LMFDB - Embedded newform 6038.2.a.c.1.9

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			1.9
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.46647 q^{3} +1.00000 q^{4} +3.27492 q^{5} +2.46647 q^{6} +3.14216 q^{7} -1.00000 q^{8} +3.08346 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.46647 q^{3} +1.00000 q^{4} +3.27492 q^{5} +2.46647 q^{6} +3.14216 q^{7} -1.00000 q^{8} +3.08346 q^{9} -3.27492 q^{10} +0.982382 q^{11} -2.46647 q^{12} -2.80579 q^{13} -3.14216 q^{14} -8.07748 q^{15} +1.00000 q^{16} -3.81446 q^{17} -3.08346 q^{18} +2.23772 q^{19} +3.27492 q^{20} -7.75003 q^{21} -0.982382 q^{22} -3.67627 q^{23} +2.46647 q^{24} +5.72510 q^{25} +2.80579 q^{26} -0.205861 q^{27} +3.14216 q^{28} +7.60920 q^{29} +8.07748 q^{30} -4.01453 q^{31} -1.00000 q^{32} -2.42301 q^{33} +3.81446 q^{34} +10.2903 q^{35} +3.08346 q^{36} +2.51377 q^{37} -2.23772 q^{38} +6.92039 q^{39} -3.27492 q^{40} -7.11195 q^{41} +7.75003 q^{42} -0.641022 q^{43} +0.982382 q^{44} +10.0981 q^{45} +3.67627 q^{46} -6.58914 q^{47} -2.46647 q^{48} +2.87314 q^{49} -5.72510 q^{50} +9.40824 q^{51} -2.80579 q^{52} -7.96225 q^{53} +0.205861 q^{54} +3.21722 q^{55} -3.14216 q^{56} -5.51926 q^{57} -7.60920 q^{58} -7.32393 q^{59} -8.07748 q^{60} -14.0080 q^{61} +4.01453 q^{62} +9.68872 q^{63} +1.00000 q^{64} -9.18873 q^{65} +2.42301 q^{66} -9.84947 q^{67} -3.81446 q^{68} +9.06741 q^{69} -10.2903 q^{70} +9.53161 q^{71} -3.08346 q^{72} -13.0297 q^{73} -2.51377 q^{74} -14.1208 q^{75} +2.23772 q^{76} +3.08680 q^{77} -6.92039 q^{78} -2.72098 q^{79} +3.27492 q^{80} -8.74264 q^{81} +7.11195 q^{82} -5.46198 q^{83} -7.75003 q^{84} -12.4920 q^{85} +0.641022 q^{86} -18.7678 q^{87} -0.982382 q^{88} +13.1741 q^{89} -10.0981 q^{90} -8.81622 q^{91} -3.67627 q^{92} +9.90170 q^{93} +6.58914 q^{94} +7.32835 q^{95} +2.46647 q^{96} -15.5698 q^{97} -2.87314 q^{98} +3.02914 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.46647	−1.42402	−0.712008	−	0.702171i	$-0.752214\pi$
$3$	−2.46647	−1.42402	−0.712008	+	0.702171i	$0.752214\pi$
$4$	1.00000	0.500000
$5$	3.27492	1.46459	0.732294	−	0.680988i	$-0.238450\pi$
$5$	3.27492	1.46459	0.732294	+	0.680988i	$0.238450\pi$
$6$	2.46647	1.00693
$7$	3.14216	1.18762	0.593812	−	0.804604i	$-0.297622\pi$
$7$	3.14216	1.18762	0.593812	+	0.804604i	$0.297622\pi$
$8$	−1.00000	−0.353553
$9$	3.08346	1.02782
$10$	−3.27492	−1.03562
$11$	0.982382	0.296199	0.148100	−	0.988972i	$-0.452684\pi$
$11$	0.982382	0.296199	0.148100	+	0.988972i	$0.452684\pi$
$12$	−2.46647	−0.712008
$13$	−2.80579	−0.778186	−0.389093	−	0.921199i	$-0.627211\pi$
$13$	−2.80579	−0.778186	−0.389093	+	0.921199i	$0.627211\pi$
$14$	−3.14216	−0.839777
$15$	−8.07748	−2.08560
$16$	1.00000	0.250000
$17$	−3.81446	−0.925142	−0.462571	−	0.886582i	$-0.653073\pi$
$17$	−3.81446	−0.925142	−0.462571	+	0.886582i	$0.653073\pi$
$18$	−3.08346	−0.726779
$19$	2.23772	0.513368	0.256684	−	0.966495i	$-0.417370\pi$
$19$	2.23772	0.513368	0.256684	+	0.966495i	$0.417370\pi$
$20$	3.27492	0.732294
$21$	−7.75003	−1.69119
$22$	−0.982382	−0.209444
$23$	−3.67627	−0.766556	−0.383278	−	0.923633i	$-0.625205\pi$
$23$	−3.67627	−0.766556	−0.383278	+	0.923633i	$0.625205\pi$
$24$	2.46647	0.503466
$25$	5.72510	1.14502
$26$	2.80579	0.550260
$27$	−0.205861	−0.0396179
$28$	3.14216	0.593812
$29$	7.60920	1.41299	0.706496	−	0.707717i	$-0.250275\pi$
$29$	7.60920	1.41299	0.706496	+	0.707717i	$0.250275\pi$
$30$	8.07748	1.47474
$31$	−4.01453	−0.721030	−0.360515	−	0.932753i	$-0.617399\pi$
$31$	−4.01453	−0.721030	−0.360515	+	0.932753i	$0.617399\pi$
$32$	−1.00000	−0.176777
$33$	−2.42301	−0.421792
$34$	3.81446	0.654174
$35$	10.2903	1.73938
$36$	3.08346	0.513911
$37$	2.51377	0.413261	0.206631	−	0.978419i	$-0.433750\pi$
$37$	2.51377	0.413261	0.206631	+	0.978419i	$0.433750\pi$
$38$	−2.23772	−0.363006
$39$	6.92039	1.10815
$40$	−3.27492	−0.517810
$41$	−7.11195	−1.11070	−0.555350	−	0.831617i	$-0.687416\pi$
$41$	−7.11195	−1.11070	−0.555350	+	0.831617i	$0.687416\pi$
$42$	7.75003	1.19586
$43$	−0.641022	−0.0977549	−0.0488775	−	0.998805i	$-0.515564\pi$
$43$	−0.641022	−0.0977549	−0.0488775	+	0.998805i	$0.515564\pi$
$44$	0.982382	0.148100
$45$	10.0981	1.50534
$46$	3.67627	0.542037
$47$	−6.58914	−0.961124	−0.480562	−	0.876961i	$-0.659567\pi$
$47$	−6.58914	−0.961124	−0.480562	+	0.876961i	$0.659567\pi$
$48$	−2.46647	−0.356004
$49$	2.87314	0.410449
$50$	−5.72510	−0.809651
$51$	9.40824	1.31742
$52$	−2.80579	−0.389093
$53$	−7.96225	−1.09370	−0.546850	−	0.837231i	$-0.684173\pi$
$53$	−7.96225	−1.09370	−0.546850	+	0.837231i	$0.684173\pi$
$54$	0.205861	0.0280141
$55$	3.21722	0.433810
$56$	−3.14216	−0.419888
$57$	−5.51926	−0.731044
$58$	−7.60920	−0.999136
$59$	−7.32393	−0.953495	−0.476748	−	0.879040i	$-0.658184\pi$
$59$	−7.32393	−0.953495	−0.476748	+	0.879040i	$0.658184\pi$
$60$	−8.07748	−1.04280
$61$	−14.0080	−1.79355	−0.896773	−	0.442490i	$-0.854095\pi$
$61$	−14.0080	−1.79355	−0.896773	+	0.442490i	$0.854095\pi$
$62$	4.01453	0.509846
$63$	9.68872	1.22066
$64$	1.00000	0.125000
$65$	−9.18873	−1.13972
$66$	2.42301	0.298252
$67$	−9.84947	−1.20330	−0.601652	−	0.798758i	$-0.705491\pi$
$67$	−9.84947	−1.20330	−0.601652	+	0.798758i	$0.705491\pi$
$68$	−3.81446	−0.462571
$69$	9.06741	1.09159
$70$	−10.2903	−1.22993
$71$	9.53161	1.13119	0.565597	−	0.824682i	$-0.308646\pi$
$71$	9.53161	1.13119	0.565597	+	0.824682i	$0.308646\pi$
$72$	−3.08346	−0.363390
$73$	−13.0297	−1.52501	−0.762505	−	0.646982i	$-0.776031\pi$
$73$	−13.0297	−1.52501	−0.762505	+	0.646982i	$0.776031\pi$
$74$	−2.51377	−0.292220
$75$	−14.1208	−1.63053
$76$	2.23772	0.256684
$77$	3.08680	0.351773
$78$	−6.92039	−0.783580
$79$	−2.72098	−0.306134	−0.153067	−	0.988216i	$-0.548915\pi$
$79$	−2.72098	−0.306134	−0.153067	+	0.988216i	$0.548915\pi$
$80$	3.27492	0.366147
$81$	−8.74264	−0.971405
$82$	7.11195	0.785384
$83$	−5.46198	−0.599530	−0.299765	−	0.954013i	$-0.596908\pi$
$83$	−5.46198	−0.599530	−0.299765	+	0.954013i	$0.596908\pi$
$84$	−7.75003	−0.845597
$85$	−12.4920	−1.35495
$86$	0.641022	0.0691232
$87$	−18.7678	−2.01212
$88$	−0.982382	−0.104722
$89$	13.1741	1.39645	0.698224	−	0.715880i	$-0.253974\pi$
$89$	13.1741	1.39645	0.698224	+	0.715880i	$0.253974\pi$
$90$	−10.0981	−1.06443
$91$	−8.81622	−0.924191
$92$	−3.67627	−0.383278
$93$	9.90170	1.02676
$94$	6.58914	0.679617
$95$	7.32835	0.751873
$96$	2.46647	0.251733
$97$	−15.5698	−1.58088	−0.790439	−	0.612541i	$-0.790148\pi$
$97$	−15.5698	−1.58088	−0.790439	+	0.612541i	$0.790148\pi$
$98$	−2.87314	−0.290231
$99$	3.02914	0.304440
$100$	5.72510	0.572510
$101$	−4.52955	−0.450707	−0.225353	−	0.974277i	$-0.572354\pi$
$101$	−4.52955	−0.450707	−0.225353	+	0.974277i	$0.572354\pi$
$102$	−9.40824	−0.931555
$103$	−7.14110	−0.703634	−0.351817	−	0.936069i	$-0.614436\pi$
$103$	−7.14110	−0.703634	−0.351817	+	0.936069i	$0.614436\pi$
$104$	2.80579	0.275130
$105$	−25.3807	−2.47690
$106$	7.96225	0.773362
$107$	5.15726	0.498571	0.249285	−	0.968430i	$-0.419804\pi$
$107$	5.15726	0.498571	0.249285	+	0.968430i	$0.419804\pi$
$108$	−0.205861	−0.0198089
$109$	15.0365	1.44024	0.720120	−	0.693850i	$-0.244087\pi$
$109$	15.0365	1.44024	0.720120	+	0.693850i	$0.244087\pi$
$110$	−3.21722	−0.306750
$111$	−6.20014	−0.588491
$112$	3.14216	0.296906
$113$	1.48840	0.140016	0.0700082	−	0.997546i	$-0.477697\pi$
$113$	1.48840	0.140016	0.0700082	+	0.997546i	$0.477697\pi$
$114$	5.51926	0.516926
$115$	−12.0395	−1.12269
$116$	7.60920	0.706496
$117$	−8.65155	−0.799836
$118$	7.32393	0.674223
$119$	−11.9856	−1.09872
$120$	8.07748	0.737370
$121$	−10.0349	−0.912266
$122$	14.0080	1.26823
$123$	17.5414	1.58165
$124$	−4.01453	−0.360515
$125$	2.37464	0.212394
$126$	−9.68872	−0.863140
$127$	0.0764772	0.00678626	0.00339313	−	0.999994i	$-0.498920\pi$
$127$	0.0764772	0.00678626	0.00339313	+	0.999994i	$0.498920\pi$
$128$	−1.00000	−0.0883883
$129$	1.58106	0.139205
$130$	9.18873	0.805905
$131$	−9.65739	−0.843771	−0.421885	−	0.906649i	$-0.638631\pi$
$131$	−9.65739	−0.843771	−0.421885	+	0.906649i	$0.638631\pi$
$132$	−2.42301	−0.210896
$133$	7.03126	0.609688
$134$	9.84947	0.850864
$135$	−0.674177	−0.0580239
$136$	3.81446	0.327087
$137$	11.0144	0.941025	0.470513	−	0.882393i	$-0.344069\pi$
$137$	11.0144	0.941025	0.470513	+	0.882393i	$0.344069\pi$
$138$	−9.06741	−0.771869
$139$	1.70100	0.144277	0.0721385	−	0.997395i	$-0.477018\pi$
$139$	1.70100	0.144277	0.0721385	+	0.997395i	$0.477018\pi$
$140$	10.2903	0.869690
$141$	16.2519	1.36866
$142$	−9.53161	−0.799875
$143$	−2.75635	−0.230498
$144$	3.08346	0.256955
$145$	24.9195	2.06945
$146$	13.0297	1.07834
$147$	−7.08652	−0.584486
$148$	2.51377	0.206631
$149$	−2.04612	−0.167625	−0.0838125	−	0.996482i	$-0.526710\pi$
$149$	−2.04612	−0.167625	−0.0838125	+	0.996482i	$0.526710\pi$
$150$	14.1208	1.15296
$151$	3.37081	0.274313	0.137156	−	0.990549i	$-0.456204\pi$
$151$	3.37081	0.274313	0.137156	+	0.990549i	$0.456204\pi$
$152$	−2.23772	−0.181503
$153$	−11.7617	−0.950881
$154$	−3.08680	−0.248741
$155$	−13.1473	−1.05601
$156$	6.92039	0.554074
$157$	7.84073	0.625758	0.312879	−	0.949793i	$-0.398706\pi$
$157$	7.84073	0.625758	0.312879	+	0.949793i	$0.398706\pi$
$158$	2.72098	0.216469
$159$	19.6386	1.55745
$160$	−3.27492	−0.258905
$161$	−11.5514	−0.910380
$162$	8.74264	0.686887
$163$	9.84755	0.771320	0.385660	−	0.922641i	$-0.373974\pi$
$163$	9.84755	0.771320	0.385660	+	0.922641i	$0.373974\pi$
$164$	−7.11195	−0.555350
$165$	−7.93517	−0.617752
$166$	5.46198	0.423932
$167$	19.8411	1.53535	0.767675	−	0.640839i	$-0.221414\pi$
$167$	19.8411	1.53535	0.767675	+	0.640839i	$0.221414\pi$
$168$	7.75003	0.597928
$169$	−5.12755	−0.394427
$170$	12.4920	0.958096
$171$	6.89992	0.527650
$172$	−0.641022	−0.0488775
$173$	−20.2718	−1.54123	−0.770617	−	0.637299i	$-0.780052\pi$
$173$	−20.2718	−1.54123	−0.770617	+	0.637299i	$0.780052\pi$
$174$	18.7678	1.42279
$175$	17.9892	1.35985
$176$	0.982382	0.0740498
$177$	18.0642	1.35779
$178$	−13.1741	−0.987437
$179$	8.48254	0.634015	0.317007	−	0.948423i	$-0.397322\pi$
$179$	8.48254	0.634015	0.317007	+	0.948423i	$0.397322\pi$
$180$	10.0981	0.752668
$181$	−18.1514	−1.34919	−0.674593	−	0.738190i	$-0.735681\pi$
$181$	−18.1514	−1.34919	−0.674593	+	0.738190i	$0.735681\pi$
$182$	8.81622	0.653502
$183$	34.5504	2.55404
$184$	3.67627	0.271018
$185$	8.23240	0.605258
$186$	−9.90170	−0.726028
$187$	−3.74726	−0.274026
$188$	−6.58914	−0.480562
$189$	−0.646846	−0.0470511
$190$	−7.32835	−0.531654
$191$	1.58086	0.114387	0.0571935	−	0.998363i	$-0.481785\pi$
$191$	1.58086	0.114387	0.0571935	+	0.998363i	$0.481785\pi$
$192$	−2.46647	−0.178002
$193$	6.71744	0.483532	0.241766	−	0.970335i	$-0.422273\pi$
$193$	6.71744	0.483532	0.241766	+	0.970335i	$0.422273\pi$
$194$	15.5698	1.11785
$195$	22.6637	1.62298
$196$	2.87314	0.205225
$197$	−21.2101	−1.51115	−0.755577	−	0.655059i	$-0.772644\pi$
$197$	−21.2101	−1.51115	−0.755577	+	0.655059i	$0.772644\pi$
$198$	−3.02914	−0.215271
$199$	−5.00444	−0.354755	−0.177378	−	0.984143i	$-0.556761\pi$
$199$	−5.00444	−0.354755	−0.177378	+	0.984143i	$0.556761\pi$
$200$	−5.72510	−0.404826
$201$	24.2934	1.71352
$202$	4.52955	0.318698
$203$	23.9093	1.67810
$204$	9.40824	0.658709
$205$	−23.2911	−1.62672
$206$	7.14110	0.497544
$207$	−11.3357	−0.787882
$208$	−2.80579	−0.194546
$209$	2.19829	0.152059
$210$	25.3807	1.75144
$211$	16.9222	1.16497	0.582487	−	0.812840i	$-0.302080\pi$
$211$	16.9222	1.16497	0.582487	+	0.812840i	$0.302080\pi$
$212$	−7.96225	−0.546850
$213$	−23.5094	−1.61084
$214$	−5.15726	−0.352543
$215$	−2.09929	−0.143171
$216$	0.205861	0.0140070
$217$	−12.6143	−0.856313
$218$	−15.0365	−1.01840
$219$	32.1373	2.17164
$220$	3.21722	0.216905
$221$	10.7026	0.719933
$222$	6.20014	0.416126
$223$	8.58313	0.574769	0.287385	−	0.957815i	$-0.407214\pi$
$223$	8.58313	0.574769	0.287385	+	0.957815i	$0.407214\pi$
$224$	−3.14216	−0.209944
$225$	17.6531	1.17688
$226$	−1.48840	−0.0990066
$227$	−6.83025	−0.453340	−0.226670	−	0.973972i	$-0.572784\pi$
$227$	−6.83025	−0.453340	−0.226670	+	0.973972i	$0.572784\pi$
$228$	−5.51926	−0.365522
$229$	14.2700	0.942990	0.471495	−	0.881869i	$-0.343714\pi$
$229$	14.2700	0.942990	0.471495	+	0.881869i	$0.343714\pi$
$230$	12.0395	0.793861
$231$	−7.61348	−0.500930
$232$	−7.60920	−0.499568
$233$	−9.05319	−0.593094	−0.296547	−	0.955018i	$-0.595835\pi$
$233$	−9.05319	−0.593094	−0.296547	+	0.955018i	$0.595835\pi$
$234$	8.65155	0.565569
$235$	−21.5789	−1.40765
$236$	−7.32393	−0.476748
$237$	6.71120	0.435939
$238$	11.9856	0.776913
$239$	6.61579	0.427940	0.213970	−	0.976840i	$-0.431361\pi$
$239$	6.61579	0.427940	0.213970	+	0.976840i	$0.431361\pi$
$240$	−8.07748	−0.521399
$241$	−30.7882	−1.98324	−0.991620	−	0.129187i	$-0.958763\pi$
$241$	−30.7882	−1.98324	−0.991620	+	0.129187i	$0.958763\pi$
$242$	10.0349	0.645069
$243$	22.1810	1.42291
$244$	−14.0080	−0.896773
$245$	9.40932	0.601139
$246$	−17.5414	−1.11840
$247$	−6.27856	−0.399495
$248$	4.01453	0.254923
$249$	13.4718	0.853740
$250$	−2.37464	−0.150186
$251$	5.78025	0.364846	0.182423	−	0.983220i	$-0.441606\pi$
$251$	5.78025	0.364846	0.182423	+	0.983220i	$0.441606\pi$
$252$	9.68872	0.610332
$253$	−3.61150	−0.227053
$254$	−0.0764772	−0.00479861
$255$	30.8112	1.92947
$256$	1.00000	0.0625000
$257$	−27.6636	−1.72561	−0.862804	−	0.505539i	$-0.831294\pi$
$257$	−27.6636	−1.72561	−0.862804	+	0.505539i	$0.831294\pi$
$258$	−1.58106	−0.0984325
$259$	7.89866	0.490799
$260$	−9.18873	−0.569861
$261$	23.4627	1.45230
$262$	9.65739	0.596636
$263$	−2.71825	−0.167614	−0.0838072	−	0.996482i	$-0.526708\pi$
$263$	−2.71825	−0.167614	−0.0838072	+	0.996482i	$0.526708\pi$
$264$	2.42301	0.149126
$265$	−26.0757	−1.60182
$266$	−7.03126	−0.431114
$267$	−32.4934	−1.98856
$268$	−9.84947	−0.601652
$269$	6.27644	0.382681	0.191341	−	0.981524i	$-0.438717\pi$
$269$	6.27644	0.382681	0.191341	+	0.981524i	$0.438717\pi$
$270$	0.674177	0.0410291
$271$	22.8796	1.38984	0.694918	−	0.719089i	$-0.255441\pi$
$271$	22.8796	1.38984	0.694918	+	0.719089i	$0.255441\pi$
$272$	−3.81446	−0.231286
$273$	21.7449	1.31606
$274$	−11.0144	−0.665405
$275$	5.62423	0.339154
$276$	9.06741	0.545794
$277$	23.9815	1.44091	0.720453	−	0.693504i	$-0.243934\pi$
$277$	23.9815	1.44091	0.720453	+	0.693504i	$0.243934\pi$
$278$	−1.70100	−0.102019
$279$	−12.3786	−0.741090
$280$	−10.2903	−0.614964
$281$	8.54627	0.509828	0.254914	−	0.966964i	$-0.417953\pi$
$281$	8.54627	0.509828	0.254914	+	0.966964i	$0.417953\pi$
$282$	−16.2519	−0.967786
$283$	−14.3583	−0.853514	−0.426757	−	0.904366i	$-0.640344\pi$
$283$	−14.3583	−0.853514	−0.426757	+	0.904366i	$0.640344\pi$
$284$	9.53161	0.565597
$285$	−18.0751	−1.07068
$286$	2.75635	0.162987
$287$	−22.3469	−1.31909
$288$	−3.08346	−0.181695
$289$	−2.44990	−0.144112
$290$	−24.9195	−1.46332
$291$	38.4025	2.25120
$292$	−13.0297	−0.762505
$293$	7.70530	0.450148	0.225074	−	0.974342i	$-0.427738\pi$
$293$	7.70530	0.450148	0.225074	+	0.974342i	$0.427738\pi$
$294$	7.08652	0.413294
$295$	−23.9853	−1.39648
$296$	−2.51377	−0.146110
$297$	−0.202234	−0.0117348
$298$	2.04612	0.118529
$299$	10.3148	0.596523
$300$	−14.1208	−0.815263
$301$	−2.01419	−0.116096
$302$	−3.37081	−0.193968
$303$	11.1720	0.641813
$304$	2.23772	0.128342
$305$	−45.8752	−2.62681
$306$	11.7617	0.672374
$307$	29.5171	1.68463	0.842314	−	0.538986i	$-0.181193\pi$
$307$	29.5171	1.68463	0.842314	+	0.538986i	$0.181193\pi$
$308$	3.08680	0.175887
$309$	17.6133	1.00199
$310$	13.1473	0.746714
$311$	−5.56501	−0.315563	−0.157781	−	0.987474i	$-0.550434\pi$
$311$	−5.56501	−0.315563	−0.157781	+	0.987474i	$0.550434\pi$
$312$	−6.92039	−0.391790
$313$	−14.8872	−0.841475	−0.420737	−	0.907182i	$-0.638229\pi$
$313$	−14.8872	−0.841475	−0.420737	+	0.907182i	$0.638229\pi$
$314$	−7.84073	−0.442478
$315$	31.7298	1.78777
$316$	−2.72098	−0.153067
$317$	18.1654	1.02027	0.510134	−	0.860095i	$-0.329596\pi$
$317$	18.1654	1.02027	0.510134	+	0.860095i	$0.329596\pi$
$318$	−19.6386	−1.10128
$319$	7.47513	0.418527
$320$	3.27492	0.183074
$321$	−12.7202	−0.709973
$322$	11.5514	0.643736
$323$	−8.53569	−0.474938
$324$	−8.74264	−0.485702
$325$	−16.0634	−0.891038
$326$	−9.84755	−0.545406
$327$	−37.0872	−2.05092
$328$	7.11195	0.392692
$329$	−20.7041	−1.14145
$330$	7.93517	0.436817
$331$	1.40218	0.0770709	0.0385355	−	0.999257i	$-0.487731\pi$
$331$	1.40218	0.0770709	0.0385355	+	0.999257i	$0.487731\pi$
$332$	−5.46198	−0.299765
$333$	7.75112	0.424759
$334$	−19.8411	−1.08566
$335$	−32.2562	−1.76234
$336$	−7.75003	−0.422799
$337$	24.9496	1.35909	0.679546	−	0.733632i	$-0.262177\pi$
$337$	24.9496	1.35909	0.679546	+	0.733632i	$0.262177\pi$
$338$	5.12755	0.278902
$339$	−3.67108	−0.199386
$340$	−12.4920	−0.677476
$341$	−3.94380	−0.213569
$342$	−6.89992	−0.373105
$343$	−12.9672	−0.700164
$344$	0.641022	0.0345616
$345$	29.6950	1.59873
$346$	20.2718	1.08982
$347$	−9.67126	−0.519180	−0.259590	−	0.965719i	$-0.583587\pi$
$347$	−9.67126	−0.519180	−0.259590	+	0.965719i	$0.583587\pi$
$348$	−18.7678	−1.00606
$349$	4.65247	0.249041	0.124521	−	0.992217i	$-0.460261\pi$
$349$	4.65247	0.249041	0.124521	+	0.992217i	$0.460261\pi$
$350$	−17.9892	−0.961561
$351$	0.577601	0.0308301
$352$	−0.982382	−0.0523611
$353$	−26.3892	−1.40456	−0.702279	−	0.711902i	$-0.747834\pi$
$353$	−26.3892	−1.40456	−0.702279	+	0.711902i	$0.747834\pi$
$354$	−18.0642	−0.960104
$355$	31.2153	1.65673
$356$	13.1741	0.698224
$357$	29.5622	1.56460
$358$	−8.48254	−0.448316
$359$	−21.8784	−1.15470	−0.577349	−	0.816498i	$-0.695913\pi$
$359$	−21.8784	−1.15470	−0.577349	+	0.816498i	$0.695913\pi$
$360$	−10.0981	−0.532216
$361$	−13.9926	−0.736453
$362$	18.1514	0.954019
$363$	24.7508	1.29908
$364$	−8.81622	−0.462096
$365$	−42.6712	−2.23351
$366$	−34.5504	−1.80598
$367$	−17.8571	−0.932133	−0.466066	−	0.884750i	$-0.654329\pi$
$367$	−17.8571	−0.932133	−0.466066	+	0.884750i	$0.654329\pi$
$368$	−3.67627	−0.191639
$369$	−21.9294	−1.14160
$370$	−8.23240	−0.427982
$371$	−25.0186	−1.29890
$372$	9.90170	0.513379
$373$	4.48849	0.232405	0.116203	−	0.993226i	$-0.462928\pi$
$373$	4.48849	0.232405	0.116203	+	0.993226i	$0.462928\pi$
$374$	3.74726	0.193766
$375$	−5.85698	−0.302453
$376$	6.58914	0.339809
$377$	−21.3498	−1.09957
$378$	0.646846	0.0332702
$379$	4.22047	0.216791	0.108395	−	0.994108i	$-0.465429\pi$
$379$	4.22047	0.216791	0.108395	+	0.994108i	$0.465429\pi$
$380$	7.32835	0.375936
$381$	−0.188629	−0.00966374
$382$	−1.58086	−0.0808838
$383$	36.2351	1.85153	0.925764	−	0.378103i	$-0.123423\pi$
$383$	36.2351	1.85153	0.925764	+	0.378103i	$0.123423\pi$
$384$	2.46647	0.125866
$385$	10.1090	0.515203
$386$	−6.71744	−0.341909
$387$	−1.97657	−0.100475
$388$	−15.5698	−0.790439
$389$	29.9540	1.51873	0.759365	−	0.650665i	$-0.225510\pi$
$389$	29.9540	1.51873	0.759365	+	0.650665i	$0.225510\pi$
$390$	−22.6637	−1.14762
$391$	14.0230	0.709173
$392$	−2.87314	−0.145116
$393$	23.8197	1.20154
$394$	21.2101	1.06855
$395$	−8.91098	−0.448360
$396$	3.02914	0.152220
$397$	−37.0826	−1.86112	−0.930561	−	0.366136i	$-0.880680\pi$
$397$	−37.0826	−1.86112	−0.930561	+	0.366136i	$0.880680\pi$
$398$	5.00444	0.250850
$399$	−17.3424	−0.868205
$400$	5.72510	0.286255
$401$	17.8027	0.889025	0.444513	−	0.895773i	$-0.353377\pi$
$401$	17.8027	0.889025	0.444513	+	0.895773i	$0.353377\pi$
$402$	−24.2934	−1.21164
$403$	11.2639	0.561096
$404$	−4.52955	−0.225353
$405$	−28.6315	−1.42271
$406$	−23.9093	−1.18660
$407$	2.46948	0.122408
$408$	−9.40824	−0.465777
$409$	−5.00761	−0.247611	−0.123805	−	0.992307i	$-0.539510\pi$
$409$	−5.00761	−0.247611	−0.123805	+	0.992307i	$0.539510\pi$
$410$	23.2911	1.15026
$411$	−27.1667	−1.34004
$412$	−7.14110	−0.351817
$413$	−23.0129	−1.13239
$414$	11.3357	0.557117
$415$	−17.8875	−0.878065
$416$	2.80579	0.137565
$417$	−4.19546	−0.205453
$418$	−2.19829	−0.107522
$419$	25.8542	1.26306	0.631529	−	0.775352i	$-0.282427\pi$
$419$	25.8542	1.26306	0.631529	+	0.775352i	$0.282427\pi$
$420$	−25.3807	−1.23845
$421$	0.365338	0.0178055	0.00890274	−	0.999960i	$-0.497166\pi$
$421$	0.365338	0.0178055	0.00890274	+	0.999960i	$0.497166\pi$
$422$	−16.9222	−0.823760
$423$	−20.3174	−0.987864
$424$	7.96225	0.386681
$425$	−21.8382	−1.05931
$426$	23.5094	1.13903
$427$	−44.0155	−2.13006
$428$	5.15726	0.249285
$429$	6.79846	0.328233
$430$	2.09929	0.101237
$431$	−10.8618	−0.523196	−0.261598	−	0.965177i	$-0.584249\pi$
$431$	−10.8618	−0.523196	−0.261598	+	0.965177i	$0.584249\pi$
$432$	−0.205861	−0.00990447
$433$	32.8872	1.58046	0.790229	−	0.612812i	$-0.209962\pi$
$433$	32.8872	1.58046	0.790229	+	0.612812i	$0.209962\pi$
$434$	12.6143	0.605504
$435$	−61.4632	−2.94693
$436$	15.0365	0.720120
$437$	−8.22646	−0.393525
$438$	−32.1373	−1.53558
$439$	−17.1786	−0.819891	−0.409945	−	0.912110i	$-0.634452\pi$
$439$	−17.1786	−0.819891	−0.409945	+	0.912110i	$0.634452\pi$
$440$	−3.21722	−0.153375
$441$	8.85924	0.421868
$442$	−10.7026	−0.509069
$443$	−8.32989	−0.395765	−0.197883	−	0.980226i	$-0.563406\pi$
$443$	−8.32989	−0.395765	−0.197883	+	0.980226i	$0.563406\pi$
$444$	−6.20014	−0.294245
$445$	43.1440	2.04522
$446$	−8.58313	−0.406423
$447$	5.04670	0.238701
$448$	3.14216	0.148453
$449$	33.1715	1.56546	0.782731	−	0.622360i	$-0.213826\pi$
$449$	33.1715	1.56546	0.782731	+	0.622360i	$0.213826\pi$
$450$	−17.6531	−0.832177
$451$	−6.98665	−0.328989
$452$	1.48840	0.0700082
$453$	−8.31400	−0.390626
$454$	6.83025	0.320560
$455$	−28.8724	−1.35356
$456$	5.51926	0.258463
$457$	−15.8107	−0.739595	−0.369798	−	0.929112i	$-0.620573\pi$
$457$	−15.8107	−0.739595	−0.369798	+	0.929112i	$0.620573\pi$
$458$	−14.2700	−0.666795
$459$	0.785247	0.0366522
$460$	−12.0395	−0.561345
$461$	−15.9938	−0.744904	−0.372452	−	0.928051i	$-0.621483\pi$
$461$	−15.9938	−0.744904	−0.372452	+	0.928051i	$0.621483\pi$
$462$	7.61348	0.354211
$463$	−22.0800	−1.02614	−0.513072	−	0.858346i	$-0.671493\pi$
$463$	−22.0800	−1.02614	−0.513072	+	0.858346i	$0.671493\pi$
$464$	7.60920	0.353248
$465$	32.4273	1.50378
$466$	9.05319	0.419381
$467$	20.6721	0.956589	0.478295	−	0.878199i	$-0.341255\pi$
$467$	20.6721	0.956589	0.478295	+	0.878199i	$0.341255\pi$
$468$	−8.65155	−0.399918
$469$	−30.9486	−1.42907
$470$	21.5789	0.995360
$471$	−19.3389	−0.891090
$472$	7.32393	0.337111
$473$	−0.629728	−0.0289549
$474$	−6.71120	−0.308256
$475$	12.8112	0.587816
$476$	−11.9856	−0.549360
$477$	−24.5513	−1.12413
$478$	−6.61579	−0.302599
$479$	29.9794	1.36979	0.684896	−	0.728641i	$-0.259848\pi$
$479$	29.9794	1.36979	0.684896	+	0.728641i	$0.259848\pi$
$480$	8.07748	0.368685
$481$	−7.05311	−0.321594
$482$	30.7882	1.40236
$483$	28.4912	1.29640
$484$	−10.0349	−0.456133
$485$	−50.9900	−2.31534
$486$	−22.1810	−1.00615
$487$	3.00064	0.135972	0.0679859	−	0.997686i	$-0.478343\pi$
$487$	3.00064	0.135972	0.0679859	+	0.997686i	$0.478343\pi$
$488$	14.0080	0.634114
$489$	−24.2887	−1.09837
$490$	−9.40932	−0.425070
$491$	21.0328	0.949197	0.474598	−	0.880203i	$-0.342593\pi$
$491$	21.0328	0.949197	0.474598	+	0.880203i	$0.342593\pi$
$492$	17.5414	0.790827
$493$	−29.0250	−1.30722
$494$	6.27856	0.282486
$495$	9.92018	0.445879
$496$	−4.01453	−0.180258
$497$	29.9498	1.34343
$498$	−13.4718	−0.603686
$499$	20.9505	0.937874	0.468937	−	0.883231i	$-0.344637\pi$
$499$	20.9505	0.937874	0.468937	+	0.883231i	$0.344637\pi$
$500$	2.37464	0.106197
$501$	−48.9374	−2.18636
$502$	−5.78025	−0.257985
$503$	12.3271	0.549639	0.274819	−	0.961496i	$-0.411382\pi$
$503$	12.3271	0.549639	0.274819	+	0.961496i	$0.411382\pi$
$504$	−9.68872	−0.431570
$505$	−14.8339	−0.660100
$506$	3.61150	0.160551
$507$	12.6469	0.561670
$508$	0.0764772	0.00339313
$509$	−29.2834	−1.29796	−0.648982	−	0.760803i	$-0.724805\pi$
$509$	−29.2834	−1.29796	−0.648982	+	0.760803i	$0.724805\pi$
$510$	−30.8112	−1.36434
$511$	−40.9413	−1.81114
$512$	−1.00000	−0.0441942
$513$	−0.460658	−0.0203385
$514$	27.6636	1.22019
$515$	−23.3865	−1.03053
$516$	1.58106	0.0696023
$517$	−6.47305	−0.284684
$518$	−7.89866	−0.347047
$519$	49.9997	2.19474
$520$	9.18873	0.402953
$521$	37.7439	1.65359	0.826795	−	0.562503i	$-0.190162\pi$
$521$	37.7439	1.65359	0.826795	+	0.562503i	$0.190162\pi$
$522$	−23.4627	−1.02693
$523$	7.07955	0.309567	0.154784	−	0.987948i	$-0.450532\pi$
$523$	7.07955	0.309567	0.154784	+	0.987948i	$0.450532\pi$
$524$	−9.65739	−0.421885
$525$	−44.3697	−1.93645
$526$	2.71825	0.118521
$527$	15.3133	0.667056
$528$	−2.42301	−0.105448
$529$	−9.48502	−0.412392
$530$	26.0757	1.13266
$531$	−22.5831	−0.980022
$532$	7.03126	0.304844
$533$	19.9546	0.864331
$534$	32.4934	1.40613
$535$	16.8896	0.730201
$536$	9.84947	0.425432
$537$	−20.9219	−0.902847
$538$	−6.27644	−0.270596
$539$	2.82252	0.121575
$540$	−0.674177	−0.0290120
$541$	−21.6214	−0.929577	−0.464789	−	0.885422i	$-0.653870\pi$
$541$	−21.6214	−0.929577	−0.464789	+	0.885422i	$0.653870\pi$
$542$	−22.8796	−0.982762
$543$	44.7700	1.92126
$544$	3.81446	0.163544
$545$	49.2435	2.10936
$546$	−21.7449	−0.930597
$547$	−0.876977	−0.0374968	−0.0187484	−	0.999824i	$-0.505968\pi$
$547$	−0.876977	−0.0374968	−0.0187484	+	0.999824i	$0.505968\pi$
$548$	11.0144	0.470513
$549$	−43.1933	−1.84345
$550$	−5.62423	−0.239818
$551$	17.0272	0.725385
$552$	−9.06741	−0.385935
$553$	−8.54973	−0.363572
$554$	−23.9815	−1.01887
$555$	−20.3049	−0.861897
$556$	1.70100	0.0721385
$557$	13.7039	0.580655	0.290327	−	0.956927i	$-0.406236\pi$
$557$	13.7039	0.580655	0.290327	+	0.956927i	$0.406236\pi$
$558$	12.3786	0.524030
$559$	1.79857	0.0760715
$560$	10.2903	0.434845
$561$	9.24248	0.390218
$562$	−8.54627	−0.360503
$563$	−30.7227	−1.29481	−0.647403	−	0.762148i	$-0.724145\pi$
$563$	−30.7227	−1.29481	−0.647403	+	0.762148i	$0.724145\pi$
$564$	16.2519	0.684328
$565$	4.87438	0.205067
$566$	14.3583	0.603526
$567$	−27.4707	−1.15366
$568$	−9.53161	−0.399937
$569$	−15.4933	−0.649512	−0.324756	−	0.945798i	$-0.605282\pi$
$569$	−15.4933	−0.649512	−0.324756	+	0.945798i	$0.605282\pi$
$570$	18.0751	0.757084
$571$	25.2074	1.05490	0.527449	−	0.849587i	$-0.323149\pi$
$571$	25.2074	1.05490	0.527449	+	0.849587i	$0.323149\pi$
$572$	−2.75635	−0.115249
$573$	−3.89914	−0.162889
$574$	22.3469	0.932740
$575$	−21.0470	−0.877722
$576$	3.08346	0.128478
$577$	7.37452	0.307005	0.153503	−	0.988148i	$-0.450945\pi$
$577$	7.37452	0.307005	0.153503	+	0.988148i	$0.450945\pi$
$578$	2.44990	0.101902
$579$	−16.5683	−0.688557
$580$	24.9195	1.03473
$581$	−17.1624	−0.712016
$582$	−38.4025	−1.59184
$583$	−7.82197	−0.323953
$584$	13.0297	0.539172
$585$	−28.3331	−1.17143
$586$	−7.70530	−0.318303
$587$	−14.5507	−0.600573	−0.300287	−	0.953849i	$-0.597082\pi$
$587$	−14.5507	−0.600573	−0.300287	+	0.953849i	$0.597082\pi$
$588$	−7.08652	−0.292243
$589$	−8.98338	−0.370154
$590$	23.9853	0.987459
$591$	52.3139	2.15191
$592$	2.51377	0.103315
$593$	12.5695	0.516168	0.258084	−	0.966123i	$-0.416909\pi$
$593$	12.5695	0.516168	0.258084	+	0.966123i	$0.416909\pi$
$594$	0.202234	0.00829775
$595$	−39.2520	−1.60917
$596$	−2.04612	−0.0838125
$597$	12.3433	0.505177
$598$	−10.3148	−0.421805
$599$	−0.440616	−0.0180031	−0.00900154	−	0.999959i	$-0.502865\pi$
$599$	−0.440616	−0.0180031	−0.00900154	+	0.999959i	$0.502865\pi$
$600$	14.1208	0.576478
$601$	3.32563	0.135655	0.0678276	−	0.997697i	$-0.478393\pi$
$601$	3.32563	0.135655	0.0678276	+	0.997697i	$0.478393\pi$
$602$	2.01419	0.0820923
$603$	−30.3705	−1.23678
$604$	3.37081	0.137156
$605$	−32.8636	−1.33609
$606$	−11.1720	−0.453831
$607$	−19.9711	−0.810602	−0.405301	−	0.914183i	$-0.632833\pi$
$607$	−19.9711	−0.810602	−0.405301	+	0.914183i	$0.632833\pi$
$608$	−2.23772	−0.0907515
$609$	−58.9715	−2.38964
$610$	45.8752	1.85743
$611$	18.4877	0.747933
$612$	−11.7617	−0.475440
$613$	−32.9728	−1.33176	−0.665879	−	0.746060i	$-0.731943\pi$
$613$	−32.9728	−1.33176	−0.665879	+	0.746060i	$0.731943\pi$
$614$	−29.5171	−1.19121
$615$	57.4467	2.31647
$616$	−3.08680	−0.124371
$617$	18.8683	0.759608	0.379804	−	0.925067i	$-0.375991\pi$
$617$	18.8683	0.759608	0.379804	+	0.925067i	$0.375991\pi$
$618$	−17.6133	−0.708511
$619$	−37.5004	−1.50727	−0.753634	−	0.657295i	$-0.771701\pi$
$619$	−37.5004	−1.50727	−0.753634	+	0.657295i	$0.771701\pi$
$620$	−13.1473	−0.528006
$621$	0.756800	0.0303693
$622$	5.56501	0.223137
$623$	41.3949	1.65845
$624$	6.92039	0.277037
$625$	−20.8487	−0.833949
$626$	14.8872	0.595012
$627$	−5.42202	−0.216535
$628$	7.84073	0.312879
$629$	−9.58868	−0.382326
$630$	−31.7298	−1.26415
$631$	−30.0362	−1.19572	−0.597862	−	0.801599i	$-0.703983\pi$
$631$	−30.0362	−1.19572	−0.597862	+	0.801599i	$0.703983\pi$
$632$	2.72098	0.108235
$633$	−41.7381	−1.65894
$634$	−18.1654	−0.721438
$635$	0.250457	0.00993907
$636$	19.6386	0.778723
$637$	−8.06143	−0.319406
$638$	−7.47513	−0.295943
$639$	29.3904	1.16267
$640$	−3.27492	−0.129453
$641$	−15.0203	−0.593266	−0.296633	−	0.954992i	$-0.595864\pi$
$641$	−15.0203	−0.593266	−0.296633	+	0.954992i	$0.595864\pi$
$642$	12.7202	0.502026
$643$	41.3653	1.63129	0.815643	−	0.578555i	$-0.196383\pi$
$643$	41.3653	1.63129	0.815643	+	0.578555i	$0.196383\pi$
$644$	−11.5514	−0.455190
$645$	5.17784	0.203877
$646$	8.53569	0.335832
$647$	5.39998	0.212295	0.106148	−	0.994350i	$-0.466148\pi$
$647$	5.39998	0.212295	0.106148	+	0.994350i	$0.466148\pi$
$648$	8.74264	0.343443
$649$	−7.19490	−0.282424
$650$	16.0634	0.630059
$651$	31.1127	1.21940
$652$	9.84755	0.385660
$653$	−35.4467	−1.38714	−0.693568	−	0.720391i	$-0.743962\pi$
$653$	−35.4467	−1.38714	−0.693568	+	0.720391i	$0.743962\pi$
$654$	37.0872	1.45022
$655$	−31.6272	−1.23578
$656$	−7.11195	−0.277675
$657$	−40.1766	−1.56744
$658$	20.7041	0.807130
$659$	20.4550	0.796813	0.398406	−	0.917209i	$-0.369563\pi$
$659$	20.4550	0.796813	0.398406	+	0.917209i	$0.369563\pi$
$660$	−7.93517	−0.308876
$661$	−46.4193	−1.80550	−0.902750	−	0.430165i	$-0.858455\pi$
$661$	−46.4193	−1.80550	−0.902750	+	0.430165i	$0.858455\pi$
$662$	−1.40218	−0.0544974
$663$	−26.3975	−1.02520
$664$	5.46198	0.211966
$665$	23.0268	0.892942
$666$	−7.75112	−0.300350
$667$	−27.9735	−1.08314
$668$	19.8411	0.767675
$669$	−21.1700	−0.818480
$670$	32.2562	1.24617
$671$	−13.7612	−0.531247
$672$	7.75003	0.298964
$673$	19.7043	0.759544	0.379772	−	0.925080i	$-0.376002\pi$
$673$	19.7043	0.759544	0.379772	+	0.925080i	$0.376002\pi$
$674$	−24.9496	−0.961024
$675$	−1.17857	−0.0453633
$676$	−5.12755	−0.197214
$677$	34.2068	1.31468	0.657338	−	0.753596i	$-0.271683\pi$
$677$	34.2068	1.31468	0.657338	+	0.753596i	$0.271683\pi$
$678$	3.67108	0.140987
$679$	−48.9229	−1.87749
$680$	12.4920	0.479048
$681$	16.8466	0.645563
$682$	3.94380	0.151016
$683$	−32.2718	−1.23484	−0.617422	−	0.786632i	$-0.711823\pi$
$683$	−32.2718	−1.23484	−0.617422	+	0.786632i	$0.711823\pi$
$684$	6.89992	0.263825
$685$	36.0713	1.37822
$686$	12.9672	0.495091
$687$	−35.1966	−1.34283
$688$	−0.641022	−0.0244387
$689$	22.3404	0.851101
$690$	−29.6950	−1.13047
$691$	−3.87743	−0.147504	−0.0737522	−	0.997277i	$-0.523497\pi$
$691$	−3.87743	−0.147504	−0.0737522	+	0.997277i	$0.523497\pi$
$692$	−20.2718	−0.770617
$693$	9.51802	0.361560
$694$	9.67126	0.367116
$695$	5.57064	0.211306
$696$	18.7678	0.711393
$697$	27.1283	1.02756
$698$	−4.65247	−0.176099
$699$	22.3294	0.844575
$700$	17.9892	0.679926
$701$	−18.3111	−0.691601	−0.345801	−	0.938308i	$-0.612393\pi$
$701$	−18.3111	−0.691601	−0.345801	+	0.938308i	$0.612393\pi$
$702$	−0.577601	−0.0218002
$703$	5.62511	0.212155
$704$	0.982382	0.0370249
$705$	53.2236	2.00452
$706$	26.3892	0.993172
$707$	−14.2325	−0.535270
$708$	18.0642	0.678896
$709$	−36.8687	−1.38463	−0.692317	−	0.721594i	$-0.743410\pi$
$709$	−36.8687	−1.38463	−0.692317	+	0.721594i	$0.743410\pi$
$710$	−31.2153	−1.17149
$711$	−8.39003	−0.314651
$712$	−13.1741	−0.493719
$713$	14.7585	0.552710
$714$	−29.5622	−1.10634
$715$	−9.02684	−0.337585
$716$	8.48254	0.317007
$717$	−16.3176	−0.609393
$718$	21.8784	0.816495
$719$	−24.5476	−0.915470	−0.457735	−	0.889089i	$-0.651339\pi$
$719$	−24.5476	−0.915470	−0.457735	+	0.889089i	$0.651339\pi$
$720$	10.0981	0.376334
$721$	−22.4385	−0.835652
$722$	13.9926	0.520751
$723$	75.9380	2.82417
$724$	−18.1514	−0.674593
$725$	43.5634	1.61790
$726$	−24.7508	−0.918589
$727$	1.43312	0.0531515	0.0265757	−	0.999647i	$-0.491540\pi$
$727$	1.43312	0.0531515	0.0265757	+	0.999647i	$0.491540\pi$
$728$	8.81622	0.326751
$729$	−28.4809	−1.05485
$730$	42.6712	1.57933
$731$	2.44515	0.0904372
$732$	34.5504	1.27702
$733$	−38.4195	−1.41906	−0.709528	−	0.704677i	$-0.751092\pi$
$733$	−38.4195	−1.41906	−0.709528	+	0.704677i	$0.751092\pi$
$734$	17.8571	0.659117
$735$	−23.2078	−0.856032
$736$	3.67627	0.135509
$737$	−9.67593	−0.356418
$738$	21.9294	0.807234
$739$	−32.3114	−1.18859	−0.594297	−	0.804246i	$-0.702570\pi$
$739$	−32.3114	−1.18859	−0.594297	+	0.804246i	$0.702570\pi$
$740$	8.23240	0.302629
$741$	15.4859	0.568888
$742$	25.0186	0.918463
$743$	−25.9135	−0.950674	−0.475337	−	0.879804i	$-0.657674\pi$
$743$	−25.9135	−0.950674	−0.475337	+	0.879804i	$0.657674\pi$
$744$	−9.90170	−0.363014
$745$	−6.70089	−0.245502
$746$	−4.48849	−0.164335
$747$	−16.8418	−0.616210
$748$	−3.74726	−0.137013
$749$	16.2049	0.592114
$750$	5.85698	0.213867
$751$	20.0499	0.731632	0.365816	−	0.930687i	$-0.380790\pi$
$751$	20.0499	0.731632	0.365816	+	0.930687i	$0.380790\pi$
$752$	−6.58914	−0.240281
$753$	−14.2568	−0.519547
$754$	21.3498	0.777514
$755$	11.0391	0.401755
$756$	−0.646846	−0.0235256
$757$	7.04341	0.255997	0.127999	−	0.991774i	$-0.459145\pi$
$757$	7.04341	0.255997	0.127999	+	0.991774i	$0.459145\pi$
$758$	−4.22047	−0.153294
$759$	8.90766	0.323327
$760$	−7.32835	−0.265827
$761$	9.66377	0.350311	0.175156	−	0.984541i	$-0.443957\pi$
$761$	9.66377	0.350311	0.175156	+	0.984541i	$0.443957\pi$
$762$	0.188629	0.00683329
$763$	47.2472	1.71046
$764$	1.58086	0.0571935
$765$	−38.5188	−1.39265
$766$	−36.2351	−1.30923
$767$	20.5494	0.741996
$768$	−2.46647	−0.0890010
$769$	−11.2994	−0.407466	−0.203733	−	0.979026i	$-0.565307\pi$
$769$	−11.2994	−0.407466	−0.203733	+	0.979026i	$0.565307\pi$
$770$	−10.1090	−0.364303
$771$	68.2313	2.45729
$772$	6.71744	0.241766
$773$	8.60726	0.309582	0.154791	−	0.987947i	$-0.450530\pi$
$773$	8.60726	0.309582	0.154791	+	0.987947i	$0.450530\pi$
$774$	1.97657	0.0710462
$775$	−22.9836	−0.825594
$776$	15.5698	0.558925
$777$	−19.4818	−0.698905
$778$	−29.9540	−1.07390
$779$	−15.9145	−0.570198
$780$	22.6637	0.811491
$781$	9.36368	0.335059
$782$	−14.0230	−0.501461
$783$	−1.56643	−0.0559798
$784$	2.87314	0.102612
$785$	25.6778	0.916479
$786$	−23.8197	−0.849619
$787$	−43.8189	−1.56197	−0.780987	−	0.624547i	$-0.785283\pi$
$787$	−43.8189	−1.56197	−0.780987	+	0.624547i	$0.785283\pi$
$788$	−21.2101	−0.755577
$789$	6.70447	0.238685
$790$	8.91098	0.317038
$791$	4.67677	0.166287
$792$	−3.02914	−0.107636
$793$	39.3036	1.39571
$794$	37.0826	1.31601
$795$	64.3150	2.28102
$796$	−5.00444	−0.177378
$797$	−1.69817	−0.0601523	−0.0300762	−	0.999548i	$-0.509575\pi$
$797$	−1.69817	−0.0601523	−0.0300762	+	0.999548i	$0.509575\pi$
$798$	17.3424	0.613914
$799$	25.1340	0.889177
$800$	−5.72510	−0.202413
$801$	40.6217	1.43530
$802$	−17.8027	−0.628636
$803$	−12.8001	−0.451707
$804$	24.2934	0.856762
$805$	−37.8300	−1.33333
$806$	−11.2639	−0.396754
$807$	−15.4806	−0.544944
$808$	4.52955	0.159349
$809$	−33.8013	−1.18839	−0.594194	−	0.804321i	$-0.702529\pi$
$809$	−33.8013	−1.18839	−0.594194	+	0.804321i	$0.702529\pi$
$810$	28.6315	1.00601
$811$	25.0039	0.878005	0.439002	−	0.898486i	$-0.355332\pi$
$811$	25.0039	0.878005	0.439002	+	0.898486i	$0.355332\pi$
$812$	23.9093	0.839051
$813$	−56.4317	−1.97915
$814$	−2.46948	−0.0865553
$815$	32.2500	1.12967
$816$	9.40824	0.329354
$817$	−1.43443	−0.0501842
$818$	5.00761	0.175087
$819$	−27.1845	−0.949904
$820$	−23.2911	−0.813360
$821$	−5.00383	−0.174635	−0.0873174	−	0.996181i	$-0.527829\pi$
$821$	−5.00383	−0.174635	−0.0873174	+	0.996181i	$0.527829\pi$
$822$	27.1667	0.947548
$823$	10.2183	0.356187	0.178093	−	0.984014i	$-0.443007\pi$
$823$	10.2183	0.356187	0.178093	+	0.984014i	$0.443007\pi$
$824$	7.14110	0.248772
$825$	−13.8720	−0.482961
$826$	23.0129	0.800723
$827$	55.1960	1.91935	0.959676	−	0.281107i	$-0.0907016\pi$
$827$	55.1960	1.91935	0.959676	+	0.281107i	$0.0907016\pi$
$828$	−11.3357	−0.393941
$829$	39.5457	1.37348	0.686740	−	0.726903i	$-0.259041\pi$
$829$	39.5457	1.37348	0.686740	+	0.726903i	$0.259041\pi$
$830$	17.8875	0.620886
$831$	−59.1495	−2.05187
$832$	−2.80579	−0.0972732
$833$	−10.9595	−0.379724
$834$	4.19546	0.145277
$835$	64.9780	2.24866
$836$	2.19829	0.0760296
$837$	0.826433	0.0285657
$838$	−25.8542	−0.893118
$839$	10.8150	0.373375	0.186687	−	0.982419i	$-0.440225\pi$
$839$	10.8150	0.373375	0.186687	+	0.982419i	$0.440225\pi$
$840$	25.3807	0.875718
$841$	28.8999	0.996547
$842$	−0.365338	−0.0125904
$843$	−21.0791	−0.726003
$844$	16.9222	0.582487
$845$	−16.7923	−0.577673
$846$	20.3174	0.698525
$847$	−31.5313	−1.08343
$848$	−7.96225	−0.273425
$849$	35.4144	1.21542
$850$	21.8382	0.749043
$851$	−9.24131	−0.316788
$852$	−23.5094	−0.805419
$853$	7.33883	0.251277	0.125638	−	0.992076i	$-0.459902\pi$
$853$	7.33883	0.251277	0.125638	+	0.992076i	$0.459902\pi$
$854$	44.0155	1.50618
$855$	22.5967	0.772791
$856$	−5.15726	−0.176271
$857$	−0.238319	−0.00814081	−0.00407041	−	0.999992i	$-0.501296\pi$
$857$	−0.238319	−0.00814081	−0.00407041	+	0.999992i	$0.501296\pi$
$858$	−6.79846	−0.232096
$859$	−1.82681	−0.0623300	−0.0311650	−	0.999514i	$-0.509922\pi$
$859$	−1.82681	−0.0623300	−0.0311650	+	0.999514i	$0.509922\pi$
$860$	−2.09929	−0.0715854
$861$	55.1178	1.87841
$862$	10.8618	0.369955
$863$	25.1335	0.855554	0.427777	−	0.903884i	$-0.359297\pi$
$863$	25.1335	0.855554	0.427777	+	0.903884i	$0.359297\pi$
$864$	0.205861	0.00700352
$865$	−66.3884	−2.25727
$866$	−32.8872	−1.11755
$867$	6.04260	0.205217
$868$	−12.6143	−0.428156
$869$	−2.67304	−0.0906766
$870$	61.4632	2.08380
$871$	27.6355	0.936394
$872$	−15.0365	−0.509202
$873$	−48.0090	−1.62486
$874$	8.22646	0.278264
$875$	7.46149	0.252245
$876$	32.1373	1.08582
$877$	−47.7324	−1.61181	−0.805905	−	0.592046i	$-0.798321\pi$
$877$	−47.7324	−1.61181	−0.805905	+	0.592046i	$0.798321\pi$
$878$	17.1786	0.579750
$879$	−19.0049	−0.641018
$880$	3.21722	0.108452
$881$	−6.32395	−0.213059	−0.106530	−	0.994310i	$-0.533974\pi$
$881$	−6.32395	−0.213059	−0.106530	+	0.994310i	$0.533974\pi$
$882$	−8.85924	−0.298306
$883$	−55.1770	−1.85685	−0.928426	−	0.371516i	$-0.878838\pi$
$883$	−55.1770	−1.85685	−0.928426	+	0.371516i	$0.878838\pi$
$884$	10.7026	0.359966
$885$	59.1590	1.98861
$886$	8.32989	0.279848
$887$	0.916817	0.0307837	0.0153919	−	0.999882i	$-0.495100\pi$
$887$	0.916817	0.0307837	0.0153919	+	0.999882i	$0.495100\pi$
$888$	6.20014	0.208063
$889$	0.240303	0.00805952
$890$	−43.1440	−1.44619
$891$	−8.58861	−0.287729
$892$	8.58313	0.287385
$893$	−14.7446	−0.493410
$894$	−5.04670	−0.168787
$895$	27.7796	0.928571
$896$	−3.14216	−0.104972
$897$	−25.4412	−0.849458
$898$	−33.1715	−1.10695
$899$	−30.5473	−1.01881
$900$	17.6531	0.588438
$901$	30.3717	1.01183
$902$	6.98665	0.232630
$903$	4.96794	0.165323
$904$	−1.48840	−0.0495033
$905$	−59.4445	−1.97600
$906$	8.31400	0.276214
$907$	−55.4329	−1.84062	−0.920310	−	0.391190i	$-0.872064\pi$
$907$	−55.4329	−1.84062	−0.920310	+	0.391190i	$0.872064\pi$
$908$	−6.83025	−0.226670
$909$	−13.9667	−0.463246
$910$	28.8724	0.957112
$911$	46.5221	1.54134	0.770672	−	0.637232i	$-0.219921\pi$
$911$	46.5221	1.54134	0.770672	+	0.637232i	$0.219921\pi$
$912$	−5.51926	−0.182761
$913$	−5.36575	−0.177580
$914$	15.8107	0.522973
$915$	113.150	3.74062
$916$	14.2700	0.471495
$917$	−30.3450	−1.00208
$918$	−0.785247	−0.0259170
$919$	39.8893	1.31583	0.657914	−	0.753093i	$-0.271439\pi$
$919$	39.8893	1.31583	0.657914	+	0.753093i	$0.271439\pi$
$920$	12.0395	0.396931
$921$	−72.8029	−2.39894
$922$	15.9938	0.526727
$923$	−26.7437	−0.880279
$924$	−7.61348	−0.250465
$925$	14.3916	0.473193
$926$	22.0800	0.725593
$927$	−22.0193	−0.723209
$928$	−7.60920	−0.249784
$929$	−14.6400	−0.480322	−0.240161	−	0.970733i	$-0.577200\pi$
$929$	−14.6400	−0.480322	−0.240161	+	0.970733i	$0.577200\pi$
$930$	−32.4273	−1.06333
$931$	6.42929	0.210711
$932$	−9.05319	−0.296547
$933$	13.7259	0.449366
$934$	−20.6721	−0.676411
$935$	−12.2720	−0.401336
$936$	8.65155	0.282785
$937$	−36.0555	−1.17788	−0.588940	−	0.808177i	$-0.700455\pi$
$937$	−36.0555	−1.17788	−0.588940	+	0.808177i	$0.700455\pi$
$938$	30.9486	1.01051
$939$	36.7188	1.19827
$940$	−21.5789	−0.703826
$941$	32.9557	1.07432	0.537162	−	0.843479i	$-0.319496\pi$
$941$	32.9557	1.07432	0.537162	+	0.843479i	$0.319496\pi$
$942$	19.3389	0.630096
$943$	26.1455	0.851414
$944$	−7.32393	−0.238374
$945$	−2.11837	−0.0689105
$946$	0.629728	0.0204742
$947$	−50.0809	−1.62741	−0.813705	−	0.581278i	$-0.802553\pi$
$947$	−50.0809	−1.62741	−0.813705	+	0.581278i	$0.802553\pi$
$948$	6.71120	0.217970
$949$	36.5586	1.18674
$950$	−12.8112	−0.415649
$951$	−44.8043	−1.45288
$952$	11.9856	0.388456
$953$	−26.2850	−0.851456	−0.425728	−	0.904851i	$-0.639982\pi$
$953$	−26.2850	−0.851456	−0.425728	+	0.904851i	$0.639982\pi$
$954$	24.5513	0.794878
$955$	5.17719	0.167530
$956$	6.61579	0.213970
$957$	−18.4372	−0.595989
$958$	−29.9794	−0.968589
$959$	34.6090	1.11758
$960$	−8.07748	−0.260700
$961$	−14.8836	−0.480115
$962$	7.05311	0.227401
$963$	15.9022	0.512442
$964$	−30.7882	−0.991620
$965$	21.9991	0.708175
$966$	−28.4912	−0.916690
$967$	22.5092	0.723847	0.361924	−	0.932208i	$-0.382120\pi$
$967$	22.5092	0.723847	0.361924	+	0.932208i	$0.382120\pi$
$968$	10.0349	0.322535
$969$	21.0530	0.676320
$970$	50.9900	1.63719
$971$	−10.2150	−0.327815	−0.163908	−	0.986476i	$-0.552410\pi$
$971$	−10.2150	−0.327815	−0.163908	+	0.986476i	$0.552410\pi$
$972$	22.1810	0.711457
$973$	5.34481	0.171347
$974$	−3.00064	−0.0961466
$975$	39.6199	1.26885
$976$	−14.0080	−0.448387
$977$	5.68069	0.181741	0.0908707	−	0.995863i	$-0.471035\pi$
$977$	5.68069	0.181741	0.0908707	+	0.995863i	$0.471035\pi$
$978$	24.2887	0.776666
$979$	12.9420	0.413627
$980$	9.40932	0.300570
$981$	46.3646	1.48031
$982$	−21.0328	−0.671183
$983$	−28.9212	−0.922444	−0.461222	−	0.887285i	$-0.652589\pi$
$983$	−28.9212	−0.922444	−0.461222	+	0.887285i	$0.652589\pi$
$984$	−17.5414	−0.559199
$985$	−69.4613	−2.21322
$986$	29.0250	0.924343
$987$	51.0660	1.62545
$988$	−6.27856	−0.199748
$989$	2.35657	0.0749346
$990$	−9.92018	−0.315284
$991$	46.6140	1.48074	0.740371	−	0.672198i	$-0.234650\pi$
$991$	46.6140	1.48074	0.740371	+	0.672198i	$0.234650\pi$
$992$	4.01453	0.127461
$993$	−3.45844	−0.109750
$994$	−29.9498	−0.949950
$995$	−16.3891	−0.519570
$996$	13.4718	0.426870
$997$	−29.9610	−0.948876	−0.474438	−	0.880289i	$-0.657349\pi$
$997$	−29.9610	−0.948876	−0.474438	+	0.880289i	$0.657349\pi$
$998$	−20.9505	−0.663177
$999$	−0.517486	−0.0163725

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6038.2.a.c.1.9	✓	57

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6038.2.a.c.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.46647 q^{3} +1.00000 q^{4} +3.27492 q^{5} +2.46647 q^{6} +3.14216 q^{7} -1.00000 q^{8} +3.08346 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.46647 q^{3} +1.00000 q^{4} +3.27492 q^{5} +2.46647 q^{6} +3.14216 q^{7} -1.00000 q^{8} +3.08346 q^{9} -3.27492 q^{10} +0.982382 q^{11} -2.46647 q^{12} -2.80579 q^{13} -3.14216 q^{14} -8.07748 q^{15} +1.00000 q^{16} -3.81446 q^{17} -3.08346 q^{18} +2.23772 q^{19} +3.27492 q^{20} -7.75003 q^{21} -0.982382 q^{22} -3.67627 q^{23} +2.46647 q^{24} +5.72510 q^{25} +2.80579 q^{26} -0.205861 q^{27} +3.14216 q^{28} +7.60920 q^{29} +8.07748 q^{30} -4.01453 q^{31} -1.00000 q^{32} -2.42301 q^{33} +3.81446 q^{34} +10.2903 q^{35} +3.08346 q^{36} +2.51377 q^{37} -2.23772 q^{38} +6.92039 q^{39} -3.27492 q^{40} -7.11195 q^{41} +7.75003 q^{42} -0.641022 q^{43} +0.982382 q^{44} +10.0981 q^{45} +3.67627 q^{46} -6.58914 q^{47} -2.46647 q^{48} +2.87314 q^{49} -5.72510 q^{50} +9.40824 q^{51} -2.80579 q^{52} -7.96225 q^{53} +0.205861 q^{54} +3.21722 q^{55} -3.14216 q^{56} -5.51926 q^{57} -7.60920 q^{58} -7.32393 q^{59} -8.07748 q^{60} -14.0080 q^{61} +4.01453 q^{62} +9.68872 q^{63} +1.00000 q^{64} -9.18873 q^{65} +2.42301 q^{66} -9.84947 q^{67} -3.81446 q^{68} +9.06741 q^{69} -10.2903 q^{70} +9.53161 q^{71} -3.08346 q^{72} -13.0297 q^{73} -2.51377 q^{74} -14.1208 q^{75} +2.23772 q^{76} +3.08680 q^{77} -6.92039 q^{78} -2.72098 q^{79} +3.27492 q^{80} -8.74264 q^{81} +7.11195 q^{82} -5.46198 q^{83} -7.75003 q^{84} -12.4920 q^{85} +0.641022 q^{86} -18.7678 q^{87} -0.982382 q^{88} +13.1741 q^{89} -10.0981 q^{90} -8.81622 q^{91} -3.67627 q^{92} +9.90170 q^{93} +6.58914 q^{94} +7.32835 q^{95} +2.46647 q^{96} -15.5698 q^{97} -2.87314 q^{98} +3.02914 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 57 q - 57 q^{2} - 5 q^{3} + 57 q^{4} - 15 q^{5} + 5 q^{6} - 28 q^{7} - 57 q^{8} + 50 q^{9}+O(q^{10}) \) 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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