LMFDB - Embedded newform 8018.2.a.h.1.1

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:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-1.00000 q^{2} -3.10704 q^{3} +1.00000 q^{4} -3.25849 q^{5} +3.10704 q^{6} +4.58720 q^{7} -1.00000 q^{8} +6.65369 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.10704 q^{3} +1.00000 q^{4} -3.25849 q^{5} +3.10704 q^{6} +4.58720 q^{7} -1.00000 q^{8} +6.65369 q^{9} +3.25849 q^{10} +0.524584 q^{11} -3.10704 q^{12} +0.0238330 q^{13} -4.58720 q^{14} +10.1242 q^{15} +1.00000 q^{16} -6.08316 q^{17} -6.65369 q^{18} -1.00000 q^{19} -3.25849 q^{20} -14.2526 q^{21} -0.524584 q^{22} -3.03031 q^{23} +3.10704 q^{24} +5.61775 q^{25} -0.0238330 q^{26} -11.3521 q^{27} +4.58720 q^{28} +2.34875 q^{29} -10.1242 q^{30} +4.38888 q^{31} -1.00000 q^{32} -1.62990 q^{33} +6.08316 q^{34} -14.9473 q^{35} +6.65369 q^{36} +2.80481 q^{37} +1.00000 q^{38} -0.0740502 q^{39} +3.25849 q^{40} -0.960139 q^{41} +14.2526 q^{42} -1.64493 q^{43} +0.524584 q^{44} -21.6810 q^{45} +3.03031 q^{46} +9.36661 q^{47} -3.10704 q^{48} +14.0424 q^{49} -5.61775 q^{50} +18.9006 q^{51} +0.0238330 q^{52} +9.05122 q^{53} +11.3521 q^{54} -1.70935 q^{55} -4.58720 q^{56} +3.10704 q^{57} -2.34875 q^{58} -8.13416 q^{59} +10.1242 q^{60} -6.52012 q^{61} -4.38888 q^{62} +30.5218 q^{63} +1.00000 q^{64} -0.0776597 q^{65} +1.62990 q^{66} +1.80218 q^{67} -6.08316 q^{68} +9.41530 q^{69} +14.9473 q^{70} -1.92187 q^{71} -6.65369 q^{72} +2.74600 q^{73} -2.80481 q^{74} -17.4545 q^{75} -1.00000 q^{76} +2.40637 q^{77} +0.0740502 q^{78} -1.95398 q^{79} -3.25849 q^{80} +15.3105 q^{81} +0.960139 q^{82} -0.196543 q^{83} -14.2526 q^{84} +19.8219 q^{85} +1.64493 q^{86} -7.29766 q^{87} -0.524584 q^{88} +0.0816219 q^{89} +21.6810 q^{90} +0.109327 q^{91} -3.03031 q^{92} -13.6364 q^{93} -9.36661 q^{94} +3.25849 q^{95} +3.10704 q^{96} +11.6239 q^{97} -14.0424 q^{98} +3.49042 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9}+O(q^{10}) $ 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9} + 9 q^{10} - 9 q^{11} + 8 q^{12} + 13 q^{13} - 7 q^{14} + 26 q^{15} + 41 q^{16} - 16 q^{17} - 43 q^{18} - 41 q^{19} - 9 q^{20} + 2 q^{21} + 9 q^{22} + 10 q^{23} - 8 q^{24} + 60 q^{25} - 13 q^{26} + 47 q^{27} + 7 q^{28} - 14 q^{29} - 26 q^{30} + 49 q^{31} - 41 q^{32} + 12 q^{33} + 16 q^{34} - 8 q^{35} + 43 q^{36} + 54 q^{37} + 41 q^{38} + 16 q^{39} + 9 q^{40} - 18 q^{41} - 2 q^{42} + 29 q^{43} - 9 q^{44} - 13 q^{45} - 10 q^{46} - 8 q^{47} + 8 q^{48} + 44 q^{49} - 60 q^{50} - 16 q^{51} + 13 q^{52} + 7 q^{53} - 47 q^{54} + 19 q^{55} - 7 q^{56} - 8 q^{57} + 14 q^{58} - 5 q^{59} + 26 q^{60} - 6 q^{61} - 49 q^{62} + 24 q^{63} + 41 q^{64} - 26 q^{65} - 12 q^{66} + 66 q^{67} - 16 q^{68} + 12 q^{69} + 8 q^{70} + 27 q^{71} - 43 q^{72} - q^{73} - 54 q^{74} + 62 q^{75} - 41 q^{76} - 8 q^{77} - 16 q^{78} + 87 q^{79} - 9 q^{80} + 73 q^{81} + 18 q^{82} - 41 q^{83} + 2 q^{84} + 14 q^{85} - 29 q^{86} + 35 q^{87} + 9 q^{88} - 4 q^{89} + 13 q^{90} + 39 q^{91} + 10 q^{92} + 17 q^{93} + 8 q^{94} + 9 q^{95} - 8 q^{96} + 64 q^{97} - 44 q^{98} + 40 q^{99}+O(q^{100}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9 + 9 * q^10 - 9 * q^11 + 8 * q^12 + 13 * q^13 - 7 * q^14 + 26 * q^15 + 41 * q^16 - 16 * q^17 - 43 * q^18 - 41 * q^19 - 9 * q^20 + 2 * q^21 + 9 * q^22 + 10 * q^23 - 8 * q^24 + 60 * q^25 - 13 * q^26 + 47 * q^27 + 7 * q^28 - 14 * q^29 - 26 * q^30 + 49 * q^31 - 41 * q^32 + 12 * q^33 + 16 * q^34 - 8 * q^35 + 43 * q^36 + 54 * q^37 + 41 * q^38 + 16 * q^39 + 9 * q^40 - 18 * q^41 - 2 * q^42 + 29 * q^43 - 9 * q^44 - 13 * q^45 - 10 * q^46 - 8 * q^47 + 8 * q^48 + 44 * q^49 - 60 * q^50 - 16 * q^51 + 13 * q^52 + 7 * q^53 - 47 * q^54 + 19 * q^55 - 7 * q^56 - 8 * q^57 + 14 * q^58 - 5 * q^59 + 26 * q^60 - 6 * q^61 - 49 * q^62 + 24 * q^63 + 41 * q^64 - 26 * q^65 - 12 * q^66 + 66 * q^67 - 16 * q^68 + 12 * q^69 + 8 * q^70 + 27 * q^71 - 43 * q^72 - q^73 - 54 * q^74 + 62 * q^75 - 41 * q^76 - 8 * q^77 - 16 * q^78 + 87 * q^79 - 9 * q^80 + 73 * q^81 + 18 * q^82 - 41 * q^83 + 2 * q^84 + 14 * q^85 - 29 * q^86 + 35 * q^87 + 9 * q^88 - 4 * q^89 + 13 * q^90 + 39 * q^91 + 10 * q^92 + 17 * q^93 + 8 * q^94 + 9 * q^95 - 8 * q^96 + 64 * q^97 - 44 * q^98 + 40 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.10704	−1.79385	−0.896925	−	0.442183i	$-0.854204\pi$
$3$	−3.10704	−1.79385	−0.896925	+	0.442183i	$0.854204\pi$
$4$	1.00000	0.500000
$5$	−3.25849	−1.45724	−0.728620	−	0.684918i	$-0.759838\pi$
$5$	−3.25849	−1.45724	−0.728620	+	0.684918i	$0.759838\pi$
$6$	3.10704	1.26844
$7$	4.58720	1.73380	0.866900	−	0.498482i	$-0.166109\pi$
$7$	4.58720	1.73380	0.866900	+	0.498482i	$0.166109\pi$
$8$	−1.00000	−0.353553
$9$	6.65369	2.21790
$10$	3.25849	1.03042
$11$	0.524584	0.158168	0.0790840	−	0.996868i	$-0.474800\pi$
$11$	0.524584	0.158168	0.0790840	+	0.996868i	$0.474800\pi$
$12$	−3.10704	−0.896925
$13$	0.0238330	0.00661010	0.00330505	−	0.999995i	$-0.498948\pi$
$13$	0.0238330	0.00661010	0.00330505	+	0.999995i	$0.498948\pi$
$14$	−4.58720	−1.22598
$15$	10.1242	2.61407
$16$	1.00000	0.250000
$17$	−6.08316	−1.47538	−0.737692	−	0.675138i	$-0.764084\pi$
$17$	−6.08316	−1.47538	−0.737692	+	0.675138i	$0.764084\pi$
$18$	−6.65369	−1.56829
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−3.25849	−0.728620
$21$	−14.2526	−3.11018
$22$	−0.524584	−0.111842
$23$	−3.03031	−0.631864	−0.315932	−	0.948782i	$-0.602317\pi$
$23$	−3.03031	−0.631864	−0.315932	+	0.948782i	$0.602317\pi$
$24$	3.10704	0.634221
$25$	5.61775	1.12355
$26$	−0.0238330	−0.00467405
$27$	−11.3521	−2.18472
$28$	4.58720	0.866900
$29$	2.34875	0.436152	0.218076	−	0.975932i	$-0.430022\pi$
$29$	2.34875	0.436152	0.218076	+	0.975932i	$0.430022\pi$
$30$	−10.1242	−1.84843
$31$	4.38888	0.788266	0.394133	−	0.919053i	$-0.371045\pi$
$31$	4.38888	0.788266	0.394133	+	0.919053i	$0.371045\pi$
$32$	−1.00000	−0.176777
$33$	−1.62990	−0.283730
$34$	6.08316	1.04325
$35$	−14.9473	−2.52656
$36$	6.65369	1.10895
$37$	2.80481	0.461108	0.230554	−	0.973060i	$-0.425946\pi$
$37$	2.80481	0.461108	0.230554	+	0.973060i	$0.425946\pi$
$38$	1.00000	0.162221
$39$	−0.0740502	−0.0118575
$40$	3.25849	0.515212
$41$	−0.960139	−0.149949	−0.0749743	−	0.997185i	$-0.523887\pi$
$41$	−0.960139	−0.149949	−0.0749743	+	0.997185i	$0.523887\pi$
$42$	14.2526	2.19923
$43$	−1.64493	−0.250849	−0.125425	−	0.992103i	$-0.540029\pi$
$43$	−1.64493	−0.250849	−0.125425	+	0.992103i	$0.540029\pi$
$44$	0.524584	0.0790840
$45$	−21.6810	−3.23201
$46$	3.03031	0.446795
$47$	9.36661	1.36626	0.683130	−	0.730297i	$-0.260618\pi$
$47$	9.36661	1.36626	0.683130	+	0.730297i	$0.260618\pi$
$48$	−3.10704	−0.448462
$49$	14.0424	2.00606
$50$	−5.61775	−0.794469
$51$	18.9006	2.64662
$52$	0.0238330	0.00330505
$53$	9.05122	1.24328	0.621641	−	0.783303i	$-0.286466\pi$
$53$	9.05122	1.24328	0.621641	+	0.783303i	$0.286466\pi$
$54$	11.3521	1.54483
$55$	−1.70935	−0.230489
$56$	−4.58720	−0.612991
$57$	3.10704	0.411537
$58$	−2.34875	−0.308406
$59$	−8.13416	−1.05898	−0.529489	−	0.848317i	$-0.677616\pi$
$59$	−8.13416	−1.05898	−0.529489	+	0.848317i	$0.677616\pi$
$60$	10.1242	1.30703
$61$	−6.52012	−0.834816	−0.417408	−	0.908719i	$-0.637061\pi$
$61$	−6.52012	−0.834816	−0.417408	+	0.908719i	$0.637061\pi$
$62$	−4.38888	−0.557388
$63$	30.5218	3.84539
$64$	1.00000	0.125000
$65$	−0.0776597	−0.00963250
$66$	1.62990	0.200627
$67$	1.80218	0.220171	0.110086	−	0.993922i	$-0.464888\pi$
$67$	1.80218	0.220171	0.110086	+	0.993922i	$0.464888\pi$
$68$	−6.08316	−0.737692
$69$	9.41530	1.13347
$70$	14.9473	1.78655
$71$	−1.92187	−0.228084	−0.114042	−	0.993476i	$-0.536380\pi$
$71$	−1.92187	−0.228084	−0.114042	+	0.993476i	$0.536380\pi$
$72$	−6.65369	−0.784144
$73$	2.74600	0.321395	0.160698	−	0.987004i	$-0.448626\pi$
$73$	2.74600	0.321395	0.160698	+	0.987004i	$0.448626\pi$
$74$	−2.80481	−0.326053
$75$	−17.4545	−2.01548
$76$	−1.00000	−0.114708
$77$	2.40637	0.274232
$78$	0.0740502	0.00838453
$79$	−1.95398	−0.219840	−0.109920	−	0.993940i	$-0.535059\pi$
$79$	−1.95398	−0.219840	−0.109920	+	0.993940i	$0.535059\pi$
$80$	−3.25849	−0.364310
$81$	15.3105	1.70116
$82$	0.960139	0.106030
$83$	−0.196543	−0.0215734	−0.0107867	−	0.999942i	$-0.503434\pi$
$83$	−0.196543	−0.0215734	−0.0107867	+	0.999942i	$0.503434\pi$
$84$	−14.2526	−1.55509
$85$	19.8219	2.14999
$86$	1.64493	0.177377
$87$	−7.29766	−0.782391
$88$	−0.524584	−0.0559209
$89$	0.0816219	0.00865191	0.00432595	−	0.999991i	$-0.498623\pi$
$89$	0.0816219	0.00865191	0.00432595	+	0.999991i	$0.498623\pi$
$90$	21.6810	2.28537
$91$	0.109327	0.0114606
$92$	−3.03031	−0.315932
$93$	−13.6364	−1.41403
$94$	−9.36661	−0.966092
$95$	3.25849	0.334314
$96$	3.10704	0.317111
$97$	11.6239	1.18022	0.590112	−	0.807321i	$-0.299084\pi$
$97$	11.6239	1.18022	0.590112	+	0.807321i	$0.299084\pi$
$98$	−14.0424	−1.41850
$99$	3.49042	0.350800
$100$	5.61775	0.561775
$101$	−7.99794	−0.795825	−0.397912	−	0.917423i	$-0.630265\pi$
$101$	−7.99794	−0.795825	−0.397912	+	0.917423i	$0.630265\pi$
$102$	−18.9006	−1.87144
$103$	−0.697399	−0.0687168	−0.0343584	−	0.999410i	$-0.510939\pi$
$103$	−0.697399	−0.0687168	−0.0343584	+	0.999410i	$0.510939\pi$
$104$	−0.0238330	−0.00233702
$105$	46.4420	4.53227
$106$	−9.05122	−0.879133
$107$	9.23443	0.892726	0.446363	−	0.894852i	$-0.352719\pi$
$107$	9.23443	0.892726	0.446363	+	0.894852i	$0.352719\pi$
$108$	−11.3521	−1.09236
$109$	2.54281	0.243557	0.121779	−	0.992557i	$-0.461140\pi$
$109$	2.54281	0.243557	0.121779	+	0.992557i	$0.461140\pi$
$110$	1.70935	0.162980
$111$	−8.71466	−0.827159
$112$	4.58720	0.433450
$113$	15.5322	1.46114	0.730572	−	0.682836i	$-0.239254\pi$
$113$	15.5322	1.46114	0.730572	+	0.682836i	$0.239254\pi$
$114$	−3.10704	−0.291001
$115$	9.87424	0.920778
$116$	2.34875	0.218076
$117$	0.158578	0.0146605
$118$	8.13416	0.748810
$119$	−27.9047	−2.55802
$120$	−10.1242	−0.924213
$121$	−10.7248	−0.974983
$122$	6.52012	0.590304
$123$	2.98319	0.268985
$124$	4.38888	0.394133
$125$	−2.01292	−0.180041
$126$	−30.5218	−2.71910
$127$	−2.72760	−0.242035	−0.121018	−	0.992650i	$-0.538616\pi$
$127$	−2.72760	−0.242035	−0.121018	+	0.992650i	$0.538616\pi$
$128$	−1.00000	−0.0883883
$129$	5.11086	0.449986
$130$	0.0776597	0.00681121
$131$	−12.5186	−1.09375	−0.546877	−	0.837213i	$-0.684184\pi$
$131$	−12.5186	−1.09375	−0.546877	+	0.837213i	$0.684184\pi$
$132$	−1.62990	−0.141865
$133$	−4.58720	−0.397761
$134$	−1.80218	−0.155685
$135$	36.9908	3.18366
$136$	6.08316	0.521627
$137$	9.94580	0.849727	0.424863	−	0.905257i	$-0.360322\pi$
$137$	9.94580	0.849727	0.424863	+	0.905257i	$0.360322\pi$
$138$	−9.41530	−0.801483
$139$	−19.0016	−1.61169	−0.805846	−	0.592126i	$-0.798289\pi$
$139$	−19.0016	−1.61169	−0.805846	+	0.592126i	$0.798289\pi$
$140$	−14.9473	−1.26328
$141$	−29.1024	−2.45086
$142$	1.92187	0.161280
$143$	0.0125024	0.00104551
$144$	6.65369	0.554474
$145$	−7.65338	−0.635578
$146$	−2.74600	−0.227261
$147$	−43.6304	−3.59857
$148$	2.80481	0.230554
$149$	−9.89077	−0.810284	−0.405142	−	0.914254i	$-0.632778\pi$
$149$	−9.89077	−0.810284	−0.405142	+	0.914254i	$0.632778\pi$
$150$	17.4545	1.42516
$151$	21.7802	1.77245	0.886226	−	0.463254i	$-0.153318\pi$
$151$	21.7802	1.77245	0.886226	+	0.463254i	$0.153318\pi$
$152$	1.00000	0.0811107
$153$	−40.4754	−3.27225
$154$	−2.40637	−0.193911
$155$	−14.3011	−1.14869
$156$	−0.0740502	−0.00592876
$157$	7.61720	0.607919	0.303959	−	0.952685i	$-0.401691\pi$
$157$	7.61720	0.607919	0.303959	+	0.952685i	$0.401691\pi$
$158$	1.95398	0.155450
$159$	−28.1225	−2.23026
$160$	3.25849	0.257606
$161$	−13.9007	−1.09553
$162$	−15.3105	−1.20290
$163$	−13.0054	−1.01866	−0.509329	−	0.860572i	$-0.670106\pi$
$163$	−13.0054	−1.01866	−0.509329	+	0.860572i	$0.670106\pi$
$164$	−0.960139	−0.0749743
$165$	5.31102	0.413462
$166$	0.196543	0.0152547
$167$	−12.0973	−0.936114	−0.468057	−	0.883698i	$-0.655046\pi$
$167$	−12.0973	−0.936114	−0.468057	+	0.883698i	$0.655046\pi$
$168$	14.2526	1.09961
$169$	−12.9994	−0.999956
$170$	−19.8219	−1.52027
$171$	−6.65369	−0.508820
$172$	−1.64493	−0.125425
$173$	−15.0351	−1.14310	−0.571548	−	0.820569i	$-0.693657\pi$
$173$	−15.0351	−1.14310	−0.571548	+	0.820569i	$0.693657\pi$
$174$	7.29766	0.553234
$175$	25.7697	1.94801
$176$	0.524584	0.0395420
$177$	25.2731	1.89965
$178$	−0.0816219	−0.00611782
$179$	−20.9126	−1.56308	−0.781541	−	0.623854i	$-0.785566\pi$
$179$	−20.9126	−1.56308	−0.781541	+	0.623854i	$0.785566\pi$
$180$	−21.6810	−1.61600
$181$	21.7506	1.61671	0.808354	−	0.588697i	$-0.200359\pi$
$181$	21.7506	1.61671	0.808354	+	0.588697i	$0.200359\pi$
$182$	−0.109327	−0.00810386
$183$	20.2583	1.49753
$184$	3.03031	0.223398
$185$	−9.13945	−0.671945
$186$	13.6364	0.999871
$187$	−3.19113	−0.233359
$188$	9.36661	0.683130
$189$	−52.0746	−3.78787
$190$	−3.25849	−0.236396
$191$	−6.63286	−0.479937	−0.239968	−	0.970781i	$-0.577137\pi$
$191$	−6.63286	−0.479937	−0.239968	+	0.970781i	$0.577137\pi$
$192$	−3.10704	−0.224231
$193$	8.17533	0.588473	0.294236	−	0.955733i	$-0.404935\pi$
$193$	8.17533	0.588473	0.294236	+	0.955733i	$0.404935\pi$
$194$	−11.6239	−0.834544
$195$	0.241292	0.0172793
$196$	14.0424	1.00303
$197$	−3.20156	−0.228101	−0.114051	−	0.993475i	$-0.536383\pi$
$197$	−3.20156	−0.228101	−0.114051	+	0.993475i	$0.536383\pi$
$198$	−3.49042	−0.248053
$199$	−20.7297	−1.46949	−0.734745	−	0.678344i	$-0.762698\pi$
$199$	−20.7297	−1.46949	−0.734745	+	0.678344i	$0.762698\pi$
$200$	−5.61775	−0.397235
$201$	−5.59944	−0.394954
$202$	7.99794	0.562733
$203$	10.7742	0.756200
$204$	18.9006	1.32331
$205$	3.12860	0.218511
$206$	0.697399	0.0485901
$207$	−20.1627	−1.40141
$208$	0.0238330	0.00165252
$209$	−0.524584	−0.0362862
$210$	−46.4420	−3.20480
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	9.05122	0.621641
$213$	5.97133	0.409149
$214$	−9.23443	−0.631252
$215$	5.35998	0.365548
$216$	11.3521	0.772415
$217$	20.1327	1.36670
$218$	−2.54281	−0.172221
$219$	−8.53193	−0.576534
$220$	−1.70935	−0.115244
$221$	−0.144980	−0.00975243
$222$	8.71466	0.584890
$223$	5.03709	0.337308	0.168654	−	0.985675i	$-0.446058\pi$
$223$	5.03709	0.337308	0.168654	+	0.985675i	$0.446058\pi$
$224$	−4.58720	−0.306495
$225$	37.3787	2.49191
$226$	−15.5322	−1.03318
$227$	19.0127	1.26192	0.630958	−	0.775817i	$-0.282662\pi$
$227$	19.0127	1.26192	0.630958	+	0.775817i	$0.282662\pi$
$228$	3.10704	0.205769
$229$	7.11596	0.470236	0.235118	−	0.971967i	$-0.424452\pi$
$229$	7.11596	0.470236	0.235118	+	0.971967i	$0.424452\pi$
$230$	−9.87424	−0.651088
$231$	−7.47670	−0.491931
$232$	−2.34875	−0.154203
$233$	8.38077	0.549042	0.274521	−	0.961581i	$-0.411481\pi$
$233$	8.38077	0.549042	0.274521	+	0.961581i	$0.411481\pi$
$234$	−0.158578	−0.0103665
$235$	−30.5210	−1.99097
$236$	−8.13416	−0.529489
$237$	6.07108	0.394359
$238$	27.9047	1.80879
$239$	−10.6122	−0.686448	−0.343224	−	0.939254i	$-0.611519\pi$
$239$	−10.6122	−0.686448	−0.343224	+	0.939254i	$0.611519\pi$
$240$	10.1242	0.653517
$241$	−4.21854	−0.271740	−0.135870	−	0.990727i	$-0.543383\pi$
$241$	−4.21854	−0.271740	−0.135870	+	0.990727i	$0.543383\pi$
$242$	10.7248	0.689417
$243$	−13.5138	−0.866911
$244$	−6.52012	−0.417408
$245$	−45.7571	−2.92332
$246$	−2.98319	−0.190201
$247$	−0.0238330	−0.00151646
$248$	−4.38888	−0.278694
$249$	0.610666	0.0386994
$250$	2.01292	0.127308
$251$	7.79421	0.491966	0.245983	−	0.969274i	$-0.420889\pi$
$251$	7.79421	0.491966	0.245983	+	0.969274i	$0.420889\pi$
$252$	30.5218	1.92269
$253$	−1.58965	−0.0999407
$254$	2.72760	0.171145
$255$	−61.5874	−3.85675
$256$	1.00000	0.0625000
$257$	−8.25944	−0.515210	−0.257605	−	0.966250i	$-0.582933\pi$
$257$	−8.25944	−0.515210	−0.257605	+	0.966250i	$0.582933\pi$
$258$	−5.11086	−0.318188
$259$	12.8662	0.799469
$260$	−0.0776597	−0.00481625
$261$	15.6278	0.967340
$262$	12.5186	0.773401
$263$	1.63608	0.100885	0.0504425	−	0.998727i	$-0.483937\pi$
$263$	1.63608	0.100885	0.0504425	+	0.998727i	$0.483937\pi$
$264$	1.62990	0.100314
$265$	−29.4933	−1.81176
$266$	4.58720	0.281260
$267$	−0.253602	−0.0155202
$268$	1.80218	0.110086
$269$	−24.1222	−1.47076	−0.735378	−	0.677657i	$-0.762995\pi$
$269$	−24.1222	−1.47076	−0.735378	+	0.677657i	$0.762995\pi$
$270$	−36.9908	−2.25119
$271$	23.2027	1.40946	0.704730	−	0.709475i	$-0.251068\pi$
$271$	23.2027	1.40946	0.704730	+	0.709475i	$0.251068\pi$
$272$	−6.08316	−0.368846
$273$	−0.339683	−0.0205586
$274$	−9.94580	−0.600848
$275$	2.94698	0.177710
$276$	9.41530	0.566734
$277$	−20.7462	−1.24652	−0.623260	−	0.782015i	$-0.714192\pi$
$277$	−20.7462	−1.24652	−0.623260	+	0.782015i	$0.714192\pi$
$278$	19.0016	1.13964
$279$	29.2022	1.74829
$280$	14.9473	0.893275
$281$	−22.5716	−1.34651	−0.673255	−	0.739410i	$-0.735104\pi$
$281$	−22.5716	−1.34651	−0.673255	+	0.739410i	$0.735104\pi$
$282$	29.1024	1.73302
$283$	1.64000	0.0974880	0.0487440	−	0.998811i	$-0.484478\pi$
$283$	1.64000	0.0974880	0.0487440	+	0.998811i	$0.484478\pi$
$284$	−1.92187	−0.114042
$285$	−10.1242	−0.599709
$286$	−0.0125024	−0.000739285 0
$287$	−4.40435	−0.259981
$288$	−6.65369	−0.392072
$289$	20.0048	1.17676
$290$	7.65338	0.449422
$291$	−36.1158	−2.11714
$292$	2.74600	0.160698
$293$	6.44853	0.376727	0.188364	−	0.982099i	$-0.439682\pi$
$293$	6.44853	0.376727	0.188364	+	0.982099i	$0.439682\pi$
$294$	43.6304	2.54458
$295$	26.5051	1.54318
$296$	−2.80481	−0.163026
$297$	−5.95515	−0.345553
$298$	9.89077	0.572957
$299$	−0.0722216	−0.00417668
$300$	−17.4545	−1.00774
$301$	−7.54563	−0.434923
$302$	−21.7802	−1.25331
$303$	24.8499	1.42759
$304$	−1.00000	−0.0573539
$305$	21.2457	1.21653
$306$	40.4754	2.31383
$307$	1.80508	0.103021	0.0515107	−	0.998672i	$-0.483596\pi$
$307$	1.80508	0.103021	0.0515107	+	0.998672i	$0.483596\pi$
$308$	2.40637	0.137116
$309$	2.16684	0.123267
$310$	14.3011	0.812249
$311$	19.2253	1.09017	0.545083	−	0.838382i	$-0.316498\pi$
$311$	19.2253	1.09017	0.545083	+	0.838382i	$0.316498\pi$
$312$	0.0740502	0.00419227
$313$	−6.46763	−0.365572	−0.182786	−	0.983153i	$-0.558512\pi$
$313$	−6.46763	−0.365572	−0.182786	+	0.983153i	$0.558512\pi$
$314$	−7.61720	−0.429864
$315$	−99.4550	−5.60365
$316$	−1.95398	−0.109920
$317$	−26.4589	−1.48608	−0.743039	−	0.669249i	$-0.766616\pi$
$317$	−26.4589	−1.48608	−0.743039	+	0.669249i	$0.766616\pi$
$318$	28.1225	1.57703
$319$	1.23212	0.0689853
$320$	−3.25849	−0.182155
$321$	−28.6917	−1.60142
$322$	13.9007	0.774654
$323$	6.08316	0.338476
$324$	15.3105	0.850582
$325$	0.133888	0.00742677
$326$	13.0054	0.720300
$327$	−7.90062	−0.436905
$328$	0.960139	0.0530148
$329$	42.9665	2.36882
$330$	−5.31102	−0.292362
$331$	0.189628	0.0104229	0.00521145	−	0.999986i	$-0.498341\pi$
$331$	0.189628	0.0104229	0.00521145	+	0.999986i	$0.498341\pi$
$332$	−0.196543	−0.0107867
$333$	18.6623	1.02269
$334$	12.0973	0.661933
$335$	−5.87238	−0.320842
$336$	−14.2526	−0.777544
$337$	−11.8279	−0.644308	−0.322154	−	0.946687i	$-0.604407\pi$
$337$	−11.8279	−0.644308	−0.322154	+	0.946687i	$0.604407\pi$
$338$	12.9994	0.707076
$339$	−48.2590	−2.62107
$340$	19.8219	1.07499
$341$	2.30234	0.124679
$342$	6.65369	0.359790
$343$	32.3051	1.74431
$344$	1.64493	0.0886887
$345$	−30.6796	−1.65174
$346$	15.0351	0.808291
$347$	35.4446	1.90276	0.951382	−	0.308014i	$-0.0996644\pi$
$347$	35.4446	1.90276	0.951382	+	0.308014i	$0.0996644\pi$
$348$	−7.29766	−0.391196
$349$	−31.1974	−1.66996	−0.834979	−	0.550282i	$-0.814520\pi$
$349$	−31.1974	−1.66996	−0.834979	+	0.550282i	$0.814520\pi$
$350$	−25.7697	−1.37745
$351$	−0.270556	−0.0144412
$352$	−0.524584	−0.0279604
$353$	−3.24647	−0.172792	−0.0863961	−	0.996261i	$-0.527535\pi$
$353$	−3.24647	−0.172792	−0.0863961	+	0.996261i	$0.527535\pi$
$354$	−25.2731	−1.34325
$355$	6.26240	0.332374
$356$	0.0816219	0.00432595
$357$	86.7010	4.58870
$358$	20.9126	1.10527
$359$	16.5126	0.871501	0.435750	−	0.900068i	$-0.356483\pi$
$359$	16.5126	0.871501	0.435750	+	0.900068i	$0.356483\pi$
$360$	21.6810	1.14269
$361$	1.00000	0.0526316
$362$	−21.7506	−1.14319
$363$	33.3224	1.74897
$364$	0.109327	0.00573029
$365$	−8.94781	−0.468350
$366$	−20.2583	−1.05892
$367$	30.3074	1.58203	0.791017	−	0.611795i	$-0.209552\pi$
$367$	30.3074	1.58203	0.791017	+	0.611795i	$0.209552\pi$
$368$	−3.03031	−0.157966
$369$	−6.38846	−0.332570
$370$	9.13945	0.475137
$371$	41.5198	2.15560
$372$	−13.6364	−0.707016
$373$	15.2515	0.789692	0.394846	−	0.918747i	$-0.370798\pi$
$373$	15.2515	0.789692	0.394846	+	0.918747i	$0.370798\pi$
$374$	3.19113	0.165009
$375$	6.25421	0.322966
$376$	−9.36661	−0.483046
$377$	0.0559779	0.00288301
$378$	52.0746	2.67843
$379$	31.6011	1.62324	0.811619	−	0.584187i	$-0.198586\pi$
$379$	31.6011	1.62324	0.811619	+	0.584187i	$0.198586\pi$
$380$	3.25849	0.167157
$381$	8.47475	0.434175
$382$	6.63286	0.339367
$383$	−8.78767	−0.449029	−0.224514	−	0.974471i	$-0.572080\pi$
$383$	−8.78767	−0.449029	−0.224514	+	0.974471i	$0.572080\pi$
$384$	3.10704	0.158555
$385$	−7.84114	−0.399622
$386$	−8.17533	−0.416113
$387$	−10.9448	−0.556358
$388$	11.6239	0.590112
$389$	−6.11134	−0.309857	−0.154929	−	0.987926i	$-0.549515\pi$
$389$	−6.11134	−0.309857	−0.154929	+	0.987926i	$0.549515\pi$
$390$	−0.241292	−0.0122183
$391$	18.4339	0.932241
$392$	−14.0424	−0.709250
$393$	38.8957	1.96203
$394$	3.20156	0.161292
$395$	6.36701	0.320359
$396$	3.49042	0.175400
$397$	−1.80012	−0.0903457	−0.0451728	−	0.998979i	$-0.514384\pi$
$397$	−1.80012	−0.0903457	−0.0451728	+	0.998979i	$0.514384\pi$
$398$	20.7297	1.03909
$399$	14.2526	0.713523
$400$	5.61775	0.280887
$401$	27.6247	1.37951	0.689755	−	0.724043i	$-0.257718\pi$
$401$	27.6247	1.37951	0.689755	+	0.724043i	$0.257718\pi$
$402$	5.59944	0.279275
$403$	0.104600	0.00521052
$404$	−7.99794	−0.397912
$405$	−49.8890	−2.47900
$406$	−10.7742	−0.534714
$407$	1.47136	0.0729326
$408$	−18.9006	−0.935720
$409$	−9.65044	−0.477184	−0.238592	−	0.971120i	$-0.576686\pi$
$409$	−9.65044	−0.477184	−0.238592	+	0.971120i	$0.576686\pi$
$410$	−3.12860	−0.154511
$411$	−30.9020	−1.52428
$412$	−0.697399	−0.0343584
$413$	−37.3130	−1.83605
$414$	20.1627	0.990945
$415$	0.640432	0.0314376
$416$	−0.0238330	−0.00116851
$417$	59.0386	2.89113
$418$	0.524584	0.0256582
$419$	3.89218	0.190145	0.0950727	−	0.995470i	$-0.469692\pi$
$419$	3.89218	0.190145	0.0950727	+	0.995470i	$0.469692\pi$
$420$	46.4420	2.26614
$421$	0.134786	0.00656907	0.00328453	−	0.999995i	$-0.498954\pi$
$421$	0.134786	0.00656907	0.00328453	+	0.999995i	$0.498954\pi$
$422$	−1.00000	−0.0486792
$423$	62.3225	3.03022
$424$	−9.05122	−0.439566
$425$	−34.1736	−1.65767
$426$	−5.97133	−0.289312
$427$	−29.9091	−1.44740
$428$	9.23443	0.446363
$429$	−0.0388456	−0.00187548
$430$	−5.35998	−0.258481
$431$	37.2240	1.79302	0.896509	−	0.443026i	$-0.146095\pi$
$431$	37.2240	1.79302	0.896509	+	0.443026i	$0.146095\pi$
$432$	−11.3521	−0.546180
$433$	−0.896009	−0.0430594	−0.0215297	−	0.999768i	$-0.506854\pi$
$433$	−0.896009	−0.0430594	−0.0215297	+	0.999768i	$0.506854\pi$
$434$	−20.1327	−0.966400
$435$	23.7793	1.14013
$436$	2.54281	0.121779
$437$	3.03031	0.144960
$438$	8.53193	0.407671
$439$	−24.5265	−1.17059	−0.585293	−	0.810822i	$-0.699021\pi$
$439$	−24.5265	−1.17059	−0.585293	+	0.810822i	$0.699021\pi$
$440$	1.70935	0.0814901
$441$	93.4340	4.44924
$442$	0.144980	0.00689601
$443$	11.5293	0.547775	0.273888	−	0.961762i	$-0.411690\pi$
$443$	11.5293	0.547775	0.273888	+	0.961762i	$0.411690\pi$
$444$	−8.71466	−0.413579
$445$	−0.265964	−0.0126079
$446$	−5.03709	−0.238513
$447$	30.7310	1.45353
$448$	4.58720	0.216725
$449$	34.5003	1.62817	0.814084	−	0.580747i	$-0.197240\pi$
$449$	34.5003	1.62817	0.814084	+	0.580747i	$0.197240\pi$
$450$	−37.3787	−1.76205
$451$	−0.503674	−0.0237171
$452$	15.5322	0.730572
$453$	−67.6720	−3.17951
$454$	−19.0127	−0.892309
$455$	−0.356241	−0.0167008
$456$	−3.10704	−0.145500
$457$	−10.8079	−0.505574	−0.252787	−	0.967522i	$-0.581347\pi$
$457$	−10.8079	−0.505574	−0.252787	+	0.967522i	$0.581347\pi$
$458$	−7.11596	−0.332507
$459$	69.0569	3.22330
$460$	9.87424	0.460389
$461$	5.51633	0.256921	0.128460	−	0.991715i	$-0.458996\pi$
$461$	5.51633	0.256921	0.128460	+	0.991715i	$0.458996\pi$
$462$	7.47670	0.347847
$463$	−10.0123	−0.465310	−0.232655	−	0.972559i	$-0.574741\pi$
$463$	−10.0123	−0.465310	−0.232655	+	0.972559i	$0.574741\pi$
$464$	2.34875	0.109038
$465$	44.4341	2.06058
$466$	−8.38077	−0.388232
$467$	−7.86217	−0.363818	−0.181909	−	0.983315i	$-0.558228\pi$
$467$	−7.86217	−0.363818	−0.181909	+	0.983315i	$0.558228\pi$
$468$	0.158578	0.00733025
$469$	8.26696	0.381733
$470$	30.5210	1.40783
$471$	−23.6669	−1.09052
$472$	8.13416	0.374405
$473$	−0.862904	−0.0396764
$474$	−6.07108	−0.278854
$475$	−5.61775	−0.257760
$476$	−27.9047	−1.27901
$477$	60.2240	2.75747
$478$	10.6122	0.485392
$479$	−25.0450	−1.14434	−0.572168	−	0.820137i	$-0.693897\pi$
$479$	−25.0450	−1.14434	−0.572168	+	0.820137i	$0.693897\pi$
$480$	−10.1242	−0.462107
$481$	0.0668472	0.00304797
$482$	4.21854	0.192149
$483$	43.1899	1.96521
$484$	−10.7248	−0.487491
$485$	−37.8762	−1.71987
$486$	13.5138	0.612999
$487$	4.19809	0.190234	0.0951169	−	0.995466i	$-0.469678\pi$
$487$	4.19809	0.190234	0.0951169	+	0.995466i	$0.469678\pi$
$488$	6.52012	0.295152
$489$	40.4082	1.82732
$490$	45.7571	2.06710
$491$	21.0084	0.948095	0.474047	−	0.880499i	$-0.342793\pi$
$491$	21.0084	0.948095	0.474047	+	0.880499i	$0.342793\pi$
$492$	2.98319	0.134493
$493$	−14.2878	−0.643491
$494$	0.0238330	0.00107230
$495$	−11.3735	−0.511200
$496$	4.38888	0.197067
$497$	−8.81602	−0.395453
$498$	−0.610666	−0.0273646
$499$	26.0412	1.16577	0.582883	−	0.812556i	$-0.301925\pi$
$499$	26.0412	1.16577	0.582883	+	0.812556i	$0.301925\pi$
$500$	−2.01292	−0.0900203
$501$	37.5867	1.67925
$502$	−7.79421	−0.347873
$503$	−43.8285	−1.95422	−0.977109	−	0.212738i	$-0.931762\pi$
$503$	−43.8285	−1.95422	−0.977109	+	0.212738i	$0.931762\pi$
$504$	−30.5218	−1.35955
$505$	26.0612	1.15971
$506$	1.58965	0.0706687
$507$	40.3897	1.79377
$508$	−2.72760	−0.121018
$509$	−17.8396	−0.790724	−0.395362	−	0.918525i	$-0.629381\pi$
$509$	−17.8396	−0.790724	−0.395362	+	0.918525i	$0.629381\pi$
$510$	61.5874	2.72714
$511$	12.5965	0.557235
$512$	−1.00000	−0.0441942
$513$	11.3521	0.501209
$514$	8.25944	0.364308
$515$	2.27247	0.100137
$516$	5.11086	0.224993
$517$	4.91357	0.216099
$518$	−12.8662	−0.565310
$519$	46.7145	2.05054
$520$	0.0776597	0.00340560
$521$	38.5093	1.68712	0.843561	−	0.537034i	$-0.180455\pi$
$521$	38.5093	1.68712	0.843561	+	0.537034i	$0.180455\pi$
$522$	−15.6278	−0.684012
$523$	−2.35442	−0.102951	−0.0514757	−	0.998674i	$-0.516392\pi$
$523$	−2.35442	−0.102951	−0.0514757	+	0.998674i	$0.516392\pi$
$524$	−12.5186	−0.546877
$525$	−80.0676	−3.49444
$526$	−1.63608	−0.0713365
$527$	−26.6983	−1.16299
$528$	−1.62990	−0.0709324
$529$	−13.8172	−0.600748
$530$	29.4933	1.28111
$531$	−54.1221	−2.34870
$532$	−4.58720	−0.198881
$533$	−0.0228830	−0.000991175 0
$534$	0.253602	0.0109745
$535$	−30.0903	−1.30092
$536$	−1.80218	−0.0778423
$537$	64.9763	2.80393
$538$	24.1222	1.03998
$539$	7.36644	0.317295
$540$	36.9908	1.59183
$541$	7.67448	0.329952	0.164976	−	0.986298i	$-0.447245\pi$
$541$	7.67448	0.329952	0.164976	+	0.986298i	$0.447245\pi$
$542$	−23.2027	−0.996639
$543$	−67.5799	−2.90013
$544$	6.08316	0.260813
$545$	−8.28573	−0.354922
$546$	0.339683	0.0145371
$547$	−9.71119	−0.415221	−0.207610	−	0.978212i	$-0.566569\pi$
$547$	−9.71119	−0.415221	−0.207610	+	0.978212i	$0.566569\pi$
$548$	9.94580	0.424863
$549$	−43.3828	−1.85153
$550$	−2.94698	−0.125660
$551$	−2.34875	−0.100060
$552$	−9.41530	−0.400742
$553$	−8.96329	−0.381158
$554$	20.7462	0.881423
$555$	28.3966	1.20537
$556$	−19.0016	−0.805846
$557$	14.8733	0.630201	0.315101	−	0.949058i	$-0.397962\pi$
$557$	14.8733	0.630201	0.315101	+	0.949058i	$0.397962\pi$
$558$	−29.2022	−1.23623
$559$	−0.0392037	−0.00165814
$560$	−14.9473	−0.631641
$561$	9.91496	0.418610
$562$	22.5716	0.952127
$563$	−30.0136	−1.26492	−0.632461	−	0.774593i	$-0.717955\pi$
$563$	−30.0136	−1.26492	−0.632461	+	0.774593i	$0.717955\pi$
$564$	−29.1024	−1.22543
$565$	−50.6114	−2.12924
$566$	−1.64000	−0.0689344
$567$	70.2323	2.94948
$568$	1.92187	0.0806400
$569$	17.7432	0.743832	0.371916	−	0.928266i	$-0.378701\pi$
$569$	17.7432	0.743832	0.371916	+	0.928266i	$0.378701\pi$
$570$	10.1242	0.424058
$571$	−24.7756	−1.03683	−0.518414	−	0.855130i	$-0.673477\pi$
$571$	−24.7756	−1.03683	−0.518414	+	0.855130i	$0.673477\pi$
$572$	0.0125024	0.000522753 0
$573$	20.6085	0.860934
$574$	4.40435	0.183834
$575$	−17.0235	−0.709930
$576$	6.65369	0.277237
$577$	42.5621	1.77188	0.885942	−	0.463797i	$-0.153513\pi$
$577$	42.5621	1.77188	0.885942	+	0.463797i	$0.153513\pi$
$578$	−20.0048	−0.832092
$579$	−25.4011	−1.05563
$580$	−7.65338	−0.317789
$581$	−0.901582	−0.0374039
$582$	36.1158	1.49705
$583$	4.74813	0.196647
$584$	−2.74600	−0.113630
$585$	−0.516723	−0.0213639
$586$	−6.44853	−0.266386
$587$	14.7820	0.610117	0.305059	−	0.952334i	$-0.401324\pi$
$587$	14.7820	0.610117	0.305059	+	0.952334i	$0.401324\pi$
$588$	−43.6304	−1.79929
$589$	−4.38888	−0.180841
$590$	−26.5051	−1.09120
$591$	9.94736	0.409180
$592$	2.80481	0.115277
$593$	28.9683	1.18958	0.594792	−	0.803879i	$-0.297234\pi$
$593$	28.9683	1.18958	0.594792	+	0.803879i	$0.297234\pi$
$594$	5.95515	0.244343
$595$	90.9271	3.72765
$596$	−9.89077	−0.405142
$597$	64.4080	2.63604
$598$	0.0722216	0.00295336
$599$	4.88072	0.199421	0.0997105	−	0.995016i	$-0.468208\pi$
$599$	4.88072	0.199421	0.0997105	+	0.995016i	$0.468208\pi$
$600$	17.4545	0.712579
$601$	−7.42378	−0.302822	−0.151411	−	0.988471i	$-0.548382\pi$
$601$	−7.42378	−0.302822	−0.151411	+	0.988471i	$0.548382\pi$
$602$	7.54563	0.307537
$603$	11.9911	0.488317
$604$	21.7802	0.886226
$605$	34.9467	1.42078
$606$	−24.8499	−1.00946
$607$	−5.97479	−0.242509	−0.121255	−	0.992621i	$-0.538692\pi$
$607$	−5.97479	−0.242509	−0.121255	+	0.992621i	$0.538692\pi$
$608$	1.00000	0.0405554
$609$	−33.4758	−1.35651
$610$	−21.2457	−0.860215
$611$	0.223235	0.00903111
$612$	−40.4754	−1.63612
$613$	42.1179	1.70112	0.850562	−	0.525874i	$-0.176262\pi$
$613$	42.1179	1.70112	0.850562	+	0.525874i	$0.176262\pi$
$614$	−1.80508	−0.0728471
$615$	−9.72068	−0.391976
$616$	−2.40637	−0.0969556
$617$	−27.3616	−1.10154	−0.550768	−	0.834658i	$-0.685665\pi$
$617$	−27.3616	−1.10154	−0.550768	+	0.834658i	$0.685665\pi$
$618$	−2.16684	−0.0871633
$619$	0.472205	0.0189795	0.00948977	−	0.999955i	$-0.496979\pi$
$619$	0.472205	0.0189795	0.00948977	+	0.999955i	$0.496979\pi$
$620$	−14.3011	−0.574347
$621$	34.4005	1.38045
$622$	−19.2253	−0.770864
$623$	0.374416	0.0150007
$624$	−0.0740502	−0.00296438
$625$	−21.5297	−0.861187
$626$	6.46763	0.258498
$627$	1.62990	0.0650920
$628$	7.61720	0.303959
$629$	−17.0621	−0.680311
$630$	99.4550	3.96238
$631$	45.8306	1.82449	0.912244	−	0.409648i	$-0.134348\pi$
$631$	45.8306	1.82449	0.912244	+	0.409648i	$0.134348\pi$
$632$	1.95398	0.0777250
$633$	−3.10704	−0.123494
$634$	26.4589	1.05082
$635$	8.88785	0.352703
$636$	−28.1225	−1.11513
$637$	0.334674	0.0132603
$638$	−1.23212	−0.0487800
$639$	−12.7875	−0.505867
$640$	3.25849	0.128803
$641$	33.4117	1.31968	0.659841	−	0.751406i	$-0.270624\pi$
$641$	33.4117	1.31968	0.659841	+	0.751406i	$0.270624\pi$
$642$	28.6917	1.13237
$643$	47.1715	1.86026	0.930132	−	0.367226i	$-0.119692\pi$
$643$	47.1715	1.86026	0.930132	+	0.367226i	$0.119692\pi$
$644$	−13.9007	−0.547763
$645$	−16.6537	−0.655738
$646$	−6.08316	−0.239339
$647$	−26.4764	−1.04090	−0.520448	−	0.853893i	$-0.674235\pi$
$647$	−26.4764	−1.04090	−0.520448	+	0.853893i	$0.674235\pi$
$648$	−15.3105	−0.601452
$649$	−4.26705	−0.167496
$650$	−0.133888	−0.00525152
$651$	−62.5530	−2.45165
$652$	−13.0054	−0.509329
$653$	−46.2301	−1.80912	−0.904562	−	0.426343i	$-0.859802\pi$
$653$	−46.2301	−1.80912	−0.904562	+	0.426343i	$0.859802\pi$
$654$	7.90062	0.308939
$655$	40.7917	1.59386
$656$	−0.960139	−0.0374871
$657$	18.2710	0.712821
$658$	−42.9665	−1.67501
$659$	−2.34336	−0.0912843	−0.0456422	−	0.998958i	$-0.514533\pi$
$659$	−2.34336	−0.0912843	−0.0456422	+	0.998958i	$0.514533\pi$
$660$	5.31102	0.206731
$661$	29.9315	1.16420	0.582100	−	0.813117i	$-0.302231\pi$
$661$	29.9315	1.16420	0.582100	+	0.813117i	$0.302231\pi$
$662$	−0.189628	−0.00737010
$663$	0.450459	0.0174944
$664$	0.196543	0.00762734
$665$	14.9473	0.579633
$666$	−18.6623	−0.723151
$667$	−7.11745	−0.275589
$668$	−12.0973	−0.468057
$669$	−15.6504	−0.605080
$670$	5.87238	0.226870
$671$	−3.42035	−0.132041
$672$	14.2526	0.549807
$673$	−17.1446	−0.660875	−0.330438	−	0.943828i	$-0.607196\pi$
$673$	−17.1446	−0.660875	−0.330438	+	0.943828i	$0.607196\pi$
$674$	11.8279	0.455595
$675$	−63.7734	−2.45464
$676$	−12.9994	−0.499978
$677$	5.93525	0.228110	0.114055	−	0.993474i	$-0.463616\pi$
$677$	5.93525	0.228110	0.114055	+	0.993474i	$0.463616\pi$
$678$	48.2590	1.85338
$679$	53.3210	2.04627
$680$	−19.8219	−0.760135
$681$	−59.0731	−2.26369
$682$	−2.30234	−0.0881611
$683$	41.1239	1.57356	0.786782	−	0.617231i	$-0.211746\pi$
$683$	41.1239	1.57356	0.786782	+	0.617231i	$0.211746\pi$
$684$	−6.65369	−0.254410
$685$	−32.4083	−1.23826
$686$	−32.3051	−1.23341
$687$	−22.1096	−0.843533
$688$	−1.64493	−0.0627124
$689$	0.215718	0.00821821
$690$	30.6796	1.16795
$691$	−15.5945	−0.593243	−0.296621	−	0.954995i	$-0.595860\pi$
$691$	−15.5945	−0.593243	−0.296621	+	0.954995i	$0.595860\pi$
$692$	−15.0351	−0.571548
$693$	16.0113	0.608217
$694$	−35.4446	−1.34546
$695$	61.9164	2.34862
$696$	7.29766	0.276617
$697$	5.84068	0.221232
$698$	31.1974	1.18084
$699$	−26.0394	−0.984899
$700$	25.7697	0.974005
$701$	−29.5070	−1.11447	−0.557233	−	0.830356i	$-0.688137\pi$
$701$	−29.5070	−1.11447	−0.557233	+	0.830356i	$0.688137\pi$
$702$	0.270556	0.0102115
$703$	−2.80481	−0.105785
$704$	0.524584	0.0197710
$705$	94.8298	3.57150
$706$	3.24647	0.122182
$707$	−36.6882	−1.37980
$708$	25.2731	0.949823
$709$	7.94266	0.298293	0.149146	−	0.988815i	$-0.452347\pi$
$709$	7.94266	0.298293	0.149146	+	0.988815i	$0.452347\pi$
$710$	−6.26240	−0.235024
$711$	−13.0012	−0.487581
$712$	−0.0816219	−0.00305891
$713$	−13.2997	−0.498077
$714$	−86.7010	−3.24470
$715$	−0.0407390	−0.00152355
$716$	−20.9126	−0.781541
$717$	32.9726	1.23138
$718$	−16.5126	−0.616244
$719$	22.3653	0.834086	0.417043	−	0.908887i	$-0.363067\pi$
$719$	22.3653	0.834086	0.417043	+	0.908887i	$0.363067\pi$
$720$	−21.6810	−0.808002
$721$	−3.19911	−0.119141
$722$	−1.00000	−0.0372161
$723$	13.1072	0.487460
$724$	21.7506	0.808354
$725$	13.1947	0.490038
$726$	−33.3224	−1.23671
$727$	−17.1587	−0.636380	−0.318190	−	0.948027i	$-0.603075\pi$
$727$	−17.1587	−0.636380	−0.318190	+	0.948027i	$0.603075\pi$
$728$	−0.109327	−0.00405193
$729$	−3.94350	−0.146056
$730$	8.94781	0.331173
$731$	10.0064	0.370099
$732$	20.2583	0.748767
$733$	4.44607	0.164219	0.0821096	−	0.996623i	$-0.473834\pi$
$733$	4.44607	0.164219	0.0821096	+	0.996623i	$0.473834\pi$
$734$	−30.3074	−1.11867
$735$	142.169	5.24399
$736$	3.03031	0.111699
$737$	0.945394	0.0348241
$738$	6.38846	0.235163
$739$	−46.5761	−1.71333	−0.856664	−	0.515875i	$-0.827467\pi$
$739$	−46.5761	−1.71333	−0.856664	+	0.515875i	$0.827467\pi$
$740$	−9.13945	−0.335973
$741$	0.0740502	0.00272030
$742$	−41.5198	−1.52424
$743$	13.9260	0.510895	0.255447	−	0.966823i	$-0.417777\pi$
$743$	13.9260	0.510895	0.255447	+	0.966823i	$0.417777\pi$
$744$	13.6364	0.499935
$745$	32.2290	1.18078
$746$	−15.2515	−0.558396
$747$	−1.30773	−0.0478475
$748$	−3.19113	−0.116679
$749$	42.3602	1.54781
$750$	−6.25421	−0.228371
$751$	−33.0234	−1.20504	−0.602521	−	0.798103i	$-0.705837\pi$
$751$	−33.0234	−1.20504	−0.602521	+	0.798103i	$0.705837\pi$
$752$	9.36661	0.341565
$753$	−24.2169	−0.882514
$754$	−0.0559779	−0.00203859
$755$	−70.9707	−2.58289
$756$	−52.0746	−1.89393
$757$	49.2773	1.79101	0.895506	−	0.445049i	$-0.146814\pi$
$757$	49.2773	1.79101	0.895506	+	0.445049i	$0.146814\pi$
$758$	−31.6011	−1.14780
$759$	4.93912	0.179279
$760$	−3.25849	−0.118198
$761$	14.5593	0.527775	0.263888	−	0.964553i	$-0.414995\pi$
$761$	14.5593	0.527775	0.263888	+	0.964553i	$0.414995\pi$
$762$	−8.47475	−0.307008
$763$	11.6644	0.422280
$764$	−6.63286	−0.239968
$765$	131.889	4.76845
$766$	8.78767	0.317511
$767$	−0.193862	−0.00699994
$768$	−3.10704	−0.112116
$769$	1.88511	0.0679787	0.0339894	−	0.999422i	$-0.489179\pi$
$769$	1.88511	0.0679787	0.0339894	+	0.999422i	$0.489179\pi$
$770$	7.84114	0.282575
$771$	25.6624	0.924208
$772$	8.17533	0.294236
$773$	−30.5670	−1.09942	−0.549709	−	0.835356i	$-0.685261\pi$
$773$	−30.5670	−1.09942	−0.549709	+	0.835356i	$0.685261\pi$
$774$	10.9448	0.393404
$775$	24.6556	0.885656
$776$	−11.6239	−0.417272
$777$	−39.9759	−1.43413
$778$	6.11134	0.219102
$779$	0.960139	0.0344006
$780$	0.241292	0.00863963
$781$	−1.00818	−0.0360757
$782$	−18.4339	−0.659194
$783$	−26.6633	−0.952870
$784$	14.0424	0.501516
$785$	−24.8206	−0.885884
$786$	−38.8957	−1.38737
$787$	−29.2975	−1.04434	−0.522172	−	0.852840i	$-0.674878\pi$
$787$	−29.2975	−1.04434	−0.522172	+	0.852840i	$0.674878\pi$
$788$	−3.20156	−0.114051
$789$	−5.08337	−0.180973
$790$	−6.36701	−0.226528
$791$	71.2492	2.53333
$792$	−3.49042	−0.124027
$793$	−0.155394	−0.00551822
$794$	1.80012	0.0638840
$795$	91.6368	3.25002
$796$	−20.7297	−0.734745
$797$	13.4969	0.478086	0.239043	−	0.971009i	$-0.423166\pi$
$797$	13.4969	0.478086	0.239043	+	0.971009i	$0.423166\pi$
$798$	−14.2526	−0.504537
$799$	−56.9786	−2.01576
$800$	−5.61775	−0.198617
$801$	0.543087	0.0191890
$802$	−27.6247	−0.975461
$803$	1.44051	0.0508344
$804$	−5.59944	−0.197477
$805$	45.2951	1.59644
$806$	−0.104600	−0.00368439
$807$	74.9486	2.63831
$808$	7.99794	0.281367
$809$	−4.23078	−0.148746	−0.0743732	−	0.997230i	$-0.523696\pi$
$809$	−4.23078	−0.148746	−0.0743732	+	0.997230i	$0.523696\pi$
$810$	49.8890	1.75292
$811$	23.7485	0.833921	0.416961	−	0.908925i	$-0.363095\pi$
$811$	23.7485	0.833921	0.416961	+	0.908925i	$0.363095\pi$
$812$	10.7742	0.378100
$813$	−72.0915	−2.52836
$814$	−1.47136	−0.0515711
$815$	42.3778	1.48443
$816$	18.9006	0.661654
$817$	1.64493	0.0575488
$818$	9.65044	0.337420
$819$	0.727428	0.0254184
$820$	3.12860	0.109256
$821$	6.58318	0.229754	0.114877	−	0.993380i	$-0.463353\pi$
$821$	6.58318	0.229754	0.114877	+	0.993380i	$0.463353\pi$
$822$	30.9020	1.07783
$823$	14.6255	0.509812	0.254906	−	0.966966i	$-0.417955\pi$
$823$	14.6255	0.509812	0.254906	+	0.966966i	$0.417955\pi$
$824$	0.697399	0.0242950
$825$	−9.15638	−0.318784
$826$	37.3130	1.29829
$827$	−34.4641	−1.19843	−0.599217	−	0.800587i	$-0.704521\pi$
$827$	−34.4641	−1.19843	−0.599217	+	0.800587i	$0.704521\pi$
$828$	−20.1627	−0.700704
$829$	11.7508	0.408122	0.204061	−	0.978958i	$-0.434586\pi$
$829$	11.7508	0.408122	0.204061	+	0.978958i	$0.434586\pi$
$830$	−0.640432	−0.0222297
$831$	64.4593	2.23607
$832$	0.0238330	0.000826262 0
$833$	−85.4224	−2.95971
$834$	−59.0386	−2.04434
$835$	39.4188	1.36414
$836$	−0.524584	−0.0181431
$837$	−49.8232	−1.72214
$838$	−3.89218	−0.134453
$839$	17.4160	0.601266	0.300633	−	0.953740i	$-0.402802\pi$
$839$	17.4160	0.601266	0.300633	+	0.953740i	$0.402802\pi$
$840$	−46.4420	−1.60240
$841$	−23.4834	−0.809771
$842$	−0.134786	−0.00464503
$843$	70.1309	2.41544
$844$	1.00000	0.0344214
$845$	42.3585	1.45718
$846$	−62.3225	−2.14269
$847$	−49.1969	−1.69043
$848$	9.05122	0.310820
$849$	−5.09555	−0.174879
$850$	34.1736	1.17215
$851$	−8.49946	−0.291358
$852$	5.97133	0.204575
$853$	−52.7951	−1.80767	−0.903835	−	0.427881i	$-0.859260\pi$
$853$	−52.7951	−1.80767	−0.903835	+	0.427881i	$0.859260\pi$
$854$	29.9091	1.02347
$855$	21.6810	0.741473
$856$	−9.23443	−0.315626
$857$	16.2002	0.553388	0.276694	−	0.960958i	$-0.410761\pi$
$857$	16.2002	0.553388	0.276694	+	0.960958i	$0.410761\pi$
$858$	0.0388456	0.00132617
$859$	−49.6905	−1.69542	−0.847709	−	0.530462i	$-0.822018\pi$
$859$	−49.6905	−1.69542	−0.847709	+	0.530462i	$0.822018\pi$
$860$	5.35998	0.182774
$861$	13.6845	0.466366
$862$	−37.2240	−1.26785
$863$	40.9452	1.39379	0.696895	−	0.717173i	$-0.254564\pi$
$863$	40.9452	1.39379	0.696895	+	0.717173i	$0.254564\pi$
$864$	11.3521	0.386208
$865$	48.9916	1.66576
$866$	0.896009	0.0304476
$867$	−62.1558	−2.11092
$868$	20.1327	0.683348
$869$	−1.02503	−0.0347716
$870$	−23.7793	−0.806195
$871$	0.0429514	0.00145535
$872$	−2.54281	−0.0861105
$873$	77.3415	2.61761
$874$	−3.03031	−0.102502
$875$	−9.23366	−0.312155
$876$	−8.53193	−0.288267
$877$	−30.8491	−1.04170	−0.520850	−	0.853648i	$-0.674385\pi$
$877$	−30.8491	−1.04170	−0.520850	+	0.853648i	$0.674385\pi$
$878$	24.5265	0.827729
$879$	−20.0358	−0.675792
$880$	−1.70935	−0.0576222
$881$	31.8666	1.07361	0.536806	−	0.843706i	$-0.319631\pi$
$881$	31.8666	1.07361	0.536806	+	0.843706i	$0.319631\pi$
$882$	−93.4340	−3.14609
$883$	44.2865	1.49036	0.745180	−	0.666863i	$-0.232364\pi$
$883$	44.2865	1.49036	0.745180	+	0.666863i	$0.232364\pi$
$884$	−0.144980	−0.00487621
$885$	−82.3522	−2.76824
$886$	−11.5293	−0.387336
$887$	−7.16581	−0.240604	−0.120302	−	0.992737i	$-0.538386\pi$
$887$	−7.16581	−0.240604	−0.120302	+	0.992737i	$0.538386\pi$
$888$	8.71466	0.292445
$889$	−12.5120	−0.419641
$890$	0.265964	0.00891514
$891$	8.03163	0.269070
$892$	5.03709	0.168654
$893$	−9.36661	−0.313442
$894$	−30.7310	−1.02780
$895$	68.1435	2.27779
$896$	−4.58720	−0.153248
$897$	0.224395	0.00749234
$898$	−34.5003	−1.15129
$899$	10.3084	0.343804
$900$	37.3787	1.24596
$901$	−55.0600	−1.83432
$902$	0.503674	0.0167705
$903$	23.4446	0.780186
$904$	−15.5322	−0.516592
$905$	−70.8740	−2.35593
$906$	67.6720	2.24825
$907$	40.5648	1.34693	0.673466	−	0.739218i	$-0.264805\pi$
$907$	40.5648	1.34693	0.673466	+	0.739218i	$0.264805\pi$
$908$	19.0127	0.630958
$909$	−53.2158	−1.76506
$910$	0.356241	0.0118093
$911$	31.3440	1.03847	0.519236	−	0.854631i	$-0.326216\pi$
$911$	31.3440	1.03847	0.519236	+	0.854631i	$0.326216\pi$
$912$	3.10704	0.102884
$913$	−0.103103	−0.00341222
$914$	10.8079	0.357495
$915$	−66.0113	−2.18227
$916$	7.11596	0.235118
$917$	−57.4253	−1.89635
$918$	−69.0569	−2.27922
$919$	−7.23379	−0.238621	−0.119310	−	0.992857i	$-0.538068\pi$
$919$	−7.23379	−0.238621	−0.119310	+	0.992857i	$0.538068\pi$
$920$	−9.87424	−0.325544
$921$	−5.60846	−0.184805
$922$	−5.51633	−0.181671
$923$	−0.0458041	−0.00150766
$924$	−7.47670	−0.245965
$925$	15.7567	0.518078
$926$	10.0123	0.329024
$927$	−4.64027	−0.152407
$928$	−2.34875	−0.0771015
$929$	−7.33265	−0.240576	−0.120288	−	0.992739i	$-0.538382\pi$
$929$	−7.33265	−0.240576	−0.120288	+	0.992739i	$0.538382\pi$
$930$	−44.4341	−1.45705
$931$	−14.0424	−0.460222
$932$	8.38077	0.274521
$933$	−59.7337	−1.95559
$934$	7.86217	0.257258
$935$	10.3983	0.340059
$936$	−0.158578	−0.00518327
$937$	−1.35428	−0.0442423	−0.0221212	−	0.999755i	$-0.507042\pi$
$937$	−1.35428	−0.0442423	−0.0221212	+	0.999755i	$0.507042\pi$
$938$	−8.26696	−0.269926
$939$	20.0952	0.655781
$940$	−30.5210	−0.995485
$941$	−42.7433	−1.39339	−0.696696	−	0.717367i	$-0.745347\pi$
$941$	−42.7433	−1.39339	−0.696696	+	0.717367i	$0.745347\pi$
$942$	23.6669	0.771111
$943$	2.90952	0.0947471
$944$	−8.13416	−0.264744
$945$	169.684	5.51983
$946$	0.862904	0.0280554
$947$	46.7346	1.51867	0.759336	−	0.650699i	$-0.225524\pi$
$947$	46.7346	1.51867	0.759336	+	0.650699i	$0.225524\pi$
$948$	6.07108	0.197180
$949$	0.0654456	0.00212445
$950$	5.61775	0.182264
$951$	82.2087	2.66580
$952$	27.9047	0.904396
$953$	19.0996	0.618695	0.309348	−	0.950949i	$-0.399889\pi$
$953$	19.0996	0.618695	0.309348	+	0.950949i	$0.399889\pi$
$954$	−60.2240	−1.94982
$955$	21.6131	0.699383
$956$	−10.6122	−0.343224
$957$	−3.82824	−0.123749
$958$	25.0450	0.809167
$959$	45.6234	1.47326
$960$	10.1242	0.326759
$961$	−11.7377	−0.378636
$962$	−0.0668472	−0.00215524
$963$	61.4430	1.97997
$964$	−4.21854	−0.135870
$965$	−26.6392	−0.857546
$966$	−43.1899	−1.38961
$967$	59.0732	1.89967	0.949834	−	0.312755i	$-0.101252\pi$
$967$	59.0732	1.89967	0.949834	+	0.312755i	$0.101252\pi$
$968$	10.7248	0.344708
$969$	−18.9006	−0.607175
$970$	37.8762	1.21613
$971$	18.6220	0.597610	0.298805	−	0.954314i	$-0.403412\pi$
$971$	18.6220	0.597610	0.298805	+	0.954314i	$0.403412\pi$
$972$	−13.5138	−0.433456
$973$	−87.1640	−2.79435
$974$	−4.19809	−0.134516
$975$	−0.415995	−0.0133225
$976$	−6.52012	−0.208704
$977$	30.2863	0.968945	0.484473	−	0.874806i	$-0.339012\pi$
$977$	30.2863	0.968945	0.484473	+	0.874806i	$0.339012\pi$
$978$	−40.4082	−1.29211
$979$	0.0428176	0.00136846
$980$	−45.7571	−1.46166
$981$	16.9191	0.540185
$982$	−21.0084	−0.670404
$983$	−33.7796	−1.07740	−0.538701	−	0.842497i	$-0.681085\pi$
$983$	−33.7796	−1.07740	−0.538701	+	0.842497i	$0.681085\pi$
$984$	−2.98319	−0.0951006
$985$	10.4322	0.332399
$986$	14.2878	0.455017
$987$	−133.499	−4.24931
$988$	−0.0238330	−0.000758230 0
$989$	4.98465	0.158503
$990$	11.3735	0.361473
$991$	23.2334	0.738033	0.369016	−	0.929423i	$-0.379695\pi$
$991$	23.2334	0.738033	0.369016	+	0.929423i	$0.379695\pi$
$992$	−4.38888	−0.139347
$993$	−0.589182	−0.0186971
$994$	8.81602	0.279627
$995$	67.5475	2.14140
$996$	0.610666	0.0193497
$997$	−6.41783	−0.203255	−0.101627	−	0.994823i	$-0.532405\pi$
$997$	−6.41783	−0.203255	−0.101627	+	0.994823i	$0.532405\pi$
$998$	−26.0412	−0.824321
$999$	−31.8406	−1.00739

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.h.1.1	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.h.1.1	✓	41	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.10704 q^{3} +1.00000 q^{4} -3.25849 q^{5} +3.10704 q^{6} +4.58720 q^{7} -1.00000 q^{8} +6.65369 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.10704 q^{3} +1.00000 q^{4} -3.25849 q^{5} +3.10704 q^{6} +4.58720 q^{7} -1.00000 q^{8} +6.65369 q^{9} +3.25849 q^{10} +0.524584 q^{11} -3.10704 q^{12} +0.0238330 q^{13} -4.58720 q^{14} +10.1242 q^{15} +1.00000 q^{16} -6.08316 q^{17} -6.65369 q^{18} -1.00000 q^{19} -3.25849 q^{20} -14.2526 q^{21} -0.524584 q^{22} -3.03031 q^{23} +3.10704 q^{24} +5.61775 q^{25} -0.0238330 q^{26} -11.3521 q^{27} +4.58720 q^{28} +2.34875 q^{29} -10.1242 q^{30} +4.38888 q^{31} -1.00000 q^{32} -1.62990 q^{33} +6.08316 q^{34} -14.9473 q^{35} +6.65369 q^{36} +2.80481 q^{37} +1.00000 q^{38} -0.0740502 q^{39} +3.25849 q^{40} -0.960139 q^{41} +14.2526 q^{42} -1.64493 q^{43} +0.524584 q^{44} -21.6810 q^{45} +3.03031 q^{46} +9.36661 q^{47} -3.10704 q^{48} +14.0424 q^{49} -5.61775 q^{50} +18.9006 q^{51} +0.0238330 q^{52} +9.05122 q^{53} +11.3521 q^{54} -1.70935 q^{55} -4.58720 q^{56} +3.10704 q^{57} -2.34875 q^{58} -8.13416 q^{59} +10.1242 q^{60} -6.52012 q^{61} -4.38888 q^{62} +30.5218 q^{63} +1.00000 q^{64} -0.0776597 q^{65} +1.62990 q^{66} +1.80218 q^{67} -6.08316 q^{68} +9.41530 q^{69} +14.9473 q^{70} -1.92187 q^{71} -6.65369 q^{72} +2.74600 q^{73} -2.80481 q^{74} -17.4545 q^{75} -1.00000 q^{76} +2.40637 q^{77} +0.0740502 q^{78} -1.95398 q^{79} -3.25849 q^{80} +15.3105 q^{81} +0.960139 q^{82} -0.196543 q^{83} -14.2526 q^{84} +19.8219 q^{85} +1.64493 q^{86} -7.29766 q^{87} -0.524584 q^{88} +0.0816219 q^{89} +21.6810 q^{90} +0.109327 q^{91} -3.03031 q^{92} -13.6364 q^{93} -9.36661 q^{94} +3.25849 q^{95} +3.10704 q^{96} +11.6239 q^{97} -14.0424 q^{98} +3.49042 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9}+O(q^{10}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9} + 9 q^{10} - 9 q^{11} + 8 q^{12} + 13 q^{13} - 7 q^{14} + 26 q^{15} + 41 q^{16} - 16 q^{17} - 43 q^{18} - 41 q^{19} - 9 q^{20} + 2 q^{21} + 9 q^{22} + 10 q^{23} - 8 q^{24} + 60 q^{25} - 13 q^{26} + 47 q^{27} + 7 q^{28} - 14 q^{29} - 26 q^{30} + 49 q^{31} - 41 q^{32} + 12 q^{33} + 16 q^{34} - 8 q^{35} + 43 q^{36} + 54 q^{37} + 41 q^{38} + 16 q^{39} + 9 q^{40} - 18 q^{41} - 2 q^{42} + 29 q^{43} - 9 q^{44} - 13 q^{45} - 10 q^{46} - 8 q^{47} + 8 q^{48} + 44 q^{49} - 60 q^{50} - 16 q^{51} + 13 q^{52} + 7 q^{53} - 47 q^{54} + 19 q^{55} - 7 q^{56} - 8 q^{57} + 14 q^{58} - 5 q^{59} + 26 q^{60} - 6 q^{61} - 49 q^{62} + 24 q^{63} + 41 q^{64} - 26 q^{65} - 12 q^{66} + 66 q^{67} - 16 q^{68} + 12 q^{69} + 8 q^{70} + 27 q^{71} - 43 q^{72} - q^{73} - 54 q^{74} + 62 q^{75} - 41 q^{76} - 8 q^{77} - 16 q^{78} + 87 q^{79} - 9 q^{80} + 73 q^{81} + 18 q^{82} - 41 q^{83} + 2 q^{84} + 14 q^{85} - 29 q^{86} + 35 q^{87} + 9 q^{88} - 4 q^{89} + 13 q^{90} + 39 q^{91} + 10 q^{92} + 17 q^{93} + 8 q^{94} + 9 q^{95} - 8 q^{96} + 64 q^{97} - 44 q^{98} + 40 q^{99}+O(q^{100}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9 + 9 * q^10 - 9 * q^11 + 8 * q^12 + 13 * q^13 - 7 * q^14 + 26 * q^15 + 41 * q^16 - 16 * q^17 - 43 * q^18 - 41 * q^19 - 9 * q^20 + 2 * q^21 + 9 * q^22 + 10 * q^23 - 8 * q^24 + 60 * q^25 - 13 * q^26 + 47 * q^27 + 7 * q^28 - 14 * q^29 - 26 * q^30 + 49 * q^31 - 41 * q^32 + 12 * q^33 + 16 * q^34 - 8 * q^35 + 43 * q^36 + 54 * q^37 + 41 * q^38 + 16 * q^39 + 9 * q^40 - 18 * q^41 - 2 * q^42 + 29 * q^43 - 9 * q^44 - 13 * q^45 - 10 * q^46 - 8 * q^47 + 8 * q^48 + 44 * q^49 - 60 * q^50 - 16 * q^51 + 13 * q^52 + 7 * q^53 - 47 * q^54 + 19 * q^55 - 7 * q^56 - 8 * q^57 + 14 * q^58 - 5 * q^59 + 26 * q^60 - 6 * q^61 - 49 * q^62 + 24 * q^63 + 41 * q^64 - 26 * q^65 - 12 * q^66 + 66 * q^67 - 16 * q^68 + 12 * q^69 + 8 * q^70 + 27 * q^71 - 43 * q^72 - q^73 - 54 * q^74 + 62 * q^75 - 41 * q^76 - 8 * q^77 - 16 * q^78 + 87 * q^79 - 9 * q^80 + 73 * q^81 + 18 * q^82 - 41 * q^83 + 2 * q^84 + 14 * q^85 - 29 * q^86 + 35 * q^87 + 9 * q^88 - 4 * q^89 + 13 * q^90 + 39 * q^91 + 10 * q^92 + 17 * q^93 + 8 * q^94 + 9 * q^95 - 8 * q^96 + 64 * q^97 - 44 * q^98 + 40 * q^99

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