$-0.689959\pi$
$541$	−26.1425	−1.12396	−0.561978	+	0.827152i	$0.689959\pi$
$542$	0.000837891 0	3.59905e−5 0
$543$	35.1234	1.50729
$544$	0.268732	0.0115218
$545$	6.39302	0.273847
$546$	−14.8590	−0.635906
$547$	−14.7845	−0.632142	−0.316071	−	0.948736i	$-0.602364\pi$
$547$	−14.7845	−0.632142	−0.316071	+	0.948736i	$0.602364\pi$
$548$	20.2203	0.863769
$549$	−10.7498	−0.458791
$550$	−7.81484	−0.333226
$551$	2.20661	0.0940047
$552$	10.7808	0.458862
$553$	28.1091	1.19532
$554$	−24.3494	−1.03451
$555$	16.7773	0.712156
$556$	−13.2878	−0.563529
$557$	−44.7943	−1.89799	−0.948997	−	0.315286i	$-0.897900\pi$
$557$	−44.7943	−1.89799	−0.948997	+	0.315286i	$0.897900\pi$
$558$	−6.23180	−0.263813
$559$	−34.4955	−1.45900
$560$	−2.55275	−0.107874
$561$	−1.00737	−0.0425314
$562$	6.62031	0.279261
$563$	−3.99585	−0.168405	−0.0842025	−	0.996449i	$-0.526834\pi$
$563$	−3.99585	−0.168405	−0.0842025	+	0.996449i	$0.526834\pi$
$564$	−14.5044	−0.610747
$565$	13.2822	0.558786
$566$	26.5408	1.11559
$567$	−27.4286	−1.15189
$568$	−5.59302	−0.234678
$569$	−45.9689	−1.92712	−0.963559	−	0.267495i	$-0.913804\pi$
$569$	−45.9689	−1.92712	−0.963559	+	0.267495i	$0.913804\pi$
$570$	−1.90907	−0.0799623
$571$	26.3443	1.10247	0.551237	−	0.834349i	$-0.314156\pi$
$571$	26.3443	1.10247	0.551237	+	0.834349i	$0.314156\pi$
$572$	5.81078	0.242961
$573$	29.0520	1.21367
$574$	−21.6793	−0.904877
$575$	22.4750	0.937272
$576$	0.717864	0.0299110
$577$	15.6273	0.650574	0.325287	−	0.945615i	$-0.394539\pi$
$577$	15.6273	0.650574	0.325287	+	0.945615i	$0.394539\pi$
$578$	−16.9278	−0.704103
$579$	5.93704	0.246735
$580$	2.18475	0.0907168
$581$	35.4677	1.47145
$582$	−11.5334	−0.478075
$583$	−0.129928	−0.00538107
$584$	−1.45928	−0.0603853
$585$	−2.12436	−0.0878314
$586$	−21.4870	−0.887619
$587$	6.26264	0.258487	0.129243	−	0.991613i	$-0.458745\pi$
$587$	6.26264	0.258487	0.129243	+	0.991613i	$0.458745\pi$
$588$	0.679464	0.0280206
$589$	8.68104	0.357696
$590$	8.97523	0.369505
$591$	−44.0399	−1.81156
$592$	8.78817	0.361192
$593$	−25.6402	−1.05292	−0.526458	−	0.850201i	$-0.676480\pi$
$593$	−25.6402	−1.05292	−0.526458	+	0.850201i	$0.676480\pi$
$594$	8.55487	0.351010
$595$	−0.686007	−0.0281235
$596$	−18.3444	−0.751418
$597$	35.0221	1.43336
$598$	−16.7114	−0.683382
$599$	29.3633	1.19975	0.599876	−	0.800093i	$-0.295217\pi$
$599$	29.3633	1.19975	0.599876	+	0.800093i	$0.295217\pi$
$600$	7.75072	0.316422
$601$	−9.47906	−0.386659	−0.193329	−	0.981134i	$-0.561929\pi$
$601$	−9.47906	−0.386659	−0.193329	+	0.981134i	$0.561929\pi$
$602$	−29.7568	−1.21280
$603$	9.70794	0.395338
$604$	−2.50997	−0.102129
$605$	7.14884	0.290642
$606$	−19.7135	−0.800808
$607$	41.5567	1.68674	0.843368	−	0.537337i	$-0.180570\pi$
$607$	41.5567	1.68674	0.843368	+	0.537337i	$0.180570\pi$
$608$	−1.00000	−0.0405554
$609$	10.9700	0.444525
$610$	14.8264	0.600303
$611$	22.4835	0.909584
$612$	0.192913	0.00779804
$613$	34.1330	1.37862	0.689309	−	0.724467i	$-0.257914\pi$
$613$	34.1330	1.37862	0.689309	+	0.724467i	$0.257914\pi$
$614$	−25.8012	−1.04125
$615$	−16.0522	−0.647289
$616$	5.01254	0.201961
$617$	5.22363	0.210296	0.105148	−	0.994457i	$-0.466468\pi$
$617$	5.22363	0.210296	0.105148	+	0.994457i	$0.466468\pi$
$618$	−0.257814	−0.0103708
$619$	−31.5763	−1.26916	−0.634579	−	0.772858i	$-0.718827\pi$
$619$	−31.5763	−1.26916	−0.634579	+	0.772858i	$0.718827\pi$
$620$	8.59504	0.345185
$621$	−24.6033	−0.987295
$622$	−3.23630	−0.129764
$623$	29.9046	1.19810
$624$	−5.76310	−0.230709
$625$	11.2567	0.450267
$626$	31.0954	1.24282
$627$	3.74862	0.149706
$628$	4.20604	0.167839
$629$	2.36166	0.0941657
$630$	−1.83253	−0.0730098
$631$	−15.0435	−0.598870	−0.299435	−	0.954117i	$-0.596798\pi$
$631$	−15.0435	−0.598870	−0.299435	+	0.954117i	$0.596798\pi$
$632$	10.9022	0.433666
$633$	−1.92818	−0.0766381
$634$	9.92367	0.394119
$635$	12.8628	0.510446
$636$	0.128862	0.00510970
$637$	−1.05325	−0.0417311
$638$	−4.28993	−0.169840
$639$	−4.01503	−0.158832
$640$	−0.990094	−0.0391369
$641$	−1.21658	−0.0480518	−0.0240259	−	0.999711i	$-0.507648\pi$
$641$	−1.21658	−0.0480518	−0.0240259	+	0.999711i	$0.507648\pi$
$642$	−6.37615	−0.251647
$643$	−32.0928	−1.26562	−0.632809	−	0.774308i	$-0.718098\pi$
$643$	−32.0928	−1.26562	−0.632809	+	0.774308i	$0.718098\pi$
$644$	−14.4158	−0.568060
$645$	−22.0331	−0.867553
$646$	−0.268732	−0.0105731
$647$	29.7835	1.17091	0.585454	−	0.810706i	$-0.300916\pi$
$647$	29.7835	1.17091	0.585454	+	0.810706i	$0.300916\pi$
$648$	−10.6383	−0.417910
$649$	−17.6236	−0.691787
$650$	−12.0145	−0.471247
$651$	43.1570	1.69146
$652$	−4.07933	−0.159759
$653$	34.7077	1.35822	0.679109	−	0.734037i	$-0.262366\pi$
$653$	34.7077	1.35822	0.679109	+	0.734037i	$0.262366\pi$
$654$	12.4502	0.486842
$655$	16.4891	0.644283
$656$	−8.40839	−0.328292
$657$	−1.04756	−0.0408693
$658$	19.3949	0.756091
$659$	5.83862	0.227441	0.113720	−	0.993513i	$-0.463723\pi$
$659$	5.83862	0.227441	0.113720	+	0.993513i	$0.463723\pi$
$660$	3.71149	0.144469
$661$	−24.2484	−0.943155	−0.471578	−	0.881825i	$-0.656315\pi$
$661$	−24.2484	−0.943155	−0.471578	+	0.881825i	$0.656315\pi$
$662$	3.11309	0.120994
$663$	−1.54873	−0.0601477
$664$	13.7562	0.533845
$665$	2.55275	0.0989916
$666$	6.30871	0.244458
$667$	12.3376	0.477713
$668$	1.93048	0.0746924
$669$	−18.1007	−0.699812
$670$	−13.3894	−0.517278
$671$	−29.1128	−1.12389
$672$	−4.97141	−0.191776
$673$	1.95212	0.0752486	0.0376243	−	0.999292i	$-0.488021\pi$
$673$	1.95212	0.0752486	0.0376243	+	0.999292i	$0.488021\pi$
$674$	24.1689	0.930952
$675$	−17.6882	−0.680819
$676$	−4.06655	−0.156406
$677$	−42.7958	−1.64477	−0.822387	−	0.568928i	$-0.807358\pi$
$677$	−42.7958	−1.64477	−0.822387	+	0.568928i	$0.807358\pi$
$678$	25.8667	0.993403
$679$	15.4221	0.591846
$680$	−0.266070	−0.0102033
$681$	−5.84113	−0.223832
$682$	−16.8771	−0.646256
$683$	−10.6292	−0.406713	−0.203357	−	0.979105i	$-0.565185\pi$
$683$	−10.6292	−0.406713	−0.203357	+	0.979105i	$0.565185\pi$
$684$	−0.717864	−0.0274482
$685$	−20.0200	−0.764925
$686$	−18.9566	−0.723768
$687$	−46.7648	−1.78419
$688$	−11.5413	−0.440006
$689$	−0.199750	−0.00760988
$690$	−10.6740	−0.406352
$691$	42.5708	1.61947	0.809736	−	0.586795i	$-0.199611\pi$
$691$	42.5708	1.61947	0.809736	+	0.586795i	$0.199611\pi$
$692$	−10.9039	−0.414505
$693$	3.59832	0.136689
$694$	−22.9811	−0.872349
$695$	13.1562	0.499043
$696$	4.25473	0.161275
$697$	−2.25960	−0.0855885
$698$	−27.2264	−1.03054
$699$	49.2642	1.86334
$700$	−10.3640	−0.391723
$701$	22.1923	0.838191	0.419096	−	0.907942i	$-0.362347\pi$
$701$	22.1923	0.838191	0.419096	+	0.907942i	$0.362347\pi$
$702$	13.1522	0.496397
$703$	−8.78817	−0.331452
$704$	1.94413	0.0732721
$705$	14.3607	0.540857
$706$	10.3747	0.390458
$707$	26.3603	0.991382
$708$	17.4790	0.656901
$709$	−21.0737	−0.791438	−0.395719	−	0.918372i	$-0.629505\pi$
$709$	−21.0737	−0.791438	−0.395719	+	0.918372i	$0.629505\pi$
$710$	5.53762	0.207823
$711$	7.82629	0.293509
$712$	11.5986	0.434676
$713$	48.5374	1.81774
$714$	−1.33598	−0.0499977
$715$	−5.75322	−0.215158
$716$	−16.0460	−0.599666
$717$	−49.7925	−1.85954
$718$	−23.6161	−0.881346
$719$	5.30813	0.197960	0.0989799	−	0.995089i	$-0.468442\pi$
$719$	5.30813	0.197960	0.0989799	+	0.995089i	$0.468442\pi$
$720$	−0.710752	−0.0264882
$721$	0.344740	0.0128388
$722$	1.00000	0.0372161
$723$	6.03508	0.224447
$724$	−18.2159	−0.676988
$725$	8.86994	0.329421
$726$	13.9221	0.516699
$727$	42.3634	1.57117	0.785586	−	0.618752i	$-0.212361\pi$
$727$	42.3634	1.57117	0.785586	+	0.618752i	$0.212361\pi$
$728$	7.70624	0.285612
$729$	17.8172	0.659896
$730$	1.44482	0.0534752
$731$	−3.10150	−0.114713
$732$	28.8739	1.06721
$733$	−27.7724	−1.02580	−0.512899	−	0.858449i	$-0.671428\pi$
$733$	−27.7724	−1.02580	−0.512899	+	0.858449i	$0.671428\pi$
$734$	−29.7471	−1.09799
$735$	−0.672733	−0.0248141
$736$	−5.59119	−0.206094
$737$	26.2912	0.968448
$738$	−6.03608	−0.222191
$739$	−2.79121	−0.102676	−0.0513381	−	0.998681i	$-0.516349\pi$
$739$	−2.79121	−0.102676	−0.0513381	+	0.998681i	$0.516349\pi$
$740$	−8.70112	−0.319859
$741$	5.76310	0.211713
$742$	−0.172310	−0.00632570
$743$	−4.38814	−0.160985	−0.0804927	−	0.996755i	$-0.525649\pi$
$743$	−4.38814	−0.160985	−0.0804927	+	0.996755i	$0.525649\pi$
$744$	16.7386	0.613666
$745$	18.1627	0.665431
$746$	−29.2991	−1.07272
$747$	9.87510	0.361311
$748$	0.522449	0.0191026
$749$	8.52599	0.311533
$750$	−17.2193	−0.628760
$751$	−26.0818	−0.951738	−0.475869	−	0.879516i	$-0.657866\pi$
$751$	−26.0818	−0.951738	−0.475869	+	0.879516i	$0.657866\pi$
$752$	7.52236	0.274312
$753$	−13.2282	−0.482062
$754$	−6.59531	−0.240187
$755$	2.48511	0.0904424
$756$	11.3454	0.412629
$757$	9.13337	0.331958	0.165979	−	0.986129i	$-0.446922\pi$
$757$	9.13337	0.331958	0.165979	+	0.986129i	$0.446922\pi$
$758$	−1.92246	−0.0698267
$759$	20.9593	0.760773
$760$	0.990094	0.0359145
$761$	4.35889	0.158010	0.0790049	−	0.996874i	$-0.474826\pi$
$761$	4.35889	0.158010	0.0790049	+	0.996874i	$0.474826\pi$
$762$	25.0500	0.907464
$763$	−16.6480	−0.602699
$764$	−15.0671	−0.545109
$765$	−0.191002	−0.00690568
$766$	14.3126	0.517136
$767$	−27.0944	−0.978321
$768$	−1.92818	−0.0695771
$769$	4.24908	0.153226	0.0766129	−	0.997061i	$-0.475589\pi$
$769$	4.24908	0.153226	0.0766129	+	0.997061i	$0.475589\pi$
$770$	−4.96288	−0.178850
$771$	10.3972	0.374444
$772$	−3.07910	−0.110819
$773$	−53.7216	−1.93223	−0.966116	−	0.258107i	$-0.916901\pi$
$773$	−53.7216	−1.93223	−0.966116	+	0.258107i	$0.916901\pi$
$774$	−8.28505	−0.297800
$775$	34.8953	1.25348
$776$	5.98151	0.214724
$777$	−43.6896	−1.56736
$778$	8.82759	0.316484
$779$	8.40839	0.301262
$780$	5.70601	0.204308
$781$	−10.8736	−0.389086
$782$	−1.50253	−0.0537304
$783$	−9.70988	−0.347003
$784$	−0.352387	−0.0125853
$785$	−4.16437	−0.148633
$786$	32.1121	1.14540
$787$	−44.6794	−1.59265	−0.796325	−	0.604869i	$-0.793226\pi$
$787$	−44.6794	−1.59265	−0.796325	+	0.604869i	$0.793226\pi$
$788$	22.8402	0.813649
$789$	0.345161	0.0122880
$790$	−10.7942	−0.384040
$791$	−34.5881	−1.22981
$792$	1.39562	0.0495912
$793$	−44.7578	−1.58940
$794$	−11.1686	−0.396359
$795$	−0.127585	−0.00452498
$796$	−18.1633	−0.643783
$797$	−12.6846	−0.449313	−0.224656	−	0.974438i	$-0.572126\pi$
$797$	−12.6846	−0.449313	−0.224656	+	0.974438i	$0.572126\pi$
$798$	4.97141	0.175986
$799$	2.02150	0.0715154
$800$	−4.01971	−0.142118
$801$	8.32621	0.294192
$802$	−23.1985	−0.819166
$803$	−2.83702	−0.100116
$804$	−26.0754	−0.919610
$805$	14.2729	0.503055
$806$	−25.9467	−0.913932
$807$	−41.0295	−1.44431
$808$	10.2239	0.359676
$809$	6.24068	0.219411	0.109705	−	0.993964i	$-0.465009\pi$
$809$	6.24068	0.219411	0.109705	+	0.993964i	$0.465009\pi$
$810$	10.5329	0.370088
$811$	49.1742	1.72674	0.863369	−	0.504572i	$-0.168350\pi$
$811$	49.1742	1.72674	0.863369	+	0.504572i	$0.168350\pi$
$812$	−5.68929	−0.199655
$813$	−0.00161560	−5.66617e−5 0
$814$	17.0853	0.598841
$815$	4.03892	0.141477
$816$	−0.518162	−0.0181393
$817$	11.5413	0.403777
$818$	−22.1636	−0.774933
$819$	5.53203	0.193305
$820$	8.32509	0.290725
$821$	−27.0355	−0.943544	−0.471772	−	0.881721i	$-0.656385\pi$
$821$	−27.0355	−0.943544	−0.471772	+	0.881721i	$0.656385\pi$
$822$	−38.9883	−1.35987
$823$	−23.8770	−0.832301	−0.416150	−	0.909296i	$-0.636621\pi$
$823$	−23.8770	−0.832301	−0.416150	+	0.909296i	$0.636621\pi$
$824$	0.133709	0.00465796
$825$	15.0684	0.524614
$826$	−23.3724	−0.813228
$827$	44.4485	1.54562	0.772812	−	0.634635i	$-0.218849\pi$
$827$	44.4485	1.54562	0.772812	+	0.634635i	$0.218849\pi$
$828$	−4.01372	−0.139486
$829$	5.07035	0.176101	0.0880503	−	0.996116i	$-0.471936\pi$
$829$	5.07035	0.176101	0.0880503	+	0.996116i	$0.471936\pi$
$830$	−13.6200	−0.472756
$831$	46.9499	1.62867
$832$	2.98889	0.103621
$833$	−0.0946976	−0.00328108
$834$	25.6213	0.887192
$835$	−1.91135	−0.0661451
$836$	−1.94413	−0.0672391
$837$	−38.1997	−1.32037
$838$	−6.45283	−0.222909
$839$	−30.0126	−1.03615	−0.518075	−	0.855335i	$-0.673351\pi$
$839$	−30.0126	−1.03615	−0.518075	+	0.855335i	$0.673351\pi$
$840$	4.92216	0.169831
$841$	−24.1309	−0.832099
$842$	−2.18675	−0.0753602
$843$	−12.7651	−0.439654
$844$	1.00000	0.0344214
$845$	4.02626	0.138508
$846$	5.40003	0.185657
$847$	−18.6162	−0.639662
$848$	−0.0668310	−0.00229498
$849$	−51.1753	−1.75633
$850$	−1.08023	−0.0370514
$851$	−49.1364	−1.68437
$852$	10.7843	0.369465
$853$	−24.9934	−0.855758	−0.427879	−	0.903836i	$-0.640739\pi$
$853$	−24.9934	−0.855758	−0.427879	+	0.903836i	$0.640739\pi$
$854$	−38.6093	−1.32118
$855$	0.710752	0.0243072
$856$	3.30683	0.113025
$857$	13.0605	0.446139	0.223069	−	0.974803i	$-0.428392\pi$
$857$	13.0605	0.446139	0.223069	+	0.974803i	$0.428392\pi$
$858$	−11.2042	−0.382505
$859$	49.9034	1.70268	0.851340	−	0.524614i	$-0.175790\pi$
$859$	49.9034	1.70268	0.851340	+	0.524614i	$0.175790\pi$
$860$	11.4269	0.389655
$861$	41.8015	1.42459
$862$	−9.17833	−0.312615
$863$	37.3166	1.27027	0.635135	−	0.772401i	$-0.280944\pi$
$863$	37.3166	1.27027	0.635135	+	0.772401i	$0.280944\pi$
$864$	4.40036	0.149703
$865$	10.7959	0.367072
$866$	−20.3563	−0.691736
$867$	32.6398	1.10850
$868$	−22.3823	−0.759705
$869$	21.1953	0.719000
$870$	−4.21258	−0.142820
$871$	40.4198	1.36957
$872$	−6.45699	−0.218661
$873$	4.29391	0.145327
$874$	5.59119	0.189125
$875$	23.0251	0.778391
$876$	2.81374	0.0950676
$877$	12.7420	0.430267	0.215134	−	0.976585i	$-0.430981\pi$
$877$	12.7420	0.430267	0.215134	+	0.976585i	$0.430981\pi$
$878$	−15.0434	−0.507689
$879$	41.4307	1.39742
$880$	−1.92487	−0.0648873
$881$	1.21211	0.0408370	0.0204185	−	0.999792i	$-0.493500\pi$
$881$	1.21211	0.0408370	0.0204185	+	0.999792i	$0.493500\pi$
$882$	−0.252966	−0.00851781
$883$	−15.8246	−0.532540	−0.266270	−	0.963899i	$-0.585791\pi$
$883$	−15.8246	−0.532540	−0.266270	+	0.963899i	$0.585791\pi$
$884$	0.803209	0.0270149
$885$	−17.3058	−0.581729
$886$	−22.3905	−0.752225
$887$	49.0205	1.64595	0.822974	−	0.568079i	$-0.192313\pi$
$887$	49.0205	1.64595	0.822974	+	0.568079i	$0.192313\pi$
$888$	−16.9452	−0.568642
$889$	−33.4960	−1.12342
$890$	−11.4837	−0.384934
$891$	−20.6821	−0.692878
$892$	9.38745	0.314315
$893$	−7.52236	−0.251726
$894$	35.3713	1.18299
$895$	15.8870	0.531044
$896$	2.57830	0.0861348
$897$	32.2226	1.07588
$898$	4.11099	0.137186
$899$	19.1557	0.638877
$900$	−2.88561	−0.0961869
$901$	−0.0179596	−0.000598321 0
$902$	−16.3470	−0.544295
$903$	57.3763	1.90936
$904$	−13.4151	−0.446179
$905$	18.0354	0.599518
$906$	4.83967	0.160787
$907$	−29.1849	−0.969070	−0.484535	−	0.874772i	$-0.661011\pi$
$907$	−29.1849	−0.969070	−0.484535	+	0.874772i	$0.661011\pi$
$908$	3.02935	0.100533
$909$	7.33939	0.243432
$910$	−7.62990	−0.252929
$911$	38.2172	1.26619	0.633096	−	0.774073i	$-0.281784\pi$
$911$	38.2172	1.26619	0.633096	+	0.774073i	$0.281784\pi$
$912$	1.92818	0.0638483
$913$	26.7439	0.885093
$914$	27.8382	0.920806
$915$	−28.5879	−0.945087
$916$	24.2534	0.801355
$917$	−42.9392	−1.41798
$918$	1.18252	0.0390289
$919$	−15.4003	−0.508008	−0.254004	−	0.967203i	$-0.581748\pi$
$919$	−15.4003	−0.508008	−0.254004	+	0.967203i	$0.581748\pi$
$920$	5.53580	0.182510
$921$	49.7493	1.63929
$922$	20.3726	0.670936
$923$	−16.7169	−0.550244
$924$	−9.66506	−0.317957
$925$	−35.3260	−1.16151
$926$	−10.7383	−0.352882
$927$	0.0959846	0.00315255
$928$	−2.20661	−0.0724355
$929$	−6.26650	−0.205597	−0.102799	−	0.994702i	$-0.532780\pi$
$929$	−6.26650	−0.205597	−0.102799	+	0.994702i	$0.532780\pi$
$930$	−16.5728	−0.543442
$931$	0.352387	0.0115490
$932$	−25.5496	−0.836906
$933$	6.24016	0.204294
$934$	12.6788	0.414864
$935$	−0.517274	−0.0169167
$936$	2.14561	0.0701316
$937$	38.0215	1.24211	0.621054	−	0.783768i	$-0.286705\pi$
$937$	38.0215	1.24211	0.621054	+	0.783768i	$0.286705\pi$
$938$	34.8673	1.13846
$939$	−59.9574	−1.95663
$940$	−7.44784	−0.242922
$941$	2.39890	0.0782019	0.0391010	−	0.999235i	$-0.487551\pi$
$941$	2.39890	0.0782019	0.0391010	+	0.999235i	$0.487551\pi$
$942$	−8.10999	−0.264238
$943$	47.0129	1.53095
$944$	−9.06504	−0.295042
$945$	−11.2330	−0.365411
$946$	−22.4377	−0.729512
$947$	17.3082	0.562442	0.281221	−	0.959643i	$-0.409261\pi$
$947$	17.3082	0.562442	0.281221	+	0.959643i	$0.409261\pi$
$948$	−21.0214	−0.682742
$949$	−4.36162	−0.141584
$950$	4.01971	0.130417
$951$	−19.1346	−0.620481
$952$	0.692870	0.0224561
$953$	−15.7494	−0.510173	−0.255087	−	0.966918i	$-0.582104\pi$
$953$	−15.7494	−0.510173	−0.255087	+	0.966918i	$0.582104\pi$
$954$	−0.0479755	−0.00155326
$955$	14.9179	0.482730
$956$	25.8236	0.835196
$957$	8.27175	0.267388
$958$	9.24974	0.298846
$959$	52.1340	1.68349
$960$	1.90907	0.0616151
$961$	44.3604	1.43098
$962$	26.2669	0.846878
$963$	2.37385	0.0764963
$964$	−3.12994	−0.100809
$965$	3.04859	0.0981377
$966$	27.7961	0.894325
$967$	45.8947	1.47588	0.737938	−	0.674869i	$-0.235800\pi$
$967$	45.8947	1.47588	0.737938	+	0.674869i	$0.235800\pi$
$968$	−7.22036	−0.232071
$969$	0.518162	0.0166458
$970$	−5.92226	−0.190152
$971$	21.3390	0.684802	0.342401	−	0.939554i	$-0.388760\pi$
$971$	21.3390	0.684802	0.342401	+	0.939554i	$0.388760\pi$
$972$	7.31136	0.234512
$973$	−34.2600	−1.09832
$974$	−27.8965	−0.893860
$975$	23.1660	0.741907
$976$	−14.9747	−0.479330
$977$	−9.47755	−0.303214	−0.151607	−	0.988441i	$-0.548445\pi$
$977$	−9.47755	−0.303214	−0.151607	+	0.988441i	$0.548445\pi$
$978$	7.86568	0.251517
$979$	22.5492	0.720674
$980$	0.348896	0.0111451
$981$	−4.63524	−0.147992
$982$	39.2733	1.25326
$983$	14.4674	0.461438	0.230719	−	0.973020i	$-0.425892\pi$
$983$	14.4674	0.461438	0.230719	+	0.973020i	$0.425892\pi$
$984$	16.2128	0.516847
$985$	−22.6139	−0.720540
$986$	−0.592986	−0.0188845
$987$	−37.3967	−1.19035
$988$	−2.98889	−0.0950892
$989$	64.5294	2.05192
$990$	−1.38179	−0.0439163
$991$	−4.12114	−0.130912	−0.0654562	−	0.997855i	$-0.520850\pi$
$991$	−4.12114	−0.130912	−0.0654562	+	0.997855i	$0.520850\pi$
$992$	−8.68104	−0.275623
$993$	−6.00260	−0.190487
$994$	−14.4205	−0.457390
$995$	17.9834	0.570113
$996$	−26.5244	−0.840459
$997$	35.7918	1.13354	0.566769	−	0.823876i	$-0.308193\pi$
$997$	35.7918	1.13354	0.566769	+	0.823876i	$0.308193\pi$
$998$	13.4691	0.426356
$999$	38.6711	1.22350

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.e.1.8	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.e.1.8	✓	32	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.92818 q^{3} +1.00000 q^{4} -0.990094 q^{5} -1.92818 q^{6} +2.57830 q^{7} +1.00000 q^{8} +0.717864 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.92818 q^{3} +1.00000 q^{4} -0.990094 q^{5} -1.92818 q^{6} +2.57830 q^{7} +1.00000 q^{8} +0.717864 q^{9} -0.990094 q^{10} +1.94413 q^{11} -1.92818 q^{12} +2.98889 q^{13} +2.57830 q^{14} +1.90907 q^{15} +1.00000 q^{16} +0.268732 q^{17} +0.717864 q^{18} -1.00000 q^{19} -0.990094 q^{20} -4.97141 q^{21} +1.94413 q^{22} -5.59119 q^{23} -1.92818 q^{24} -4.01971 q^{25} +2.98889 q^{26} +4.40036 q^{27} +2.57830 q^{28} -2.20661 q^{29} +1.90907 q^{30} -8.68104 q^{31} +1.00000 q^{32} -3.74862 q^{33} +0.268732 q^{34} -2.55275 q^{35} +0.717864 q^{36} +8.78817 q^{37} -1.00000 q^{38} -5.76310 q^{39} -0.990094 q^{40} -8.40839 q^{41} -4.97141 q^{42} -11.5413 q^{43} +1.94413 q^{44} -0.710752 q^{45} -5.59119 q^{46} +7.52236 q^{47} -1.92818 q^{48} -0.352387 q^{49} -4.01971 q^{50} -0.518162 q^{51} +2.98889 q^{52} -0.0668310 q^{53} +4.40036 q^{54} -1.92487 q^{55} +2.57830 q^{56} +1.92818 q^{57} -2.20661 q^{58} -9.06504 q^{59} +1.90907 q^{60} -14.9747 q^{61} -8.68104 q^{62} +1.85087 q^{63} +1.00000 q^{64} -2.95928 q^{65} -3.74862 q^{66} +13.5234 q^{67} +0.268732 q^{68} +10.7808 q^{69} -2.55275 q^{70} -5.59302 q^{71} +0.717864 q^{72} -1.45928 q^{73} +8.78817 q^{74} +7.75072 q^{75} -1.00000 q^{76} +5.01254 q^{77} -5.76310 q^{78} +10.9022 q^{79} -0.990094 q^{80} -10.6383 q^{81} -8.40839 q^{82} +13.7562 q^{83} -4.97141 q^{84} -0.266070 q^{85} -11.5413 q^{86} +4.25473 q^{87} +1.94413 q^{88} +11.5986 q^{89} -0.710752 q^{90} +7.70624 q^{91} -5.59119 q^{92} +16.7386 q^{93} +7.52236 q^{94} +0.990094 q^{95} -1.92818 q^{96} +5.98151 q^{97} -0.352387 q^{98} +1.39562 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9}+O(q^{10}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9} - 6 q^{10} - 21 q^{11} - 7 q^{12} - 19 q^{13} - 5 q^{14} - 14 q^{15} + 32 q^{16} - 14 q^{17} + 15 q^{18} - 32 q^{19} - 6 q^{20} - 26 q^{21} - 21 q^{22} - 13 q^{23} - 7 q^{24} - 10 q^{25} - 19 q^{26} - 25 q^{27} - 5 q^{28} - 42 q^{29} - 14 q^{30} - 15 q^{31} + 32 q^{32} - 32 q^{33} - 14 q^{34} - 22 q^{35} + 15 q^{36} - 54 q^{37} - 32 q^{38} - 32 q^{39} - 6 q^{40} - 16 q^{41} - 26 q^{42} - 37 q^{43} - 21 q^{44} - 46 q^{45} - 13 q^{46} - 9 q^{47} - 7 q^{48} - 7 q^{49} - 10 q^{50} - 32 q^{51} - 19 q^{52} - 53 q^{53} - 25 q^{54} - 17 q^{55} - 5 q^{56} + 7 q^{57} - 42 q^{58} - 34 q^{59} - 14 q^{60} - 33 q^{61} - 15 q^{62} + 18 q^{63} + 32 q^{64} - 50 q^{65} - 32 q^{66} - 53 q^{67} - 14 q^{68} - 40 q^{69} - 22 q^{70} - 27 q^{71} + 15 q^{72} - 43 q^{73} - 54 q^{74} + 5 q^{75} - 32 q^{76} - 56 q^{77} - 32 q^{78} - 11 q^{79} - 6 q^{80} - 8 q^{81} - 16 q^{82} - 17 q^{83} - 26 q^{84} - 30 q^{85} - 37 q^{86} + 3 q^{87} - 21 q^{88} - 21 q^{89} - 46 q^{90} - 67 q^{91} - 13 q^{92} - 31 q^{93} - 9 q^{94} + 6 q^{95} - 7 q^{96} - 51 q^{97} - 7 q^{98} - 32 q^{99}+O(q^{100}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9 - 6 * q^10 - 21 * q^11 - 7 * q^12 - 19 * q^13 - 5 * q^14 - 14 * q^15 + 32 * q^16 - 14 * q^17 + 15 * q^18 - 32 * q^19 - 6 * q^20 - 26 * q^21 - 21 * q^22 - 13 * q^23 - 7 * q^24 - 10 * q^25 - 19 * q^26 - 25 * q^27 - 5 * q^28 - 42 * q^29 - 14 * q^30 - 15 * q^31 + 32 * q^32 - 32 * q^33 - 14 * q^34 - 22 * q^35 + 15 * q^36 - 54 * q^37 - 32 * q^38 - 32 * q^39 - 6 * q^40 - 16 * q^41 - 26 * q^42 - 37 * q^43 - 21 * q^44 - 46 * q^45 - 13 * q^46 - 9 * q^47 - 7 * q^48 - 7 * q^49 - 10 * q^50 - 32 * q^51 - 19 * q^52 - 53 * q^53 - 25 * q^54 - 17 * q^55 - 5 * q^56 + 7 * q^57 - 42 * q^58 - 34 * q^59 - 14 * q^60 - 33 * q^61 - 15 * q^62 + 18 * q^63 + 32 * q^64 - 50 * q^65 - 32 * q^66 - 53 * q^67 - 14 * q^68 - 40 * q^69 - 22 * q^70 - 27 * q^71 + 15 * q^72 - 43 * q^73 - 54 * q^74 + 5 * q^75 - 32 * q^76 - 56 * q^77 - 32 * q^78 - 11 * q^79 - 6 * q^80 - 8 * q^81 - 16 * q^82 - 17 * q^83 - 26 * q^84 - 30 * q^85 - 37 * q^86 + 3 * q^87 - 21 * q^88 - 21 * q^89 - 46 * q^90 - 67 * q^91 - 13 * q^92 - 31 * q^93 - 9 * q^94 + 6 * q^95 - 7 * q^96 - 51 * q^97 - 7 * q^98 - 32 * q^99

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