LMFDB - Embedded newform 6038.2.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6038,2,Mod(1,6038)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6038, 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("6038.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6038 = 2 \cdot 3019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6038.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:	$48.2136727404$
Analytic rank:	$1$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6038.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.27315 q^{3} +1.00000 q^{4} -2.64091 q^{5} -2.27315 q^{6} +0.657447 q^{7} +1.00000 q^{8} +2.16722 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.27315 q^{3} +1.00000 q^{4} -2.64091 q^{5} -2.27315 q^{6} +0.657447 q^{7} +1.00000 q^{8} +2.16722 q^{9} -2.64091 q^{10} +1.55337 q^{11} -2.27315 q^{12} -1.82768 q^{13} +0.657447 q^{14} +6.00320 q^{15} +1.00000 q^{16} -1.72736 q^{17} +2.16722 q^{18} -5.42951 q^{19} -2.64091 q^{20} -1.49448 q^{21} +1.55337 q^{22} +8.39759 q^{23} -2.27315 q^{24} +1.97443 q^{25} -1.82768 q^{26} +1.89303 q^{27} +0.657447 q^{28} -1.74099 q^{29} +6.00320 q^{30} +3.57279 q^{31} +1.00000 q^{32} -3.53105 q^{33} -1.72736 q^{34} -1.73626 q^{35} +2.16722 q^{36} +6.12228 q^{37} -5.42951 q^{38} +4.15459 q^{39} -2.64091 q^{40} -3.44609 q^{41} -1.49448 q^{42} +6.18853 q^{43} +1.55337 q^{44} -5.72345 q^{45} +8.39759 q^{46} -4.64596 q^{47} -2.27315 q^{48} -6.56776 q^{49} +1.97443 q^{50} +3.92655 q^{51} -1.82768 q^{52} +7.12897 q^{53} +1.89303 q^{54} -4.10232 q^{55} +0.657447 q^{56} +12.3421 q^{57} -1.74099 q^{58} +3.41618 q^{59} +6.00320 q^{60} -4.62524 q^{61} +3.57279 q^{62} +1.42484 q^{63} +1.00000 q^{64} +4.82674 q^{65} -3.53105 q^{66} +6.31396 q^{67} -1.72736 q^{68} -19.0890 q^{69} -1.73626 q^{70} -13.5701 q^{71} +2.16722 q^{72} -1.03519 q^{73} +6.12228 q^{74} -4.48818 q^{75} -5.42951 q^{76} +1.02126 q^{77} +4.15459 q^{78} +3.92954 q^{79} -2.64091 q^{80} -10.8048 q^{81} -3.44609 q^{82} +2.25995 q^{83} -1.49448 q^{84} +4.56181 q^{85} +6.18853 q^{86} +3.95755 q^{87} +1.55337 q^{88} -1.61639 q^{89} -5.72345 q^{90} -1.20160 q^{91} +8.39759 q^{92} -8.12150 q^{93} -4.64596 q^{94} +14.3389 q^{95} -2.27315 q^{96} -0.598127 q^{97} -6.56776 q^{98} +3.36651 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 54 q^{2} - 21 q^{3} + 54 q^{4} - 14 q^{5} - 21 q^{6} - 44 q^{7} + 54 q^{8} + 39 q^{9}+O(q^{10}) $ 54 * q + 54 * q^2 - 21 * q^3 + 54 * q^4 - 14 * q^5 - 21 * q^6 - 44 * q^7 + 54 * q^8 + 39 * q^9	\( 54 q + 54 q^{2} - 21 q^{3} + 54 q^{4} - 14 q^{5} - 21 q^{6} - 44 q^{7} + 54 q^{8} + 39 q^{9} - 14 q^{10} - 31 q^{11} - 21 q^{12} - 34 q^{13} - 44 q^{14} - 22 q^{15} + 54 q^{16} - 40 q^{17} + 39 q^{18} - 44 q^{19} - 14 q^{20} - 3 q^{21} - 31 q^{22} - 33 q^{23} - 21 q^{24} + 14 q^{25} - 34 q^{26} - 66 q^{27} - 44 q^{28} - 22 q^{30} - 65 q^{31} + 54 q^{32} - 43 q^{33} - 40 q^{34} - 46 q^{35} + 39 q^{36} - 58 q^{37} - 44 q^{38} - 36 q^{39} - 14 q^{40} - 49 q^{41} - 3 q^{42} - 47 q^{43} - 31 q^{44} - 45 q^{45} - 33 q^{46} - 66 q^{47} - 21 q^{48} + 16 q^{49} + 14 q^{50} - 33 q^{51} - 34 q^{52} - 16 q^{53} - 66 q^{54} - 50 q^{55} - 44 q^{56} - 33 q^{57} - 70 q^{59} - 22 q^{60} - 40 q^{61} - 65 q^{62} - 117 q^{63} + 54 q^{64} - 33 q^{65} - 43 q^{66} - 82 q^{67} - 40 q^{68} - q^{69} - 46 q^{70} - 60 q^{71} + 39 q^{72} - 92 q^{73} - 58 q^{74} - 68 q^{75} - 44 q^{76} + 13 q^{77} - 36 q^{78} - 57 q^{79} - 14 q^{80} + 26 q^{81} - 49 q^{82} - 77 q^{83} - 3 q^{84} - 24 q^{85} - 47 q^{86} - 61 q^{87} - 31 q^{88} - 54 q^{89} - 45 q^{90} - 46 q^{91} - 33 q^{92} - 24 q^{93} - 66 q^{94} - 66 q^{95} - 21 q^{96} - 137 q^{97} + 16 q^{98} - 71 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 21 * q^3 + 54 * q^4 - 14 * q^5 - 21 * q^6 - 44 * q^7 + 54 * q^8 + 39 * q^9 - 14 * q^10 - 31 * q^11 - 21 * q^12 - 34 * q^13 - 44 * q^14 - 22 * q^15 + 54 * q^16 - 40 * q^17 + 39 * q^18 - 44 * q^19 - 14 * q^20 - 3 * q^21 - 31 * q^22 - 33 * q^23 - 21 * q^24 + 14 * q^25 - 34 * q^26 - 66 * q^27 - 44 * q^28 - 22 * q^30 - 65 * q^31 + 54 * q^32 - 43 * q^33 - 40 * q^34 - 46 * q^35 + 39 * q^36 - 58 * q^37 - 44 * q^38 - 36 * q^39 - 14 * q^40 - 49 * q^41 - 3 * q^42 - 47 * q^43 - 31 * q^44 - 45 * q^45 - 33 * q^46 - 66 * q^47 - 21 * q^48 + 16 * q^49 + 14 * q^50 - 33 * q^51 - 34 * q^52 - 16 * q^53 - 66 * q^54 - 50 * q^55 - 44 * q^56 - 33 * q^57 - 70 * q^59 - 22 * q^60 - 40 * q^61 - 65 * q^62 - 117 * q^63 + 54 * q^64 - 33 * q^65 - 43 * q^66 - 82 * q^67 - 40 * q^68 - q^69 - 46 * q^70 - 60 * q^71 + 39 * q^72 - 92 * q^73 - 58 * q^74 - 68 * q^75 - 44 * q^76 + 13 * q^77 - 36 * q^78 - 57 * q^79 - 14 * q^80 + 26 * q^81 - 49 * q^82 - 77 * q^83 - 3 * q^84 - 24 * q^85 - 47 * q^86 - 61 * q^87 - 31 * q^88 - 54 * q^89 - 45 * q^90 - 46 * q^91 - 33 * q^92 - 24 * q^93 - 66 * q^94 - 66 * q^95 - 21 * q^96 - 137 * q^97 + 16 * q^98 - 71 * 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
$3$	−2.27315	−1.31241	−0.656203	−	0.754585i	$-0.727838\pi$
$3$	−2.27315	−1.31241	−0.656203	+	0.754585i	$0.727838\pi$
$4$	1.00000	0.500000
$5$	−2.64091	−1.18105	−0.590526	−	0.807018i	$-0.701080\pi$
$5$	−2.64091	−1.18105	−0.590526	+	0.807018i	$0.701080\pi$
$6$	−2.27315	−0.928011
$7$	0.657447	0.248492	0.124246	−	0.992251i	$-0.460349\pi$
$7$	0.657447	0.248492	0.124246	+	0.992251i	$0.460349\pi$
$8$	1.00000	0.353553
$9$	2.16722	0.722408
$10$	−2.64091	−0.835131
$11$	1.55337	0.468359	0.234180	−	0.972193i	$-0.424760\pi$
$11$	1.55337	0.468359	0.234180	+	0.972193i	$0.424760\pi$
$12$	−2.27315	−0.656203
$13$	−1.82768	−0.506907	−0.253454	−	0.967348i	$-0.581566\pi$
$13$	−1.82768	−0.506907	−0.253454	+	0.967348i	$0.581566\pi$
$14$	0.657447	0.175710
$15$	6.00320	1.55002
$16$	1.00000	0.250000
$17$	−1.72736	−0.418946	−0.209473	−	0.977814i	$-0.567175\pi$
$17$	−1.72736	−0.418946	−0.209473	+	0.977814i	$0.567175\pi$
$18$	2.16722	0.510820
$19$	−5.42951	−1.24562	−0.622808	−	0.782375i	$-0.714008\pi$
$19$	−5.42951	−1.24562	−0.622808	+	0.782375i	$0.714008\pi$
$20$	−2.64091	−0.590526
$21$	−1.49448	−0.326122
$22$	1.55337	0.331180
$23$	8.39759	1.75102	0.875509	−	0.483202i	$-0.160526\pi$
$23$	8.39759	1.75102	0.875509	+	0.483202i	$0.160526\pi$
$24$	−2.27315	−0.464005
$25$	1.97443	0.394886
$26$	−1.82768	−0.358437
$27$	1.89303	0.364313
$28$	0.657447	0.124246
$29$	−1.74099	−0.323295	−0.161647	−	0.986849i	$-0.551681\pi$
$29$	−1.74099	−0.323295	−0.161647	+	0.986849i	$0.551681\pi$
$30$	6.00320	1.09603
$31$	3.57279	0.641692	0.320846	−	0.947131i	$-0.396033\pi$
$31$	3.57279	0.641692	0.320846	+	0.947131i	$0.396033\pi$
$32$	1.00000	0.176777
$33$	−3.53105	−0.614677
$34$	−1.72736	−0.296240
$35$	−1.73626	−0.293482
$36$	2.16722	0.361204
$37$	6.12228	1.00650	0.503248	−	0.864142i	$-0.332138\pi$
$37$	6.12228	1.00650	0.503248	+	0.864142i	$0.332138\pi$
$38$	−5.42951	−0.880783
$39$	4.15459	0.665268
$40$	−2.64091	−0.417565
$41$	−3.44609	−0.538189	−0.269094	−	0.963114i	$-0.586724\pi$
$41$	−3.44609	−0.538189	−0.269094	+	0.963114i	$0.586724\pi$
$42$	−1.49448	−0.230603
$43$	6.18853	0.943742	0.471871	−	0.881668i	$-0.343579\pi$
$43$	6.18853	0.943742	0.471871	+	0.881668i	$0.343579\pi$
$44$	1.55337	0.234180
$45$	−5.72345	−0.853202
$46$	8.39759	1.23816
$47$	−4.64596	−0.677682	−0.338841	−	0.940844i	$-0.610035\pi$
$47$	−4.64596	−0.677682	−0.338841	+	0.940844i	$0.610035\pi$
$48$	−2.27315	−0.328101
$49$	−6.56776	−0.938252
$50$	1.97443	0.279227
$51$	3.92655	0.549828
$52$	−1.82768	−0.253454
$53$	7.12897	0.979239	0.489619	−	0.871936i	$-0.337136\pi$
$53$	7.12897	0.979239	0.489619	+	0.871936i	$0.337136\pi$
$54$	1.89303	0.257608
$55$	−4.10232	−0.553157
$56$	0.657447	0.0878551
$57$	12.3421	1.63475
$58$	−1.74099	−0.228604
$59$	3.41618	0.444748	0.222374	−	0.974961i	$-0.428619\pi$
$59$	3.41618	0.444748	0.222374	+	0.974961i	$0.428619\pi$
$60$	6.00320	0.775010
$61$	−4.62524	−0.592201	−0.296101	−	0.955157i	$-0.595686\pi$
$61$	−4.62524	−0.592201	−0.296101	+	0.955157i	$0.595686\pi$
$62$	3.57279	0.453745
$63$	1.42484	0.179512
$64$	1.00000	0.125000
$65$	4.82674	0.598684
$66$	−3.53105	−0.434642
$67$	6.31396	0.771373	0.385686	−	0.922630i	$-0.373965\pi$
$67$	6.31396	0.771373	0.385686	+	0.922630i	$0.373965\pi$
$68$	−1.72736	−0.209473
$69$	−19.0890	−2.29805
$70$	−1.73626	−0.207523
$71$	−13.5701	−1.61048	−0.805239	−	0.592950i	$-0.797963\pi$
$71$	−13.5701	−1.61048	−0.805239	+	0.592950i	$0.797963\pi$
$72$	2.16722	0.255410
$73$	−1.03519	−0.121160	−0.0605799	−	0.998163i	$-0.519295\pi$
$73$	−1.03519	−0.121160	−0.0605799	+	0.998163i	$0.519295\pi$
$74$	6.12228	0.711700
$75$	−4.48818	−0.518251
$76$	−5.42951	−0.622808
$77$	1.02126	0.116383
$78$	4.15459	0.470415
$79$	3.92954	0.442108	0.221054	−	0.975262i	$-0.429050\pi$
$79$	3.92954	0.442108	0.221054	+	0.975262i	$0.429050\pi$
$80$	−2.64091	−0.295263
$81$	−10.8048	−1.20053
$82$	−3.44609	−0.380557
$83$	2.25995	0.248062	0.124031	−	0.992278i	$-0.460418\pi$
$83$	2.25995	0.248062	0.124031	+	0.992278i	$0.460418\pi$
$84$	−1.49448	−0.163061
$85$	4.56181	0.494798
$86$	6.18853	0.667327
$87$	3.95755	0.424294
$88$	1.55337	0.165590
$89$	−1.61639	−0.171337	−0.0856684	−	0.996324i	$-0.527303\pi$
$89$	−1.61639	−0.171337	−0.0856684	+	0.996324i	$0.527303\pi$
$90$	−5.72345	−0.603305
$91$	−1.20160	−0.125962
$92$	8.39759	0.875509
$93$	−8.12150	−0.842161
$94$	−4.64596	−0.479194
$95$	14.3389	1.47114
$96$	−2.27315	−0.232003
$97$	−0.598127	−0.0607306	−0.0303653	−	0.999539i	$-0.509667\pi$
$97$	−0.598127	−0.0607306	−0.0303653	+	0.999539i	$0.509667\pi$
$98$	−6.56776	−0.663444
$99$	3.36651	0.338346
$100$	1.97443	0.197443
$101$	−10.9834	−1.09289	−0.546443	−	0.837496i	$-0.684019\pi$
$101$	−10.9834	−1.09289	−0.546443	+	0.837496i	$0.684019\pi$
$102$	3.92655	0.388787
$103$	6.81817	0.671814	0.335907	−	0.941895i	$-0.390957\pi$
$103$	6.81817	0.671814	0.335907	+	0.941895i	$0.390957\pi$
$104$	−1.82768	−0.179219
$105$	3.94679	0.385167
$106$	7.12897	0.692427
$107$	−2.77432	−0.268203	−0.134102	−	0.990968i	$-0.542815\pi$
$107$	−2.77432	−0.268203	−0.134102	+	0.990968i	$0.542815\pi$
$108$	1.89303	0.182157
$109$	5.81411	0.556891	0.278445	−	0.960452i	$-0.410181\pi$
$109$	5.81411	0.556891	0.278445	+	0.960452i	$0.410181\pi$
$110$	−4.10232	−0.391141
$111$	−13.9169	−1.32093
$112$	0.657447	0.0621229
$113$	10.0367	0.944172	0.472086	−	0.881553i	$-0.343501\pi$
$113$	10.0367	0.944172	0.472086	+	0.881553i	$0.343501\pi$
$114$	12.3421	1.15594
$115$	−22.1773	−2.06804
$116$	−1.74099	−0.161647
$117$	−3.96099	−0.366194
$118$	3.41618	0.314484
$119$	−1.13565	−0.104105
$120$	6.00320	0.548015
$121$	−8.58704	−0.780640
$122$	−4.62524	−0.418749
$123$	7.83349	0.706322
$124$	3.57279	0.320846
$125$	7.99027	0.714672
$126$	1.42484	0.126934
$127$	−13.9182	−1.23504	−0.617520	−	0.786555i	$-0.711863\pi$
$127$	−13.9182	−1.23504	−0.617520	+	0.786555i	$0.711863\pi$
$128$	1.00000	0.0883883
$129$	−14.0675	−1.23857
$130$	4.82674	0.423334
$131$	9.46225	0.826721	0.413360	−	0.910568i	$-0.364355\pi$
$131$	9.46225	0.826721	0.413360	+	0.910568i	$0.364355\pi$
$132$	−3.53105	−0.307339
$133$	−3.56962	−0.309525
$134$	6.31396	0.545443
$135$	−4.99932	−0.430273
$136$	−1.72736	−0.148120
$137$	−15.7641	−1.34682	−0.673409	−	0.739270i	$-0.735171\pi$
$137$	−15.7641	−1.34682	−0.673409	+	0.739270i	$0.735171\pi$
$138$	−19.0890	−1.62496
$139$	10.3790	0.880333	0.440166	−	0.897916i	$-0.354919\pi$
$139$	10.3790	0.880333	0.440166	+	0.897916i	$0.354919\pi$
$140$	−1.73626	−0.146741
$141$	10.5610	0.889394
$142$	−13.5701	−1.13878
$143$	−2.83907	−0.237415
$144$	2.16722	0.180602
$145$	4.59782	0.381828
$146$	−1.03519	−0.0856729
$147$	14.9295	1.23137
$148$	6.12228	0.503248
$149$	10.7806	0.883183	0.441591	−	0.897216i	$-0.354414\pi$
$149$	10.7806	0.883183	0.441591	+	0.897216i	$0.354414\pi$
$150$	−4.48818	−0.366458
$151$	−4.55943	−0.371041	−0.185520	−	0.982640i	$-0.559397\pi$
$151$	−4.55943	−0.371041	−0.185520	+	0.982640i	$0.559397\pi$
$152$	−5.42951	−0.440391
$153$	−3.74358	−0.302650
$154$	1.02126	0.0822955
$155$	−9.43544	−0.757873
$156$	4.15459	0.332634
$157$	2.28635	0.182471	0.0912355	−	0.995829i	$-0.470918\pi$
$157$	2.28635	0.182471	0.0912355	+	0.995829i	$0.470918\pi$
$158$	3.92954	0.312618
$159$	−16.2052	−1.28516
$160$	−2.64091	−0.208783
$161$	5.52097	0.435114
$162$	−10.8048	−0.848906
$163$	2.22381	0.174182	0.0870909	−	0.996200i	$-0.472243\pi$
$163$	2.22381	0.174182	0.0870909	+	0.996200i	$0.472243\pi$
$164$	−3.44609	−0.269094
$165$	9.32521	0.725966
$166$	2.25995	0.175406
$167$	−16.7518	−1.29629	−0.648145	−	0.761517i	$-0.724455\pi$
$167$	−16.7518	−1.29629	−0.648145	+	0.761517i	$0.724455\pi$
$168$	−1.49448	−0.115302
$169$	−9.65959	−0.743045
$170$	4.56181	0.349875
$171$	−11.7670	−0.899843
$172$	6.18853	0.471871
$173$	−23.8463	−1.81300	−0.906502	−	0.422202i	$-0.861257\pi$
$173$	−23.8463	−1.81300	−0.906502	+	0.422202i	$0.861257\pi$
$174$	3.95755	0.300021
$175$	1.29808	0.0981259
$176$	1.55337	0.117090
$177$	−7.76549	−0.583690
$178$	−1.61639	−0.121153
$179$	7.81216	0.583908	0.291954	−	0.956432i	$-0.405695\pi$
$179$	7.81216	0.583908	0.291954	+	0.956432i	$0.405695\pi$
$180$	−5.72345	−0.426601
$181$	6.10790	0.453997	0.226998	−	0.973895i	$-0.427109\pi$
$181$	6.10790	0.453997	0.226998	+	0.973895i	$0.427109\pi$
$182$	−1.20160	−0.0890687
$183$	10.5139	0.777208
$184$	8.39759	0.619078
$185$	−16.1684	−1.18873
$186$	−8.12150	−0.595497
$187$	−2.68323	−0.196217
$188$	−4.64596	−0.338841
$189$	1.24457	0.0905288
$190$	14.3389	1.04025
$191$	5.66168	0.409665	0.204832	−	0.978797i	$-0.434335\pi$
$191$	5.66168	0.409665	0.204832	+	0.978797i	$0.434335\pi$
$192$	−2.27315	−0.164051
$193$	−24.1444	−1.73795	−0.868977	−	0.494853i	$-0.835222\pi$
$193$	−24.1444	−1.73795	−0.868977	+	0.494853i	$0.835222\pi$
$194$	−0.598127	−0.0429430
$195$	−10.9719	−0.785716
$196$	−6.56776	−0.469126
$197$	16.9370	1.20671	0.603354	−	0.797474i	$-0.293831\pi$
$197$	16.9370	1.20671	0.603354	+	0.797474i	$0.293831\pi$
$198$	3.36651	0.239247
$199$	−15.3078	−1.08514	−0.542570	−	0.840010i	$-0.682549\pi$
$199$	−15.3078	−1.08514	−0.542570	+	0.840010i	$0.682549\pi$
$200$	1.97443	0.139613
$201$	−14.3526	−1.01235
$202$	−10.9834	−0.772788
$203$	−1.14461	−0.0803361
$204$	3.92655	0.274914
$205$	9.10083	0.635629
$206$	6.81817	0.475045
$207$	18.1995	1.26495
$208$	−1.82768	−0.126727
$209$	−8.43405	−0.583395
$210$	3.94679	0.272354
$211$	−15.7436	−1.08383	−0.541916	−	0.840433i	$-0.682301\pi$
$211$	−15.7436	−1.08383	−0.541916	+	0.840433i	$0.682301\pi$
$212$	7.12897	0.489619
$213$	30.8470	2.11360
$214$	−2.77432	−0.189648
$215$	−16.3434	−1.11461
$216$	1.89303	0.128804
$217$	2.34892	0.159455
$218$	5.81411	0.393781
$219$	2.35314	0.159011
$220$	−4.10232	−0.276578
$221$	3.15706	0.212367
$222$	−13.9169	−0.934040
$223$	−19.7260	−1.32095	−0.660477	−	0.750846i	$-0.729646\pi$
$223$	−19.7260	−1.32095	−0.660477	+	0.750846i	$0.729646\pi$
$224$	0.657447	0.0439276
$225$	4.27903	0.285269
$226$	10.0367	0.667630
$227$	8.78507	0.583085	0.291543	−	0.956558i	$-0.405831\pi$
$227$	8.78507	0.583085	0.291543	+	0.956558i	$0.405831\pi$
$228$	12.3421	0.817376
$229$	−21.2228	−1.40244	−0.701220	−	0.712945i	$-0.747361\pi$
$229$	−21.2228	−1.40244	−0.701220	+	0.712945i	$0.747361\pi$
$230$	−22.1773	−1.46233
$231$	−2.32148	−0.152742
$232$	−1.74099	−0.114302
$233$	1.64873	0.108012	0.0540061	−	0.998541i	$-0.482801\pi$
$233$	1.64873	0.108012	0.0540061	+	0.998541i	$0.482801\pi$
$234$	−3.96099	−0.258938
$235$	12.2696	0.800379
$236$	3.41618	0.222374
$237$	−8.93245	−0.580225
$238$	−1.13565	−0.0736132
$239$	−23.0885	−1.49347	−0.746735	−	0.665121i	$-0.768380\pi$
$239$	−23.0885	−1.49347	−0.746735	+	0.665121i	$0.768380\pi$
$240$	6.00320	0.387505
$241$	18.8167	1.21209	0.606046	−	0.795429i	$-0.292755\pi$
$241$	18.8167	1.21209	0.606046	+	0.795429i	$0.292755\pi$
$242$	−8.58704	−0.551996
$243$	18.8819	1.21128
$244$	−4.62524	−0.296101
$245$	17.3449	1.10813
$246$	7.83349	0.499445
$247$	9.92340	0.631411
$248$	3.57279	0.226873
$249$	−5.13722	−0.325558
$250$	7.99027	0.505349
$251$	−16.3774	−1.03373	−0.516865	−	0.856067i	$-0.672901\pi$
$251$	−16.3774	−1.03373	−0.516865	+	0.856067i	$0.672901\pi$
$252$	1.42484	0.0897562
$253$	13.0446	0.820105
$254$	−13.9182	−0.873306
$255$	−10.3697	−0.649376
$256$	1.00000	0.0625000
$257$	5.62339	0.350777	0.175389	−	0.984499i	$-0.443882\pi$
$257$	5.62339	0.350777	0.175389	+	0.984499i	$0.443882\pi$
$258$	−14.0675	−0.875803
$259$	4.02508	0.250106
$260$	4.82674	0.299342
$261$	−3.77313	−0.233551
$262$	9.46225	0.584580
$263$	−6.36888	−0.392722	−0.196361	−	0.980532i	$-0.562912\pi$
$263$	−6.36888	−0.392722	−0.196361	+	0.980532i	$0.562912\pi$
$264$	−3.53105	−0.217321
$265$	−18.8270	−1.15653
$266$	−3.56962	−0.218867
$267$	3.67430	0.224863
$268$	6.31396	0.385686
$269$	−23.1218	−1.40976	−0.704880	−	0.709327i	$-0.748999\pi$
$269$	−23.1218	−1.40976	−0.704880	+	0.709327i	$0.748999\pi$
$270$	−4.99932	−0.304249
$271$	15.3822	0.934404	0.467202	−	0.884151i	$-0.345262\pi$
$271$	15.3822	0.934404	0.467202	+	0.884151i	$0.345262\pi$
$272$	−1.72736	−0.104737
$273$	2.73143	0.165314
$274$	−15.7641	−0.952344
$275$	3.06702	0.184948
$276$	−19.0890	−1.14902
$277$	−14.5746	−0.875702	−0.437851	−	0.899048i	$-0.644260\pi$
$277$	−14.5746	−0.875702	−0.437851	+	0.899048i	$0.644260\pi$
$278$	10.3790	0.622489
$279$	7.74304	0.463564
$280$	−1.73626	−0.103762
$281$	−15.8561	−0.945893	−0.472946	−	0.881091i	$-0.656810\pi$
$281$	−15.8561	−0.945893	−0.472946	+	0.881091i	$0.656810\pi$
$282$	10.5610	0.628896
$283$	−2.78988	−0.165841	−0.0829207	−	0.996556i	$-0.526425\pi$
$283$	−2.78988	−0.165841	−0.0829207	+	0.996556i	$0.526425\pi$
$284$	−13.5701	−0.805239
$285$	−32.5945	−1.93073
$286$	−2.83907	−0.167877
$287$	−2.26562	−0.133735
$288$	2.16722	0.127705
$289$	−14.0162	−0.824484
$290$	4.59782	0.269993
$291$	1.35963	0.0797032
$292$	−1.03519	−0.0605799
$293$	−8.24195	−0.481500	−0.240750	−	0.970587i	$-0.577393\pi$
$293$	−8.24195	−0.481500	−0.240750	+	0.970587i	$0.577393\pi$
$294$	14.9295	0.870708
$295$	−9.02183	−0.525271
$296$	6.12228	0.355850
$297$	2.94057	0.170629
$298$	10.7806	0.624504
$299$	−15.3481	−0.887603
$300$	−4.48818	−0.259125
$301$	4.06863	0.234512
$302$	−4.55943	−0.262366
$303$	24.9669	1.43431
$304$	−5.42951	−0.311404
$305$	12.2149	0.699421
$306$	−3.74358	−0.214006
$307$	−12.2223	−0.697564	−0.348782	−	0.937204i	$-0.613405\pi$
$307$	−12.2223	−0.697564	−0.348782	+	0.937204i	$0.613405\pi$
$308$	1.02126	0.0581917
$309$	−15.4987	−0.881693
$310$	−9.43544	−0.535897
$311$	−24.6834	−1.39967	−0.699834	−	0.714305i	$-0.746743\pi$
$311$	−24.6834	−1.39967	−0.699834	+	0.714305i	$0.746743\pi$
$312$	4.15459	0.235208
$313$	−24.6748	−1.39470	−0.697351	−	0.716729i	$-0.745638\pi$
$313$	−24.6748	−1.39470	−0.697351	+	0.716729i	$0.745638\pi$
$314$	2.28635	0.129026
$315$	−3.76287	−0.212014
$316$	3.92954	0.221054
$317$	−10.9079	−0.612649	−0.306325	−	0.951927i	$-0.599099\pi$
$317$	−10.9079	−0.612649	−0.306325	+	0.951927i	$0.599099\pi$
$318$	−16.2052	−0.908744
$319$	−2.70441	−0.151418
$320$	−2.64091	−0.147632
$321$	6.30645	0.351992
$322$	5.52097	0.307672
$323$	9.37872	0.521846
$324$	−10.8048	−0.600267
$325$	−3.60862	−0.200170
$326$	2.22381	0.123165
$327$	−13.2164	−0.730867
$328$	−3.44609	−0.190278
$329$	−3.05447	−0.168398
$330$	9.32521	0.513336
$331$	−22.1325	−1.21651	−0.608256	−	0.793741i	$-0.708131\pi$
$331$	−22.1325	−1.21651	−0.608256	+	0.793741i	$0.708131\pi$
$332$	2.25995	0.124031
$333$	13.2684	0.727101
$334$	−16.7518	−0.916616
$335$	−16.6746	−0.911032
$336$	−1.49448	−0.0815305
$337$	−17.2023	−0.937068	−0.468534	−	0.883445i	$-0.655218\pi$
$337$	−17.2023	−0.937068	−0.468534	+	0.883445i	$0.655218\pi$
$338$	−9.65959	−0.525412
$339$	−22.8149	−1.23914
$340$	4.56181	0.247399
$341$	5.54987	0.300543
$342$	−11.7670	−0.636285
$343$	−8.92009	−0.481640
$344$	6.18853	0.333663
$345$	50.4124	2.71411
$346$	−23.8463	−1.28199
$347$	−4.73832	−0.254367	−0.127183	−	0.991879i	$-0.540594\pi$
$347$	−4.73832	−0.254367	−0.127183	+	0.991879i	$0.540594\pi$
$348$	3.95755	0.212147
$349$	32.5972	1.74489	0.872443	−	0.488715i	$-0.162534\pi$
$349$	32.5972	1.74489	0.872443	+	0.488715i	$0.162534\pi$
$350$	1.29808	0.0693855
$351$	−3.45984	−0.184673
$352$	1.55337	0.0827950
$353$	1.28824	0.0685661	0.0342830	−	0.999412i	$-0.489085\pi$
$353$	1.28824	0.0685661	0.0342830	+	0.999412i	$0.489085\pi$
$354$	−7.76549	−0.412731
$355$	35.8375	1.90206
$356$	−1.61639	−0.0856684
$357$	2.58150	0.136628
$358$	7.81216	0.412885
$359$	−32.5123	−1.71593	−0.857966	−	0.513707i	$-0.828272\pi$
$359$	−32.5123	−1.71593	−0.857966	+	0.513707i	$0.828272\pi$
$360$	−5.72345	−0.301653
$361$	10.4796	0.551557
$362$	6.10790	0.321024
$363$	19.5196	1.02452
$364$	−1.20160	−0.0629811
$365$	2.73385	0.143096
$366$	10.5139	0.549569
$367$	−17.6111	−0.919291	−0.459646	−	0.888102i	$-0.652024\pi$
$367$	−17.6111	−0.919291	−0.459646	+	0.888102i	$0.652024\pi$
$368$	8.39759	0.437754
$369$	−7.46845	−0.388792
$370$	−16.1684	−0.840556
$371$	4.68692	0.243333
$372$	−8.12150	−0.421080
$373$	−16.5282	−0.855800	−0.427900	−	0.903826i	$-0.640746\pi$
$373$	−16.5282	−0.855800	−0.427900	+	0.903826i	$0.640746\pi$
$374$	−2.68323	−0.138747
$375$	−18.1631	−0.937939
$376$	−4.64596	−0.239597
$377$	3.18198	0.163880
$378$	1.24457	0.0640135
$379$	22.8025	1.17129	0.585643	−	0.810569i	$-0.300842\pi$
$379$	22.8025	1.17129	0.585643	+	0.810569i	$0.300842\pi$
$380$	14.3389	0.735569
$381$	31.6382	1.62087
$382$	5.66168	0.289677
$383$	−23.0327	−1.17691	−0.588457	−	0.808528i	$-0.700264\pi$
$383$	−23.0327	−1.17691	−0.588457	+	0.808528i	$0.700264\pi$
$384$	−2.27315	−0.116001
$385$	−2.69706	−0.137455
$386$	−24.1444	−1.22892
$387$	13.4119	0.681767
$388$	−0.598127	−0.0303653
$389$	21.1274	1.07120	0.535600	−	0.844472i	$-0.320086\pi$
$389$	21.1274	1.07120	0.535600	+	0.844472i	$0.320086\pi$
$390$	−10.9719	−0.555585
$391$	−14.5057	−0.733583
$392$	−6.56776	−0.331722
$393$	−21.5091	−1.08499
$394$	16.9370	0.853271
$395$	−10.3776	−0.522153
$396$	3.36651	0.169173
$397$	27.9814	1.40434	0.702172	−	0.712007i	$-0.252214\pi$
$397$	27.9814	1.40434	0.702172	+	0.712007i	$0.252214\pi$
$398$	−15.3078	−0.767310
$399$	8.11429	0.406222
$400$	1.97443	0.0987215
$401$	10.8916	0.543898	0.271949	−	0.962312i	$-0.412332\pi$
$401$	10.8916	0.543898	0.271949	+	0.962312i	$0.412332\pi$
$402$	−14.3526	−0.715842
$403$	−6.52992	−0.325278
$404$	−10.9834	−0.546443
$405$	28.5346	1.41789
$406$	−1.14461	−0.0568062
$407$	9.51017	0.471402
$408$	3.92655	0.194393
$409$	−14.5290	−0.718411	−0.359206	−	0.933258i	$-0.616952\pi$
$409$	−14.5290	−0.718411	−0.359206	+	0.933258i	$0.616952\pi$
$410$	9.10083	0.449458
$411$	35.8342	1.76757
$412$	6.81817	0.335907
$413$	2.24596	0.110516
$414$	18.1995	0.894454
$415$	−5.96834	−0.292974
$416$	−1.82768	−0.0896093
$417$	−23.5930	−1.15535
$418$	−8.43405	−0.412523
$419$	23.6782	1.15675	0.578377	−	0.815770i	$-0.303686\pi$
$419$	23.6782	1.15675	0.578377	+	0.815770i	$0.303686\pi$
$420$	3.94679	0.192584
$421$	−15.8392	−0.771953	−0.385977	−	0.922509i	$-0.626135\pi$
$421$	−15.8392	−0.771953	−0.385977	+	0.922509i	$0.626135\pi$
$422$	−15.7436	−0.766385
$423$	−10.0688	−0.489563
$424$	7.12897	0.346213
$425$	−3.41055	−0.165436
$426$	30.8470	1.49454
$427$	−3.04085	−0.147157
$428$	−2.77432	−0.134102
$429$	6.45363	0.311584
$430$	−16.3434	−0.788148
$431$	37.8359	1.82249	0.911244	−	0.411866i	$-0.135123\pi$
$431$	37.8359	1.82249	0.911244	+	0.411866i	$0.135123\pi$
$432$	1.89303	0.0910783
$433$	20.3440	0.977669	0.488835	−	0.872376i	$-0.337422\pi$
$433$	20.3440	0.977669	0.488835	+	0.872376i	$0.337422\pi$
$434$	2.34892	0.112752
$435$	−10.4515	−0.501113
$436$	5.81411	0.278445
$437$	−45.5948	−2.18109
$438$	2.35314	0.112438
$439$	23.6799	1.13018	0.565091	−	0.825029i	$-0.308841\pi$
$439$	23.6799	1.13018	0.565091	+	0.825029i	$0.308841\pi$
$440$	−4.10232	−0.195571
$441$	−14.2338	−0.677801
$442$	3.15706	0.150166
$443$	−6.25011	−0.296952	−0.148476	−	0.988916i	$-0.547437\pi$
$443$	−6.25011	−0.296952	−0.148476	+	0.988916i	$0.547437\pi$
$444$	−13.9169	−0.660466
$445$	4.26874	0.202358
$446$	−19.7260	−0.934056
$447$	−24.5060	−1.15909
$448$	0.657447	0.0310615
$449$	26.0214	1.22803	0.614013	−	0.789296i	$-0.289554\pi$
$449$	26.0214	1.22803	0.614013	+	0.789296i	$0.289554\pi$
$450$	4.27903	0.201716
$451$	−5.35306	−0.252066
$452$	10.0367	0.472086
$453$	10.3643	0.486956
$454$	8.78507	0.412304
$455$	3.17333	0.148768
$456$	12.3421	0.577972
$457$	−8.49000	−0.397146	−0.198573	−	0.980086i	$-0.563631\pi$
$457$	−8.49000	−0.397146	−0.198573	+	0.980086i	$0.563631\pi$
$458$	−21.2228	−0.991674
$459$	−3.26994	−0.152628
$460$	−22.1773	−1.03402
$461$	34.6065	1.61179	0.805893	−	0.592061i	$-0.201686\pi$
$461$	34.6065	1.61179	0.805893	+	0.592061i	$0.201686\pi$
$462$	−2.32148	−0.108005
$463$	−18.4180	−0.855957	−0.427979	−	0.903789i	$-0.640774\pi$
$463$	−18.4180	−0.855957	−0.427979	+	0.903789i	$0.640774\pi$
$464$	−1.74099	−0.0808237
$465$	21.4482	0.994636
$466$	1.64873	0.0763761
$467$	−4.53126	−0.209682	−0.104841	−	0.994489i	$-0.533433\pi$
$467$	−4.53126	−0.209682	−0.104841	+	0.994489i	$0.533433\pi$
$468$	−3.96099	−0.183097
$469$	4.15110	0.191680
$470$	12.2696	0.565953
$471$	−5.19723	−0.239476
$472$	3.41618	0.157242
$473$	9.61309	0.442010
$474$	−8.93245	−0.410281
$475$	−10.7202	−0.491876
$476$	−1.13565	−0.0520524
$477$	15.4501	0.707410
$478$	−23.0885	−1.05604
$479$	−17.6485	−0.806382	−0.403191	−	0.915116i	$-0.632099\pi$
$479$	−17.6485	−0.806382	−0.403191	+	0.915116i	$0.632099\pi$
$480$	6.00320	0.274007
$481$	−11.1896	−0.510200
$482$	18.8167	0.857079
$483$	−12.5500	−0.571045
$484$	−8.58704	−0.390320
$485$	1.57960	0.0717261
$486$	18.8819	0.856501
$487$	1.19388	0.0540999	0.0270500	−	0.999634i	$-0.491389\pi$
$487$	1.19388	0.0540999	0.0270500	+	0.999634i	$0.491389\pi$
$488$	−4.62524	−0.209375
$489$	−5.05505	−0.228597
$490$	17.3449	0.783563
$491$	4.14028	0.186848	0.0934242	−	0.995626i	$-0.470219\pi$
$491$	4.14028	0.186848	0.0934242	+	0.995626i	$0.470219\pi$
$492$	7.83349	0.353161
$493$	3.00733	0.135443
$494$	9.92340	0.446475
$495$	−8.89065	−0.399605
$496$	3.57279	0.160423
$497$	−8.92165	−0.400190
$498$	−5.13722	−0.230204
$499$	6.33456	0.283574	0.141787	−	0.989897i	$-0.454715\pi$
$499$	6.33456	0.283574	0.141787	+	0.989897i	$0.454715\pi$
$500$	7.99027	0.357336
$501$	38.0793	1.70126
$502$	−16.3774	−0.730958
$503$	−24.2503	−1.08127	−0.540633	−	0.841259i	$-0.681815\pi$
$503$	−24.2503	−1.08127	−0.540633	+	0.841259i	$0.681815\pi$
$504$	1.42484	0.0634672
$505$	29.0062	1.29076
$506$	13.0446	0.579902
$507$	21.9577	0.975177
$508$	−13.9182	−0.617520
$509$	−26.4683	−1.17319	−0.586593	−	0.809882i	$-0.699531\pi$
$509$	−26.4683	−1.17319	−0.586593	+	0.809882i	$0.699531\pi$
$510$	−10.3697	−0.459178
$511$	−0.680583	−0.0301072
$512$	1.00000	0.0441942
$513$	−10.2782	−0.453794
$514$	5.62339	0.248037
$515$	−18.0062	−0.793448
$516$	−14.0675	−0.619286
$517$	−7.21690	−0.317399
$518$	4.02508	0.176852
$519$	54.2064	2.37940
$520$	4.82674	0.211667
$521$	−12.9777	−0.568564	−0.284282	−	0.958741i	$-0.591755\pi$
$521$	−12.9777	−0.568564	−0.284282	+	0.958741i	$0.591755\pi$
$522$	−3.77313	−0.165145
$523$	−28.1323	−1.23014	−0.615069	−	0.788473i	$-0.710872\pi$
$523$	−28.1323	−1.23014	−0.615069	+	0.788473i	$0.710872\pi$
$524$	9.46225	0.413360
$525$	−2.95074	−0.128781
$526$	−6.36888	−0.277696
$527$	−6.17150	−0.268835
$528$	−3.53105	−0.153669
$529$	47.5195	2.06606
$530$	−18.8270	−0.817792
$531$	7.40362	0.321290
$532$	−3.56962	−0.154763
$533$	6.29835	0.272812
$534$	3.67430	0.159002
$535$	7.32673	0.316762
$536$	6.31396	0.272721
$537$	−17.7582	−0.766324
$538$	−23.1218	−0.996851
$539$	−10.2022	−0.439439
$540$	−4.99932	−0.215136
$541$	−23.8926	−1.02722	−0.513611	−	0.858023i	$-0.671693\pi$
$541$	−23.8926	−1.02722	−0.513611	+	0.858023i	$0.671693\pi$
$542$	15.3822	0.660723
$543$	−13.8842	−0.595828
$544$	−1.72736	−0.0740600
$545$	−15.3546	−0.657718
$546$	2.73143	0.116894
$547$	−16.5753	−0.708711	−0.354355	−	0.935111i	$-0.615300\pi$
$547$	−16.5753	−0.708711	−0.354355	+	0.935111i	$0.615300\pi$
$548$	−15.7641	−0.673409
$549$	−10.0239	−0.427811
$550$	3.06702	0.130778
$551$	9.45275	0.402701
$552$	−19.0890	−0.812482
$553$	2.58347	0.109860
$554$	−14.5746	−0.619214
$555$	36.7533	1.56009
$556$	10.3790	0.440166
$557$	−1.45409	−0.0616119	−0.0308060	−	0.999525i	$-0.509807\pi$
$557$	−1.45409	−0.0616119	−0.0308060	+	0.999525i	$0.509807\pi$
$558$	7.74304	0.327789
$559$	−11.3107	−0.478390
$560$	−1.73626	−0.0733705
$561$	6.09940	0.257517
$562$	−15.8561	−0.668847
$563$	37.4591	1.57871	0.789356	−	0.613935i	$-0.210414\pi$
$563$	37.4591	1.57871	0.789356	+	0.613935i	$0.210414\pi$
$564$	10.5610	0.444697
$565$	−26.5060	−1.11512
$566$	−2.78988	−0.117268
$567$	−7.10360	−0.298323
$568$	−13.5701	−0.569390
$569$	47.0188	1.97113	0.985565	−	0.169299i	$-0.0541505\pi$
$569$	47.0188	1.97113	0.985565	+	0.169299i	$0.0541505\pi$
$570$	−32.5945	−1.36523
$571$	−24.1914	−1.01238	−0.506189	−	0.862423i	$-0.668946\pi$
$571$	−24.1914	−1.01238	−0.506189	+	0.862423i	$0.668946\pi$
$572$	−2.83907	−0.118707
$573$	−12.8699	−0.537646
$574$	−2.26562	−0.0945653
$575$	16.5804	0.691452
$576$	2.16722	0.0903010
$577$	15.2011	0.632829	0.316414	−	0.948621i	$-0.397521\pi$
$577$	15.2011	0.632829	0.316414	+	0.948621i	$0.397521\pi$
$578$	−14.0162	−0.582998
$579$	54.8840	2.28090
$580$	4.59782	0.190914
$581$	1.48580	0.0616414
$582$	1.35963	0.0563587
$583$	11.0739	0.458636
$584$	−1.03519	−0.0428365
$585$	10.4606	0.432494
$586$	−8.24195	−0.340472
$587$	−42.2321	−1.74310	−0.871552	−	0.490303i	$-0.836886\pi$
$587$	−42.2321	−1.74310	−0.871552	+	0.490303i	$0.836886\pi$
$588$	14.9295	0.615683
$589$	−19.3985	−0.799302
$590$	−9.02183	−0.371423
$591$	−38.5003	−1.58369
$592$	6.12228	0.251624
$593$	42.4237	1.74213	0.871066	−	0.491166i	$-0.163429\pi$
$593$	42.4237	1.74213	0.871066	+	0.491166i	$0.163429\pi$
$594$	2.94057	0.120653
$595$	2.99915	0.122953
$596$	10.7806	0.441591
$597$	34.7970	1.42414
$598$	−15.3481	−0.627630
$599$	29.1997	1.19307	0.596533	−	0.802588i	$-0.296544\pi$
$599$	29.1997	1.19307	0.596533	+	0.802588i	$0.296544\pi$
$600$	−4.48818	−0.183229
$601$	35.0701	1.43054	0.715269	−	0.698849i	$-0.246304\pi$
$601$	35.0701	1.43054	0.715269	+	0.698849i	$0.246304\pi$
$602$	4.06863	0.165825
$603$	13.6838	0.557246
$604$	−4.55943	−0.185520
$605$	22.6776	0.921977
$606$	24.9669	1.01421
$607$	−0.222805	−0.00904338	−0.00452169	−	0.999990i	$-0.501439\pi$
$607$	−0.222805	−0.00904338	−0.00452169	+	0.999990i	$0.501439\pi$
$608$	−5.42951	−0.220196
$609$	2.60188	0.105433
$610$	12.2149	0.494565
$611$	8.49132	0.343522
$612$	−3.74358	−0.151325
$613$	3.29661	0.133149	0.0665743	−	0.997781i	$-0.478793\pi$
$613$	3.29661	0.133149	0.0665743	+	0.997781i	$0.478793\pi$
$614$	−12.2223	−0.493252
$615$	−20.6876	−0.834204
$616$	1.02126	0.0411477
$617$	48.8161	1.96526	0.982631	−	0.185571i	$-0.0594136\pi$
$617$	48.8161	1.96526	0.982631	+	0.185571i	$0.0594136\pi$
$618$	−15.4987	−0.623451
$619$	20.2188	0.812664	0.406332	−	0.913726i	$-0.366808\pi$
$619$	20.2188	0.812664	0.406332	+	0.913726i	$0.366808\pi$
$620$	−9.43544	−0.378936
$621$	15.8969	0.637919
$622$	−24.6834	−0.989715
$623$	−1.06269	−0.0425758
$624$	4.15459	0.166317
$625$	−30.9738	−1.23895
$626$	−24.6748	−0.986204
$627$	19.1719	0.765651
$628$	2.28635	0.0912355
$629$	−10.5754	−0.421668
$630$	−3.76287	−0.149916
$631$	−23.8343	−0.948829	−0.474414	−	0.880302i	$-0.657340\pi$
$631$	−23.8343	−0.948829	−0.474414	+	0.880302i	$0.657340\pi$
$632$	3.92954	0.156309
$633$	35.7876	1.42243
$634$	−10.9079	−0.433209
$635$	36.7568	1.45865
$636$	−16.2052	−0.642579
$637$	12.0038	0.475606
$638$	−2.70441	−0.107069
$639$	−29.4095	−1.16342
$640$	−2.64091	−0.104391
$641$	33.1764	1.31039	0.655195	−	0.755459i	$-0.272586\pi$
$641$	33.1764	1.31039	0.655195	+	0.755459i	$0.272586\pi$
$642$	6.30645	0.248896
$643$	34.3426	1.35434	0.677170	−	0.735827i	$-0.263206\pi$
$643$	34.3426	1.35434	0.677170	+	0.735827i	$0.263206\pi$
$644$	5.52097	0.217557
$645$	37.1510	1.46282
$646$	9.37872	0.369001
$647$	7.65765	0.301053	0.150527	−	0.988606i	$-0.451903\pi$
$647$	7.65765	0.301053	0.150527	+	0.988606i	$0.451903\pi$
$648$	−10.8048	−0.424453
$649$	5.30659	0.208302
$650$	−3.60862	−0.141542
$651$	−5.33946	−0.209270
$652$	2.22381	0.0870909
$653$	−11.4872	−0.449531	−0.224765	−	0.974413i	$-0.572162\pi$
$653$	−11.4872	−0.449531	−0.224765	+	0.974413i	$0.572162\pi$
$654$	−13.2164	−0.516801
$655$	−24.9890	−0.976401
$656$	−3.44609	−0.134547
$657$	−2.24349	−0.0875268
$658$	−3.05447	−0.119076
$659$	43.9887	1.71356	0.856779	−	0.515684i	$-0.172462\pi$
$659$	43.9887	1.71356	0.856779	+	0.515684i	$0.172462\pi$
$660$	9.32521	0.362983
$661$	−31.1220	−1.21050	−0.605252	−	0.796034i	$-0.706928\pi$
$661$	−31.1220	−1.21050	−0.605252	+	0.796034i	$0.706928\pi$
$662$	−22.1325	−0.860204
$663$	−7.17648	−0.278712
$664$	2.25995	0.0877032
$665$	9.42705	0.365565
$666$	13.2684	0.514138
$667$	−14.6202	−0.566095
$668$	−16.7518	−0.648145
$669$	44.8403	1.73363
$670$	−16.6746	−0.644197
$671$	−7.18472	−0.277363
$672$	−1.49448	−0.0576508
$673$	−22.2516	−0.857736	−0.428868	−	0.903367i	$-0.641087\pi$
$673$	−22.2516	−0.857736	−0.428868	+	0.903367i	$0.641087\pi$
$674$	−17.2023	−0.662607
$675$	3.73765	0.143862
$676$	−9.65959	−0.371523
$677$	6.56381	0.252268	0.126134	−	0.992013i	$-0.459743\pi$
$677$	6.56381	0.252268	0.126134	+	0.992013i	$0.459743\pi$
$678$	−22.8149	−0.876202
$679$	−0.393237	−0.0150911
$680$	4.56181	0.174937
$681$	−19.9698	−0.765245
$682$	5.54987	0.212516
$683$	−25.9641	−0.993489	−0.496745	−	0.867897i	$-0.665471\pi$
$683$	−25.9641	−0.993489	−0.496745	+	0.867897i	$0.665471\pi$
$684$	−11.7670	−0.449921
$685$	41.6316	1.59066
$686$	−8.92009	−0.340571
$687$	48.2426	1.84057
$688$	6.18853	0.235936
$689$	−13.0295	−0.496383
$690$	50.4124	1.91917
$691$	26.0646	0.991545	0.495773	−	0.868452i	$-0.334885\pi$
$691$	26.0646	0.991545	0.495773	+	0.868452i	$0.334885\pi$
$692$	−23.8463	−0.906502
$693$	2.21330	0.0840763
$694$	−4.73832	−0.179864
$695$	−27.4100	−1.03972
$696$	3.95755	0.150010
$697$	5.95264	0.225472
$698$	32.5972	1.23382
$699$	−3.74782	−0.141756
$700$	1.29808	0.0490630
$701$	25.7304	0.971823	0.485912	−	0.874008i	$-0.338488\pi$
$701$	25.7304	0.971823	0.485912	+	0.874008i	$0.338488\pi$
$702$	−3.45984	−0.130583
$703$	−33.2410	−1.25371
$704$	1.55337	0.0585449
$705$	−27.8906	−1.05042
$706$	1.28824	0.0484835
$707$	−7.22099	−0.271573
$708$	−7.76549	−0.291845
$709$	−4.00154	−0.150281	−0.0751405	−	0.997173i	$-0.523941\pi$
$709$	−4.00154	−0.150281	−0.0751405	+	0.997173i	$0.523941\pi$
$710$	35.8375	1.34496
$711$	8.51620	0.319383
$712$	−1.61639	−0.0605767
$713$	30.0028	1.12361
$714$	2.58150	0.0966103
$715$	7.49773	0.280399
$716$	7.81216	0.291954
$717$	52.4837	1.96004
$718$	−32.5123	−1.21335
$719$	23.8899	0.890943	0.445471	−	0.895296i	$-0.353036\pi$
$719$	23.8899	0.890943	0.445471	+	0.895296i	$0.353036\pi$
$720$	−5.72345	−0.213301
$721$	4.48259	0.166940
$722$	10.4796	0.390010
$723$	−42.7733	−1.59076
$724$	6.10790	0.226998
$725$	−3.43747	−0.127665
$726$	19.5196	0.724442
$727$	28.7526	1.06637	0.533187	−	0.845998i	$-0.320994\pi$
$727$	28.7526	1.06637	0.533187	+	0.845998i	$0.320994\pi$
$728$	−1.20160	−0.0445344
$729$	−10.5070	−0.389150
$730$	2.73385	0.101184
$731$	−10.6898	−0.395377
$732$	10.5139	0.388604
$733$	12.7984	0.472720	0.236360	−	0.971666i	$-0.424046\pi$
$733$	12.7984	0.472720	0.236360	+	0.971666i	$0.424046\pi$
$734$	−17.6111	−0.650037
$735$	−39.4276	−1.45431
$736$	8.39759	0.309539
$737$	9.80792	0.361280
$738$	−7.46845	−0.274917
$739$	−4.33808	−0.159579	−0.0797894	−	0.996812i	$-0.525425\pi$
$739$	−4.33808	−0.159579	−0.0797894	+	0.996812i	$0.525425\pi$
$740$	−16.1684	−0.594363
$741$	−22.5574	−0.828667
$742$	4.68692	0.172062
$743$	6.17370	0.226491	0.113246	−	0.993567i	$-0.463875\pi$
$743$	6.17370	0.226491	0.113246	+	0.993567i	$0.463875\pi$
$744$	−8.12150	−0.297749
$745$	−28.4707	−1.04309
$746$	−16.5282	−0.605142
$747$	4.89783	0.179202
$748$	−2.68323	−0.0981087
$749$	−1.82397	−0.0666463
$750$	−18.1631	−0.663223
$751$	−15.9009	−0.580231	−0.290115	−	0.956992i	$-0.593694\pi$
$751$	−15.9009	−0.580231	−0.290115	+	0.956992i	$0.593694\pi$
$752$	−4.64596	−0.169421
$753$	37.2283	1.35667
$754$	3.18198	0.115881
$755$	12.0411	0.438219
$756$	1.24457	0.0452644
$757$	−9.16251	−0.333017	−0.166508	−	0.986040i	$-0.553249\pi$
$757$	−9.16251	−0.333017	−0.166508	+	0.986040i	$0.553249\pi$
$758$	22.8025	0.828224
$759$	−29.6523	−1.07631
$760$	14.3389	0.520126
$761$	5.96548	0.216249	0.108124	−	0.994137i	$-0.465516\pi$
$761$	5.96548	0.216249	0.108124	+	0.994137i	$0.465516\pi$
$762$	31.6382	1.14613
$763$	3.82247	0.138383
$764$	5.66168	0.204832
$765$	9.88647	0.357446
$766$	−23.0327	−0.832204
$767$	−6.24367	−0.225446
$768$	−2.27315	−0.0820253
$769$	24.9537	0.899854	0.449927	−	0.893065i	$-0.351450\pi$
$769$	24.9537	0.899854	0.449927	+	0.893065i	$0.351450\pi$
$770$	−2.69706	−0.0971953
$771$	−12.7828	−0.460362
$772$	−24.1444	−0.868977
$773$	−10.5017	−0.377722	−0.188861	−	0.982004i	$-0.560479\pi$
$773$	−10.5017	−0.377722	−0.188861	+	0.982004i	$0.560479\pi$
$774$	13.4119	0.482082
$775$	7.05423	0.253395
$776$	−0.598127	−0.0214715
$777$	−9.14961	−0.328241
$778$	21.1274	0.757453
$779$	18.7106	0.670376
$780$	−10.9719	−0.392858
$781$	−21.0795	−0.754282
$782$	−14.5057	−0.518721
$783$	−3.29575	−0.117780
$784$	−6.56776	−0.234563
$785$	−6.03807	−0.215508
$786$	−21.5091	−0.767206
$787$	−26.6683	−0.950621	−0.475311	−	0.879818i	$-0.657664\pi$
$787$	−26.6683	−0.950621	−0.475311	+	0.879818i	$0.657664\pi$
$788$	16.9370	0.603354
$789$	14.4774	0.515411
$790$	−10.3776	−0.369218
$791$	6.59859	0.234619
$792$	3.36651	0.119624
$793$	8.45345	0.300191
$794$	27.9814	0.993021
$795$	42.7966	1.51784
$796$	−15.3078	−0.542570
$797$	−1.31901	−0.0467216	−0.0233608	−	0.999727i	$-0.507437\pi$
$797$	−1.31901	−0.0467216	−0.0233608	+	0.999727i	$0.507437\pi$
$798$	8.11429	0.287243
$799$	8.02524	0.283913
$800$	1.97443	0.0698066
$801$	−3.50308	−0.123775
$802$	10.8916	0.384594
$803$	−1.60803	−0.0567463
$804$	−14.3526	−0.506177
$805$	−14.5804	−0.513892
$806$	−6.52992	−0.230007
$807$	52.5594	1.85018
$808$	−10.9834	−0.386394
$809$	0.659191	0.0231759	0.0115880	−	0.999933i	$-0.496311\pi$
$809$	0.659191	0.0231759	0.0115880	+	0.999933i	$0.496311\pi$
$810$	28.5346	1.00260
$811$	−37.6070	−1.32056	−0.660281	−	0.751019i	$-0.729563\pi$
$811$	−37.6070	−1.32056	−0.660281	+	0.751019i	$0.729563\pi$
$812$	−1.14461	−0.0401680
$813$	−34.9662	−1.22632
$814$	9.51017	0.333331
$815$	−5.87288	−0.205718
$816$	3.92655	0.137457
$817$	−33.6007	−1.17554
$818$	−14.5290	−0.507993
$819$	−2.60414	−0.0909961
$820$	9.10083	0.317815
$821$	18.9451	0.661187	0.330594	−	0.943773i	$-0.392751\pi$
$821$	18.9451	0.661187	0.330594	+	0.943773i	$0.392751\pi$
$822$	35.8342	1.24986
$823$	35.7038	1.24455	0.622277	−	0.782797i	$-0.286208\pi$
$823$	35.7038	1.24455	0.622277	+	0.782797i	$0.286208\pi$
$824$	6.81817	0.237522
$825$	−6.97181	−0.242727
$826$	2.24596	0.0781468
$827$	11.1685	0.388365	0.194183	−	0.980965i	$-0.437795\pi$
$827$	11.1685	0.388365	0.194183	+	0.980965i	$0.437795\pi$
$828$	18.1995	0.632475
$829$	−12.6187	−0.438264	−0.219132	−	0.975695i	$-0.570323\pi$
$829$	−12.6187	−0.438264	−0.219132	+	0.975695i	$0.570323\pi$
$830$	−5.96834	−0.207164
$831$	33.1302	1.14928
$832$	−1.82768	−0.0633634
$833$	11.3449	0.393077
$834$	−23.5930	−0.816958
$835$	44.2400	1.53099
$836$	−8.43405	−0.291698
$837$	6.76339	0.233777
$838$	23.6782	0.817948
$839$	31.0352	1.07145	0.535726	−	0.844392i	$-0.320038\pi$
$839$	31.0352	1.07145	0.535726	+	0.844392i	$0.320038\pi$
$840$	3.94679	0.136177
$841$	−25.9689	−0.895481
$842$	−15.8392	−0.545853
$843$	36.0432	1.24140
$844$	−15.7436	−0.541916
$845$	25.5101	0.877576
$846$	−10.0688	−0.346173
$847$	−5.64552	−0.193983
$848$	7.12897	0.244810
$849$	6.34183	0.217651
$850$	−3.41055	−0.116981
$851$	51.4124	1.76239
$852$	30.8470	1.05680
$853$	−10.6107	−0.363304	−0.181652	−	0.983363i	$-0.558144\pi$
$853$	−10.6107	−0.363304	−0.181652	+	0.983363i	$0.558144\pi$
$854$	−3.04085	−0.104056
$855$	31.0756	1.06276
$856$	−2.77432	−0.0948242
$857$	−36.0007	−1.22976	−0.614880	−	0.788621i	$-0.710796\pi$
$857$	−36.0007	−1.22976	−0.614880	+	0.788621i	$0.710796\pi$
$858$	6.45363	0.220323
$859$	4.09997	0.139889	0.0699446	−	0.997551i	$-0.477718\pi$
$859$	4.09997	0.139889	0.0699446	+	0.997551i	$0.477718\pi$
$860$	−16.3434	−0.557305
$861$	5.15011	0.175515
$862$	37.8359	1.28869
$863$	30.1993	1.02800	0.513998	−	0.857791i	$-0.328164\pi$
$863$	30.1993	1.02800	0.513998	+	0.857791i	$0.328164\pi$
$864$	1.89303	0.0644021
$865$	62.9761	2.14125
$866$	20.3440	0.691317
$867$	31.8610	1.08206
$868$	2.34892	0.0797276
$869$	6.10404	0.207065
$870$	−10.4515	−0.354341
$871$	−11.5399	−0.391014
$872$	5.81411	0.196891
$873$	−1.29628	−0.0438723
$874$	−45.5948	−1.54227
$875$	5.25318	0.177590
$876$	2.35314	0.0795054
$877$	12.1925	0.411713	0.205856	−	0.978582i	$-0.434002\pi$
$877$	12.1925	0.411713	0.205856	+	0.978582i	$0.434002\pi$
$878$	23.6799	0.799159
$879$	18.7352	0.631923
$880$	−4.10232	−0.138289
$881$	−31.4621	−1.05999	−0.529993	−	0.848002i	$-0.677805\pi$
$881$	−31.4621	−1.05999	−0.529993	+	0.848002i	$0.677805\pi$
$882$	−14.2338	−0.479278
$883$	−33.2948	−1.12046	−0.560229	−	0.828338i	$-0.689287\pi$
$883$	−33.2948	−1.12046	−0.560229	+	0.828338i	$0.689287\pi$
$884$	3.15706	0.106183
$885$	20.5080	0.689369
$886$	−6.25011	−0.209977
$887$	−30.7374	−1.03206	−0.516031	−	0.856570i	$-0.672591\pi$
$887$	−30.7374	−1.03206	−0.516031	+	0.856570i	$0.672591\pi$
$888$	−13.9169	−0.467020
$889$	−9.15049	−0.306897
$890$	4.26874	0.143089
$891$	−16.7839	−0.562281
$892$	−19.7260	−0.660477
$893$	25.2253	0.844131
$894$	−24.5060	−0.819603
$895$	−20.6312	−0.689627
$896$	0.657447	0.0219638
$897$	34.8886	1.16490
$898$	26.0214	0.868345
$899$	−6.22021	−0.207456
$900$	4.27903	0.142634
$901$	−12.3143	−0.410249
$902$	−5.35306	−0.178237
$903$	−9.24863	−0.307775
$904$	10.0367	0.333815
$905$	−16.1304	−0.536194
$906$	10.3643	0.344330
$907$	−28.9266	−0.960492	−0.480246	−	0.877134i	$-0.659453\pi$
$907$	−28.9266	−0.960492	−0.480246	+	0.877134i	$0.659453\pi$
$908$	8.78507	0.291543
$909$	−23.8034	−0.789510
$910$	3.17333	0.105195
$911$	−11.9067	−0.394485	−0.197243	−	0.980355i	$-0.563199\pi$
$911$	−11.9067	−0.394485	−0.197243	+	0.980355i	$0.563199\pi$
$912$	12.3421	0.408688
$913$	3.51055	0.116182
$914$	−8.49000	−0.280824
$915$	−27.7662	−0.917924
$916$	−21.2228	−0.701220
$917$	6.22093	0.205433
$918$	−3.26994	−0.107924
$919$	41.0309	1.35348	0.676742	−	0.736220i	$-0.263391\pi$
$919$	41.0309	1.35348	0.676742	+	0.736220i	$0.263391\pi$
$920$	−22.1773	−0.731164
$921$	27.7832	0.915486
$922$	34.6065	1.13970
$923$	24.8018	0.816363
$924$	−2.32148	−0.0763711
$925$	12.0880	0.397451
$926$	−18.4180	−0.605253
$927$	14.7765	0.485324
$928$	−1.74099	−0.0571510
$929$	34.9728	1.14742	0.573709	−	0.819059i	$-0.305504\pi$
$929$	34.9728	1.14742	0.573709	+	0.819059i	$0.305504\pi$
$930$	21.4482	0.703314
$931$	35.6597	1.16870
$932$	1.64873	0.0540061
$933$	56.1092	1.83693
$934$	−4.53126	−0.148268
$935$	7.08619	0.231743
$936$	−3.96099	−0.129469
$937$	−26.3748	−0.861629	−0.430814	−	0.902441i	$-0.641774\pi$
$937$	−26.3748	−0.861629	−0.430814	+	0.902441i	$0.641774\pi$
$938$	4.15110	0.135538
$939$	56.0896	1.83042
$940$	12.2696	0.400189
$941$	20.0761	0.654461	0.327230	−	0.944945i	$-0.393885\pi$
$941$	20.0761	0.654461	0.327230	+	0.944945i	$0.393885\pi$
$942$	−5.19723	−0.169335
$943$	−28.9388	−0.942378
$944$	3.41618	0.111187
$945$	−3.28679	−0.106919
$946$	9.61309	0.312549
$947$	−43.5686	−1.41579	−0.707895	−	0.706318i	$-0.750355\pi$
$947$	−43.5686	−1.41579	−0.707895	+	0.706318i	$0.750355\pi$
$948$	−8.93245	−0.290113
$949$	1.89200	0.0614168
$950$	−10.7202	−0.347809
$951$	24.7954	0.804044
$952$	−1.13565	−0.0368066
$953$	−44.8665	−1.45337	−0.726684	−	0.686972i	$-0.758940\pi$
$953$	−44.8665	−1.45337	−0.726684	+	0.686972i	$0.758940\pi$
$954$	15.4501	0.500215
$955$	−14.9520	−0.483836
$956$	−23.0885	−0.746735
$957$	6.14754	0.198722
$958$	−17.6485	−0.570198
$959$	−10.3641	−0.334673
$960$	6.00320	0.193753
$961$	−18.2352	−0.588231
$962$	−11.1896	−0.360766
$963$	−6.01257	−0.193752
$964$	18.8167	0.606046
$965$	63.7633	2.05261
$966$	−12.5500	−0.403790
$967$	−29.3786	−0.944751	−0.472375	−	0.881397i	$-0.656603\pi$
$967$	−29.3786	−0.944751	−0.472375	+	0.881397i	$0.656603\pi$
$968$	−8.58704	−0.275998
$969$	−21.3193	−0.684874
$970$	1.57960	0.0507180
$971$	5.31218	0.170476	0.0852379	−	0.996361i	$-0.472835\pi$
$971$	5.31218	0.170476	0.0852379	+	0.996361i	$0.472835\pi$
$972$	18.8819	0.605638
$973$	6.82363	0.218755
$974$	1.19388	0.0382544
$975$	8.20296	0.262705
$976$	−4.62524	−0.148050
$977$	8.66781	0.277308	0.138654	−	0.990341i	$-0.455722\pi$
$977$	8.66781	0.277308	0.138654	+	0.990341i	$0.455722\pi$
$978$	−5.05505	−0.161643
$979$	−2.51085	−0.0802471
$980$	17.3449	0.554063
$981$	12.6005	0.402303
$982$	4.14028	0.132122
$983$	−28.5869	−0.911780	−0.455890	−	0.890036i	$-0.650679\pi$
$983$	−28.5869	−0.911780	−0.455890	+	0.890036i	$0.650679\pi$
$984$	7.83349	0.249723
$985$	−44.7290	−1.42519
$986$	3.00733	0.0957728
$987$	6.94328	0.221007
$988$	9.92340	0.315706
$989$	51.9687	1.65251
$990$	−8.89065	−0.282563
$991$	−47.9291	−1.52252	−0.761259	−	0.648448i	$-0.775418\pi$
$991$	−47.9291	−1.52252	−0.761259	+	0.648448i	$0.775418\pi$
$992$	3.57279	0.113436
$993$	50.3105	1.59656
$994$	−8.92165	−0.282977
$995$	40.4266	1.28161
$996$	−5.13722	−0.162779
$997$	−52.0847	−1.64954	−0.824769	−	0.565469i	$-0.808695\pi$
$997$	−52.0847	−1.64954	−0.824769	+	0.565469i	$0.808695\pi$
$998$	6.33456	0.200517
$999$	11.5896	0.366680

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6038.2.a.b.1.12	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6038.2.a.b.1.12	✓	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:	\( N \)	\(=\)	\( 6038 = 2 \cdot 3019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6038.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.27315 q^{3} +1.00000 q^{4} -2.64091 q^{5} -2.27315 q^{6} +0.657447 q^{7} +1.00000 q^{8} +2.16722 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.27315 q^{3} +1.00000 q^{4} -2.64091 q^{5} -2.27315 q^{6} +0.657447 q^{7} +1.00000 q^{8} +2.16722 q^{9} -2.64091 q^{10} +1.55337 q^{11} -2.27315 q^{12} -1.82768 q^{13} +0.657447 q^{14} +6.00320 q^{15} +1.00000 q^{16} -1.72736 q^{17} +2.16722 q^{18} -5.42951 q^{19} -2.64091 q^{20} -1.49448 q^{21} +1.55337 q^{22} +8.39759 q^{23} -2.27315 q^{24} +1.97443 q^{25} -1.82768 q^{26} +1.89303 q^{27} +0.657447 q^{28} -1.74099 q^{29} +6.00320 q^{30} +3.57279 q^{31} +1.00000 q^{32} -3.53105 q^{33} -1.72736 q^{34} -1.73626 q^{35} +2.16722 q^{36} +6.12228 q^{37} -5.42951 q^{38} +4.15459 q^{39} -2.64091 q^{40} -3.44609 q^{41} -1.49448 q^{42} +6.18853 q^{43} +1.55337 q^{44} -5.72345 q^{45} +8.39759 q^{46} -4.64596 q^{47} -2.27315 q^{48} -6.56776 q^{49} +1.97443 q^{50} +3.92655 q^{51} -1.82768 q^{52} +7.12897 q^{53} +1.89303 q^{54} -4.10232 q^{55} +0.657447 q^{56} +12.3421 q^{57} -1.74099 q^{58} +3.41618 q^{59} +6.00320 q^{60} -4.62524 q^{61} +3.57279 q^{62} +1.42484 q^{63} +1.00000 q^{64} +4.82674 q^{65} -3.53105 q^{66} +6.31396 q^{67} -1.72736 q^{68} -19.0890 q^{69} -1.73626 q^{70} -13.5701 q^{71} +2.16722 q^{72} -1.03519 q^{73} +6.12228 q^{74} -4.48818 q^{75} -5.42951 q^{76} +1.02126 q^{77} +4.15459 q^{78} +3.92954 q^{79} -2.64091 q^{80} -10.8048 q^{81} -3.44609 q^{82} +2.25995 q^{83} -1.49448 q^{84} +4.56181 q^{85} +6.18853 q^{86} +3.95755 q^{87} +1.55337 q^{88} -1.61639 q^{89} -5.72345 q^{90} -1.20160 q^{91} +8.39759 q^{92} -8.12150 q^{93} -4.64596 q^{94} +14.3389 q^{95} -2.27315 q^{96} -0.598127 q^{97} -6.56776 q^{98} +3.36651 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 54 q^{2} - 21 q^{3} + 54 q^{4} - 14 q^{5} - 21 q^{6} - 44 q^{7} + 54 q^{8} + 39 q^{9}+O(q^{10}) \) 54 * q + 54 * q^2 - 21 * q^3 + 54 * q^4 - 14 * q^5 - 21 * q^6 - 44 * q^7 + 54 * q^8 + 39 * q^9	\( 54 q + 54 q^{2} - 21 q^{3} + 54 q^{4} - 14 q^{5} - 21 q^{6} - 44 q^{7} + 54 q^{8} + 39 q^{9} - 14 q^{10} - 31 q^{11} - 21 q^{12} - 34 q^{13} - 44 q^{14} - 22 q^{15} + 54 q^{16} - 40 q^{17} + 39 q^{18} - 44 q^{19} - 14 q^{20} - 3 q^{21} - 31 q^{22} - 33 q^{23} - 21 q^{24} + 14 q^{25} - 34 q^{26} - 66 q^{27} - 44 q^{28} - 22 q^{30} - 65 q^{31} + 54 q^{32} - 43 q^{33} - 40 q^{34} - 46 q^{35} + 39 q^{36} - 58 q^{37} - 44 q^{38} - 36 q^{39} - 14 q^{40} - 49 q^{41} - 3 q^{42} - 47 q^{43} - 31 q^{44} - 45 q^{45} - 33 q^{46} - 66 q^{47} - 21 q^{48} + 16 q^{49} + 14 q^{50} - 33 q^{51} - 34 q^{52} - 16 q^{53} - 66 q^{54} - 50 q^{55} - 44 q^{56} - 33 q^{57} - 70 q^{59} - 22 q^{60} - 40 q^{61} - 65 q^{62} - 117 q^{63} + 54 q^{64} - 33 q^{65} - 43 q^{66} - 82 q^{67} - 40 q^{68} - q^{69} - 46 q^{70} - 60 q^{71} + 39 q^{72} - 92 q^{73} - 58 q^{74} - 68 q^{75} - 44 q^{76} + 13 q^{77} - 36 q^{78} - 57 q^{79} - 14 q^{80} + 26 q^{81} - 49 q^{82} - 77 q^{83} - 3 q^{84} - 24 q^{85} - 47 q^{86} - 61 q^{87} - 31 q^{88} - 54 q^{89} - 45 q^{90} - 46 q^{91} - 33 q^{92} - 24 q^{93} - 66 q^{94} - 66 q^{95} - 21 q^{96} - 137 q^{97} + 16 q^{98} - 71 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 21 * q^3 + 54 * q^4 - 14 * q^5 - 21 * q^6 - 44 * q^7 + 54 * q^8 + 39 * q^9 - 14 * q^10 - 31 * q^11 - 21 * q^12 - 34 * q^13 - 44 * q^14 - 22 * q^15 + 54 * q^16 - 40 * q^17 + 39 * q^18 - 44 * q^19 - 14 * q^20 - 3 * q^21 - 31 * q^22 - 33 * q^23 - 21 * q^24 + 14 * q^25 - 34 * q^26 - 66 * q^27 - 44 * q^28 - 22 * q^30 - 65 * q^31 + 54 * q^32 - 43 * q^33 - 40 * q^34 - 46 * q^35 + 39 * q^36 - 58 * q^37 - 44 * q^38 - 36 * q^39 - 14 * q^40 - 49 * q^41 - 3 * q^42 - 47 * q^43 - 31 * q^44 - 45 * q^45 - 33 * q^46 - 66 * q^47 - 21 * q^48 + 16 * q^49 + 14 * q^50 - 33 * q^51 - 34 * q^52 - 16 * q^53 - 66 * q^54 - 50 * q^55 - 44 * q^56 - 33 * q^57 - 70 * q^59 - 22 * q^60 - 40 * q^61 - 65 * q^62 - 117 * q^63 + 54 * q^64 - 33 * q^65 - 43 * q^66 - 82 * q^67 - 40 * q^68 - q^69 - 46 * q^70 - 60 * q^71 + 39 * q^72 - 92 * q^73 - 58 * q^74 - 68 * q^75 - 44 * q^76 + 13 * q^77 - 36 * q^78 - 57 * q^79 - 14 * q^80 + 26 * q^81 - 49 * q^82 - 77 * q^83 - 3 * q^84 - 24 * q^85 - 47 * q^86 - 61 * q^87 - 31 * q^88 - 54 * q^89 - 45 * q^90 - 46 * q^91 - 33 * q^92 - 24 * q^93 - 66 * q^94 - 66 * q^95 - 21 * q^96 - 137 * q^97 + 16 * q^98 - 71 * q^99

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