LMFDB - Embedded newform 8029.2.a.h.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8029,2,Mod(1,8029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8029, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8029 = 7 \cdot 31 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8029.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:	$64.1118877829$
Analytic rank:	$0$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.56268 q^{2} -3.23783 q^{3} +0.441960 q^{4} -3.23512 q^{5} +5.05968 q^{6} -1.00000 q^{7} +2.43471 q^{8} +7.48352 q^{9} +O(q^{10})$	\(q-1.56268 q^{2} -3.23783 q^{3} +0.441960 q^{4} -3.23512 q^{5} +5.05968 q^{6} -1.00000 q^{7} +2.43471 q^{8} +7.48352 q^{9} +5.05544 q^{10} -2.06333 q^{11} -1.43099 q^{12} -1.53365 q^{13} +1.56268 q^{14} +10.4748 q^{15} -4.68859 q^{16} -3.75531 q^{17} -11.6943 q^{18} -0.618795 q^{19} -1.42979 q^{20} +3.23783 q^{21} +3.22432 q^{22} -4.39108 q^{23} -7.88318 q^{24} +5.46599 q^{25} +2.39660 q^{26} -14.5169 q^{27} -0.441960 q^{28} +2.01265 q^{29} -16.3687 q^{30} -1.00000 q^{31} +2.45733 q^{32} +6.68070 q^{33} +5.86834 q^{34} +3.23512 q^{35} +3.30742 q^{36} +1.00000 q^{37} +0.966977 q^{38} +4.96569 q^{39} -7.87659 q^{40} +2.30095 q^{41} -5.05968 q^{42} -0.429913 q^{43} -0.911908 q^{44} -24.2101 q^{45} +6.86183 q^{46} +10.5840 q^{47} +15.1808 q^{48} +1.00000 q^{49} -8.54157 q^{50} +12.1591 q^{51} -0.677811 q^{52} +4.24059 q^{53} +22.6852 q^{54} +6.67511 q^{55} -2.43471 q^{56} +2.00355 q^{57} -3.14513 q^{58} -2.02906 q^{59} +4.62942 q^{60} +8.21207 q^{61} +1.56268 q^{62} -7.48352 q^{63} +5.53718 q^{64} +4.96154 q^{65} -10.4398 q^{66} -5.32872 q^{67} -1.65970 q^{68} +14.2175 q^{69} -5.05544 q^{70} +11.1413 q^{71} +18.2202 q^{72} -16.6715 q^{73} -1.56268 q^{74} -17.6979 q^{75} -0.273482 q^{76} +2.06333 q^{77} -7.75977 q^{78} +6.63202 q^{79} +15.1681 q^{80} +24.5526 q^{81} -3.59564 q^{82} +8.11577 q^{83} +1.43099 q^{84} +12.1489 q^{85} +0.671815 q^{86} -6.51663 q^{87} -5.02362 q^{88} -15.6086 q^{89} +37.8325 q^{90} +1.53365 q^{91} -1.94068 q^{92} +3.23783 q^{93} -16.5393 q^{94} +2.00187 q^{95} -7.95639 q^{96} -16.1127 q^{97} -1.56268 q^{98} -15.4410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9}+O(q^{10}) $ 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9} + 4 q^{10} + 57 q^{11} + 21 q^{12} - 20 q^{13} - 6 q^{14} + 22 q^{15} + 88 q^{16} - 19 q^{17} + q^{18} + 23 q^{19} + 25 q^{20} - 8 q^{21} + 18 q^{22} + 34 q^{23} + 15 q^{24} + 81 q^{25} - 13 q^{26} + 20 q^{27} - 78 q^{28} + 16 q^{29} + 6 q^{30} - 71 q^{31} + 47 q^{32} - 16 q^{33} + 32 q^{34} + 125 q^{36} + 71 q^{37} + 13 q^{38} + 30 q^{39} + 31 q^{40} + 17 q^{41} - 5 q^{42} + 38 q^{43} + 80 q^{44} - q^{45} + 26 q^{46} + 32 q^{47} + 61 q^{48} + 71 q^{49} + 47 q^{50} + 73 q^{51} - 23 q^{52} + 31 q^{53} + 47 q^{54} + 11 q^{55} - 18 q^{56} + 17 q^{57} - 2 q^{58} + 97 q^{59} + 103 q^{60} - q^{61} - 6 q^{62} - 87 q^{63} + 100 q^{64} + 46 q^{65} + 43 q^{66} + 75 q^{67} - 43 q^{68} + 10 q^{69} - 4 q^{70} + 131 q^{71} - 11 q^{72} - 15 q^{73} + 6 q^{74} + 76 q^{75} + 41 q^{76} - 57 q^{77} + 89 q^{78} + 8 q^{79} + 10 q^{80} + 171 q^{81} + 14 q^{82} + 18 q^{83} - 21 q^{84} + 47 q^{85} + 90 q^{86} - 59 q^{87} + 13 q^{88} + 18 q^{89} + 69 q^{90} + 20 q^{91} + 110 q^{92} - 8 q^{93} + 39 q^{94} + 72 q^{95} + 100 q^{96} + 23 q^{97} + 6 q^{98} + 168 q^{99}+O(q^{100}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9 + 4 * q^10 + 57 * q^11 + 21 * q^12 - 20 * q^13 - 6 * q^14 + 22 * q^15 + 88 * q^16 - 19 * q^17 + q^18 + 23 * q^19 + 25 * q^20 - 8 * q^21 + 18 * q^22 + 34 * q^23 + 15 * q^24 + 81 * q^25 - 13 * q^26 + 20 * q^27 - 78 * q^28 + 16 * q^29 + 6 * q^30 - 71 * q^31 + 47 * q^32 - 16 * q^33 + 32 * q^34 + 125 * q^36 + 71 * q^37 + 13 * q^38 + 30 * q^39 + 31 * q^40 + 17 * q^41 - 5 * q^42 + 38 * q^43 + 80 * q^44 - q^45 + 26 * q^46 + 32 * q^47 + 61 * q^48 + 71 * q^49 + 47 * q^50 + 73 * q^51 - 23 * q^52 + 31 * q^53 + 47 * q^54 + 11 * q^55 - 18 * q^56 + 17 * q^57 - 2 * q^58 + 97 * q^59 + 103 * q^60 - q^61 - 6 * q^62 - 87 * q^63 + 100 * q^64 + 46 * q^65 + 43 * q^66 + 75 * q^67 - 43 * q^68 + 10 * q^69 - 4 * q^70 + 131 * q^71 - 11 * q^72 - 15 * q^73 + 6 * q^74 + 76 * q^75 + 41 * q^76 - 57 * q^77 + 89 * q^78 + 8 * q^79 + 10 * q^80 + 171 * q^81 + 14 * q^82 + 18 * q^83 - 21 * q^84 + 47 * q^85 + 90 * q^86 - 59 * q^87 + 13 * q^88 + 18 * q^89 + 69 * q^90 + 20 * q^91 + 110 * q^92 - 8 * q^93 + 39 * q^94 + 72 * q^95 + 100 * q^96 + 23 * q^97 + 6 * q^98 + 168 * 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 $

$2$	−1.56268	−1.10498	−0.552490	−	0.833520i	$-0.686322\pi$
$2$	−1.56268	−1.10498	−0.552490	+	0.833520i	$0.686322\pi$
$3$	−3.23783	−1.86936	−0.934680	−	0.355490i	$-0.884314\pi$
$3$	−3.23783	−1.86936	−0.934680	+	0.355490i	$0.884314\pi$
$4$	0.441960	0.220980
$5$	−3.23512	−1.44679	−0.723394	−	0.690435i	$-0.757419\pi$
$5$	−3.23512	−1.44679	−0.723394	+	0.690435i	$0.757419\pi$
$6$	5.05968	2.06560
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.43471	0.860801
$9$	7.48352	2.49451
$10$	5.05544	1.59867
$11$	−2.06333	−0.622117	−0.311059	−	0.950391i	$-0.600684\pi$
$11$	−2.06333	−0.622117	−0.311059	+	0.950391i	$0.600684\pi$
$12$	−1.43099	−0.413091
$13$	−1.53365	−0.425358	−0.212679	−	0.977122i	$-0.568219\pi$
$13$	−1.53365	−0.425358	−0.212679	+	0.977122i	$0.568219\pi$
$14$	1.56268	0.417643
$15$	10.4748	2.70457
$16$	−4.68859	−1.17215
$17$	−3.75531	−0.910797	−0.455399	−	0.890288i	$-0.650503\pi$
$17$	−3.75531	−0.910797	−0.455399	+	0.890288i	$0.650503\pi$
$18$	−11.6943	−2.75638
$19$	−0.618795	−0.141961	−0.0709806	−	0.997478i	$-0.522613\pi$
$19$	−0.618795	−0.141961	−0.0709806	+	0.997478i	$0.522613\pi$
$20$	−1.42979	−0.319711
$21$	3.23783	0.706552
$22$	3.22432	0.687427
$23$	−4.39108	−0.915603	−0.457801	−	0.889054i	$-0.651363\pi$
$23$	−4.39108	−0.915603	−0.457801	+	0.889054i	$0.651363\pi$
$24$	−7.88318	−1.60915
$25$	5.46599	1.09320
$26$	2.39660	0.470012
$27$	−14.5169	−2.79377
$28$	−0.441960	−0.0835225
$29$	2.01265	0.373741	0.186870	−	0.982385i	$-0.440166\pi$
$29$	2.01265	0.373741	0.186870	+	0.982385i	$0.440166\pi$
$30$	−16.3687	−2.98849
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	2.45733	0.434398
$33$	6.68070	1.16296
$34$	5.86834	1.00641
$35$	3.23512	0.546835
$36$	3.30742	0.551236
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	0.966977	0.156864
$39$	4.96569	0.795147
$40$	−7.87659	−1.24540
$41$	2.30095	0.359348	0.179674	−	0.983726i	$-0.442496\pi$
$41$	2.30095	0.359348	0.179674	+	0.983726i	$0.442496\pi$
$42$	−5.05968	−0.780725
$43$	−0.429913	−0.0655611	−0.0327806	−	0.999463i	$-0.510436\pi$
$43$	−0.429913	−0.0655611	−0.0327806	+	0.999463i	$0.510436\pi$
$44$	−0.911908	−0.137475
$45$	−24.2101	−3.60903
$46$	6.86183	1.01172
$47$	10.5840	1.54383	0.771915	−	0.635726i	$-0.219299\pi$
$47$	10.5840	1.54383	0.771915	+	0.635726i	$0.219299\pi$
$48$	15.1808	2.19117
$49$	1.00000	0.142857
$50$	−8.54157	−1.20796
$51$	12.1591	1.70261
$52$	−0.677811	−0.0939955
$53$	4.24059	0.582489	0.291245	−	0.956649i	$-0.405931\pi$
$53$	4.24059	0.582489	0.291245	+	0.956649i	$0.405931\pi$
$54$	22.6852	3.08706
$55$	6.67511	0.900072
$56$	−2.43471	−0.325352
$57$	2.00355	0.265377
$58$	−3.14513	−0.412976
$59$	−2.02906	−0.264161	−0.132080	−	0.991239i	$-0.542166\pi$
$59$	−2.02906	−0.264161	−0.132080	+	0.991239i	$0.542166\pi$
$60$	4.62942	0.597655
$61$	8.21207	1.05145	0.525724	−	0.850655i	$-0.323794\pi$
$61$	8.21207	1.05145	0.525724	+	0.850655i	$0.323794\pi$
$62$	1.56268	0.198460
$63$	−7.48352	−0.942835
$64$	5.53718	0.692147
$65$	4.96154	0.615403
$66$	−10.4398	−1.28505
$67$	−5.32872	−0.651007	−0.325504	−	0.945541i	$-0.605534\pi$
$67$	−5.32872	−0.651007	−0.325504	+	0.945541i	$0.605534\pi$
$68$	−1.65970	−0.201268
$69$	14.2175	1.71159
$70$	−5.05544	−0.604241
$71$	11.1413	1.32223	0.661113	−	0.750287i	$-0.270084\pi$
$71$	11.1413	1.32223	0.661113	+	0.750287i	$0.270084\pi$
$72$	18.2202	2.14728
$73$	−16.6715	−1.95125	−0.975625	−	0.219446i	$-0.929575\pi$
$73$	−16.6715	−1.95125	−0.975625	+	0.219446i	$0.929575\pi$
$74$	−1.56268	−0.181658
$75$	−17.6979	−2.04358
$76$	−0.273482	−0.0313706
$77$	2.06333	0.235138
$78$	−7.75977	−0.878621
$79$	6.63202	0.746160	0.373080	−	0.927799i	$-0.378302\pi$
$79$	6.63202	0.746160	0.373080	+	0.927799i	$0.378302\pi$
$80$	15.1681	1.69585
$81$	24.5526	2.72806
$82$	−3.59564	−0.397072
$83$	8.11577	0.890821	0.445411	−	0.895326i	$-0.353058\pi$
$83$	8.11577	0.890821	0.445411	+	0.895326i	$0.353058\pi$
$84$	1.43099	0.156134
$85$	12.1489	1.31773
$86$	0.671815	0.0724437
$87$	−6.51663	−0.698656
$88$	−5.02362	−0.535519
$89$	−15.6086	−1.65451	−0.827257	−	0.561824i	$-0.810100\pi$
$89$	−15.6086	−1.65451	−0.827257	+	0.561824i	$0.810100\pi$
$90$	37.8325	3.98790
$91$	1.53365	0.160770
$92$	−1.94068	−0.202330
$93$	3.23783	0.335747
$94$	−16.5393	−1.70590
$95$	2.00187	0.205388
$96$	−7.95639	−0.812046
$97$	−16.1127	−1.63599	−0.817997	−	0.575223i	$-0.804915\pi$
$97$	−16.1127	−1.63599	−0.817997	+	0.575223i	$0.804915\pi$
$98$	−1.56268	−0.157854
$99$	−15.4410	−1.55188
$100$	2.41575	0.241575
$101$	−13.9008	−1.38318	−0.691589	−	0.722291i	$-0.743089\pi$
$101$	−13.9008	−1.38318	−0.691589	+	0.722291i	$0.743089\pi$
$102$	−19.0007	−1.88135
$103$	−10.4548	−1.03014	−0.515071	−	0.857148i	$-0.672234\pi$
$103$	−10.4548	−1.03014	−0.515071	+	0.857148i	$0.672234\pi$
$104$	−3.73400	−0.366149
$105$	−10.4748	−1.02223
$106$	−6.62667	−0.643639
$107$	15.1670	1.46625	0.733124	−	0.680095i	$-0.238061\pi$
$107$	15.1670	1.46625	0.733124	+	0.680095i	$0.238061\pi$
$108$	−6.41587	−0.617368
$109$	10.6178	1.01700	0.508501	−	0.861061i	$-0.330200\pi$
$109$	10.6178	1.01700	0.508501	+	0.861061i	$0.330200\pi$
$110$	−10.4310	−0.994561
$111$	−3.23783	−0.307321
$112$	4.68859	0.443030
$113$	−2.11859	−0.199300	−0.0996500	−	0.995023i	$-0.531772\pi$
$113$	−2.11859	−0.199300	−0.0996500	+	0.995023i	$0.531772\pi$
$114$	−3.13090	−0.293236
$115$	14.2057	1.32468
$116$	0.889512	0.0825891
$117$	−11.4771	−1.06106
$118$	3.17076	0.291892
$119$	3.75531	0.344249
$120$	25.5030	2.32810
$121$	−6.74267	−0.612970
$122$	−12.8328	−1.16183
$123$	−7.45007	−0.671750
$124$	−0.441960	−0.0396891
$125$	−1.50753	−0.134837
$126$	11.6943	1.04181
$127$	−20.2532	−1.79718	−0.898592	−	0.438786i	$-0.855409\pi$
$127$	−20.2532	−1.79718	−0.898592	+	0.438786i	$0.855409\pi$
$128$	−13.5675	−1.19921
$129$	1.39198	0.122557
$130$	−7.75328	−0.680008
$131$	−2.90702	−0.253988	−0.126994	−	0.991904i	$-0.540533\pi$
$131$	−2.90702	−0.253988	−0.126994	+	0.991904i	$0.540533\pi$
$132$	2.95260	0.256991
$133$	0.618795	0.0536563
$134$	8.32707	0.719350
$135$	46.9638	4.04200
$136$	−9.14311	−0.784015
$137$	−12.9941	−1.11016	−0.555080	−	0.831797i	$-0.687312\pi$
$137$	−12.9941	−1.11016	−0.555080	+	0.831797i	$0.687312\pi$
$138$	−22.2174	−1.89127
$139$	0.428721	0.0363636	0.0181818	−	0.999835i	$-0.494212\pi$
$139$	0.428721	0.0363636	0.0181818	+	0.999835i	$0.494212\pi$
$140$	1.42979	0.120839
$141$	−34.2690	−2.88597
$142$	−17.4102	−1.46103
$143$	3.16442	0.264622
$144$	−35.0872	−2.92393
$145$	−6.51117	−0.540724
$146$	26.0521	2.15609
$147$	−3.23783	−0.267051
$148$	0.441960	0.0363289
$149$	−4.54847	−0.372625	−0.186313	−	0.982491i	$-0.559654\pi$
$149$	−4.54847	−0.372625	−0.186313	+	0.982491i	$0.559654\pi$
$150$	27.6561	2.25811
$151$	−7.51673	−0.611703	−0.305852	−	0.952079i	$-0.598941\pi$
$151$	−7.51673	−0.611703	−0.305852	+	0.952079i	$0.598941\pi$
$152$	−1.50659	−0.122200
$153$	−28.1030	−2.27199
$154$	−3.22432	−0.259823
$155$	3.23512	0.259851
$156$	2.19463	0.175711
$157$	14.7458	1.17684	0.588420	−	0.808555i	$-0.299750\pi$
$157$	14.7458	1.17684	0.588420	+	0.808555i	$0.299750\pi$
$158$	−10.3637	−0.824492
$159$	−13.7303	−1.08888
$160$	−7.94974	−0.628482
$161$	4.39108	0.346065
$162$	−38.3677	−3.01445
$163$	2.68607	0.210389	0.105195	−	0.994452i	$-0.466453\pi$
$163$	2.68607	0.210389	0.105195	+	0.994452i	$0.466453\pi$
$164$	1.01693	0.0794086
$165$	−21.6129	−1.68256
$166$	−12.6823	−0.984339
$167$	−6.13562	−0.474788	−0.237394	−	0.971413i	$-0.576293\pi$
$167$	−6.13562	−0.474788	−0.237394	+	0.971413i	$0.576293\pi$
$168$	7.88318	0.608201
$169$	−10.6479	−0.819071
$170$	−18.9848	−1.45607
$171$	−4.63077	−0.354124
$172$	−0.190004	−0.0144877
$173$	12.4154	0.943926	0.471963	−	0.881618i	$-0.343546\pi$
$173$	12.4154	0.943926	0.471963	+	0.881618i	$0.343546\pi$
$174$	10.1834	0.772000
$175$	−5.46599	−0.413190
$176$	9.67411	0.729213
$177$	6.56973	0.493811
$178$	24.3913	1.82820
$179$	5.46829	0.408719	0.204359	−	0.978896i	$-0.434489\pi$
$179$	5.46829	0.408719	0.204359	+	0.978896i	$0.434489\pi$
$180$	−10.6999	−0.797522
$181$	−7.85578	−0.583916	−0.291958	−	0.956431i	$-0.594307\pi$
$181$	−7.85578	−0.583916	−0.291958	+	0.956431i	$0.594307\pi$
$182$	−2.39660	−0.177648
$183$	−26.5893	−1.96554
$184$	−10.6910	−0.788152
$185$	−3.23512	−0.237851
$186$	−5.05968	−0.370994
$187$	7.74845	0.566623
$188$	4.67768	0.341155
$189$	14.5169	1.05595
$190$	−3.12828	−0.226950
$191$	−11.9810	−0.866915	−0.433457	−	0.901174i	$-0.642707\pi$
$191$	−11.9810	−0.866915	−0.433457	+	0.901174i	$0.642707\pi$
$192$	−17.9284	−1.29387
$193$	−13.3914	−0.963934	−0.481967	−	0.876189i	$-0.660077\pi$
$193$	−13.3914	−0.963934	−0.481967	+	0.876189i	$0.660077\pi$
$194$	25.1789	1.80774
$195$	−16.0646	−1.15041
$196$	0.441960	0.0315685
$197$	−4.37104	−0.311424	−0.155712	−	0.987803i	$-0.549767\pi$
$197$	−4.37104	−0.311424	−0.155712	+	0.987803i	$0.549767\pi$
$198$	24.1293	1.71479
$199$	−17.2269	−1.22119	−0.610593	−	0.791945i	$-0.709069\pi$
$199$	−17.2269	−1.22119	−0.610593	+	0.791945i	$0.709069\pi$
$200$	13.3081	0.941026
$201$	17.2535	1.21697
$202$	21.7224	1.52838
$203$	−2.01265	−0.141261
$204$	5.37381	0.376242
$205$	−7.44384	−0.519900
$206$	16.3375	1.13829
$207$	−32.8607	−2.28398
$208$	7.19065	0.498582
$209$	1.27678	0.0883166
$210$	16.3687	1.12954
$211$	16.8169	1.15772	0.578862	−	0.815426i	$-0.303497\pi$
$211$	16.8169	1.15772	0.578862	+	0.815426i	$0.303497\pi$
$212$	1.87417	0.128718
$213$	−36.0735	−2.47172
$214$	−23.7011	−1.62017
$215$	1.39082	0.0948531
$216$	−35.3444	−2.40488
$217$	1.00000	0.0678844
$218$	−16.5922	−1.12377
$219$	53.9794	3.64759
$220$	2.95013	0.198898
$221$	5.75933	0.387415
$222$	5.05968	0.339583
$223$	−8.92446	−0.597626	−0.298813	−	0.954312i	$-0.596591\pi$
$223$	−8.92446	−0.597626	−0.298813	+	0.954312i	$0.596591\pi$
$224$	−2.45733	−0.164187
$225$	40.9049	2.72699
$226$	3.31067	0.220222
$227$	−7.10267	−0.471421	−0.235711	−	0.971823i	$-0.575742\pi$
$227$	−7.10267	−0.471421	−0.235711	+	0.971823i	$0.575742\pi$
$228$	0.885488	0.0586429
$229$	−24.3431	−1.60864	−0.804320	−	0.594196i	$-0.797470\pi$
$229$	−24.3431	−1.60864	−0.804320	+	0.594196i	$0.797470\pi$
$230$	−22.1988	−1.46375
$231$	−6.68070	−0.439558
$232$	4.90024	0.321716
$233$	−8.79617	−0.576256	−0.288128	−	0.957592i	$-0.593033\pi$
$233$	−8.79617	−0.576256	−0.288128	+	0.957592i	$0.593033\pi$
$234$	17.9350	1.17245
$235$	−34.2404	−2.23360
$236$	−0.896761	−0.0583742
$237$	−21.4733	−1.39484
$238$	−5.86834	−0.380388
$239$	1.03544	0.0669771	0.0334886	−	0.999439i	$-0.489338\pi$
$239$	1.03544	0.0669771	0.0334886	+	0.999439i	$0.489338\pi$
$240$	−49.1118	−3.17015
$241$	2.19865	0.141627	0.0708137	−	0.997490i	$-0.477440\pi$
$241$	2.19865	0.141627	0.0708137	+	0.997490i	$0.477440\pi$
$242$	10.5366	0.677319
$243$	−35.9463	−2.30596
$244$	3.62940	0.232349
$245$	−3.23512	−0.206684
$246$	11.6421	0.742270
$247$	0.949014	0.0603843
$248$	−2.43471	−0.154604
$249$	−26.2774	−1.66527
$250$	2.35578	0.148992
$251$	3.11415	0.196564	0.0982818	−	0.995159i	$-0.468665\pi$
$251$	3.11415	0.196564	0.0982818	+	0.995159i	$0.468665\pi$
$252$	−3.30742	−0.208348
$253$	9.06024	0.569612
$254$	31.6493	1.98585
$255$	−39.3360	−2.46331
$256$	10.1272	0.632951
$257$	−25.7010	−1.60319	−0.801593	−	0.597871i	$-0.796014\pi$
$257$	−25.7010	−1.60319	−0.801593	+	0.597871i	$0.796014\pi$
$258$	−2.17522	−0.135423
$259$	−1.00000	−0.0621370
$260$	2.19280	0.135992
$261$	15.0617	0.932299
$262$	4.54274	0.280651
$263$	12.1970	0.752101	0.376050	−	0.926599i	$-0.377282\pi$
$263$	12.1970	0.752101	0.376050	+	0.926599i	$0.377282\pi$
$264$	16.2656	1.00108
$265$	−13.7188	−0.842739
$266$	−0.966977	−0.0592891
$267$	50.5381	3.09288
$268$	−2.35508	−0.143859
$269$	11.3732	0.693438	0.346719	−	0.937969i	$-0.387296\pi$
$269$	11.3732	0.693438	0.346719	+	0.937969i	$0.387296\pi$
$270$	−73.3893	−4.46633
$271$	17.4858	1.06219	0.531095	−	0.847312i	$-0.321781\pi$
$271$	17.4858	1.06219	0.531095	+	0.847312i	$0.321781\pi$
$272$	17.6071	1.06759
$273$	−4.96569	−0.300537
$274$	20.3055	1.22670
$275$	−11.2781	−0.680097
$276$	6.28358	0.378227
$277$	−23.1538	−1.39118	−0.695588	−	0.718441i	$-0.744856\pi$
$277$	−23.1538	−1.39118	−0.695588	+	0.718441i	$0.744856\pi$
$278$	−0.669952	−0.0401811
$279$	−7.48352	−0.448027
$280$	7.87659	0.470716
$281$	−4.75059	−0.283397	−0.141698	−	0.989910i	$-0.545256\pi$
$281$	−4.75059	−0.283397	−0.141698	+	0.989910i	$0.545256\pi$
$282$	53.5515	3.18894
$283$	−11.2187	−0.666885	−0.333443	−	0.942770i	$-0.608210\pi$
$283$	−11.2187	−0.666885	−0.333443	+	0.942770i	$0.608210\pi$
$284$	4.92399	0.292185
$285$	−6.48172	−0.383944
$286$	−4.94497	−0.292402
$287$	−2.30095	−0.135821
$288$	18.3895	1.08361
$289$	−2.89763	−0.170449
$290$	10.1749	0.597489
$291$	52.1700	3.05826
$292$	−7.36812	−0.431187
$293$	−7.78900	−0.455038	−0.227519	−	0.973774i	$-0.573061\pi$
$293$	−7.78900	−0.455038	−0.227519	+	0.973774i	$0.573061\pi$
$294$	5.05968	0.295086
$295$	6.56424	0.382185
$296$	2.43471	0.141515
$297$	29.9531	1.73806
$298$	7.10779	0.411743
$299$	6.73437	0.389459
$300$	−7.82177	−0.451590
$301$	0.429913	0.0247798
$302$	11.7462	0.675920
$303$	45.0083	2.58566
$304$	2.90128	0.166400
$305$	−26.5670	−1.52122
$306$	43.9159	2.51050
$307$	−0.469566	−0.0267995	−0.0133998	−	0.999910i	$-0.504265\pi$
$307$	−0.469566	−0.0267995	−0.0133998	+	0.999910i	$0.504265\pi$
$308$	0.911908	0.0519608
$309$	33.8508	1.92571
$310$	−5.05544	−0.287130
$311$	−14.1946	−0.804903	−0.402451	−	0.915441i	$-0.631842\pi$
$311$	−14.1946	−0.804903	−0.402451	+	0.915441i	$0.631842\pi$
$312$	12.0900	0.684464
$313$	20.8437	1.17816	0.589078	−	0.808076i	$-0.299491\pi$
$313$	20.8437	1.17816	0.589078	+	0.808076i	$0.299491\pi$
$314$	−23.0429	−1.30038
$315$	24.2101	1.36408
$316$	2.93108	0.164886
$317$	1.39761	0.0784978	0.0392489	−	0.999229i	$-0.487503\pi$
$317$	1.39761	0.0784978	0.0392489	+	0.999229i	$0.487503\pi$
$318$	21.4560	1.20319
$319$	−4.15277	−0.232510
$320$	−17.9134	−1.00139
$321$	−49.1081	−2.74095
$322$	−6.86183	−0.382395
$323$	2.32377	0.129298
$324$	10.8512	0.602847
$325$	−8.38291	−0.465000
$326$	−4.19746	−0.232476
$327$	−34.3787	−1.90114
$328$	5.60215	0.309327
$329$	−10.5840	−0.583513
$330$	33.7739	1.85919
$331$	−17.7201	−0.973988	−0.486994	−	0.873405i	$-0.661907\pi$
$331$	−17.7201	−0.973988	−0.486994	+	0.873405i	$0.661907\pi$
$332$	3.58684	0.196853
$333$	7.48352	0.410095
$334$	9.58799	0.524631
$335$	17.2391	0.941870
$336$	−15.1808	−0.828183
$337$	3.79674	0.206822	0.103411	−	0.994639i	$-0.467024\pi$
$337$	3.79674	0.206822	0.103411	+	0.994639i	$0.467024\pi$
$338$	16.6393	0.905056
$339$	6.85962	0.372563
$340$	5.36931	0.291192
$341$	2.06333	0.111736
$342$	7.23639	0.391299
$343$	−1.00000	−0.0539949
$344$	−1.04672	−0.0564351
$345$	−45.9954	−2.47631
$346$	−19.4013	−1.04302
$347$	−5.03273	−0.270171	−0.135085	−	0.990834i	$-0.543131\pi$
$347$	−5.03273	−0.270171	−0.135085	+	0.990834i	$0.543131\pi$
$348$	−2.88009	−0.154389
$349$	14.3031	0.765627	0.382813	−	0.923826i	$-0.374955\pi$
$349$	14.3031	0.765627	0.382813	+	0.923826i	$0.374955\pi$
$350$	8.54157	0.456566
$351$	22.2638	1.18835
$352$	−5.07027	−0.270246
$353$	−5.03351	−0.267907	−0.133953	−	0.990988i	$-0.542767\pi$
$353$	−5.03351	−0.267907	−0.133953	+	0.990988i	$0.542767\pi$
$354$	−10.2664	−0.545651
$355$	−36.0433	−1.91298
$356$	−6.89839	−0.365614
$357$	−12.1591	−0.643525
$358$	−8.54516	−0.451626
$359$	37.3430	1.97089	0.985444	−	0.170001i	$-0.0543770\pi$
$359$	37.3430	1.97089	0.985444	+	0.170001i	$0.0543770\pi$
$360$	−58.9446	−3.10665
$361$	−18.6171	−0.979847
$362$	12.2761	0.645215
$363$	21.8316	1.14586
$364$	0.677811	0.0355270
$365$	53.9342	2.82305
$366$	41.5504	2.17188
$367$	−33.9137	−1.77028	−0.885141	−	0.465323i	$-0.845938\pi$
$367$	−33.9137	−1.77028	−0.885141	+	0.465323i	$0.845938\pi$
$368$	20.5880	1.07322
$369$	17.2192	0.896396
$370$	5.05544	0.262820
$371$	−4.24059	−0.220160
$372$	1.43099	0.0741933
$373$	4.05306	0.209859	0.104930	−	0.994480i	$-0.466538\pi$
$373$	4.05306	0.209859	0.104930	+	0.994480i	$0.466538\pi$
$374$	−12.1083	−0.626106
$375$	4.88111	0.252059
$376$	25.7689	1.32893
$377$	−3.08671	−0.158973
$378$	−22.6852	−1.16680
$379$	5.63496	0.289448	0.144724	−	0.989472i	$-0.453771\pi$
$379$	5.63496	0.289448	0.144724	+	0.989472i	$0.453771\pi$
$380$	0.884748	0.0453866
$381$	65.5765	3.35958
$382$	18.7224	0.957923
$383$	−5.86651	−0.299765	−0.149882	−	0.988704i	$-0.547890\pi$
$383$	−5.86651	−0.299765	−0.149882	+	0.988704i	$0.547890\pi$
$384$	43.9291	2.24175
$385$	−6.67511	−0.340195
$386$	20.9264	1.06513
$387$	−3.21726	−0.163543
$388$	−7.12115	−0.361522
$389$	8.50969	0.431459	0.215729	−	0.976453i	$-0.430787\pi$
$389$	8.50969	0.431459	0.215729	+	0.976453i	$0.430787\pi$
$390$	25.1038	1.27118
$391$	16.4899	0.833928
$392$	2.43471	0.122972
$393$	9.41243	0.474794
$394$	6.83052	0.344117
$395$	−21.4554	−1.07954
$396$	−6.82429	−0.342933
$397$	−16.4934	−0.827779	−0.413890	−	0.910327i	$-0.635830\pi$
$397$	−16.4934	−0.827779	−0.413890	+	0.910327i	$0.635830\pi$
$398$	26.9201	1.34938
$399$	−2.00355	−0.100303
$400$	−25.6278	−1.28139
$401$	−21.0265	−1.05001	−0.525006	−	0.851099i	$-0.675937\pi$
$401$	−21.0265	−1.05001	−0.525006	+	0.851099i	$0.675937\pi$
$402$	−26.9616	−1.34472
$403$	1.53365	0.0763965
$404$	−6.14358	−0.305655
$405$	−79.4304	−3.94693
$406$	3.14513	0.156090
$407$	−2.06333	−0.102275
$408$	29.6038	1.46561
$409$	−30.1507	−1.49085	−0.745427	−	0.666587i	$-0.767755\pi$
$409$	−30.1507	−1.49085	−0.745427	+	0.666587i	$0.767755\pi$
$410$	11.6323	0.574479
$411$	42.0726	2.07529
$412$	−4.62060	−0.227641
$413$	2.02906	0.0998433
$414$	51.3507	2.52375
$415$	−26.2555	−1.28883
$416$	−3.76868	−0.184775
$417$	−1.38812	−0.0679767
$418$	−1.99519	−0.0975880
$419$	14.2576	0.696528	0.348264	−	0.937397i	$-0.386771\pi$
$419$	14.2576	0.696528	0.348264	+	0.937397i	$0.386771\pi$
$420$	−4.62942	−0.225892
$421$	−15.7699	−0.768579	−0.384289	−	0.923213i	$-0.625553\pi$
$421$	−15.7699	−0.768579	−0.384289	+	0.923213i	$0.625553\pi$
$422$	−26.2794	−1.27926
$423$	79.2054	3.85110
$424$	10.3246	0.501408
$425$	−20.5265	−0.995681
$426$	56.3712	2.73120
$427$	−8.21207	−0.397410
$428$	6.70320	0.324011
$429$	−10.2459	−0.494675
$430$	−2.17340	−0.104811
$431$	20.5869	0.991636	0.495818	−	0.868426i	$-0.334868\pi$
$431$	20.5869	0.991636	0.495818	+	0.868426i	$0.334868\pi$
$432$	68.0637	3.27472
$433$	−4.83000	−0.232115	−0.116057	−	0.993242i	$-0.537026\pi$
$433$	−4.83000	−0.232115	−0.116057	+	0.993242i	$0.537026\pi$
$434$	−1.56268	−0.0750109
$435$	21.0821	1.01081
$436$	4.69265	0.224737
$437$	2.71718	0.129980
$438$	−84.3523	−4.03051
$439$	34.8044	1.66112	0.830562	−	0.556926i	$-0.188019\pi$
$439$	34.8044	1.66112	0.830562	+	0.556926i	$0.188019\pi$
$440$	16.2520	0.774783
$441$	7.48352	0.356358
$442$	−8.99998	−0.428085
$443$	−28.1866	−1.33919	−0.669593	−	0.742728i	$-0.733532\pi$
$443$	−28.1866	−1.33919	−0.669593	+	0.742728i	$0.733532\pi$
$444$	−1.43099	−0.0679117
$445$	50.4958	2.39373
$446$	13.9461	0.660365
$447$	14.7272	0.696571
$448$	−5.53718	−0.261607
$449$	8.47254	0.399844	0.199922	−	0.979812i	$-0.435931\pi$
$449$	8.47254	0.399844	0.199922	+	0.979812i	$0.435931\pi$
$450$	−63.9211	−3.01327
$451$	−4.74761	−0.223556
$452$	−0.936330	−0.0440413
$453$	24.3379	1.14349
$454$	11.0992	0.520911
$455$	−4.96154	−0.232600
$456$	4.87807	0.228437
$457$	27.0219	1.26403	0.632017	−	0.774955i	$-0.282227\pi$
$457$	27.0219	1.26403	0.632017	+	0.774955i	$0.282227\pi$
$458$	38.0405	1.77751
$459$	54.5154	2.54456
$460$	6.27832	0.292728
$461$	2.44687	0.113962	0.0569811	−	0.998375i	$-0.481853\pi$
$461$	2.44687	0.113962	0.0569811	+	0.998375i	$0.481853\pi$
$462$	10.4398	0.485703
$463$	5.66907	0.263464	0.131732	−	0.991285i	$-0.457946\pi$
$463$	5.66907	0.263464	0.131732	+	0.991285i	$0.457946\pi$
$464$	−9.43651	−0.438079
$465$	−10.4748	−0.485755
$466$	13.7456	0.636751
$467$	−32.7565	−1.51579	−0.757896	−	0.652375i	$-0.773773\pi$
$467$	−32.7565	−1.51579	−0.757896	+	0.652375i	$0.773773\pi$
$468$	−5.07242	−0.234472
$469$	5.32872	0.246058
$470$	53.5066	2.46808
$471$	−47.7442	−2.19994
$472$	−4.94017	−0.227390
$473$	0.887052	0.0407867
$474$	33.5559	1.54127
$475$	−3.38233	−0.155192
$476$	1.65970	0.0760721
$477$	31.7345	1.45302
$478$	−1.61806	−0.0740083
$479$	−22.5983	−1.03254	−0.516272	−	0.856425i	$-0.672681\pi$
$479$	−22.5983	−1.03254	−0.516272	+	0.856425i	$0.672681\pi$
$480$	25.7399	1.17486
$481$	−1.53365	−0.0699284
$482$	−3.43578	−0.156495
$483$	−14.2175	−0.646921
$484$	−2.97999	−0.135454
$485$	52.1264	2.36694
$486$	56.1725	2.54804
$487$	10.2544	0.464673	0.232336	−	0.972635i	$-0.425363\pi$
$487$	10.2544	0.464673	0.232336	+	0.972635i	$0.425363\pi$
$488$	19.9941	0.905088
$489$	−8.69703	−0.393293
$490$	5.05544	0.228382
$491$	−15.9581	−0.720180	−0.360090	−	0.932918i	$-0.617254\pi$
$491$	−15.9581	−0.720180	−0.360090	+	0.932918i	$0.617254\pi$
$492$	−3.29263	−0.148443
$493$	−7.55815	−0.340402
$494$	−1.48300	−0.0667235
$495$	49.9534	2.24524
$496$	4.68859	0.210524
$497$	−11.1413	−0.499754
$498$	41.0632	1.84008
$499$	−20.4260	−0.914394	−0.457197	−	0.889365i	$-0.651147\pi$
$499$	−20.4260	−0.914394	−0.457197	+	0.889365i	$0.651147\pi$
$500$	−0.666265	−0.0297963
$501$	19.8661	0.887551
$502$	−4.86641	−0.217199
$503$	−38.2514	−1.70555	−0.852773	−	0.522282i	$-0.825081\pi$
$503$	−38.2514	−1.70555	−0.852773	+	0.522282i	$0.825081\pi$
$504$	−18.2202	−0.811594
$505$	44.9707	2.00117
$506$	−14.1582	−0.629410
$507$	34.4761	1.53114
$508$	−8.95111	−0.397141
$509$	4.17215	0.184927	0.0924637	−	0.995716i	$-0.470526\pi$
$509$	4.17215	0.184927	0.0924637	+	0.995716i	$0.470526\pi$
$510$	61.4694	2.72191
$511$	16.6715	0.737503
$512$	11.3094	0.499808
$513$	8.98297	0.396608
$514$	40.1624	1.77149
$515$	33.8225	1.49040
$516$	0.615201	0.0270827
$517$	−21.8382	−0.960443
$518$	1.56268	0.0686601
$519$	−40.1989	−1.76454
$520$	12.0799	0.529740
$521$	16.1162	0.706066	0.353033	−	0.935611i	$-0.385150\pi$
$521$	16.1162	0.706066	0.353033	+	0.935611i	$0.385150\pi$
$522$	−23.5366	−1.03017
$523$	−31.7752	−1.38943	−0.694716	−	0.719285i	$-0.744470\pi$
$523$	−31.7752	−1.38943	−0.694716	+	0.719285i	$0.744470\pi$
$524$	−1.28479	−0.0561261
$525$	17.6979	0.772401
$526$	−19.0600	−0.831056
$527$	3.75531	0.163584
$528$	−31.3231	−1.36316
$529$	−3.71845	−0.161672
$530$	21.4380	0.931209
$531$	−15.1845	−0.658951
$532$	0.273482	0.0118570
$533$	−3.52885	−0.152851
$534$	−78.9747	−3.41757
$535$	−49.0670	−2.12135
$536$	−12.9739	−0.560388
$537$	−17.7054	−0.764043
$538$	−17.7727	−0.766235
$539$	−2.06333	−0.0888739
$540$	20.7561	0.893200
$541$	19.3517	0.831995	0.415997	−	0.909366i	$-0.363433\pi$
$541$	19.3517	0.831995	0.415997	+	0.909366i	$0.363433\pi$
$542$	−27.3247	−1.17370
$543$	25.4357	1.09155
$544$	−9.22802	−0.395648
$545$	−34.3499	−1.47139
$546$	7.75977	0.332088
$547$	−10.4263	−0.445797	−0.222899	−	0.974842i	$-0.571552\pi$
$547$	−10.4263	−0.445797	−0.222899	+	0.974842i	$0.571552\pi$
$548$	−5.74286	−0.245323
$549$	61.4553	2.62285
$550$	17.6241	0.751493
$551$	−1.24542	−0.0530567
$552$	34.6157	1.47334
$553$	−6.63202	−0.282022
$554$	36.1819	1.53722
$555$	10.4748	0.444628
$556$	0.189477	0.00803563
$557$	−32.0117	−1.35638	−0.678190	−	0.734886i	$-0.737236\pi$
$557$	−32.0117	−1.35638	−0.678190	+	0.734886i	$0.737236\pi$
$558$	11.6943	0.495061
$559$	0.659336	0.0278869
$560$	−15.1681	−0.640971
$561$	−25.0881	−1.05922
$562$	7.42364	0.313148
$563$	20.2238	0.852334	0.426167	−	0.904645i	$-0.359864\pi$
$563$	20.2238	0.852334	0.426167	+	0.904645i	$0.359864\pi$
$564$	−15.1455	−0.637742
$565$	6.85388	0.288345
$566$	17.5313	0.736895
$567$	−24.5526	−1.03111
$568$	27.1258	1.13817
$569$	−0.337041	−0.0141295	−0.00706476	−	0.999975i	$-0.502249\pi$
$569$	−0.337041	−0.0141295	−0.00706476	+	0.999975i	$0.502249\pi$
$570$	10.1288	0.424250
$571$	−7.57659	−0.317071	−0.158535	−	0.987353i	$-0.550677\pi$
$571$	−7.57659	−0.317071	−0.158535	+	0.987353i	$0.550677\pi$
$572$	1.39855	0.0584762
$573$	38.7924	1.62058
$574$	3.59564	0.150079
$575$	−24.0016	−1.00093
$576$	41.4376	1.72657
$577$	−23.3873	−0.973626	−0.486813	−	0.873506i	$-0.661841\pi$
$577$	−23.3873	−0.973626	−0.486813	+	0.873506i	$0.661841\pi$
$578$	4.52806	0.188342
$579$	43.3590	1.80194
$580$	−2.87768	−0.119489
$581$	−8.11577	−0.336699
$582$	−81.5249	−3.37932
$583$	−8.74973	−0.362377
$584$	−40.5903	−1.67964
$585$	37.1298	1.53513
$586$	12.1717	0.502808
$587$	38.8374	1.60299	0.801496	−	0.598001i	$-0.204038\pi$
$587$	38.8374	1.60299	0.801496	+	0.598001i	$0.204038\pi$
$588$	−1.43099	−0.0590130
$589$	0.618795	0.0254970
$590$	−10.2578	−0.422306
$591$	14.1527	0.582163
$592$	−4.68859	−0.192700
$593$	−22.7046	−0.932368	−0.466184	−	0.884688i	$-0.654371\pi$
$593$	−22.7046	−0.932368	−0.466184	+	0.884688i	$0.654371\pi$
$594$	−46.8070	−1.92052
$595$	−12.1489	−0.498055
$596$	−2.01024	−0.0823426
$597$	55.7778	2.28284
$598$	−10.5236	−0.430344
$599$	−30.7598	−1.25681	−0.628407	−	0.777885i	$-0.716293\pi$
$599$	−30.7598	−1.25681	−0.628407	+	0.777885i	$0.716293\pi$
$600$	−43.0894	−1.75912
$601$	−6.49381	−0.264888	−0.132444	−	0.991190i	$-0.542282\pi$
$601$	−6.49381	−0.264888	−0.132444	+	0.991190i	$0.542282\pi$
$602$	−0.671815	−0.0273811
$603$	−39.8776	−1.62394
$604$	−3.32209	−0.135174
$605$	21.8133	0.886838
$606$	−70.3335	−2.85710
$607$	3.89474	0.158083	0.0790413	−	0.996871i	$-0.474814\pi$
$607$	3.89474	0.158083	0.0790413	+	0.996871i	$0.474814\pi$
$608$	−1.52058	−0.0616677
$609$	6.51663	0.264067
$610$	41.5157	1.68092
$611$	−16.2321	−0.656680
$612$	−12.4204	−0.502064
$613$	−11.4913	−0.464130	−0.232065	−	0.972700i	$-0.574548\pi$
$613$	−11.4913	−0.464130	−0.232065	+	0.972700i	$0.574548\pi$
$614$	0.733780	0.0296130
$615$	24.1019	0.971881
$616$	5.02362	0.202407
$617$	27.1492	1.09298	0.546492	−	0.837464i	$-0.315963\pi$
$617$	27.1492	1.09298	0.546492	+	0.837464i	$0.315963\pi$
$618$	−52.8979	−2.12787
$619$	−12.1402	−0.487957	−0.243979	−	0.969781i	$-0.578453\pi$
$619$	−12.1402	−0.487957	−0.243979	+	0.969781i	$0.578453\pi$
$620$	1.42979	0.0574218
$621$	63.7447	2.55799
$622$	22.1816	0.889401
$623$	15.6086	0.625347
$624$	−23.2821	−0.932030
$625$	−22.4529	−0.898117
$626$	−32.5720	−1.30184
$627$	−4.13399	−0.165095
$628$	6.51703	0.260058
$629$	−3.75531	−0.149734
$630$	−37.8325	−1.50728
$631$	−30.2059	−1.20248	−0.601239	−	0.799069i	$-0.705326\pi$
$631$	−30.2059	−1.20248	−0.601239	+	0.799069i	$0.705326\pi$
$632$	16.1471	0.642296
$633$	−54.4502	−2.16420
$634$	−2.18402	−0.0867384
$635$	65.5216	2.60014
$636$	−6.06823	−0.240621
$637$	−1.53365	−0.0607654
$638$	6.48944	0.256919
$639$	83.3760	3.29830
$640$	43.8924	1.73500
$641$	12.1077	0.478224	0.239112	−	0.970992i	$-0.423144\pi$
$641$	12.1077	0.478224	0.239112	+	0.970992i	$0.423144\pi$
$642$	76.7401	3.02869
$643$	40.5402	1.59875	0.799375	−	0.600832i	$-0.205164\pi$
$643$	40.5402	1.59875	0.799375	+	0.600832i	$0.205164\pi$
$644$	1.94068	0.0764734
$645$	−4.50323	−0.177315
$646$	−3.63130	−0.142872
$647$	32.8330	1.29080	0.645399	−	0.763845i	$-0.276691\pi$
$647$	32.8330	1.29080	0.645399	+	0.763845i	$0.276691\pi$
$648$	59.7785	2.34832
$649$	4.18661	0.164339
$650$	13.0998	0.513816
$651$	−3.23783	−0.126900
$652$	1.18713	0.0464918
$653$	−44.5320	−1.74267	−0.871336	−	0.490686i	$-0.836746\pi$
$653$	−44.5320	−1.74267	−0.871336	+	0.490686i	$0.836746\pi$
$654$	53.7228	2.10073
$655$	9.40456	0.367466
$656$	−10.7882	−0.421209
$657$	−124.761	−4.86741
$658$	16.5393	0.644770
$659$	1.59432	0.0621059	0.0310530	−	0.999518i	$-0.490114\pi$
$659$	1.59432	0.0621059	0.0310530	+	0.999518i	$0.490114\pi$
$660$	−9.55201	−0.371812
$661$	−22.0948	−0.859388	−0.429694	−	0.902975i	$-0.641379\pi$
$661$	−22.0948	−0.859388	−0.429694	+	0.902975i	$0.641379\pi$
$662$	27.6909	1.07624
$663$	−18.6477	−0.724218
$664$	19.7596	0.766820
$665$	−2.00187	−0.0776294
$666$	−11.6943	−0.453146
$667$	−8.83772	−0.342198
$668$	−2.71170	−0.104919
$669$	28.8959	1.11718
$670$	−26.9391	−1.04075
$671$	−16.9442	−0.654124
$672$	7.95639	0.306925
$673$	−12.2773	−0.473256	−0.236628	−	0.971600i	$-0.576042\pi$
$673$	−12.2773	−0.473256	−0.236628	+	0.971600i	$0.576042\pi$
$674$	−5.93308	−0.228534
$675$	−79.3491	−3.05415
$676$	−4.70595	−0.180998
$677$	−36.1299	−1.38858	−0.694292	−	0.719694i	$-0.744282\pi$
$677$	−36.1299	−1.38858	−0.694292	+	0.719694i	$0.744282\pi$
$678$	−10.7194	−0.411675
$679$	16.1127	0.618347
$680$	29.5790	1.13430
$681$	22.9972	0.881256
$682$	−3.22432	−0.123466
$683$	39.0365	1.49369	0.746845	−	0.664999i	$-0.231568\pi$
$683$	39.0365	1.49369	0.746845	+	0.664999i	$0.231568\pi$
$684$	−2.04661	−0.0782541
$685$	42.0374	1.60617
$686$	1.56268	0.0596633
$687$	78.8189	3.00713
$688$	2.01569	0.0768473
$689$	−6.50357	−0.247766
$690$	71.8760	2.73627
$691$	26.5498	1.01000	0.505001	−	0.863119i	$-0.331492\pi$
$691$	26.5498	1.01000	0.505001	+	0.863119i	$0.331492\pi$
$692$	5.48711	0.208589
$693$	15.4410	0.586554
$694$	7.86453	0.298533
$695$	−1.38696	−0.0526105
$696$	−15.8661	−0.601404
$697$	−8.64078	−0.327293
$698$	−22.3511	−0.846002
$699$	28.4805	1.07723
$700$	−2.41575	−0.0913066
$701$	31.2158	1.17901	0.589503	−	0.807767i	$-0.299324\pi$
$701$	31.2158	1.17901	0.589503	+	0.807767i	$0.299324\pi$
$702$	−34.7911	−1.31311
$703$	−0.618795	−0.0233383
$704$	−11.4250	−0.430597
$705$	110.864	4.17540
$706$	7.86575	0.296032
$707$	13.9008	0.522793
$708$	2.90356	0.109122
$709$	7.78825	0.292494	0.146247	−	0.989248i	$-0.453281\pi$
$709$	7.78825	0.292494	0.146247	+	0.989248i	$0.453281\pi$
$710$	56.3241	2.11380
$711$	49.6309	1.86130
$712$	−38.0026	−1.42421
$713$	4.39108	0.164447
$714$	19.0007	0.711082
$715$	−10.2373	−0.382853
$716$	2.41676	0.0903186
$717$	−3.35258	−0.125204
$718$	−58.3550	−2.17779
$719$	−33.7447	−1.25847	−0.629233	−	0.777217i	$-0.716631\pi$
$719$	−33.7447	−1.25847	−0.629233	+	0.777217i	$0.716631\pi$
$720$	113.511	4.23031
$721$	10.4548	0.389357
$722$	29.0925	1.08271
$723$	−7.11884	−0.264753
$724$	−3.47194	−0.129034
$725$	11.0011	0.408572
$726$	−34.1157	−1.26615
$727$	−23.9205	−0.887162	−0.443581	−	0.896234i	$-0.646292\pi$
$727$	−23.9205	−0.887162	−0.443581	+	0.896234i	$0.646292\pi$
$728$	3.73400	0.138391
$729$	42.7303	1.58260
$730$	−84.2818	−3.11941
$731$	1.61446	0.0597129
$732$	−11.7514	−0.434344
$733$	20.7261	0.765534	0.382767	−	0.923845i	$-0.374971\pi$
$733$	20.7261	0.765534	0.382767	+	0.923845i	$0.374971\pi$
$734$	52.9962	1.95613
$735$	10.4748	0.386367
$736$	−10.7903	−0.397736
$737$	10.9949	0.405003
$738$	−26.9080	−0.990499
$739$	34.7233	1.27732	0.638658	−	0.769491i	$-0.279490\pi$
$739$	34.7233	1.27732	0.638658	+	0.769491i	$0.279490\pi$
$740$	−1.42979	−0.0525602
$741$	−3.07274	−0.112880
$742$	6.62667	0.243273
$743$	4.57159	0.167716	0.0838578	−	0.996478i	$-0.473276\pi$
$743$	4.57159	0.167716	0.0838578	+	0.996478i	$0.473276\pi$
$744$	7.88318	0.289012
$745$	14.7148	0.539110
$746$	−6.33362	−0.231890
$747$	60.7345	2.22216
$748$	3.42450	0.125212
$749$	−15.1670	−0.554190
$750$	−7.62759	−0.278520
$751$	8.31213	0.303314	0.151657	−	0.988433i	$-0.451539\pi$
$751$	8.31213	0.303314	0.151657	+	0.988433i	$0.451539\pi$
$752$	−49.6239	−1.80960
$753$	−10.0831	−0.367448
$754$	4.82353	0.175662
$755$	24.3175	0.885005
$756$	6.41587	0.233343
$757$	30.4562	1.10695	0.553475	−	0.832866i	$-0.313302\pi$
$757$	30.4562	1.10695	0.553475	+	0.832866i	$0.313302\pi$
$758$	−8.80562	−0.319834
$759$	−29.3355	−1.06481
$760$	4.87399	0.176798
$761$	11.1664	0.404780	0.202390	−	0.979305i	$-0.435129\pi$
$761$	11.1664	0.404780	0.202390	+	0.979305i	$0.435129\pi$
$762$	−102.475	−3.71227
$763$	−10.6178	−0.384391
$764$	−5.29512	−0.191571
$765$	90.9164	3.28709
$766$	9.16747	0.331234
$767$	3.11186	0.112363
$768$	−32.7902	−1.18321
$769$	−17.2592	−0.622381	−0.311191	−	0.950347i	$-0.600728\pi$
$769$	−17.2592	−0.622381	−0.311191	+	0.950347i	$0.600728\pi$
$770$	10.4310	0.375909
$771$	83.2154	2.99693
$772$	−5.91846	−0.213010
$773$	−18.1646	−0.653335	−0.326667	−	0.945139i	$-0.605926\pi$
$773$	−18.1646	−0.653335	−0.326667	+	0.945139i	$0.605926\pi$
$774$	5.02754	0.180711
$775$	−5.46599	−0.196344
$776$	−39.2297	−1.40827
$777$	3.23783	0.116156
$778$	−13.2979	−0.476753
$779$	−1.42381	−0.0510135
$780$	−7.09990	−0.254217
$781$	−22.9881	−0.822579
$782$	−25.7683	−0.921474
$783$	−29.2175	−1.04415
$784$	−4.68859	−0.167450
$785$	−47.7043	−1.70264
$786$	−14.7086	−0.524638
$787$	−51.8022	−1.84655	−0.923274	−	0.384142i	$-0.874497\pi$
$787$	−51.8022	−1.84655	−0.923274	+	0.384142i	$0.874497\pi$
$788$	−1.93182	−0.0688183
$789$	−39.4918	−1.40595
$790$	33.5278	1.19287
$791$	2.11859	0.0753283
$792$	−37.5944	−1.33586
$793$	−12.5944	−0.447242
$794$	25.7738	0.914679
$795$	44.4191	1.57538
$796$	−7.61361	−0.269857
$797$	−30.0934	−1.06596	−0.532982	−	0.846127i	$-0.678929\pi$
$797$	−30.0934	−1.06596	−0.532982	+	0.846127i	$0.678929\pi$
$798$	3.13090	0.110833
$799$	−39.7461	−1.40612
$800$	13.4317	0.474883
$801$	−116.808	−4.12720
$802$	32.8576	1.16024
$803$	34.3988	1.21391
$804$	7.62534	0.268925
$805$	−14.2057	−0.500683
$806$	−2.39660	−0.0844166
$807$	−36.8245	−1.29629
$808$	−33.8444	−1.19064
$809$	11.1464	0.391885	0.195943	−	0.980615i	$-0.437223\pi$
$809$	11.1464	0.391885	0.195943	+	0.980615i	$0.437223\pi$
$810$	124.124	4.36128
$811$	−13.1227	−0.460802	−0.230401	−	0.973096i	$-0.574004\pi$
$811$	−13.1227	−0.460802	−0.230401	+	0.973096i	$0.574004\pi$
$812$	−0.889512	−0.0312157
$813$	−56.6161	−1.98561
$814$	3.22432	0.113012
$815$	−8.68976	−0.304389
$816$	−57.0088	−1.99571
$817$	0.266028	0.00930714
$818$	47.1158	1.64736
$819$	11.4771	0.401042
$820$	−3.28988	−0.114887
$821$	36.6279	1.27832	0.639162	−	0.769072i	$-0.279281\pi$
$821$	36.6279	1.27832	0.639162	+	0.769072i	$0.279281\pi$
$822$	−65.7459	−2.29315
$823$	−1.22404	−0.0426673	−0.0213336	−	0.999772i	$-0.506791\pi$
$823$	−1.22404	−0.0426673	−0.0213336	+	0.999772i	$0.506791\pi$
$824$	−25.4544	−0.886747
$825$	36.5166	1.27135
$826$	−3.17076	−0.110325
$827$	−28.4347	−0.988771	−0.494385	−	0.869243i	$-0.664607\pi$
$827$	−28.4347	−0.988771	−0.494385	+	0.869243i	$0.664607\pi$
$828$	−14.5231	−0.504713
$829$	−53.0785	−1.84349	−0.921746	−	0.387794i	$-0.873237\pi$
$829$	−53.0785	−1.84349	−0.921746	+	0.387794i	$0.873237\pi$
$830$	41.0288	1.42413
$831$	74.9680	2.60061
$832$	−8.49209	−0.294410
$833$	−3.75531	−0.130114
$834$	2.16919	0.0751129
$835$	19.8494	0.686918
$836$	0.564284	0.0195162
$837$	14.5169	0.501777
$838$	−22.2800	−0.769649
$839$	10.0939	0.348481	0.174240	−	0.984703i	$-0.444253\pi$
$839$	10.0939	0.348481	0.174240	+	0.984703i	$0.444253\pi$
$840$	−25.5030	−0.879938
$841$	−24.9492	−0.860318
$842$	24.6433	0.849264
$843$	15.3816	0.529771
$844$	7.43239	0.255833
$845$	34.4473	1.18502
$846$	−123.772	−4.25538
$847$	6.74267	0.231681
$848$	−19.8824	−0.682763
$849$	36.3244	1.24665
$850$	32.0763	1.10021
$851$	−4.39108	−0.150524
$852$	−15.9430	−0.546199
$853$	29.7971	1.02023	0.510117	−	0.860105i	$-0.329602\pi$
$853$	29.7971	1.02023	0.510117	+	0.860105i	$0.329602\pi$
$854$	12.8328	0.439130
$855$	14.9811	0.512342
$856$	36.9273	1.26215
$857$	20.2597	0.692059	0.346030	−	0.938224i	$-0.387530\pi$
$857$	20.2597	0.692059	0.346030	+	0.938224i	$0.387530\pi$
$858$	16.0110	0.546605
$859$	−34.5973	−1.18045	−0.590223	−	0.807240i	$-0.700960\pi$
$859$	−34.5973	−1.18045	−0.590223	+	0.807240i	$0.700960\pi$
$860$	0.614686	0.0209606
$861$	7.45007	0.253898
$862$	−32.1707	−1.09574
$863$	4.49541	0.153026	0.0765128	−	0.997069i	$-0.475621\pi$
$863$	4.49541	0.153026	0.0765128	+	0.997069i	$0.475621\pi$
$864$	−35.6727	−1.21361
$865$	−40.1653	−1.36566
$866$	7.54773	0.256482
$867$	9.38202	0.318630
$868$	0.441960	0.0150011
$869$	−13.6840	−0.464199
$870$	−32.9444	−1.11692
$871$	8.17239	0.276911
$872$	25.8514	0.875437
$873$	−120.580	−4.08100
$874$	−4.24607	−0.143625
$875$	1.50753	0.0509637
$876$	23.8567	0.806043
$877$	−39.8068	−1.34418	−0.672090	−	0.740469i	$-0.734603\pi$
$877$	−39.8068	−1.34418	−0.672090	+	0.740469i	$0.734603\pi$
$878$	−54.3881	−1.83551
$879$	25.2194	0.850631
$880$	−31.2969	−1.05502
$881$	−8.67028	−0.292109	−0.146055	−	0.989277i	$-0.546658\pi$
$881$	−8.67028	−0.292109	−0.146055	+	0.989277i	$0.546658\pi$
$882$	−11.6943	−0.393769
$883$	6.64225	0.223529	0.111765	−	0.993735i	$-0.464350\pi$
$883$	6.64225	0.223529	0.111765	+	0.993735i	$0.464350\pi$
$884$	2.54539	0.0856108
$885$	−21.2539	−0.714441
$886$	44.0466	1.47977
$887$	34.5167	1.15896	0.579480	−	0.814987i	$-0.303256\pi$
$887$	34.5167	1.15896	0.579480	+	0.814987i	$0.303256\pi$
$888$	−7.88318	−0.264542
$889$	20.2532	0.679272
$890$	−78.9086	−2.64502
$891$	−50.6600	−1.69717
$892$	−3.94425	−0.132063
$893$	−6.54930	−0.219164
$894$	−23.0138	−0.769696
$895$	−17.6905	−0.591330
$896$	13.5675	0.453257
$897$	−21.8047	−0.728039
$898$	−13.2398	−0.441819
$899$	−2.01265	−0.0671258
$900$	18.0783	0.602610
$901$	−15.9247	−0.530530
$902$	7.41899	0.247025
$903$	−1.39198	−0.0463223
$904$	−5.15816	−0.171558
$905$	25.4144	0.844803
$906$	−38.0323	−1.26354
$907$	−1.31967	−0.0438191	−0.0219095	−	0.999760i	$-0.506975\pi$
$907$	−1.31967	−0.0438191	−0.0219095	+	0.999760i	$0.506975\pi$
$908$	−3.13910	−0.104175
$909$	−104.027	−3.45035
$910$	7.75328	0.257019
$911$	−46.2738	−1.53312	−0.766561	−	0.642172i	$-0.778033\pi$
$911$	−46.2738	−1.53312	−0.766561	+	0.642172i	$0.778033\pi$
$912$	−9.39383	−0.311061
$913$	−16.7455	−0.554195
$914$	−42.2266	−1.39673
$915$	86.0194	2.84371
$916$	−10.7587	−0.355477
$917$	2.90702	0.0959983
$918$	−85.1900	−2.81169
$919$	30.3414	1.00087	0.500435	−	0.865774i	$-0.333173\pi$
$919$	30.3414	1.00087	0.500435	+	0.865774i	$0.333173\pi$
$920$	34.5867	1.14029
$921$	1.52037	0.0500980
$922$	−3.82367	−0.125926
$923$	−17.0868	−0.562419
$924$	−2.95260	−0.0971335
$925$	5.46599	0.179721
$926$	−8.85892	−0.291122
$927$	−78.2387	−2.56970
$928$	4.94575	0.162352
$929$	49.3519	1.61918	0.809592	−	0.586993i	$-0.199688\pi$
$929$	49.3519	1.61918	0.809592	+	0.586993i	$0.199688\pi$
$930$	16.3687	0.536749
$931$	−0.618795	−0.0202802
$932$	−3.88755	−0.127341
$933$	45.9597	1.50465
$934$	51.1879	1.67492
$935$	−25.0671	−0.819783
$936$	−27.9435	−0.913361
$937$	48.1097	1.57168	0.785838	−	0.618433i	$-0.212232\pi$
$937$	48.1097	1.57168	0.785838	+	0.618433i	$0.212232\pi$
$938$	−8.32707	−0.271889
$939$	−67.4884	−2.20240
$940$	−15.1329	−0.493580
$941$	25.7849	0.840565	0.420283	−	0.907393i	$-0.361931\pi$
$941$	25.7849	0.840565	0.420283	+	0.907393i	$0.361931\pi$
$942$	74.6088	2.43089
$943$	−10.1036	−0.329020
$944$	9.51341	0.309635
$945$	−46.9638	−1.52773
$946$	−1.38618	−0.0450685
$947$	−10.3723	−0.337053	−0.168526	−	0.985697i	$-0.553901\pi$
$947$	−10.3723	−0.337053	−0.168526	+	0.985697i	$0.553901\pi$
$948$	−9.49034	−0.308232
$949$	25.5682	0.829979
$950$	5.28548	0.171484
$951$	−4.52523	−0.146741
$952$	9.14311	0.296330
$953$	−25.0172	−0.810387	−0.405193	−	0.914231i	$-0.632796\pi$
$953$	−25.0172	−0.810387	−0.405193	+	0.914231i	$0.632796\pi$
$954$	−49.5908	−1.60556
$955$	38.7600	1.25424
$956$	0.457623	0.0148006
$957$	13.4459	0.434646
$958$	35.3139	1.14094
$959$	12.9941	0.419601
$960$	58.0005	1.87196
$961$	1.00000	0.0322581
$962$	2.39660	0.0772694
$963$	113.503	3.65757
$964$	0.971714	0.0312968
$965$	43.3228	1.39461
$966$	22.2174	0.714834
$967$	−1.14983	−0.0369761	−0.0184880	−	0.999829i	$-0.505885\pi$
$967$	−1.14983	−0.0369761	−0.0184880	+	0.999829i	$0.505885\pi$
$968$	−16.4165	−0.527646
$969$	−7.52396	−0.241704
$970$	−81.4567	−2.61542
$971$	28.4218	0.912100	0.456050	−	0.889954i	$-0.349264\pi$
$971$	28.4218	0.912100	0.456050	+	0.889954i	$0.349264\pi$
$972$	−15.8868	−0.509570
$973$	−0.428721	−0.0137442
$974$	−16.0244	−0.513454
$975$	27.1424	0.869253
$976$	−38.5031	−1.23245
$977$	−4.45915	−0.142661	−0.0713305	−	0.997453i	$-0.522725\pi$
$977$	−4.45915	−0.142661	−0.0713305	+	0.997453i	$0.522725\pi$
$978$	13.5907	0.434581
$979$	32.2058	1.02930
$980$	−1.42979	−0.0456730
$981$	79.4587	2.53692
$982$	24.9374	0.795784
$983$	58.1977	1.85622	0.928109	−	0.372309i	$-0.121434\pi$
$983$	58.1977	1.85622	0.928109	+	0.372309i	$0.121434\pi$
$984$	−18.1388	−0.578244
$985$	14.1408	0.450564
$986$	11.8109	0.376137
$987$	34.2690	1.09080
$988$	0.419426	0.0133437
$989$	1.88778	0.0600279
$990$	−78.0610	−2.48094
$991$	−56.8210	−1.80498	−0.902490	−	0.430712i	$-0.858263\pi$
$991$	−56.8210	−1.80498	−0.902490	+	0.430712i	$0.858263\pi$
$992$	−2.45733	−0.0780202
$993$	57.3748	1.82073
$994$	17.4102	0.552218
$995$	55.7312	1.76680
$996$	−11.6136	−0.367990
$997$	27.5742	0.873285	0.436642	−	0.899635i	$-0.356167\pi$
$997$	27.5742	0.873285	0.436642	+	0.899635i	$0.356167\pi$
$998$	31.9193	1.01039
$999$	−14.5169	−0.459294

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.h.1.17	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.h.1.17	✓	71	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:	\( N \)	\(=\)	\( 8029 = 7 \cdot 31 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.56268 q^{2} -3.23783 q^{3} +0.441960 q^{4} -3.23512 q^{5} +5.05968 q^{6} -1.00000 q^{7} +2.43471 q^{8} +7.48352 q^{9} +O(q^{10})\)	\(q-1.56268 q^{2} -3.23783 q^{3} +0.441960 q^{4} -3.23512 q^{5} +5.05968 q^{6} -1.00000 q^{7} +2.43471 q^{8} +7.48352 q^{9} +5.05544 q^{10} -2.06333 q^{11} -1.43099 q^{12} -1.53365 q^{13} +1.56268 q^{14} +10.4748 q^{15} -4.68859 q^{16} -3.75531 q^{17} -11.6943 q^{18} -0.618795 q^{19} -1.42979 q^{20} +3.23783 q^{21} +3.22432 q^{22} -4.39108 q^{23} -7.88318 q^{24} +5.46599 q^{25} +2.39660 q^{26} -14.5169 q^{27} -0.441960 q^{28} +2.01265 q^{29} -16.3687 q^{30} -1.00000 q^{31} +2.45733 q^{32} +6.68070 q^{33} +5.86834 q^{34} +3.23512 q^{35} +3.30742 q^{36} +1.00000 q^{37} +0.966977 q^{38} +4.96569 q^{39} -7.87659 q^{40} +2.30095 q^{41} -5.05968 q^{42} -0.429913 q^{43} -0.911908 q^{44} -24.2101 q^{45} +6.86183 q^{46} +10.5840 q^{47} +15.1808 q^{48} +1.00000 q^{49} -8.54157 q^{50} +12.1591 q^{51} -0.677811 q^{52} +4.24059 q^{53} +22.6852 q^{54} +6.67511 q^{55} -2.43471 q^{56} +2.00355 q^{57} -3.14513 q^{58} -2.02906 q^{59} +4.62942 q^{60} +8.21207 q^{61} +1.56268 q^{62} -7.48352 q^{63} +5.53718 q^{64} +4.96154 q^{65} -10.4398 q^{66} -5.32872 q^{67} -1.65970 q^{68} +14.2175 q^{69} -5.05544 q^{70} +11.1413 q^{71} +18.2202 q^{72} -16.6715 q^{73} -1.56268 q^{74} -17.6979 q^{75} -0.273482 q^{76} +2.06333 q^{77} -7.75977 q^{78} +6.63202 q^{79} +15.1681 q^{80} +24.5526 q^{81} -3.59564 q^{82} +8.11577 q^{83} +1.43099 q^{84} +12.1489 q^{85} +0.671815 q^{86} -6.51663 q^{87} -5.02362 q^{88} -15.6086 q^{89} +37.8325 q^{90} +1.53365 q^{91} -1.94068 q^{92} +3.23783 q^{93} -16.5393 q^{94} +2.00187 q^{95} -7.95639 q^{96} -16.1127 q^{97} -1.56268 q^{98} -15.4410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9}+O(q^{10}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9} + 4 q^{10} + 57 q^{11} + 21 q^{12} - 20 q^{13} - 6 q^{14} + 22 q^{15} + 88 q^{16} - 19 q^{17} + q^{18} + 23 q^{19} + 25 q^{20} - 8 q^{21} + 18 q^{22} + 34 q^{23} + 15 q^{24} + 81 q^{25} - 13 q^{26} + 20 q^{27} - 78 q^{28} + 16 q^{29} + 6 q^{30} - 71 q^{31} + 47 q^{32} - 16 q^{33} + 32 q^{34} + 125 q^{36} + 71 q^{37} + 13 q^{38} + 30 q^{39} + 31 q^{40} + 17 q^{41} - 5 q^{42} + 38 q^{43} + 80 q^{44} - q^{45} + 26 q^{46} + 32 q^{47} + 61 q^{48} + 71 q^{49} + 47 q^{50} + 73 q^{51} - 23 q^{52} + 31 q^{53} + 47 q^{54} + 11 q^{55} - 18 q^{56} + 17 q^{57} - 2 q^{58} + 97 q^{59} + 103 q^{60} - q^{61} - 6 q^{62} - 87 q^{63} + 100 q^{64} + 46 q^{65} + 43 q^{66} + 75 q^{67} - 43 q^{68} + 10 q^{69} - 4 q^{70} + 131 q^{71} - 11 q^{72} - 15 q^{73} + 6 q^{74} + 76 q^{75} + 41 q^{76} - 57 q^{77} + 89 q^{78} + 8 q^{79} + 10 q^{80} + 171 q^{81} + 14 q^{82} + 18 q^{83} - 21 q^{84} + 47 q^{85} + 90 q^{86} - 59 q^{87} + 13 q^{88} + 18 q^{89} + 69 q^{90} + 20 q^{91} + 110 q^{92} - 8 q^{93} + 39 q^{94} + 72 q^{95} + 100 q^{96} + 23 q^{97} + 6 q^{98} + 168 q^{99}+O(q^{100}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9 + 4 * q^10 + 57 * q^11 + 21 * q^12 - 20 * q^13 - 6 * q^14 + 22 * q^15 + 88 * q^16 - 19 * q^17 + q^18 + 23 * q^19 + 25 * q^20 - 8 * q^21 + 18 * q^22 + 34 * q^23 + 15 * q^24 + 81 * q^25 - 13 * q^26 + 20 * q^27 - 78 * q^28 + 16 * q^29 + 6 * q^30 - 71 * q^31 + 47 * q^32 - 16 * q^33 + 32 * q^34 + 125 * q^36 + 71 * q^37 + 13 * q^38 + 30 * q^39 + 31 * q^40 + 17 * q^41 - 5 * q^42 + 38 * q^43 + 80 * q^44 - q^45 + 26 * q^46 + 32 * q^47 + 61 * q^48 + 71 * q^49 + 47 * q^50 + 73 * q^51 - 23 * q^52 + 31 * q^53 + 47 * q^54 + 11 * q^55 - 18 * q^56 + 17 * q^57 - 2 * q^58 + 97 * q^59 + 103 * q^60 - q^61 - 6 * q^62 - 87 * q^63 + 100 * q^64 + 46 * q^65 + 43 * q^66 + 75 * q^67 - 43 * q^68 + 10 * q^69 - 4 * q^70 + 131 * q^71 - 11 * q^72 - 15 * q^73 + 6 * q^74 + 76 * q^75 + 41 * q^76 - 57 * q^77 + 89 * q^78 + 8 * q^79 + 10 * q^80 + 171 * q^81 + 14 * q^82 + 18 * q^83 - 21 * q^84 + 47 * q^85 + 90 * q^86 - 59 * q^87 + 13 * q^88 + 18 * q^89 + 69 * q^90 + 20 * q^91 + 110 * q^92 - 8 * q^93 + 39 * q^94 + 72 * q^95 + 100 * q^96 + 23 * q^97 + 6 * q^98 + 168 * q^99

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