LMFDB - Embedded newform 6038.2.a.b.1.13

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			1.13
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.11795 q^{3} +1.00000 q^{4} +1.57843 q^{5} -2.11795 q^{6} +1.37381 q^{7} +1.00000 q^{8} +1.48570 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.11795 q^{3} +1.00000 q^{4} +1.57843 q^{5} -2.11795 q^{6} +1.37381 q^{7} +1.00000 q^{8} +1.48570 q^{9} +1.57843 q^{10} -2.38527 q^{11} -2.11795 q^{12} +1.78007 q^{13} +1.37381 q^{14} -3.34303 q^{15} +1.00000 q^{16} -2.37925 q^{17} +1.48570 q^{18} +3.65698 q^{19} +1.57843 q^{20} -2.90966 q^{21} -2.38527 q^{22} -9.35820 q^{23} -2.11795 q^{24} -2.50856 q^{25} +1.78007 q^{26} +3.20721 q^{27} +1.37381 q^{28} -1.09404 q^{29} -3.34303 q^{30} +2.30877 q^{31} +1.00000 q^{32} +5.05188 q^{33} -2.37925 q^{34} +2.16847 q^{35} +1.48570 q^{36} -5.21531 q^{37} +3.65698 q^{38} -3.77009 q^{39} +1.57843 q^{40} +12.2751 q^{41} -2.90966 q^{42} -5.45174 q^{43} -2.38527 q^{44} +2.34507 q^{45} -9.35820 q^{46} -11.1379 q^{47} -2.11795 q^{48} -5.11264 q^{49} -2.50856 q^{50} +5.03912 q^{51} +1.78007 q^{52} -0.957432 q^{53} +3.20721 q^{54} -3.76499 q^{55} +1.37381 q^{56} -7.74530 q^{57} -1.09404 q^{58} -9.60099 q^{59} -3.34303 q^{60} -8.50861 q^{61} +2.30877 q^{62} +2.04107 q^{63} +1.00000 q^{64} +2.80971 q^{65} +5.05188 q^{66} -4.77368 q^{67} -2.37925 q^{68} +19.8202 q^{69} +2.16847 q^{70} +3.00736 q^{71} +1.48570 q^{72} +14.1019 q^{73} -5.21531 q^{74} +5.31300 q^{75} +3.65698 q^{76} -3.27692 q^{77} -3.77009 q^{78} -7.36452 q^{79} +1.57843 q^{80} -11.2498 q^{81} +12.2751 q^{82} +3.39907 q^{83} -2.90966 q^{84} -3.75548 q^{85} -5.45174 q^{86} +2.31712 q^{87} -2.38527 q^{88} +16.4629 q^{89} +2.34507 q^{90} +2.44548 q^{91} -9.35820 q^{92} -4.88985 q^{93} -11.1379 q^{94} +5.77229 q^{95} -2.11795 q^{96} +3.90931 q^{97} -5.11264 q^{98} -3.54380 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.11795	−1.22280	−0.611399	−	0.791323i	$-0.709393\pi$
$3$	−2.11795	−1.22280	−0.611399	+	0.791323i	$0.709393\pi$
$4$	1.00000	0.500000
$5$	1.57843	0.705895	0.352948	−	0.935643i	$-0.385179\pi$
$5$	1.57843	0.705895	0.352948	+	0.935643i	$0.385179\pi$
$6$	−2.11795	−0.864648
$7$	1.37381	0.519253	0.259626	−	0.965709i	$-0.416401\pi$
$7$	1.37381	0.519253	0.259626	+	0.965709i	$0.416401\pi$
$8$	1.00000	0.353553
$9$	1.48570	0.495233
$10$	1.57843	0.499143
$11$	−2.38527	−0.719187	−0.359593	−	0.933109i	$-0.617085\pi$
$11$	−2.38527	−0.719187	−0.359593	+	0.933109i	$0.617085\pi$
$12$	−2.11795	−0.611399
$13$	1.78007	0.493702	0.246851	−	0.969053i	$-0.420604\pi$
$13$	1.78007	0.493702	0.246851	+	0.969053i	$0.420604\pi$
$14$	1.37381	0.367167
$15$	−3.34303	−0.863167
$16$	1.00000	0.250000
$17$	−2.37925	−0.577053	−0.288526	−	0.957472i	$-0.593165\pi$
$17$	−2.37925	−0.577053	−0.288526	+	0.957472i	$0.593165\pi$
$18$	1.48570	0.350183
$19$	3.65698	0.838970	0.419485	−	0.907762i	$-0.362211\pi$
$19$	3.65698	0.838970	0.419485	+	0.907762i	$0.362211\pi$
$20$	1.57843	0.352948
$21$	−2.90966	−0.634941
$22$	−2.38527	−0.508542
$23$	−9.35820	−1.95132	−0.975660	−	0.219291i	$-0.929626\pi$
$23$	−9.35820	−1.95132	−0.975660	+	0.219291i	$0.929626\pi$
$24$	−2.11795	−0.432324
$25$	−2.50856	−0.501712
$26$	1.78007	0.349100
$27$	3.20721	0.617228
$28$	1.37381	0.259626
$29$	−1.09404	−0.203158	−0.101579	−	0.994827i	$-0.532389\pi$
$29$	−1.09404	−0.203158	−0.101579	+	0.994827i	$0.532389\pi$
$30$	−3.34303	−0.610351
$31$	2.30877	0.414667	0.207333	−	0.978270i	$-0.433521\pi$
$31$	2.30877	0.414667	0.207333	+	0.978270i	$0.433521\pi$
$32$	1.00000	0.176777
$33$	5.05188	0.879420
$34$	−2.37925	−0.408038
$35$	2.16847	0.366538
$36$	1.48570	0.247616
$37$	−5.21531	−0.857392	−0.428696	−	0.903449i	$-0.641027\pi$
$37$	−5.21531	−0.857392	−0.428696	+	0.903449i	$0.641027\pi$
$38$	3.65698	0.593241
$39$	−3.77009	−0.603697
$40$	1.57843	0.249572
$41$	12.2751	1.91704	0.958522	−	0.285019i	$-0.0919999\pi$
$41$	12.2751	1.91704	0.958522	+	0.285019i	$0.0919999\pi$
$42$	−2.90966	−0.448971
$43$	−5.45174	−0.831383	−0.415692	−	0.909506i	$-0.636460\pi$
$43$	−5.45174	−0.831383	−0.415692	+	0.909506i	$0.636460\pi$
$44$	−2.38527	−0.359593
$45$	2.34507	0.349583
$46$	−9.35820	−1.37979
$47$	−11.1379	−1.62464	−0.812318	−	0.583214i	$-0.801795\pi$
$47$	−11.1379	−1.62464	−0.812318	+	0.583214i	$0.801795\pi$
$48$	−2.11795	−0.305699
$49$	−5.11264	−0.730377
$50$	−2.50856	−0.354764
$51$	5.03912	0.705618
$52$	1.78007	0.246851
$53$	−0.957432	−0.131513	−0.0657567	−	0.997836i	$-0.520946\pi$
$53$	−0.957432	−0.131513	−0.0657567	+	0.997836i	$0.520946\pi$
$54$	3.20721	0.436446
$55$	−3.76499	−0.507671
$56$	1.37381	0.183584
$57$	−7.74530	−1.02589
$58$	−1.09404	−0.143654
$59$	−9.60099	−1.24994	−0.624971	−	0.780648i	$-0.714889\pi$
$59$	−9.60099	−1.24994	−0.624971	+	0.780648i	$0.714889\pi$
$60$	−3.34303	−0.431583
$61$	−8.50861	−1.08942	−0.544708	−	0.838626i	$-0.683359\pi$
$61$	−8.50861	−1.08942	−0.544708	+	0.838626i	$0.683359\pi$
$62$	2.30877	0.293214
$63$	2.04107	0.257151
$64$	1.00000	0.125000
$65$	2.80971	0.348502
$66$	5.05188	0.621844
$67$	−4.77368	−0.583198	−0.291599	−	0.956541i	$-0.594187\pi$
$67$	−4.77368	−0.583198	−0.291599	+	0.956541i	$0.594187\pi$
$68$	−2.37925	−0.288526
$69$	19.8202	2.38607
$70$	2.16847	0.259181
$71$	3.00736	0.356908	0.178454	−	0.983948i	$-0.442891\pi$
$71$	3.00736	0.356908	0.178454	+	0.983948i	$0.442891\pi$
$72$	1.48570	0.175091
$73$	14.1019	1.65050	0.825250	−	0.564768i	$-0.191034\pi$
$73$	14.1019	1.65050	0.825250	+	0.564768i	$0.191034\pi$
$74$	−5.21531	−0.606268
$75$	5.31300	0.613492
$76$	3.65698	0.419485
$77$	−3.27692	−0.373440
$78$	−3.77009	−0.426878
$79$	−7.36452	−0.828573	−0.414287	−	0.910147i	$-0.635969\pi$
$79$	−7.36452	−0.828573	−0.414287	+	0.910147i	$0.635969\pi$
$80$	1.57843	0.176474
$81$	−11.2498	−1.24998
$82$	12.2751	1.35555
$83$	3.39907	0.373097	0.186548	−	0.982446i	$-0.440270\pi$
$83$	3.39907	0.373097	0.186548	+	0.982446i	$0.440270\pi$
$84$	−2.90966	−0.317470
$85$	−3.75548	−0.407339
$86$	−5.45174	−0.587877
$87$	2.31712	0.248421
$88$	−2.38527	−0.254271
$89$	16.4629	1.74506	0.872531	−	0.488559i	$-0.162477\pi$
$89$	16.4629	1.74506	0.872531	+	0.488559i	$0.162477\pi$
$90$	2.34507	0.247192
$91$	2.44548	0.256356
$92$	−9.35820	−0.975660
$93$	−4.88985	−0.507054
$94$	−11.1379	−1.14879
$95$	5.77229	0.592225
$96$	−2.11795	−0.216162
$97$	3.90931	0.396931	0.198465	−	0.980108i	$-0.436404\pi$
$97$	3.90931	0.396931	0.198465	+	0.980108i	$0.436404\pi$
$98$	−5.11264	−0.516454
$99$	−3.54380	−0.356165
$100$	−2.50856	−0.250856
$101$	6.02268	0.599279	0.299639	−	0.954053i	$-0.403134\pi$
$101$	6.02268	0.599279	0.299639	+	0.954053i	$0.403134\pi$
$102$	5.03912	0.498948
$103$	3.08807	0.304276	0.152138	−	0.988359i	$-0.451384\pi$
$103$	3.08807	0.304276	0.152138	+	0.988359i	$0.451384\pi$
$104$	1.78007	0.174550
$105$	−4.59270	−0.448202
$106$	−0.957432	−0.0929940
$107$	−14.0423	−1.35752	−0.678760	−	0.734360i	$-0.737482\pi$
$107$	−14.0423	−1.35752	−0.678760	+	0.734360i	$0.737482\pi$
$108$	3.20721	0.308614
$109$	−9.22515	−0.883609	−0.441805	−	0.897111i	$-0.645662\pi$
$109$	−9.22515	−0.883609	−0.441805	+	0.897111i	$0.645662\pi$
$110$	−3.76499	−0.358977
$111$	11.0458	1.04842
$112$	1.37381	0.129813
$113$	−15.1176	−1.42215	−0.711074	−	0.703117i	$-0.751791\pi$
$113$	−15.1176	−1.42215	−0.711074	+	0.703117i	$0.751791\pi$
$114$	−7.74530	−0.725414
$115$	−14.7713	−1.37743
$116$	−1.09404	−0.101579
$117$	2.64464	0.244497
$118$	−9.60099	−0.883843
$119$	−3.26864	−0.299636
$120$	−3.34303	−0.305176
$121$	−5.31047	−0.482770
$122$	−8.50861	−0.770333
$123$	−25.9979	−2.34416
$124$	2.30877	0.207333
$125$	−11.8517	−1.06005
$126$	2.04107	0.181833
$127$	−6.51130	−0.577784	−0.288892	−	0.957362i	$-0.593287\pi$
$127$	−6.51130	−0.577784	−0.288892	+	0.957362i	$0.593287\pi$
$128$	1.00000	0.0883883
$129$	11.5465	1.01661
$130$	2.80971	0.246428
$131$	9.90482	0.865388	0.432694	−	0.901541i	$-0.357563\pi$
$131$	9.90482	0.865388	0.432694	+	0.901541i	$0.357563\pi$
$132$	5.05188	0.439710
$133$	5.02401	0.435637
$134$	−4.77368	−0.412383
$135$	5.06235	0.435698
$136$	−2.37925	−0.204019
$137$	−4.02313	−0.343720	−0.171860	−	0.985121i	$-0.554978\pi$
$137$	−4.02313	−0.343720	−0.171860	+	0.985121i	$0.554978\pi$
$138$	19.8202	1.68720
$139$	9.33753	0.791999	0.396000	−	0.918251i	$-0.370398\pi$
$139$	9.33753	0.791999	0.396000	+	0.918251i	$0.370398\pi$
$140$	2.16847	0.183269
$141$	23.5896	1.98660
$142$	3.00736	0.252372
$143$	−4.24595	−0.355064
$144$	1.48570	0.123808
$145$	−1.72686	−0.143408
$146$	14.1019	1.16708
$147$	10.8283	0.893103
$148$	−5.21531	−0.428696
$149$	15.7420	1.28963	0.644816	−	0.764337i	$-0.276934\pi$
$149$	15.7420	1.28963	0.644816	+	0.764337i	$0.276934\pi$
$150$	5.31300	0.433804
$151$	−1.93378	−0.157368	−0.0786842	−	0.996900i	$-0.525072\pi$
$151$	−1.93378	−0.157368	−0.0786842	+	0.996900i	$0.525072\pi$
$152$	3.65698	0.296621
$153$	−3.53485	−0.285775
$154$	−3.27692	−0.264062
$155$	3.64423	0.292711
$156$	−3.77009	−0.301849
$157$	−1.22984	−0.0981523	−0.0490762	−	0.998795i	$-0.515628\pi$
$157$	−1.22984	−0.0981523	−0.0490762	+	0.998795i	$0.515628\pi$
$158$	−7.36452	−0.585890
$159$	2.02779	0.160814
$160$	1.57843	0.124786
$161$	−12.8564	−1.01323
$162$	−11.2498	−0.883867
$163$	−18.6692	−1.46229	−0.731143	−	0.682224i	$-0.761013\pi$
$163$	−18.6692	−1.46229	−0.731143	+	0.682224i	$0.761013\pi$
$164$	12.2751	0.958522
$165$	7.97404	0.620778
$166$	3.39907	0.263819
$167$	9.21663	0.713204	0.356602	−	0.934256i	$-0.383935\pi$
$167$	9.21663	0.713204	0.356602	+	0.934256i	$0.383935\pi$
$168$	−2.90966	−0.224485
$169$	−9.83136	−0.756259
$170$	−3.75548	−0.288032
$171$	5.43318	0.415485
$172$	−5.45174	−0.415692
$173$	−9.97229	−0.758179	−0.379090	−	0.925360i	$-0.623763\pi$
$173$	−9.97229	−0.758179	−0.379090	+	0.925360i	$0.623763\pi$
$174$	2.31712	0.175660
$175$	−3.44629	−0.260515
$176$	−2.38527	−0.179797
$177$	20.3344	1.52843
$178$	16.4629	1.23394
$179$	20.2780	1.51565	0.757823	−	0.652461i	$-0.226263\pi$
$179$	20.2780	1.51565	0.757823	+	0.652461i	$0.226263\pi$
$180$	2.34507	0.174791
$181$	9.15638	0.680589	0.340294	−	0.940319i	$-0.389473\pi$
$181$	9.15638	0.680589	0.340294	+	0.940319i	$0.389473\pi$
$182$	2.44548	0.181271
$183$	18.0208	1.33213
$184$	−9.35820	−0.689896
$185$	−8.23200	−0.605229
$186$	−4.88985	−0.358541
$187$	5.67516	0.415009
$188$	−11.1379	−0.812318
$189$	4.40611	0.320497
$190$	5.77229	0.418766
$191$	16.4070	1.18717	0.593586	−	0.804771i	$-0.297712\pi$
$191$	16.4070	1.18717	0.593586	+	0.804771i	$0.297712\pi$
$192$	−2.11795	−0.152850
$193$	−17.7169	−1.27529	−0.637646	−	0.770329i	$-0.720092\pi$
$193$	−17.7169	−1.27529	−0.637646	+	0.770329i	$0.720092\pi$
$194$	3.90931	0.280672
$195$	−5.95082	−0.426147
$196$	−5.11264	−0.365188
$197$	5.20693	0.370978	0.185489	−	0.982646i	$-0.440613\pi$
$197$	5.20693	0.370978	0.185489	+	0.982646i	$0.440613\pi$
$198$	−3.54380	−0.251847
$199$	−5.66973	−0.401917	−0.200958	−	0.979600i	$-0.564406\pi$
$199$	−5.66973	−0.401917	−0.200958	+	0.979600i	$0.564406\pi$
$200$	−2.50856	−0.177382
$201$	10.1104	0.713132
$202$	6.02268	0.423754
$203$	−1.50301	−0.105490
$204$	5.03912	0.352809
$205$	19.3753	1.35323
$206$	3.08807	0.215156
$207$	−13.9035	−0.966358
$208$	1.78007	0.123425
$209$	−8.72291	−0.603376
$210$	−4.59270	−0.316926
$211$	−11.3289	−0.779912	−0.389956	−	0.920833i	$-0.627510\pi$
$211$	−11.3289	−0.779912	−0.389956	+	0.920833i	$0.627510\pi$
$212$	−0.957432	−0.0657567
$213$	−6.36942	−0.436425
$214$	−14.0423	−0.959912
$215$	−8.60520	−0.586870
$216$	3.20721	0.218223
$217$	3.17182	0.215317
$218$	−9.22515	−0.624806
$219$	−29.8670	−2.01823
$220$	−3.76499	−0.253835
$221$	−4.23522	−0.284892
$222$	11.0458	0.741342
$223$	−7.97845	−0.534277	−0.267138	−	0.963658i	$-0.586078\pi$
$223$	−7.97845	−0.534277	−0.267138	+	0.963658i	$0.586078\pi$
$224$	1.37381	0.0917918
$225$	−3.72696	−0.248464
$226$	−15.1176	−1.00561
$227$	−13.3038	−0.883003	−0.441502	−	0.897260i	$-0.645554\pi$
$227$	−13.3038	−0.883003	−0.441502	+	0.897260i	$0.645554\pi$
$228$	−7.74530	−0.512945
$229$	−15.3638	−1.01527	−0.507636	−	0.861572i	$-0.669480\pi$
$229$	−15.3638	−1.01527	−0.507636	+	0.861572i	$0.669480\pi$
$230$	−14.7713	−0.973988
$231$	6.94034	0.456641
$232$	−1.09404	−0.0718272
$233$	19.0112	1.24546	0.622732	−	0.782435i	$-0.286023\pi$
$233$	19.0112	1.24546	0.622732	+	0.782435i	$0.286023\pi$
$234$	2.64464	0.172886
$235$	−17.5805	−1.14682
$236$	−9.60099	−0.624971
$237$	15.5977	1.01318
$238$	−3.26864	−0.211875
$239$	17.5268	1.13371	0.566856	−	0.823817i	$-0.308160\pi$
$239$	17.5268	1.13371	0.566856	+	0.823817i	$0.308160\pi$
$240$	−3.34303	−0.215792
$241$	−25.3661	−1.63398	−0.816988	−	0.576655i	$-0.804358\pi$
$241$	−25.3661	−1.63398	−0.816988	+	0.576655i	$0.804358\pi$
$242$	−5.31047	−0.341370
$243$	14.2048	0.911241
$244$	−8.50861	−0.544708
$245$	−8.06994	−0.515570
$246$	−25.9979	−1.65757
$247$	6.50968	0.414201
$248$	2.30877	0.146607
$249$	−7.19906	−0.456222
$250$	−11.8517	−0.749569
$251$	5.39268	0.340383	0.170191	−	0.985411i	$-0.445561\pi$
$251$	5.39268	0.340383	0.170191	+	0.985411i	$0.445561\pi$
$252$	2.04107	0.128575
$253$	22.3219	1.40336
$254$	−6.51130	−0.408555
$255$	7.95390	0.498093
$256$	1.00000	0.0625000
$257$	−0.0615105	−0.00383692	−0.00191846	−	0.999998i	$-0.500611\pi$
$257$	−0.0615105	−0.00383692	−0.00191846	+	0.999998i	$0.500611\pi$
$258$	11.5465	0.718854
$259$	−7.16486	−0.445203
$260$	2.80971	0.174251
$261$	−1.62541	−0.100611
$262$	9.90482	0.611922
$263$	−7.00833	−0.432152	−0.216076	−	0.976377i	$-0.569326\pi$
$263$	−7.00833	−0.432152	−0.216076	+	0.976377i	$0.569326\pi$
$264$	5.05188	0.310922
$265$	−1.51124	−0.0928347
$266$	5.02401	0.308042
$267$	−34.8675	−2.13386
$268$	−4.77368	−0.291599
$269$	7.73544	0.471638	0.235819	−	0.971797i	$-0.424223\pi$
$269$	7.73544	0.471638	0.235819	+	0.971797i	$0.424223\pi$
$270$	5.06235	0.308085
$271$	−18.0364	−1.09563	−0.547817	−	0.836598i	$-0.684541\pi$
$271$	−18.0364	−1.09563	−0.547817	+	0.836598i	$0.684541\pi$
$272$	−2.37925	−0.144263
$273$	−5.17939	−0.313471
$274$	−4.02313	−0.243046
$275$	5.98360	0.360825
$276$	19.8202	1.19303
$277$	16.3985	0.985290	0.492645	−	0.870230i	$-0.336030\pi$
$277$	16.3985	0.985290	0.492645	+	0.870230i	$0.336030\pi$
$278$	9.33753	0.560028
$279$	3.43013	0.205357
$280$	2.16847	0.129591
$281$	−9.74257	−0.581193	−0.290597	−	0.956846i	$-0.593854\pi$
$281$	−9.74257	−0.581193	−0.290597	+	0.956846i	$0.593854\pi$
$282$	23.5896	1.40474
$283$	−21.2223	−1.26153	−0.630766	−	0.775973i	$-0.717259\pi$
$283$	−21.2223	−1.26153	−0.630766	+	0.775973i	$0.717259\pi$
$284$	3.00736	0.178454
$285$	−12.2254	−0.724171
$286$	−4.24595	−0.251068
$287$	16.8637	0.995430
$288$	1.48570	0.0875456
$289$	−11.3392	−0.667010
$290$	−1.72686	−0.101405
$291$	−8.27972	−0.485366
$292$	14.1019	0.825250
$293$	9.41311	0.549920	0.274960	−	0.961456i	$-0.411335\pi$
$293$	9.41311	0.549920	0.274960	+	0.961456i	$0.411335\pi$
$294$	10.8283	0.631519
$295$	−15.1545	−0.882329
$296$	−5.21531	−0.303134
$297$	−7.65007	−0.443902
$298$	15.7420	0.911908
$299$	−16.6582	−0.963370
$300$	5.31300	0.306746
$301$	−7.48968	−0.431698
$302$	−1.93378	−0.111276
$303$	−12.7557	−0.732796
$304$	3.65698	0.209742
$305$	−13.4302	−0.769014
$306$	−3.53485	−0.202074
$307$	−29.3285	−1.67387	−0.836933	−	0.547306i	$-0.815653\pi$
$307$	−29.3285	−1.67387	−0.836933	+	0.547306i	$0.815653\pi$
$308$	−3.27692	−0.186720
$309$	−6.54036	−0.372068
$310$	3.64423	0.206978
$311$	−13.6875	−0.776147	−0.388074	−	0.921628i	$-0.626859\pi$
$311$	−13.6875	−0.776147	−0.388074	+	0.921628i	$0.626859\pi$
$312$	−3.77009	−0.213439
$313$	−2.59688	−0.146785	−0.0733923	−	0.997303i	$-0.523383\pi$
$313$	−2.59688	−0.146785	−0.0733923	+	0.997303i	$0.523383\pi$
$314$	−1.22984	−0.0694042
$315$	3.22169	0.181522
$316$	−7.36452	−0.414287
$317$	−12.1478	−0.682290	−0.341145	−	0.940011i	$-0.610815\pi$
$317$	−12.1478	−0.682290	−0.341145	+	0.940011i	$0.610815\pi$
$318$	2.02779	0.113713
$319$	2.60958	0.146109
$320$	1.57843	0.0882369
$321$	29.7408	1.65997
$322$	−12.8564	−0.716460
$323$	−8.70088	−0.484130
$324$	−11.2498	−0.624989
$325$	−4.46540	−0.247696
$326$	−18.6692	−1.03399
$327$	19.5384	1.08047
$328$	12.2751	0.677777
$329$	−15.3015	−0.843597
$330$	7.97404	0.438957
$331$	−30.9589	−1.70166	−0.850828	−	0.525444i	$-0.823899\pi$
$331$	−30.9589	−1.70166	−0.850828	+	0.525444i	$0.823899\pi$
$332$	3.39907	0.186548
$333$	−7.74838	−0.424609
$334$	9.21663	0.504311
$335$	−7.53492	−0.411676
$336$	−2.90966	−0.158735
$337$	−9.89564	−0.539050	−0.269525	−	0.962993i	$-0.586867\pi$
$337$	−9.89564	−0.539050	−0.269525	+	0.962993i	$0.586867\pi$
$338$	−9.83136	−0.534756
$339$	32.0183	1.73900
$340$	−3.75548	−0.203669
$341$	−5.50704	−0.298223
$342$	5.43318	0.293793
$343$	−16.6405	−0.898503
$344$	−5.45174	−0.293938
$345$	31.2847	1.68431
$346$	−9.97229	−0.536114
$347$	32.8557	1.76379	0.881893	−	0.471449i	$-0.156269\pi$
$347$	32.8557	1.76379	0.881893	+	0.471449i	$0.156269\pi$
$348$	2.31712	0.124211
$349$	−23.4315	−1.25426	−0.627130	−	0.778915i	$-0.715771\pi$
$349$	−23.4315	−1.25426	−0.627130	+	0.778915i	$0.715771\pi$
$350$	−3.44629	−0.184212
$351$	5.70905	0.304726
$352$	−2.38527	−0.127135
$353$	35.0330	1.86462	0.932310	−	0.361660i	$-0.117790\pi$
$353$	35.0330	1.86462	0.932310	+	0.361660i	$0.117790\pi$
$354$	20.3344	1.08076
$355$	4.74690	0.251939
$356$	16.4629	0.872531
$357$	6.92281	0.366394
$358$	20.2780	1.07172
$359$	−19.2455	−1.01574	−0.507871	−	0.861433i	$-0.669567\pi$
$359$	−19.2455	−1.01574	−0.507871	+	0.861433i	$0.669567\pi$
$360$	2.34507	0.123596
$361$	−5.62647	−0.296130
$362$	9.15638	0.481249
$363$	11.2473	0.590330
$364$	2.44548	0.128178
$365$	22.2588	1.16508
$366$	18.0208	0.941961
$367$	−14.4879	−0.756260	−0.378130	−	0.925752i	$-0.623433\pi$
$367$	−14.4879	−0.756260	−0.378130	+	0.925752i	$0.623433\pi$
$368$	−9.35820	−0.487830
$369$	18.2371	0.949383
$370$	−8.23200	−0.427962
$371$	−1.31533	−0.0682887
$372$	−4.88985	−0.253527
$373$	23.1254	1.19739	0.598695	−	0.800977i	$-0.295686\pi$
$373$	23.1254	1.19739	0.598695	+	0.800977i	$0.295686\pi$
$374$	5.67516	0.293455
$375$	25.1013	1.29623
$376$	−11.1379	−0.574396
$377$	−1.94746	−0.100299
$378$	4.40611	0.226626
$379$	−22.2730	−1.14409	−0.572043	−	0.820223i	$-0.693849\pi$
$379$	−22.2730	−1.14409	−0.572043	+	0.820223i	$0.693849\pi$
$380$	5.77229	0.296112
$381$	13.7906	0.706513
$382$	16.4070	0.839457
$383$	−23.9652	−1.22457	−0.612283	−	0.790639i	$-0.709748\pi$
$383$	−23.9652	−1.22457	−0.612283	+	0.790639i	$0.709748\pi$
$384$	−2.11795	−0.108081
$385$	−5.17239	−0.263609
$386$	−17.7169	−0.901768
$387$	−8.09965	−0.411728
$388$	3.90931	0.198465
$389$	8.31701	0.421689	0.210845	−	0.977520i	$-0.432379\pi$
$389$	8.31701	0.421689	0.210845	+	0.977520i	$0.432379\pi$
$390$	−5.95082	−0.301331
$391$	22.2655	1.12601
$392$	−5.11264	−0.258227
$393$	−20.9779	−1.05819
$394$	5.20693	0.262321
$395$	−11.6244	−0.584886
$396$	−3.54380	−0.178083
$397$	−2.49805	−0.125374	−0.0626868	−	0.998033i	$-0.519967\pi$
$397$	−2.49805	−0.125374	−0.0626868	+	0.998033i	$0.519967\pi$
$398$	−5.66973	−0.284198
$399$	−10.6406	−0.532696
$400$	−2.50856	−0.125428
$401$	−3.08484	−0.154050	−0.0770249	−	0.997029i	$-0.524542\pi$
$401$	−3.08484	−0.154050	−0.0770249	+	0.997029i	$0.524542\pi$
$402$	10.1104	0.504261
$403$	4.10976	0.204722
$404$	6.02268	0.299639
$405$	−17.7570	−0.882353
$406$	−1.50301	−0.0745929
$407$	12.4399	0.616625
$408$	5.03912	0.249474
$409$	32.2923	1.59675	0.798375	−	0.602161i	$-0.205693\pi$
$409$	32.2923	1.59675	0.798375	+	0.602161i	$0.205693\pi$
$410$	19.3753	0.956880
$411$	8.52078	0.420299
$412$	3.08807	0.152138
$413$	−13.1900	−0.649036
$414$	−13.9035	−0.683318
$415$	5.36520	0.263367
$416$	1.78007	0.0872750
$417$	−19.7764	−0.968454
$418$	−8.72291	−0.426651
$419$	25.2513	1.23361	0.616803	−	0.787117i	$-0.288427\pi$
$419$	25.2513	1.23361	0.616803	+	0.787117i	$0.288427\pi$
$420$	−4.59270	−0.224101
$421$	−0.907578	−0.0442326	−0.0221163	−	0.999755i	$-0.507040\pi$
$421$	−0.907578	−0.0442326	−0.0221163	+	0.999755i	$0.507040\pi$
$422$	−11.3289	−0.551481
$423$	−16.5476	−0.804574
$424$	−0.957432	−0.0464970
$425$	5.96849	0.289514
$426$	−6.36942	−0.308599
$427$	−11.6892	−0.565682
$428$	−14.0423	−0.678760
$429$	8.99269	0.434171
$430$	−8.60520	−0.414979
$431$	30.0671	1.44828	0.724141	−	0.689652i	$-0.242237\pi$
$431$	30.0671	1.44828	0.724141	+	0.689652i	$0.242237\pi$
$432$	3.20721	0.154307
$433$	0.00327995	0.000157624 0	7.88121e−5	−	1.00000i	$-0.499975\pi$
$433$	0.00327995	0.000157624 0	7.88121e−5		1.00000i	$0.499975\pi$
$434$	3.17182	0.152252
$435$	3.65741	0.175359
$436$	−9.22515	−0.441805
$437$	−34.2228	−1.63710
$438$	−29.8670	−1.42710
$439$	−24.7471	−1.18112	−0.590558	−	0.806995i	$-0.701092\pi$
$439$	−24.7471	−1.18112	−0.590558	+	0.806995i	$0.701092\pi$
$440$	−3.76499	−0.179489
$441$	−7.59584	−0.361707
$442$	−4.23522	−0.201449
$443$	−16.5484	−0.786237	−0.393119	−	0.919488i	$-0.628604\pi$
$443$	−16.5484	−0.786237	−0.393119	+	0.919488i	$0.628604\pi$
$444$	11.0458	0.524208
$445$	25.9855	1.23183
$446$	−7.97845	−0.377791
$447$	−33.3407	−1.57696
$448$	1.37381	0.0649066
$449$	−9.41118	−0.444141	−0.222071	−	0.975031i	$-0.571282\pi$
$449$	−9.41118	−0.444141	−0.222071	+	0.975031i	$0.571282\pi$
$450$	−3.72696	−0.175691
$451$	−29.2794	−1.37871
$452$	−15.1176	−0.711074
$453$	4.09563	0.192430
$454$	−13.3038	−0.624377
$455$	3.86002	0.180960
$456$	−7.74530	−0.362707
$457$	17.1934	0.804273	0.402137	−	0.915580i	$-0.368268\pi$
$457$	17.1934	0.804273	0.402137	+	0.915580i	$0.368268\pi$
$458$	−15.3638	−0.717905
$459$	−7.63075	−0.356173
$460$	−14.7713	−0.688714
$461$	−12.3316	−0.574339	−0.287169	−	0.957880i	$-0.592714\pi$
$461$	−12.3316	−0.574339	−0.287169	+	0.957880i	$0.592714\pi$
$462$	6.94034	0.322894
$463$	−13.5765	−0.630956	−0.315478	−	0.948933i	$-0.602165\pi$
$463$	−13.5765	−0.630956	−0.315478	+	0.948933i	$0.602165\pi$
$464$	−1.09404	−0.0507895
$465$	−7.71828	−0.357927
$466$	19.0112	0.880676
$467$	−36.5206	−1.68997	−0.844987	−	0.534787i	$-0.820392\pi$
$467$	−36.5206	−1.68997	−0.844987	+	0.534787i	$0.820392\pi$
$468$	2.64464	0.122249
$469$	−6.55814	−0.302827
$470$	−17.5805	−0.810927
$471$	2.60475	0.120020
$472$	−9.60099	−0.441921
$473$	13.0039	0.597920
$474$	15.5977	0.716424
$475$	−9.17376	−0.420921
$476$	−3.26864	−0.149818
$477$	−1.42246	−0.0651298
$478$	17.5268	0.801656
$479$	2.26825	0.103639	0.0518195	−	0.998656i	$-0.483498\pi$
$479$	2.26825	0.103639	0.0518195	+	0.998656i	$0.483498\pi$
$480$	−3.34303	−0.152588
$481$	−9.28360	−0.423296
$482$	−25.3661	−1.15540
$483$	27.2292	1.23897
$484$	−5.31047	−0.241385
$485$	6.17058	0.280191
$486$	14.2048	0.644345
$487$	−15.9273	−0.721737	−0.360868	−	0.932617i	$-0.617520\pi$
$487$	−15.9273	−0.721737	−0.360868	+	0.932617i	$0.617520\pi$
$488$	−8.50861	−0.385167
$489$	39.5404	1.78808
$490$	−8.06994	−0.364563
$491$	1.42701	0.0644000	0.0322000	−	0.999481i	$-0.489749\pi$
$491$	1.42701	0.0644000	0.0322000	+	0.999481i	$0.489749\pi$
$492$	−25.9979	−1.17208
$493$	2.60299	0.117233
$494$	6.50968	0.292884
$495$	−5.59364	−0.251415
$496$	2.30877	0.103667
$497$	4.13155	0.185325
$498$	−7.19906	−0.322598
$499$	17.4712	0.782119	0.391060	−	0.920365i	$-0.372109\pi$
$499$	17.4712	0.782119	0.391060	+	0.920365i	$0.372109\pi$
$500$	−11.8517	−0.530026
$501$	−19.5203	−0.872104
$502$	5.39268	0.240687
$503$	−2.37821	−0.106039	−0.0530195	−	0.998593i	$-0.516885\pi$
$503$	−2.37821	−0.106039	−0.0530195	+	0.998593i	$0.516885\pi$
$504$	2.04107	0.0909166
$505$	9.50637	0.423028
$506$	22.3219	0.992328
$507$	20.8223	0.924751
$508$	−6.51130	−0.288892
$509$	30.3143	1.34366	0.671829	−	0.740707i	$-0.265509\pi$
$509$	30.3143	1.34366	0.671829	+	0.740707i	$0.265509\pi$
$510$	7.95390	0.352205
$511$	19.3733	0.857026
$512$	1.00000	0.0441942
$513$	11.7287	0.517835
$514$	−0.0615105	−0.00271311
$515$	4.87430	0.214787
$516$	11.5465	0.508307
$517$	26.5671	1.16842
$518$	−7.16486	−0.314806
$519$	21.1208	0.927100
$520$	2.80971	0.123214
$521$	21.5422	0.943781	0.471891	−	0.881657i	$-0.343572\pi$
$521$	21.5422	0.943781	0.471891	+	0.881657i	$0.343572\pi$
$522$	−1.62541	−0.0711424
$523$	−8.87247	−0.387966	−0.193983	−	0.981005i	$-0.562141\pi$
$523$	−8.87247	−0.387966	−0.193983	+	0.981005i	$0.562141\pi$
$524$	9.90482	0.432694
$525$	7.29906	0.318557
$526$	−7.00833	−0.305578
$527$	−5.49313	−0.239285
$528$	5.05188	0.219855
$529$	64.5759	2.80765
$530$	−1.51124	−0.0656440
$531$	−14.2642	−0.619013
$532$	5.02401	0.217819
$533$	21.8504	0.946448
$534$	−34.8675	−1.50886
$535$	−22.1648	−0.958267
$536$	−4.77368	−0.206191
$537$	−42.9476	−1.85333
$538$	7.73544	0.333498
$539$	12.1950	0.525277
$540$	5.06235	0.217849
$541$	15.7165	0.675703	0.337852	−	0.941199i	$-0.390300\pi$
$541$	15.7165	0.675703	0.337852	+	0.941199i	$0.390300\pi$
$542$	−18.0364	−0.774730
$543$	−19.3927	−0.832222
$544$	−2.37925	−0.102009
$545$	−14.5613	−0.623735
$546$	−5.17939	−0.221658
$547$	−7.59858	−0.324892	−0.162446	−	0.986717i	$-0.551938\pi$
$547$	−7.59858	−0.324892	−0.162446	+	0.986717i	$0.551938\pi$
$548$	−4.02313	−0.171860
$549$	−12.6412	−0.539515
$550$	5.98360	0.255142
$551$	−4.00089	−0.170443
$552$	19.8202	0.843602
$553$	−10.1175	−0.430239
$554$	16.3985	0.696706
$555$	17.4349	0.740072
$556$	9.33753	0.396000
$557$	−18.7578	−0.794793	−0.397396	−	0.917647i	$-0.630086\pi$
$557$	−18.7578	−0.794793	−0.397396	+	0.917647i	$0.630086\pi$
$558$	3.43013	0.145209
$559$	−9.70447	−0.410455
$560$	2.16847	0.0916345
$561$	−12.0197	−0.507471
$562$	−9.74257	−0.410966
$563$	−14.4797	−0.610245	−0.305123	−	0.952313i	$-0.598697\pi$
$563$	−14.4797	−0.610245	−0.305123	+	0.952313i	$0.598697\pi$
$564$	23.5896	0.993301
$565$	−23.8621	−1.00389
$566$	−21.2223	−0.892038
$567$	−15.4551	−0.649054
$568$	3.00736	0.126186
$569$	−26.4720	−1.10977	−0.554883	−	0.831929i	$-0.687237\pi$
$569$	−26.4720	−1.10977	−0.554883	+	0.831929i	$0.687237\pi$
$570$	−12.2254	−0.512066
$571$	−35.1507	−1.47101	−0.735505	−	0.677520i	$-0.763055\pi$
$571$	−35.1507	−1.47101	−0.735505	+	0.677520i	$0.763055\pi$
$572$	−4.24595	−0.177532
$573$	−34.7492	−1.45167
$574$	16.8637	0.703875
$575$	23.4756	0.979000
$576$	1.48570	0.0619041
$577$	27.1515	1.13033	0.565167	−	0.824977i	$-0.308812\pi$
$577$	27.1515	1.13033	0.565167	+	0.824977i	$0.308812\pi$
$578$	−11.3392	−0.471647
$579$	37.5235	1.55942
$580$	−1.72686	−0.0717042
$581$	4.66969	0.193732
$582$	−8.27972	−0.343205
$583$	2.28374	0.0945827
$584$	14.1019	0.583540
$585$	4.17438	0.172590
$586$	9.41311	0.388852
$587$	−18.8826	−0.779368	−0.389684	−	0.920949i	$-0.627416\pi$
$587$	−18.8826	−0.779368	−0.389684	+	0.920949i	$0.627416\pi$
$588$	10.8283	0.446551
$589$	8.44313	0.347893
$590$	−15.1545	−0.623901
$591$	−11.0280	−0.453631
$592$	−5.21531	−0.214348
$593$	17.5396	0.720267	0.360133	−	0.932901i	$-0.382731\pi$
$593$	17.5396	0.720267	0.360133	+	0.932901i	$0.382731\pi$
$594$	−7.65007	−0.313886
$595$	−5.15932	−0.211512
$596$	15.7420	0.644816
$597$	12.0082	0.491463
$598$	−16.6582	−0.681205
$599$	−33.0730	−1.35133	−0.675663	−	0.737210i	$-0.736143\pi$
$599$	−33.0730	−1.35133	−0.675663	+	0.737210i	$0.736143\pi$
$600$	5.31300	0.216902
$601$	20.7619	0.846896	0.423448	−	0.905920i	$-0.360820\pi$
$601$	20.7619	0.846896	0.423448	+	0.905920i	$0.360820\pi$
$602$	−7.48968	−0.305256
$603$	−7.09225	−0.288819
$604$	−1.93378	−0.0786842
$605$	−8.38221	−0.340785
$606$	−12.7557	−0.518165
$607$	38.4773	1.56174	0.780872	−	0.624691i	$-0.214775\pi$
$607$	38.4773	1.56174	0.780872	+	0.624691i	$0.214775\pi$
$608$	3.65698	0.148310
$609$	3.18329	0.128993
$610$	−13.4302	−0.543775
$611$	−19.8263	−0.802086
$612$	−3.53485	−0.142888
$613$	25.3109	1.02230	0.511149	−	0.859492i	$-0.329220\pi$
$613$	25.3109	1.02230	0.511149	+	0.859492i	$0.329220\pi$
$614$	−29.3285	−1.18360
$615$	−41.0359	−1.65473
$616$	−3.27692	−0.132031
$617$	0.219707	0.00884507	0.00442254	−	0.999990i	$-0.498592\pi$
$617$	0.219707	0.00884507	0.00442254	+	0.999990i	$0.498592\pi$
$618$	−6.54036	−0.263092
$619$	−22.5949	−0.908165	−0.454082	−	0.890960i	$-0.650033\pi$
$619$	−22.5949	−0.908165	−0.454082	+	0.890960i	$0.650033\pi$
$620$	3.64423	0.146356
$621$	−30.0137	−1.20441
$622$	−13.6875	−0.548819
$623$	22.6169	0.906128
$624$	−3.77009	−0.150924
$625$	−6.16434	−0.246573
$626$	−2.59688	−0.103792
$627$	18.4747	0.737807
$628$	−1.22984	−0.0490762
$629$	12.4085	0.494760
$630$	3.22169	0.128355
$631$	−1.77841	−0.0707974	−0.0353987	−	0.999373i	$-0.511270\pi$
$631$	−1.77841	−0.0707974	−0.0353987	+	0.999373i	$0.511270\pi$
$632$	−7.36452	−0.292945
$633$	23.9940	0.953674
$634$	−12.1478	−0.482452
$635$	−10.2776	−0.407855
$636$	2.02779	0.0804071
$637$	−9.10084	−0.360588
$638$	2.60958	0.103314
$639$	4.46803	0.176752
$640$	1.57843	0.0623929
$641$	−21.3194	−0.842067	−0.421034	−	0.907045i	$-0.638333\pi$
$641$	−21.3194	−0.842067	−0.421034	+	0.907045i	$0.638333\pi$
$642$	29.7408	1.17378
$643$	20.2227	0.797504	0.398752	−	0.917059i	$-0.369443\pi$
$643$	20.2227	0.797504	0.398752	+	0.917059i	$0.369443\pi$
$644$	−12.8564	−0.506614
$645$	18.2253	0.717622
$646$	−8.70088	−0.342331
$647$	20.0294	0.787435	0.393718	−	0.919231i	$-0.371189\pi$
$647$	20.0294	0.787435	0.393718	+	0.919231i	$0.371189\pi$
$648$	−11.2498	−0.441934
$649$	22.9010	0.898942
$650$	−4.46540	−0.175148
$651$	−6.71774	−0.263289
$652$	−18.6692	−0.731143
$653$	7.45172	0.291608	0.145804	−	0.989313i	$-0.453423\pi$
$653$	7.45172	0.291608	0.145804	+	0.989313i	$0.453423\pi$
$654$	19.5384	0.764011
$655$	15.6341	0.610873
$656$	12.2751	0.479261
$657$	20.9511	0.817382
$658$	−15.3015	−0.596513
$659$	8.09488	0.315332	0.157666	−	0.987493i	$-0.449603\pi$
$659$	8.09488	0.315332	0.157666	+	0.987493i	$0.449603\pi$
$660$	7.97404	0.310389
$661$	14.8213	0.576482	0.288241	−	0.957558i	$-0.406930\pi$
$661$	14.8213	0.576482	0.288241	+	0.957558i	$0.406930\pi$
$662$	−30.9589	−1.20325
$663$	8.96998	0.348365
$664$	3.39907	0.131910
$665$	7.93005	0.307514
$666$	−7.74838	−0.300244
$667$	10.2382	0.396426
$668$	9.21663	0.356602
$669$	16.8979	0.653312
$670$	−7.53492	−0.291099
$671$	20.2954	0.783494
$672$	−2.90966	−0.112243
$673$	31.6820	1.22125	0.610626	−	0.791919i	$-0.290918\pi$
$673$	31.6820	1.22125	0.610626	+	0.791919i	$0.290918\pi$
$674$	−9.89564	−0.381166
$675$	−8.04547	−0.309670
$676$	−9.83136	−0.378129
$677$	3.82740	0.147099	0.0735495	−	0.997292i	$-0.476567\pi$
$677$	3.82740	0.147099	0.0735495	+	0.997292i	$0.476567\pi$
$678$	32.0183	1.22966
$679$	5.37067	0.206107
$680$	−3.75548	−0.144016
$681$	28.1767	1.07973
$682$	−5.50704	−0.210876
$683$	−8.41003	−0.321801	−0.160900	−	0.986971i	$-0.551440\pi$
$683$	−8.41003	−0.321801	−0.160900	+	0.986971i	$0.551440\pi$
$684$	5.43318	0.207743
$685$	−6.35023	−0.242630
$686$	−16.6405	−0.635337
$687$	32.5398	1.24147
$688$	−5.45174	−0.207846
$689$	−1.70429	−0.0649284
$690$	31.2847	1.19099
$691$	−7.35416	−0.279765	−0.139883	−	0.990168i	$-0.544673\pi$
$691$	−7.35416	−0.279765	−0.139883	+	0.990168i	$0.544673\pi$
$692$	−9.97229	−0.379090
$693$	−4.86852	−0.184940
$694$	32.8557	1.24719
$695$	14.7386	0.559068
$696$	2.31712	0.0878301
$697$	−29.2054	−1.10624
$698$	−23.4315	−0.886896
$699$	−40.2647	−1.52295
$700$	−3.44629	−0.130258
$701$	−0.531042	−0.0200572	−0.0100286	−	0.999950i	$-0.503192\pi$
$701$	−0.531042	−0.0200572	−0.0100286	+	0.999950i	$0.503192\pi$
$702$	5.70905	0.215474
$703$	−19.0723	−0.719326
$704$	−2.38527	−0.0898984
$705$	37.2345	1.40233
$706$	35.0330	1.31849
$707$	8.27403	0.311177
$708$	20.3344	0.764213
$709$	36.0282	1.35307	0.676533	−	0.736412i	$-0.263482\pi$
$709$	36.0282	1.35307	0.676533	+	0.736412i	$0.263482\pi$
$710$	4.74690	0.178148
$711$	−10.9415	−0.410337
$712$	16.4629	0.616972
$713$	−21.6059	−0.809148
$714$	6.92281	0.259080
$715$	−6.70193	−0.250638
$716$	20.2780	0.757823
$717$	−37.1208	−1.38630
$718$	−19.2455	−0.718237
$719$	18.3644	0.684877	0.342438	−	0.939540i	$-0.388747\pi$
$719$	18.3644	0.684877	0.342438	+	0.939540i	$0.388747\pi$
$720$	2.34507	0.0873957
$721$	4.24243	0.157996
$722$	−5.62647	−0.209395
$723$	53.7241	1.99802
$724$	9.15638	0.340294
$725$	2.74446	0.101927
$726$	11.2473	0.417426
$727$	26.3330	0.976635	0.488318	−	0.872666i	$-0.337611\pi$
$727$	26.3330	0.976635	0.488318	+	0.872666i	$0.337611\pi$
$728$	2.44548	0.0906355
$729$	3.66429	0.135714
$730$	22.2588	0.823836
$731$	12.9711	0.479752
$732$	18.0208	0.666067
$733$	28.2580	1.04373	0.521867	−	0.853027i	$-0.325236\pi$
$733$	28.2580	1.04373	0.521867	+	0.853027i	$0.325236\pi$
$734$	−14.4879	−0.534757
$735$	17.0917	0.630437
$736$	−9.35820	−0.344948
$737$	11.3865	0.419428
$738$	18.2371	0.671315
$739$	−10.0867	−0.371045	−0.185523	−	0.982640i	$-0.559398\pi$
$739$	−10.0867	−0.371045	−0.185523	+	0.982640i	$0.559398\pi$
$740$	−8.23200	−0.302614
$741$	−13.7871	−0.506484
$742$	−1.31533	−0.0482874
$743$	12.8663	0.472019	0.236010	−	0.971751i	$-0.424160\pi$
$743$	12.8663	0.472019	0.236010	+	0.971751i	$0.424160\pi$
$744$	−4.88985	−0.179271
$745$	24.8476	0.910346
$746$	23.1254	0.846683
$747$	5.05000	0.184770
$748$	5.67516	0.207504
$749$	−19.2915	−0.704896
$750$	25.1013	0.916571
$751$	−21.3767	−0.780048	−0.390024	−	0.920805i	$-0.627533\pi$
$751$	−21.3767	−0.780048	−0.390024	+	0.920805i	$0.627533\pi$
$752$	−11.1379	−0.406159
$753$	−11.4214	−0.416219
$754$	−1.94746	−0.0709224
$755$	−3.05233	−0.111086
$756$	4.40611	0.160249
$757$	45.2474	1.64455	0.822273	−	0.569093i	$-0.192706\pi$
$757$	45.2474	1.64455	0.822273	+	0.569093i	$0.192706\pi$
$758$	−22.2730	−0.808992
$759$	−47.2765	−1.71603
$760$	5.77229	0.209383
$761$	−42.7692	−1.55038	−0.775191	−	0.631727i	$-0.782346\pi$
$761$	−42.7692	−1.55038	−0.775191	+	0.631727i	$0.782346\pi$
$762$	13.7906	0.499580
$763$	−12.6736	−0.458816
$764$	16.4070	0.593586
$765$	−5.57951	−0.201728
$766$	−23.9652	−0.865898
$767$	−17.0904	−0.617099
$768$	−2.11795	−0.0764248
$769$	−14.6668	−0.528898	−0.264449	−	0.964400i	$-0.585190\pi$
$769$	−14.6668	−0.528898	−0.264449	+	0.964400i	$0.585190\pi$
$770$	−5.17239	−0.186400
$771$	0.130276	0.00469177
$772$	−17.7169	−0.637646
$773$	18.5081	0.665691	0.332845	−	0.942981i	$-0.391991\pi$
$773$	18.5081	0.665691	0.332845	+	0.942981i	$0.391991\pi$
$774$	−8.09965	−0.291136
$775$	−5.79168	−0.208043
$776$	3.90931	0.140336
$777$	15.1748	0.544393
$778$	8.31701	0.298179
$779$	44.8897	1.60834
$780$	−5.95082	−0.213073
$781$	−7.17337	−0.256683
$782$	22.2655	0.796212
$783$	−3.50881	−0.125395
$784$	−5.11264	−0.182594
$785$	−1.94122	−0.0692852
$786$	−20.9779	−0.748256
$787$	21.0383	0.749934	0.374967	−	0.927038i	$-0.377654\pi$
$787$	21.0383	0.749934	0.374967	+	0.927038i	$0.377654\pi$
$788$	5.20693	0.185489
$789$	14.8433	0.528434
$790$	−11.6244	−0.413577
$791$	−20.7688	−0.738454
$792$	−3.54380	−0.125923
$793$	−15.1459	−0.537846
$794$	−2.49805	−0.0886525
$795$	3.20072	0.113518
$796$	−5.66973	−0.200958
$797$	4.99291	0.176858	0.0884289	−	0.996082i	$-0.471815\pi$
$797$	4.99291	0.176858	0.0884289	+	0.996082i	$0.471815\pi$
$798$	−10.6406	−0.376673
$799$	26.5000	0.937501
$800$	−2.50856	−0.0886910
$801$	24.4589	0.864212
$802$	−3.08484	−0.108930
$803$	−33.6368	−1.18702
$804$	10.1104	0.356566
$805$	−20.2929	−0.715233
$806$	4.10976	0.144760
$807$	−16.3832	−0.576718
$808$	6.02268	0.211877
$809$	35.5372	1.24942	0.624710	−	0.780857i	$-0.285217\pi$
$809$	35.5372	1.24942	0.624710	+	0.780857i	$0.285217\pi$
$810$	−17.7570	−0.623918
$811$	35.4038	1.24319	0.621597	−	0.783337i	$-0.286484\pi$
$811$	35.4038	1.24319	0.621597	+	0.783337i	$0.286484\pi$
$812$	−1.50301	−0.0527452
$813$	38.2002	1.33974
$814$	12.4399	0.436020
$815$	−29.4680	−1.03222
$816$	5.03912	0.176405
$817$	−19.9369	−0.697505
$818$	32.2923	1.12907
$819$	3.63325	0.126956
$820$	19.3753	0.676616
$821$	−33.5971	−1.17255	−0.586273	−	0.810114i	$-0.699405\pi$
$821$	−33.5971	−1.17255	−0.586273	+	0.810114i	$0.699405\pi$
$822$	8.52078	0.297196
$823$	45.1962	1.57544	0.787719	−	0.616034i	$-0.211262\pi$
$823$	45.1962	1.57544	0.787719	+	0.616034i	$0.211262\pi$
$824$	3.08807	0.107578
$825$	−12.6729	−0.441215
$826$	−13.1900	−0.458938
$827$	27.9090	0.970491	0.485245	−	0.874378i	$-0.338730\pi$
$827$	27.9090	0.970491	0.485245	+	0.874378i	$0.338730\pi$
$828$	−13.9035	−0.483179
$829$	25.9050	0.899718	0.449859	−	0.893100i	$-0.351474\pi$
$829$	25.9050	0.899718	0.449859	+	0.893100i	$0.351474\pi$
$830$	5.36520	0.186229
$831$	−34.7312	−1.20481
$832$	1.78007	0.0617127
$833$	12.1642	0.421466
$834$	−19.7764	−0.684801
$835$	14.5478	0.503447
$836$	−8.72291	−0.301688
$837$	7.40470	0.255944
$838$	25.2513	0.872292
$839$	21.8386	0.753951	0.376976	−	0.926223i	$-0.376964\pi$
$839$	21.8386	0.753951	0.376976	+	0.926223i	$0.376964\pi$
$840$	−4.59270	−0.158463
$841$	−27.8031	−0.958727
$842$	−0.907578	−0.0312772
$843$	20.6342	0.710681
$844$	−11.3289	−0.389956
$845$	−15.5181	−0.533839
$846$	−16.5476	−0.568920
$847$	−7.29560	−0.250680
$848$	−0.957432	−0.0328783
$849$	44.9476	1.54260
$850$	5.96849	0.204717
$851$	48.8059	1.67305
$852$	−6.36942	−0.218213
$853$	−27.9353	−0.956486	−0.478243	−	0.878227i	$-0.658726\pi$
$853$	−27.9353	−0.956486	−0.478243	+	0.878227i	$0.658726\pi$
$854$	−11.6892	−0.399998
$855$	8.57589	0.293289
$856$	−14.0423	−0.479956
$857$	7.09747	0.242445	0.121223	−	0.992625i	$-0.461319\pi$
$857$	7.09747	0.242445	0.121223	+	0.992625i	$0.461319\pi$
$858$	8.99269	0.307005
$859$	41.7275	1.42372	0.711862	−	0.702319i	$-0.247852\pi$
$859$	41.7275	1.42372	0.711862	+	0.702319i	$0.247852\pi$
$860$	−8.60520	−0.293435
$861$	−35.7163	−1.21721
$862$	30.0671	1.02409
$863$	−8.94215	−0.304394	−0.152197	−	0.988350i	$-0.548635\pi$
$863$	−8.94215	−0.304394	−0.152197	+	0.988350i	$0.548635\pi$
$864$	3.20721	0.109111
$865$	−15.7406	−0.535195
$866$	0.00327995	0.000111457 0
$867$	24.0158	0.815618
$868$	3.17182	0.107658
$869$	17.5664	0.595899
$870$	3.65741	0.123998
$871$	−8.49747	−0.287926
$872$	−9.22515	−0.312403
$873$	5.80806	0.196573
$874$	−34.2228	−1.15760
$875$	−16.2821	−0.550434
$876$	−29.8670	−1.00911
$877$	30.5112	1.03029	0.515146	−	0.857103i	$-0.327738\pi$
$877$	30.5112	1.03029	0.515146	+	0.857103i	$0.327738\pi$
$878$	−24.7471	−0.835176
$879$	−19.9365	−0.672440
$880$	−3.76499	−0.126918
$881$	−29.1237	−0.981202	−0.490601	−	0.871384i	$-0.663223\pi$
$881$	−29.1237	−0.981202	−0.490601	+	0.871384i	$0.663223\pi$
$882$	−7.59584	−0.255765
$883$	−14.9501	−0.503112	−0.251556	−	0.967843i	$-0.580942\pi$
$883$	−14.9501	−0.503112	−0.251556	+	0.967843i	$0.580942\pi$
$884$	−4.23522	−0.142446
$885$	32.0964	1.07891
$886$	−16.5484	−0.555954
$887$	6.76777	0.227239	0.113620	−	0.993524i	$-0.463755\pi$
$887$	6.76777	0.227239	0.113620	+	0.993524i	$0.463755\pi$
$888$	11.0458	0.370671
$889$	−8.94531	−0.300016
$890$	25.9855	0.871036
$891$	26.8338	0.898967
$892$	−7.97845	−0.267138
$893$	−40.7313	−1.36302
$894$	−33.3407	−1.11508
$895$	32.0073	1.06989
$896$	1.37381	0.0458959
$897$	35.2812	1.17801
$898$	−9.41118	−0.314055
$899$	−2.52588	−0.0842429
$900$	−3.72696	−0.124232
$901$	2.27797	0.0758901
$902$	−29.2794	−0.974897
$903$	15.8627	0.527879
$904$	−15.1176	−0.502805
$905$	14.4527	0.480424
$906$	4.09563	0.136068
$907$	−8.56064	−0.284251	−0.142126	−	0.989849i	$-0.545394\pi$
$907$	−8.56064	−0.284251	−0.142126	+	0.989849i	$0.545394\pi$
$908$	−13.3038	−0.441502
$909$	8.94788	0.296783
$910$	3.86002	0.127958
$911$	−3.57692	−0.118509	−0.0592543	−	0.998243i	$-0.518872\pi$
$911$	−3.57692	−0.118509	−0.0592543	+	0.998243i	$0.518872\pi$
$912$	−7.74530	−0.256472
$913$	−8.10772	−0.268326
$914$	17.1934	0.568707
$915$	28.4445	0.940348
$916$	−15.3638	−0.507636
$917$	13.6074	0.449355
$918$	−7.63075	−0.251852
$919$	51.5278	1.69974	0.849872	−	0.526989i	$-0.176679\pi$
$919$	51.5278	1.69974	0.849872	+	0.526989i	$0.176679\pi$
$920$	−14.7713	−0.486994
$921$	62.1162	2.04680
$922$	−12.3316	−0.406119
$923$	5.35329	0.176206
$924$	6.94034	0.228320
$925$	13.0829	0.430164
$926$	−13.5765	−0.446153
$927$	4.58794	0.150688
$928$	−1.09404	−0.0359136
$929$	28.2425	0.926608	0.463304	−	0.886199i	$-0.346664\pi$
$929$	28.2425	0.926608	0.463304	+	0.886199i	$0.346664\pi$
$930$	−7.71828	−0.253092
$931$	−18.6968	−0.612764
$932$	19.0112	0.622732
$933$	28.9894	0.949071
$934$	−36.5206	−1.19499
$935$	8.95784	0.292953
$936$	2.64464	0.0864429
$937$	22.6244	0.739106	0.369553	−	0.929210i	$-0.379511\pi$
$937$	22.6244	0.739106	0.369553	+	0.929210i	$0.379511\pi$
$938$	−6.55814	−0.214131
$939$	5.50006	0.179488
$940$	−17.5805	−0.573412
$941$	−30.8966	−1.00720	−0.503599	−	0.863937i	$-0.667991\pi$
$941$	−30.8966	−1.00720	−0.503599	+	0.863937i	$0.667991\pi$
$942$	2.60475	0.0848672
$943$	−114.873	−3.74076
$944$	−9.60099	−0.312486
$945$	6.95473	0.226237
$946$	13.0039	0.422793
$947$	26.8350	0.872021	0.436011	−	0.899942i	$-0.356391\pi$
$947$	26.8350	0.872021	0.436011	+	0.899942i	$0.356391\pi$
$948$	15.5977	0.506588
$949$	25.1023	0.814855
$950$	−9.17376	−0.297636
$951$	25.7285	0.834302
$952$	−3.26864	−0.105937
$953$	−56.8200	−1.84058	−0.920291	−	0.391235i	$-0.872048\pi$
$953$	−56.8200	−1.84058	−0.920291	+	0.391235i	$0.872048\pi$
$954$	−1.42246	−0.0460537
$955$	25.8974	0.838019
$956$	17.5268	0.566856
$957$	−5.52696	−0.178661
$958$	2.26825	0.0732838
$959$	−5.52703	−0.178477
$960$	−3.34303	−0.107896
$961$	−25.6696	−0.828051
$962$	−9.28360	−0.299315
$963$	−20.8626	−0.672289
$964$	−25.3661	−0.816988
$965$	−27.9649	−0.900223
$966$	27.2292	0.876085
$967$	−40.2373	−1.29395	−0.646973	−	0.762513i	$-0.723965\pi$
$967$	−40.2373	−1.29395	−0.646973	+	0.762513i	$0.723965\pi$
$968$	−5.31047	−0.170685
$969$	18.4280	0.591992
$970$	6.17058	0.198125
$971$	−12.9797	−0.416540	−0.208270	−	0.978071i	$-0.566783\pi$
$971$	−12.9797	−0.416540	−0.208270	+	0.978071i	$0.566783\pi$
$972$	14.2048	0.455621
$973$	12.8280	0.411248
$974$	−15.9273	−0.510345
$975$	9.45749	0.302882
$976$	−8.50861	−0.272354
$977$	−36.9036	−1.18065	−0.590326	−	0.807165i	$-0.701001\pi$
$977$	−36.9036	−1.18065	−0.590326	+	0.807165i	$0.701001\pi$
$978$	39.5404	1.26436
$979$	−39.2685	−1.25503
$980$	−8.06994	−0.257785
$981$	−13.7058	−0.437592
$982$	1.42701	0.0455377
$983$	−34.7446	−1.10818	−0.554091	−	0.832456i	$-0.686934\pi$
$983$	−34.7446	−1.10818	−0.554091	+	0.832456i	$0.686934\pi$
$984$	−25.9979	−0.828784
$985$	8.21877	0.261872
$986$	2.60299	0.0828962
$987$	32.4077	1.03155
$988$	6.50968	0.207100
$989$	51.0185	1.62229
$990$	−5.59364	−0.177777
$991$	−22.2167	−0.705737	−0.352869	−	0.935673i	$-0.614794\pi$
$991$	−22.2167	−0.705737	−0.352869	+	0.935673i	$0.614794\pi$
$992$	2.30877	0.0733034
$993$	65.5693	2.08078
$994$	4.13155	0.131045
$995$	−8.94928	−0.283711
$996$	−7.19906	−0.228111
$997$	−46.4598	−1.47140	−0.735699	−	0.677309i	$-0.763146\pi$
$997$	−46.4598	−1.47140	−0.735699	+	0.677309i	$0.763146\pi$
$998$	17.4712	0.553042
$999$	−16.7266	−0.529206

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6038.2.a.b.1.13	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6038.2.a.b.1.13	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.11795 q^{3} +1.00000 q^{4} +1.57843 q^{5} -2.11795 q^{6} +1.37381 q^{7} +1.00000 q^{8} +1.48570 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.11795 q^{3} +1.00000 q^{4} +1.57843 q^{5} -2.11795 q^{6} +1.37381 q^{7} +1.00000 q^{8} +1.48570 q^{9} +1.57843 q^{10} -2.38527 q^{11} -2.11795 q^{12} +1.78007 q^{13} +1.37381 q^{14} -3.34303 q^{15} +1.00000 q^{16} -2.37925 q^{17} +1.48570 q^{18} +3.65698 q^{19} +1.57843 q^{20} -2.90966 q^{21} -2.38527 q^{22} -9.35820 q^{23} -2.11795 q^{24} -2.50856 q^{25} +1.78007 q^{26} +3.20721 q^{27} +1.37381 q^{28} -1.09404 q^{29} -3.34303 q^{30} +2.30877 q^{31} +1.00000 q^{32} +5.05188 q^{33} -2.37925 q^{34} +2.16847 q^{35} +1.48570 q^{36} -5.21531 q^{37} +3.65698 q^{38} -3.77009 q^{39} +1.57843 q^{40} +12.2751 q^{41} -2.90966 q^{42} -5.45174 q^{43} -2.38527 q^{44} +2.34507 q^{45} -9.35820 q^{46} -11.1379 q^{47} -2.11795 q^{48} -5.11264 q^{49} -2.50856 q^{50} +5.03912 q^{51} +1.78007 q^{52} -0.957432 q^{53} +3.20721 q^{54} -3.76499 q^{55} +1.37381 q^{56} -7.74530 q^{57} -1.09404 q^{58} -9.60099 q^{59} -3.34303 q^{60} -8.50861 q^{61} +2.30877 q^{62} +2.04107 q^{63} +1.00000 q^{64} +2.80971 q^{65} +5.05188 q^{66} -4.77368 q^{67} -2.37925 q^{68} +19.8202 q^{69} +2.16847 q^{70} +3.00736 q^{71} +1.48570 q^{72} +14.1019 q^{73} -5.21531 q^{74} +5.31300 q^{75} +3.65698 q^{76} -3.27692 q^{77} -3.77009 q^{78} -7.36452 q^{79} +1.57843 q^{80} -11.2498 q^{81} +12.2751 q^{82} +3.39907 q^{83} -2.90966 q^{84} -3.75548 q^{85} -5.45174 q^{86} +2.31712 q^{87} -2.38527 q^{88} +16.4629 q^{89} +2.34507 q^{90} +2.44548 q^{91} -9.35820 q^{92} -4.88985 q^{93} -11.1379 q^{94} +5.77229 q^{95} -2.11795 q^{96} +3.90931 q^{97} -5.11264 q^{98} -3.54380 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 54 q^{2} - 21 q^{3} + 54 q^{4} - 14 q^{5} - 21 q^{6} - 44 q^{7} + 54 q^{8} + 39 q^{9}+O(q^{10}) \) 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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