LMFDB - Embedded newform 4334.2.a.e.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.15892 q^{3} +1.00000 q^{4} -2.65435 q^{5} +1.15892 q^{6} +4.05701 q^{7} -1.00000 q^{8} -1.65690 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.15892 q^{3} +1.00000 q^{4} -2.65435 q^{5} +1.15892 q^{6} +4.05701 q^{7} -1.00000 q^{8} -1.65690 q^{9} +2.65435 q^{10} -1.00000 q^{11} -1.15892 q^{12} +3.70680 q^{13} -4.05701 q^{14} +3.07619 q^{15} +1.00000 q^{16} +5.32788 q^{17} +1.65690 q^{18} +8.24949 q^{19} -2.65435 q^{20} -4.70176 q^{21} +1.00000 q^{22} +2.73836 q^{23} +1.15892 q^{24} +2.04559 q^{25} -3.70680 q^{26} +5.39699 q^{27} +4.05701 q^{28} -3.70508 q^{29} -3.07619 q^{30} -5.17111 q^{31} -1.00000 q^{32} +1.15892 q^{33} -5.32788 q^{34} -10.7687 q^{35} -1.65690 q^{36} +5.48223 q^{37} -8.24949 q^{38} -4.29590 q^{39} +2.65435 q^{40} -0.230412 q^{41} +4.70176 q^{42} +8.38813 q^{43} -1.00000 q^{44} +4.39798 q^{45} -2.73836 q^{46} +2.07974 q^{47} -1.15892 q^{48} +9.45931 q^{49} -2.04559 q^{50} -6.17460 q^{51} +3.70680 q^{52} -13.5722 q^{53} -5.39699 q^{54} +2.65435 q^{55} -4.05701 q^{56} -9.56053 q^{57} +3.70508 q^{58} -10.9380 q^{59} +3.07619 q^{60} -9.71142 q^{61} +5.17111 q^{62} -6.72204 q^{63} +1.00000 q^{64} -9.83915 q^{65} -1.15892 q^{66} +13.5804 q^{67} +5.32788 q^{68} -3.17356 q^{69} +10.7687 q^{70} +5.94670 q^{71} +1.65690 q^{72} +7.14279 q^{73} -5.48223 q^{74} -2.37068 q^{75} +8.24949 q^{76} -4.05701 q^{77} +4.29590 q^{78} -10.8780 q^{79} -2.65435 q^{80} -1.28401 q^{81} +0.230412 q^{82} +0.246945 q^{83} -4.70176 q^{84} -14.1421 q^{85} -8.38813 q^{86} +4.29390 q^{87} +1.00000 q^{88} +0.350969 q^{89} -4.39798 q^{90} +15.0385 q^{91} +2.73836 q^{92} +5.99292 q^{93} -2.07974 q^{94} -21.8971 q^{95} +1.15892 q^{96} -10.7197 q^{97} -9.45931 q^{98} +1.65690 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{6} + 7 q^{7} - 24 q^{8} + 28 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^6 + 7 * q^7 - 24 * q^8 + 28 * q^9	\( 24 q - 24 q^{2} - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{6} + 7 q^{7} - 24 q^{8} + 28 q^{9} + 4 q^{10} - 24 q^{11} - 4 q^{12} + 21 q^{13} - 7 q^{14} - 2 q^{15} + 24 q^{16} + 15 q^{17} - 28 q^{18} + 21 q^{19} - 4 q^{20} + 15 q^{21} + 24 q^{22} - 17 q^{23} + 4 q^{24} + 46 q^{25} - 21 q^{26} - 19 q^{27} + 7 q^{28} + 9 q^{29} + 2 q^{30} + 27 q^{31} - 24 q^{32} + 4 q^{33} - 15 q^{34} - 2 q^{35} + 28 q^{36} + 5 q^{37} - 21 q^{38} + 17 q^{39} + 4 q^{40} + 16 q^{41} - 15 q^{42} + 3 q^{43} - 24 q^{44} - 21 q^{45} + 17 q^{46} - 24 q^{47} - 4 q^{48} + 55 q^{49} - 46 q^{50} - 12 q^{51} + 21 q^{52} - 26 q^{53} + 19 q^{54} + 4 q^{55} - 7 q^{56} + 30 q^{57} - 9 q^{58} - 17 q^{59} - 2 q^{60} + 44 q^{61} - 27 q^{62} + 4 q^{63} + 24 q^{64} + 35 q^{65} - 4 q^{66} + 10 q^{67} + 15 q^{68} + 3 q^{69} + 2 q^{70} - 6 q^{71} - 28 q^{72} + 77 q^{73} - 5 q^{74} - 32 q^{75} + 21 q^{76} - 7 q^{77} - 17 q^{78} + 43 q^{79} - 4 q^{80} + 48 q^{81} - 16 q^{82} - 20 q^{83} + 15 q^{84} + 35 q^{85} - 3 q^{86} + 36 q^{87} + 24 q^{88} + 3 q^{89} + 21 q^{90} + 63 q^{91} - 17 q^{92} + 36 q^{93} + 24 q^{94} - 3 q^{95} + 4 q^{96} + 16 q^{97} - 55 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^6 + 7 * q^7 - 24 * q^8 + 28 * q^9 + 4 * q^10 - 24 * q^11 - 4 * q^12 + 21 * q^13 - 7 * q^14 - 2 * q^15 + 24 * q^16 + 15 * q^17 - 28 * q^18 + 21 * q^19 - 4 * q^20 + 15 * q^21 + 24 * q^22 - 17 * q^23 + 4 * q^24 + 46 * q^25 - 21 * q^26 - 19 * q^27 + 7 * q^28 + 9 * q^29 + 2 * q^30 + 27 * q^31 - 24 * q^32 + 4 * q^33 - 15 * q^34 - 2 * q^35 + 28 * q^36 + 5 * q^37 - 21 * q^38 + 17 * q^39 + 4 * q^40 + 16 * q^41 - 15 * q^42 + 3 * q^43 - 24 * q^44 - 21 * q^45 + 17 * q^46 - 24 * q^47 - 4 * q^48 + 55 * q^49 - 46 * q^50 - 12 * q^51 + 21 * q^52 - 26 * q^53 + 19 * q^54 + 4 * q^55 - 7 * q^56 + 30 * q^57 - 9 * q^58 - 17 * q^59 - 2 * q^60 + 44 * q^61 - 27 * q^62 + 4 * q^63 + 24 * q^64 + 35 * q^65 - 4 * q^66 + 10 * q^67 + 15 * q^68 + 3 * q^69 + 2 * q^70 - 6 * q^71 - 28 * q^72 + 77 * q^73 - 5 * q^74 - 32 * q^75 + 21 * q^76 - 7 * q^77 - 17 * q^78 + 43 * q^79 - 4 * q^80 + 48 * q^81 - 16 * q^82 - 20 * q^83 + 15 * q^84 + 35 * q^85 - 3 * q^86 + 36 * q^87 + 24 * q^88 + 3 * q^89 + 21 * q^90 + 63 * q^91 - 17 * q^92 + 36 * q^93 + 24 * q^94 - 3 * q^95 + 4 * q^96 + 16 * q^97 - 55 * q^98 - 28 * 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
$3$	−1.15892	−0.669105	−0.334552	−	0.942377i	$-0.608585\pi$
$3$	−1.15892	−0.669105	−0.334552	+	0.942377i	$0.608585\pi$
$4$	1.00000	0.500000
$5$	−2.65435	−1.18706	−0.593531	−	0.804811i	$-0.702267\pi$
$5$	−2.65435	−1.18706	−0.593531	+	0.804811i	$0.702267\pi$
$6$	1.15892	0.473129
$7$	4.05701	1.53340	0.766702	−	0.642003i	$-0.221896\pi$
$7$	4.05701	1.53340	0.766702	+	0.642003i	$0.221896\pi$
$8$	−1.00000	−0.353553
$9$	−1.65690	−0.552299
$10$	2.65435	0.839380
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.15892	−0.334552
$13$	3.70680	1.02808	0.514040	−	0.857766i	$-0.328148\pi$
$13$	3.70680	1.02808	0.514040	+	0.857766i	$0.328148\pi$
$14$	−4.05701	−1.08428
$15$	3.07619	0.794269
$16$	1.00000	0.250000
$17$	5.32788	1.29220	0.646100	−	0.763253i	$-0.276399\pi$
$17$	5.32788	1.29220	0.646100	+	0.763253i	$0.276399\pi$
$18$	1.65690	0.390534
$19$	8.24949	1.89256	0.946282	−	0.323343i	$-0.104807\pi$
$19$	8.24949	1.89256	0.946282	+	0.323343i	$0.104807\pi$
$20$	−2.65435	−0.593531
$21$	−4.70176	−1.02601
$22$	1.00000	0.213201
$23$	2.73836	0.570988	0.285494	−	0.958380i	$-0.407842\pi$
$23$	2.73836	0.570988	0.285494	+	0.958380i	$0.407842\pi$
$24$	1.15892	0.236564
$25$	2.04559	0.409117
$26$	−3.70680	−0.726963
$27$	5.39699	1.03865
$28$	4.05701	0.766702
$29$	−3.70508	−0.688016	−0.344008	−	0.938967i	$-0.611785\pi$
$29$	−3.70508	−0.688016	−0.344008	+	0.938967i	$0.611785\pi$
$30$	−3.07619	−0.561633
$31$	−5.17111	−0.928758	−0.464379	−	0.885636i	$-0.653723\pi$
$31$	−5.17111	−0.928758	−0.464379	+	0.885636i	$0.653723\pi$
$32$	−1.00000	−0.176777
$33$	1.15892	0.201743
$34$	−5.32788	−0.913723
$35$	−10.7687	−1.82025
$36$	−1.65690	−0.276149
$37$	5.48223	0.901273	0.450637	−	0.892708i	$-0.351197\pi$
$37$	5.48223	0.901273	0.450637	+	0.892708i	$0.351197\pi$
$38$	−8.24949	−1.33824
$39$	−4.29590	−0.687894
$40$	2.65435	0.419690
$41$	−0.230412	−0.0359843	−0.0179921	−	0.999838i	$-0.505727\pi$
$41$	−0.230412	−0.0359843	−0.0179921	+	0.999838i	$0.505727\pi$
$42$	4.70176	0.725498
$43$	8.38813	1.27918	0.639589	−	0.768717i	$-0.279104\pi$
$43$	8.38813	1.27918	0.639589	+	0.768717i	$0.279104\pi$
$44$	−1.00000	−0.150756
$45$	4.39798	0.655613
$46$	−2.73836	−0.403750
$47$	2.07974	0.303361	0.151680	−	0.988430i	$-0.451532\pi$
$47$	2.07974	0.303361	0.151680	+	0.988430i	$0.451532\pi$
$48$	−1.15892	−0.167276
$49$	9.45931	1.35133
$50$	−2.04559	−0.289290
$51$	−6.17460	−0.864617
$52$	3.70680	0.514040
$53$	−13.5722	−1.86429	−0.932144	−	0.362088i	$-0.882064\pi$
$53$	−13.5722	−1.86429	−0.932144	+	0.362088i	$0.882064\pi$
$54$	−5.39699	−0.734437
$55$	2.65435	0.357913
$56$	−4.05701	−0.542140
$57$	−9.56053	−1.26632
$58$	3.70508	0.486501
$59$	−10.9380	−1.42400	−0.712001	−	0.702178i	$-0.752211\pi$
$59$	−10.9380	−1.42400	−0.712001	+	0.702178i	$0.752211\pi$
$60$	3.07619	0.397135
$61$	−9.71142	−1.24342	−0.621710	−	0.783248i	$-0.713562\pi$
$61$	−9.71142	−1.24342	−0.621710	+	0.783248i	$0.713562\pi$
$62$	5.17111	0.656731
$63$	−6.72204	−0.846897
$64$	1.00000	0.125000
$65$	−9.83915	−1.22040
$66$	−1.15892	−0.142654
$67$	13.5804	1.65912	0.829558	−	0.558421i	$-0.188592\pi$
$67$	13.5804	1.65912	0.829558	+	0.558421i	$0.188592\pi$
$68$	5.32788	0.646100
$69$	−3.17356	−0.382051
$70$	10.7687	1.28711
$71$	5.94670	0.705744	0.352872	−	0.935672i	$-0.385205\pi$
$71$	5.94670	0.705744	0.352872	+	0.935672i	$0.385205\pi$
$72$	1.65690	0.195267
$73$	7.14279	0.836000	0.418000	−	0.908447i	$-0.362731\pi$
$73$	7.14279	0.836000	0.418000	+	0.908447i	$0.362731\pi$
$74$	−5.48223	−0.637296
$75$	−2.37068	−0.273742
$76$	8.24949	0.946282
$77$	−4.05701	−0.462339
$78$	4.29590	0.486414
$79$	−10.8780	−1.22387	−0.611937	−	0.790907i	$-0.709609\pi$
$79$	−10.8780	−1.22387	−0.611937	+	0.790907i	$0.709609\pi$
$80$	−2.65435	−0.296766
$81$	−1.28401	−0.142668
$82$	0.230412	0.0254447
$83$	0.246945	0.0271057	0.0135528	−	0.999908i	$-0.495686\pi$
$83$	0.246945	0.0271057	0.0135528	+	0.999908i	$0.495686\pi$
$84$	−4.70176	−0.513004
$85$	−14.1421	−1.53392
$86$	−8.38813	−0.904516
$87$	4.29390	0.460355
$88$	1.00000	0.106600
$89$	0.350969	0.0372026	0.0186013	−	0.999827i	$-0.494079\pi$
$89$	0.350969	0.0372026	0.0186013	+	0.999827i	$0.494079\pi$
$90$	−4.39798	−0.463588
$91$	15.0385	1.57646
$92$	2.73836	0.285494
$93$	5.99292	0.621437
$94$	−2.07974	−0.214508
$95$	−21.8971	−2.24659
$96$	1.15892	0.118282
$97$	−10.7197	−1.08842	−0.544208	−	0.838950i	$-0.683170\pi$
$97$	−10.7197	−1.08842	−0.544208	+	0.838950i	$0.683170\pi$
$98$	−9.45931	−0.955535
$99$	1.65690	0.166524
$100$	2.04559	0.204559
$101$	7.86002	0.782101	0.391051	−	0.920369i	$-0.372112\pi$
$101$	7.86002	0.782101	0.391051	+	0.920369i	$0.372112\pi$
$102$	6.17460	0.611377
$103$	7.00720	0.690440	0.345220	−	0.938522i	$-0.387804\pi$
$103$	7.00720	0.690440	0.345220	+	0.938522i	$0.387804\pi$
$104$	−3.70680	−0.363481
$105$	12.4801	1.21794
$106$	13.5722	1.31825
$107$	9.18064	0.887526	0.443763	−	0.896144i	$-0.353643\pi$
$107$	9.18064	0.887526	0.443763	+	0.896144i	$0.353643\pi$
$108$	5.39699	0.519325
$109$	−9.85461	−0.943900	−0.471950	−	0.881625i	$-0.656450\pi$
$109$	−9.85461	−0.943900	−0.471950	+	0.881625i	$0.656450\pi$
$110$	−2.65435	−0.253083
$111$	−6.35349	−0.603046
$112$	4.05701	0.383351
$113$	14.6875	1.38168	0.690842	−	0.723006i	$-0.257240\pi$
$113$	14.6875	1.38168	0.690842	+	0.723006i	$0.257240\pi$
$114$	9.56053	0.895426
$115$	−7.26858	−0.677799
$116$	−3.70508	−0.344008
$117$	−6.14178	−0.567807
$118$	10.9380	1.00692
$119$	21.6152	1.98147
$120$	−3.07619	−0.280817
$121$	1.00000	0.0909091
$122$	9.71142	0.879230
$123$	0.267030	0.0240772
$124$	−5.17111	−0.464379
$125$	7.84205	0.701415
$126$	6.72204	0.598847
$127$	−14.2986	−1.26880	−0.634400	−	0.773005i	$-0.718753\pi$
$127$	−14.2986	−1.26880	−0.634400	+	0.773005i	$0.718753\pi$
$128$	−1.00000	−0.0883883
$129$	−9.72121	−0.855905
$130$	9.83915	0.862950
$131$	21.4059	1.87025	0.935123	−	0.354325i	$-0.115289\pi$
$131$	21.4059	1.87025	0.935123	+	0.354325i	$0.115289\pi$
$132$	1.15892	0.100871
$133$	33.4683	2.90207
$134$	−13.5804	−1.17317
$135$	−14.3255	−1.23294
$136$	−5.32788	−0.456862
$137$	−2.24745	−0.192012	−0.0960062	−	0.995381i	$-0.530607\pi$
$137$	−2.24745	−0.192012	−0.0960062	+	0.995381i	$0.530607\pi$
$138$	3.17356	0.270151
$139$	−12.9753	−1.10055	−0.550275	−	0.834983i	$-0.685477\pi$
$139$	−12.9753	−1.10055	−0.550275	+	0.834983i	$0.685477\pi$
$140$	−10.7687	−0.910124
$141$	−2.41026	−0.202980
$142$	−5.94670	−0.499036
$143$	−3.70680	−0.309978
$144$	−1.65690	−0.138075
$145$	9.83459	0.816718
$146$	−7.14279	−0.591141
$147$	−10.9626	−0.904182
$148$	5.48223	0.450637
$149$	−23.0709	−1.89004	−0.945021	−	0.327009i	$-0.893959\pi$
$149$	−23.0709	−1.89004	−0.945021	+	0.327009i	$0.893959\pi$
$150$	2.37068	0.193565
$151$	5.43769	0.442513	0.221256	−	0.975216i	$-0.428984\pi$
$151$	5.43769	0.442513	0.221256	+	0.975216i	$0.428984\pi$
$152$	−8.24949	−0.669122
$153$	−8.82773	−0.713680
$154$	4.05701	0.326923
$155$	13.7259	1.10249
$156$	−4.29590	−0.343947
$157$	−10.6991	−0.853882	−0.426941	−	0.904279i	$-0.640409\pi$
$157$	−10.6991	−0.853882	−0.426941	+	0.904279i	$0.640409\pi$
$158$	10.8780	0.865409
$159$	15.7292	1.24740
$160$	2.65435	0.209845
$161$	11.1096	0.875557
$162$	1.28401	0.100881
$163$	20.9479	1.64077	0.820383	−	0.571815i	$-0.193760\pi$
$163$	20.9479	1.64077	0.820383	+	0.571815i	$0.193760\pi$
$164$	−0.230412	−0.0179921
$165$	−3.07619	−0.239481
$166$	−0.246945	−0.0191666
$167$	3.84985	0.297910	0.148955	−	0.988844i	$-0.452409\pi$
$167$	3.84985	0.297910	0.148955	+	0.988844i	$0.452409\pi$
$168$	4.70176	0.362749
$169$	0.740348	0.0569498
$170$	14.1421	1.08465
$171$	−13.6685	−1.04526
$172$	8.38813	0.639589
$173$	−20.5881	−1.56528	−0.782641	−	0.622474i	$-0.786128\pi$
$173$	−20.5881	−1.56528	−0.782641	+	0.622474i	$0.786128\pi$
$174$	−4.29390	−0.325520
$175$	8.29896	0.627343
$176$	−1.00000	−0.0753778
$177$	12.6763	0.952807
$178$	−0.350969	−0.0263062
$179$	3.98975	0.298208	0.149104	−	0.988822i	$-0.452361\pi$
$179$	3.98975	0.298208	0.149104	+	0.988822i	$0.452361\pi$
$180$	4.39798	0.327806
$181$	−6.76900	−0.503136	−0.251568	−	0.967840i	$-0.580946\pi$
$181$	−6.76900	−0.503136	−0.251568	+	0.967840i	$0.580946\pi$
$182$	−15.0385	−1.11473
$183$	11.2548	0.831978
$184$	−2.73836	−0.201875
$185$	−14.5518	−1.06987
$186$	−5.99292	−0.439422
$187$	−5.32788	−0.389613
$188$	2.07974	0.151680
$189$	21.8956	1.59267
$190$	21.8971	1.58858
$191$	17.4252	1.26085	0.630423	−	0.776252i	$-0.282881\pi$
$191$	17.4252	1.26085	0.630423	+	0.776252i	$0.282881\pi$
$192$	−1.15892	−0.0836381
$193$	18.4925	1.33112	0.665561	−	0.746343i	$-0.268192\pi$
$193$	18.4925	1.33112	0.665561	+	0.746343i	$0.268192\pi$
$194$	10.7197	0.769627
$195$	11.4028	0.816573
$196$	9.45931	0.675665
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	−1.65690	−0.117750
$199$	−20.3727	−1.44419	−0.722093	−	0.691796i	$-0.756820\pi$
$199$	−20.3727	−1.44419	−0.722093	+	0.691796i	$0.756820\pi$
$200$	−2.04559	−0.144645
$201$	−15.7387	−1.11012
$202$	−7.86002	−0.553029
$203$	−15.0315	−1.05501
$204$	−6.17460	−0.432309
$205$	0.611594	0.0427156
$206$	−7.00720	−0.488215
$207$	−4.53718	−0.315356
$208$	3.70680	0.257020
$209$	−8.24949	−0.570629
$210$	−12.4801	−0.861211
$211$	4.31085	0.296771	0.148386	−	0.988930i	$-0.452592\pi$
$211$	4.31085	0.296771	0.148386	+	0.988930i	$0.452592\pi$
$212$	−13.5722	−0.932144
$213$	−6.89178	−0.472217
$214$	−9.18064	−0.627576
$215$	−22.2651	−1.51846
$216$	−5.39699	−0.367218
$217$	−20.9792	−1.42416
$218$	9.85461	0.667438
$219$	−8.27795	−0.559372
$220$	2.65435	0.178956
$221$	19.7494	1.32849
$222$	6.35349	0.426418
$223$	20.5981	1.37935	0.689674	−	0.724120i	$-0.257754\pi$
$223$	20.5981	1.37935	0.689674	+	0.724120i	$0.257754\pi$
$224$	−4.05701	−0.271070
$225$	−3.38932	−0.225955
$226$	−14.6875	−0.976998
$227$	−5.21374	−0.346048	−0.173024	−	0.984918i	$-0.555354\pi$
$227$	−5.21374	−0.346048	−0.173024	+	0.984918i	$0.555354\pi$
$228$	−9.56053	−0.633162
$229$	−29.2764	−1.93464	−0.967320	−	0.253559i	$-0.918399\pi$
$229$	−29.2764	−1.93464	−0.967320	+	0.253559i	$0.918399\pi$
$230$	7.26858	0.479276
$231$	4.70176	0.309353
$232$	3.70508	0.243250
$233$	27.8302	1.82322	0.911610	−	0.411057i	$-0.134840\pi$
$233$	27.8302	1.82322	0.911610	+	0.411057i	$0.134840\pi$
$234$	6.14178	0.401500
$235$	−5.52035	−0.360108
$236$	−10.9380	−0.712001
$237$	12.6068	0.818900
$238$	−21.6152	−1.40111
$239$	10.4670	0.677051	0.338526	−	0.940957i	$-0.390072\pi$
$239$	10.4670	0.677051	0.338526	+	0.940957i	$0.390072\pi$
$240$	3.07619	0.198567
$241$	4.72586	0.304419	0.152210	−	0.988348i	$-0.451361\pi$
$241$	4.72586	0.304419	0.152210	+	0.988348i	$0.451361\pi$
$242$	−1.00000	−0.0642824
$243$	−14.7029	−0.943191
$244$	−9.71142	−0.621710
$245$	−25.1083	−1.60411
$246$	−0.267030	−0.0170252
$247$	30.5792	1.94571
$248$	5.17111	0.328366
$249$	−0.286190	−0.0181366
$250$	−7.84205	−0.495975
$251$	−10.7118	−0.676124	−0.338062	−	0.941124i	$-0.609771\pi$
$251$	−10.7118	−0.676124	−0.338062	+	0.941124i	$0.609771\pi$
$252$	−6.72204	−0.423449
$253$	−2.73836	−0.172160
$254$	14.2986	0.897176
$255$	16.3896	1.02635
$256$	1.00000	0.0625000
$257$	21.8175	1.36094	0.680469	−	0.732777i	$-0.261776\pi$
$257$	21.8175	1.36094	0.680469	+	0.732777i	$0.261776\pi$
$258$	9.72121	0.605216
$259$	22.2414	1.38202
$260$	−9.83915	−0.610198
$261$	6.13893	0.379990
$262$	−21.4059	−1.32246
$263$	17.9149	1.10468	0.552340	−	0.833619i	$-0.313735\pi$
$263$	17.9149	1.10468	0.552340	+	0.833619i	$0.313735\pi$
$264$	−1.15892	−0.0713268
$265$	36.0255	2.21303
$266$	−33.4683	−2.05207
$267$	−0.406746	−0.0248925
$268$	13.5804	0.829558
$269$	20.5261	1.25150	0.625750	−	0.780023i	$-0.284793\pi$
$269$	20.5261	1.25150	0.625750	+	0.780023i	$0.284793\pi$
$270$	14.3255	0.871823
$271$	22.0189	1.33755	0.668776	−	0.743464i	$-0.266819\pi$
$271$	22.0189	1.33755	0.668776	+	0.743464i	$0.266819\pi$
$272$	5.32788	0.323050
$273$	−17.4285	−1.05482
$274$	2.24745	0.135773
$275$	−2.04559	−0.123354
$276$	−3.17356	−0.191026
$277$	7.96961	0.478848	0.239424	−	0.970915i	$-0.423041\pi$
$277$	7.96961	0.478848	0.239424	+	0.970915i	$0.423041\pi$
$278$	12.9753	0.778206
$279$	8.56799	0.512952
$280$	10.7687	0.643555
$281$	−28.6247	−1.70760	−0.853802	−	0.520598i	$-0.825709\pi$
$281$	−28.6247	−1.70760	−0.853802	+	0.520598i	$0.825709\pi$
$282$	2.41026	0.143529
$283$	17.1786	1.02116	0.510582	−	0.859829i	$-0.329430\pi$
$283$	17.1786	1.02116	0.510582	+	0.859829i	$0.329430\pi$
$284$	5.94670	0.352872
$285$	25.3770	1.50321
$286$	3.70680	0.219188
$287$	−0.934782	−0.0551784
$288$	1.65690	0.0976335
$289$	11.3863	0.669781
$290$	−9.83459	−0.577507
$291$	12.4233	0.728265
$292$	7.14279	0.418000
$293$	−28.4745	−1.66350	−0.831748	−	0.555154i	$-0.812659\pi$
$293$	−28.4745	−1.66350	−0.831748	+	0.555154i	$0.812659\pi$
$294$	10.9626	0.639353
$295$	29.0332	1.69038
$296$	−5.48223	−0.318648
$297$	−5.39699	−0.313165
$298$	23.0709	1.33646
$299$	10.1506	0.587022
$300$	−2.37068	−0.136871
$301$	34.0307	1.96150
$302$	−5.43769	−0.312904
$303$	−9.10917	−0.523308
$304$	8.24949	0.473141
$305$	25.7775	1.47602
$306$	8.82773	0.504648
$307$	−15.3985	−0.878838	−0.439419	−	0.898282i	$-0.644816\pi$
$307$	−15.3985	−0.878838	−0.439419	+	0.898282i	$0.644816\pi$
$308$	−4.05701	−0.231169
$309$	−8.12081	−0.461977
$310$	−13.7259	−0.779581
$311$	11.4502	0.649280	0.324640	−	0.945838i	$-0.394757\pi$
$311$	11.4502	0.649280	0.324640	+	0.945838i	$0.394757\pi$
$312$	4.29590	0.243207
$313$	13.8442	0.782523	0.391261	−	0.920280i	$-0.372039\pi$
$313$	13.8442	0.782523	0.391261	+	0.920280i	$0.372039\pi$
$314$	10.6991	0.603786
$315$	17.8427	1.00532
$316$	−10.8780	−0.611937
$317$	26.6908	1.49911	0.749554	−	0.661944i	$-0.230268\pi$
$317$	26.6908	1.49911	0.749554	+	0.661944i	$0.230268\pi$
$318$	−15.7292	−0.882048
$319$	3.70508	0.207445
$320$	−2.65435	−0.148383
$321$	−10.6397	−0.593848
$322$	−11.1096	−0.619112
$323$	43.9523	2.44557
$324$	−1.28401	−0.0713339
$325$	7.58258	0.420606
$326$	−20.9479	−1.16020
$327$	11.4207	0.631568
$328$	0.230412	0.0127224
$329$	8.43751	0.465175
$330$	3.07619	0.169339
$331$	−4.53047	−0.249017	−0.124509	−	0.992219i	$-0.539735\pi$
$331$	−4.53047	−0.249017	−0.124509	+	0.992219i	$0.539735\pi$
$332$	0.246945	0.0135528
$333$	−9.08348	−0.497772
$334$	−3.84985	−0.210654
$335$	−36.0473	−1.96947
$336$	−4.70176	−0.256502
$337$	15.1582	0.825717	0.412859	−	0.910795i	$-0.364530\pi$
$337$	15.1582	0.825717	0.412859	+	0.910795i	$0.364530\pi$
$338$	−0.740348	−0.0402696
$339$	−17.0217	−0.924491
$340$	−14.1421	−0.766961
$341$	5.17111	0.280031
$342$	13.6685	0.739110
$343$	9.97745	0.538732
$344$	−8.38813	−0.452258
$345$	8.42374	0.453519
$346$	20.5881	1.10682
$347$	−7.30301	−0.392046	−0.196023	−	0.980599i	$-0.562803\pi$
$347$	−7.30301	−0.392046	−0.196023	+	0.980599i	$0.562803\pi$
$348$	4.29390	0.230177
$349$	−13.5570	−0.725689	−0.362844	−	0.931850i	$-0.618194\pi$
$349$	−13.5570	−0.725689	−0.362844	+	0.931850i	$0.618194\pi$
$350$	−8.29896	−0.443598
$351$	20.0055	1.06782
$352$	1.00000	0.0533002
$353$	−37.2409	−1.98213	−0.991066	−	0.133369i	$-0.957420\pi$
$353$	−37.2409	−1.98213	−0.991066	+	0.133369i	$0.957420\pi$
$354$	−12.6763	−0.673736
$355$	−15.7846	−0.837762
$356$	0.350969	0.0186013
$357$	−25.0504	−1.32581
$358$	−3.98975	−0.210865
$359$	23.4423	1.23724	0.618619	−	0.785691i	$-0.287693\pi$
$359$	23.4423	1.23724	0.618619	+	0.785691i	$0.287693\pi$
$360$	−4.39798	−0.231794
$361$	49.0541	2.58180
$362$	6.76900	0.355771
$363$	−1.15892	−0.0608277
$364$	15.0385	0.788232
$365$	−18.9595	−0.992385
$366$	−11.2548	−0.588297
$367$	25.6885	1.34093	0.670464	−	0.741942i	$-0.266095\pi$
$367$	25.6885	1.34093	0.670464	+	0.741942i	$0.266095\pi$
$368$	2.73836	0.142747
$369$	0.381768	0.0198741
$370$	14.5518	0.756510
$371$	−55.0626	−2.85871
$372$	5.99292	0.310718
$373$	9.43503	0.488527	0.244264	−	0.969709i	$-0.421454\pi$
$373$	9.43503	0.488527	0.244264	+	0.969709i	$0.421454\pi$
$374$	5.32788	0.275498
$375$	−9.08834	−0.469320
$376$	−2.07974	−0.107254
$377$	−13.7340	−0.707336
$378$	−21.8956	−1.12619
$379$	−8.83706	−0.453929	−0.226965	−	0.973903i	$-0.572880\pi$
$379$	−8.83706	−0.453929	−0.226965	+	0.973903i	$0.572880\pi$
$380$	−21.8971	−1.12330
$381$	16.5710	0.848960
$382$	−17.4252	−0.891553
$383$	0.753351	0.0384944	0.0192472	−	0.999815i	$-0.493873\pi$
$383$	0.753351	0.0384944	0.0192472	+	0.999815i	$0.493873\pi$
$384$	1.15892	0.0591411
$385$	10.7687	0.548825
$386$	−18.4925	−0.941245
$387$	−13.8983	−0.706488
$388$	−10.7197	−0.544208
$389$	3.59230	0.182137	0.0910683	−	0.995845i	$-0.470972\pi$
$389$	3.59230	0.182137	0.0910683	+	0.995845i	$0.470972\pi$
$390$	−11.4028	−0.577404
$391$	14.5897	0.737831
$392$	−9.45931	−0.477767
$393$	−24.8078	−1.25139
$394$	−1.00000	−0.0503793
$395$	28.8741	1.45281
$396$	1.65690	0.0832621
$397$	32.9977	1.65611	0.828055	−	0.560647i	$-0.189448\pi$
$397$	32.9977	1.65611	0.828055	+	0.560647i	$0.189448\pi$
$398$	20.3727	1.02119
$399$	−38.7872	−1.94179
$400$	2.04559	0.102279
$401$	16.7781	0.837858	0.418929	−	0.908019i	$-0.362406\pi$
$401$	16.7781	0.837858	0.418929	+	0.908019i	$0.362406\pi$
$402$	15.7387	0.784975
$403$	−19.1683	−0.954839
$404$	7.86002	0.391051
$405$	3.40822	0.169356
$406$	15.0315	0.746003
$407$	−5.48223	−0.271744
$408$	6.17460	0.305688
$409$	9.26235	0.457994	0.228997	−	0.973427i	$-0.426455\pi$
$409$	9.26235	0.457994	0.228997	+	0.973427i	$0.426455\pi$
$410$	−0.611594	−0.0302045
$411$	2.60462	0.128477
$412$	7.00720	0.345220
$413$	−44.3754	−2.18357
$414$	4.53718	0.222990
$415$	−0.655478	−0.0321762
$416$	−3.70680	−0.181741
$417$	15.0374	0.736383
$418$	8.24949	0.403496
$419$	9.88437	0.482883	0.241442	−	0.970415i	$-0.422380\pi$
$419$	9.88437	0.482883	0.241442	+	0.970415i	$0.422380\pi$
$420$	12.4801	0.608968
$421$	0.582236	0.0283764	0.0141882	−	0.999899i	$-0.495484\pi$
$421$	0.582236	0.0283764	0.0141882	+	0.999899i	$0.495484\pi$
$422$	−4.31085	−0.209849
$423$	−3.44591	−0.167546
$424$	13.5722	0.659125
$425$	10.8986	0.528661
$426$	6.89178	0.333908
$427$	−39.3993	−1.90667
$428$	9.18064	0.443763
$429$	4.29590	0.207408
$430$	22.2651	1.07372
$431$	−24.3853	−1.17460	−0.587299	−	0.809370i	$-0.699809\pi$
$431$	−24.3853	−1.17460	−0.587299	+	0.809370i	$0.699809\pi$
$432$	5.39699	0.259663
$433$	8.40621	0.403976	0.201988	−	0.979388i	$-0.435260\pi$
$433$	8.40621	0.403976	0.201988	+	0.979388i	$0.435260\pi$
$434$	20.9792	1.00704
$435$	−11.3975	−0.546470
$436$	−9.85461	−0.471950
$437$	22.5901	1.08063
$438$	8.27795	0.395536
$439$	−23.6212	−1.12738	−0.563688	−	0.825988i	$-0.690618\pi$
$439$	−23.6212	−1.12738	−0.563688	+	0.825988i	$0.690618\pi$
$440$	−2.65435	−0.126541
$441$	−15.6731	−0.746338
$442$	−19.7494	−0.939381
$443$	−7.82712	−0.371878	−0.185939	−	0.982561i	$-0.559533\pi$
$443$	−7.82712	−0.371878	−0.185939	+	0.982561i	$0.559533\pi$
$444$	−6.35349	−0.301523
$445$	−0.931596	−0.0441619
$446$	−20.5981	−0.975346
$447$	26.7374	1.26464
$448$	4.05701	0.191676
$449$	37.4769	1.76864	0.884321	−	0.466879i	$-0.154622\pi$
$449$	37.4769	1.76864	0.884321	+	0.466879i	$0.154622\pi$
$450$	3.38932	0.159774
$451$	0.230412	0.0108497
$452$	14.6875	0.690842
$453$	−6.30187	−0.296088
$454$	5.21374	0.244693
$455$	−39.9175	−1.87136
$456$	9.56053	0.447713
$457$	12.8091	0.599184	0.299592	−	0.954067i	$-0.403149\pi$
$457$	12.8091	0.599184	0.299592	+	0.954067i	$0.403149\pi$
$458$	29.2764	1.36800
$459$	28.7545	1.34214
$460$	−7.26858	−0.338900
$461$	38.2807	1.78291	0.891456	−	0.453107i	$-0.149685\pi$
$461$	38.2807	1.78291	0.891456	+	0.453107i	$0.149685\pi$
$462$	−4.70176	−0.218746
$463$	−5.12160	−0.238021	−0.119011	−	0.992893i	$-0.537972\pi$
$463$	−5.12160	−0.238021	−0.119011	+	0.992893i	$0.537972\pi$
$464$	−3.70508	−0.172004
$465$	−15.9073	−0.737684
$466$	−27.8302	−1.28921
$467$	11.7973	0.545915	0.272958	−	0.962026i	$-0.411998\pi$
$467$	11.7973	0.545915	0.272958	+	0.962026i	$0.411998\pi$
$468$	−6.14178	−0.283904
$469$	55.0960	2.54410
$470$	5.52035	0.254635
$471$	12.3995	0.571337
$472$	10.9380	0.503461
$473$	−8.38813	−0.385687
$474$	−12.6068	−0.579050
$475$	16.8751	0.774281
$476$	21.6152	0.990733
$477$	22.4878	1.02964
$478$	−10.4670	−0.478748
$479$	4.93099	0.225303	0.112651	−	0.993635i	$-0.464066\pi$
$479$	4.93099	0.225303	0.112651	+	0.993635i	$0.464066\pi$
$480$	−3.07619	−0.140408
$481$	20.3215	0.926581
$482$	−4.72586	−0.215257
$483$	−12.8751	−0.585839
$484$	1.00000	0.0454545
$485$	28.4538	1.29202
$486$	14.7029	0.666937
$487$	−18.2507	−0.827020	−0.413510	−	0.910500i	$-0.635697\pi$
$487$	−18.2507	−0.827020	−0.413510	+	0.910500i	$0.635697\pi$
$488$	9.71142	0.439615
$489$	−24.2770	−1.09784
$490$	25.1083	1.13428
$491$	30.5197	1.37733	0.688667	−	0.725078i	$-0.258196\pi$
$491$	30.5197	1.37733	0.688667	+	0.725078i	$0.258196\pi$
$492$	0.267030	0.0120386
$493$	−19.7402	−0.889054
$494$	−30.5792	−1.37582
$495$	−4.39798	−0.197675
$496$	−5.17111	−0.232190
$497$	24.1258	1.08219
$498$	0.286190	0.0128245
$499$	−5.60170	−0.250766	−0.125383	−	0.992108i	$-0.540016\pi$
$499$	−5.60170	−0.250766	−0.125383	+	0.992108i	$0.540016\pi$
$500$	7.84205	0.350707
$501$	−4.46168	−0.199333
$502$	10.7118	0.478092
$503$	−36.2141	−1.61471	−0.807354	−	0.590068i	$-0.799101\pi$
$503$	−36.2141	−1.61471	−0.807354	+	0.590068i	$0.799101\pi$
$504$	6.72204	0.299423
$505$	−20.8633	−0.928403
$506$	2.73836	0.121735
$507$	−0.858007	−0.0381054
$508$	−14.2986	−0.634400
$509$	−33.9597	−1.50524	−0.752618	−	0.658457i	$-0.771209\pi$
$509$	−33.9597	−1.50524	−0.752618	+	0.658457i	$0.771209\pi$
$510$	−16.3896	−0.725742
$511$	28.9784	1.28193
$512$	−1.00000	−0.0441942
$513$	44.5224	1.96571
$514$	−21.8175	−0.962328
$515$	−18.5996	−0.819595
$516$	−9.72121	−0.427952
$517$	−2.07974	−0.0914667
$518$	−22.2414	−0.977233
$519$	23.8600	1.04734
$520$	9.83915	0.431475
$521$	11.8315	0.518347	0.259173	−	0.965831i	$-0.416550\pi$
$521$	11.8315	0.518347	0.259173	+	0.965831i	$0.416550\pi$
$522$	−6.13893	−0.268694
$523$	27.1527	1.18731	0.593653	−	0.804721i	$-0.297685\pi$
$523$	27.1527	1.18731	0.593653	+	0.804721i	$0.297685\pi$
$524$	21.4059	0.935123
$525$	−9.61787	−0.419758
$526$	−17.9149	−0.781127
$527$	−27.5510	−1.20014
$528$	1.15892	0.0504357
$529$	−15.5014	−0.673972
$530$	−36.0255	−1.56485
$531$	18.1231	0.786474
$532$	33.4683	1.45103
$533$	−0.854089	−0.0369947
$534$	0.406746	0.0176016
$535$	−24.3687	−1.05355
$536$	−13.5804	−0.586586
$537$	−4.62382	−0.199533
$538$	−20.5261	−0.884945
$539$	−9.45931	−0.407441
$540$	−14.3255	−0.616472
$541$	−28.5718	−1.22840	−0.614199	−	0.789151i	$-0.710521\pi$
$541$	−28.5718	−1.22840	−0.614199	+	0.789151i	$0.710521\pi$
$542$	−22.0189	−0.945792
$543$	7.84476	0.336651
$544$	−5.32788	−0.228431
$545$	26.1576	1.12047
$546$	17.4285	0.745870
$547$	−37.6526	−1.60991	−0.804954	−	0.593337i	$-0.797810\pi$
$547$	−37.6526	−1.60991	−0.804954	+	0.593337i	$0.797810\pi$
$548$	−2.24745	−0.0960062
$549$	16.0908	0.686739
$550$	2.04559	0.0872241
$551$	−30.5650	−1.30211
$552$	3.17356	0.135076
$553$	−44.1322	−1.87669
$554$	−7.96961	−0.338596
$555$	16.8644	0.715854
$556$	−12.9753	−0.550275
$557$	−10.1622	−0.430588	−0.215294	−	0.976549i	$-0.569071\pi$
$557$	−10.1622	−0.430588	−0.215294	+	0.976549i	$0.569071\pi$
$558$	−8.56799	−0.362712
$559$	31.0931	1.31510
$560$	−10.7687	−0.455062
$561$	6.17460	0.260692
$562$	28.6247	1.20746
$563$	11.9183	0.502297	0.251148	−	0.967949i	$-0.419192\pi$
$563$	11.9183	0.502297	0.251148	+	0.967949i	$0.419192\pi$
$564$	−2.41026	−0.101490
$565$	−38.9858	−1.64014
$566$	−17.1786	−0.722071
$567$	−5.20924	−0.218768
$568$	−5.94670	−0.249518
$569$	−13.0335	−0.546393	−0.273196	−	0.961958i	$-0.588081\pi$
$569$	−13.0335	−0.546393	−0.273196	+	0.961958i	$0.588081\pi$
$570$	−25.3770	−1.06293
$571$	−43.3059	−1.81229	−0.906147	−	0.422963i	$-0.860990\pi$
$571$	−43.3059	−1.81229	−0.906147	+	0.422963i	$0.860990\pi$
$572$	−3.70680	−0.154989
$573$	−20.1945	−0.843638
$574$	0.934782	0.0390170
$575$	5.60156	0.233601
$576$	−1.65690	−0.0690373
$577$	10.8483	0.451622	0.225811	−	0.974171i	$-0.427497\pi$
$577$	10.8483	0.451622	0.225811	+	0.974171i	$0.427497\pi$
$578$	−11.3863	−0.473606
$579$	−21.4314	−0.890660
$580$	9.83459	0.408359
$581$	1.00186	0.0415640
$582$	−12.4233	−0.514961
$583$	13.5722	0.562104
$584$	−7.14279	−0.295571
$585$	16.3024	0.674023
$586$	28.4745	1.17627
$587$	−21.3477	−0.881112	−0.440556	−	0.897725i	$-0.645219\pi$
$587$	−21.3477	−0.881112	−0.440556	+	0.897725i	$0.645219\pi$
$588$	−10.9626	−0.452091
$589$	−42.6590	−1.75773
$590$	−29.0332	−1.19528
$591$	−1.15892	−0.0476718
$592$	5.48223	0.225318
$593$	41.2844	1.69535	0.847675	−	0.530517i	$-0.178002\pi$
$593$	41.2844	1.69535	0.847675	+	0.530517i	$0.178002\pi$
$594$	5.39699	0.221441
$595$	−57.3745	−2.35212
$596$	−23.0709	−0.945021
$597$	23.6105	0.966312
$598$	−10.1506	−0.415087
$599$	42.3032	1.72846	0.864230	−	0.503096i	$-0.167806\pi$
$599$	42.3032	1.72846	0.864230	+	0.503096i	$0.167806\pi$
$600$	2.37068	0.0967826
$601$	37.1941	1.51718	0.758588	−	0.651570i	$-0.225889\pi$
$601$	37.1941	1.51718	0.758588	+	0.651570i	$0.225889\pi$
$602$	−34.0307	−1.38699
$603$	−22.5014	−0.916327
$604$	5.43769	0.221256
$605$	−2.65435	−0.107915
$606$	9.10917	0.370035
$607$	24.0666	0.976831	0.488416	−	0.872611i	$-0.337575\pi$
$607$	24.0666	0.976831	0.488416	+	0.872611i	$0.337575\pi$
$608$	−8.24949	−0.334561
$609$	17.4204	0.705910
$610$	−25.7775	−1.04370
$611$	7.70916	0.311879
$612$	−8.82773	−0.356840
$613$	36.4474	1.47209	0.736047	−	0.676930i	$-0.236690\pi$
$613$	36.4474	1.47209	0.736047	+	0.676930i	$0.236690\pi$
$614$	15.3985	0.621432
$615$	−0.708791	−0.0285812
$616$	4.05701	0.163462
$617$	−18.9498	−0.762889	−0.381444	−	0.924392i	$-0.624573\pi$
$617$	−18.9498	−0.762889	−0.381444	+	0.924392i	$0.624573\pi$
$618$	8.12081	0.326667
$619$	−14.3495	−0.576754	−0.288377	−	0.957517i	$-0.593116\pi$
$619$	−14.3495	−0.576754	−0.288377	+	0.957517i	$0.593116\pi$
$620$	13.7259	0.551247
$621$	14.7789	0.593058
$622$	−11.4502	−0.459110
$623$	1.42388	0.0570467
$624$	−4.29590	−0.171973
$625$	−31.0435	−1.24174
$626$	−13.8442	−0.553327
$627$	9.56053	0.381811
$628$	−10.6991	−0.426941
$629$	29.2086	1.16462
$630$	−17.8427	−0.710869
$631$	18.0318	0.717834	0.358917	−	0.933370i	$-0.383146\pi$
$631$	18.0318	0.717834	0.358917	+	0.933370i	$0.383146\pi$
$632$	10.8780	0.432705
$633$	−4.99594	−0.198571
$634$	−26.6908	−1.06003
$635$	37.9536	1.50614
$636$	15.7292	0.623702
$637$	35.0638	1.38928
$638$	−3.70508	−0.146685
$639$	−9.85306	−0.389781
$640$	2.65435	0.104922
$641$	3.91330	0.154566	0.0772831	−	0.997009i	$-0.475375\pi$
$641$	3.91330	0.154566	0.0772831	+	0.997009i	$0.475375\pi$
$642$	10.6397	0.419914
$643$	20.6341	0.813730	0.406865	−	0.913488i	$-0.366622\pi$
$643$	20.6341	0.813730	0.406865	+	0.913488i	$0.366622\pi$
$644$	11.1096	0.437778
$645$	25.8035	1.01601
$646$	−43.9523	−1.72928
$647$	−13.8083	−0.542860	−0.271430	−	0.962458i	$-0.587497\pi$
$647$	−13.8083	−0.542860	−0.271430	+	0.962458i	$0.587497\pi$
$648$	1.28401	0.0504407
$649$	10.9380	0.429353
$650$	−7.58258	−0.297413
$651$	24.3133	0.952914
$652$	20.9479	0.820383
$653$	−27.1120	−1.06097	−0.530487	−	0.847693i	$-0.677991\pi$
$653$	−27.1120	−1.06097	−0.530487	+	0.847693i	$0.677991\pi$
$654$	−11.4207	−0.446586
$655$	−56.8189	−2.22010
$656$	−0.230412	−0.00899606
$657$	−11.8349	−0.461722
$658$	−8.43751	−0.328928
$659$	26.3503	1.02646	0.513231	−	0.858251i	$-0.328449\pi$
$659$	26.3503	1.02646	0.513231	+	0.858251i	$0.328449\pi$
$660$	−3.07619	−0.119741
$661$	−16.6010	−0.645704	−0.322852	−	0.946450i	$-0.604642\pi$
$661$	−16.6010	−0.645704	−0.322852	+	0.946450i	$0.604642\pi$
$662$	4.53047	0.176082
$663$	−22.8880	−0.888896
$664$	−0.246945	−0.00958331
$665$	−88.8365	−3.44493
$666$	9.08348	0.351978
$667$	−10.1459	−0.392849
$668$	3.84985	0.148955
$669$	−23.8716	−0.922928
$670$	36.0473	1.39263
$671$	9.71142	0.374905
$672$	4.70176	0.181374
$673$	−49.4672	−1.90682	−0.953409	−	0.301679i	$-0.902453\pi$
$673$	−49.4672	−1.90682	−0.953409	+	0.301679i	$0.902453\pi$
$674$	−15.1582	−0.583870
$675$	11.0400	0.424930
$676$	0.740348	0.0284749
$677$	−23.3353	−0.896850	−0.448425	−	0.893821i	$-0.648015\pi$
$677$	−23.3353	−0.896850	−0.448425	+	0.893821i	$0.648015\pi$
$678$	17.0217	0.653714
$679$	−43.4897	−1.66898
$680$	14.1421	0.542323
$681$	6.04233	0.231542
$682$	−5.17111	−0.198012
$683$	−24.1750	−0.925030	−0.462515	−	0.886611i	$-0.653053\pi$
$683$	−24.1750	−0.925030	−0.462515	+	0.886611i	$0.653053\pi$
$684$	−13.6685	−0.522630
$685$	5.96552	0.227931
$686$	−9.97745	−0.380941
$687$	33.9291	1.29448
$688$	8.38813	0.319795
$689$	−50.3095	−1.91664
$690$	−8.42374	−0.320686
$691$	6.32501	0.240615	0.120307	−	0.992737i	$-0.461612\pi$
$691$	6.32501	0.240615	0.120307	+	0.992737i	$0.461612\pi$
$692$	−20.5881	−0.782641
$693$	6.72204	0.255349
$694$	7.30301	0.277219
$695$	34.4410	1.30642
$696$	−4.29390	−0.162760
$697$	−1.22760	−0.0464988
$698$	13.5570	0.513139
$699$	−32.2531	−1.21993
$700$	8.29896	0.313671
$701$	12.5333	0.473375	0.236687	−	0.971586i	$-0.423938\pi$
$701$	12.5333	0.473375	0.236687	+	0.971586i	$0.423938\pi$
$702$	−20.0055	−0.755060
$703$	45.2256	1.70572
$704$	−1.00000	−0.0376889
$705$	6.39767	0.240950
$706$	37.2409	1.40158
$707$	31.8882	1.19928
$708$	12.6763	0.476403
$709$	32.2244	1.21021	0.605107	−	0.796144i	$-0.293130\pi$
$709$	32.2244	1.21021	0.605107	+	0.796144i	$0.293130\pi$
$710$	15.7846	0.592387
$711$	18.0238	0.675944
$712$	−0.350969	−0.0131531
$713$	−14.1604	−0.530310
$714$	25.0504	0.937488
$715$	9.83915	0.367963
$716$	3.98975	0.149104
$717$	−12.1304	−0.453019
$718$	−23.4423	−0.874859
$719$	−11.3868	−0.424657	−0.212329	−	0.977198i	$-0.568105\pi$
$719$	−11.3868	−0.424657	−0.212329	+	0.977198i	$0.568105\pi$
$720$	4.39798	0.163903
$721$	28.4283	1.05872
$722$	−49.0541	−1.82561
$723$	−5.47691	−0.203688
$724$	−6.76900	−0.251568
$725$	−7.57906	−0.281479
$726$	1.15892	0.0430117
$727$	32.8154	1.21706	0.608529	−	0.793532i	$-0.291760\pi$
$727$	32.8154	1.21706	0.608529	+	0.793532i	$0.291760\pi$
$728$	−15.0385	−0.557364
$729$	20.8916	0.773762
$730$	18.9595	0.701722
$731$	44.6909	1.65295
$732$	11.2548	0.415989
$733$	3.42840	0.126631	0.0633154	−	0.997994i	$-0.479833\pi$
$733$	3.42840	0.126631	0.0633154	+	0.997994i	$0.479833\pi$
$734$	−25.6885	−0.948179
$735$	29.0987	1.07332
$736$	−2.73836	−0.100937
$737$	−13.5804	−0.500242
$738$	−0.381768	−0.0140531
$739$	17.3863	0.639565	0.319783	−	0.947491i	$-0.396390\pi$
$739$	17.3863	0.639565	0.319783	+	0.947491i	$0.396390\pi$
$740$	−14.5518	−0.534934
$741$	−35.4390	−1.30188
$742$	55.0626	2.02141
$743$	−24.1659	−0.886560	−0.443280	−	0.896383i	$-0.646185\pi$
$743$	−24.1659	−0.886560	−0.443280	+	0.896383i	$0.646185\pi$
$744$	−5.99292	−0.219711
$745$	61.2383	2.24360
$746$	−9.43503	−0.345441
$747$	−0.409161	−0.0149704
$748$	−5.32788	−0.194806
$749$	37.2459	1.36094
$750$	9.08834	0.331859
$751$	−47.4694	−1.73218	−0.866091	−	0.499886i	$-0.833375\pi$
$751$	−47.4694	−1.73218	−0.866091	+	0.499886i	$0.833375\pi$
$752$	2.07974	0.0758402
$753$	12.4142	0.452398
$754$	13.7340	0.500162
$755$	−14.4335	−0.525291
$756$	21.8956	0.796336
$757$	−11.5498	−0.419784	−0.209892	−	0.977725i	$-0.567311\pi$
$757$	−11.5498	−0.419784	−0.209892	+	0.977725i	$0.567311\pi$
$758$	8.83706	0.320977
$759$	3.17356	0.115193
$760$	21.8971	0.794290
$761$	52.4015	1.89955	0.949777	−	0.312927i	$-0.101309\pi$
$761$	52.4015	1.89955	0.949777	+	0.312927i	$0.101309\pi$
$762$	−16.5710	−0.600305
$763$	−39.9802	−1.44738
$764$	17.4252	0.630423
$765$	23.4319	0.847183
$766$	−0.753351	−0.0272197
$767$	−40.5448	−1.46399
$768$	−1.15892	−0.0418191
$769$	−34.1905	−1.23294	−0.616471	−	0.787377i	$-0.711438\pi$
$769$	−34.1905	−1.23294	−0.616471	+	0.787377i	$0.711438\pi$
$770$	−10.7687	−0.388078
$771$	−25.2848	−0.910610
$772$	18.4925	0.665561
$773$	−3.99067	−0.143534	−0.0717672	−	0.997421i	$-0.522864\pi$
$773$	−3.99067	−0.143534	−0.0717672	+	0.997421i	$0.522864\pi$
$774$	13.8983	0.499563
$775$	−10.5780	−0.379971
$776$	10.7197	0.384813
$777$	−25.7761	−0.924714
$778$	−3.59230	−0.128790
$779$	−1.90078	−0.0681025
$780$	11.4028	0.408287
$781$	−5.94670	−0.212790
$782$	−14.5897	−0.521725
$783$	−19.9963	−0.714608
$784$	9.45931	0.337833
$785$	28.3992	1.01361
$786$	24.8078	0.884867
$787$	−12.2014	−0.434931	−0.217466	−	0.976068i	$-0.569779\pi$
$787$	−12.2014	−0.434931	−0.217466	+	0.976068i	$0.569779\pi$
$788$	1.00000	0.0356235
$789$	−20.7620	−0.739147
$790$	−28.8741	−1.02729
$791$	59.5873	2.11868
$792$	−1.65690	−0.0588752
$793$	−35.9983	−1.27834
$794$	−32.9977	−1.17105
$795$	−41.7508	−1.48075
$796$	−20.3727	−0.722093
$797$	7.58763	0.268768	0.134384	−	0.990929i	$-0.457094\pi$
$797$	7.58763	0.268768	0.134384	+	0.990929i	$0.457094\pi$
$798$	38.7872	1.37305
$799$	11.0806	0.392003
$800$	−2.04559	−0.0723224
$801$	−0.581519	−0.0205470
$802$	−16.7781	−0.592455
$803$	−7.14279	−0.252064
$804$	−15.7387	−0.555061
$805$	−29.4887	−1.03934
$806$	19.1683	0.675173
$807$	−23.7882	−0.837386
$808$	−7.86002	−0.276515
$809$	38.6828	1.36002	0.680008	−	0.733205i	$-0.261976\pi$
$809$	38.6828	1.36002	0.680008	+	0.733205i	$0.261976\pi$
$810$	−3.40822	−0.119753
$811$	−13.3919	−0.470254	−0.235127	−	0.971965i	$-0.575551\pi$
$811$	−13.3919	−0.470254	−0.235127	+	0.971965i	$0.575551\pi$
$812$	−15.0315	−0.527503
$813$	−25.5182	−0.894962
$814$	5.48223	0.192152
$815$	−55.6031	−1.94769
$816$	−6.17460	−0.216154
$817$	69.1978	2.42093
$818$	−9.26235	−0.323850
$819$	−24.9172	−0.870679
$820$	0.611594	0.0213578
$821$	25.1042	0.876144	0.438072	−	0.898940i	$-0.355661\pi$
$821$	25.1042	0.876144	0.438072	+	0.898940i	$0.355661\pi$
$822$	−2.60462	−0.0908466
$823$	9.03203	0.314837	0.157418	−	0.987532i	$-0.449683\pi$
$823$	9.03203	0.314837	0.157418	+	0.987532i	$0.449683\pi$
$824$	−7.00720	−0.244107
$825$	2.37068	0.0825365
$826$	44.3754	1.54402
$827$	−26.1380	−0.908909	−0.454454	−	0.890770i	$-0.650166\pi$
$827$	−26.1380	−0.908909	−0.454454	+	0.890770i	$0.650166\pi$
$828$	−4.53718	−0.157678
$829$	−17.7390	−0.616101	−0.308050	−	0.951370i	$-0.599677\pi$
$829$	−17.7390	−0.616101	−0.308050	+	0.951370i	$0.599677\pi$
$830$	0.655478	0.0227520
$831$	−9.23617	−0.320399
$832$	3.70680	0.128510
$833$	50.3980	1.74619
$834$	−15.0374	−0.520702
$835$	−10.2189	−0.353638
$836$	−8.24949	−0.285315
$837$	−27.9084	−0.964656
$838$	−9.88437	−0.341450
$839$	11.8829	0.410243	0.205122	−	0.978737i	$-0.434241\pi$
$839$	11.8829	0.410243	0.205122	+	0.978737i	$0.434241\pi$
$840$	−12.4801	−0.430606
$841$	−15.2724	−0.526634
$842$	−0.582236	−0.0200652
$843$	33.1738	1.14257
$844$	4.31085	0.148386
$845$	−1.96514	−0.0676030
$846$	3.44591	0.118473
$847$	4.05701	0.139400
$848$	−13.5722	−0.466072
$849$	−19.9087	−0.683265
$850$	−10.8986	−0.373820
$851$	15.0123	0.514617
$852$	−6.89178	−0.236108
$853$	−19.6403	−0.672472	−0.336236	−	0.941778i	$-0.609154\pi$
$853$	−19.6403	−0.672472	−0.336236	+	0.941778i	$0.609154\pi$
$854$	39.3993	1.34822
$855$	36.2811	1.24079
$856$	−9.18064	−0.313788
$857$	−31.5674	−1.07832	−0.539161	−	0.842203i	$-0.681259\pi$
$857$	−31.5674	−1.07832	−0.539161	+	0.842203i	$0.681259\pi$
$858$	−4.29590	−0.146659
$859$	−3.79770	−0.129576	−0.0647879	−	0.997899i	$-0.520637\pi$
$859$	−3.79770	−0.129576	−0.0647879	+	0.997899i	$0.520637\pi$
$860$	−22.2651	−0.759232
$861$	1.08334	0.0369202
$862$	24.3853	0.830567
$863$	−0.104563	−0.00355936	−0.00177968	−	0.999998i	$-0.500566\pi$
$863$	−0.104563	−0.00355936	−0.00177968	+	0.999998i	$0.500566\pi$
$864$	−5.39699	−0.183609
$865$	54.6480	1.85809
$866$	−8.40621	−0.285654
$867$	−13.1958	−0.448153
$868$	−20.9792	−0.712081
$869$	10.8780	0.369012
$870$	11.3975	0.386413
$871$	50.3400	1.70570
$872$	9.85461	0.333719
$873$	17.7614	0.601131
$874$	−22.5901	−0.764122
$875$	31.8153	1.07555
$876$	−8.27795	−0.279686
$877$	46.8958	1.58356	0.791779	−	0.610808i	$-0.209155\pi$
$877$	46.8958	1.58356	0.791779	+	0.610808i	$0.209155\pi$
$878$	23.6212	0.797176
$879$	32.9997	1.11305
$880$	2.65435	0.0894782
$881$	11.3135	0.381161	0.190580	−	0.981672i	$-0.438963\pi$
$881$	11.3135	0.381161	0.190580	+	0.981672i	$0.438963\pi$
$882$	15.6731	0.527740
$883$	5.16554	0.173834	0.0869172	−	0.996216i	$-0.472298\pi$
$883$	5.16554	0.173834	0.0869172	+	0.996216i	$0.472298\pi$
$884$	19.7494	0.664243
$885$	−33.6473	−1.13104
$886$	7.82712	0.262957
$887$	56.2312	1.88806	0.944030	−	0.329860i	$-0.107002\pi$
$887$	56.2312	1.88806	0.944030	+	0.329860i	$0.107002\pi$
$888$	6.35349	0.213209
$889$	−58.0097	−1.94558
$890$	0.931596	0.0312272
$891$	1.28401	0.0430160
$892$	20.5981	0.689674
$893$	17.1568	0.574129
$894$	−26.7374	−0.894233
$895$	−10.5902	−0.353992
$896$	−4.05701	−0.135535
$897$	−11.7637	−0.392779
$898$	−37.4769	−1.25062
$899$	19.1594	0.639001
$900$	−3.38932	−0.112977
$901$	−72.3111	−2.40903
$902$	−0.230412	−0.00767187
$903$	−39.4390	−1.31245
$904$	−14.6875	−0.488499
$905$	17.9673	0.597254
$906$	6.30187	0.209366
$907$	−37.9543	−1.26025	−0.630127	−	0.776492i	$-0.716997\pi$
$907$	−37.9543	−1.26025	−0.630127	+	0.776492i	$0.716997\pi$
$908$	−5.21374	−0.173024
$909$	−13.0232	−0.431953
$910$	39.9175	1.32325
$911$	−56.5826	−1.87467	−0.937333	−	0.348435i	$-0.886713\pi$
$911$	−56.5826	−1.87467	−0.937333	+	0.348435i	$0.886713\pi$
$912$	−9.56053	−0.316581
$913$	−0.246945	−0.00817267
$914$	−12.8091	−0.423687
$915$	−29.8742	−0.987610
$916$	−29.2764	−0.967320
$917$	86.8440	2.86784
$918$	−28.7545	−0.949039
$919$	−20.9127	−0.689845	−0.344922	−	0.938631i	$-0.612095\pi$
$919$	−20.9127	−0.689845	−0.344922	+	0.938631i	$0.612095\pi$
$920$	7.26858	0.239638
$921$	17.8457	0.588035
$922$	−38.2807	−1.26071
$923$	22.0432	0.725561
$924$	4.70176	0.154677
$925$	11.2144	0.368726
$926$	5.12160	0.168306
$927$	−11.6102	−0.381329
$928$	3.70508	0.121625
$929$	30.4663	0.999567	0.499784	−	0.866150i	$-0.333413\pi$
$929$	30.4663	0.999567	0.499784	+	0.866150i	$0.333413\pi$
$930$	15.9073	0.521622
$931$	78.0345	2.55748
$932$	27.8302	0.911610
$933$	−13.2699	−0.434436
$934$	−11.7973	−0.386021
$935$	14.1421	0.462495
$936$	6.14178	0.200750
$937$	−13.3411	−0.435836	−0.217918	−	0.975967i	$-0.569927\pi$
$937$	−13.3411	−0.435836	−0.217918	+	0.975967i	$0.569927\pi$
$938$	−55.0960	−1.79895
$939$	−16.0444	−0.523590
$940$	−5.52035	−0.180054
$941$	−52.3925	−1.70795	−0.853973	−	0.520317i	$-0.825814\pi$
$941$	−52.3925	−1.70795	−0.853973	+	0.520317i	$0.825814\pi$
$942$	−12.3995	−0.403996
$943$	−0.630951	−0.0205466
$944$	−10.9380	−0.356000
$945$	−58.1187	−1.89060
$946$	8.38813	0.272722
$947$	28.2907	0.919325	0.459663	−	0.888094i	$-0.347970\pi$
$947$	28.2907	0.919325	0.459663	+	0.888094i	$0.347970\pi$
$948$	12.6068	0.409450
$949$	26.4769	0.859476
$950$	−16.8751	−0.547499
$951$	−30.9327	−1.00306
$952$	−21.6152	−0.700554
$953$	−11.5466	−0.374032	−0.187016	−	0.982357i	$-0.559882\pi$
$953$	−11.5466	−0.374032	−0.187016	+	0.982357i	$0.559882\pi$
$954$	−22.4878	−0.728068
$955$	−46.2527	−1.49670
$956$	10.4670	0.338526
$957$	−4.29390	−0.138802
$958$	−4.93099	−0.159313
$959$	−9.11792	−0.294433
$960$	3.07619	0.0992837
$961$	−4.25964	−0.137408
$962$	−20.3215	−0.655192
$963$	−15.2114	−0.490179
$964$	4.72586	0.152210
$965$	−49.0857	−1.58013
$966$	12.8751	0.414251
$967$	−4.71847	−0.151736	−0.0758679	−	0.997118i	$-0.524173\pi$
$967$	−4.71847	−0.151736	−0.0758679	+	0.997118i	$0.524173\pi$
$968$	−1.00000	−0.0321412
$969$	−50.9373	−1.63634
$970$	−28.4538	−0.913595
$971$	−34.3864	−1.10351	−0.551757	−	0.834005i	$-0.686042\pi$
$971$	−34.3864	−1.10351	−0.551757	+	0.834005i	$0.686042\pi$
$972$	−14.7029	−0.471595
$973$	−52.6409	−1.68759
$974$	18.2507	0.584792
$975$	−8.78763	−0.281429
$976$	−9.71142	−0.310855
$977$	−39.7279	−1.27101	−0.635504	−	0.772098i	$-0.719208\pi$
$977$	−39.7279	−1.27101	−0.635504	+	0.772098i	$0.719208\pi$
$978$	24.2770	0.776293
$979$	−0.350969	−0.0112170
$980$	−25.1083	−0.802057
$981$	16.3281	0.521315
$982$	−30.5197	−0.973922
$983$	27.5433	0.878495	0.439248	−	0.898366i	$-0.355245\pi$
$983$	27.5433	0.878495	0.439248	+	0.898366i	$0.355245\pi$
$984$	−0.267030	−0.00851259
$985$	−2.65435	−0.0845747
$986$	19.7402	0.628656
$987$	−9.77843	−0.311251
$988$	30.5792	0.972854
$989$	22.9698	0.730396
$990$	4.39798	0.139777
$991$	33.0244	1.04906	0.524528	−	0.851393i	$-0.324242\pi$
$991$	33.0244	1.04906	0.524528	+	0.851393i	$0.324242\pi$
$992$	5.17111	0.164183
$993$	5.25047	0.166619
$994$	−24.1258	−0.765224
$995$	54.0765	1.71434
$996$	−0.286190	−0.00906828
$997$	34.5134	1.09305	0.546525	−	0.837443i	$-0.315950\pi$
$997$	34.5134	1.09305	0.546525	+	0.837443i	$0.315950\pi$
$998$	5.60170	0.177319
$999$	29.5875	0.936108

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.e.1.9	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.e.1.9	✓	24	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.15892 q^{3} +1.00000 q^{4} -2.65435 q^{5} +1.15892 q^{6} +4.05701 q^{7} -1.00000 q^{8} -1.65690 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.15892 q^{3} +1.00000 q^{4} -2.65435 q^{5} +1.15892 q^{6} +4.05701 q^{7} -1.00000 q^{8} -1.65690 q^{9} +2.65435 q^{10} -1.00000 q^{11} -1.15892 q^{12} +3.70680 q^{13} -4.05701 q^{14} +3.07619 q^{15} +1.00000 q^{16} +5.32788 q^{17} +1.65690 q^{18} +8.24949 q^{19} -2.65435 q^{20} -4.70176 q^{21} +1.00000 q^{22} +2.73836 q^{23} +1.15892 q^{24} +2.04559 q^{25} -3.70680 q^{26} +5.39699 q^{27} +4.05701 q^{28} -3.70508 q^{29} -3.07619 q^{30} -5.17111 q^{31} -1.00000 q^{32} +1.15892 q^{33} -5.32788 q^{34} -10.7687 q^{35} -1.65690 q^{36} +5.48223 q^{37} -8.24949 q^{38} -4.29590 q^{39} +2.65435 q^{40} -0.230412 q^{41} +4.70176 q^{42} +8.38813 q^{43} -1.00000 q^{44} +4.39798 q^{45} -2.73836 q^{46} +2.07974 q^{47} -1.15892 q^{48} +9.45931 q^{49} -2.04559 q^{50} -6.17460 q^{51} +3.70680 q^{52} -13.5722 q^{53} -5.39699 q^{54} +2.65435 q^{55} -4.05701 q^{56} -9.56053 q^{57} +3.70508 q^{58} -10.9380 q^{59} +3.07619 q^{60} -9.71142 q^{61} +5.17111 q^{62} -6.72204 q^{63} +1.00000 q^{64} -9.83915 q^{65} -1.15892 q^{66} +13.5804 q^{67} +5.32788 q^{68} -3.17356 q^{69} +10.7687 q^{70} +5.94670 q^{71} +1.65690 q^{72} +7.14279 q^{73} -5.48223 q^{74} -2.37068 q^{75} +8.24949 q^{76} -4.05701 q^{77} +4.29590 q^{78} -10.8780 q^{79} -2.65435 q^{80} -1.28401 q^{81} +0.230412 q^{82} +0.246945 q^{83} -4.70176 q^{84} -14.1421 q^{85} -8.38813 q^{86} +4.29390 q^{87} +1.00000 q^{88} +0.350969 q^{89} -4.39798 q^{90} +15.0385 q^{91} +2.73836 q^{92} +5.99292 q^{93} -2.07974 q^{94} -21.8971 q^{95} +1.15892 q^{96} -10.7197 q^{97} -9.45931 q^{98} +1.65690 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{6} + 7 q^{7} - 24 q^{8} + 28 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^6 + 7 * q^7 - 24 * q^8 + 28 * q^9	\( 24 q - 24 q^{2} - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{6} + 7 q^{7} - 24 q^{8} + 28 q^{9} + 4 q^{10} - 24 q^{11} - 4 q^{12} + 21 q^{13} - 7 q^{14} - 2 q^{15} + 24 q^{16} + 15 q^{17} - 28 q^{18} + 21 q^{19} - 4 q^{20} + 15 q^{21} + 24 q^{22} - 17 q^{23} + 4 q^{24} + 46 q^{25} - 21 q^{26} - 19 q^{27} + 7 q^{28} + 9 q^{29} + 2 q^{30} + 27 q^{31} - 24 q^{32} + 4 q^{33} - 15 q^{34} - 2 q^{35} + 28 q^{36} + 5 q^{37} - 21 q^{38} + 17 q^{39} + 4 q^{40} + 16 q^{41} - 15 q^{42} + 3 q^{43} - 24 q^{44} - 21 q^{45} + 17 q^{46} - 24 q^{47} - 4 q^{48} + 55 q^{49} - 46 q^{50} - 12 q^{51} + 21 q^{52} - 26 q^{53} + 19 q^{54} + 4 q^{55} - 7 q^{56} + 30 q^{57} - 9 q^{58} - 17 q^{59} - 2 q^{60} + 44 q^{61} - 27 q^{62} + 4 q^{63} + 24 q^{64} + 35 q^{65} - 4 q^{66} + 10 q^{67} + 15 q^{68} + 3 q^{69} + 2 q^{70} - 6 q^{71} - 28 q^{72} + 77 q^{73} - 5 q^{74} - 32 q^{75} + 21 q^{76} - 7 q^{77} - 17 q^{78} + 43 q^{79} - 4 q^{80} + 48 q^{81} - 16 q^{82} - 20 q^{83} + 15 q^{84} + 35 q^{85} - 3 q^{86} + 36 q^{87} + 24 q^{88} + 3 q^{89} + 21 q^{90} + 63 q^{91} - 17 q^{92} + 36 q^{93} + 24 q^{94} - 3 q^{95} + 4 q^{96} + 16 q^{97} - 55 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^6 + 7 * q^7 - 24 * q^8 + 28 * q^9 + 4 * q^10 - 24 * q^11 - 4 * q^12 + 21 * q^13 - 7 * q^14 - 2 * q^15 + 24 * q^16 + 15 * q^17 - 28 * q^18 + 21 * q^19 - 4 * q^20 + 15 * q^21 + 24 * q^22 - 17 * q^23 + 4 * q^24 + 46 * q^25 - 21 * q^26 - 19 * q^27 + 7 * q^28 + 9 * q^29 + 2 * q^30 + 27 * q^31 - 24 * q^32 + 4 * q^33 - 15 * q^34 - 2 * q^35 + 28 * q^36 + 5 * q^37 - 21 * q^38 + 17 * q^39 + 4 * q^40 + 16 * q^41 - 15 * q^42 + 3 * q^43 - 24 * q^44 - 21 * q^45 + 17 * q^46 - 24 * q^47 - 4 * q^48 + 55 * q^49 - 46 * q^50 - 12 * q^51 + 21 * q^52 - 26 * q^53 + 19 * q^54 + 4 * q^55 - 7 * q^56 + 30 * q^57 - 9 * q^58 - 17 * q^59 - 2 * q^60 + 44 * q^61 - 27 * q^62 + 4 * q^63 + 24 * q^64 + 35 * q^65 - 4 * q^66 + 10 * q^67 + 15 * q^68 + 3 * q^69 + 2 * q^70 - 6 * q^71 - 28 * q^72 + 77 * q^73 - 5 * q^74 - 32 * q^75 + 21 * q^76 - 7 * q^77 - 17 * q^78 + 43 * q^79 - 4 * q^80 + 48 * q^81 - 16 * q^82 - 20 * q^83 + 15 * q^84 + 35 * q^85 - 3 * q^86 + 36 * q^87 + 24 * q^88 + 3 * q^89 + 21 * q^90 + 63 * q^91 - 17 * q^92 + 36 * q^93 + 24 * q^94 - 3 * q^95 + 4 * q^96 + 16 * q^97 - 55 * q^98 - 28 * q^99

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