LMFDB - Embedded newform 6038.2.a.c.1.7

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:	$57$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.75036 q^{3} +1.00000 q^{4} +0.139827 q^{5} +2.75036 q^{6} +0.205180 q^{7} -1.00000 q^{8} +4.56449 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.75036 q^{3} +1.00000 q^{4} +0.139827 q^{5} +2.75036 q^{6} +0.205180 q^{7} -1.00000 q^{8} +4.56449 q^{9} -0.139827 q^{10} +5.82885 q^{11} -2.75036 q^{12} +3.51826 q^{13} -0.205180 q^{14} -0.384574 q^{15} +1.00000 q^{16} +4.12505 q^{17} -4.56449 q^{18} +7.10360 q^{19} +0.139827 q^{20} -0.564320 q^{21} -5.82885 q^{22} -7.36792 q^{23} +2.75036 q^{24} -4.98045 q^{25} -3.51826 q^{26} -4.30292 q^{27} +0.205180 q^{28} +0.351393 q^{29} +0.384574 q^{30} -10.9511 q^{31} -1.00000 q^{32} -16.0314 q^{33} -4.12505 q^{34} +0.0286897 q^{35} +4.56449 q^{36} -10.8319 q^{37} -7.10360 q^{38} -9.67648 q^{39} -0.139827 q^{40} +2.38303 q^{41} +0.564320 q^{42} +4.45574 q^{43} +5.82885 q^{44} +0.638238 q^{45} +7.36792 q^{46} -9.65219 q^{47} -2.75036 q^{48} -6.95790 q^{49} +4.98045 q^{50} -11.3454 q^{51} +3.51826 q^{52} -10.0176 q^{53} +4.30292 q^{54} +0.815029 q^{55} -0.205180 q^{56} -19.5375 q^{57} -0.351393 q^{58} +10.7513 q^{59} -0.384574 q^{60} +9.90076 q^{61} +10.9511 q^{62} +0.936544 q^{63} +1.00000 q^{64} +0.491946 q^{65} +16.0314 q^{66} +5.14435 q^{67} +4.12505 q^{68} +20.2644 q^{69} -0.0286897 q^{70} -16.2569 q^{71} -4.56449 q^{72} -14.2704 q^{73} +10.8319 q^{74} +13.6980 q^{75} +7.10360 q^{76} +1.19597 q^{77} +9.67648 q^{78} +5.54979 q^{79} +0.139827 q^{80} -1.85889 q^{81} -2.38303 q^{82} -2.19354 q^{83} -0.564320 q^{84} +0.576792 q^{85} -4.45574 q^{86} -0.966457 q^{87} -5.82885 q^{88} +13.9985 q^{89} -0.638238 q^{90} +0.721878 q^{91} -7.36792 q^{92} +30.1195 q^{93} +9.65219 q^{94} +0.993274 q^{95} +2.75036 q^{96} -15.1828 q^{97} +6.95790 q^{98} +26.6057 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 57 q - 57 q^{2} - 5 q^{3} + 57 q^{4} - 15 q^{5} + 5 q^{6} - 28 q^{7} - 57 q^{8} + 50 q^{9}+O(q^{10}) $ 57 * q - 57 * q^2 - 5 * q^3 + 57 * q^4 - 15 * q^5 + 5 * q^6 - 28 * q^7 - 57 * q^8 + 50 * q^9	\( 57 q - 57 q^{2} - 5 q^{3} + 57 q^{4} - 15 q^{5} + 5 q^{6} - 28 q^{7} - 57 q^{8} + 50 q^{9} + 15 q^{10} + 13 q^{11} - 5 q^{12} - 43 q^{13} + 28 q^{14} - 10 q^{15} + 57 q^{16} - 50 q^{18} - 6 q^{19} - 15 q^{20} - 23 q^{21} - 13 q^{22} - q^{23} + 5 q^{24} + 20 q^{25} + 43 q^{26} - 20 q^{27} - 28 q^{28} - 4 q^{29} + 10 q^{30} - 34 q^{31} - 57 q^{32} - 43 q^{33} + 26 q^{35} + 50 q^{36} - 64 q^{37} + 6 q^{38} + 8 q^{39} + 15 q^{40} + 27 q^{41} + 23 q^{42} - 29 q^{43} + 13 q^{44} - 76 q^{45} + q^{46} - 25 q^{47} - 5 q^{48} + 7 q^{49} - 20 q^{50} + 27 q^{51} - 43 q^{52} - 34 q^{53} + 20 q^{54} - 36 q^{55} + 28 q^{56} - 33 q^{57} + 4 q^{58} + 19 q^{59} - 10 q^{60} - 58 q^{61} + 34 q^{62} - 65 q^{63} + 57 q^{64} + 17 q^{65} + 43 q^{66} - 84 q^{67} - 33 q^{69} - 26 q^{70} + 22 q^{71} - 50 q^{72} - 82 q^{73} + 64 q^{74} + 8 q^{75} - 6 q^{76} - 41 q^{77} - 8 q^{78} + 8 q^{79} - 15 q^{80} + 25 q^{81} - 27 q^{82} - 23 q^{83} - 23 q^{84} - 58 q^{85} + 29 q^{86} - 17 q^{87} - 13 q^{88} + 18 q^{89} + 76 q^{90} - 4 q^{91} - q^{92} - 60 q^{93} + 25 q^{94} + 36 q^{95} + 5 q^{96} - 156 q^{97} - 7 q^{98} + 25 q^{99}+O(q^{100}) \) 57 * q - 57 * q^2 - 5 * q^3 + 57 * q^4 - 15 * q^5 + 5 * q^6 - 28 * q^7 - 57 * q^8 + 50 * q^9 + 15 * q^10 + 13 * q^11 - 5 * q^12 - 43 * q^13 + 28 * q^14 - 10 * q^15 + 57 * q^16 - 50 * q^18 - 6 * q^19 - 15 * q^20 - 23 * q^21 - 13 * q^22 - q^23 + 5 * q^24 + 20 * q^25 + 43 * q^26 - 20 * q^27 - 28 * q^28 - 4 * q^29 + 10 * q^30 - 34 * q^31 - 57 * q^32 - 43 * q^33 + 26 * q^35 + 50 * q^36 - 64 * q^37 + 6 * q^38 + 8 * q^39 + 15 * q^40 + 27 * q^41 + 23 * q^42 - 29 * q^43 + 13 * q^44 - 76 * q^45 + q^46 - 25 * q^47 - 5 * q^48 + 7 * q^49 - 20 * q^50 + 27 * q^51 - 43 * q^52 - 34 * q^53 + 20 * q^54 - 36 * q^55 + 28 * q^56 - 33 * q^57 + 4 * q^58 + 19 * q^59 - 10 * q^60 - 58 * q^61 + 34 * q^62 - 65 * q^63 + 57 * q^64 + 17 * q^65 + 43 * q^66 - 84 * q^67 - 33 * q^69 - 26 * q^70 + 22 * q^71 - 50 * q^72 - 82 * q^73 + 64 * q^74 + 8 * q^75 - 6 * q^76 - 41 * q^77 - 8 * q^78 + 8 * q^79 - 15 * q^80 + 25 * q^81 - 27 * q^82 - 23 * q^83 - 23 * q^84 - 58 * q^85 + 29 * q^86 - 17 * q^87 - 13 * q^88 + 18 * q^89 + 76 * q^90 - 4 * q^91 - q^92 - 60 * q^93 + 25 * q^94 + 36 * q^95 + 5 * q^96 - 156 * q^97 - 7 * q^98 + 25 * 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
$3$	−2.75036	−1.58792	−0.793961	−	0.607969i	$-0.791985\pi$
$3$	−2.75036	−1.58792	−0.793961	+	0.607969i	$0.791985\pi$
$4$	1.00000	0.500000
$5$	0.139827	0.0625324	0.0312662	−	0.999511i	$-0.490046\pi$
$5$	0.139827	0.0625324	0.0312662	+	0.999511i	$0.490046\pi$
$6$	2.75036	1.12283
$7$	0.205180	0.0775509	0.0387755	−	0.999248i	$-0.487654\pi$
$7$	0.205180	0.0775509	0.0387755	+	0.999248i	$0.487654\pi$
$8$	−1.00000	−0.353553
$9$	4.56449	1.52150
$10$	−0.139827	−0.0442171
$11$	5.82885	1.75746	0.878732	−	0.477315i	$-0.158390\pi$
$11$	5.82885	1.75746	0.878732	+	0.477315i	$0.158390\pi$
$12$	−2.75036	−0.793961
$13$	3.51826	0.975789	0.487895	−	0.872903i	$-0.337765\pi$
$13$	3.51826	0.975789	0.487895	+	0.872903i	$0.337765\pi$
$14$	−0.205180	−0.0548368
$15$	−0.384574	−0.0992966
$16$	1.00000	0.250000
$17$	4.12505	1.00047	0.500235	−	0.865889i	$-0.333247\pi$
$17$	4.12505	1.00047	0.500235	+	0.865889i	$0.333247\pi$
$18$	−4.56449	−1.07586
$19$	7.10360	1.62968	0.814839	−	0.579687i	$-0.196825\pi$
$19$	7.10360	1.62968	0.814839	+	0.579687i	$0.196825\pi$
$20$	0.139827	0.0312662
$21$	−0.564320	−0.123145
$22$	−5.82885	−1.24272
$23$	−7.36792	−1.53632	−0.768159	−	0.640260i	$-0.778827\pi$
$23$	−7.36792	−1.53632	−0.768159	+	0.640260i	$0.778827\pi$
$24$	2.75036	0.561415
$25$	−4.98045	−0.996090
$26$	−3.51826	−0.689987
$27$	−4.30292	−0.828097
$28$	0.205180	0.0387755
$29$	0.351393	0.0652520	0.0326260	−	0.999468i	$-0.489613\pi$
$29$	0.351393	0.0652520	0.0326260	+	0.999468i	$0.489613\pi$
$30$	0.384574	0.0702133
$31$	−10.9511	−1.96688	−0.983439	−	0.181241i	$-0.941989\pi$
$31$	−10.9511	−1.96688	−0.983439	+	0.181241i	$0.941989\pi$
$32$	−1.00000	−0.176777
$33$	−16.0314	−2.79072
$34$	−4.12505	−0.707440
$35$	0.0286897	0.00484945
$36$	4.56449	0.760749
$37$	−10.8319	−1.78075	−0.890375	−	0.455227i	$-0.849558\pi$
$37$	−10.8319	−1.78075	−0.890375	+	0.455227i	$0.849558\pi$
$38$	−7.10360	−1.15236
$39$	−9.67648	−1.54948
$40$	−0.139827	−0.0221085
$41$	2.38303	0.372166	0.186083	−	0.982534i	$-0.440421\pi$
$41$	2.38303	0.372166	0.186083	+	0.982534i	$0.440421\pi$
$42$	0.564320	0.0870765
$43$	4.45574	0.679494	0.339747	−	0.940517i	$-0.389659\pi$
$43$	4.45574	0.679494	0.339747	+	0.940517i	$0.389659\pi$
$44$	5.82885	0.878732
$45$	0.638238	0.0951429
$46$	7.36792	1.08634
$47$	−9.65219	−1.40792	−0.703959	−	0.710241i	$-0.748586\pi$
$47$	−9.65219	−1.40792	−0.703959	+	0.710241i	$0.748586\pi$
$48$	−2.75036	−0.396981
$49$	−6.95790	−0.993986
$50$	4.98045	0.704342
$51$	−11.3454	−1.58867
$52$	3.51826	0.487895
$53$	−10.0176	−1.37603	−0.688015	−	0.725697i	$-0.741518\pi$
$53$	−10.0176	−1.37603	−0.688015	+	0.725697i	$0.741518\pi$
$54$	4.30292	0.585553
$55$	0.815029	0.109898
$56$	−0.205180	−0.0274184
$57$	−19.5375	−2.58780
$58$	−0.351393	−0.0461401
$59$	10.7513	1.39970	0.699848	−	0.714292i	$-0.253251\pi$
$59$	10.7513	1.39970	0.699848	+	0.714292i	$0.253251\pi$
$60$	−0.384574	−0.0496483
$61$	9.90076	1.26766	0.633831	−	0.773471i	$-0.281481\pi$
$61$	9.90076	1.26766	0.633831	+	0.773471i	$0.281481\pi$
$62$	10.9511	1.39079
$63$	0.936544	0.117993
$64$	1.00000	0.125000
$65$	0.491946	0.0610184
$66$	16.0314	1.97333
$67$	5.14435	0.628483	0.314241	−	0.949343i	$-0.398250\pi$
$67$	5.14435	0.628483	0.314241	+	0.949343i	$0.398250\pi$
$68$	4.12505	0.500235
$69$	20.2644	2.43955
$70$	−0.0286897	−0.00342908
$71$	−16.2569	−1.92934	−0.964669	−	0.263465i	$-0.915135\pi$
$71$	−16.2569	−1.92934	−0.964669	+	0.263465i	$0.915135\pi$
$72$	−4.56449	−0.537930
$73$	−14.2704	−1.67022	−0.835111	−	0.550081i	$-0.814597\pi$
$73$	−14.2704	−1.67022	−0.835111	+	0.550081i	$0.814597\pi$
$74$	10.8319	1.25918
$75$	13.6980	1.58171
$76$	7.10360	0.814839
$77$	1.19597	0.136293
$78$	9.67648	1.09565
$79$	5.54979	0.624400	0.312200	−	0.950016i	$-0.398934\pi$
$79$	5.54979	0.624400	0.312200	+	0.950016i	$0.398934\pi$
$80$	0.139827	0.0156331
$81$	−1.85889	−0.206544
$82$	−2.38303	−0.263161
$83$	−2.19354	−0.240772	−0.120386	−	0.992727i	$-0.538413\pi$
$83$	−2.19354	−0.240772	−0.120386	+	0.992727i	$0.538413\pi$
$84$	−0.564320	−0.0615724
$85$	0.576792	0.0625618
$86$	−4.45574	−0.480475
$87$	−0.966457	−0.103615
$88$	−5.82885	−0.621358
$89$	13.9985	1.48384	0.741921	−	0.670487i	$-0.233915\pi$
$89$	13.9985	1.48384	0.741921	+	0.670487i	$0.233915\pi$
$90$	−0.638238	−0.0672762
$91$	0.721878	0.0756733
$92$	−7.36792	−0.768159
$93$	30.1195	3.12325
$94$	9.65219	0.995548
$95$	0.993274	0.101908
$96$	2.75036	0.280708
$97$	−15.1828	−1.54158	−0.770789	−	0.637091i	$-0.780138\pi$
$97$	−15.1828	−1.54158	−0.770789	+	0.637091i	$0.780138\pi$
$98$	6.95790	0.702854
$99$	26.6057	2.67398
$100$	−4.98045	−0.498045
$101$	−10.0986	−1.00485	−0.502424	−	0.864621i	$-0.667558\pi$
$101$	−10.0986	−1.00485	−0.502424	+	0.864621i	$0.667558\pi$
$102$	11.3454	1.12336
$103$	6.70894	0.661051	0.330526	−	0.943797i	$-0.392774\pi$
$103$	6.70894	0.661051	0.330526	+	0.943797i	$0.392774\pi$
$104$	−3.51826	−0.344994
$105$	−0.0789071	−0.00770054
$106$	10.0176	0.973000
$107$	−5.56255	−0.537752	−0.268876	−	0.963175i	$-0.586652\pi$
$107$	−5.56255	−0.537752	−0.268876	+	0.963175i	$0.586652\pi$
$108$	−4.30292	−0.414048
$109$	−0.205629	−0.0196957	−0.00984785	−	0.999952i	$-0.503135\pi$
$109$	−0.205629	−0.0196957	−0.00984785	+	0.999952i	$0.503135\pi$
$110$	−0.815029	−0.0777100
$111$	29.7916	2.82769
$112$	0.205180	0.0193877
$113$	−20.0217	−1.88348	−0.941740	−	0.336342i	$-0.890810\pi$
$113$	−20.0217	−1.88348	−0.941740	+	0.336342i	$0.890810\pi$
$114$	19.5375	1.82985
$115$	−1.03023	−0.0960696
$116$	0.351393	0.0326260
$117$	16.0591	1.48466
$118$	−10.7513	−0.989734
$119$	0.846379	0.0775874
$120$	0.384574	0.0351066
$121$	22.9755	2.08868
$122$	−9.90076	−0.896373
$123$	−6.55418	−0.590971
$124$	−10.9511	−0.983439
$125$	−1.39553	−0.124820
$126$	−0.936544	−0.0834340
$127$	18.1676	1.61212	0.806058	−	0.591837i	$-0.201597\pi$
$127$	18.1676	1.61212	0.806058	+	0.591837i	$0.201597\pi$
$128$	−1.00000	−0.0883883
$129$	−12.2549	−1.07898
$130$	−0.491946	−0.0431466
$131$	0.512869	0.0448096	0.0224048	−	0.999749i	$-0.492868\pi$
$131$	0.512869	0.0448096	0.0224048	+	0.999749i	$0.492868\pi$
$132$	−16.0314	−1.39536
$133$	1.45752	0.126383
$134$	−5.14435	−0.444404
$135$	−0.601663	−0.0517829
$136$	−4.12505	−0.353720
$137$	−3.91550	−0.334524	−0.167262	−	0.985913i	$-0.553493\pi$
$137$	−3.91550	−0.334524	−0.167262	+	0.985913i	$0.553493\pi$
$138$	−20.2644	−1.72502
$139$	−6.50175	−0.551471	−0.275736	−	0.961233i	$-0.588921\pi$
$139$	−6.50175	−0.551471	−0.275736	+	0.961233i	$0.588921\pi$
$140$	0.0286897	0.00242472
$141$	26.5470	2.23566
$142$	16.2569	1.36425
$143$	20.5074	1.71491
$144$	4.56449	0.380374
$145$	0.0491341	0.00408036
$146$	14.2704	1.18103
$147$	19.1367	1.57837
$148$	−10.8319	−0.890375
$149$	−22.0292	−1.80471	−0.902353	−	0.430998i	$-0.858162\pi$
$149$	−22.0292	−1.80471	−0.902353	+	0.430998i	$0.858162\pi$
$150$	−13.6980	−1.11844
$151$	−20.1283	−1.63802	−0.819008	−	0.573783i	$-0.805475\pi$
$151$	−20.1283	−1.63802	−0.819008	+	0.573783i	$0.805475\pi$
$152$	−7.10360	−0.576178
$153$	18.8287	1.52221
$154$	−1.19597	−0.0963737
$155$	−1.53126	−0.122994
$156$	−9.67648	−0.774739
$157$	−0.265018	−0.0211508	−0.0105754	−	0.999944i	$-0.503366\pi$
$157$	−0.265018	−0.0211508	−0.0105754	+	0.999944i	$0.503366\pi$
$158$	−5.54979	−0.441518
$159$	27.5522	2.18503
$160$	−0.139827	−0.0110543
$161$	−1.51175	−0.119143
$162$	1.85889	0.146048
$163$	−17.9317	−1.40452	−0.702259	−	0.711921i	$-0.747825\pi$
$163$	−17.9317	−1.40452	−0.702259	+	0.711921i	$0.747825\pi$
$164$	2.38303	0.186083
$165$	−2.24162	−0.174510
$166$	2.19354	0.170251
$167$	−9.35183	−0.723667	−0.361833	−	0.932243i	$-0.617849\pi$
$167$	−9.35183	−0.723667	−0.361833	+	0.932243i	$0.617849\pi$
$168$	0.564320	0.0435383
$169$	−0.621863	−0.0478356
$170$	−0.576792	−0.0442379
$171$	32.4243	2.47955
$172$	4.45574	0.339747
$173$	18.7867	1.42832	0.714161	−	0.699981i	$-0.246808\pi$
$173$	18.7867	1.42832	0.714161	+	0.699981i	$0.246808\pi$
$174$	0.966457	0.0732669
$175$	−1.02189	−0.0772477
$176$	5.82885	0.439366
$177$	−29.5699	−2.22261
$178$	−13.9985	−1.04923
$179$	14.3255	1.07074	0.535369	−	0.844618i	$-0.320173\pi$
$179$	14.3255	1.07074	0.535369	+	0.844618i	$0.320173\pi$
$180$	0.638238	0.0475714
$181$	−11.6353	−0.864843	−0.432422	−	0.901672i	$-0.642341\pi$
$181$	−11.6353	−0.864843	−0.432422	+	0.901672i	$0.642341\pi$
$182$	−0.721878	−0.0535091
$183$	−27.2307	−2.01295
$184$	7.36792	0.543170
$185$	−1.51459	−0.111355
$186$	−30.1195	−2.20847
$187$	24.0443	1.75829
$188$	−9.65219	−0.703959
$189$	−0.882874	−0.0642197
$190$	−0.993274	−0.0720596
$191$	−15.8438	−1.14642	−0.573208	−	0.819410i	$-0.694301\pi$
$191$	−15.8438	−1.14642	−0.573208	+	0.819410i	$0.694301\pi$
$192$	−2.75036	−0.198490
$193$	−11.7524	−0.845958	−0.422979	−	0.906140i	$-0.639016\pi$
$193$	−11.7524	−0.845958	−0.422979	+	0.906140i	$0.639016\pi$
$194$	15.1828	1.09006
$195$	−1.35303	−0.0968925
$196$	−6.95790	−0.496993
$197$	7.23573	0.515525	0.257762	−	0.966208i	$-0.417015\pi$
$197$	7.23573	0.515525	0.257762	+	0.966208i	$0.417015\pi$
$198$	−26.6057	−1.89079
$199$	5.81890	0.412491	0.206245	−	0.978500i	$-0.433875\pi$
$199$	5.81890	0.412491	0.206245	+	0.978500i	$0.433875\pi$
$200$	4.98045	0.352171
$201$	−14.1488	−0.997982
$202$	10.0986	0.710535
$203$	0.0720989	0.00506035
$204$	−11.3454	−0.794335
$205$	0.333211	0.0232724
$206$	−6.70894	−0.467434
$207$	−33.6308	−2.33750
$208$	3.51826	0.243947
$209$	41.4058	2.86410
$210$	0.0789071	0.00544511
$211$	−5.78786	−0.398453	−0.199226	−	0.979953i	$-0.563843\pi$
$211$	−5.78786	−0.398453	−0.199226	+	0.979953i	$0.563843\pi$
$212$	−10.0176	−0.688015
$213$	44.7123	3.06364
$214$	5.56255	0.380248
$215$	0.623031	0.0424904
$216$	4.30292	0.292776
$217$	−2.24695	−0.152533
$218$	0.205629	0.0139270
$219$	39.2487	2.65218
$220$	0.815029	0.0549492
$221$	14.5130	0.976249
$222$	−29.7916	−1.99948
$223$	2.50246	0.167577	0.0837887	−	0.996484i	$-0.473298\pi$
$223$	2.50246	0.167577	0.0837887	+	0.996484i	$0.473298\pi$
$224$	−0.205180	−0.0137092
$225$	−22.7332	−1.51555
$226$	20.0217	1.33182
$227$	4.79374	0.318172	0.159086	−	0.987265i	$-0.449145\pi$
$227$	4.79374	0.318172	0.159086	+	0.987265i	$0.449145\pi$
$228$	−19.5375	−1.29390
$229$	−25.1371	−1.66111	−0.830553	−	0.556940i	$-0.811975\pi$
$229$	−25.1371	−1.66111	−0.830553	+	0.556940i	$0.811975\pi$
$230$	1.03023	0.0679315
$231$	−3.28934	−0.216423
$232$	−0.351393	−0.0230700
$233$	7.96330	0.521693	0.260847	−	0.965380i	$-0.415998\pi$
$233$	7.96330	0.521693	0.260847	+	0.965380i	$0.415998\pi$
$234$	−16.0591	−1.04981
$235$	−1.34963	−0.0880405
$236$	10.7513	0.699848
$237$	−15.2639	−0.991499
$238$	−0.846379	−0.0548626
$239$	−4.66859	−0.301986	−0.150993	−	0.988535i	$-0.548247\pi$
$239$	−4.66859	−0.301986	−0.150993	+	0.988535i	$0.548247\pi$
$240$	−0.384574	−0.0248241
$241$	−12.3748	−0.797130	−0.398565	−	0.917140i	$-0.630492\pi$
$241$	−12.3748	−0.797130	−0.398565	+	0.917140i	$0.630492\pi$
$242$	−22.9755	−1.47692
$243$	18.0214	1.15607
$244$	9.90076	0.633831
$245$	−0.972900	−0.0621563
$246$	6.55418	0.417879
$247$	24.9923	1.59022
$248$	10.9511	0.695396
$249$	6.03302	0.382327
$250$	1.39553	0.0882613
$251$	11.7959	0.744548	0.372274	−	0.928123i	$-0.378578\pi$
$251$	11.7959	0.744548	0.372274	+	0.928123i	$0.378578\pi$
$252$	0.936544	0.0589967
$253$	−42.9465	−2.70002
$254$	−18.1676	−1.13994
$255$	−1.58639	−0.0993433
$256$	1.00000	0.0625000
$257$	24.1688	1.50761	0.753806	−	0.657097i	$-0.228216\pi$
$257$	24.1688	1.50761	0.753806	+	0.657097i	$0.228216\pi$
$258$	12.2549	0.762957
$259$	−2.22249	−0.138099
$260$	0.491946	0.0305092
$261$	1.60393	0.0992807
$262$	−0.512869	−0.0316852
$263$	9.06964	0.559258	0.279629	−	0.960108i	$-0.409789\pi$
$263$	9.06964	0.559258	0.279629	+	0.960108i	$0.409789\pi$
$264$	16.0314	0.986667
$265$	−1.40073	−0.0860464
$266$	−1.45752	−0.0893663
$267$	−38.5010	−2.35623
$268$	5.14435	0.314241
$269$	−1.34821	−0.0822019	−0.0411009	−	0.999155i	$-0.513087\pi$
$269$	−1.34821	−0.0822019	−0.0411009	+	0.999155i	$0.513087\pi$
$270$	0.601663	0.0366160
$271$	−30.1423	−1.83101	−0.915507	−	0.402303i	$-0.868210\pi$
$271$	−30.1423	−1.83101	−0.915507	+	0.402303i	$0.868210\pi$
$272$	4.12505	0.250118
$273$	−1.98542	−0.120163
$274$	3.91550	0.236544
$275$	−29.0303	−1.75059
$276$	20.2644	1.21978
$277$	−25.5182	−1.53324	−0.766619	−	0.642103i	$-0.778062\pi$
$277$	−25.5182	−1.53324	−0.766619	+	0.642103i	$0.778062\pi$
$278$	6.50175	0.389949
$279$	−49.9862	−2.99260
$280$	−0.0286897	−0.00171454
$281$	0.152561	0.00910100	0.00455050	−	0.999990i	$-0.498552\pi$
$281$	0.152561	0.00910100	0.00455050	+	0.999990i	$0.498552\pi$
$282$	−26.5470	−1.58085
$283$	12.1357	0.721395	0.360697	−	0.932683i	$-0.382539\pi$
$283$	12.1357	0.721395	0.360697	+	0.932683i	$0.382539\pi$
$284$	−16.2569	−0.964669
$285$	−2.73186	−0.161822
$286$	−20.5074	−1.21263
$287$	0.488950	0.0288618
$288$	−4.56449	−0.268965
$289$	0.0160113	0.000941841 0
$290$	−0.0491341	−0.00288525
$291$	41.7581	2.44790
$292$	−14.2704	−0.835111
$293$	4.74021	0.276926	0.138463	−	0.990368i	$-0.455784\pi$
$293$	4.74021	0.276926	0.138463	+	0.990368i	$0.455784\pi$
$294$	−19.1367	−1.11608
$295$	1.50331	0.0875263
$296$	10.8319	0.629590
$297$	−25.0811	−1.45535
$298$	22.0292	1.27612
$299$	−25.9222	−1.49912
$300$	13.6980	0.790857
$301$	0.914231	0.0526954
$302$	20.1283	1.15825
$303$	27.7748	1.59562
$304$	7.10360	0.407420
$305$	1.38439	0.0792700
$306$	−18.8287	−1.07637
$307$	−0.311211	−0.0177618	−0.00888088	−	0.999961i	$-0.502827\pi$
$307$	−0.311211	−0.0177618	−0.00888088	+	0.999961i	$0.502827\pi$
$308$	1.19597	0.0681465
$309$	−18.4520	−1.04970
$310$	1.53126	0.0869696
$311$	23.6539	1.34129	0.670645	−	0.741779i	$-0.266017\pi$
$311$	23.6539	1.34129	0.670645	+	0.741779i	$0.266017\pi$
$312$	9.67648	0.547823
$313$	7.33315	0.414494	0.207247	−	0.978289i	$-0.433550\pi$
$313$	7.33315	0.414494	0.207247	+	0.978289i	$0.433550\pi$
$314$	0.265018	0.0149559
$315$	0.130954	0.00737842
$316$	5.54979	0.312200
$317$	30.4342	1.70935	0.854676	−	0.519162i	$-0.173756\pi$
$317$	30.4342	1.70935	0.854676	+	0.519162i	$0.173756\pi$
$318$	−27.5522	−1.54505
$319$	2.04821	0.114678
$320$	0.139827	0.00781655
$321$	15.2990	0.853908
$322$	1.51175	0.0842467
$323$	29.3027	1.63045
$324$	−1.85889	−0.103272
$325$	−17.5225	−0.971973
$326$	17.9317	0.993145
$327$	0.565555	0.0312753
$328$	−2.38303	−0.131581
$329$	−1.98044	−0.109185
$330$	2.24162	0.123397
$331$	19.0988	1.04977	0.524883	−	0.851174i	$-0.324109\pi$
$331$	19.0988	1.04977	0.524883	+	0.851174i	$0.324109\pi$
$332$	−2.19354	−0.120386
$333$	−49.4420	−2.70941
$334$	9.35183	0.511709
$335$	0.719318	0.0393005
$336$	−0.564320	−0.0307862
$337$	24.7261	1.34692	0.673458	−	0.739226i	$-0.264808\pi$
$337$	24.7261	1.34692	0.673458	+	0.739226i	$0.264808\pi$
$338$	0.621863	0.0338249
$339$	55.0668	2.99082
$340$	0.576792	0.0312809
$341$	−63.8324	−3.45672
$342$	−32.4243	−1.75331
$343$	−2.86389	−0.154635
$344$	−4.45574	−0.240237
$345$	2.83351	0.152551
$346$	−18.7867	−1.00998
$347$	14.4100	0.773568	0.386784	−	0.922170i	$-0.373586\pi$
$347$	14.4100	0.773568	0.386784	+	0.922170i	$0.373586\pi$
$348$	−0.966457	−0.0518075
$349$	1.55575	0.0832774	0.0416387	−	0.999133i	$-0.486742\pi$
$349$	1.55575	0.0832774	0.0416387	+	0.999133i	$0.486742\pi$
$350$	1.02189	0.0546224
$351$	−15.1388	−0.808048
$352$	−5.82885	−0.310679
$353$	−30.3310	−1.61436	−0.807178	−	0.590309i	$-0.799006\pi$
$353$	−30.3310	−1.61436	−0.807178	+	0.590309i	$0.799006\pi$
$354$	29.5699	1.57162
$355$	−2.27315	−0.120646
$356$	13.9985	0.741921
$357$	−2.32785	−0.123203
$358$	−14.3255	−0.757126
$359$	−2.08821	−0.110212	−0.0551058	−	0.998481i	$-0.517550\pi$
$359$	−2.08821	−0.110212	−0.0551058	+	0.998481i	$0.517550\pi$
$360$	−0.638238	−0.0336381
$361$	31.4612	1.65585
$362$	11.6353	0.611537
$363$	−63.1909	−3.31666
$364$	0.721878	0.0378367
$365$	−1.99538	−0.104443
$366$	27.2307	1.42337
$367$	−34.2450	−1.78758	−0.893788	−	0.448490i	$-0.851962\pi$
$367$	−34.2450	−1.78758	−0.893788	+	0.448490i	$0.851962\pi$
$368$	−7.36792	−0.384079
$369$	10.8773	0.566249
$370$	1.51459	0.0787396
$371$	−2.05542	−0.106712
$372$	30.1195	1.56162
$373$	23.9926	1.24229	0.621146	−	0.783695i	$-0.286667\pi$
$373$	23.9926	1.24229	0.621146	+	0.783695i	$0.286667\pi$
$374$	−24.0443	−1.24330
$375$	3.83822	0.198205
$376$	9.65219	0.497774
$377$	1.23629	0.0636721
$378$	0.882874	0.0454102
$379$	14.6136	0.750652	0.375326	−	0.926893i	$-0.377531\pi$
$379$	14.6136	0.750652	0.375326	+	0.926893i	$0.377531\pi$
$380$	0.993274	0.0509539
$381$	−49.9675	−2.55991
$382$	15.8438	0.810638
$383$	13.6315	0.696537	0.348268	−	0.937395i	$-0.386770\pi$
$383$	13.6315	0.696537	0.348268	+	0.937395i	$0.386770\pi$
$384$	2.75036	0.140354
$385$	0.167228	0.00852273
$386$	11.7524	0.598182
$387$	20.3382	1.03385
$388$	−15.1828	−0.770789
$389$	11.6272	0.589522	0.294761	−	0.955571i	$-0.404760\pi$
$389$	11.6272	0.589522	0.294761	+	0.955571i	$0.404760\pi$
$390$	1.35303	0.0685134
$391$	−30.3930	−1.53704
$392$	6.95790	0.351427
$393$	−1.41058	−0.0711541
$394$	−7.23573	−0.364531
$395$	0.776009	0.0390452
$396$	26.6057	1.33699
$397$	−35.0550	−1.75936	−0.879681	−	0.475565i	$-0.842244\pi$
$397$	−35.0550	−1.75936	−0.879681	+	0.475565i	$0.842244\pi$
$398$	−5.81890	−0.291675
$399$	−4.00871	−0.200686
$400$	−4.98045	−0.249022
$401$	−8.90713	−0.444801	−0.222400	−	0.974955i	$-0.571389\pi$
$401$	−8.90713	−0.444801	−0.222400	+	0.974955i	$0.571389\pi$
$402$	14.1488	0.705680
$403$	−38.5288	−1.91926
$404$	−10.0986	−0.502424
$405$	−0.259923	−0.0129157
$406$	−0.0720989	−0.00357821
$407$	−63.1374	−3.12961
$408$	11.3454	0.561680
$409$	−17.8232	−0.881300	−0.440650	−	0.897679i	$-0.645252\pi$
$409$	−17.8232	−0.881300	−0.440650	+	0.897679i	$0.645252\pi$
$410$	−0.333211	−0.0164561
$411$	10.7690	0.531198
$412$	6.70894	0.330526
$413$	2.20595	0.108548
$414$	33.6308	1.65286
$415$	−0.306715	−0.0150560
$416$	−3.51826	−0.172497
$417$	17.8822	0.875694
$418$	−41.4058	−2.02523
$419$	3.04373	0.148696	0.0743480	−	0.997232i	$-0.476312\pi$
$419$	3.04373	0.148696	0.0743480	+	0.997232i	$0.476312\pi$
$420$	−0.0789071	−0.00385027
$421$	0.157779	0.00768969	0.00384485	−	0.999993i	$-0.498776\pi$
$421$	0.157779	0.00768969	0.00384485	+	0.999993i	$0.498776\pi$
$422$	5.78786	0.281749
$423$	−44.0574	−2.14214
$424$	10.0176	0.486500
$425$	−20.5446	−0.996559
$426$	−44.7123	−2.16632
$427$	2.03144	0.0983084
$428$	−5.56255	−0.268876
$429$	−56.4028	−2.72315
$430$	−0.623031	−0.0300452
$431$	26.2841	1.26606	0.633030	−	0.774127i	$-0.281811\pi$
$431$	26.2841	1.26606	0.633030	+	0.774127i	$0.281811\pi$
$432$	−4.30292	−0.207024
$433$	−17.8872	−0.859602	−0.429801	−	0.902924i	$-0.641416\pi$
$433$	−17.8872	−0.859602	−0.429801	+	0.902924i	$0.641416\pi$
$434$	2.24695	0.107857
$435$	−0.135136	−0.00647930
$436$	−0.205629	−0.00984785
$437$	−52.3388	−2.50370
$438$	−39.2487	−1.87538
$439$	−32.4342	−1.54800	−0.773999	−	0.633187i	$-0.781747\pi$
$439$	−32.4342	−1.54800	−0.773999	+	0.633187i	$0.781747\pi$
$440$	−0.815029	−0.0388550
$441$	−31.7593	−1.51235
$442$	−14.5130	−0.690312
$443$	−14.0723	−0.668597	−0.334299	−	0.942467i	$-0.608499\pi$
$443$	−14.0723	−0.668597	−0.334299	+	0.942467i	$0.608499\pi$
$444$	29.7916	1.41385
$445$	1.95737	0.0927882
$446$	−2.50246	−0.118495
$447$	60.5884	2.86573
$448$	0.205180	0.00969386
$449$	−37.2436	−1.75763	−0.878817	−	0.477159i	$-0.841667\pi$
$449$	−37.2436	−1.75763	−0.878817	+	0.477159i	$0.841667\pi$
$450$	22.7332	1.07165
$451$	13.8903	0.654068
$452$	−20.0217	−0.941740
$453$	55.3600	2.60104
$454$	−4.79374	−0.224981
$455$	0.100938	0.00473204
$456$	19.5375	0.914927
$457$	21.0681	0.985524	0.492762	−	0.870164i	$-0.335987\pi$
$457$	21.0681	0.985524	0.492762	+	0.870164i	$0.335987\pi$
$458$	25.1371	1.17458
$459$	−17.7497	−0.828487
$460$	−1.03023	−0.0480348
$461$	0.650814	0.0303114	0.0151557	−	0.999885i	$-0.495176\pi$
$461$	0.650814	0.0303114	0.0151557	+	0.999885i	$0.495176\pi$
$462$	3.28934	0.153034
$463$	16.7424	0.778086	0.389043	−	0.921220i	$-0.372806\pi$
$463$	16.7424	0.778086	0.389043	+	0.921220i	$0.372806\pi$
$464$	0.351393	0.0163130
$465$	4.21151	0.195304
$466$	−7.96330	−0.368893
$467$	−7.56177	−0.349917	−0.174958	−	0.984576i	$-0.555979\pi$
$467$	−7.56177	−0.349917	−0.174958	+	0.984576i	$0.555979\pi$
$468$	16.0591	0.742330
$469$	1.05552	0.0487394
$470$	1.34963	0.0622540
$471$	0.728897	0.0335858
$472$	−10.7513	−0.494867
$473$	25.9718	1.19419
$474$	15.2639	0.701096
$475$	−35.3791	−1.62331
$476$	0.846379	0.0387937
$477$	−45.7255	−2.09362
$478$	4.66859	0.213536
$479$	−4.57217	−0.208908	−0.104454	−	0.994530i	$-0.533309\pi$
$479$	−4.57217	−0.208908	−0.104454	+	0.994530i	$0.533309\pi$
$480$	0.384574	0.0175533
$481$	−38.1094	−1.73764
$482$	12.3748	0.563656
$483$	4.15787	0.189190
$484$	22.9755	1.04434
$485$	−2.12296	−0.0963985
$486$	−18.0214	−0.817466
$487$	−13.2621	−0.600962	−0.300481	−	0.953788i	$-0.597147\pi$
$487$	−13.2621	−0.600962	−0.300481	+	0.953788i	$0.597147\pi$
$488$	−9.90076	−0.448187
$489$	49.3187	2.23027
$490$	0.972900	0.0439512
$491$	−0.100551	−0.00453779	−0.00226890	−	0.999997i	$-0.500722\pi$
$491$	−0.100551	−0.00453779	−0.00226890	+	0.999997i	$0.500722\pi$
$492$	−6.55418	−0.295485
$493$	1.44951	0.0652827
$494$	−24.9923	−1.12446
$495$	3.72019	0.167210
$496$	−10.9511	−0.491719
$497$	−3.33560	−0.149622
$498$	−6.03302	−0.270346
$499$	−9.72618	−0.435404	−0.217702	−	0.976015i	$-0.569856\pi$
$499$	−9.72618	−0.435404	−0.217702	+	0.976015i	$0.569856\pi$
$500$	−1.39553	−0.0624101
$501$	25.7209	1.14913
$502$	−11.7959	−0.526475
$503$	−22.8330	−1.01807	−0.509037	−	0.860745i	$-0.669998\pi$
$503$	−22.8330	−1.01807	−0.509037	+	0.860745i	$0.669998\pi$
$504$	−0.936544	−0.0417170
$505$	−1.41205	−0.0628355
$506$	42.9465	1.90920
$507$	1.71035	0.0759592
$508$	18.1676	0.806058
$509$	36.3460	1.61101	0.805503	−	0.592592i	$-0.201895\pi$
$509$	36.3460	1.61101	0.805503	+	0.592592i	$0.201895\pi$
$510$	1.58639	0.0702464
$511$	−2.92800	−0.129527
$512$	−1.00000	−0.0441942
$513$	−30.5662	−1.34953
$514$	−24.1688	−1.06604
$515$	0.938088	0.0413371
$516$	−12.2549	−0.539492
$517$	−56.2612	−2.47436
$518$	2.22249	0.0976506
$519$	−51.6701	−2.26807
$520$	−0.491946	−0.0215733
$521$	−7.82838	−0.342968	−0.171484	−	0.985187i	$-0.554856\pi$
$521$	−7.82838	−0.342968	−0.171484	+	0.985187i	$0.554856\pi$
$522$	−1.60393	−0.0702020
$523$	21.7761	0.952201	0.476101	−	0.879391i	$-0.342050\pi$
$523$	21.7761	0.952201	0.476101	+	0.879391i	$0.342050\pi$
$524$	0.512869	0.0224048
$525$	2.81057	0.122663
$526$	−9.06964	−0.395455
$527$	−45.1738	−1.96780
$528$	−16.0314	−0.697679
$529$	31.2862	1.36027
$530$	1.40073	0.0608440
$531$	49.0740	2.12963
$532$	1.45752	0.0631915
$533$	8.38410	0.363156
$534$	38.5010	1.66610
$535$	−0.777792	−0.0336269
$536$	−5.14435	−0.222202
$537$	−39.4003	−1.70025
$538$	1.34821	0.0581255
$539$	−40.5566	−1.74689
$540$	−0.601663	−0.0258914
$541$	3.54986	0.152620	0.0763102	−	0.997084i	$-0.475686\pi$
$541$	3.54986	0.152620	0.0763102	+	0.997084i	$0.475686\pi$
$542$	30.1423	1.29472
$543$	32.0012	1.37330
$544$	−4.12505	−0.176860
$545$	−0.0287525	−0.00123162
$546$	1.98542	0.0849683
$547$	23.4240	1.00154	0.500769	−	0.865581i	$-0.333051\pi$
$547$	23.4240	1.00154	0.500769	+	0.865581i	$0.333051\pi$
$548$	−3.91550	−0.167262
$549$	45.1919	1.92875
$550$	29.0303	1.23786
$551$	2.49615	0.106340
$552$	−20.2644	−0.862512
$553$	1.13871	0.0484228
$554$	25.5182	1.08416
$555$	4.16566	0.176822
$556$	−6.50175	−0.275736
$557$	−35.4930	−1.50389	−0.751944	−	0.659227i	$-0.770884\pi$
$557$	−35.4930	−1.50389	−0.751944	+	0.659227i	$0.770884\pi$
$558$	49.9862	2.11609
$559$	15.6764	0.663043
$560$	0.0286897	0.00121236
$561$	−66.1305	−2.79203
$562$	−0.152561	−0.00643538
$563$	23.7889	1.00258	0.501292	−	0.865278i	$-0.332858\pi$
$563$	23.7889	1.00258	0.501292	+	0.865278i	$0.332858\pi$
$564$	26.5470	1.11783
$565$	−2.79956	−0.117779
$566$	−12.1357	−0.510103
$567$	−0.381409	−0.0160177
$568$	16.2569	0.682124
$569$	4.57035	0.191599	0.0957996	−	0.995401i	$-0.469459\pi$
$569$	4.57035	0.191599	0.0957996	+	0.995401i	$0.469459\pi$
$570$	2.73186	0.114425
$571$	40.4024	1.69079	0.845395	−	0.534142i	$-0.179365\pi$
$571$	40.4024	1.69079	0.845395	+	0.534142i	$0.179365\pi$
$572$	20.5074	0.857457
$573$	43.5761	1.82042
$574$	−0.488950	−0.0204084
$575$	36.6955	1.53031
$576$	4.56449	0.190187
$577$	−27.6237	−1.14999	−0.574996	−	0.818157i	$-0.694996\pi$
$577$	−27.6237	−1.14999	−0.574996	+	0.818157i	$0.694996\pi$
$578$	−0.0160113	−0.000665983 0
$579$	32.3234	1.34332
$580$	0.0491341	0.00204018
$581$	−0.450071	−0.0186721
$582$	−41.7581	−1.73093
$583$	−58.3914	−2.41832
$584$	14.2704	0.590513
$585$	2.24548	0.0928394
$586$	−4.74021	−0.195816
$587$	−22.2377	−0.917849	−0.458925	−	0.888475i	$-0.651765\pi$
$587$	−22.2377	−0.917849	−0.458925	+	0.888475i	$0.651765\pi$
$588$	19.1367	0.789186
$589$	−77.7924	−3.20538
$590$	−1.50331	−0.0618904
$591$	−19.9009	−0.818613
$592$	−10.8319	−0.445188
$593$	26.6781	1.09554	0.547770	−	0.836629i	$-0.315477\pi$
$593$	26.6781	1.09554	0.547770	+	0.836629i	$0.315477\pi$
$594$	25.0811	1.02909
$595$	0.118346	0.00485173
$596$	−22.0292	−0.902353
$597$	−16.0041	−0.655003
$598$	25.9222	1.06004
$599$	39.5196	1.61473	0.807363	−	0.590055i	$-0.200894\pi$
$599$	39.5196	1.61473	0.807363	+	0.590055i	$0.200894\pi$
$600$	−13.6980	−0.559220
$601$	5.13651	0.209522	0.104761	−	0.994497i	$-0.466592\pi$
$601$	5.13651	0.209522	0.104761	+	0.994497i	$0.466592\pi$
$602$	−0.914231	−0.0372613
$603$	23.4814	0.956235
$604$	−20.1283	−0.819008
$605$	3.21259	0.130610
$606$	−27.7748	−1.12827
$607$	27.4796	1.11536	0.557680	−	0.830056i	$-0.311691\pi$
$607$	27.4796	1.11536	0.557680	+	0.830056i	$0.311691\pi$
$608$	−7.10360	−0.288089
$609$	−0.198298	−0.00803544
$610$	−1.38439	−0.0560524
$611$	−33.9589	−1.37383
$612$	18.8287	0.761107
$613$	22.8146	0.921472	0.460736	−	0.887537i	$-0.347586\pi$
$613$	22.8146	0.921472	0.460736	+	0.887537i	$0.347586\pi$
$614$	0.311211	0.0125595
$615$	−0.916450	−0.0369548
$616$	−1.19597	−0.0481868
$617$	−10.4874	−0.422207	−0.211103	−	0.977464i	$-0.567706\pi$
$617$	−10.4874	−0.422207	−0.211103	+	0.977464i	$0.567706\pi$
$618$	18.4520	0.742248
$619$	9.85379	0.396057	0.198029	−	0.980196i	$-0.436546\pi$
$619$	9.85379	0.396057	0.198029	+	0.980196i	$0.436546\pi$
$620$	−1.53126	−0.0614968
$621$	31.7035	1.27222
$622$	−23.6539	−0.948435
$623$	2.87223	0.115073
$624$	−9.67648	−0.387369
$625$	24.7071	0.988284
$626$	−7.33315	−0.293092
$627$	−113.881	−4.54797
$628$	−0.265018	−0.0105754
$629$	−44.6820	−1.78159
$630$	−0.130954	−0.00521733
$631$	20.0144	0.796759	0.398379	−	0.917221i	$-0.369573\pi$
$631$	20.0144	0.796759	0.398379	+	0.917221i	$0.369573\pi$
$632$	−5.54979	−0.220759
$633$	15.9187	0.632712
$634$	−30.4342	−1.20869
$635$	2.54032	0.100809
$636$	27.5522	1.09251
$637$	−24.4797	−0.969921
$638$	−2.04821	−0.0810896
$639$	−74.2044	−2.93548
$640$	−0.139827	−0.00552714
$641$	13.9225	0.549904	0.274952	−	0.961458i	$-0.411338\pi$
$641$	13.9225	0.549904	0.274952	+	0.961458i	$0.411338\pi$
$642$	−15.2990	−0.603804
$643$	−42.7949	−1.68766	−0.843832	−	0.536607i	$-0.819706\pi$
$643$	−42.7949	−1.68766	−0.843832	+	0.536607i	$0.819706\pi$
$644$	−1.51175	−0.0595714
$645$	−1.71356	−0.0674714
$646$	−29.3027	−1.15290
$647$	28.6344	1.12573	0.562867	−	0.826548i	$-0.309698\pi$
$647$	28.6344	1.12573	0.562867	+	0.826548i	$0.309698\pi$
$648$	1.85889	0.0730242
$649$	62.6675	2.45991
$650$	17.5225	0.687289
$651$	6.17994	0.242211
$652$	−17.9317	−0.702259
$653$	−2.75307	−0.107736	−0.0538680	−	0.998548i	$-0.517155\pi$
$653$	−2.75307	−0.107736	−0.0538680	+	0.998548i	$0.517155\pi$
$654$	−0.565555	−0.0221149
$655$	0.0717128	0.00280205
$656$	2.38303	0.0930415
$657$	−65.1371	−2.54124
$658$	1.98044	0.0772057
$659$	9.01228	0.351069	0.175534	−	0.984473i	$-0.443835\pi$
$659$	9.01228	0.351069	0.175534	+	0.984473i	$0.443835\pi$
$660$	−2.24162	−0.0872551
$661$	−33.7558	−1.31295	−0.656475	−	0.754348i	$-0.727953\pi$
$661$	−33.7558	−1.31295	−0.656475	+	0.754348i	$0.727953\pi$
$662$	−19.0988	−0.742297
$663$	−39.9159	−1.55021
$664$	2.19354	0.0851257
$665$	0.203800	0.00790304
$666$	49.4420	1.91584
$667$	−2.58903	−0.100248
$668$	−9.35183	−0.361833
$669$	−6.88268	−0.266100
$670$	−0.719318	−0.0277897
$671$	57.7101	2.22787
$672$	0.564320	0.0217691
$673$	−25.3504	−0.977186	−0.488593	−	0.872512i	$-0.662490\pi$
$673$	−25.3504	−0.977186	−0.488593	+	0.872512i	$0.662490\pi$
$674$	−24.7261	−0.952413
$675$	21.4305	0.824859
$676$	−0.621863	−0.0239178
$677$	−15.0707	−0.579214	−0.289607	−	0.957146i	$-0.593525\pi$
$677$	−15.0707	−0.579214	−0.289607	+	0.957146i	$0.593525\pi$
$678$	−55.0668	−2.11483
$679$	−3.11521	−0.119551
$680$	−0.576792	−0.0221190
$681$	−13.1845	−0.505232
$682$	63.8324	2.44427
$683$	−9.74623	−0.372929	−0.186465	−	0.982462i	$-0.559703\pi$
$683$	−9.74623	−0.372929	−0.186465	+	0.982462i	$0.559703\pi$
$684$	32.4243	1.23978
$685$	−0.547491	−0.0209186
$686$	2.86389	0.109344
$687$	69.1361	2.63771
$688$	4.45574	0.169873
$689$	−35.2447	−1.34271
$690$	−2.83351	−0.107870
$691$	−13.8425	−0.526595	−0.263297	−	0.964715i	$-0.584810\pi$
$691$	−13.8425	−0.526595	−0.263297	+	0.964715i	$0.584810\pi$
$692$	18.7867	0.714161
$693$	5.45898	0.207369
$694$	−14.4100	−0.546995
$695$	−0.909119	−0.0344848
$696$	0.966457	0.0366334
$697$	9.83009	0.372341
$698$	−1.55575	−0.0588860
$699$	−21.9020	−0.828408
$700$	−1.02189	−0.0386238
$701$	24.8805	0.939724	0.469862	−	0.882740i	$-0.344304\pi$
$701$	24.8805	0.939724	0.469862	+	0.882740i	$0.344304\pi$
$702$	15.1388	0.571376
$703$	−76.9454	−2.90205
$704$	5.82885	0.219683
$705$	3.71198	0.139801
$706$	30.3310	1.14152
$707$	−2.07203	−0.0779269
$708$	−29.5699	−1.11130
$709$	−15.4971	−0.582005	−0.291002	−	0.956722i	$-0.593989\pi$
$709$	−15.4971	−0.582005	−0.291002	+	0.956722i	$0.593989\pi$
$710$	2.27315	0.0853097
$711$	25.3320	0.950023
$712$	−13.9985	−0.524617
$713$	80.6869	3.02175
$714$	2.32785	0.0871175
$715$	2.86748	0.107238
$716$	14.3255	0.535369
$717$	12.8403	0.479530
$718$	2.08821	0.0779314
$719$	−20.7007	−0.772005	−0.386002	−	0.922498i	$-0.626144\pi$
$719$	−20.7007	−0.772005	−0.386002	+	0.922498i	$0.626144\pi$
$720$	0.638238	0.0237857
$721$	1.37654	0.0512651
$722$	−31.4612	−1.17086
$723$	34.0351	1.26578
$724$	−11.6353	−0.432422
$725$	−1.75009	−0.0649968
$726$	63.1909	2.34524
$727$	−1.87632	−0.0695889	−0.0347945	−	0.999394i	$-0.511078\pi$
$727$	−1.87632	−0.0695889	−0.0347945	+	0.999394i	$0.511078\pi$
$728$	−0.721878	−0.0267546
$729$	−43.9886	−1.62921
$730$	1.99538	0.0738524
$731$	18.3801	0.679814
$732$	−27.2307	−1.00648
$733$	−20.2996	−0.749782	−0.374891	−	0.927069i	$-0.622320\pi$
$733$	−20.2996	−0.749782	−0.374891	+	0.927069i	$0.622320\pi$
$734$	34.2450	1.26401
$735$	2.67583	0.0986994
$736$	7.36792	0.271585
$737$	29.9857	1.10454
$738$	−10.8773	−0.400399
$739$	−13.2711	−0.488186	−0.244093	−	0.969752i	$-0.578490\pi$
$739$	−13.2711	−0.488186	−0.244093	+	0.969752i	$0.578490\pi$
$740$	−1.51459	−0.0556773
$741$	−68.7379	−2.52515
$742$	2.05542	0.0754570
$743$	−52.0116	−1.90812	−0.954060	−	0.299615i	$-0.903142\pi$
$743$	−52.0116	−1.90812	−0.954060	+	0.299615i	$0.903142\pi$
$744$	−30.1195	−1.10424
$745$	−3.08028	−0.112853
$746$	−23.9926	−0.878433
$747$	−10.0124	−0.366334
$748$	24.0443	0.879146
$749$	−1.14133	−0.0417031
$750$	−3.83822	−0.140152
$751$	22.1638	0.808769	0.404385	−	0.914589i	$-0.367486\pi$
$751$	22.1638	0.808769	0.404385	+	0.914589i	$0.367486\pi$
$752$	−9.65219	−0.351979
$753$	−32.4429	−1.18229
$754$	−1.23629	−0.0450230
$755$	−2.81447	−0.102429
$756$	−0.882874	−0.0321098
$757$	−8.40429	−0.305459	−0.152730	−	0.988268i	$-0.548806\pi$
$757$	−8.40429	−0.305459	−0.152730	+	0.988268i	$0.548806\pi$
$758$	−14.6136	−0.530791
$759$	118.118	4.28743
$760$	−0.993274	−0.0360298
$761$	20.0067	0.725241	0.362620	−	0.931937i	$-0.381882\pi$
$761$	20.0067	0.725241	0.362620	+	0.931937i	$0.381882\pi$
$762$	49.9675	1.81013
$763$	−0.0421911	−0.00152742
$764$	−15.8438	−0.573208
$765$	2.63276	0.0951877
$766$	−13.6315	−0.492526
$767$	37.8257	1.36581
$768$	−2.75036	−0.0992451
$769$	−4.05334	−0.146167	−0.0730837	−	0.997326i	$-0.523284\pi$
$769$	−4.05334	−0.146167	−0.0730837	+	0.997326i	$0.523284\pi$
$770$	−0.167228	−0.00602648
$771$	−66.4731	−2.39397
$772$	−11.7524	−0.422979
$773$	−16.6856	−0.600139	−0.300070	−	0.953917i	$-0.597010\pi$
$773$	−16.6856	−0.600139	−0.300070	+	0.953917i	$0.597010\pi$
$774$	−20.3382	−0.731041
$775$	54.5414	1.95919
$776$	15.1828	0.545030
$777$	6.11265	0.219290
$778$	−11.6272	−0.416855
$779$	16.9281	0.606511
$780$	−1.35303	−0.0484463
$781$	−94.7590	−3.39074
$782$	30.3930	1.08685
$783$	−1.51201	−0.0540349
$784$	−6.95790	−0.248496
$785$	−0.0370567	−0.00132261
$786$	1.41058	0.0503136
$787$	6.70328	0.238946	0.119473	−	0.992837i	$-0.461879\pi$
$787$	6.70328	0.238946	0.119473	+	0.992837i	$0.461879\pi$
$788$	7.23573	0.257762
$789$	−24.9448	−0.888058
$790$	−0.776009	−0.0276092
$791$	−4.10805	−0.146066
$792$	−26.6057	−0.945394
$793$	34.8334	1.23697
$794$	35.0550	1.24406
$795$	3.85253	0.136635
$796$	5.81890	0.206245
$797$	2.49881	0.0885125	0.0442562	−	0.999020i	$-0.485908\pi$
$797$	2.49881	0.0885125	0.0442562	+	0.999020i	$0.485908\pi$
$798$	4.00871	0.141907
$799$	−39.8158	−1.40858
$800$	4.98045	0.176085
$801$	63.8962	2.25766
$802$	8.90713	0.314522
$803$	−83.1800	−2.93536
$804$	−14.1488	−0.498991
$805$	−0.211383	−0.00745029
$806$	38.5288	1.35712
$807$	3.70807	0.130530
$808$	10.0986	0.355267
$809$	2.29781	0.0807865	0.0403933	−	0.999184i	$-0.487139\pi$
$809$	2.29781	0.0807865	0.0403933	+	0.999184i	$0.487139\pi$
$810$	0.259923	0.00913276
$811$	8.11466	0.284944	0.142472	−	0.989799i	$-0.454495\pi$
$811$	8.11466	0.284944	0.142472	+	0.989799i	$0.454495\pi$
$812$	0.0720989	0.00253017
$813$	82.9022	2.90751
$814$	63.1374	2.21297
$815$	−2.50733	−0.0878279
$816$	−11.3454	−0.397167
$817$	31.6518	1.10736
$818$	17.8232	0.623173
$819$	3.29500	0.115137
$820$	0.333211	0.0116362
$821$	12.0792	0.421567	0.210784	−	0.977533i	$-0.432398\pi$
$821$	12.0792	0.421567	0.210784	+	0.977533i	$0.432398\pi$
$822$	−10.7690	−0.375613
$823$	38.0998	1.32807	0.664037	−	0.747699i	$-0.268842\pi$
$823$	38.0998	1.32807	0.664037	+	0.747699i	$0.268842\pi$
$824$	−6.70894	−0.233717
$825$	79.8438	2.77980
$826$	−2.20595	−0.0767548
$827$	−9.88602	−0.343770	−0.171885	−	0.985117i	$-0.554986\pi$
$827$	−9.88602	−0.343770	−0.171885	+	0.985117i	$0.554986\pi$
$828$	−33.6308	−1.16875
$829$	−15.0081	−0.521252	−0.260626	−	0.965440i	$-0.583929\pi$
$829$	−15.0081	−0.521252	−0.260626	+	0.965440i	$0.583929\pi$
$830$	0.306715	0.0106462
$831$	70.1842	2.43466
$832$	3.51826	0.121974
$833$	−28.7017	−0.994454
$834$	−17.8822	−0.619209
$835$	−1.30764	−0.0452526
$836$	41.4058	1.43205
$837$	47.1217	1.62876
$838$	−3.04373	−0.105144
$839$	−0.111708	−0.00385657	−0.00192829	−	0.999998i	$-0.500614\pi$
$839$	−0.111708	−0.00385657	−0.00192829	+	0.999998i	$0.500614\pi$
$840$	0.0789071	0.00272255
$841$	−28.8765	−0.995742
$842$	−0.157779	−0.00543743
$843$	−0.419597	−0.0144517
$844$	−5.78786	−0.199226
$845$	−0.0869530	−0.00299127
$846$	44.0574	1.51472
$847$	4.71412	0.161979
$848$	−10.0176	−0.344007
$849$	−33.3777	−1.14552
$850$	20.5446	0.704673
$851$	79.8084	2.73580
$852$	44.7123	1.53182
$853$	−14.0227	−0.480127	−0.240063	−	0.970757i	$-0.577168\pi$
$853$	−14.0227	−0.480127	−0.240063	+	0.970757i	$0.577168\pi$
$854$	−2.03144	−0.0695145
$855$	4.53379	0.155052
$856$	5.56255	0.190124
$857$	−51.8868	−1.77242	−0.886210	−	0.463284i	$-0.846671\pi$
$857$	−51.8868	−1.77242	−0.886210	+	0.463284i	$0.846671\pi$
$858$	56.4028	1.92556
$859$	13.4775	0.459846	0.229923	−	0.973209i	$-0.426153\pi$
$859$	13.4775	0.459846	0.229923	+	0.973209i	$0.426153\pi$
$860$	0.623031	0.0212452
$861$	−1.34479	−0.0458303
$862$	−26.2841	−0.895240
$863$	−6.42614	−0.218748	−0.109374	−	0.994001i	$-0.534885\pi$
$863$	−6.42614	−0.218748	−0.109374	+	0.994001i	$0.534885\pi$
$864$	4.30292	0.146388
$865$	2.62688	0.0893165
$866$	17.8872	0.607831
$867$	−0.0440369	−0.00149557
$868$	−2.24695	−0.0762666
$869$	32.3489	1.09736
$870$	0.135136	0.00458155
$871$	18.0992	0.613267
$872$	0.205629	0.00696348
$873$	−69.3016	−2.34551
$874$	52.3388	1.77039
$875$	−0.286336	−0.00967993
$876$	39.2487	1.32609
$877$	4.56348	0.154098	0.0770490	−	0.997027i	$-0.475450\pi$
$877$	4.56348	0.154098	0.0770490	+	0.997027i	$0.475450\pi$
$878$	32.4342	1.09460
$879$	−13.0373	−0.439737
$880$	0.815029	0.0274746
$881$	5.11130	0.172204	0.0861021	−	0.996286i	$-0.472559\pi$
$881$	5.11130	0.172204	0.0861021	+	0.996286i	$0.472559\pi$
$882$	31.7593	1.06939
$883$	1.78270	0.0599926	0.0299963	−	0.999550i	$-0.490450\pi$
$883$	1.78270	0.0599926	0.0299963	+	0.999550i	$0.490450\pi$
$884$	14.5130	0.488124
$885$	−4.13466	−0.138985
$886$	14.0723	0.472770
$887$	46.9794	1.57742	0.788708	−	0.614768i	$-0.210751\pi$
$887$	46.9794	1.57742	0.788708	+	0.614768i	$0.210751\pi$
$888$	−29.7916	−0.999741
$889$	3.72764	0.125021
$890$	−1.95737	−0.0656112
$891$	−10.8352	−0.362993
$892$	2.50246	0.0837887
$893$	−68.5654	−2.29445
$894$	−60.5884	−2.02638
$895$	2.00309	0.0669558
$896$	−0.205180	−0.00685460
$897$	71.2955	2.38049
$898$	37.2436	1.24283
$899$	−3.84814	−0.128343
$900$	−22.7332	−0.757774
$901$	−41.3233	−1.37668
$902$	−13.8903	−0.462496
$903$	−2.51447	−0.0836762
$904$	20.0217	0.665911
$905$	−1.62692	−0.0540807
$906$	−55.3600	−1.83921
$907$	13.0501	0.433322	0.216661	−	0.976247i	$-0.430483\pi$
$907$	13.0501	0.433322	0.216661	+	0.976247i	$0.430483\pi$
$908$	4.79374	0.159086
$909$	−46.0949	−1.52887
$910$	−0.100938	−0.00334605
$911$	−9.47642	−0.313968	−0.156984	−	0.987601i	$-0.550177\pi$
$911$	−9.47642	−0.313968	−0.156984	+	0.987601i	$0.550177\pi$
$912$	−19.5375	−0.646951
$913$	−12.7858	−0.423148
$914$	−21.0681	−0.696871
$915$	−3.80758	−0.125875
$916$	−25.1371	−0.830553
$917$	0.105231	0.00347502
$918$	17.7497	0.585829
$919$	44.7274	1.47542	0.737710	−	0.675118i	$-0.235907\pi$
$919$	44.7274	1.47542	0.737710	+	0.675118i	$0.235907\pi$
$920$	1.03023	0.0339657
$921$	0.855943	0.0282043
$922$	−0.650814	−0.0214334
$923$	−57.1959	−1.88263
$924$	−3.28934	−0.108211
$925$	53.9476	1.77379
$926$	−16.7424	−0.550190
$927$	30.6229	1.00579
$928$	−0.351393	−0.0115350
$929$	22.6136	0.741927	0.370964	−	0.928647i	$-0.379027\pi$
$929$	22.6136	0.741927	0.370964	+	0.928647i	$0.379027\pi$
$930$	−4.21151	−0.138101
$931$	−49.4262	−1.61988
$932$	7.96330	0.260847
$933$	−65.0568	−2.12986
$934$	7.56177	0.247429
$935$	3.36203	0.109950
$936$	−16.0591	−0.524907
$937$	−25.3583	−0.828420	−0.414210	−	0.910181i	$-0.635942\pi$
$937$	−25.3583	−0.828420	−0.414210	+	0.910181i	$0.635942\pi$
$938$	−1.05552	−0.0344640
$939$	−20.1688	−0.658185
$940$	−1.34963	−0.0440202
$941$	33.0608	1.07775	0.538875	−	0.842386i	$-0.318850\pi$
$941$	33.0608	1.07775	0.538875	+	0.842386i	$0.318850\pi$
$942$	−0.728897	−0.0237487
$943$	−17.5579	−0.571765
$944$	10.7513	0.349924
$945$	−0.123449	−0.00401581
$946$	−25.9718	−0.844417
$947$	−16.6015	−0.539475	−0.269738	−	0.962934i	$-0.586937\pi$
$947$	−16.6015	−0.539475	−0.269738	+	0.962934i	$0.586937\pi$
$948$	−15.2639	−0.495749
$949$	−50.2069	−1.62979
$950$	35.3791	1.14785
$951$	−83.7049	−2.71432
$952$	−0.846379	−0.0274313
$953$	6.09459	0.197423	0.0987116	−	0.995116i	$-0.468528\pi$
$953$	6.09459	0.197423	0.0987116	+	0.995116i	$0.468528\pi$
$954$	45.7255	1.48042
$955$	−2.21538	−0.0716881
$956$	−4.66859	−0.150993
$957$	−5.63333	−0.182100
$958$	4.57217	0.147720
$959$	−0.803384	−0.0259426
$960$	−0.384574	−0.0124121
$961$	88.9268	2.86861
$962$	38.1094	1.22870
$963$	−25.3902	−0.818187
$964$	−12.3748	−0.398565
$965$	−1.64330	−0.0528998
$966$	−4.15787	−0.133777
$967$	−16.6447	−0.535259	−0.267629	−	0.963522i	$-0.586240\pi$
$967$	−16.6447	−0.535259	−0.267629	+	0.963522i	$0.586240\pi$
$968$	−22.9755	−0.738460
$969$	−80.5930	−2.58902
$970$	2.12296	0.0681641
$971$	42.6367	1.36828	0.684138	−	0.729352i	$-0.260178\pi$
$971$	42.6367	1.36828	0.684138	+	0.729352i	$0.260178\pi$
$972$	18.0214	0.578036
$973$	−1.33403	−0.0427671
$974$	13.2621	0.424944
$975$	48.1932	1.54342
$976$	9.90076	0.316916
$977$	55.5093	1.77590	0.887950	−	0.459941i	$-0.152129\pi$
$977$	55.5093	1.77590	0.887950	+	0.459941i	$0.152129\pi$
$978$	−49.3187	−1.57704
$979$	81.5954	2.60780
$980$	−0.972900	−0.0310782
$981$	−0.938593	−0.0299670
$982$	0.100551	0.00320871
$983$	−8.43801	−0.269131	−0.134565	−	0.990905i	$-0.542964\pi$
$983$	−8.43801	−0.269131	−0.134565	+	0.990905i	$0.542964\pi$
$984$	6.55418	0.208940
$985$	1.01175	0.0322370
$986$	−1.44951	−0.0461618
$987$	5.44693	0.173378
$988$	24.9923	0.795111
$989$	−32.8295	−1.04392
$990$	−3.72019	−0.118235
$991$	6.17107	0.196030	0.0980152	−	0.995185i	$-0.468751\pi$
$991$	6.17107	0.196030	0.0980152	+	0.995185i	$0.468751\pi$
$992$	10.9511	0.347698
$993$	−52.5287	−1.66695
$994$	3.33560	0.105799
$995$	0.813638	0.0257940
$996$	6.03302	0.191164
$997$	−16.9988	−0.538359	−0.269179	−	0.963090i	$-0.586752\pi$
$997$	−16.9988	−0.538359	−0.269179	+	0.963090i	$0.586752\pi$
$998$	9.72618	0.307877
$999$	46.6087	1.47463

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6038.2.a.c.1.7	✓	57

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6038.2.a.c.1.7	✓	57	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.75036 q^{3} +1.00000 q^{4} +0.139827 q^{5} +2.75036 q^{6} +0.205180 q^{7} -1.00000 q^{8} +4.56449 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.75036 q^{3} +1.00000 q^{4} +0.139827 q^{5} +2.75036 q^{6} +0.205180 q^{7} -1.00000 q^{8} +4.56449 q^{9} -0.139827 q^{10} +5.82885 q^{11} -2.75036 q^{12} +3.51826 q^{13} -0.205180 q^{14} -0.384574 q^{15} +1.00000 q^{16} +4.12505 q^{17} -4.56449 q^{18} +7.10360 q^{19} +0.139827 q^{20} -0.564320 q^{21} -5.82885 q^{22} -7.36792 q^{23} +2.75036 q^{24} -4.98045 q^{25} -3.51826 q^{26} -4.30292 q^{27} +0.205180 q^{28} +0.351393 q^{29} +0.384574 q^{30} -10.9511 q^{31} -1.00000 q^{32} -16.0314 q^{33} -4.12505 q^{34} +0.0286897 q^{35} +4.56449 q^{36} -10.8319 q^{37} -7.10360 q^{38} -9.67648 q^{39} -0.139827 q^{40} +2.38303 q^{41} +0.564320 q^{42} +4.45574 q^{43} +5.82885 q^{44} +0.638238 q^{45} +7.36792 q^{46} -9.65219 q^{47} -2.75036 q^{48} -6.95790 q^{49} +4.98045 q^{50} -11.3454 q^{51} +3.51826 q^{52} -10.0176 q^{53} +4.30292 q^{54} +0.815029 q^{55} -0.205180 q^{56} -19.5375 q^{57} -0.351393 q^{58} +10.7513 q^{59} -0.384574 q^{60} +9.90076 q^{61} +10.9511 q^{62} +0.936544 q^{63} +1.00000 q^{64} +0.491946 q^{65} +16.0314 q^{66} +5.14435 q^{67} +4.12505 q^{68} +20.2644 q^{69} -0.0286897 q^{70} -16.2569 q^{71} -4.56449 q^{72} -14.2704 q^{73} +10.8319 q^{74} +13.6980 q^{75} +7.10360 q^{76} +1.19597 q^{77} +9.67648 q^{78} +5.54979 q^{79} +0.139827 q^{80} -1.85889 q^{81} -2.38303 q^{82} -2.19354 q^{83} -0.564320 q^{84} +0.576792 q^{85} -4.45574 q^{86} -0.966457 q^{87} -5.82885 q^{88} +13.9985 q^{89} -0.638238 q^{90} +0.721878 q^{91} -7.36792 q^{92} +30.1195 q^{93} +9.65219 q^{94} +0.993274 q^{95} +2.75036 q^{96} -15.1828 q^{97} +6.95790 q^{98} +26.6057 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 57 q - 57 q^{2} - 5 q^{3} + 57 q^{4} - 15 q^{5} + 5 q^{6} - 28 q^{7} - 57 q^{8} + 50 q^{9}+O(q^{10}) \) 57 * q - 57 * q^2 - 5 * q^3 + 57 * q^4 - 15 * q^5 + 5 * q^6 - 28 * q^7 - 57 * q^8 + 50 * q^9	\( 57 q - 57 q^{2} - 5 q^{3} + 57 q^{4} - 15 q^{5} + 5 q^{6} - 28 q^{7} - 57 q^{8} + 50 q^{9} + 15 q^{10} + 13 q^{11} - 5 q^{12} - 43 q^{13} + 28 q^{14} - 10 q^{15} + 57 q^{16} - 50 q^{18} - 6 q^{19} - 15 q^{20} - 23 q^{21} - 13 q^{22} - q^{23} + 5 q^{24} + 20 q^{25} + 43 q^{26} - 20 q^{27} - 28 q^{28} - 4 q^{29} + 10 q^{30} - 34 q^{31} - 57 q^{32} - 43 q^{33} + 26 q^{35} + 50 q^{36} - 64 q^{37} + 6 q^{38} + 8 q^{39} + 15 q^{40} + 27 q^{41} + 23 q^{42} - 29 q^{43} + 13 q^{44} - 76 q^{45} + q^{46} - 25 q^{47} - 5 q^{48} + 7 q^{49} - 20 q^{50} + 27 q^{51} - 43 q^{52} - 34 q^{53} + 20 q^{54} - 36 q^{55} + 28 q^{56} - 33 q^{57} + 4 q^{58} + 19 q^{59} - 10 q^{60} - 58 q^{61} + 34 q^{62} - 65 q^{63} + 57 q^{64} + 17 q^{65} + 43 q^{66} - 84 q^{67} - 33 q^{69} - 26 q^{70} + 22 q^{71} - 50 q^{72} - 82 q^{73} + 64 q^{74} + 8 q^{75} - 6 q^{76} - 41 q^{77} - 8 q^{78} + 8 q^{79} - 15 q^{80} + 25 q^{81} - 27 q^{82} - 23 q^{83} - 23 q^{84} - 58 q^{85} + 29 q^{86} - 17 q^{87} - 13 q^{88} + 18 q^{89} + 76 q^{90} - 4 q^{91} - q^{92} - 60 q^{93} + 25 q^{94} + 36 q^{95} + 5 q^{96} - 156 q^{97} - 7 q^{98} + 25 q^{99}+O(q^{100}) \) 57 * q - 57 * q^2 - 5 * q^3 + 57 * q^4 - 15 * q^5 + 5 * q^6 - 28 * q^7 - 57 * q^8 + 50 * q^9 + 15 * q^10 + 13 * q^11 - 5 * q^12 - 43 * q^13 + 28 * q^14 - 10 * q^15 + 57 * q^16 - 50 * q^18 - 6 * q^19 - 15 * q^20 - 23 * q^21 - 13 * q^22 - q^23 + 5 * q^24 + 20 * q^25 + 43 * q^26 - 20 * q^27 - 28 * q^28 - 4 * q^29 + 10 * q^30 - 34 * q^31 - 57 * q^32 - 43 * q^33 + 26 * q^35 + 50 * q^36 - 64 * q^37 + 6 * q^38 + 8 * q^39 + 15 * q^40 + 27 * q^41 + 23 * q^42 - 29 * q^43 + 13 * q^44 - 76 * q^45 + q^46 - 25 * q^47 - 5 * q^48 + 7 * q^49 - 20 * q^50 + 27 * q^51 - 43 * q^52 - 34 * q^53 + 20 * q^54 - 36 * q^55 + 28 * q^56 - 33 * q^57 + 4 * q^58 + 19 * q^59 - 10 * q^60 - 58 * q^61 + 34 * q^62 - 65 * q^63 + 57 * q^64 + 17 * q^65 + 43 * q^66 - 84 * q^67 - 33 * q^69 - 26 * q^70 + 22 * q^71 - 50 * q^72 - 82 * q^73 + 64 * q^74 + 8 * q^75 - 6 * q^76 - 41 * q^77 - 8 * q^78 + 8 * q^79 - 15 * q^80 + 25 * q^81 - 27 * q^82 - 23 * q^83 - 23 * q^84 - 58 * q^85 + 29 * q^86 - 17 * q^87 - 13 * q^88 + 18 * q^89 + 76 * q^90 - 4 * q^91 - q^92 - 60 * q^93 + 25 * q^94 + 36 * q^95 + 5 * q^96 - 156 * q^97 - 7 * q^98 + 25 * q^99

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