LMFDB - Embedded newform 6022.2.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$1$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.44368 q^{3} +1.00000 q^{4} +2.22438 q^{5} -2.44368 q^{6} -3.70978 q^{7} +1.00000 q^{8} +2.97155 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.44368 q^{3} +1.00000 q^{4} +2.22438 q^{5} -2.44368 q^{6} -3.70978 q^{7} +1.00000 q^{8} +2.97155 q^{9} +2.22438 q^{10} -3.25312 q^{11} -2.44368 q^{12} +2.91578 q^{13} -3.70978 q^{14} -5.43567 q^{15} +1.00000 q^{16} -7.11480 q^{17} +2.97155 q^{18} +1.25786 q^{19} +2.22438 q^{20} +9.06549 q^{21} -3.25312 q^{22} +4.45063 q^{23} -2.44368 q^{24} -0.0521290 q^{25} +2.91578 q^{26} +0.0695181 q^{27} -3.70978 q^{28} +8.73119 q^{29} -5.43567 q^{30} +6.91124 q^{31} +1.00000 q^{32} +7.94956 q^{33} -7.11480 q^{34} -8.25195 q^{35} +2.97155 q^{36} +8.09170 q^{37} +1.25786 q^{38} -7.12522 q^{39} +2.22438 q^{40} -2.57872 q^{41} +9.06549 q^{42} -0.0975097 q^{43} -3.25312 q^{44} +6.60986 q^{45} +4.45063 q^{46} -6.83550 q^{47} -2.44368 q^{48} +6.76244 q^{49} -0.0521290 q^{50} +17.3863 q^{51} +2.91578 q^{52} +11.5864 q^{53} +0.0695181 q^{54} -7.23617 q^{55} -3.70978 q^{56} -3.07381 q^{57} +8.73119 q^{58} -11.2272 q^{59} -5.43567 q^{60} -14.2853 q^{61} +6.91124 q^{62} -11.0238 q^{63} +1.00000 q^{64} +6.48580 q^{65} +7.94956 q^{66} -13.6280 q^{67} -7.11480 q^{68} -10.8759 q^{69} -8.25195 q^{70} -16.1719 q^{71} +2.97155 q^{72} -0.211146 q^{73} +8.09170 q^{74} +0.127386 q^{75} +1.25786 q^{76} +12.0683 q^{77} -7.12522 q^{78} +6.04642 q^{79} +2.22438 q^{80} -9.08454 q^{81} -2.57872 q^{82} -10.9278 q^{83} +9.06549 q^{84} -15.8260 q^{85} -0.0975097 q^{86} -21.3362 q^{87} -3.25312 q^{88} +13.5804 q^{89} +6.60986 q^{90} -10.8169 q^{91} +4.45063 q^{92} -16.8888 q^{93} -6.83550 q^{94} +2.79797 q^{95} -2.44368 q^{96} +5.95915 q^{97} +6.76244 q^{98} -9.66681 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9}+O(q^{10}) $ 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9} - 14 q^{10} - 22 q^{11} - 22 q^{12} - 24 q^{13} - 20 q^{14} - 32 q^{15} + 54 q^{16} - 67 q^{17} + 32 q^{18} - 54 q^{19} - 14 q^{20} - 18 q^{21} - 22 q^{22} - 52 q^{23} - 22 q^{24} + 20 q^{25} - 24 q^{26} - 82 q^{27} - 20 q^{28} - 30 q^{29} - 32 q^{30} - 78 q^{31} + 54 q^{32} - 48 q^{33} - 67 q^{34} - 71 q^{35} + 32 q^{36} - 15 q^{37} - 54 q^{38} - 39 q^{39} - 14 q^{40} - 61 q^{41} - 18 q^{42} - 53 q^{43} - 22 q^{44} - 14 q^{45} - 52 q^{46} - 96 q^{47} - 22 q^{48} + 6 q^{49} + 20 q^{50} - 13 q^{51} - 24 q^{52} - 39 q^{53} - 82 q^{54} - 75 q^{55} - 20 q^{56} - 17 q^{57} - 30 q^{58} - 78 q^{59} - 32 q^{60} - 23 q^{61} - 78 q^{62} - 52 q^{63} + 54 q^{64} - 43 q^{65} - 48 q^{66} - 54 q^{67} - 67 q^{68} + 7 q^{69} - 71 q^{70} - 41 q^{71} + 32 q^{72} - 62 q^{73} - 15 q^{74} - 81 q^{75} - 54 q^{76} - 85 q^{77} - 39 q^{78} - 45 q^{79} - 14 q^{80} + 22 q^{81} - 61 q^{82} - 117 q^{83} - 18 q^{84} - 53 q^{86} - 84 q^{87} - 22 q^{88} - 60 q^{89} - 14 q^{90} - 60 q^{91} - 52 q^{92} + 26 q^{93} - 96 q^{94} - 44 q^{95} - 22 q^{96} - 48 q^{97} + 6 q^{98} + 7 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9 - 14 * q^10 - 22 * q^11 - 22 * q^12 - 24 * q^13 - 20 * q^14 - 32 * q^15 + 54 * q^16 - 67 * q^17 + 32 * q^18 - 54 * q^19 - 14 * q^20 - 18 * q^21 - 22 * q^22 - 52 * q^23 - 22 * q^24 + 20 * q^25 - 24 * q^26 - 82 * q^27 - 20 * q^28 - 30 * q^29 - 32 * q^30 - 78 * q^31 + 54 * q^32 - 48 * q^33 - 67 * q^34 - 71 * q^35 + 32 * q^36 - 15 * q^37 - 54 * q^38 - 39 * q^39 - 14 * q^40 - 61 * q^41 - 18 * q^42 - 53 * q^43 - 22 * q^44 - 14 * q^45 - 52 * q^46 - 96 * q^47 - 22 * q^48 + 6 * q^49 + 20 * q^50 - 13 * q^51 - 24 * q^52 - 39 * q^53 - 82 * q^54 - 75 * q^55 - 20 * q^56 - 17 * q^57 - 30 * q^58 - 78 * q^59 - 32 * q^60 - 23 * q^61 - 78 * q^62 - 52 * q^63 + 54 * q^64 - 43 * q^65 - 48 * q^66 - 54 * q^67 - 67 * q^68 + 7 * q^69 - 71 * q^70 - 41 * q^71 + 32 * q^72 - 62 * q^73 - 15 * q^74 - 81 * q^75 - 54 * q^76 - 85 * q^77 - 39 * q^78 - 45 * q^79 - 14 * q^80 + 22 * q^81 - 61 * q^82 - 117 * q^83 - 18 * q^84 - 53 * q^86 - 84 * q^87 - 22 * q^88 - 60 * q^89 - 14 * q^90 - 60 * q^91 - 52 * q^92 + 26 * q^93 - 96 * q^94 - 44 * q^95 - 22 * q^96 - 48 * q^97 + 6 * q^98 + 7 * 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
$3$	−2.44368	−1.41086	−0.705428	−	0.708781i	$-0.749245\pi$
$3$	−2.44368	−1.41086	−0.705428	+	0.708781i	$0.749245\pi$
$4$	1.00000	0.500000
$5$	2.22438	0.994773	0.497387	−	0.867529i	$-0.334293\pi$
$5$	2.22438	0.994773	0.497387	+	0.867529i	$0.334293\pi$
$6$	−2.44368	−0.997627
$7$	−3.70978	−1.40216	−0.701082	−	0.713081i	$-0.747299\pi$
$7$	−3.70978	−1.40216	−0.701082	+	0.713081i	$0.747299\pi$
$8$	1.00000	0.353553
$9$	2.97155	0.990517
$10$	2.22438	0.703411
$11$	−3.25312	−0.980852	−0.490426	−	0.871483i	$-0.663159\pi$
$11$	−3.25312	−0.980852	−0.490426	+	0.871483i	$0.663159\pi$
$12$	−2.44368	−0.705428
$13$	2.91578	0.808691	0.404346	−	0.914606i	$-0.367499\pi$
$13$	2.91578	0.808691	0.404346	+	0.914606i	$0.367499\pi$
$14$	−3.70978	−0.991479
$15$	−5.43567	−1.40348
$16$	1.00000	0.250000
$17$	−7.11480	−1.72559	−0.862796	−	0.505553i	$-0.831289\pi$
$17$	−7.11480	−1.72559	−0.862796	+	0.505553i	$0.831289\pi$
$18$	2.97155	0.700401
$19$	1.25786	0.288574	0.144287	−	0.989536i	$-0.453911\pi$
$19$	1.25786	0.288574	0.144287	+	0.989536i	$0.453911\pi$
$20$	2.22438	0.497387
$21$	9.06549	1.97825
$22$	−3.25312	−0.693567
$23$	4.45063	0.928021	0.464011	−	0.885830i	$-0.346410\pi$
$23$	4.45063	0.928021	0.464011	+	0.885830i	$0.346410\pi$
$24$	−2.44368	−0.498813
$25$	−0.0521290	−0.0104258
$26$	2.91578	0.571831
$27$	0.0695181	0.0133788
$28$	−3.70978	−0.701082
$29$	8.73119	1.62134	0.810671	−	0.585502i	$-0.199103\pi$
$29$	8.73119	1.62134	0.810671	+	0.585502i	$0.199103\pi$
$30$	−5.43567	−0.992412
$31$	6.91124	1.24129	0.620647	−	0.784090i	$-0.286870\pi$
$31$	6.91124	1.24129	0.620647	+	0.784090i	$0.286870\pi$
$32$	1.00000	0.176777
$33$	7.94956	1.38384
$34$	−7.11480	−1.22018
$35$	−8.25195	−1.39483
$36$	2.97155	0.495259
$37$	8.09170	1.33027	0.665133	−	0.746725i	$-0.268375\pi$
$37$	8.09170	1.33027	0.665133	+	0.746725i	$0.268375\pi$
$38$	1.25786	0.204052
$39$	−7.12522	−1.14095
$40$	2.22438	0.351706
$41$	−2.57872	−0.402728	−0.201364	−	0.979516i	$-0.564537\pi$
$41$	−2.57872	−0.402728	−0.201364	+	0.979516i	$0.564537\pi$
$42$	9.06549	1.39884
$43$	−0.0975097	−0.0148701	−0.00743505	−	0.999972i	$-0.502367\pi$
$43$	−0.0975097	−0.0148701	−0.00743505	+	0.999972i	$0.502367\pi$
$44$	−3.25312	−0.490426
$45$	6.60986	0.985340
$46$	4.45063	0.656210
$47$	−6.83550	−0.997061	−0.498530	−	0.866872i	$-0.666127\pi$
$47$	−6.83550	−0.997061	−0.498530	+	0.866872i	$0.666127\pi$
$48$	−2.44368	−0.352714
$49$	6.76244	0.966062
$50$	−0.0521290	−0.00737215
$51$	17.3863	2.43456
$52$	2.91578	0.404346
$53$	11.5864	1.59152	0.795760	−	0.605612i	$-0.207072\pi$
$53$	11.5864	1.59152	0.795760	+	0.605612i	$0.207072\pi$
$54$	0.0695181	0.00946021
$55$	−7.23617	−0.975725
$56$	−3.70978	−0.495740
$57$	−3.07381	−0.407136
$58$	8.73119	1.14646
$59$	−11.2272	−1.46166	−0.730830	−	0.682559i	$-0.760867\pi$
$59$	−11.2272	−1.46166	−0.730830	+	0.682559i	$0.760867\pi$
$60$	−5.43567	−0.701742
$61$	−14.2853	−1.82905	−0.914524	−	0.404532i	$-0.867434\pi$
$61$	−14.2853	−1.82905	−0.914524	+	0.404532i	$0.867434\pi$
$62$	6.91124	0.877728
$63$	−11.0238	−1.38887
$64$	1.00000	0.125000
$65$	6.48580	0.804465
$66$	7.94956	0.978524
$67$	−13.6280	−1.66493	−0.832464	−	0.554079i	$-0.813071\pi$
$67$	−13.6280	−1.66493	−0.832464	+	0.554079i	$0.813071\pi$
$68$	−7.11480	−0.862796
$69$	−10.8759	−1.30931
$70$	−8.25195	−0.986297
$71$	−16.1719	−1.91925	−0.959627	−	0.281276i	$-0.909242\pi$
$71$	−16.1719	−1.91925	−0.959627	+	0.281276i	$0.909242\pi$
$72$	2.97155	0.350201
$73$	−0.211146	−0.0247127	−0.0123564	−	0.999924i	$-0.503933\pi$
$73$	−0.211146	−0.0247127	−0.0123564	+	0.999924i	$0.503933\pi$
$74$	8.09170	0.940641
$75$	0.127386	0.0147093
$76$	1.25786	0.144287
$77$	12.0683	1.37531
$78$	−7.12522	−0.806772
$79$	6.04642	0.680276	0.340138	−	0.940376i	$-0.389526\pi$
$79$	6.04642	0.680276	0.340138	+	0.940376i	$0.389526\pi$
$80$	2.22438	0.248693
$81$	−9.08454	−1.00939
$82$	−2.57872	−0.284772
$83$	−10.9278	−1.19948	−0.599741	−	0.800194i	$-0.704730\pi$
$83$	−10.9278	−1.19948	−0.599741	+	0.800194i	$0.704730\pi$
$84$	9.06549	0.989126
$85$	−15.8260	−1.71657
$86$	−0.0975097	−0.0105147
$87$	−21.3362	−2.28748
$88$	−3.25312	−0.346783
$89$	13.5804	1.43952	0.719759	−	0.694224i	$-0.244252\pi$
$89$	13.5804	1.43952	0.719759	+	0.694224i	$0.244252\pi$
$90$	6.60986	0.696741
$91$	−10.8169	−1.13392
$92$	4.45063	0.464011
$93$	−16.8888	−1.75129
$94$	−6.83550	−0.705028
$95$	2.79797	0.287066
$96$	−2.44368	−0.249407
$97$	5.95915	0.605060	0.302530	−	0.953140i	$-0.402169\pi$
$97$	5.95915	0.605060	0.302530	+	0.953140i	$0.402169\pi$
$98$	6.76244	0.683109
$99$	−9.66681	−0.971551
$100$	−0.0521290	−0.00521290
$101$	−6.79231	−0.675860	−0.337930	−	0.941171i	$-0.609727\pi$
$101$	−6.79231	−0.675860	−0.337930	+	0.941171i	$0.609727\pi$
$102$	17.3863	1.72150
$103$	−4.98516	−0.491203	−0.245601	−	0.969371i	$-0.578985\pi$
$103$	−4.98516	−0.491203	−0.245601	+	0.969371i	$0.578985\pi$
$104$	2.91578	0.285916
$105$	20.1651	1.96791
$106$	11.5864	1.12537
$107$	−13.7678	−1.33098	−0.665489	−	0.746407i	$-0.731777\pi$
$107$	−13.7678	−1.33098	−0.665489	+	0.746407i	$0.731777\pi$
$108$	0.0695181	0.00668938
$109$	15.3351	1.46883	0.734417	−	0.678698i	$-0.237456\pi$
$109$	15.3351	1.46883	0.734417	+	0.678698i	$0.237456\pi$
$110$	−7.23617	−0.689942
$111$	−19.7735	−1.87682
$112$	−3.70978	−0.350541
$113$	−16.1922	−1.52323	−0.761615	−	0.648029i	$-0.775593\pi$
$113$	−16.1922	−1.52323	−0.761615	+	0.648029i	$0.775593\pi$
$114$	−3.07381	−0.287889
$115$	9.89991	0.923171
$116$	8.73119	0.810671
$117$	8.66438	0.801023
$118$	−11.2272	−1.03355
$119$	26.3943	2.41956
$120$	−5.43567	−0.496206
$121$	−0.417230	−0.0379300
$122$	−14.2853	−1.29333
$123$	6.30155	0.568192
$124$	6.91124	0.620647
$125$	−11.2379	−1.00514
$126$	−11.0238	−0.982077
$127$	14.9734	1.32868	0.664338	−	0.747433i	$-0.268714\pi$
$127$	14.9734	1.32868	0.664338	+	0.747433i	$0.268714\pi$
$128$	1.00000	0.0883883
$129$	0.238282	0.0209796
$130$	6.48580	0.568842
$131$	7.93540	0.693320	0.346660	−	0.937991i	$-0.387316\pi$
$131$	7.93540	0.693320	0.346660	+	0.937991i	$0.387316\pi$
$132$	7.94956	0.691921
$133$	−4.66639	−0.404628
$134$	−13.6280	−1.17728
$135$	0.154635	0.0133088
$136$	−7.11480	−0.610089
$137$	7.82687	0.668695	0.334347	−	0.942450i	$-0.391484\pi$
$137$	7.82687	0.668695	0.334347	+	0.942450i	$0.391484\pi$
$138$	−10.8759	−0.925819
$139$	−2.39909	−0.203488	−0.101744	−	0.994811i	$-0.532442\pi$
$139$	−2.39909	−0.203488	−0.101744	+	0.994811i	$0.532442\pi$
$140$	−8.25195	−0.697417
$141$	16.7038	1.40671
$142$	−16.1719	−1.35712
$143$	−9.48537	−0.793206
$144$	2.97155	0.247629
$145$	19.4215	1.61287
$146$	−0.211146	−0.0174745
$147$	−16.5252	−1.36298
$148$	8.09170	0.665133
$149$	−6.83042	−0.559570	−0.279785	−	0.960063i	$-0.590263\pi$
$149$	−6.83042	−0.559570	−0.279785	+	0.960063i	$0.590263\pi$
$150$	0.127386	0.0104011
$151$	22.6048	1.83956	0.919778	−	0.392440i	$-0.128369\pi$
$151$	22.6048	1.83956	0.919778	+	0.392440i	$0.128369\pi$
$152$	1.25786	0.102026
$153$	−21.1420	−1.70923
$154$	12.0683	0.972494
$155$	15.3732	1.23481
$156$	−7.12522	−0.570474
$157$	−10.6645	−0.851116	−0.425558	−	0.904931i	$-0.639922\pi$
$157$	−10.6645	−0.851116	−0.425558	+	0.904931i	$0.639922\pi$
$158$	6.04642	0.481028
$159$	−28.3135	−2.24541
$160$	2.22438	0.175853
$161$	−16.5109	−1.30124
$162$	−9.08454	−0.713748
$163$	−16.2325	−1.27143	−0.635713	−	0.771925i	$-0.719294\pi$
$163$	−16.2325	−1.27143	−0.635713	+	0.771925i	$0.719294\pi$
$164$	−2.57872	−0.201364
$165$	17.6829	1.37661
$166$	−10.9278	−0.848162
$167$	−18.7635	−1.45196	−0.725982	−	0.687714i	$-0.758614\pi$
$167$	−18.7635	−1.45196	−0.725982	+	0.687714i	$0.758614\pi$
$168$	9.06549	0.699418
$169$	−4.49824	−0.346019
$170$	−15.8260	−1.21380
$171$	3.73781	0.285837
$172$	−0.0975097	−0.00743505
$173$	−13.3957	−1.01845	−0.509227	−	0.860632i	$-0.670069\pi$
$173$	−13.3957	−1.01845	−0.509227	+	0.860632i	$0.670069\pi$
$174$	−21.3362	−1.61749
$175$	0.193387	0.0146187
$176$	−3.25312	−0.245213
$177$	27.4357	2.06219
$178$	13.5804	1.01789
$179$	3.12550	0.233611	0.116805	−	0.993155i	$-0.462735\pi$
$179$	3.12550	0.233611	0.116805	+	0.993155i	$0.462735\pi$
$180$	6.60986	0.492670
$181$	−15.3402	−1.14023	−0.570113	−	0.821566i	$-0.693101\pi$
$181$	−15.3402	−1.14023	−0.570113	+	0.821566i	$0.693101\pi$
$182$	−10.8169	−0.801801
$183$	34.9087	2.58052
$184$	4.45063	0.328105
$185$	17.9990	1.32331
$186$	−16.8888	−1.23835
$187$	23.1453	1.69255
$188$	−6.83550	−0.498530
$189$	−0.257897	−0.0187592
$190$	2.79797	0.202986
$191$	−1.12631	−0.0814972	−0.0407486	−	0.999169i	$-0.512974\pi$
$191$	−1.12631	−0.0814972	−0.0407486	+	0.999169i	$0.512974\pi$
$192$	−2.44368	−0.176357
$193$	−6.64460	−0.478289	−0.239144	−	0.970984i	$-0.576867\pi$
$193$	−6.64460	−0.478289	−0.239144	+	0.970984i	$0.576867\pi$
$194$	5.95915	0.427842
$195$	−15.8492	−1.13498
$196$	6.76244	0.483031
$197$	−23.1689	−1.65072	−0.825359	−	0.564608i	$-0.809027\pi$
$197$	−23.1689	−1.65072	−0.825359	+	0.564608i	$0.809027\pi$
$198$	−9.66681	−0.686990
$199$	14.3676	1.01850	0.509248	−	0.860620i	$-0.329924\pi$
$199$	14.3676	1.01850	0.509248	+	0.860620i	$0.329924\pi$
$200$	−0.0521290	−0.00368608
$201$	33.3025	2.34898
$202$	−6.79231	−0.477905
$203$	−32.3908	−2.27339
$204$	17.3863	1.21728
$205$	−5.73605	−0.400623
$206$	−4.98516	−0.347333
$207$	13.2253	0.919221
$208$	2.91578	0.202173
$209$	−4.09198	−0.283048
$210$	20.1651	1.39152
$211$	−16.6854	−1.14867	−0.574335	−	0.818620i	$-0.694739\pi$
$211$	−16.6854	−1.14867	−0.574335	+	0.818620i	$0.694739\pi$
$212$	11.5864	0.795760
$213$	39.5189	2.70779
$214$	−13.7678	−0.941144
$215$	−0.216899	−0.0147924
$216$	0.0695181	0.00473011
$217$	−25.6391	−1.74050
$218$	15.3351	1.03862
$219$	0.515972	0.0348661
$220$	−7.23617	−0.487863
$221$	−20.7452	−1.39547
$222$	−19.7735	−1.32711
$223$	4.14931	0.277858	0.138929	−	0.990302i	$-0.455634\pi$
$223$	4.14931	0.277858	0.138929	+	0.990302i	$0.455634\pi$
$224$	−3.70978	−0.247870
$225$	−0.154904	−0.0103269
$226$	−16.1922	−1.07709
$227$	−8.16173	−0.541713	−0.270856	−	0.962620i	$-0.587307\pi$
$227$	−8.16173	−0.541713	−0.270856	+	0.962620i	$0.587307\pi$
$228$	−3.07381	−0.203568
$229$	19.8594	1.31235	0.656173	−	0.754610i	$-0.272174\pi$
$229$	19.8594	1.31235	0.656173	+	0.754610i	$0.272174\pi$
$230$	9.89991	0.652780
$231$	−29.4911	−1.94037
$232$	8.73119	0.573231
$233$	11.3094	0.740904	0.370452	−	0.928852i	$-0.379203\pi$
$233$	11.3094	0.740904	0.370452	+	0.928852i	$0.379203\pi$
$234$	8.66438	0.566409
$235$	−15.2048	−0.991849
$236$	−11.2272	−0.730830
$237$	−14.7755	−0.959772
$238$	26.3943	1.71089
$239$	−10.7716	−0.696756	−0.348378	−	0.937354i	$-0.613268\pi$
$239$	−10.7716	−0.696756	−0.348378	+	0.937354i	$0.613268\pi$
$240$	−5.43567	−0.350871
$241$	−9.73144	−0.626857	−0.313429	−	0.949612i	$-0.601478\pi$
$241$	−9.73144	−0.626857	−0.313429	+	0.949612i	$0.601478\pi$
$242$	−0.417230	−0.0268206
$243$	21.9911	1.41073
$244$	−14.2853	−0.914524
$245$	15.0422	0.961013
$246$	6.30155	0.401772
$247$	3.66765	0.233367
$248$	6.91124	0.438864
$249$	26.7040	1.69230
$250$	−11.2379	−0.710745
$251$	7.11176	0.448890	0.224445	−	0.974487i	$-0.427943\pi$
$251$	7.11176	0.448890	0.224445	+	0.974487i	$0.427943\pi$
$252$	−11.0238	−0.694434
$253$	−14.4784	−0.910251
$254$	14.9734	0.939515
$255$	38.6737	2.42184
$256$	1.00000	0.0625000
$257$	4.75551	0.296640	0.148320	−	0.988939i	$-0.452613\pi$
$257$	4.75551	0.296640	0.148320	+	0.988939i	$0.452613\pi$
$258$	0.238282	0.0148348
$259$	−30.0184	−1.86525
$260$	6.48580	0.402232
$261$	25.9452	1.60597
$262$	7.93540	0.490251
$263$	−3.50639	−0.216213	−0.108107	−	0.994139i	$-0.534479\pi$
$263$	−3.50639	−0.216213	−0.108107	+	0.994139i	$0.534479\pi$
$264$	7.94956	0.489262
$265$	25.7727	1.58320
$266$	−4.66639	−0.286115
$267$	−33.1861	−2.03095
$268$	−13.6280	−0.832464
$269$	−14.6958	−0.896020	−0.448010	−	0.894029i	$-0.647867\pi$
$269$	−14.6958	−0.896020	−0.448010	+	0.894029i	$0.647867\pi$
$270$	0.154635	0.00941077
$271$	−14.0230	−0.851834	−0.425917	−	0.904762i	$-0.640048\pi$
$271$	−14.0230	−0.851834	−0.425917	+	0.904762i	$0.640048\pi$
$272$	−7.11480	−0.431398
$273$	26.4330	1.59980
$274$	7.82687	0.472838
$275$	0.169582	0.0102262
$276$	−10.8759	−0.654653
$277$	−17.1636	−1.03126	−0.515629	−	0.856812i	$-0.672442\pi$
$277$	−17.1636	−1.03126	−0.515629	+	0.856812i	$0.672442\pi$
$278$	−2.39909	−0.143888
$279$	20.5371	1.22952
$280$	−8.25195	−0.493149
$281$	9.89869	0.590506	0.295253	−	0.955419i	$-0.404596\pi$
$281$	9.89869	0.590506	0.295253	+	0.955419i	$0.404596\pi$
$282$	16.7038	0.994694
$283$	20.0346	1.19093	0.595466	−	0.803381i	$-0.296968\pi$
$283$	20.0346	1.19093	0.595466	+	0.803381i	$0.296968\pi$
$284$	−16.1719	−0.959627
$285$	−6.83733	−0.405008
$286$	−9.48537	−0.560881
$287$	9.56646	0.564690
$288$	2.97155	0.175100
$289$	33.6203	1.97767
$290$	19.4215	1.14047
$291$	−14.5622	−0.853653
$292$	−0.211146	−0.0123564
$293$	−5.36350	−0.313339	−0.156669	−	0.987651i	$-0.550076\pi$
$293$	−5.36350	−0.313339	−0.156669	+	0.987651i	$0.550076\pi$
$294$	−16.5252	−0.963769
$295$	−24.9736	−1.45402
$296$	8.09170	0.470320
$297$	−0.226150	−0.0131226
$298$	−6.83042	−0.395676
$299$	12.9771	0.750483
$300$	0.127386	0.00735465
$301$	0.361739	0.0208503
$302$	22.6048	1.30076
$303$	16.5982	0.953541
$304$	1.25786	0.0721435
$305$	−31.7760	−1.81949
$306$	−21.1420	−1.20861
$307$	−17.1581	−0.979267	−0.489633	−	0.871928i	$-0.662869\pi$
$307$	−17.1581	−0.979267	−0.489633	+	0.871928i	$0.662869\pi$
$308$	12.0683	0.687657
$309$	12.1821	0.693017
$310$	15.3732	0.873140
$311$	−14.0060	−0.794206	−0.397103	−	0.917774i	$-0.629984\pi$
$311$	−14.0060	−0.794206	−0.397103	+	0.917774i	$0.629984\pi$
$312$	−7.12522	−0.403386
$313$	0.435482	0.0246149	0.0123074	−	0.999924i	$-0.496082\pi$
$313$	0.435482	0.0246149	0.0123074	+	0.999924i	$0.496082\pi$
$314$	−10.6645	−0.601830
$315$	−24.5211	−1.38161
$316$	6.04642	0.340138
$317$	23.8380	1.33887	0.669437	−	0.742869i	$-0.266535\pi$
$317$	23.8380	1.33887	0.669437	+	0.742869i	$0.266535\pi$
$318$	−28.3135	−1.58774
$319$	−28.4036	−1.59030
$320$	2.22438	0.124347
$321$	33.6439	1.87782
$322$	−16.5109	−0.920114
$323$	−8.94945	−0.497961
$324$	−9.08454	−0.504696
$325$	−0.151997	−0.00843125
$326$	−16.2325	−0.899035
$327$	−37.4740	−2.07232
$328$	−2.57872	−0.142386
$329$	25.3582	1.39804
$330$	17.6829	0.973409
$331$	−9.98961	−0.549078	−0.274539	−	0.961576i	$-0.588525\pi$
$331$	−9.98961	−0.549078	−0.274539	+	0.961576i	$0.588525\pi$
$332$	−10.9278	−0.599741
$333$	24.0449	1.31765
$334$	−18.7635	−1.02669
$335$	−30.3139	−1.65623
$336$	9.06549	0.494563
$337$	−24.3987	−1.32908	−0.664540	−	0.747252i	$-0.731373\pi$
$337$	−24.3987	−1.32908	−0.664540	+	0.747252i	$0.731373\pi$
$338$	−4.49824	−0.244672
$339$	39.5684	2.14906
$340$	−15.8260	−0.858286
$341$	−22.4831	−1.21753
$342$	3.73781	0.202118
$343$	0.881307	0.0475861
$344$	−0.0975097	−0.00525737
$345$	−24.1922	−1.30246
$346$	−13.3957	−0.720156
$347$	13.9044	0.746426	0.373213	−	0.927746i	$-0.378256\pi$
$347$	13.9044	0.746426	0.373213	+	0.927746i	$0.378256\pi$
$348$	−21.3362	−1.14374
$349$	5.86275	0.313826	0.156913	−	0.987612i	$-0.449846\pi$
$349$	5.86275	0.313826	0.156913	+	0.987612i	$0.449846\pi$
$350$	0.193387	0.0103370
$351$	0.202699	0.0108193
$352$	−3.25312	−0.173392
$353$	25.5418	1.35945	0.679726	−	0.733466i	$-0.262099\pi$
$353$	25.5418	1.35945	0.679726	+	0.733466i	$0.262099\pi$
$354$	27.4357	1.45819
$355$	−35.9725	−1.90922
$356$	13.5804	0.719759
$357$	−64.4991	−3.41365
$358$	3.12550	0.165188
$359$	0.0397099	0.00209581	0.00104790	−	0.999999i	$-0.499666\pi$
$359$	0.0397099	0.00209581	0.00104790	+	0.999999i	$0.499666\pi$
$360$	6.60986	0.348370
$361$	−17.4178	−0.916725
$362$	−15.3402	−0.806262
$363$	1.01958	0.0535138
$364$	−10.8169	−0.566959
$365$	−0.469668	−0.0245836
$366$	34.9087	1.82471
$367$	8.48536	0.442932	0.221466	−	0.975168i	$-0.428916\pi$
$367$	8.48536	0.442932	0.221466	+	0.975168i	$0.428916\pi$
$368$	4.45063	0.232005
$369$	−7.66279	−0.398909
$370$	17.9990	0.935724
$371$	−42.9831	−2.23157
$372$	−16.8888	−0.875645
$373$	6.71091	0.347478	0.173739	−	0.984792i	$-0.444415\pi$
$373$	6.71091	0.347478	0.173739	+	0.984792i	$0.444415\pi$
$374$	23.1453	1.19681
$375$	27.4617	1.41812
$376$	−6.83550	−0.352514
$377$	25.4582	1.31117
$378$	−0.257897	−0.0132648
$379$	28.4000	1.45881	0.729405	−	0.684082i	$-0.239797\pi$
$379$	28.4000	1.45881	0.729405	+	0.684082i	$0.239797\pi$
$380$	2.79797	0.143533
$381$	−36.5902	−1.87457
$382$	−1.12631	−0.0576273
$383$	−34.4357	−1.75958	−0.879791	−	0.475361i	$-0.842318\pi$
$383$	−34.4357	−1.75958	−0.879791	+	0.475361i	$0.842318\pi$
$384$	−2.44368	−0.124703
$385$	26.8446	1.36813
$386$	−6.64460	−0.338201
$387$	−0.289755	−0.0147291
$388$	5.95915	0.302530
$389$	−17.3602	−0.880196	−0.440098	−	0.897950i	$-0.645056\pi$
$389$	−17.3602	−0.880196	−0.440098	+	0.897950i	$0.645056\pi$
$390$	−15.8492	−0.802555
$391$	−31.6654	−1.60139
$392$	6.76244	0.341555
$393$	−19.3916	−0.978175
$394$	−23.1689	−1.16723
$395$	13.4496	0.676720
$396$	−9.66681	−0.485775
$397$	−9.40968	−0.472258	−0.236129	−	0.971722i	$-0.575879\pi$
$397$	−9.40968	−0.472258	−0.236129	+	0.971722i	$0.575879\pi$
$398$	14.3676	0.720185
$399$	11.4032	0.570872
$400$	−0.0521290	−0.00260645
$401$	−25.3090	−1.26387	−0.631935	−	0.775021i	$-0.717739\pi$
$401$	−25.3090	−1.26387	−0.631935	+	0.775021i	$0.717739\pi$
$402$	33.3025	1.66098
$403$	20.1516	1.00382
$404$	−6.79231	−0.337930
$405$	−20.2075	−1.00412
$406$	−32.3908	−1.60753
$407$	−26.3232	−1.30479
$408$	17.3863	0.860748
$409$	−34.6128	−1.71149	−0.855747	−	0.517395i	$-0.826902\pi$
$409$	−34.6128	−1.71149	−0.855747	+	0.517395i	$0.826902\pi$
$410$	−5.73605	−0.283283
$411$	−19.1263	−0.943432
$412$	−4.98516	−0.245601
$413$	41.6505	2.04949
$414$	13.2253	0.649988
$415$	−24.3076	−1.19321
$416$	2.91578	0.142958
$417$	5.86260	0.287093
$418$	−4.09198	−0.200145
$419$	16.5466	0.808356	0.404178	−	0.914680i	$-0.367558\pi$
$419$	16.5466	0.808356	0.404178	+	0.914680i	$0.367558\pi$
$420$	20.1651	0.983956
$421$	−37.3580	−1.82072	−0.910358	−	0.413821i	$-0.864194\pi$
$421$	−37.3580	−1.82072	−0.910358	+	0.413821i	$0.864194\pi$
$422$	−16.6854	−0.812233
$423$	−20.3121	−0.987606
$424$	11.5864	0.562687
$425$	0.370887	0.0179907
$426$	39.5189	1.91470
$427$	52.9953	2.56462
$428$	−13.7678	−0.665489
$429$	23.1792	1.11910
$430$	−0.216899	−0.0104598
$431$	−1.37686	−0.0663208	−0.0331604	−	0.999450i	$-0.510557\pi$
$431$	−1.37686	−0.0663208	−0.0331604	+	0.999450i	$0.510557\pi$
$432$	0.0695181	0.00334469
$433$	24.4390	1.17446	0.587232	−	0.809419i	$-0.300218\pi$
$433$	24.4390	1.17446	0.587232	+	0.809419i	$0.300218\pi$
$434$	−25.6391	−1.23072
$435$	−47.4599	−2.27553
$436$	15.3351	0.734417
$437$	5.59829	0.267803
$438$	0.515972	0.0246541
$439$	−7.12686	−0.340146	−0.170073	−	0.985431i	$-0.554400\pi$
$439$	−7.12686	−0.340146	−0.170073	+	0.985431i	$0.554400\pi$
$440$	−7.23617	−0.344971
$441$	20.0949	0.956901
$442$	−20.7452	−0.986747
$443$	−15.7642	−0.748981	−0.374490	−	0.927231i	$-0.622182\pi$
$443$	−15.7642	−0.748981	−0.374490	+	0.927231i	$0.622182\pi$
$444$	−19.7735	−0.938408
$445$	30.2080	1.43199
$446$	4.14931	0.196476
$447$	16.6913	0.789473
$448$	−3.70978	−0.175270
$449$	26.5711	1.25397	0.626984	−	0.779032i	$-0.284289\pi$
$449$	26.5711	1.25397	0.626984	+	0.779032i	$0.284289\pi$
$450$	−0.154904	−0.00730224
$451$	8.38887	0.395016
$452$	−16.1922	−0.761615
$453$	−55.2389	−2.59535
$454$	−8.16173	−0.383049
$455$	−24.0609	−1.12799
$456$	−3.07381	−0.143944
$457$	10.9605	0.512711	0.256356	−	0.966583i	$-0.417478\pi$
$457$	10.9605	0.512711	0.256356	+	0.966583i	$0.417478\pi$
$458$	19.8594	0.927969
$459$	−0.494607	−0.0230863
$460$	9.89991	0.461585
$461$	9.41129	0.438328	0.219164	−	0.975688i	$-0.429667\pi$
$461$	9.41129	0.438328	0.219164	+	0.975688i	$0.429667\pi$
$462$	−29.4911	−1.37205
$463$	−7.98331	−0.371016	−0.185508	−	0.982643i	$-0.559393\pi$
$463$	−7.98331	−0.371016	−0.185508	+	0.982643i	$0.559393\pi$
$464$	8.73119	0.405336
$465$	−37.5672	−1.74214
$466$	11.3094	0.523898
$467$	−41.3887	−1.91524	−0.957620	−	0.288034i	$-0.906998\pi$
$467$	−41.3887	−1.91524	−0.957620	+	0.288034i	$0.906998\pi$
$468$	8.66438	0.400511
$469$	50.5569	2.33450
$470$	−15.2048	−0.701343
$471$	26.0605	1.20080
$472$	−11.2272	−0.516775
$473$	0.317211	0.0145854
$474$	−14.7755	−0.678661
$475$	−0.0655712	−0.00300861
$476$	26.3943	1.20978
$477$	34.4297	1.57643
$478$	−10.7716	−0.492681
$479$	21.6848	0.990804	0.495402	−	0.868664i	$-0.335021\pi$
$479$	21.6848	0.990804	0.495402	+	0.868664i	$0.335021\pi$
$480$	−5.43567	−0.248103
$481$	23.5936	1.07578
$482$	−9.73144	−0.443255
$483$	40.3472	1.83586
$484$	−0.417230	−0.0189650
$485$	13.2554	0.601897
$486$	21.9911	0.997537
$487$	−29.9367	−1.35656	−0.678281	−	0.734803i	$-0.737275\pi$
$487$	−29.9367	−1.35656	−0.678281	+	0.734803i	$0.737275\pi$
$488$	−14.2853	−0.646666
$489$	39.6670	1.79380
$490$	15.0422	0.679539
$491$	11.7819	0.531712	0.265856	−	0.964013i	$-0.414345\pi$
$491$	11.7819	0.531712	0.265856	+	0.964013i	$0.414345\pi$
$492$	6.30155	0.284096
$493$	−62.1207	−2.79777
$494$	3.66765	0.165015
$495$	−21.5027	−0.966473
$496$	6.91124	0.310324
$497$	59.9942	2.69111
$498$	26.7040	1.19664
$499$	24.0080	1.07474	0.537372	−	0.843345i	$-0.319417\pi$
$499$	24.0080	1.07474	0.537372	+	0.843345i	$0.319417\pi$
$500$	−11.2379	−0.502572
$501$	45.8519	2.04851
$502$	7.11176	0.317413
$503$	−0.270262	−0.0120504	−0.00602519	−	0.999982i	$-0.501918\pi$
$503$	−0.270262	−0.0120504	−0.00602519	+	0.999982i	$0.501918\pi$
$504$	−11.0238	−0.491039
$505$	−15.1087	−0.672327
$506$	−14.4784	−0.643645
$507$	10.9922	0.488183
$508$	14.9734	0.664338
$509$	−4.22785	−0.187396	−0.0936980	−	0.995601i	$-0.529869\pi$
$509$	−4.22785	−0.187396	−0.0936980	+	0.995601i	$0.529869\pi$
$510$	38.6737	1.71250
$511$	0.783303	0.0346513
$512$	1.00000	0.0441942
$513$	0.0874443	0.00386076
$514$	4.75551	0.209756
$515$	−11.0889	−0.488636
$516$	0.238282	0.0104898
$517$	22.2367	0.977969
$518$	−30.0184	−1.31893
$519$	32.7347	1.43689
$520$	6.48580	0.284421
$521$	30.0629	1.31708	0.658540	−	0.752546i	$-0.271174\pi$
$521$	30.0629	1.31708	0.658540	+	0.752546i	$0.271174\pi$
$522$	25.9452	1.13559
$523$	−3.80926	−0.166568	−0.0832838	−	0.996526i	$-0.526541\pi$
$523$	−3.80926	−0.166568	−0.0832838	+	0.996526i	$0.526541\pi$
$524$	7.93540	0.346660
$525$	−0.472575	−0.0206249
$526$	−3.50639	−0.152886
$527$	−49.1720	−2.14197
$528$	7.94956	0.345960
$529$	−3.19186	−0.138776
$530$	25.7727	1.11949
$531$	−33.3623	−1.44780
$532$	−4.66639	−0.202314
$533$	−7.51897	−0.325683
$534$	−33.1861	−1.43610
$535$	−30.6247	−1.32402
$536$	−13.6280	−0.588641
$537$	−7.63771	−0.329591
$538$	−14.6958	−0.633582
$539$	−21.9990	−0.947564
$540$	0.154635	0.00665442
$541$	20.9610	0.901184	0.450592	−	0.892730i	$-0.351213\pi$
$541$	20.9610	0.901184	0.450592	+	0.892730i	$0.351213\pi$
$542$	−14.0230	−0.602337
$543$	37.4864	1.60870
$544$	−7.11480	−0.305044
$545$	34.1111	1.46116
$546$	26.4330	1.13123
$547$	−16.5561	−0.707888	−0.353944	−	0.935267i	$-0.615160\pi$
$547$	−16.5561	−0.707888	−0.353944	+	0.935267i	$0.615160\pi$
$548$	7.82687	0.334347
$549$	−42.4496	−1.81170
$550$	0.169582	0.00723099
$551$	10.9827	0.467877
$552$	−10.8759	−0.462909
$553$	−22.4309	−0.953858
$554$	−17.1636	−0.729209
$555$	−43.9838	−1.86701
$556$	−2.39909	−0.101744
$557$	−21.2958	−0.902333	−0.451167	−	0.892440i	$-0.648992\pi$
$557$	−21.2958	−0.902333	−0.451167	+	0.892440i	$0.648992\pi$
$558$	20.5371	0.869405
$559$	−0.284317	−0.0120253
$560$	−8.25195	−0.348709
$561$	−56.5595	−2.38794
$562$	9.89869	0.417551
$563$	30.6537	1.29190	0.645949	−	0.763380i	$-0.276462\pi$
$563$	30.6537	1.29190	0.645949	+	0.763380i	$0.276462\pi$
$564$	16.7038	0.703355
$565$	−36.0175	−1.51527
$566$	20.0346	0.842115
$567$	33.7016	1.41533
$568$	−16.1719	−0.678559
$569$	−18.3326	−0.768543	−0.384272	−	0.923220i	$-0.625547\pi$
$569$	−18.3326	−0.768543	−0.384272	+	0.923220i	$0.625547\pi$
$570$	−6.83733	−0.286384
$571$	10.6534	0.445829	0.222915	−	0.974838i	$-0.428443\pi$
$571$	10.6534	0.445829	0.222915	+	0.974838i	$0.428443\pi$
$572$	−9.48537	−0.396603
$573$	2.75235	0.114981
$574$	9.56646	0.399296
$575$	−0.232007	−0.00967536
$576$	2.97155	0.123815
$577$	44.9729	1.87225	0.936123	−	0.351673i	$-0.114387\pi$
$577$	44.9729	1.87225	0.936123	+	0.351673i	$0.114387\pi$
$578$	33.6203	1.39842
$579$	16.2372	0.674797
$580$	19.4215	0.806434
$581$	40.5397	1.68187
$582$	−14.5622	−0.603624
$583$	−37.6921	−1.56105
$584$	−0.211146	−0.00873727
$585$	19.2729	0.796836
$586$	−5.36350	−0.221564
$587$	−46.2704	−1.90978	−0.954891	−	0.296957i	$-0.904028\pi$
$587$	−46.2704	−1.90978	−0.954891	+	0.296957i	$0.904028\pi$
$588$	−16.5252	−0.681488
$589$	8.69339	0.358205
$590$	−24.9736	−1.02815
$591$	56.6174	2.32893
$592$	8.09170	0.332567
$593$	−13.6203	−0.559319	−0.279660	−	0.960099i	$-0.590222\pi$
$593$	−13.6203	−0.559319	−0.279660	+	0.960099i	$0.590222\pi$
$594$	−0.226150	−0.00927907
$595$	58.7110	2.40692
$596$	−6.83042	−0.279785
$597$	−35.1099	−1.43695
$598$	12.9771	0.530671
$599$	12.9535	0.529265	0.264633	−	0.964349i	$-0.414749\pi$
$599$	12.9535	0.529265	0.264633	+	0.964349i	$0.414749\pi$
$600$	0.127386	0.00520053
$601$	−35.8466	−1.46221	−0.731106	−	0.682264i	$-0.760996\pi$
$601$	−35.8466	−1.46221	−0.731106	+	0.682264i	$0.760996\pi$
$602$	0.361739	0.0147434
$603$	−40.4964	−1.64914
$604$	22.6048	0.919778
$605$	−0.928079	−0.0377318
$606$	16.5982	0.674256
$607$	−24.5320	−0.995725	−0.497862	−	0.867256i	$-0.665882\pi$
$607$	−24.5320	−0.995725	−0.497862	+	0.867256i	$0.665882\pi$
$608$	1.25786	0.0510131
$609$	79.1526	3.20742
$610$	−31.7760	−1.28657
$611$	−19.9308	−0.806314
$612$	−21.1420	−0.854614
$613$	5.17266	0.208922	0.104461	−	0.994529i	$-0.466688\pi$
$613$	5.17266	0.208922	0.104461	+	0.994529i	$0.466688\pi$
$614$	−17.1581	−0.692446
$615$	14.0170	0.565222
$616$	12.0683	0.486247
$617$	3.94381	0.158772	0.0793860	−	0.996844i	$-0.474704\pi$
$617$	3.94381	0.158772	0.0793860	+	0.996844i	$0.474704\pi$
$618$	12.1821	0.490037
$619$	29.6170	1.19041	0.595204	−	0.803575i	$-0.297071\pi$
$619$	29.6170	1.19041	0.595204	+	0.803575i	$0.297071\pi$
$620$	15.3732	0.617403
$621$	0.309400	0.0124158
$622$	−14.0060	−0.561589
$623$	−50.3802	−2.01844
$624$	−7.12522	−0.285237
$625$	−24.7366	−0.989466
$626$	0.435482	0.0174053
$627$	9.99947	0.399340
$628$	−10.6645	−0.425558
$629$	−57.5708	−2.29550
$630$	−24.5211	−0.976944
$631$	−27.5244	−1.09573	−0.547865	−	0.836567i	$-0.684559\pi$
$631$	−27.5244	−1.09573	−0.547865	+	0.836567i	$0.684559\pi$
$632$	6.04642	0.240514
$633$	40.7737	1.62061
$634$	23.8380	0.946727
$635$	33.3066	1.32173
$636$	−28.3135	−1.12270
$637$	19.7178	0.781246
$638$	−28.4036	−1.12451
$639$	−48.0557	−1.90105
$640$	2.22438	0.0879264
$641$	24.0727	0.950813	0.475407	−	0.879766i	$-0.342301\pi$
$641$	24.0727	0.950813	0.475407	+	0.879766i	$0.342301\pi$
$642$	33.6439	1.32782
$643$	29.0226	1.14454	0.572270	−	0.820065i	$-0.306063\pi$
$643$	29.0226	1.14454	0.572270	+	0.820065i	$0.306063\pi$
$644$	−16.5109	−0.650619
$645$	0.530030	0.0208699
$646$	−8.94945	−0.352111
$647$	3.66375	0.144037	0.0720185	−	0.997403i	$-0.477056\pi$
$647$	3.66375	0.144037	0.0720185	+	0.997403i	$0.477056\pi$
$648$	−9.08454	−0.356874
$649$	36.5235	1.43367
$650$	−0.151997	−0.00596179
$651$	62.6537	2.45559
$652$	−16.2325	−0.635713
$653$	−1.74913	−0.0684488	−0.0342244	−	0.999414i	$-0.510896\pi$
$653$	−1.74913	−0.0684488	−0.0342244	+	0.999414i	$0.510896\pi$
$654$	−37.4740	−1.46535
$655$	17.6514	0.689696
$656$	−2.57872	−0.100682
$657$	−0.627430	−0.0244784
$658$	25.3582	0.988565
$659$	3.45920	0.134751	0.0673756	−	0.997728i	$-0.478537\pi$
$659$	3.45920	0.134751	0.0673756	+	0.997728i	$0.478537\pi$
$660$	17.6829	0.688304
$661$	35.7136	1.38910	0.694550	−	0.719445i	$-0.255604\pi$
$661$	35.7136	1.38910	0.694550	+	0.719445i	$0.255604\pi$
$662$	−9.98961	−0.388257
$663$	50.6945	1.96881
$664$	−10.9278	−0.424081
$665$	−10.3798	−0.402513
$666$	24.0449	0.931721
$667$	38.8593	1.50464
$668$	−18.7635	−0.725982
$669$	−10.1396	−0.392018
$670$	−30.3139	−1.17113
$671$	46.4718	1.79402
$672$	9.06549	0.349709
$673$	3.35020	0.129141	0.0645703	−	0.997913i	$-0.479432\pi$
$673$	3.35020	0.129141	0.0645703	+	0.997913i	$0.479432\pi$
$674$	−24.3987	−0.939802
$675$	−0.00362391	−0.000139484 0
$676$	−4.49824	−0.173009
$677$	24.3330	0.935193	0.467596	−	0.883942i	$-0.345120\pi$
$677$	24.3330	0.935193	0.467596	+	0.883942i	$0.345120\pi$
$678$	39.5684	1.51962
$679$	−22.1071	−0.848393
$680$	−15.8260	−0.606900
$681$	19.9446	0.764279
$682$	−22.4831	−0.860921
$683$	5.77260	0.220882	0.110441	−	0.993883i	$-0.464774\pi$
$683$	5.77260	0.220882	0.110441	+	0.993883i	$0.464774\pi$
$684$	3.73781	0.142919
$685$	17.4099	0.665200
$686$	0.881307	0.0336485
$687$	−48.5300	−1.85153
$688$	−0.0975097	−0.00371752
$689$	33.7835	1.28705
$690$	−24.1922	−0.920980
$691$	−3.39881	−0.129297	−0.0646484	−	0.997908i	$-0.520593\pi$
$691$	−3.39881	−0.129297	−0.0646484	+	0.997908i	$0.520593\pi$
$692$	−13.3957	−0.509227
$693$	35.8617	1.36227
$694$	13.9044	0.527803
$695$	−5.33649	−0.202425
$696$	−21.3362	−0.808747
$697$	18.3470	0.694944
$698$	5.86275	0.221908
$699$	−27.6365	−1.04531
$700$	0.193387	0.00730934
$701$	12.9676	0.489780	0.244890	−	0.969551i	$-0.421248\pi$
$701$	12.9676	0.489780	0.244890	+	0.969551i	$0.421248\pi$
$702$	0.202699	0.00765039
$703$	10.1783	0.383880
$704$	−3.25312	−0.122606
$705$	37.1555	1.39936
$706$	25.5418	0.961278
$707$	25.1979	0.947666
$708$	27.4357	1.03110
$709$	18.9456	0.711515	0.355758	−	0.934578i	$-0.384223\pi$
$709$	18.9456	0.711515	0.355758	+	0.934578i	$0.384223\pi$
$710$	−35.9725	−1.35002
$711$	17.9673	0.673825
$712$	13.5804	0.508947
$713$	30.7594	1.15195
$714$	−64.4991	−2.41382
$715$	−21.0991	−0.789060
$716$	3.12550	0.116805
$717$	26.3223	0.983024
$718$	0.0397099	0.00148196
$719$	38.7639	1.44565	0.722826	−	0.691030i	$-0.242843\pi$
$719$	38.7639	1.44565	0.722826	+	0.691030i	$0.242843\pi$
$720$	6.60986	0.246335
$721$	18.4938	0.688747
$722$	−17.4178	−0.648223
$723$	23.7805	0.884406
$724$	−15.3402	−0.570113
$725$	−0.455148	−0.0169038
$726$	1.01958	0.0378400
$727$	−51.6338	−1.91499	−0.957495	−	0.288449i	$-0.906860\pi$
$727$	−51.6338	−1.91499	−0.957495	+	0.288449i	$0.906860\pi$
$728$	−10.8169	−0.400900
$729$	−26.4855	−0.980945
$730$	−0.469668	−0.0173832
$731$	0.693762	0.0256597
$732$	34.9087	1.29026
$733$	−48.4497	−1.78953	−0.894765	−	0.446537i	$-0.852657\pi$
$733$	−48.4497	−1.78953	−0.894765	+	0.446537i	$0.852657\pi$
$734$	8.48536	0.313200
$735$	−36.7583	−1.35585
$736$	4.45063	0.164053
$737$	44.3336	1.63305
$738$	−7.66279	−0.282071
$739$	−0.168357	−0.00619312	−0.00309656	−	0.999995i	$-0.500986\pi$
$739$	−0.168357	−0.00619312	−0.00309656	+	0.999995i	$0.500986\pi$
$740$	17.9990	0.661657
$741$	−8.96255	−0.329248
$742$	−42.9831	−1.57796
$743$	34.5393	1.26712	0.633561	−	0.773692i	$-0.281592\pi$
$743$	34.5393	1.26712	0.633561	+	0.773692i	$0.281592\pi$
$744$	−16.8888	−0.619174
$745$	−15.1935	−0.556646
$746$	6.71091	0.245704
$747$	−32.4726	−1.18811
$748$	23.1453	0.846275
$749$	51.0753	1.86625
$750$	27.4617	1.00276
$751$	−13.0979	−0.477951	−0.238975	−	0.971026i	$-0.576812\pi$
$751$	−13.0979	−0.477951	−0.238975	+	0.971026i	$0.576812\pi$
$752$	−6.83550	−0.249265
$753$	−17.3788	−0.633320
$754$	25.4582	0.927134
$755$	50.2818	1.82994
$756$	−0.257897	−0.00937961
$757$	49.3186	1.79251	0.896257	−	0.443535i	$-0.146276\pi$
$757$	49.3186	1.79251	0.896257	+	0.443535i	$0.146276\pi$
$758$	28.4000	1.03153
$759$	35.3806	1.28423
$760$	2.79797	0.101493
$761$	5.35698	0.194191	0.0970953	−	0.995275i	$-0.469045\pi$
$761$	5.35698	0.194191	0.0970953	+	0.995275i	$0.469045\pi$
$762$	−36.5902	−1.32552
$763$	−56.8897	−2.05955
$764$	−1.12631	−0.0407486
$765$	−47.0278	−1.70029
$766$	−34.4357	−1.24421
$767$	−32.7361	−1.18203
$768$	−2.44368	−0.0881786
$769$	−28.9325	−1.04333	−0.521666	−	0.853150i	$-0.674689\pi$
$769$	−28.9325	−1.04333	−0.521666	+	0.853150i	$0.674689\pi$
$770$	26.8446	0.967411
$771$	−11.6209	−0.418517
$772$	−6.64460	−0.239144
$773$	−24.3998	−0.877599	−0.438800	−	0.898585i	$-0.644596\pi$
$773$	−24.3998	−0.877599	−0.438800	+	0.898585i	$0.644596\pi$
$774$	−0.289755	−0.0104150
$775$	−0.360276	−0.0129415
$776$	5.95915	0.213921
$777$	73.3552	2.63160
$778$	−17.3602	−0.622393
$779$	−3.24368	−0.116217
$780$	−15.8492	−0.567492
$781$	52.6091	1.88250
$782$	−31.6654	−1.13235
$783$	0.606976	0.0216916
$784$	6.76244	0.241516
$785$	−23.7218	−0.846668
$786$	−19.3916	−0.691674
$787$	−31.2715	−1.11471	−0.557354	−	0.830275i	$-0.688183\pi$
$787$	−31.2715	−1.11471	−0.557354	+	0.830275i	$0.688183\pi$
$788$	−23.1689	−0.825359
$789$	8.56849	0.305046
$790$	13.4496	0.478514
$791$	60.0693	2.13582
$792$	−9.66681	−0.343495
$793$	−41.6528	−1.47913
$794$	−9.40968	−0.333937
$795$	−62.9800	−2.23367
$796$	14.3676	0.509248
$797$	−41.5471	−1.47167	−0.735837	−	0.677159i	$-0.763211\pi$
$797$	−41.5471	−1.47167	−0.735837	+	0.677159i	$0.763211\pi$
$798$	11.4032	0.403667
$799$	48.6332	1.72052
$800$	−0.0521290	−0.00184304
$801$	40.3548	1.42587
$802$	−25.3090	−0.893692
$803$	0.686882	0.0242395
$804$	33.3025	1.17449
$805$	−36.7264	−1.29444
$806$	20.1516	0.709811
$807$	35.9118	1.26416
$808$	−6.79231	−0.238953
$809$	−20.3306	−0.714786	−0.357393	−	0.933954i	$-0.616334\pi$
$809$	−20.3306	−0.714786	−0.357393	+	0.933954i	$0.616334\pi$
$810$	−20.2075	−0.710018
$811$	30.8822	1.08442	0.542211	−	0.840243i	$-0.317587\pi$
$811$	30.8822	1.08442	0.542211	+	0.840243i	$0.317587\pi$
$812$	−32.3908	−1.13669
$813$	34.2675	1.20182
$814$	−26.3232	−0.922629
$815$	−36.1073	−1.26478
$816$	17.3863	0.608641
$817$	−0.122654	−0.00429112
$818$	−34.6128	−1.21021
$819$	−32.1429	−1.12316
$820$	−5.73605	−0.200312
$821$	0.759691	0.0265134	0.0132567	−	0.999912i	$-0.495780\pi$
$821$	0.759691	0.0265134	0.0132567	+	0.999912i	$0.495780\pi$
$822$	−19.1263	−0.667107
$823$	−38.5882	−1.34510	−0.672550	−	0.740051i	$-0.734801\pi$
$823$	−38.5882	−1.34510	−0.672550	+	0.740051i	$0.734801\pi$
$824$	−4.98516	−0.173666
$825$	−0.414403	−0.0144277
$826$	41.6505	1.44921
$827$	−8.65662	−0.301020	−0.150510	−	0.988608i	$-0.548092\pi$
$827$	−8.65662	−0.301020	−0.150510	+	0.988608i	$0.548092\pi$
$828$	13.2253	0.459611
$829$	27.3836	0.951071	0.475536	−	0.879696i	$-0.342254\pi$
$829$	27.3836	0.951071	0.475536	+	0.879696i	$0.342254\pi$
$830$	−24.3076	−0.843729
$831$	41.9422	1.45496
$832$	2.91578	0.101086
$833$	−48.1134	−1.66703
$834$	5.86260	0.203005
$835$	−41.7372	−1.44437
$836$	−4.09198	−0.141524
$837$	0.480456	0.0166070
$838$	16.5466	0.571594
$839$	−30.7830	−1.06275	−0.531373	−	0.847138i	$-0.678324\pi$
$839$	−30.7830	−1.06275	−0.531373	+	0.847138i	$0.678324\pi$
$840$	20.1651	0.695762
$841$	47.2338	1.62875
$842$	−37.3580	−1.28744
$843$	−24.1892	−0.833120
$844$	−16.6854	−0.574335
$845$	−10.0058	−0.344210
$846$	−20.3121	−0.698343
$847$	1.54783	0.0531841
$848$	11.5864	0.397880
$849$	−48.9580	−1.68023
$850$	0.370887	0.0127213
$851$	36.0132	1.23452
$852$	39.5189	1.35390
$853$	21.3492	0.730984	0.365492	−	0.930815i	$-0.380901\pi$
$853$	21.3492	0.730984	0.365492	+	0.930815i	$0.380901\pi$
$854$	52.9953	1.81346
$855$	8.31431	0.284343
$856$	−13.7678	−0.470572
$857$	38.8087	1.32568	0.662840	−	0.748761i	$-0.269351\pi$
$857$	38.8087	1.32568	0.662840	+	0.748761i	$0.269351\pi$
$858$	23.1792	0.791323
$859$	−37.3625	−1.27479	−0.637397	−	0.770536i	$-0.719989\pi$
$859$	−37.3625	−1.27479	−0.637397	+	0.770536i	$0.719989\pi$
$860$	−0.216899	−0.00739619
$861$	−23.3773	−0.796697
$862$	−1.37686	−0.0468959
$863$	−43.1377	−1.46842	−0.734212	−	0.678920i	$-0.762448\pi$
$863$	−43.1377	−1.46842	−0.734212	+	0.678920i	$0.762448\pi$
$864$	0.0695181	0.00236505
$865$	−29.7971	−1.01313
$866$	24.4390	0.830471
$867$	−82.1572	−2.79020
$868$	−25.6391	−0.870249
$869$	−19.6697	−0.667250
$870$	−47.4599	−1.60904
$871$	−39.7363	−1.34641
$872$	15.3351	0.519311
$873$	17.7079	0.599322
$874$	5.59829	0.189365
$875$	41.6899	1.40938
$876$	0.515972	0.0174331
$877$	18.6794	0.630758	0.315379	−	0.948966i	$-0.397868\pi$
$877$	18.6794	0.630758	0.315379	+	0.948966i	$0.397868\pi$
$878$	−7.12686	−0.240520
$879$	13.1067	0.442076
$880$	−7.23617	−0.243931
$881$	−39.4639	−1.32957	−0.664786	−	0.747034i	$-0.731477\pi$
$881$	−39.4639	−1.32957	−0.664786	+	0.747034i	$0.731477\pi$
$882$	20.0949	0.676632
$883$	39.6310	1.33369	0.666845	−	0.745196i	$-0.267644\pi$
$883$	39.6310	1.33369	0.666845	+	0.745196i	$0.267644\pi$
$884$	−20.7452	−0.697735
$885$	61.0274	2.05142
$886$	−15.7642	−0.529609
$887$	10.0173	0.336347	0.168173	−	0.985757i	$-0.446213\pi$
$887$	10.0173	0.336347	0.168173	+	0.985757i	$0.446213\pi$
$888$	−19.7735	−0.663555
$889$	−55.5480	−1.86302
$890$	30.2080	1.01257
$891$	29.5531	0.990065
$892$	4.14931	0.138929
$893$	−8.59813	−0.287726
$894$	16.6913	0.558242
$895$	6.95230	0.232390
$896$	−3.70978	−0.123935
$897$	−31.7117	−1.05882
$898$	26.5711	0.886689
$899$	60.3433	2.01256
$900$	−0.154904	−0.00516347
$901$	−82.4352	−2.74631
$902$	8.38887	0.279319
$903$	−0.883973	−0.0294168
$904$	−16.1922	−0.538543
$905$	−34.1224	−1.13427
$906$	−55.2389	−1.83519
$907$	−41.8012	−1.38799	−0.693993	−	0.719982i	$-0.744150\pi$
$907$	−41.8012	−1.38799	−0.693993	+	0.719982i	$0.744150\pi$
$908$	−8.16173	−0.270856
$909$	−20.1837	−0.669451
$910$	−24.0609	−0.797610
$911$	44.8543	1.48609	0.743045	−	0.669241i	$-0.233381\pi$
$911$	44.8543	1.48609	0.743045	+	0.669241i	$0.233381\pi$
$912$	−3.07381	−0.101784
$913$	35.5494	1.17651
$914$	10.9605	0.362542
$915$	77.6502	2.56704
$916$	19.8594	0.656173
$917$	−29.4386	−0.972147
$918$	−0.494607	−0.0163245
$919$	5.87657	0.193850	0.0969250	−	0.995292i	$-0.469099\pi$
$919$	5.87657	0.193850	0.0969250	+	0.995292i	$0.469099\pi$
$920$	9.89991	0.326390
$921$	41.9289	1.38161
$922$	9.41129	0.309944
$923$	−47.1537	−1.55208
$924$	−29.4911	−0.970186
$925$	−0.421812	−0.0138691
$926$	−7.98331	−0.262348
$927$	−14.8137	−0.486545
$928$	8.73119	0.286615
$929$	−33.9815	−1.11490	−0.557448	−	0.830212i	$-0.688219\pi$
$929$	−33.9815	−1.11490	−0.557448	+	0.830212i	$0.688219\pi$
$930$	−37.5672	−1.23188
$931$	8.50623	0.278780
$932$	11.3094	0.370452
$933$	34.2261	1.12051
$934$	−41.3887	−1.35428
$935$	51.4839	1.68370
$936$	8.66438	0.283204
$937$	−31.4515	−1.02747	−0.513737	−	0.857947i	$-0.671739\pi$
$937$	−31.4515	−1.02747	−0.513737	+	0.857947i	$0.671739\pi$
$938$	50.5569	1.65074
$939$	−1.06418	−0.0347281
$940$	−15.2048	−0.495925
$941$	−12.2224	−0.398440	−0.199220	−	0.979955i	$-0.563841\pi$
$941$	−12.2224	−0.398440	−0.199220	+	0.979955i	$0.563841\pi$
$942$	26.0605	0.849096
$943$	−11.4769	−0.373740
$944$	−11.2272	−0.365415
$945$	−0.573660	−0.0186612
$946$	0.317211	0.0103134
$947$	−25.9450	−0.843100	−0.421550	−	0.906805i	$-0.638514\pi$
$947$	−25.9450	−0.843100	−0.421550	+	0.906805i	$0.638514\pi$
$948$	−14.7755	−0.479886
$949$	−0.615654	−0.0199850
$950$	−0.0655712	−0.00212741
$951$	−58.2523	−1.88896
$952$	26.3943	0.855444
$953$	−29.4691	−0.954598	−0.477299	−	0.878741i	$-0.658384\pi$
$953$	−29.4691	−0.954598	−0.477299	+	0.878741i	$0.658384\pi$
$954$	34.4297	1.11470
$955$	−2.50535	−0.0810713
$956$	−10.7716	−0.348378
$957$	69.4092	2.24368
$958$	21.6848	0.700604
$959$	−29.0359	−0.937619
$960$	−5.43567	−0.175435
$961$	16.7652	0.540812
$962$	23.5936	0.760688
$963$	−40.9116	−1.31836
$964$	−9.73144	−0.313429
$965$	−14.7801	−0.475789
$966$	40.3472	1.29815
$967$	−7.01448	−0.225571	−0.112785	−	0.993619i	$-0.535977\pi$
$967$	−7.01448	−0.225571	−0.112785	+	0.993619i	$0.535977\pi$
$968$	−0.417230	−0.0134103
$969$	21.8695	0.702551
$970$	13.2554	0.425606
$971$	50.7801	1.62961	0.814805	−	0.579735i	$-0.196844\pi$
$971$	50.7801	1.62961	0.814805	+	0.579735i	$0.196844\pi$
$972$	21.9911	0.705365
$973$	8.90008	0.285324
$974$	−29.9367	−0.959234
$975$	0.371430	0.0118953
$976$	−14.2853	−0.457262
$977$	18.6514	0.596712	0.298356	−	0.954455i	$-0.403562\pi$
$977$	18.6514	0.596712	0.298356	+	0.954455i	$0.403562\pi$
$978$	39.6670	1.26841
$979$	−44.1786	−1.41195
$980$	15.0422	0.480507
$981$	45.5690	1.45491
$982$	11.7819	0.375977
$983$	−8.39074	−0.267623	−0.133812	−	0.991007i	$-0.542722\pi$
$983$	−8.39074	−0.267623	−0.133812	+	0.991007i	$0.542722\pi$
$984$	6.30155	0.200886
$985$	−51.5365	−1.64209
$986$	−62.1207	−1.97833
$987$	−61.9672	−1.97244
$988$	3.66765	0.116684
$989$	−0.433980	−0.0137998
$990$	−21.5027	−0.683399
$991$	48.2709	1.53337	0.766687	−	0.642021i	$-0.221904\pi$
$991$	48.2709	1.53337	0.766687	+	0.642021i	$0.221904\pi$
$992$	6.91124	0.219432
$993$	24.4114	0.774671
$994$	59.9942	1.90290
$995$	31.9591	1.01317
$996$	26.7040	0.846149
$997$	−41.2770	−1.30725	−0.653627	−	0.756817i	$-0.726754\pi$
$997$	−41.2770	−1.30725	−0.653627	+	0.756817i	$0.726754\pi$
$998$	24.0080	0.759959
$999$	0.562519	0.0177973

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.b.1.11	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.b.1.11	✓	54	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.44368 q^{3} +1.00000 q^{4} +2.22438 q^{5} -2.44368 q^{6} -3.70978 q^{7} +1.00000 q^{8} +2.97155 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.44368 q^{3} +1.00000 q^{4} +2.22438 q^{5} -2.44368 q^{6} -3.70978 q^{7} +1.00000 q^{8} +2.97155 q^{9} +2.22438 q^{10} -3.25312 q^{11} -2.44368 q^{12} +2.91578 q^{13} -3.70978 q^{14} -5.43567 q^{15} +1.00000 q^{16} -7.11480 q^{17} +2.97155 q^{18} +1.25786 q^{19} +2.22438 q^{20} +9.06549 q^{21} -3.25312 q^{22} +4.45063 q^{23} -2.44368 q^{24} -0.0521290 q^{25} +2.91578 q^{26} +0.0695181 q^{27} -3.70978 q^{28} +8.73119 q^{29} -5.43567 q^{30} +6.91124 q^{31} +1.00000 q^{32} +7.94956 q^{33} -7.11480 q^{34} -8.25195 q^{35} +2.97155 q^{36} +8.09170 q^{37} +1.25786 q^{38} -7.12522 q^{39} +2.22438 q^{40} -2.57872 q^{41} +9.06549 q^{42} -0.0975097 q^{43} -3.25312 q^{44} +6.60986 q^{45} +4.45063 q^{46} -6.83550 q^{47} -2.44368 q^{48} +6.76244 q^{49} -0.0521290 q^{50} +17.3863 q^{51} +2.91578 q^{52} +11.5864 q^{53} +0.0695181 q^{54} -7.23617 q^{55} -3.70978 q^{56} -3.07381 q^{57} +8.73119 q^{58} -11.2272 q^{59} -5.43567 q^{60} -14.2853 q^{61} +6.91124 q^{62} -11.0238 q^{63} +1.00000 q^{64} +6.48580 q^{65} +7.94956 q^{66} -13.6280 q^{67} -7.11480 q^{68} -10.8759 q^{69} -8.25195 q^{70} -16.1719 q^{71} +2.97155 q^{72} -0.211146 q^{73} +8.09170 q^{74} +0.127386 q^{75} +1.25786 q^{76} +12.0683 q^{77} -7.12522 q^{78} +6.04642 q^{79} +2.22438 q^{80} -9.08454 q^{81} -2.57872 q^{82} -10.9278 q^{83} +9.06549 q^{84} -15.8260 q^{85} -0.0975097 q^{86} -21.3362 q^{87} -3.25312 q^{88} +13.5804 q^{89} +6.60986 q^{90} -10.8169 q^{91} +4.45063 q^{92} -16.8888 q^{93} -6.83550 q^{94} +2.79797 q^{95} -2.44368 q^{96} +5.95915 q^{97} +6.76244 q^{98} -9.66681 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9}+O(q^{10}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9} - 14 q^{10} - 22 q^{11} - 22 q^{12} - 24 q^{13} - 20 q^{14} - 32 q^{15} + 54 q^{16} - 67 q^{17} + 32 q^{18} - 54 q^{19} - 14 q^{20} - 18 q^{21} - 22 q^{22} - 52 q^{23} - 22 q^{24} + 20 q^{25} - 24 q^{26} - 82 q^{27} - 20 q^{28} - 30 q^{29} - 32 q^{30} - 78 q^{31} + 54 q^{32} - 48 q^{33} - 67 q^{34} - 71 q^{35} + 32 q^{36} - 15 q^{37} - 54 q^{38} - 39 q^{39} - 14 q^{40} - 61 q^{41} - 18 q^{42} - 53 q^{43} - 22 q^{44} - 14 q^{45} - 52 q^{46} - 96 q^{47} - 22 q^{48} + 6 q^{49} + 20 q^{50} - 13 q^{51} - 24 q^{52} - 39 q^{53} - 82 q^{54} - 75 q^{55} - 20 q^{56} - 17 q^{57} - 30 q^{58} - 78 q^{59} - 32 q^{60} - 23 q^{61} - 78 q^{62} - 52 q^{63} + 54 q^{64} - 43 q^{65} - 48 q^{66} - 54 q^{67} - 67 q^{68} + 7 q^{69} - 71 q^{70} - 41 q^{71} + 32 q^{72} - 62 q^{73} - 15 q^{74} - 81 q^{75} - 54 q^{76} - 85 q^{77} - 39 q^{78} - 45 q^{79} - 14 q^{80} + 22 q^{81} - 61 q^{82} - 117 q^{83} - 18 q^{84} - 53 q^{86} - 84 q^{87} - 22 q^{88} - 60 q^{89} - 14 q^{90} - 60 q^{91} - 52 q^{92} + 26 q^{93} - 96 q^{94} - 44 q^{95} - 22 q^{96} - 48 q^{97} + 6 q^{98} + 7 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9 - 14 * q^10 - 22 * q^11 - 22 * q^12 - 24 * q^13 - 20 * q^14 - 32 * q^15 + 54 * q^16 - 67 * q^17 + 32 * q^18 - 54 * q^19 - 14 * q^20 - 18 * q^21 - 22 * q^22 - 52 * q^23 - 22 * q^24 + 20 * q^25 - 24 * q^26 - 82 * q^27 - 20 * q^28 - 30 * q^29 - 32 * q^30 - 78 * q^31 + 54 * q^32 - 48 * q^33 - 67 * q^34 - 71 * q^35 + 32 * q^36 - 15 * q^37 - 54 * q^38 - 39 * q^39 - 14 * q^40 - 61 * q^41 - 18 * q^42 - 53 * q^43 - 22 * q^44 - 14 * q^45 - 52 * q^46 - 96 * q^47 - 22 * q^48 + 6 * q^49 + 20 * q^50 - 13 * q^51 - 24 * q^52 - 39 * q^53 - 82 * q^54 - 75 * q^55 - 20 * q^56 - 17 * q^57 - 30 * q^58 - 78 * q^59 - 32 * q^60 - 23 * q^61 - 78 * q^62 - 52 * q^63 + 54 * q^64 - 43 * q^65 - 48 * q^66 - 54 * q^67 - 67 * q^68 + 7 * q^69 - 71 * q^70 - 41 * q^71 + 32 * q^72 - 62 * q^73 - 15 * q^74 - 81 * q^75 - 54 * q^76 - 85 * q^77 - 39 * q^78 - 45 * q^79 - 14 * q^80 + 22 * q^81 - 61 * q^82 - 117 * q^83 - 18 * q^84 - 53 * q^86 - 84 * q^87 - 22 * q^88 - 60 * q^89 - 14 * q^90 - 60 * q^91 - 52 * q^92 + 26 * q^93 - 96 * q^94 - 44 * q^95 - 22 * q^96 - 48 * q^97 + 6 * q^98 + 7 * q^99

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