LMFDB - Embedded newform 4031.2.a.c.1.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.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:	$32.1876970548$
Analytic rank:	$1$
Dimension:	$61$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.23
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.727508 q^{2} +2.55135 q^{3} -1.47073 q^{4} +1.88009 q^{5} -1.85613 q^{6} -3.30412 q^{7} +2.52498 q^{8} +3.50938 q^{9} +O(q^{10})$	\(q-0.727508 q^{2} +2.55135 q^{3} -1.47073 q^{4} +1.88009 q^{5} -1.85613 q^{6} -3.30412 q^{7} +2.52498 q^{8} +3.50938 q^{9} -1.36778 q^{10} +3.99856 q^{11} -3.75235 q^{12} -3.84765 q^{13} +2.40377 q^{14} +4.79677 q^{15} +1.10452 q^{16} -6.88880 q^{17} -2.55310 q^{18} -3.14778 q^{19} -2.76511 q^{20} -8.42996 q^{21} -2.90899 q^{22} +6.97776 q^{23} +6.44212 q^{24} -1.46526 q^{25} +2.79919 q^{26} +1.29962 q^{27} +4.85948 q^{28} -1.00000 q^{29} -3.48969 q^{30} -4.04279 q^{31} -5.85352 q^{32} +10.2017 q^{33} +5.01165 q^{34} -6.21205 q^{35} -5.16137 q^{36} -2.32300 q^{37} +2.29004 q^{38} -9.81669 q^{39} +4.74720 q^{40} +0.551042 q^{41} +6.13286 q^{42} -1.16844 q^{43} -5.88082 q^{44} +6.59796 q^{45} -5.07637 q^{46} -4.20588 q^{47} +2.81802 q^{48} +3.91721 q^{49} +1.06599 q^{50} -17.5757 q^{51} +5.65886 q^{52} -1.62481 q^{53} -0.945481 q^{54} +7.51766 q^{55} -8.34285 q^{56} -8.03110 q^{57} +0.727508 q^{58} +2.94617 q^{59} -7.05477 q^{60} -1.29481 q^{61} +2.94116 q^{62} -11.5954 q^{63} +2.04944 q^{64} -7.23393 q^{65} -7.42184 q^{66} +1.01233 q^{67} +10.1316 q^{68} +17.8027 q^{69} +4.51931 q^{70} -10.7801 q^{71} +8.86114 q^{72} -5.65214 q^{73} +1.69000 q^{74} -3.73838 q^{75} +4.62955 q^{76} -13.2117 q^{77} +7.14172 q^{78} -6.01250 q^{79} +2.07660 q^{80} -7.21237 q^{81} -0.400887 q^{82} -3.30215 q^{83} +12.3982 q^{84} -12.9516 q^{85} +0.850052 q^{86} -2.55135 q^{87} +10.0963 q^{88} +5.98023 q^{89} -4.80007 q^{90} +12.7131 q^{91} -10.2624 q^{92} -10.3146 q^{93} +3.05981 q^{94} -5.91812 q^{95} -14.9344 q^{96} +9.64879 q^{97} -2.84980 q^{98} +14.0325 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) $ 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9} - 16 q^{10} - 3 q^{11} - 18 q^{12} - 28 q^{13} - 14 q^{14} - 12 q^{15} + 11 q^{16} - 21 q^{17} - 17 q^{18} - 36 q^{19} - 16 q^{20} - 12 q^{21} - 42 q^{22} - 15 q^{23} - 28 q^{24} - 16 q^{25} - 13 q^{26} - 10 q^{27} - 25 q^{28} - 61 q^{29} - 12 q^{30} - 18 q^{31} - 3 q^{32} - 42 q^{33} - 22 q^{34} - 29 q^{35} - 38 q^{36} - 30 q^{37} - 27 q^{38} - 31 q^{39} - 22 q^{40} - 28 q^{41} - 9 q^{42} - 58 q^{43} - 2 q^{44} - 31 q^{45} - 40 q^{46} - 6 q^{47} - 37 q^{48} - 37 q^{49} - 15 q^{50} - 44 q^{51} - 43 q^{52} - 27 q^{53} - 18 q^{54} - 38 q^{55} - 22 q^{56} - 50 q^{57} + q^{58} - 24 q^{59} + 6 q^{60} - 76 q^{61} - 17 q^{62} - 6 q^{63} - 60 q^{64} - 65 q^{65} - 7 q^{66} - 45 q^{67} - 31 q^{68} - 16 q^{69} - 48 q^{70} - 28 q^{71} - 40 q^{72} - 50 q^{73} - 17 q^{74} - 35 q^{75} - 100 q^{76} + q^{77} - 6 q^{78} - 66 q^{79} - 10 q^{80} - 63 q^{81} - 5 q^{82} - 9 q^{83} - 24 q^{84} - 77 q^{85} + 29 q^{86} + 4 q^{87} - 62 q^{88} - 30 q^{89} + 50 q^{90} - 52 q^{91} - 53 q^{92} - 42 q^{93} - 92 q^{94} - 20 q^{95} - 47 q^{96} - 34 q^{97} + 36 q^{98} - 29 q^{99}+O(q^{100}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9 - 16 * q^10 - 3 * q^11 - 18 * q^12 - 28 * q^13 - 14 * q^14 - 12 * q^15 + 11 * q^16 - 21 * q^17 - 17 * q^18 - 36 * q^19 - 16 * q^20 - 12 * q^21 - 42 * q^22 - 15 * q^23 - 28 * q^24 - 16 * q^25 - 13 * q^26 - 10 * q^27 - 25 * q^28 - 61 * q^29 - 12 * q^30 - 18 * q^31 - 3 * q^32 - 42 * q^33 - 22 * q^34 - 29 * q^35 - 38 * q^36 - 30 * q^37 - 27 * q^38 - 31 * q^39 - 22 * q^40 - 28 * q^41 - 9 * q^42 - 58 * q^43 - 2 * q^44 - 31 * q^45 - 40 * q^46 - 6 * q^47 - 37 * q^48 - 37 * q^49 - 15 * q^50 - 44 * q^51 - 43 * q^52 - 27 * q^53 - 18 * q^54 - 38 * q^55 - 22 * q^56 - 50 * q^57 + q^58 - 24 * q^59 + 6 * q^60 - 76 * q^61 - 17 * q^62 - 6 * q^63 - 60 * q^64 - 65 * q^65 - 7 * q^66 - 45 * q^67 - 31 * q^68 - 16 * q^69 - 48 * q^70 - 28 * q^71 - 40 * q^72 - 50 * q^73 - 17 * q^74 - 35 * q^75 - 100 * q^76 + q^77 - 6 * q^78 - 66 * q^79 - 10 * q^80 - 63 * q^81 - 5 * q^82 - 9 * q^83 - 24 * q^84 - 77 * q^85 + 29 * q^86 + 4 * q^87 - 62 * q^88 - 30 * q^89 + 50 * q^90 - 52 * q^91 - 53 * q^92 - 42 * q^93 - 92 * q^94 - 20 * q^95 - 47 * q^96 - 34 * q^97 + 36 * q^98 - 29 * 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 $

$2$	−0.727508	−0.514426	−0.257213	−	0.966355i	$-0.582804\pi$
$2$	−0.727508	−0.514426	−0.257213	+	0.966355i	$0.582804\pi$
$3$	2.55135	1.47302	0.736511	−	0.676425i	$-0.236472\pi$
$3$	2.55135	1.47302	0.736511	+	0.676425i	$0.236472\pi$
$4$	−1.47073	−0.735366
$5$	1.88009	0.840802	0.420401	−	0.907338i	$-0.361889\pi$
$5$	1.88009	0.840802	0.420401	+	0.907338i	$0.361889\pi$
$6$	−1.85613	−0.757760
$7$	−3.30412	−1.24884	−0.624420	−	0.781089i	$-0.714665\pi$
$7$	−3.30412	−1.24884	−0.624420	+	0.781089i	$0.714665\pi$
$8$	2.52498	0.892717
$9$	3.50938	1.16979
$10$	−1.36778	−0.432530
$11$	3.99856	1.20561	0.602806	−	0.797888i	$-0.294049\pi$
$11$	3.99856	1.20561	0.602806	+	0.797888i	$0.294049\pi$
$12$	−3.75235	−1.08321
$13$	−3.84765	−1.06715	−0.533573	−	0.845754i	$-0.679151\pi$
$13$	−3.84765	−1.06715	−0.533573	+	0.845754i	$0.679151\pi$
$14$	2.40377	0.642435
$15$	4.79677	1.23852
$16$	1.10452	0.276130
$17$	−6.88880	−1.67078	−0.835390	−	0.549658i	$-0.814758\pi$
$17$	−6.88880	−1.67078	−0.835390	+	0.549658i	$0.814758\pi$
$18$	−2.55310	−0.601772
$19$	−3.14778	−0.722151	−0.361076	−	0.932537i	$-0.617590\pi$
$19$	−3.14778	−0.722151	−0.361076	+	0.932537i	$0.617590\pi$
$20$	−2.76511	−0.618298
$21$	−8.42996	−1.83957
$22$	−2.90899	−0.620198
$23$	6.97776	1.45496	0.727482	−	0.686127i	$-0.240691\pi$
$23$	6.97776	1.45496	0.727482	+	0.686127i	$0.240691\pi$
$24$	6.44212	1.31499
$25$	−1.46526	−0.293051
$26$	2.79919	0.548967
$27$	1.29962	0.250111
$28$	4.85948	0.918355
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−3.48969	−0.637127
$31$	−4.04279	−0.726107	−0.363054	−	0.931768i	$-0.618266\pi$
$31$	−4.04279	−0.726107	−0.363054	+	0.931768i	$0.618266\pi$
$32$	−5.85352	−1.03477
$33$	10.2017	1.77589
$34$	5.01165	0.859492
$35$	−6.21205	−1.05003
$36$	−5.16137	−0.860228
$37$	−2.32300	−0.381899	−0.190949	−	0.981600i	$-0.561157\pi$
$37$	−2.32300	−0.381899	−0.190949	+	0.981600i	$0.561157\pi$
$38$	2.29004	0.371493
$39$	−9.81669	−1.57193
$40$	4.74720	0.750599
$41$	0.551042	0.0860583	0.0430292	−	0.999074i	$-0.486299\pi$
$41$	0.551042	0.0860583	0.0430292	+	0.999074i	$0.486299\pi$
$42$	6.13286	0.946321
$43$	−1.16844	−0.178186	−0.0890930	−	0.996023i	$-0.528397\pi$
$43$	−1.16844	−0.178186	−0.0890930	+	0.996023i	$0.528397\pi$
$44$	−5.88082	−0.886566
$45$	6.59796	0.983566
$46$	−5.07637	−0.748470
$47$	−4.20588	−0.613491	−0.306746	−	0.951792i	$-0.599240\pi$
$47$	−4.20588	−0.613491	−0.306746	+	0.951792i	$0.599240\pi$
$48$	2.81802	0.406745
$49$	3.91721	0.559601
$50$	1.06599	0.150753
$51$	−17.5757	−2.46109
$52$	5.65886	0.784743
$53$	−1.62481	−0.223185	−0.111592	−	0.993754i	$-0.535595\pi$
$53$	−1.62481	−0.223185	−0.111592	+	0.993754i	$0.535595\pi$
$54$	−0.945481	−0.128664
$55$	7.51766	1.01368
$56$	−8.34285	−1.11486
$57$	−8.03110	−1.06374
$58$	0.727508	0.0955264
$59$	2.94617	0.383559	0.191779	−	0.981438i	$-0.438574\pi$
$59$	2.94617	0.383559	0.191779	+	0.981438i	$0.438574\pi$
$60$	−7.05477	−0.910766
$61$	−1.29481	−0.165783	−0.0828917	−	0.996559i	$-0.526416\pi$
$61$	−1.29481	−0.165783	−0.0828917	+	0.996559i	$0.526416\pi$
$62$	2.94116	0.373528
$63$	−11.5954	−1.46089
$64$	2.04944	0.256180
$65$	−7.23393	−0.897259
$66$	−7.42184	−0.913565
$67$	1.01233	0.123675	0.0618376	−	0.998086i	$-0.480304\pi$
$67$	1.01233	0.123675	0.0618376	+	0.998086i	$0.480304\pi$
$68$	10.1316	1.22863
$69$	17.8027	2.14319
$70$	4.51931	0.540161
$71$	−10.7801	−1.27936	−0.639681	−	0.768641i	$-0.720933\pi$
$71$	−10.7801	−1.27936	−0.639681	+	0.768641i	$0.720933\pi$
$72$	8.86114	1.04430
$73$	−5.65214	−0.661533	−0.330766	−	0.943713i	$-0.607307\pi$
$73$	−5.65214	−0.661533	−0.330766	+	0.943713i	$0.607307\pi$
$74$	1.69000	0.196459
$75$	−3.73838	−0.431671
$76$	4.62955	0.531046
$77$	−13.2117	−1.50562
$78$	7.14172	0.808641
$79$	−6.01250	−0.676459	−0.338230	−	0.941064i	$-0.609828\pi$
$79$	−6.01250	−0.676459	−0.338230	+	0.941064i	$0.609828\pi$
$80$	2.07660	0.232171
$81$	−7.21237	−0.801375
$82$	−0.400887	−0.0442706
$83$	−3.30215	−0.362458	−0.181229	−	0.983441i	$-0.558007\pi$
$83$	−3.30215	−0.362458	−0.181229	+	0.983441i	$0.558007\pi$
$84$	12.3982	1.35276
$85$	−12.9516	−1.40480
$86$	0.850052	0.0916634
$87$	−2.55135	−0.273533
$88$	10.0963	1.07627
$89$	5.98023	0.633903	0.316951	−	0.948442i	$-0.397341\pi$
$89$	5.98023	0.633903	0.316951	+	0.948442i	$0.397341\pi$
$90$	−4.80007	−0.505972
$91$	12.7131	1.33269
$92$	−10.2624	−1.06993
$93$	−10.3146	−1.06957
$94$	3.05981	0.315595
$95$	−5.91812	−0.607186
$96$	−14.9344	−1.52423
$97$	9.64879	0.979686	0.489843	−	0.871811i	$-0.337054\pi$
$97$	9.64879	0.979686	0.489843	+	0.871811i	$0.337054\pi$
$98$	−2.84980	−0.287873
$99$	14.0325	1.41032
$100$	2.15500	0.215500
$101$	3.49869	0.348132	0.174066	−	0.984734i	$-0.444309\pi$
$101$	3.49869	0.348132	0.174066	+	0.984734i	$0.444309\pi$
$102$	12.7865	1.26605
$103$	−4.35182	−0.428798	−0.214399	−	0.976746i	$-0.568779\pi$
$103$	−4.35182	−0.428798	−0.214399	+	0.976746i	$0.568779\pi$
$104$	−9.71525	−0.952659
$105$	−15.8491	−1.54671
$106$	1.18206	0.114812
$107$	−9.31327	−0.900348	−0.450174	−	0.892941i	$-0.648638\pi$
$107$	−9.31327	−0.900348	−0.450174	+	0.892941i	$0.648638\pi$
$108$	−1.91139	−0.183924
$109$	13.5294	1.29588	0.647942	−	0.761690i	$-0.275630\pi$
$109$	13.5294	1.29588	0.647942	+	0.761690i	$0.275630\pi$
$110$	−5.46916	−0.521464
$111$	−5.92679	−0.562546
$112$	−3.64947	−0.344842
$113$	−2.20190	−0.207137	−0.103569	−	0.994622i	$-0.533026\pi$
$113$	−2.20190	−0.207137	−0.103569	+	0.994622i	$0.533026\pi$
$114$	5.84268	0.547217
$115$	13.1188	1.22334
$116$	1.47073	0.136554
$117$	−13.5029	−1.24834
$118$	−2.14336	−0.197312
$119$	22.7614	2.08654
$120$	12.1118	1.10565
$121$	4.98850	0.453500
$122$	0.941984	0.0852832
$123$	1.40590	0.126766
$124$	5.94587	0.533955
$125$	−12.1553	−1.08720
$126$	8.43576	0.751517
$127$	20.0076	1.77539	0.887695	−	0.460432i	$-0.152305\pi$
$127$	20.0076	1.77539	0.887695	+	0.460432i	$0.152305\pi$
$128$	10.2160	0.902980
$129$	−2.98111	−0.262472
$130$	5.26274	0.461573
$131$	−9.75001	−0.851863	−0.425931	−	0.904756i	$-0.640053\pi$
$131$	−9.75001	−0.851863	−0.425931	+	0.904756i	$0.640053\pi$
$132$	−15.0040	−1.30593
$133$	10.4007	0.901851
$134$	−0.736475	−0.0636217
$135$	2.44340	0.210294
$136$	−17.3941	−1.49153
$137$	2.58885	0.221180	0.110590	−	0.993866i	$-0.464726\pi$
$137$	2.58885	0.221180	0.110590	+	0.993866i	$0.464726\pi$
$138$	−12.9516	−1.10251
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	9.13626	0.772155
$141$	−10.7307	−0.903686
$142$	7.84260	0.658136
$143$	−15.3851	−1.28656
$144$	3.87618	0.323015
$145$	−1.88009	−0.156133
$146$	4.11197	0.340309
$147$	9.99417	0.824305
$148$	3.41651	0.280836
$149$	−13.1792	−1.07968	−0.539841	−	0.841767i	$-0.681516\pi$
$149$	−13.1792	−1.07968	−0.539841	+	0.841767i	$0.681516\pi$
$150$	2.71970	0.222063
$151$	0.0927162	0.00754514	0.00377257	−	0.999993i	$-0.498799\pi$
$151$	0.0927162	0.00754514	0.00377257	+	0.999993i	$0.498799\pi$
$152$	−7.94810	−0.644676
$153$	−24.1754	−1.95447
$154$	9.61164	0.774528
$155$	−7.60082	−0.610513
$156$	14.4377	1.15594
$157$	6.55362	0.523036	0.261518	−	0.965199i	$-0.415777\pi$
$157$	6.55362	0.523036	0.261518	+	0.965199i	$0.415777\pi$
$158$	4.37414	0.347988
$159$	−4.14546	−0.328756
$160$	−11.0051	−0.870033
$161$	−23.0554	−1.81702
$162$	5.24706	0.412248
$163$	−16.3164	−1.27800	−0.638999	−	0.769208i	$-0.720651\pi$
$163$	−16.3164	−1.27800	−0.638999	+	0.769208i	$0.720651\pi$
$164$	−0.810436	−0.0632844
$165$	19.1802	1.49318
$166$	2.40234	0.186457
$167$	−15.4681	−1.19696	−0.598479	−	0.801139i	$-0.704228\pi$
$167$	−15.4681	−1.19696	−0.598479	+	0.801139i	$0.704228\pi$
$168$	−21.2855	−1.64221
$169$	1.80440	0.138800
$170$	9.42237	0.722663
$171$	−11.0468	−0.844768
$172$	1.71847	0.131032
$173$	14.9245	1.13469	0.567343	−	0.823481i	$-0.307971\pi$
$173$	14.9245	1.13469	0.567343	+	0.823481i	$0.307971\pi$
$174$	1.85613	0.140713
$175$	4.84138	0.365974
$176$	4.41649	0.332906
$177$	7.51671	0.564991
$178$	−4.35066	−0.326096
$179$	0.0910591	0.00680608	0.00340304	−	0.999994i	$-0.498917\pi$
$179$	0.0910591	0.00680608	0.00340304	+	0.999994i	$0.498917\pi$
$180$	−9.70384	−0.723281
$181$	−5.51699	−0.410075	−0.205037	−	0.978754i	$-0.565732\pi$
$181$	−5.51699	−0.410075	−0.205037	+	0.978754i	$0.565732\pi$
$182$	−9.24887	−0.685572
$183$	−3.30351	−0.244203
$184$	17.6187	1.29887
$185$	−4.36745	−0.321102
$186$	7.50394	0.550215
$187$	−27.5453	−2.01431
$188$	6.18573	0.451141
$189$	−4.29409	−0.312349
$190$	4.30548	0.312352
$191$	2.25482	0.163153	0.0815764	−	0.996667i	$-0.474005\pi$
$191$	2.25482	0.163153	0.0815764	+	0.996667i	$0.474005\pi$
$192$	5.22883	0.377359
$193$	−4.01975	−0.289348	−0.144674	−	0.989479i	$-0.546213\pi$
$193$	−4.01975	−0.289348	−0.144674	+	0.989479i	$0.546213\pi$
$194$	−7.01957	−0.503976
$195$	−18.4563	−1.32168
$196$	−5.76117	−0.411512
$197$	−1.41200	−0.100601	−0.0503003	−	0.998734i	$-0.516018\pi$
$197$	−1.41200	−0.100601	−0.0503003	+	0.998734i	$0.516018\pi$
$198$	−10.2087	−0.725504
$199$	−0.593815	−0.0420944	−0.0210472	−	0.999778i	$-0.506700\pi$
$199$	−0.593815	−0.0420944	−0.0210472	+	0.999778i	$0.506700\pi$
$200$	−3.69975	−0.261612
$201$	2.58280	0.182176
$202$	−2.54532	−0.179088
$203$	3.30412	0.231904
$204$	25.8492	1.80981
$205$	1.03601	0.0723581
$206$	3.16599	0.220585
$207$	24.4876	1.70201
$208$	−4.24980	−0.294671
$209$	−12.5866	−0.870634
$210$	11.5303	0.795669
$211$	−27.7354	−1.90939	−0.954693	−	0.297594i	$-0.903816\pi$
$211$	−27.7354	−1.90939	−0.954693	+	0.297594i	$0.903816\pi$
$212$	2.38966	0.164123
$213$	−27.5038	−1.88453
$214$	6.77548	0.463162
$215$	−2.19678	−0.149819
$216$	3.28151	0.223279
$217$	13.3579	0.906792
$218$	−9.84276	−0.666636
$219$	−14.4206	−0.974453
$220$	−11.0565	−0.745427
$221$	26.5057	1.78296
$222$	4.31178	0.289388
$223$	6.45359	0.432165	0.216082	−	0.976375i	$-0.430672\pi$
$223$	6.45359	0.432165	0.216082	+	0.976375i	$0.430672\pi$
$224$	19.3407	1.29226
$225$	−5.14215	−0.342810
$226$	1.60190	0.106557
$227$	−11.5994	−0.769877	−0.384939	−	0.922942i	$-0.625777\pi$
$227$	−11.5994	−0.769877	−0.384939	+	0.922942i	$0.625777\pi$
$228$	11.8116	0.782242
$229$	21.3222	1.40901	0.704507	−	0.709697i	$-0.251168\pi$
$229$	21.3222	1.40901	0.704507	+	0.709697i	$0.251168\pi$
$230$	−9.54405	−0.629316
$231$	−33.7077	−2.21781
$232$	−2.52498	−0.165773
$233$	7.55271	0.494794	0.247397	−	0.968914i	$-0.420425\pi$
$233$	7.55271	0.494794	0.247397	+	0.968914i	$0.420425\pi$
$234$	9.82345	0.642179
$235$	−7.90744	−0.515825
$236$	−4.33303	−0.282056
$237$	−15.3400	−0.996440
$238$	−16.5591	−1.07337
$239$	−22.1508	−1.43281	−0.716407	−	0.697683i	$-0.754214\pi$
$239$	−22.1508	−1.43281	−0.716407	+	0.697683i	$0.754214\pi$
$240$	5.29813	0.341993
$241$	−6.71294	−0.432419	−0.216209	−	0.976347i	$-0.569369\pi$
$241$	−6.71294	−0.432419	−0.216209	+	0.976347i	$0.569369\pi$
$242$	−3.62918	−0.233292
$243$	−22.3001	−1.43055
$244$	1.90432	0.121912
$245$	7.36471	0.470514
$246$	−1.02280	−0.0652116
$247$	12.1116	0.770640
$248$	−10.2080	−0.648208
$249$	−8.42493	−0.533908
$250$	8.84305	0.559284
$251$	−13.9618	−0.881258	−0.440629	−	0.897689i	$-0.645245\pi$
$251$	−13.9618	−0.881258	−0.440629	+	0.897689i	$0.645245\pi$
$252$	17.0538	1.07429
$253$	27.9010	1.75412
$254$	−14.5557	−0.913306
$255$	−33.0440	−2.06929
$256$	−11.5311	−0.720696
$257$	12.6868	0.791380	0.395690	−	0.918384i	$-0.370505\pi$
$257$	12.6868	0.791380	0.395690	+	0.918384i	$0.370505\pi$
$258$	2.16878	0.135022
$259$	7.67547	0.476931
$260$	10.6392	0.659814
$261$	−3.50938	−0.217225
$262$	7.09321	0.438220
$263$	−18.4824	−1.13967	−0.569837	−	0.821757i	$-0.692994\pi$
$263$	−18.4824	−1.13967	−0.569837	+	0.821757i	$0.692994\pi$
$264$	25.7592	1.58537
$265$	−3.05479	−0.187654
$266$	−7.56656	−0.463935
$267$	15.2576	0.933753
$268$	−1.48886	−0.0909466
$269$	−22.8028	−1.39031	−0.695155	−	0.718860i	$-0.744664\pi$
$269$	−22.8028	−1.39031	−0.695155	+	0.718860i	$0.744664\pi$
$270$	−1.77759	−0.108181
$271$	11.3649	0.690366	0.345183	−	0.938535i	$-0.387817\pi$
$271$	11.3649	0.690366	0.345183	+	0.938535i	$0.387817\pi$
$272$	−7.60881	−0.461352
$273$	32.4355	1.96309
$274$	−1.88341	−0.113781
$275$	−5.85892	−0.353306
$276$	−26.1830	−1.57603
$277$	22.0331	1.32384	0.661921	−	0.749574i	$-0.269742\pi$
$277$	22.0331	1.32384	0.661921	+	0.749574i	$0.269742\pi$
$278$	0.727508	0.0436330
$279$	−14.1877	−0.849396
$280$	−15.6853	−0.937377
$281$	8.27139	0.493429	0.246715	−	0.969088i	$-0.420649\pi$
$281$	8.27139	0.493429	0.246715	+	0.969088i	$0.420649\pi$
$282$	7.80665	0.464879
$283$	9.83756	0.584782	0.292391	−	0.956299i	$-0.405549\pi$
$283$	9.83756	0.584782	0.292391	+	0.956299i	$0.405549\pi$
$284$	15.8546	0.940799
$285$	−15.0992	−0.894399
$286$	11.1928	0.661841
$287$	−1.82071	−0.107473
$288$	−20.5422	−1.21046
$289$	30.4555	1.79150
$290$	1.36778	0.0803189
$291$	24.6174	1.44310
$292$	8.31279	0.486469
$293$	17.0781	0.997714	0.498857	−	0.866684i	$-0.333753\pi$
$293$	17.0781	0.997714	0.498857	+	0.866684i	$0.333753\pi$
$294$	−7.27083	−0.424044
$295$	5.53907	0.322497
$296$	−5.86554	−0.340928
$297$	5.19660	0.301537
$298$	9.58796	0.555416
$299$	−26.8480	−1.55266
$300$	5.49816	0.317436
$301$	3.86068	0.222526
$302$	−0.0674517	−0.00388141
$303$	8.92637	0.512806
$304$	−3.47679	−0.199407
$305$	−2.43436	−0.139391
$306$	17.5878	1.00543
$307$	13.0928	0.747245	0.373623	−	0.927581i	$-0.378116\pi$
$307$	13.0928	0.747245	0.373623	+	0.927581i	$0.378116\pi$
$308$	19.4309	1.10718
$309$	−11.1030	−0.631629
$310$	5.52966	0.314063
$311$	3.79188	0.215018	0.107509	−	0.994204i	$-0.465713\pi$
$311$	3.79188	0.215018	0.107509	+	0.994204i	$0.465713\pi$
$312$	−24.7870	−1.40329
$313$	−15.7444	−0.889929	−0.444964	−	0.895548i	$-0.646784\pi$
$313$	−15.7444	−0.889929	−0.444964	+	0.895548i	$0.646784\pi$
$314$	−4.76781	−0.269063
$315$	−21.8005	−1.22832
$316$	8.84278	0.497445
$317$	26.9876	1.51578	0.757888	−	0.652385i	$-0.226231\pi$
$317$	26.9876	1.51578	0.757888	+	0.652385i	$0.226231\pi$
$318$	3.01585	0.169121
$319$	−3.99856	−0.223877
$320$	3.85313	0.215397
$321$	−23.7614	−1.32623
$322$	16.7729	0.934720
$323$	21.6844	1.20655
$324$	10.6075	0.589304
$325$	5.63779	0.312728
$326$	11.8703	0.657435
$327$	34.5183	1.90887
$328$	1.39137	0.0768257
$329$	13.8967	0.766152
$330$	−13.9537	−0.768128
$331$	−7.51854	−0.413256	−0.206628	−	0.978420i	$-0.566249\pi$
$331$	−7.51854	−0.413256	−0.206628	+	0.978420i	$0.566249\pi$
$332$	4.85657	0.266539
$333$	−8.15230	−0.446743
$334$	11.2532	0.615746
$335$	1.90326	0.103986
$336$	−9.31106	−0.507960
$337$	−2.80726	−0.152921	−0.0764606	−	0.997073i	$-0.524362\pi$
$337$	−2.80726	−0.152921	−0.0764606	+	0.997073i	$0.524362\pi$
$338$	−1.31271	−0.0714021
$339$	−5.61782	−0.305118
$340$	19.0483	1.03304
$341$	−16.1654	−0.875404
$342$	8.03662	0.434571
$343$	10.1859	0.549988
$344$	−2.95030	−0.159070
$345$	33.4707	1.80200
$346$	−10.8577	−0.583712
$347$	−17.2394	−0.925461	−0.462730	−	0.886499i	$-0.653130\pi$
$347$	−17.2394	−0.925461	−0.462730	+	0.886499i	$0.653130\pi$
$348$	3.75235	0.201147
$349$	−27.8469	−1.49061	−0.745306	−	0.666722i	$-0.767697\pi$
$349$	−27.8469	−1.49061	−0.745306	+	0.666722i	$0.767697\pi$
$350$	−3.52214	−0.188266
$351$	−5.00047	−0.266905
$352$	−23.4056	−1.24753
$353$	21.1612	1.12630	0.563149	−	0.826356i	$-0.309590\pi$
$353$	21.1612	1.12630	0.563149	+	0.826356i	$0.309590\pi$
$354$	−5.46847	−0.290646
$355$	−20.2676	−1.07569
$356$	−8.79531	−0.466151
$357$	58.0723	3.07351
$358$	−0.0662462	−0.00350122
$359$	−0.120939	−0.00638294	−0.00319147	−	0.999995i	$-0.501016\pi$
$359$	−0.120939	−0.00638294	−0.00319147	+	0.999995i	$0.501016\pi$
$360$	16.6598	0.878046
$361$	−9.09146	−0.478498
$362$	4.01365	0.210953
$363$	12.7274	0.668016
$364$	−18.6976	−0.980018
$365$	−10.6265	−0.556218
$366$	2.40333	0.125624
$367$	17.4352	0.910109	0.455055	−	0.890464i	$-0.349620\pi$
$367$	17.4352	0.910109	0.455055	+	0.890464i	$0.349620\pi$
$368$	7.70707	0.401759
$369$	1.93382	0.100671
$370$	3.17736	0.165183
$371$	5.36857	0.278722
$372$	15.1700	0.786527
$373$	11.4225	0.591434	0.295717	−	0.955276i	$-0.404441\pi$
$373$	11.4225	0.591434	0.295717	+	0.955276i	$0.404441\pi$
$374$	20.0394	1.03621
$375$	−31.0123	−1.60147
$376$	−10.6198	−0.547674
$377$	3.84765	0.198164
$378$	3.12398	0.160680
$379$	37.1029	1.90585	0.952925	−	0.303207i	$-0.0980574\pi$
$379$	37.1029	1.90585	0.952925	+	0.303207i	$0.0980574\pi$
$380$	8.70397	0.446504
$381$	51.0465	2.61519
$382$	−1.64040	−0.0839300
$383$	16.7096	0.853819	0.426910	−	0.904294i	$-0.359602\pi$
$383$	16.7096	0.853819	0.426910	+	0.904294i	$0.359602\pi$
$384$	26.0647	1.33011
$385$	−24.8393	−1.26593
$386$	2.92440	0.148848
$387$	−4.10052	−0.208441
$388$	−14.1908	−0.720428
$389$	30.3544	1.53903	0.769515	−	0.638629i	$-0.220498\pi$
$389$	30.3544	1.53903	0.769515	+	0.638629i	$0.220498\pi$
$390$	13.4271	0.679907
$391$	−48.0684	−2.43092
$392$	9.89089	0.499565
$393$	−24.8757	−1.25481
$394$	1.02724	0.0517515
$395$	−11.3041	−0.568769
$396$	−20.6380	−1.03710
$397$	26.6108	1.33556	0.667778	−	0.744361i	$-0.267246\pi$
$397$	26.6108	1.33556	0.667778	+	0.744361i	$0.267246\pi$
$398$	0.432005	0.0216545
$399$	26.5357	1.32845
$400$	−1.61840	−0.0809202
$401$	−33.3666	−1.66625	−0.833124	−	0.553087i	$-0.813450\pi$
$401$	−33.3666	−1.66625	−0.833124	+	0.553087i	$0.813450\pi$
$402$	−1.87900	−0.0937162
$403$	15.5552	0.774862
$404$	−5.14563	−0.256005
$405$	−13.5599	−0.673798
$406$	−2.40377	−0.119297
$407$	−9.28866	−0.460422
$408$	−44.3785	−2.19706
$409$	−33.5312	−1.65801	−0.829006	−	0.559240i	$-0.811093\pi$
$409$	−33.5312	−1.65801	−0.829006	+	0.559240i	$0.811093\pi$
$410$	−0.753705	−0.0372228
$411$	6.60506	0.325804
$412$	6.40037	0.315324
$413$	−9.73450	−0.479004
$414$	−17.8149	−0.875557
$415$	−6.20834	−0.304755
$416$	22.5223	1.10425
$417$	−2.55135	−0.124940
$418$	9.15685	0.447876
$419$	−29.7622	−1.45398	−0.726989	−	0.686649i	$-0.759081\pi$
$419$	−29.7622	−1.45398	−0.726989	+	0.686649i	$0.759081\pi$
$420$	23.3098	1.13740
$421$	−34.8294	−1.69748	−0.848741	−	0.528809i	$-0.822639\pi$
$421$	−34.8294	−1.69748	−0.848741	+	0.528809i	$0.822639\pi$
$422$	20.1777	0.982237
$423$	−14.7601	−0.717659
$424$	−4.10262	−0.199241
$425$	10.0939	0.489624
$426$	20.0092	0.969449
$427$	4.27821	0.207037
$428$	13.6973	0.662086
$429$	−39.2527	−1.89514
$430$	1.59817	0.0770708
$431$	8.41553	0.405362	0.202681	−	0.979245i	$-0.435035\pi$
$431$	8.41553	0.405362	0.202681	+	0.979245i	$0.435035\pi$
$432$	1.43545	0.0690632
$433$	−22.0003	−1.05727	−0.528633	−	0.848851i	$-0.677295\pi$
$433$	−22.0003	−1.05727	−0.528633	+	0.848851i	$0.677295\pi$
$434$	−9.71796	−0.466477
$435$	−4.79677	−0.229988
$436$	−19.8982	−0.952949
$437$	−21.9645	−1.05070
$438$	10.4911	0.501283
$439$	25.6957	1.22639	0.613195	−	0.789932i	$-0.289884\pi$
$439$	25.6957	1.22639	0.613195	+	0.789932i	$0.289884\pi$
$440$	18.9820	0.904931
$441$	13.7470	0.654619
$442$	−19.2831	−0.917203
$443$	2.24249	0.106544	0.0532720	−	0.998580i	$-0.483035\pi$
$443$	2.24249	0.106544	0.0532720	+	0.998580i	$0.483035\pi$
$444$	8.71672	0.413677
$445$	11.2434	0.532987
$446$	−4.69504	−0.222317
$447$	−33.6247	−1.59039
$448$	−6.77159	−0.319928
$449$	−17.4491	−0.823476	−0.411738	−	0.911302i	$-0.635078\pi$
$449$	−17.4491	−0.823476	−0.411738	+	0.911302i	$0.635078\pi$
$450$	3.74095	0.176350
$451$	2.20338	0.103753
$452$	3.23841	0.152322
$453$	0.236551	0.0111142
$454$	8.43863	0.396045
$455$	23.9018	1.12053
$456$	−20.2784	−0.949623
$457$	−22.3781	−1.04680	−0.523401	−	0.852087i	$-0.675337\pi$
$457$	−22.3781	−1.04680	−0.523401	+	0.852087i	$0.675337\pi$
$458$	−15.5121	−0.724833
$459$	−8.95280	−0.417881
$460$	−19.2943	−0.899601
$461$	−6.50616	−0.303022	−0.151511	−	0.988456i	$-0.548414\pi$
$461$	−6.50616	−0.303022	−0.151511	+	0.988456i	$0.548414\pi$
$462$	24.5226	1.14090
$463$	−25.0969	−1.16635	−0.583176	−	0.812345i	$-0.698190\pi$
$463$	−25.0969	−1.16635	−0.583176	+	0.812345i	$0.698190\pi$
$464$	−1.10452	−0.0512760
$465$	−19.3924	−0.899299
$466$	−5.49465	−0.254535
$467$	7.64649	0.353837	0.176919	−	0.984225i	$-0.443387\pi$
$467$	7.64649	0.353837	0.176919	+	0.984225i	$0.443387\pi$
$468$	19.8591	0.917988
$469$	−3.34485	−0.154451
$470$	5.75273	0.265353
$471$	16.7206	0.770443
$472$	7.43904	0.342409
$473$	−4.67209	−0.214823
$474$	11.1600	0.512594
$475$	4.61231	0.211627
$476$	−33.4760	−1.53437
$477$	−5.70208	−0.261080
$478$	16.1148	0.737076
$479$	−17.9926	−0.822103	−0.411052	−	0.911612i	$-0.634838\pi$
$479$	−17.9926	−0.822103	−0.411052	+	0.911612i	$0.634838\pi$
$480$	−28.0780	−1.28158
$481$	8.93809	0.407542
$482$	4.88372	0.222447
$483$	−58.8223	−2.67651
$484$	−7.33676	−0.333489
$485$	18.1406	0.823723
$486$	16.2235	0.735914
$487$	−5.07928	−0.230164	−0.115082	−	0.993356i	$-0.536713\pi$
$487$	−5.07928	−0.230164	−0.115082	+	0.993356i	$0.536713\pi$
$488$	−3.26938	−0.147998
$489$	−41.6288	−1.88252
$490$	−5.35788	−0.242044
$491$	21.6017	0.974870	0.487435	−	0.873159i	$-0.337933\pi$
$491$	21.6017	0.974870	0.487435	+	0.873159i	$0.337933\pi$
$492$	−2.06770	−0.0932193
$493$	6.88880	0.310256
$494$	−8.81125	−0.396437
$495$	26.3824	1.18580
$496$	−4.46534	−0.200500
$497$	35.6187	1.59772
$498$	6.12920	0.274656
$499$	24.9564	1.11720	0.558602	−	0.829436i	$-0.311338\pi$
$499$	24.9564	1.11720	0.558602	+	0.829436i	$0.311338\pi$
$500$	17.8772	0.799491
$501$	−39.4645	−1.76315
$502$	10.1573	0.453342
$503$	12.7083	0.566635	0.283318	−	0.959026i	$-0.408565\pi$
$503$	12.7083	0.566635	0.283318	+	0.959026i	$0.408565\pi$
$504$	−29.2783	−1.30416
$505$	6.57785	0.292710
$506$	−20.2982	−0.902365
$507$	4.60364	0.204455
$508$	−29.4259	−1.30556
$509$	10.9157	0.483829	0.241914	−	0.970298i	$-0.422225\pi$
$509$	10.9157	0.483829	0.241914	+	0.970298i	$0.422225\pi$
$510$	24.0398	1.06450
$511$	18.6753	0.826149
$512$	−12.0431	−0.532235
$513$	−4.09091	−0.180618
$514$	−9.22974	−0.407106
$515$	−8.18183	−0.360534
$516$	4.38441	0.193013
$517$	−16.8175	−0.739632
$518$	−5.58397	−0.245345
$519$	38.0775	1.67142
$520$	−18.2656	−0.800998
$521$	−22.4000	−0.981364	−0.490682	−	0.871339i	$-0.663252\pi$
$521$	−22.4000	−0.981364	−0.490682	+	0.871339i	$0.663252\pi$
$522$	2.55310	0.111746
$523$	38.9295	1.70227	0.851133	−	0.524950i	$-0.175916\pi$
$523$	38.9295	1.70227	0.851133	+	0.524950i	$0.175916\pi$
$524$	14.3397	0.626431
$525$	12.3521	0.539088
$526$	13.4461	0.586278
$527$	27.8500	1.21316
$528$	11.2680	0.490377
$529$	25.6891	1.11692
$530$	2.22238	0.0965342
$531$	10.3392	0.448685
$532$	−15.2966	−0.663191
$533$	−2.12022	−0.0918368
$534$	−11.1001	−0.480346
$535$	−17.5098	−0.757015
$536$	2.55611	0.110407
$537$	0.232324	0.0100255
$538$	16.5892	0.715211
$539$	15.6632	0.674662
$540$	−3.59359	−0.154643
$541$	−44.0292	−1.89296	−0.946482	−	0.322757i	$-0.895390\pi$
$541$	−44.0292	−1.89296	−0.946482	+	0.322757i	$0.895390\pi$
$542$	−8.26802	−0.355142
$543$	−14.0758	−0.604049
$544$	40.3237	1.72886
$545$	25.4365	1.08958
$546$	−23.5971	−1.00986
$547$	−6.72198	−0.287411	−0.143705	−	0.989620i	$-0.545902\pi$
$547$	−6.72198	−0.287411	−0.143705	+	0.989620i	$0.545902\pi$
$548$	−3.80751	−0.162649
$549$	−4.54399	−0.193933
$550$	4.26241	0.181750
$551$	3.14778	0.134100
$552$	44.9516	1.91327
$553$	19.8660	0.844790
$554$	−16.0293	−0.681018
$555$	−11.1429	−0.472990
$556$	1.47073	0.0623730
$557$	−13.8522	−0.586938	−0.293469	−	0.955969i	$-0.594810\pi$
$557$	−13.8522	−0.586938	−0.293469	+	0.955969i	$0.594810\pi$
$558$	10.3217	0.436951
$559$	4.49576	0.190150
$560$	−6.86133	−0.289944
$561$	−70.2777	−2.96713
$562$	−6.01750	−0.253833
$563$	34.4171	1.45051	0.725253	−	0.688483i	$-0.241723\pi$
$563$	34.4171	1.45051	0.725253	+	0.688483i	$0.241723\pi$
$564$	15.7820	0.664540
$565$	−4.13978	−0.174162
$566$	−7.15690	−0.300827
$567$	23.8306	1.00079
$568$	−27.2196	−1.14211
$569$	−9.29053	−0.389479	−0.194740	−	0.980855i	$-0.562386\pi$
$569$	−9.29053	−0.389479	−0.194740	+	0.980855i	$0.562386\pi$
$570$	10.9848	0.460102
$571$	11.5305	0.482535	0.241268	−	0.970459i	$-0.422437\pi$
$571$	11.5305	0.482535	0.241268	+	0.970459i	$0.422437\pi$
$572$	22.6273	0.946095
$573$	5.75283	0.240328
$574$	1.32458	0.0552869
$575$	−10.2242	−0.426379
$576$	7.19227	0.299678
$577$	8.74851	0.364205	0.182103	−	0.983280i	$-0.441710\pi$
$577$	8.74851	0.364205	0.182103	+	0.983280i	$0.441710\pi$
$578$	−22.1566	−0.921595
$579$	−10.2558	−0.426216
$580$	2.76511	0.114815
$581$	10.9107	0.452652
$582$	−17.9094	−0.742367
$583$	−6.49691	−0.269074
$584$	−14.2716	−0.590562
$585$	−25.3866	−1.04961
$586$	−12.4245	−0.513250
$587$	7.44062	0.307107	0.153554	−	0.988140i	$-0.450928\pi$
$587$	7.44062	0.307107	0.153554	+	0.988140i	$0.450928\pi$
$588$	−14.6987	−0.606166
$589$	12.7258	0.524359
$590$	−4.02972	−0.165901
$591$	−3.60249	−0.148187
$592$	−2.56580	−0.105454
$593$	3.15013	0.129360	0.0646801	−	0.997906i	$-0.479397\pi$
$593$	3.15013	0.129360	0.0646801	+	0.997906i	$0.479397\pi$
$594$	−3.78057	−0.155119
$595$	42.7935	1.75436
$596$	19.3831	0.793961
$597$	−1.51503	−0.0620060
$598$	19.5321	0.798727
$599$	−9.53642	−0.389647	−0.194824	−	0.980838i	$-0.562413\pi$
$599$	−9.53642	−0.389647	−0.194824	+	0.980838i	$0.562413\pi$
$600$	−9.43935	−0.385360
$601$	−9.23751	−0.376806	−0.188403	−	0.982092i	$-0.560331\pi$
$601$	−9.23751	−0.376806	−0.188403	+	0.982092i	$0.560331\pi$
$602$	−2.80867	−0.114473
$603$	3.55264	0.144675
$604$	−0.136361	−0.00554844
$605$	9.37885	0.381304
$606$	−6.49400	−0.263801
$607$	−30.6784	−1.24520	−0.622599	−	0.782541i	$-0.713923\pi$
$607$	−30.6784	−1.24520	−0.622599	+	0.782541i	$0.713923\pi$
$608$	18.4256	0.747257
$609$	8.42996	0.341599
$610$	1.77102	0.0717064
$611$	16.1828	0.654684
$612$	35.5556	1.43725
$613$	−2.62938	−0.106200	−0.0530998	−	0.998589i	$-0.516910\pi$
$613$	−2.62938	−0.106200	−0.0530998	+	0.998589i	$0.516910\pi$
$614$	−9.52511	−0.384402
$615$	2.64322	0.106585
$616$	−33.3594	−1.34409
$617$	22.3427	0.899483	0.449741	−	0.893159i	$-0.351516\pi$
$617$	22.3427	0.899483	0.449741	+	0.893159i	$0.351516\pi$
$618$	8.07754	0.324926
$619$	−48.0446	−1.93108	−0.965539	−	0.260260i	$-0.916192\pi$
$619$	−48.0446	−1.93108	−0.965539	+	0.260260i	$0.916192\pi$
$620$	11.1788	0.448950
$621$	9.06842	0.363903
$622$	−2.75862	−0.110611
$623$	−19.7594	−0.791643
$624$	−10.8427	−0.434057
$625$	−15.5267	−0.621070
$626$	11.4542	0.457802
$627$	−32.1128	−1.28246
$628$	−9.63862	−0.384623
$629$	16.0027	0.638069
$630$	15.8600	0.631878
$631$	9.73250	0.387445	0.193722	−	0.981056i	$-0.437944\pi$
$631$	9.73250	0.387445	0.193722	+	0.981056i	$0.437944\pi$
$632$	−15.1815	−0.603887
$633$	−70.7628	−2.81257
$634$	−19.6337	−0.779754
$635$	37.6162	1.49275
$636$	6.09686	0.241756
$637$	−15.0720	−0.597176
$638$	2.90899	0.115168
$639$	−37.8315	−1.49659
$640$	19.2071	0.759228
$641$	−18.2291	−0.720005	−0.360003	−	0.932951i	$-0.617224\pi$
$641$	−18.2291	−0.720005	−0.360003	+	0.932951i	$0.617224\pi$
$642$	17.2866	0.682248
$643$	45.2667	1.78514	0.892572	−	0.450905i	$-0.148899\pi$
$643$	45.2667	1.78514	0.892572	+	0.450905i	$0.148899\pi$
$644$	33.9083	1.33617
$645$	−5.60475	−0.220687
$646$	−15.7756	−0.620683
$647$	−1.33611	−0.0525279	−0.0262639	−	0.999655i	$-0.508361\pi$
$647$	−1.33611	−0.0525279	−0.0262639	+	0.999655i	$0.508361\pi$
$648$	−18.2111	−0.715401
$649$	11.7805	0.462423
$650$	−4.10154	−0.160875
$651$	34.0806	1.33572
$652$	23.9970	0.939797
$653$	42.4385	1.66075	0.830373	−	0.557208i	$-0.188127\pi$
$653$	42.4385	1.66075	0.830373	+	0.557208i	$0.188127\pi$
$654$	−25.1123	−0.981969
$655$	−18.3309	−0.716248
$656$	0.608637	0.0237633
$657$	−19.8355	−0.773858
$658$	−10.1100	−0.394128
$659$	−6.08914	−0.237199	−0.118600	−	0.992942i	$-0.537841\pi$
$659$	−6.08914	−0.237199	−0.118600	+	0.992942i	$0.537841\pi$
$660$	−28.2089	−1.09803
$661$	37.1677	1.44565	0.722827	−	0.691029i	$-0.242842\pi$
$661$	37.1677	1.44565	0.722827	+	0.691029i	$0.242842\pi$
$662$	5.46979	0.212590
$663$	67.6252	2.62635
$664$	−8.33787	−0.323572
$665$	19.5542	0.758279
$666$	5.93086	0.229816
$667$	−6.97776	−0.270180
$668$	22.7494	0.880202
$669$	16.4654	0.636588
$670$	−1.38464	−0.0534933
$671$	−5.17738	−0.199871
$672$	49.3449	1.90352
$673$	30.9980	1.19488	0.597442	−	0.801912i	$-0.296184\pi$
$673$	30.9980	1.19488	0.597442	+	0.801912i	$0.296184\pi$
$674$	2.04230	0.0786666
$675$	−1.90427	−0.0732955
$676$	−2.65378	−0.102069
$677$	−3.20104	−0.123026	−0.0615130	−	0.998106i	$-0.519593\pi$
$677$	−3.20104	−0.123026	−0.0615130	+	0.998106i	$0.519593\pi$
$678$	4.08701	0.156961
$679$	−31.8808	−1.22347
$680$	−32.7025	−1.25408
$681$	−29.5940	−1.13405
$682$	11.7604	0.450330
$683$	48.6765	1.86255	0.931277	−	0.364312i	$-0.118696\pi$
$683$	48.6765	1.86255	0.931277	+	0.364312i	$0.118696\pi$
$684$	16.2469	0.621214
$685$	4.86727	0.185969
$686$	−7.41033	−0.282928
$687$	54.4005	2.07551
$688$	−1.29057	−0.0492025
$689$	6.25170	0.238171
$690$	−24.3502	−0.926996
$691$	26.9756	1.02620	0.513100	−	0.858329i	$-0.328497\pi$
$691$	26.9756	1.02620	0.513100	+	0.858329i	$0.328497\pi$
$692$	−21.9499	−0.834410
$693$	−46.3650	−1.76126
$694$	12.5418	0.476081
$695$	−1.88009	−0.0713159
$696$	−6.44212	−0.244188
$697$	−3.79602	−0.143784
$698$	20.2589	0.766809
$699$	19.2696	0.728843
$700$	−7.12038	−0.269125
$701$	−28.2595	−1.06735	−0.533673	−	0.845691i	$-0.679189\pi$
$701$	−28.2595	−1.06735	−0.533673	+	0.845691i	$0.679189\pi$
$702$	3.63788	0.137303
$703$	7.31230	0.275789
$704$	8.19481	0.308853
$705$	−20.1747	−0.759821
$706$	−15.3949	−0.579396
$707$	−11.5601	−0.434761
$708$	−11.0551	−0.415475
$709$	−38.6135	−1.45016	−0.725079	−	0.688665i	$-0.758197\pi$
$709$	−38.6135	−1.45016	−0.725079	+	0.688665i	$0.758197\pi$
$710$	14.7448	0.553363
$711$	−21.1002	−0.791319
$712$	15.1000	0.565896
$713$	−28.2096	−1.05646
$714$	−42.2481	−1.58109
$715$	−28.9253	−1.08175
$716$	−0.133924	−0.00500496
$717$	−56.5143	−2.11057
$718$	0.0879844	0.00328355
$719$	41.1856	1.53596	0.767982	−	0.640472i	$-0.221261\pi$
$719$	41.1856	1.53596	0.767982	+	0.640472i	$0.221261\pi$
$720$	7.28758	0.271592
$721$	14.3790	0.535500
$722$	6.61411	0.246152
$723$	−17.1271	−0.636963
$724$	8.11402	0.301555
$725$	1.46526	0.0544183
$726$	−9.25930	−0.343645
$727$	−2.47646	−0.0918470	−0.0459235	−	0.998945i	$-0.514623\pi$
$727$	−2.47646	−0.0918470	−0.0459235	+	0.998945i	$0.514623\pi$
$728$	32.1004	1.18972
$729$	−35.2583	−1.30586
$730$	7.73089	0.286133
$731$	8.04917	0.297709
$732$	4.85858	0.179578
$733$	8.90296	0.328838	0.164419	−	0.986391i	$-0.447425\pi$
$733$	8.90296	0.328838	0.164419	+	0.986391i	$0.447425\pi$
$734$	−12.6842	−0.468183
$735$	18.7900	0.693078
$736$	−40.8444	−1.50555
$737$	4.04785	0.149104
$738$	−1.40687	−0.0517875
$739$	−13.0725	−0.480878	−0.240439	−	0.970664i	$-0.577291\pi$
$739$	−13.0725	−0.480878	−0.240439	+	0.970664i	$0.577291\pi$
$740$	6.42336	0.236127
$741$	30.9008	1.13517
$742$	−3.90567	−0.143382
$743$	−19.7140	−0.723238	−0.361619	−	0.932326i	$-0.617776\pi$
$743$	−19.7140	−0.723238	−0.361619	+	0.932326i	$0.617776\pi$
$744$	−26.0442	−0.954825
$745$	−24.7781	−0.907799
$746$	−8.30995	−0.304249
$747$	−11.5885	−0.424001
$748$	40.5118	1.48126
$749$	30.7722	1.12439
$750$	22.5617	0.823838
$751$	−36.1056	−1.31751	−0.658757	−	0.752356i	$-0.728917\pi$
$751$	−36.1056	−1.31751	−0.658757	+	0.752356i	$0.728917\pi$
$752$	−4.64548	−0.169403
$753$	−35.6213	−1.29811
$754$	−2.79919	−0.101941
$755$	0.174315	0.00634397
$756$	6.31546	0.229691
$757$	11.6462	0.423288	0.211644	−	0.977347i	$-0.432118\pi$
$757$	11.6462	0.423288	0.211644	+	0.977347i	$0.432118\pi$
$758$	−26.9927	−0.980418
$759$	71.1852	2.58386
$760$	−14.9432	−0.542045
$761$	−44.6856	−1.61985	−0.809925	−	0.586533i	$-0.800492\pi$
$761$	−44.6856	−1.61985	−0.809925	+	0.586533i	$0.800492\pi$
$762$	−37.1367	−1.34532
$763$	−44.7028	−1.61835
$764$	−3.31623	−0.119977
$765$	−45.4520	−1.64332
$766$	−12.1563	−0.439227
$767$	−11.3358	−0.409313
$768$	−29.4199	−1.06160
$769$	35.2250	1.27025	0.635123	−	0.772411i	$-0.280949\pi$
$769$	35.2250	1.27025	0.635123	+	0.772411i	$0.280949\pi$
$770$	18.0708	0.651225
$771$	32.3684	1.16572
$772$	5.91198	0.212777
$773$	22.7742	0.819131	0.409565	−	0.912281i	$-0.365680\pi$
$773$	22.7742	0.819131	0.409565	+	0.912281i	$0.365680\pi$
$774$	2.98316	0.107227
$775$	5.92373	0.212787
$776$	24.3630	0.874582
$777$	19.5828	0.702529
$778$	−22.0831	−0.791717
$779$	−1.73456	−0.0621471
$780$	27.1443	0.971920
$781$	−43.1049	−1.54241
$782$	34.9701	1.25053
$783$	−1.29962	−0.0464445
$784$	4.32663	0.154523
$785$	12.3214	0.439770
$786$	18.0973	0.645508
$787$	−22.4796	−0.801310	−0.400655	−	0.916229i	$-0.631217\pi$
$787$	−22.4796	−0.801310	−0.400655	+	0.916229i	$0.631217\pi$
$788$	2.07667	0.0739782
$789$	−47.1551	−1.67877
$790$	8.22379	0.292589
$791$	7.27535	0.258682
$792$	35.4318	1.25902
$793$	4.98197	0.176915
$794$	−19.3595	−0.687044
$795$	−7.79384	−0.276419
$796$	0.873343	0.0309548
$797$	−10.2768	−0.364023	−0.182012	−	0.983296i	$-0.558261\pi$
$797$	−10.2768	−0.364023	−0.182012	+	0.983296i	$0.558261\pi$
$798$	−19.3049	−0.683387
$799$	28.9735	1.02501
$800$	8.57690	0.303239
$801$	20.9869	0.741536
$802$	24.2744	0.857160
$803$	−22.6004	−0.797552
$804$	−3.79860	−0.133966
$805$	−43.3462	−1.52775
$806$	−11.3166	−0.398609
$807$	−58.1779	−2.04796
$808$	8.83413	0.310783
$809$	−24.8691	−0.874351	−0.437176	−	0.899376i	$-0.644021\pi$
$809$	−24.8691	−0.874351	−0.437176	+	0.899376i	$0.644021\pi$
$810$	9.86495	0.346619
$811$	51.3917	1.80461	0.902304	−	0.431101i	$-0.141875\pi$
$811$	51.3917	1.80461	0.902304	+	0.431101i	$0.141875\pi$
$812$	−4.85948	−0.170534
$813$	28.9957	1.01692
$814$	6.75757	0.236853
$815$	−30.6763	−1.07454
$816$	−19.4127	−0.679582
$817$	3.67801	0.128677
$818$	24.3942	0.852923
$819$	44.6151	1.55898
$820$	−1.52369	−0.0532097
$821$	−20.4801	−0.714762	−0.357381	−	0.933959i	$-0.616330\pi$
$821$	−20.4801	−0.714762	−0.357381	+	0.933959i	$0.616330\pi$
$822$	−4.80523	−0.167602
$823$	−4.48485	−0.156332	−0.0781661	−	0.996940i	$-0.524906\pi$
$823$	−4.48485	−0.156332	−0.0781661	+	0.996940i	$0.524906\pi$
$824$	−10.9883	−0.382795
$825$	−14.9482	−0.520428
$826$	7.08193	0.246412
$827$	−17.4615	−0.607197	−0.303598	−	0.952800i	$-0.598188\pi$
$827$	−17.4615	−0.607197	−0.303598	+	0.952800i	$0.598188\pi$
$828$	−36.0148	−1.25160
$829$	−54.5184	−1.89350	−0.946751	−	0.321966i	$-0.895656\pi$
$829$	−54.5184	−1.89350	−0.946751	+	0.321966i	$0.895656\pi$
$830$	4.51661	0.156774
$831$	56.2142	1.95005
$832$	−7.88552	−0.273381
$833$	−26.9849	−0.934970
$834$	1.85613	0.0642724
$835$	−29.0814	−1.00640
$836$	18.5115	0.640235
$837$	−5.25408	−0.181608
$838$	21.6522	0.747964
$839$	17.2102	0.594161	0.297080	−	0.954853i	$-0.403987\pi$
$839$	17.2102	0.594161	0.297080	+	0.954853i	$0.403987\pi$
$840$	−40.0187	−1.38078
$841$	1.00000	0.0344828
$842$	25.3387	0.873228
$843$	21.1032	0.726833
$844$	40.7914	1.40410
$845$	3.39243	0.116703
$846$	10.7381	0.369182
$847$	−16.4826	−0.566349
$848$	−1.79463	−0.0616280
$849$	25.0991	0.861397
$850$	−7.34336	−0.251875
$851$	−16.2093	−0.555649
$852$	40.4507	1.38582
$853$	37.4844	1.28344	0.641721	−	0.766938i	$-0.278221\pi$
$853$	37.4844	1.28344	0.641721	+	0.766938i	$0.278221\pi$
$854$	−3.11243	−0.106505
$855$	−20.7690	−0.710283
$856$	−23.5159	−0.803756
$857$	−18.6686	−0.637706	−0.318853	−	0.947804i	$-0.603298\pi$
$857$	−18.6686	−0.637706	−0.318853	+	0.947804i	$0.603298\pi$
$858$	28.5566	0.974907
$859$	38.9730	1.32974	0.664871	−	0.746958i	$-0.268486\pi$
$859$	38.9730	1.32974	0.664871	+	0.746958i	$0.268486\pi$
$860$	3.23088	0.110172
$861$	−4.64527	−0.158310
$862$	−6.12236	−0.208529
$863$	−48.1630	−1.63949	−0.819744	−	0.572730i	$-0.805884\pi$
$863$	−48.1630	−1.63949	−0.819744	+	0.572730i	$0.805884\pi$
$864$	−7.60733	−0.258807
$865$	28.0594	0.954047
$866$	16.0054	0.543885
$867$	77.7027	2.63892
$868$	−19.6459	−0.666824
$869$	−24.0414	−0.815548
$870$	3.48969	0.118311
$871$	−3.89507	−0.131980
$872$	34.1616	1.15686
$873$	33.8613	1.14603
$874$	15.9793	0.540509
$875$	40.1625	1.35774
$876$	21.2088	0.716580
$877$	−47.8553	−1.61596	−0.807980	−	0.589210i	$-0.799439\pi$
$877$	−47.8553	−1.61596	−0.807980	+	0.589210i	$0.799439\pi$
$878$	−18.6938	−0.630886
$879$	43.5722	1.46966
$880$	8.30341	0.279908
$881$	36.9447	1.24470	0.622349	−	0.782740i	$-0.286178\pi$
$881$	36.9447	1.24470	0.622349	+	0.782740i	$0.286178\pi$
$882$	−10.0010	−0.336753
$883$	−0.899332	−0.0302649	−0.0151325	−	0.999885i	$-0.504817\pi$
$883$	−0.899332	−0.0302649	−0.0151325	+	0.999885i	$0.504817\pi$
$884$	−38.9828	−1.31113
$885$	14.1321	0.475046
$886$	−1.63143	−0.0548090
$887$	42.9010	1.44047	0.720237	−	0.693728i	$-0.244033\pi$
$887$	42.9010	1.44047	0.720237	+	0.693728i	$0.244033\pi$
$888$	−14.9650	−0.502194
$889$	−66.1076	−2.21718
$890$	−8.17964	−0.274182
$891$	−28.8391	−0.966147
$892$	−9.49151	−0.317799
$893$	13.2392	0.443033
$894$	24.4622	0.818140
$895$	0.171199	0.00572257
$896$	−33.7551	−1.12768
$897$	−68.4985	−2.28710
$898$	12.6944	0.423617
$899$	4.04279	0.134835
$900$	7.56272	0.252091
$901$	11.1930	0.372893
$902$	−1.60297	−0.0533732
$903$	9.84994	0.327785
$904$	−5.55977	−0.184915
$905$	−10.3724	−0.344792
$906$	−0.172093	−0.00571741
$907$	−11.2856	−0.374731	−0.187366	−	0.982290i	$-0.559995\pi$
$907$	−11.2856	−0.374731	−0.187366	+	0.982290i	$0.559995\pi$
$908$	17.0596	0.566142
$909$	12.2782	0.407243
$910$	−17.3887	−0.576431
$911$	38.7822	1.28491	0.642455	−	0.766323i	$-0.277916\pi$
$911$	38.7822	1.28491	0.642455	+	0.766323i	$0.277916\pi$
$912$	−8.87050	−0.293732
$913$	−13.2038	−0.436983
$914$	16.2802	0.538501
$915$	−6.21091	−0.205326
$916$	−31.3593	−1.03614
$917$	32.2152	1.06384
$918$	6.51323	0.214969
$919$	25.1781	0.830550	0.415275	−	0.909696i	$-0.363685\pi$
$919$	25.1781	0.830550	0.415275	+	0.909696i	$0.363685\pi$
$920$	33.1248	1.09209
$921$	33.4043	1.10071
$922$	4.73328	0.155882
$923$	41.4780	1.36526
$924$	49.5751	1.63090
$925$	3.40379	0.111916
$926$	18.2582	0.600002
$927$	−15.2722	−0.501606
$928$	5.85352	0.192151
$929$	54.2416	1.77961	0.889805	−	0.456342i	$-0.150841\pi$
$929$	54.2416	1.77961	0.889805	+	0.456342i	$0.150841\pi$
$930$	14.1081	0.462622
$931$	−12.3305	−0.404117
$932$	−11.1080	−0.363855
$933$	9.67442	0.316726
$934$	−5.56288	−0.182023
$935$	−51.7877	−1.69364
$936$	−34.0946	−1.11442
$937$	−1.30622	−0.0426725	−0.0213362	−	0.999772i	$-0.506792\pi$
$937$	−1.30622	−0.0426725	−0.0213362	+	0.999772i	$0.506792\pi$
$938$	2.43340	0.0794533
$939$	−40.1696	−1.31088
$940$	11.6297	0.379320
$941$	13.2446	0.431762	0.215881	−	0.976420i	$-0.430738\pi$
$941$	13.2446	0.431762	0.215881	+	0.976420i	$0.430738\pi$
$942$	−12.1643	−0.396336
$943$	3.84504	0.125212
$944$	3.25410	0.105912
$945$	−8.07328	−0.262624
$946$	3.39898	0.110511
$947$	−0.716485	−0.0232826	−0.0116413	−	0.999932i	$-0.503706\pi$
$947$	−0.716485	−0.0232826	−0.0116413	+	0.999932i	$0.503706\pi$
$948$	22.5610	0.732748
$949$	21.7474	0.705952
$950$	−3.35549	−0.108866
$951$	68.8549	2.23277
$952$	57.4722	1.86269
$953$	−47.6724	−1.54426	−0.772131	−	0.635463i	$-0.780809\pi$
$953$	−47.6724	−1.54426	−0.772131	+	0.635463i	$0.780809\pi$
$954$	4.14831	0.134306
$955$	4.23926	0.137179
$956$	32.5778	1.05364
$957$	−10.2017	−0.329775
$958$	13.0898	0.422911
$959$	−8.55387	−0.276219
$960$	9.83068	0.317284
$961$	−14.6558	−0.472768
$962$	−6.50253	−0.209650
$963$	−32.6839	−1.05322
$964$	9.87295	0.317986
$965$	−7.55751	−0.243285
$966$	42.7937	1.37686
$967$	−2.62146	−0.0843004	−0.0421502	−	0.999111i	$-0.513421\pi$
$967$	−2.62146	−0.0843004	−0.0421502	+	0.999111i	$0.513421\pi$
$968$	12.5959	0.404847
$969$	55.3246	1.77728
$970$	−13.1974	−0.423744
$971$	34.7582	1.11544	0.557722	−	0.830028i	$-0.311675\pi$
$971$	34.7582	1.11544	0.557722	+	0.830028i	$0.311675\pi$
$972$	32.7975	1.05198
$973$	3.30412	0.105925
$974$	3.69522	0.118402
$975$	14.3840	0.460656
$976$	−1.43014	−0.0457778
$977$	51.6897	1.65370	0.826851	−	0.562421i	$-0.190130\pi$
$977$	51.6897	1.65370	0.826851	+	0.562421i	$0.190130\pi$
$978$	30.2853	0.968416
$979$	23.9123	0.764241
$980$	−10.8315	−0.346000
$981$	47.4799	1.51592
$982$	−15.7154	−0.501498
$983$	56.2972	1.79560	0.897800	−	0.440402i	$-0.145164\pi$
$983$	56.2972	1.79560	0.897800	+	0.440402i	$0.145164\pi$
$984$	3.54988	0.113166
$985$	−2.65468	−0.0845852
$986$	−5.01165	−0.159604
$987$	35.4554	1.12856
$988$	−17.8129	−0.566703
$989$	−8.15312	−0.259254
$990$	−19.1934	−0.610006
$991$	34.3874	1.09235	0.546176	−	0.837670i	$-0.316083\pi$
$991$	34.3874	1.09235	0.546176	+	0.837670i	$0.316083\pi$
$992$	23.6646	0.751350
$993$	−19.1824	−0.608736
$994$	−25.9129	−0.821907
$995$	−1.11643	−0.0353931
$996$	12.3908	0.392618
$997$	22.3604	0.708162	0.354081	−	0.935215i	$-0.384794\pi$
$997$	22.3604	0.708162	0.354081	+	0.935215i	$0.384794\pi$
$998$	−18.1560	−0.574718
$999$	−3.01901	−0.0955173

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.c.1.23	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.c.1.23	✓	61	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-0.727508 q^{2} +2.55135 q^{3} -1.47073 q^{4} +1.88009 q^{5} -1.85613 q^{6} -3.30412 q^{7} +2.52498 q^{8} +3.50938 q^{9} +O(q^{10})\)	\(q-0.727508 q^{2} +2.55135 q^{3} -1.47073 q^{4} +1.88009 q^{5} -1.85613 q^{6} -3.30412 q^{7} +2.52498 q^{8} +3.50938 q^{9} -1.36778 q^{10} +3.99856 q^{11} -3.75235 q^{12} -3.84765 q^{13} +2.40377 q^{14} +4.79677 q^{15} +1.10452 q^{16} -6.88880 q^{17} -2.55310 q^{18} -3.14778 q^{19} -2.76511 q^{20} -8.42996 q^{21} -2.90899 q^{22} +6.97776 q^{23} +6.44212 q^{24} -1.46526 q^{25} +2.79919 q^{26} +1.29962 q^{27} +4.85948 q^{28} -1.00000 q^{29} -3.48969 q^{30} -4.04279 q^{31} -5.85352 q^{32} +10.2017 q^{33} +5.01165 q^{34} -6.21205 q^{35} -5.16137 q^{36} -2.32300 q^{37} +2.29004 q^{38} -9.81669 q^{39} +4.74720 q^{40} +0.551042 q^{41} +6.13286 q^{42} -1.16844 q^{43} -5.88082 q^{44} +6.59796 q^{45} -5.07637 q^{46} -4.20588 q^{47} +2.81802 q^{48} +3.91721 q^{49} +1.06599 q^{50} -17.5757 q^{51} +5.65886 q^{52} -1.62481 q^{53} -0.945481 q^{54} +7.51766 q^{55} -8.34285 q^{56} -8.03110 q^{57} +0.727508 q^{58} +2.94617 q^{59} -7.05477 q^{60} -1.29481 q^{61} +2.94116 q^{62} -11.5954 q^{63} +2.04944 q^{64} -7.23393 q^{65} -7.42184 q^{66} +1.01233 q^{67} +10.1316 q^{68} +17.8027 q^{69} +4.51931 q^{70} -10.7801 q^{71} +8.86114 q^{72} -5.65214 q^{73} +1.69000 q^{74} -3.73838 q^{75} +4.62955 q^{76} -13.2117 q^{77} +7.14172 q^{78} -6.01250 q^{79} +2.07660 q^{80} -7.21237 q^{81} -0.400887 q^{82} -3.30215 q^{83} +12.3982 q^{84} -12.9516 q^{85} +0.850052 q^{86} -2.55135 q^{87} +10.0963 q^{88} +5.98023 q^{89} -4.80007 q^{90} +12.7131 q^{91} -10.2624 q^{92} -10.3146 q^{93} +3.05981 q^{94} -5.91812 q^{95} -14.9344 q^{96} +9.64879 q^{97} -2.84980 q^{98} +14.0325 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9} - 16 q^{10} - 3 q^{11} - 18 q^{12} - 28 q^{13} - 14 q^{14} - 12 q^{15} + 11 q^{16} - 21 q^{17} - 17 q^{18} - 36 q^{19} - 16 q^{20} - 12 q^{21} - 42 q^{22} - 15 q^{23} - 28 q^{24} - 16 q^{25} - 13 q^{26} - 10 q^{27} - 25 q^{28} - 61 q^{29} - 12 q^{30} - 18 q^{31} - 3 q^{32} - 42 q^{33} - 22 q^{34} - 29 q^{35} - 38 q^{36} - 30 q^{37} - 27 q^{38} - 31 q^{39} - 22 q^{40} - 28 q^{41} - 9 q^{42} - 58 q^{43} - 2 q^{44} - 31 q^{45} - 40 q^{46} - 6 q^{47} - 37 q^{48} - 37 q^{49} - 15 q^{50} - 44 q^{51} - 43 q^{52} - 27 q^{53} - 18 q^{54} - 38 q^{55} - 22 q^{56} - 50 q^{57} + q^{58} - 24 q^{59} + 6 q^{60} - 76 q^{61} - 17 q^{62} - 6 q^{63} - 60 q^{64} - 65 q^{65} - 7 q^{66} - 45 q^{67} - 31 q^{68} - 16 q^{69} - 48 q^{70} - 28 q^{71} - 40 q^{72} - 50 q^{73} - 17 q^{74} - 35 q^{75} - 100 q^{76} + q^{77} - 6 q^{78} - 66 q^{79} - 10 q^{80} - 63 q^{81} - 5 q^{82} - 9 q^{83} - 24 q^{84} - 77 q^{85} + 29 q^{86} + 4 q^{87} - 62 q^{88} - 30 q^{89} + 50 q^{90} - 52 q^{91} - 53 q^{92} - 42 q^{93} - 92 q^{94} - 20 q^{95} - 47 q^{96} - 34 q^{97} + 36 q^{98} - 29 q^{99}+O(q^{100}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9 - 16 * q^10 - 3 * q^11 - 18 * q^12 - 28 * q^13 - 14 * q^14 - 12 * q^15 + 11 * q^16 - 21 * q^17 - 17 * q^18 - 36 * q^19 - 16 * q^20 - 12 * q^21 - 42 * q^22 - 15 * q^23 - 28 * q^24 - 16 * q^25 - 13 * q^26 - 10 * q^27 - 25 * q^28 - 61 * q^29 - 12 * q^30 - 18 * q^31 - 3 * q^32 - 42 * q^33 - 22 * q^34 - 29 * q^35 - 38 * q^36 - 30 * q^37 - 27 * q^38 - 31 * q^39 - 22 * q^40 - 28 * q^41 - 9 * q^42 - 58 * q^43 - 2 * q^44 - 31 * q^45 - 40 * q^46 - 6 * q^47 - 37 * q^48 - 37 * q^49 - 15 * q^50 - 44 * q^51 - 43 * q^52 - 27 * q^53 - 18 * q^54 - 38 * q^55 - 22 * q^56 - 50 * q^57 + q^58 - 24 * q^59 + 6 * q^60 - 76 * q^61 - 17 * q^62 - 6 * q^63 - 60 * q^64 - 65 * q^65 - 7 * q^66 - 45 * q^67 - 31 * q^68 - 16 * q^69 - 48 * q^70 - 28 * q^71 - 40 * q^72 - 50 * q^73 - 17 * q^74 - 35 * q^75 - 100 * q^76 + q^77 - 6 * q^78 - 66 * q^79 - 10 * q^80 - 63 * q^81 - 5 * q^82 - 9 * q^83 - 24 * q^84 - 77 * q^85 + 29 * q^86 + 4 * q^87 - 62 * q^88 - 30 * q^89 + 50 * q^90 - 52 * q^91 - 53 * q^92 - 42 * q^93 - 92 * q^94 - 20 * q^95 - 47 * q^96 - 34 * q^97 + 36 * q^98 - 29 * q^99

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