LMFDB - Embedded newform 8049.2.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8049,2,Mod(1,8049)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, 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("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8049 = 3 \cdot 2683 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8049.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.2715885869$
Analytic rank:	$1$
Dimension:	$95$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67709 q^{2} +1.00000 q^{3} +5.16680 q^{4} +1.53691 q^{5} -2.67709 q^{6} +1.80566 q^{7} -8.47779 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.67709 q^{2} +1.00000 q^{3} +5.16680 q^{4} +1.53691 q^{5} -2.67709 q^{6} +1.80566 q^{7} -8.47779 q^{8} +1.00000 q^{9} -4.11445 q^{10} -1.56831 q^{11} +5.16680 q^{12} -5.72621 q^{13} -4.83390 q^{14} +1.53691 q^{15} +12.3622 q^{16} -0.930070 q^{17} -2.67709 q^{18} +3.29243 q^{19} +7.94092 q^{20} +1.80566 q^{21} +4.19849 q^{22} +3.70821 q^{23} -8.47779 q^{24} -2.63789 q^{25} +15.3296 q^{26} +1.00000 q^{27} +9.32947 q^{28} +1.66160 q^{29} -4.11445 q^{30} -9.20024 q^{31} -16.1391 q^{32} -1.56831 q^{33} +2.48988 q^{34} +2.77514 q^{35} +5.16680 q^{36} -8.61718 q^{37} -8.81412 q^{38} -5.72621 q^{39} -13.0296 q^{40} +7.27294 q^{41} -4.83390 q^{42} -2.21917 q^{43} -8.10311 q^{44} +1.53691 q^{45} -9.92720 q^{46} +4.42933 q^{47} +12.3622 q^{48} -3.73960 q^{49} +7.06187 q^{50} -0.930070 q^{51} -29.5862 q^{52} +2.31352 q^{53} -2.67709 q^{54} -2.41035 q^{55} -15.3080 q^{56} +3.29243 q^{57} -4.44824 q^{58} -2.40029 q^{59} +7.94092 q^{60} -13.6526 q^{61} +24.6299 q^{62} +1.80566 q^{63} +18.4813 q^{64} -8.80070 q^{65} +4.19849 q^{66} +8.38233 q^{67} -4.80548 q^{68} +3.70821 q^{69} -7.42930 q^{70} +11.9609 q^{71} -8.47779 q^{72} -6.31125 q^{73} +23.0689 q^{74} -2.63789 q^{75} +17.0113 q^{76} -2.83182 q^{77} +15.3296 q^{78} +13.3217 q^{79} +18.9996 q^{80} +1.00000 q^{81} -19.4703 q^{82} +14.1171 q^{83} +9.32947 q^{84} -1.42944 q^{85} +5.94091 q^{86} +1.66160 q^{87} +13.2958 q^{88} -11.8526 q^{89} -4.11445 q^{90} -10.3396 q^{91} +19.1596 q^{92} -9.20024 q^{93} -11.8577 q^{94} +5.06018 q^{95} -16.1391 q^{96} +10.5041 q^{97} +10.0112 q^{98} -1.56831 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 95 q - 9 q^{2} + 95 q^{3} + 65 q^{4} - 15 q^{5} - 9 q^{6} - 36 q^{7} - 27 q^{8} + 95 q^{9}+O(q^{10}) $ 95 * q - 9 * q^2 + 95 * q^3 + 65 * q^4 - 15 * q^5 - 9 * q^6 - 36 * q^7 - 27 * q^8 + 95 * q^9	\( 95 q - 9 q^{2} + 95 q^{3} + 65 q^{4} - 15 q^{5} - 9 q^{6} - 36 q^{7} - 27 q^{8} + 95 q^{9} - 36 q^{10} - 48 q^{11} + 65 q^{12} - 73 q^{13} - 17 q^{14} - 15 q^{15} + 13 q^{16} - 9 q^{17} - 9 q^{18} - 66 q^{19} - 35 q^{20} - 36 q^{21} - 37 q^{22} - 58 q^{23} - 27 q^{24} + 24 q^{25} - 25 q^{26} + 95 q^{27} - 75 q^{28} - 31 q^{29} - 36 q^{30} - 129 q^{31} - 53 q^{32} - 48 q^{33} - 61 q^{34} - 38 q^{35} + 65 q^{36} - 127 q^{37} + q^{38} - 73 q^{39} - 74 q^{40} - 31 q^{41} - 17 q^{42} - 62 q^{43} - 76 q^{44} - 15 q^{45} - 60 q^{46} - 75 q^{47} + 13 q^{48} + 5 q^{49} - 30 q^{50} - 9 q^{51} - 137 q^{52} - 28 q^{53} - 9 q^{54} - 117 q^{55} - 23 q^{56} - 66 q^{57} - 90 q^{58} - 60 q^{59} - 35 q^{60} - 96 q^{61} + 10 q^{62} - 36 q^{63} - 75 q^{64} - 28 q^{65} - 37 q^{66} - 116 q^{67} + 3 q^{68} - 58 q^{69} - 73 q^{70} - 144 q^{71} - 27 q^{72} - 121 q^{73} - 16 q^{74} + 24 q^{75} - 118 q^{76} - 3 q^{77} - 25 q^{78} - 135 q^{79} - 36 q^{80} + 95 q^{81} - 102 q^{82} - 21 q^{83} - 75 q^{84} - 129 q^{85} - 46 q^{86} - 31 q^{87} - 77 q^{88} - 63 q^{89} - 36 q^{90} - 123 q^{91} - 42 q^{92} - 129 q^{93} - 44 q^{94} - 80 q^{95} - 53 q^{96} - 144 q^{97} + 10 q^{98} - 48 q^{99}+O(q^{100}) \) 95 * q - 9 * q^2 + 95 * q^3 + 65 * q^4 - 15 * q^5 - 9 * q^6 - 36 * q^7 - 27 * q^8 + 95 * q^9 - 36 * q^10 - 48 * q^11 + 65 * q^12 - 73 * q^13 - 17 * q^14 - 15 * q^15 + 13 * q^16 - 9 * q^17 - 9 * q^18 - 66 * q^19 - 35 * q^20 - 36 * q^21 - 37 * q^22 - 58 * q^23 - 27 * q^24 + 24 * q^25 - 25 * q^26 + 95 * q^27 - 75 * q^28 - 31 * q^29 - 36 * q^30 - 129 * q^31 - 53 * q^32 - 48 * q^33 - 61 * q^34 - 38 * q^35 + 65 * q^36 - 127 * q^37 + q^38 - 73 * q^39 - 74 * q^40 - 31 * q^41 - 17 * q^42 - 62 * q^43 - 76 * q^44 - 15 * q^45 - 60 * q^46 - 75 * q^47 + 13 * q^48 + 5 * q^49 - 30 * q^50 - 9 * q^51 - 137 * q^52 - 28 * q^53 - 9 * q^54 - 117 * q^55 - 23 * q^56 - 66 * q^57 - 90 * q^58 - 60 * q^59 - 35 * q^60 - 96 * q^61 + 10 * q^62 - 36 * q^63 - 75 * q^64 - 28 * q^65 - 37 * q^66 - 116 * q^67 + 3 * q^68 - 58 * q^69 - 73 * q^70 - 144 * q^71 - 27 * q^72 - 121 * q^73 - 16 * q^74 + 24 * q^75 - 118 * q^76 - 3 * q^77 - 25 * q^78 - 135 * q^79 - 36 * q^80 + 95 * q^81 - 102 * q^82 - 21 * q^83 - 75 * q^84 - 129 * q^85 - 46 * q^86 - 31 * q^87 - 77 * q^88 - 63 * q^89 - 36 * q^90 - 123 * q^91 - 42 * q^92 - 129 * q^93 - 44 * q^94 - 80 * q^95 - 53 * q^96 - 144 * q^97 + 10 * q^98 - 48 * 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 $

$2$	−2.67709	−1.89299	−0.946493	−	0.322724i	$-0.895402\pi$
$2$	−2.67709	−1.89299	−0.946493	+	0.322724i	$0.895402\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.16680	2.58340
$5$	1.53691	0.687329	0.343665	−	0.939092i	$-0.388332\pi$
$5$	1.53691	0.687329	0.343665	+	0.939092i	$0.388332\pi$
$6$	−2.67709	−1.09292
$7$	1.80566	0.682475	0.341237	−	0.939977i	$-0.389154\pi$
$7$	1.80566	0.682475	0.341237	+	0.939977i	$0.389154\pi$
$8$	−8.47779	−2.99735
$9$	1.00000	0.333333
$10$	−4.11445	−1.30110
$11$	−1.56831	−0.472862	−0.236431	−	0.971648i	$-0.575978\pi$
$11$	−1.56831	−0.472862	−0.236431	+	0.971648i	$0.575978\pi$
$12$	5.16680	1.49153
$13$	−5.72621	−1.58817	−0.794083	−	0.607809i	$-0.792048\pi$
$13$	−5.72621	−1.58817	−0.794083	+	0.607809i	$0.792048\pi$
$14$	−4.83390	−1.29192
$15$	1.53691	0.396830
$16$	12.3622	3.09055
$17$	−0.930070	−0.225575	−0.112788	−	0.993619i	$-0.535978\pi$
$17$	−0.930070	−0.225575	−0.112788	+	0.993619i	$0.535978\pi$
$18$	−2.67709	−0.630995
$19$	3.29243	0.755335	0.377667	−	0.925941i	$-0.376726\pi$
$19$	3.29243	0.755335	0.377667	+	0.925941i	$0.376726\pi$
$20$	7.94092	1.77564
$21$	1.80566	0.394027
$22$	4.19849	0.895121
$23$	3.70821	0.773215	0.386607	−	0.922244i	$-0.373647\pi$
$23$	3.70821	0.773215	0.386607	+	0.922244i	$0.373647\pi$
$24$	−8.47779	−1.73052
$25$	−2.63789	−0.527579
$26$	15.3296	3.00638
$27$	1.00000	0.192450
$28$	9.32947	1.76310
$29$	1.66160	0.308551	0.154275	−	0.988028i	$-0.450696\pi$
$29$	1.66160	0.308551	0.154275	+	0.988028i	$0.450696\pi$
$30$	−4.11445	−0.751193
$31$	−9.20024	−1.65241	−0.826206	−	0.563368i	$-0.809505\pi$
$31$	−9.20024	−1.65241	−0.826206	+	0.563368i	$0.809505\pi$
$32$	−16.1391	−2.85301
$33$	−1.56831	−0.273007
$34$	2.48988	0.427010
$35$	2.77514	0.469085
$36$	5.16680	0.861133
$37$	−8.61718	−1.41666	−0.708328	−	0.705884i	$-0.750550\pi$
$37$	−8.61718	−1.41666	−0.708328	+	0.705884i	$0.750550\pi$
$38$	−8.81412	−1.42984
$39$	−5.72621	−0.916928
$40$	−13.0296	−2.06017
$41$	7.27294	1.13584	0.567921	−	0.823083i	$-0.307748\pi$
$41$	7.27294	1.13584	0.567921	+	0.823083i	$0.307748\pi$
$42$	−4.83390	−0.745888
$43$	−2.21917	−0.338420	−0.169210	−	0.985580i	$-0.554122\pi$
$43$	−2.21917	−0.338420	−0.169210	+	0.985580i	$0.554122\pi$
$44$	−8.10311	−1.22159
$45$	1.53691	0.229110
$46$	−9.92720	−1.46369
$47$	4.42933	0.646083	0.323042	−	0.946385i	$-0.395295\pi$
$47$	4.42933	0.646083	0.323042	+	0.946385i	$0.395295\pi$
$48$	12.3622	1.78433
$49$	−3.73960	−0.534228
$50$	7.06187	0.998699
$51$	−0.930070	−0.130236
$52$	−29.5862	−4.10286
$53$	2.31352	0.317787	0.158893	−	0.987296i	$-0.449207\pi$
$53$	2.31352	0.317787	0.158893	+	0.987296i	$0.449207\pi$
$54$	−2.67709	−0.364305
$55$	−2.41035	−0.325012
$56$	−15.3080	−2.04562
$57$	3.29243	0.436093
$58$	−4.44824	−0.584082
$59$	−2.40029	−0.312491	−0.156245	−	0.987718i	$-0.549939\pi$
$59$	−2.40029	−0.312491	−0.156245	+	0.987718i	$0.549939\pi$
$60$	7.94092	1.02517
$61$	−13.6526	−1.74804	−0.874020	−	0.485890i	$-0.838495\pi$
$61$	−13.6526	−1.74804	−0.874020	+	0.485890i	$0.838495\pi$
$62$	24.6299	3.12799
$63$	1.80566	0.227492
$64$	18.4813	2.31017
$65$	−8.80070	−1.09159
$66$	4.19849	0.516799
$67$	8.38233	1.02406	0.512032	−	0.858966i	$-0.328893\pi$
$67$	8.38233	1.02406	0.512032	+	0.858966i	$0.328893\pi$
$68$	−4.80548	−0.582750
$69$	3.70821	0.446416
$70$	−7.42930	−0.887971
$71$	11.9609	1.41950	0.709751	−	0.704452i	$-0.248807\pi$
$71$	11.9609	1.41950	0.709751	+	0.704452i	$0.248807\pi$
$72$	−8.47779	−0.999117
$73$	−6.31125	−0.738676	−0.369338	−	0.929295i	$-0.620415\pi$
$73$	−6.31125	−0.738676	−0.369338	+	0.929295i	$0.620415\pi$
$74$	23.0689	2.68171
$75$	−2.63789	−0.304598
$76$	17.0113	1.95133
$77$	−2.83182	−0.322716
$78$	15.3296	1.73573
$79$	13.3217	1.49881	0.749403	−	0.662114i	$-0.230340\pi$
$79$	13.3217	1.49881	0.749403	+	0.662114i	$0.230340\pi$
$80$	18.9996	2.12422
$81$	1.00000	0.111111
$82$	−19.4703	−2.15013
$83$	14.1171	1.54956	0.774779	−	0.632233i	$-0.217861\pi$
$83$	14.1171	1.54956	0.774779	+	0.632233i	$0.217861\pi$
$84$	9.32947	1.01793
$85$	−1.42944	−0.155044
$86$	5.94091	0.640625
$87$	1.66160	0.178142
$88$	13.2958	1.41733
$89$	−11.8526	−1.25637	−0.628187	−	0.778063i	$-0.716203\pi$
$89$	−11.8526	−1.25637	−0.628187	+	0.778063i	$0.716203\pi$
$90$	−4.11445	−0.433702
$91$	−10.3396	−1.08388
$92$	19.1596	1.99752
$93$	−9.20024	−0.954021
$94$	−11.8577	−1.22303
$95$	5.06018	0.519164
$96$	−16.1391	−1.64719
$97$	10.5041	1.06653	0.533267	−	0.845947i	$-0.320964\pi$
$97$	10.5041	1.06653	0.533267	+	0.845947i	$0.320964\pi$
$98$	10.0112	1.01129
$99$	−1.56831	−0.157621
$100$	−13.6295	−1.36295
$101$	−0.448956	−0.0446728	−0.0223364	−	0.999751i	$-0.507110\pi$
$101$	−0.448956	−0.0446728	−0.0223364	+	0.999751i	$0.507110\pi$
$102$	2.48988	0.246535
$103$	−4.48084	−0.441511	−0.220755	−	0.975329i	$-0.570852\pi$
$103$	−4.48084	−0.441511	−0.220755	+	0.975329i	$0.570852\pi$
$104$	48.5456	4.76029
$105$	2.77514	0.270826
$106$	−6.19351	−0.601566
$107$	17.5022	1.69200	0.846002	−	0.533179i	$-0.179003\pi$
$107$	17.5022	1.69200	0.846002	+	0.533179i	$0.179003\pi$
$108$	5.16680	0.497175
$109$	−11.1490	−1.06788	−0.533941	−	0.845522i	$-0.679289\pi$
$109$	−11.1490	−1.06788	−0.533941	+	0.845522i	$0.679289\pi$
$110$	6.45272	0.615243
$111$	−8.61718	−0.817906
$112$	22.3219	2.10922
$113$	−13.8153	−1.29963	−0.649817	−	0.760091i	$-0.725154\pi$
$113$	−13.8153	−1.29963	−0.649817	+	0.760091i	$0.725154\pi$
$114$	−8.81412	−0.825518
$115$	5.69920	0.531453
$116$	8.58512	0.797109
$117$	−5.72621	−0.529389
$118$	6.42578	0.591541
$119$	−1.67939	−0.153949
$120$	−13.0296	−1.18944
$121$	−8.54042	−0.776402
$122$	36.5493	3.30902
$123$	7.27294	0.655779
$124$	−47.5358	−4.26884
$125$	−11.7388	−1.04995
$126$	−4.83390	−0.430638
$127$	0.584049	0.0518260	0.0259130	−	0.999664i	$-0.491751\pi$
$127$	0.584049	0.0518260	0.0259130	+	0.999664i	$0.491751\pi$
$128$	−17.1980	−1.52010
$129$	−2.21917	−0.195387
$130$	23.5602	2.06637
$131$	−18.7440	−1.63768	−0.818838	−	0.574025i	$-0.805381\pi$
$131$	−18.7440	−1.63768	−0.818838	+	0.574025i	$0.805381\pi$
$132$	−8.10311	−0.705286
$133$	5.94500	0.515497
$134$	−22.4402	−1.93854
$135$	1.53691	0.132277
$136$	7.88493	0.676127
$137$	−10.7365	−0.917283	−0.458642	−	0.888621i	$-0.651664\pi$
$137$	−10.7365	−0.917283	−0.458642	+	0.888621i	$0.651664\pi$
$138$	−9.92720	−0.845059
$139$	4.78105	0.405524	0.202762	−	0.979228i	$-0.435008\pi$
$139$	4.78105	0.405524	0.202762	+	0.979228i	$0.435008\pi$
$140$	14.3386	1.21183
$141$	4.42933	0.373016
$142$	−32.0205	−2.68710
$143$	8.98045	0.750983
$144$	12.3622	1.03018
$145$	2.55373	0.212076
$146$	16.8958	1.39830
$147$	−3.73960	−0.308437
$148$	−44.5232	−3.65978
$149$	−20.6445	−1.69126	−0.845631	−	0.533767i	$-0.820776\pi$
$149$	−20.6445	−1.69126	−0.845631	+	0.533767i	$0.820776\pi$
$150$	7.06187	0.576599
$151$	11.3835	0.926380	0.463190	−	0.886259i	$-0.346705\pi$
$151$	11.3835	0.926380	0.463190	+	0.886259i	$0.346705\pi$
$152$	−27.9125	−2.26400
$153$	−0.930070	−0.0751917
$154$	7.58104	0.610898
$155$	−14.1400	−1.13575
$156$	−29.5862	−2.36879
$157$	2.06058	0.164452	0.0822260	−	0.996614i	$-0.473797\pi$
$157$	2.06058	0.164452	0.0822260	+	0.996614i	$0.473797\pi$
$158$	−35.6633	−2.83722
$159$	2.31352	0.183474
$160$	−24.8044	−1.96096
$161$	6.69576	0.527700
$162$	−2.67709	−0.210332
$163$	17.4738	1.36866	0.684329	−	0.729174i	$-0.260095\pi$
$163$	17.4738	1.36866	0.684329	+	0.729174i	$0.260095\pi$
$164$	37.5778	2.93433
$165$	−2.41035	−0.187646
$166$	−37.7928	−2.93329
$167$	−8.37585	−0.648143	−0.324071	−	0.946033i	$-0.605052\pi$
$167$	−8.37585	−0.648143	−0.324071	+	0.946033i	$0.605052\pi$
$168$	−15.3080	−1.18104
$169$	19.7895	1.52227
$170$	3.82673	0.293497
$171$	3.29243	0.251778
$172$	−11.4660	−0.874274
$173$	10.6309	0.808253	0.404126	−	0.914703i	$-0.367576\pi$
$173$	10.6309	0.808253	0.404126	+	0.914703i	$0.367576\pi$
$174$	−4.44824	−0.337220
$175$	−4.76313	−0.360059
$176$	−19.3877	−1.46140
$177$	−2.40029	−0.180417
$178$	31.7305	2.37830
$179$	−24.7023	−1.84634	−0.923169	−	0.384395i	$-0.874410\pi$
$179$	−24.7023	−1.84634	−0.923169	+	0.384395i	$0.874410\pi$
$180$	7.94092	0.591881
$181$	−17.7835	−1.32184	−0.660918	−	0.750458i	$-0.729833\pi$
$181$	−17.7835	−1.32184	−0.660918	+	0.750458i	$0.729833\pi$
$182$	27.6800	2.05178
$183$	−13.6526	−1.00923
$184$	−31.4374	−2.31760
$185$	−13.2439	−0.973709
$186$	24.6299	1.80595
$187$	1.45863	0.106666
$188$	22.8854	1.66909
$189$	1.80566	0.131342
$190$	−13.5465	−0.982770
$191$	−25.8084	−1.86743	−0.933716	−	0.358014i	$-0.883454\pi$
$191$	−25.8084	−1.86743	−0.933716	+	0.358014i	$0.883454\pi$
$192$	18.4813	1.33377
$193$	9.93312	0.715002	0.357501	−	0.933913i	$-0.383629\pi$
$193$	9.93312	0.715002	0.357501	+	0.933913i	$0.383629\pi$
$194$	−28.1205	−2.01893
$195$	−8.80070	−0.630231
$196$	−19.3217	−1.38012
$197$	−22.5268	−1.60497	−0.802485	−	0.596672i	$-0.796489\pi$
$197$	−22.5268	−1.60497	−0.802485	+	0.596672i	$0.796489\pi$
$198$	4.19849	0.298374
$199$	−12.4375	−0.881674	−0.440837	−	0.897587i	$-0.645318\pi$
$199$	−12.4375	−0.881674	−0.440837	+	0.897587i	$0.645318\pi$
$200$	22.3635	1.58134
$201$	8.38233	0.591244
$202$	1.20189	0.0845650
$203$	3.00027	0.210578
$204$	−4.80548	−0.336451
$205$	11.1779	0.780697
$206$	11.9956	0.835774
$207$	3.70821	0.257738
$208$	−70.7885	−4.90830
$209$	−5.16353	−0.357169
$210$	−7.42930	−0.512670
$211$	6.90125	0.475101	0.237551	−	0.971375i	$-0.423655\pi$
$211$	6.90125	0.475101	0.237551	+	0.971375i	$0.423655\pi$
$212$	11.9535	0.820970
$213$	11.9609	0.819550
$214$	−46.8550	−3.20294
$215$	−3.41068	−0.232606
$216$	−8.47779	−0.576840
$217$	−16.6125	−1.12773
$218$	29.8469	2.02148
$219$	−6.31125	−0.426475
$220$	−12.4538	−0.839635
$221$	5.32578	0.358251
$222$	23.0689	1.54829
$223$	−27.9702	−1.87302	−0.936510	−	0.350640i	$-0.885964\pi$
$223$	−27.9702	−1.87302	−0.936510	+	0.350640i	$0.885964\pi$
$224$	−29.1416	−1.94711
$225$	−2.63789	−0.175860
$226$	36.9847	2.46019
$227$	8.37837	0.556092	0.278046	−	0.960568i	$-0.410313\pi$
$227$	8.37837	0.556092	0.278046	+	0.960568i	$0.410313\pi$
$228$	17.0113	1.12660
$229$	−1.51179	−0.0999016	−0.0499508	−	0.998752i	$-0.515906\pi$
$229$	−1.51179	−0.0999016	−0.0499508	+	0.998752i	$0.515906\pi$
$230$	−15.2573	−1.00603
$231$	−2.83182	−0.186320
$232$	−14.0867	−0.924834
$233$	16.5694	1.08550	0.542748	−	0.839896i	$-0.317384\pi$
$233$	16.5694	1.08550	0.542748	+	0.839896i	$0.317384\pi$
$234$	15.3296	1.00213
$235$	6.80749	0.444072
$236$	−12.4018	−0.807288
$237$	13.3217	0.865336
$238$	4.49587	0.291424
$239$	−21.1997	−1.37129	−0.685646	−	0.727935i	$-0.740480\pi$
$239$	−21.1997	−1.37129	−0.685646	+	0.727935i	$0.740480\pi$
$240$	18.9996	1.22642
$241$	−6.44436	−0.415118	−0.207559	−	0.978223i	$-0.566552\pi$
$241$	−6.44436	−0.415118	−0.207559	+	0.978223i	$0.566552\pi$
$242$	22.8634	1.46972
$243$	1.00000	0.0641500
$244$	−70.5403	−4.51588
$245$	−5.74744	−0.367191
$246$	−19.4703	−1.24138
$247$	−18.8531	−1.19960
$248$	77.9977	4.95286
$249$	14.1171	0.894637
$250$	31.4258	1.98754
$251$	−16.9119	−1.06747	−0.533733	−	0.845653i	$-0.679211\pi$
$251$	−16.9119	−1.06747	−0.533733	+	0.845653i	$0.679211\pi$
$252$	9.32947	0.587701
$253$	−5.81560	−0.365624
$254$	−1.56355	−0.0981059
$255$	−1.42944	−0.0895149
$256$	9.07783	0.567364
$257$	1.32265	0.0825046	0.0412523	−	0.999149i	$-0.486865\pi$
$257$	1.32265	0.0825046	0.0412523	+	0.999149i	$0.486865\pi$
$258$	5.94091	0.369865
$259$	−15.5597	−0.966832
$260$	−45.4714	−2.82002
$261$	1.66160	0.102850
$262$	50.1794	3.10010
$263$	27.7364	1.71030	0.855150	−	0.518380i	$-0.173465\pi$
$263$	27.7364	1.71030	0.855150	+	0.518380i	$0.173465\pi$
$264$	13.2958	0.818298
$265$	3.55569	0.218424
$266$	−15.9153	−0.975829
$267$	−11.8526	−0.725368
$268$	43.3098	2.64557
$269$	13.4354	0.819170	0.409585	−	0.912272i	$-0.365673\pi$
$269$	13.4354	0.819170	0.409585	+	0.912272i	$0.365673\pi$
$270$	−4.11445	−0.250398
$271$	9.90902	0.601930	0.300965	−	0.953635i	$-0.402691\pi$
$271$	9.90902	0.601930	0.300965	+	0.953635i	$0.402691\pi$
$272$	−11.4977	−0.697150
$273$	−10.3396	−0.625780
$274$	28.7426	1.73641
$275$	4.13702	0.249472
$276$	19.1596	1.15327
$277$	−24.8777	−1.49476	−0.747379	−	0.664398i	$-0.768688\pi$
$277$	−24.8777	−1.49476	−0.747379	+	0.664398i	$0.768688\pi$
$278$	−12.7993	−0.767651
$279$	−9.20024	−0.550804
$280$	−23.5271	−1.40601
$281$	−3.56213	−0.212499	−0.106249	−	0.994340i	$-0.533884\pi$
$281$	−3.56213	−0.212499	−0.106249	+	0.994340i	$0.533884\pi$
$282$	−11.8577	−0.706115
$283$	5.57616	0.331468	0.165734	−	0.986170i	$-0.447001\pi$
$283$	5.57616	0.331468	0.165734	+	0.986170i	$0.447001\pi$
$284$	61.7997	3.66714
$285$	5.06018	0.299739
$286$	−24.0415	−1.42160
$287$	13.1324	0.775183
$288$	−16.1391	−0.951004
$289$	−16.1350	−0.949116
$290$	−6.83656	−0.401457
$291$	10.5041	0.615763
$292$	−32.6089	−1.90829
$293$	−1.90328	−0.111191	−0.0555955	−	0.998453i	$-0.517706\pi$
$293$	−1.90328	−0.111191	−0.0555955	+	0.998453i	$0.517706\pi$
$294$	10.0112	0.583867
$295$	−3.68904	−0.214784
$296$	73.0546	4.24621
$297$	−1.56831	−0.0910023
$298$	55.2671	3.20154
$299$	−21.2340	−1.22799
$300$	−13.6295	−0.786897
$301$	−4.00706	−0.230963
$302$	−30.4748	−1.75362
$303$	−0.448956	−0.0257918
$304$	40.7016	2.33440
$305$	−20.9829	−1.20148
$306$	2.48988	0.142337
$307$	−27.6618	−1.57874	−0.789372	−	0.613915i	$-0.789594\pi$
$307$	−27.6618	−1.57874	−0.789372	+	0.613915i	$0.789594\pi$
$308$	−14.6315	−0.833705
$309$	−4.48084	−0.254906
$310$	37.8540	2.14996
$311$	−3.32329	−0.188447	−0.0942233	−	0.995551i	$-0.530037\pi$
$311$	−3.32329	−0.188447	−0.0942233	+	0.995551i	$0.530037\pi$
$312$	48.5456	2.74835
$313$	−30.5188	−1.72503	−0.862514	−	0.506034i	$-0.831111\pi$
$313$	−30.5188	−1.72503	−0.862514	+	0.506034i	$0.831111\pi$
$314$	−5.51635	−0.311306
$315$	2.77514	0.156362
$316$	68.8304	3.87201
$317$	21.8763	1.22870	0.614349	−	0.789034i	$-0.289419\pi$
$317$	21.8763	1.22870	0.614349	+	0.789034i	$0.289419\pi$
$318$	−6.19351	−0.347315
$319$	−2.60589	−0.145902
$320$	28.4042	1.58784
$321$	17.5022	0.976879
$322$	−17.9251	−0.998928
$323$	−3.06219	−0.170385
$324$	5.16680	0.287044
$325$	15.1051	0.837882
$326$	−46.7790	−2.59085
$327$	−11.1490	−0.616541
$328$	−61.6584	−3.40452
$329$	7.99785	0.440936
$330$	6.45272	0.355211
$331$	−25.2174	−1.38607	−0.693037	−	0.720902i	$-0.743728\pi$
$331$	−25.2174	−1.38607	−0.693037	+	0.720902i	$0.743728\pi$
$332$	72.9404	4.00312
$333$	−8.61718	−0.472219
$334$	22.4229	1.22693
$335$	12.8829	0.703870
$336$	22.3219	1.21776
$337$	−11.4878	−0.625778	−0.312889	−	0.949790i	$-0.601297\pi$
$337$	−11.4878	−0.625778	−0.312889	+	0.949790i	$0.601297\pi$
$338$	−52.9783	−2.88164
$339$	−13.8153	−0.750344
$340$	−7.38561	−0.400541
$341$	14.4288	0.781363
$342$	−8.81412	−0.476613
$343$	−19.3920	−1.04707
$344$	18.8137	1.01436
$345$	5.69920	0.306835
$346$	−28.4599	−1.53001
$347$	2.26547	0.121617	0.0608084	−	0.998149i	$-0.480632\pi$
$347$	2.26547	0.121617	0.0608084	+	0.998149i	$0.480632\pi$
$348$	8.58512	0.460211
$349$	33.2731	1.78107	0.890534	−	0.454917i	$-0.150331\pi$
$349$	33.2731	1.78107	0.890534	+	0.454917i	$0.150331\pi$
$350$	12.7513	0.681587
$351$	−5.72621	−0.305643
$352$	25.3110	1.34908
$353$	−30.1877	−1.60673	−0.803364	−	0.595488i	$-0.796959\pi$
$353$	−30.1877	−1.60673	−0.803364	+	0.595488i	$0.796959\pi$
$354$	6.42578	0.341526
$355$	18.3829	0.975665
$356$	−61.2400	−3.24571
$357$	−1.67939	−0.0888826
$358$	66.1302	3.49509
$359$	−17.7447	−0.936528	−0.468264	−	0.883589i	$-0.655120\pi$
$359$	−17.7447	−0.936528	−0.468264	+	0.883589i	$0.655120\pi$
$360$	−13.0296	−0.686722
$361$	−8.15992	−0.429469
$362$	47.6080	2.50222
$363$	−8.54042	−0.448256
$364$	−53.4225	−2.80010
$365$	−9.69985	−0.507713
$366$	36.5493	1.91046
$367$	−14.2503	−0.743859	−0.371929	−	0.928261i	$-0.621304\pi$
$367$	−14.2503	−0.743859	−0.371929	+	0.928261i	$0.621304\pi$
$368$	45.8415	2.38966
$369$	7.27294	0.378614
$370$	35.4550	1.84322
$371$	4.17743	0.216882
$372$	−47.5358	−2.46462
$373$	15.0339	0.778424	0.389212	−	0.921148i	$-0.372747\pi$
$373$	15.0339	0.778424	0.389212	+	0.921148i	$0.372747\pi$
$374$	−3.90489	−0.201917
$375$	−11.7388	−0.606189
$376$	−37.5509	−1.93654
$377$	−9.51465	−0.490029
$378$	−4.83390	−0.248629
$379$	28.9764	1.48842	0.744208	−	0.667948i	$-0.232827\pi$
$379$	28.9764	1.48842	0.744208	+	0.667948i	$0.232827\pi$
$380$	26.1449	1.34121
$381$	0.584049	0.0299217
$382$	69.0914	3.53502
$383$	−27.4710	−1.40370	−0.701851	−	0.712324i	$-0.747643\pi$
$383$	−27.4710	−1.40370	−0.701851	+	0.712324i	$0.747643\pi$
$384$	−17.1980	−0.877630
$385$	−4.35227	−0.221812
$386$	−26.5918	−1.35349
$387$	−2.21917	−0.112807
$388$	54.2727	2.75528
$389$	9.48553	0.480935	0.240468	−	0.970657i	$-0.422699\pi$
$389$	9.48553	0.480935	0.240468	+	0.970657i	$0.422699\pi$
$390$	23.5602	1.19302
$391$	−3.44889	−0.174418
$392$	31.7035	1.60127
$393$	−18.7440	−0.945512
$394$	60.3063	3.03819
$395$	20.4743	1.03017
$396$	−8.10311	−0.407197
$397$	−6.61778	−0.332137	−0.166068	−	0.986114i	$-0.553107\pi$
$397$	−6.61778	−0.332137	−0.166068	+	0.986114i	$0.553107\pi$
$398$	33.2964	1.66900
$399$	5.94500	0.297622
$400$	−32.6101	−1.63051
$401$	−0.343746	−0.0171659	−0.00858293	−	0.999963i	$-0.502732\pi$
$401$	−0.343746	−0.0171659	−0.00858293	+	0.999963i	$0.502732\pi$
$402$	−22.4402	−1.11922
$403$	52.6826	2.62431
$404$	−2.31966	−0.115408
$405$	1.53691	0.0763699
$406$	−8.03200	−0.398621
$407$	13.5144	0.669883
$408$	7.88493	0.390362
$409$	36.9106	1.82511	0.912556	−	0.408953i	$-0.134106\pi$
$409$	36.9106	1.82511	0.912556	+	0.408953i	$0.134106\pi$
$410$	−29.9242	−1.47785
$411$	−10.7365	−0.529594
$412$	−23.1516	−1.14060
$413$	−4.33410	−0.213267
$414$	−9.92720	−0.487895
$415$	21.6968	1.06506
$416$	92.4157	4.53105
$417$	4.78105	0.234129
$418$	13.8232	0.676116
$419$	26.8783	1.31309	0.656546	−	0.754286i	$-0.272017\pi$
$419$	26.8783	1.31309	0.656546	+	0.754286i	$0.272017\pi$
$420$	14.3386	0.699652
$421$	−25.7839	−1.25663	−0.628316	−	0.777958i	$-0.716256\pi$
$421$	−25.7839	−1.25663	−0.628316	+	0.777958i	$0.716256\pi$
$422$	−18.4752	−0.899360
$423$	4.42933	0.215361
$424$	−19.6136	−0.952519
$425$	2.45342	0.119009
$426$	−32.0205	−1.55140
$427$	−24.6520	−1.19299
$428$	90.4304	4.37112
$429$	8.98045	0.433580
$430$	9.13068	0.440320
$431$	−12.4278	−0.598624	−0.299312	−	0.954155i	$-0.596757\pi$
$431$	−12.4278	−0.598624	−0.299312	+	0.954155i	$0.596757\pi$
$432$	12.3622	0.594776
$433$	28.8816	1.38796	0.693981	−	0.719993i	$-0.255855\pi$
$433$	28.8816	1.38796	0.693981	+	0.719993i	$0.255855\pi$
$434$	44.4731	2.13478
$435$	2.55373	0.122442
$436$	−57.6046	−2.75876
$437$	12.2090	0.584036
$438$	16.8958	0.807311
$439$	−12.0141	−0.573403	−0.286701	−	0.958020i	$-0.592559\pi$
$439$	−12.0141	−0.573403	−0.286701	+	0.958020i	$0.592559\pi$
$440$	20.4345	0.974174
$441$	−3.73960	−0.178076
$442$	−14.2576	−0.678163
$443$	−7.43030	−0.353024	−0.176512	−	0.984298i	$-0.556481\pi$
$443$	−7.43030	−0.353024	−0.176512	+	0.984298i	$0.556481\pi$
$444$	−44.5232	−2.11298
$445$	−18.2164	−0.863542
$446$	74.8785	3.54560
$447$	−20.6445	−0.976451
$448$	33.3710	1.57663
$449$	1.67862	0.0792189	0.0396094	−	0.999215i	$-0.487389\pi$
$449$	1.67862	0.0792189	0.0396094	+	0.999215i	$0.487389\pi$
$450$	7.06187	0.332900
$451$	−11.4062	−0.537096
$452$	−71.3808	−3.35747
$453$	11.3835	0.534846
$454$	−22.4296	−1.05268
$455$	−15.8911	−0.744984
$456$	−27.9125	−1.30712
$457$	−27.9421	−1.30708	−0.653539	−	0.756893i	$-0.726717\pi$
$457$	−27.9421	−1.30708	−0.653539	+	0.756893i	$0.726717\pi$
$458$	4.04718	0.189112
$459$	−0.930070	−0.0434119
$460$	29.4466	1.37295
$461$	−20.4916	−0.954388	−0.477194	−	0.878798i	$-0.658346\pi$
$461$	−20.4916	−0.954388	−0.477194	+	0.878798i	$0.658346\pi$
$462$	7.58104	0.352702
$463$	29.9342	1.39116	0.695580	−	0.718448i	$-0.255147\pi$
$463$	29.9342	1.39116	0.695580	+	0.718448i	$0.255147\pi$
$464$	20.5409	0.953590
$465$	−14.1400	−0.655726
$466$	−44.3576	−2.05483
$467$	13.3524	0.617878	0.308939	−	0.951082i	$-0.400026\pi$
$467$	13.3524	0.617878	0.308939	+	0.951082i	$0.400026\pi$
$468$	−29.5862	−1.36762
$469$	15.1356	0.698898
$470$	−18.2243	−0.840622
$471$	2.06058	0.0949465
$472$	20.3491	0.936644
$473$	3.48034	0.160026
$474$	−35.6633	−1.63807
$475$	−8.68508	−0.398499
$476$	−8.67705	−0.397712
$477$	2.31352	0.105929
$478$	56.7534	2.59584
$479$	−1.06875	−0.0488323	−0.0244162	−	0.999702i	$-0.507773\pi$
$479$	−1.06875	−0.0488323	−0.0244162	+	0.999702i	$0.507773\pi$
$480$	−24.8044	−1.13216
$481$	49.3438	2.24988
$482$	17.2521	0.785812
$483$	6.69576	0.304667
$484$	−44.1266	−2.00575
$485$	16.1440	0.733059
$486$	−2.67709	−0.121435
$487$	−28.0374	−1.27050	−0.635249	−	0.772308i	$-0.719102\pi$
$487$	−28.0374	−1.27050	−0.635249	+	0.772308i	$0.719102\pi$
$488$	115.744	5.23949
$489$	17.4738	0.790195
$490$	15.3864	0.695087
$491$	10.6444	0.480374	0.240187	−	0.970727i	$-0.422791\pi$
$491$	10.6444	0.480374	0.240187	+	0.970727i	$0.422791\pi$
$492$	37.5778	1.69414
$493$	−1.54540	−0.0696013
$494$	50.4715	2.27082
$495$	−2.41035	−0.108337
$496$	−113.735	−5.10686
$497$	21.5974	0.968775
$498$	−37.7928	−1.69354
$499$	−13.7994	−0.617744	−0.308872	−	0.951104i	$-0.599952\pi$
$499$	−13.7994	−0.617744	−0.308872	+	0.951104i	$0.599952\pi$
$500$	−60.6519	−2.71244
$501$	−8.37585	−0.374205
$502$	45.2745	2.02070
$503$	34.9666	1.55908	0.779542	−	0.626350i	$-0.215452\pi$
$503$	34.9666	1.55908	0.779542	+	0.626350i	$0.215452\pi$
$504$	−15.3080	−0.681872
$505$	−0.690007	−0.0307049
$506$	15.5689	0.692121
$507$	19.7895	0.878883
$508$	3.01766	0.133887
$509$	−7.80998	−0.346171	−0.173086	−	0.984907i	$-0.555374\pi$
$509$	−7.80998	−0.346171	−0.173086	+	0.984907i	$0.555374\pi$
$510$	3.82673	0.169450
$511$	−11.3960	−0.504127
$512$	10.0938	0.446087
$513$	3.29243	0.145364
$514$	−3.54085	−0.156180
$515$	−6.88668	−0.303463
$516$	−11.4660	−0.504763
$517$	−6.94654	−0.305508
$518$	41.6546	1.83020
$519$	10.6309	0.466645
$520$	74.6105	3.27189
$521$	18.5948	0.814652	0.407326	−	0.913283i	$-0.366461\pi$
$521$	18.5948	0.814652	0.407326	+	0.913283i	$0.366461\pi$
$522$	−4.44824	−0.194694
$523$	−18.2168	−0.796565	−0.398282	−	0.917263i	$-0.630394\pi$
$523$	−18.2168	−0.796565	−0.398282	+	0.917263i	$0.630394\pi$
$524$	−96.8467	−4.23077
$525$	−4.76313	−0.207880
$526$	−74.2528	−3.23758
$527$	8.55687	0.372743
$528$	−19.3877	−0.843741
$529$	−9.24919	−0.402139
$530$	−9.51889	−0.413474
$531$	−2.40029	−0.104164
$532$	30.7166	1.33173
$533$	−41.6464	−1.80391
$534$	31.7305	1.37311
$535$	26.8994	1.16296
$536$	−71.0636	−3.06948
$537$	−24.7023	−1.06598
$538$	−35.9677	−1.55068
$539$	5.86483	0.252616
$540$	7.94092	0.341723
$541$	13.6783	0.588074	0.294037	−	0.955794i	$-0.405001\pi$
$541$	13.6783	0.588074	0.294037	+	0.955794i	$0.405001\pi$
$542$	−26.5273	−1.13945
$543$	−17.7835	−0.763163
$544$	15.0105	0.643568
$545$	−17.1351	−0.733986
$546$	27.6800	1.18459
$547$	−26.0437	−1.11355	−0.556773	−	0.830664i	$-0.687961\pi$
$547$	−26.0437	−1.11355	−0.556773	+	0.830664i	$0.687961\pi$
$548$	−55.4734	−2.36971
$549$	−13.6526	−0.582680
$550$	−11.0752	−0.472247
$551$	5.47068	0.233059
$552$	−31.4374	−1.33806
$553$	24.0544	1.02290
$554$	66.5999	2.82956
$555$	−13.2439	−0.562171
$556$	24.7027	1.04763
$557$	−39.3147	−1.66582	−0.832908	−	0.553411i	$-0.813326\pi$
$557$	−39.3147	−1.66582	−0.832908	+	0.553411i	$0.813326\pi$
$558$	24.6299	1.04266
$559$	12.7074	0.537468
$560$	34.3068	1.44973
$561$	1.45863	0.0615836
$562$	9.53612	0.402257
$563$	22.4159	0.944718	0.472359	−	0.881406i	$-0.343403\pi$
$563$	22.4159	0.944718	0.472359	+	0.881406i	$0.343403\pi$
$564$	22.8854	0.963650
$565$	−21.2329	−0.893276
$566$	−14.9279	−0.627465
$567$	1.80566	0.0758305
$568$	−101.402	−4.25475
$569$	2.19105	0.0918534	0.0459267	−	0.998945i	$-0.485376\pi$
$569$	2.19105	0.0918534	0.0459267	+	0.998945i	$0.485376\pi$
$570$	−13.5465	−0.567402
$571$	40.6954	1.70305	0.851524	−	0.524315i	$-0.175679\pi$
$571$	40.6954	1.70305	0.851524	+	0.524315i	$0.175679\pi$
$572$	46.4002	1.94009
$573$	−25.8084	−1.07816
$574$	−35.1567	−1.46741
$575$	−9.78186	−0.407932
$576$	18.4813	0.770055
$577$	−2.00985	−0.0836711	−0.0418355	−	0.999125i	$-0.513321\pi$
$577$	−2.00985	−0.0836711	−0.0418355	+	0.999125i	$0.513321\pi$
$578$	43.1947	1.79666
$579$	9.93312	0.412806
$580$	13.1946	0.547876
$581$	25.4907	1.05753
$582$	−28.1205	−1.16563
$583$	−3.62831	−0.150269
$584$	53.5054	2.21407
$585$	−8.80070	−0.363864
$586$	5.09525	0.210483
$587$	1.49821	0.0618378	0.0309189	−	0.999522i	$-0.490157\pi$
$587$	1.49821	0.0618378	0.0309189	+	0.999522i	$0.490157\pi$
$588$	−19.3217	−0.796815
$589$	−30.2911	−1.24812
$590$	9.87587	0.406583
$591$	−22.5268	−0.926630
$592$	−106.527	−4.37824
$593$	−1.55593	−0.0638945	−0.0319472	−	0.999490i	$-0.510171\pi$
$593$	−1.55593	−0.0638945	−0.0319472	+	0.999490i	$0.510171\pi$
$594$	4.19849	0.172266
$595$	−2.58108	−0.105814
$596$	−106.666	−4.36920
$597$	−12.4375	−0.509034
$598$	56.8452	2.32457
$599$	36.2975	1.48307	0.741537	−	0.670912i	$-0.234097\pi$
$599$	36.2975	1.48307	0.741537	+	0.670912i	$0.234097\pi$
$600$	22.3635	0.912986
$601$	−11.2186	−0.457618	−0.228809	−	0.973471i	$-0.573483\pi$
$601$	−11.2186	−0.457618	−0.228809	+	0.973471i	$0.573483\pi$
$602$	10.7273	0.437210
$603$	8.38233	0.341355
$604$	58.8165	2.39321
$605$	−13.1259	−0.533643
$606$	1.20189	0.0488236
$607$	37.4308	1.51927	0.759634	−	0.650351i	$-0.225378\pi$
$607$	37.4308	1.51927	0.759634	+	0.650351i	$0.225378\pi$
$608$	−53.1367	−2.15498
$609$	3.00027	0.121577
$610$	56.1731	2.27438
$611$	−25.3633	−1.02609
$612$	−4.80548	−0.194250
$613$	−8.24353	−0.332953	−0.166476	−	0.986045i	$-0.553239\pi$
$613$	−8.24353	−0.332953	−0.166476	+	0.986045i	$0.553239\pi$
$614$	74.0531	2.98854
$615$	11.1779	0.450736
$616$	24.0076	0.967294
$617$	−33.0635	−1.33109	−0.665543	−	0.746359i	$-0.731800\pi$
$617$	−33.0635	−1.33109	−0.665543	+	0.746359i	$0.731800\pi$
$618$	11.9956	0.482534
$619$	47.6524	1.91531	0.957655	−	0.287919i	$-0.0929633\pi$
$619$	47.6524	1.91531	0.957655	+	0.287919i	$0.0929633\pi$
$620$	−73.0584	−2.93410
$621$	3.70821	0.148805
$622$	8.89674	0.356727
$623$	−21.4018	−0.857443
$624$	−70.7885	−2.83381
$625$	−4.85205	−0.194082
$626$	81.7016	3.26545
$627$	−5.16353	−0.206212
$628$	10.6466	0.424845
$629$	8.01458	0.319562
$630$	−7.42930	−0.295990
$631$	−22.0119	−0.876278	−0.438139	−	0.898907i	$-0.644362\pi$
$631$	−22.0119	−0.876278	−0.438139	+	0.898907i	$0.644362\pi$
$632$	−112.938	−4.49245
$633$	6.90125	0.274300
$634$	−58.5649	−2.32591
$635$	0.897634	0.0356215
$636$	11.9535	0.473987
$637$	21.4137	0.848443
$638$	6.97619	0.276190
$639$	11.9609	0.473168
$640$	−26.4318	−1.04481
$641$	−29.8292	−1.17818	−0.589091	−	0.808067i	$-0.700514\pi$
$641$	−29.8292	−1.17818	−0.589091	+	0.808067i	$0.700514\pi$
$642$	−46.8550	−1.84922
$643$	3.20129	0.126247	0.0631233	−	0.998006i	$-0.479894\pi$
$643$	3.20129	0.126247	0.0631233	+	0.998006i	$0.479894\pi$
$644$	34.5956	1.36326
$645$	−3.41068	−0.134295
$646$	8.19774	0.322536
$647$	35.5067	1.39591	0.697955	−	0.716141i	$-0.254093\pi$
$647$	35.5067	1.39591	0.697955	+	0.716141i	$0.254093\pi$
$648$	−8.47779	−0.333039
$649$	3.76438	0.147765
$650$	−40.4378	−1.58610
$651$	−16.6125	−0.651095
$652$	90.2838	3.53579
$653$	9.40204	0.367930	0.183965	−	0.982933i	$-0.441107\pi$
$653$	9.40204	0.367930	0.183965	+	0.982933i	$0.441107\pi$
$654$	29.8469	1.16710
$655$	−28.8080	−1.12562
$656$	89.9094	3.51037
$657$	−6.31125	−0.246225
$658$	−21.4109	−0.834685
$659$	40.9865	1.59661	0.798304	−	0.602255i	$-0.205731\pi$
$659$	40.9865	1.59661	0.798304	+	0.602255i	$0.205731\pi$
$660$	−12.4538	−0.484763
$661$	22.6171	0.879701	0.439851	−	0.898071i	$-0.355031\pi$
$661$	22.6171	0.879701	0.439851	+	0.898071i	$0.355031\pi$
$662$	67.5092	2.62382
$663$	5.32578	0.206836
$664$	−119.682	−4.64457
$665$	9.13696	0.354316
$666$	23.0689	0.893903
$667$	6.16154	0.238576
$668$	−43.2763	−1.67441
$669$	−27.9702	−1.08139
$670$	−34.4887	−1.33242
$671$	21.4115	0.826581
$672$	−29.1416	−1.12416
$673$	19.3213	0.744781	0.372391	−	0.928076i	$-0.378538\pi$
$673$	19.3213	0.744781	0.372391	+	0.928076i	$0.378538\pi$
$674$	30.7537	1.18459
$675$	−2.63789	−0.101533
$676$	102.248	3.93263
$677$	20.0890	0.772082	0.386041	−	0.922482i	$-0.373842\pi$
$677$	20.0890	0.772082	0.386041	+	0.922482i	$0.373842\pi$
$678$	36.9847	1.42039
$679$	18.9669	0.727882
$680$	12.1185	0.464722
$681$	8.37837	0.321060
$682$	−38.6271	−1.47911
$683$	−2.17958	−0.0833994	−0.0416997	−	0.999130i	$-0.513277\pi$
$683$	−2.17958	−0.0833994	−0.0416997	+	0.999130i	$0.513277\pi$
$684$	17.0113	0.650443
$685$	−16.5011	−0.630476
$686$	51.9142	1.98209
$687$	−1.51179	−0.0576782
$688$	−27.4338	−1.04590
$689$	−13.2477	−0.504698
$690$	−15.2573	−0.580834
$691$	1.41654	0.0538876	0.0269438	−	0.999637i	$-0.491422\pi$
$691$	1.41654	0.0538876	0.0269438	+	0.999637i	$0.491422\pi$
$692$	54.9277	2.08804
$693$	−2.83182	−0.107572
$694$	−6.06486	−0.230219
$695$	7.34807	0.278728
$696$	−14.0867	−0.533953
$697$	−6.76434	−0.256218
$698$	−89.0749	−3.37154
$699$	16.5694	0.626711
$700$	−24.6101	−0.930176
$701$	30.2490	1.14249	0.571244	−	0.820780i	$-0.306461\pi$
$701$	30.2490	1.14249	0.571244	+	0.820780i	$0.306461\pi$
$702$	15.3296	0.578577
$703$	−28.3714	−1.07005
$704$	−28.9844	−1.09239
$705$	6.80749	0.256385
$706$	80.8150	3.04151
$707$	−0.810661	−0.0304881
$708$	−12.4018	−0.466088
$709$	−26.5017	−0.995291	−0.497645	−	0.867381i	$-0.665802\pi$
$709$	−26.5017	−0.995291	−0.497645	+	0.867381i	$0.665802\pi$
$710$	−49.2127	−1.84692
$711$	13.3217	0.499602
$712$	100.484	3.76579
$713$	−34.1164	−1.27767
$714$	4.49587	0.168254
$715$	13.8022	0.516173
$716$	−127.632	−4.76982
$717$	−21.1997	−0.791716
$718$	47.5041	1.77284
$719$	−50.1885	−1.87172	−0.935858	−	0.352378i	$-0.885373\pi$
$719$	−50.1885	−1.87172	−0.935858	+	0.352378i	$0.885373\pi$
$720$	18.9996	0.708074
$721$	−8.09087	−0.301320
$722$	21.8448	0.812979
$723$	−6.44436	−0.239668
$724$	−91.8837	−3.41483
$725$	−4.38311	−0.162785
$726$	22.8634	0.848542
$727$	−5.77783	−0.214288	−0.107144	−	0.994244i	$-0.534171\pi$
$727$	−5.77783	−0.214288	−0.107144	+	0.994244i	$0.534171\pi$
$728$	87.6568	3.24878
$729$	1.00000	0.0370370
$730$	25.9673	0.961094
$731$	2.06398	0.0763392
$732$	−70.5403	−2.60725
$733$	−11.9507	−0.441408	−0.220704	−	0.975341i	$-0.570836\pi$
$733$	−11.9507	−0.441408	−0.220704	+	0.975341i	$0.570836\pi$
$734$	38.1492	1.40811
$735$	−5.74744	−0.211998
$736$	−59.8470	−2.20599
$737$	−13.1461	−0.484241
$738$	−19.4703	−0.716711
$739$	−30.2867	−1.11411	−0.557057	−	0.830474i	$-0.688069\pi$
$739$	−30.2867	−1.11411	−0.557057	+	0.830474i	$0.688069\pi$
$740$	−68.4284	−2.51548
$741$	−18.8531	−0.692588
$742$	−11.1834	−0.410554
$743$	43.8304	1.60798	0.803991	−	0.594641i	$-0.202706\pi$
$743$	43.8304	1.60798	0.803991	+	0.594641i	$0.202706\pi$
$744$	77.9977	2.85953
$745$	−31.7288	−1.16245
$746$	−40.2470	−1.47355
$747$	14.1171	0.516519
$748$	7.53646	0.275560
$749$	31.6030	1.15475
$750$	31.4258	1.14751
$751$	−38.3075	−1.39786	−0.698930	−	0.715190i	$-0.746340\pi$
$751$	−38.3075	−1.39786	−0.698930	+	0.715190i	$0.746340\pi$
$752$	54.7561	1.99675
$753$	−16.9119	−0.616302
$754$	25.4715	0.927619
$755$	17.4955	0.636728
$756$	9.32947	0.339309
$757$	39.1558	1.42314	0.711571	−	0.702615i	$-0.247984\pi$
$757$	39.1558	1.42314	0.711571	+	0.702615i	$0.247984\pi$
$758$	−77.5723	−2.81755
$759$	−5.81560	−0.211093
$760$	−42.8991	−1.55612
$761$	5.78591	0.209739	0.104870	−	0.994486i	$-0.466558\pi$
$761$	5.78591	0.209739	0.104870	+	0.994486i	$0.466558\pi$
$762$	−1.56355	−0.0566415
$763$	−20.1313	−0.728802
$764$	−133.347	−4.82432
$765$	−1.42944	−0.0516814
$766$	73.5422	2.65719
$767$	13.7446	0.496287
$768$	9.07783	0.327568
$769$	2.55374	0.0920901	0.0460450	−	0.998939i	$-0.485338\pi$
$769$	2.55374	0.0920901	0.0460450	+	0.998939i	$0.485338\pi$
$770$	11.6514	0.419888
$771$	1.32265	0.0476341
$772$	51.3224	1.84713
$773$	−14.4581	−0.520021	−0.260011	−	0.965606i	$-0.583726\pi$
$773$	−14.4581	−0.520021	−0.260011	+	0.965606i	$0.583726\pi$
$774$	5.94091	0.213542
$775$	24.2693	0.871778
$776$	−89.0518	−3.19677
$777$	−15.5597	−0.558201
$778$	−25.3936	−0.910404
$779$	23.9456	0.857941
$780$	−45.4714	−1.62814
$781$	−18.7584	−0.671229
$782$	9.23298	0.330171
$783$	1.66160	0.0593806
$784$	−46.2296	−1.65106
$785$	3.16693	0.113033
$786$	50.1794	1.78984
$787$	−17.4688	−0.622696	−0.311348	−	0.950296i	$-0.600781\pi$
$787$	−17.4688	−0.622696	−0.311348	+	0.950296i	$0.600781\pi$
$788$	−116.392	−4.14628
$789$	27.7364	0.987442
$790$	−54.8115	−1.95010
$791$	−24.9457	−0.886967
$792$	13.2958	0.472444
$793$	78.1778	2.77618
$794$	17.7164	0.628730
$795$	3.55569	0.126107
$796$	−64.2622	−2.27771
$797$	34.9491	1.23796	0.618980	−	0.785407i	$-0.287546\pi$
$797$	34.9491	1.23796	0.618980	+	0.785407i	$0.287546\pi$
$798$	−15.9153	−0.563395
$799$	−4.11958	−0.145740
$800$	42.5731	1.50519
$801$	−11.8526	−0.418791
$802$	0.920238	0.0324947
$803$	9.89797	0.349292
$804$	43.3098	1.52742
$805$	10.2908	0.362703
$806$	−141.036	−4.96777
$807$	13.4354	0.472948
$808$	3.80615	0.133900
$809$	−14.5668	−0.512141	−0.256071	−	0.966658i	$-0.582428\pi$
$809$	−14.5668	−0.512141	−0.256071	+	0.966658i	$0.582428\pi$
$810$	−4.11445	−0.144567
$811$	6.34903	0.222945	0.111472	−	0.993768i	$-0.464443\pi$
$811$	6.34903	0.222945	0.111472	+	0.993768i	$0.464443\pi$
$812$	15.5018	0.544007
$813$	9.90902	0.347525
$814$	−36.1792	−1.26808
$815$	26.8558	0.940718
$816$	−11.4977	−0.402500
$817$	−7.30646	−0.255621
$818$	−98.8129	−3.45491
$819$	−10.3396	−0.361294
$820$	57.7538	2.01685
$821$	−49.5221	−1.72833	−0.864167	−	0.503206i	$-0.832154\pi$
$821$	−49.5221	−1.72833	−0.864167	+	0.503206i	$0.832154\pi$
$822$	28.7426	1.00251
$823$	21.3399	0.743861	0.371930	−	0.928261i	$-0.378696\pi$
$823$	21.3399	0.743861	0.371930	+	0.928261i	$0.378696\pi$
$824$	37.9876	1.32336
$825$	4.13702	0.144033
$826$	11.6028	0.403712
$827$	−41.9955	−1.46033	−0.730164	−	0.683272i	$-0.760556\pi$
$827$	−41.9955	−1.46033	−0.730164	+	0.683272i	$0.760556\pi$
$828$	19.1596	0.665840
$829$	16.3212	0.566858	0.283429	−	0.958993i	$-0.408528\pi$
$829$	16.3212	0.566858	0.283429	+	0.958993i	$0.408528\pi$
$830$	−58.0843	−2.01614
$831$	−24.8777	−0.862999
$832$	−105.828	−3.66893
$833$	3.47809	0.120509
$834$	−12.7993	−0.443203
$835$	−12.8730	−0.445487
$836$	−26.6789	−0.922710
$837$	−9.20024	−0.318007
$838$	−71.9556	−2.48567
$839$	9.18737	0.317183	0.158592	−	0.987344i	$-0.449305\pi$
$839$	9.18737	0.317183	0.158592	+	0.987344i	$0.449305\pi$
$840$	−23.5271	−0.811761
$841$	−26.2391	−0.904797
$842$	69.0258	2.37879
$843$	−3.56213	−0.122686
$844$	35.6573	1.22738
$845$	30.4148	1.04630
$846$	−11.8577	−0.407676
$847$	−15.4211	−0.529874
$848$	28.6002	0.982135
$849$	5.57616	0.191373
$850$	−6.56803	−0.225282
$851$	−31.9543	−1.09538
$852$	61.7997	2.11722
$853$	17.9402	0.614262	0.307131	−	0.951667i	$-0.400631\pi$
$853$	17.9402	0.614262	0.307131	+	0.951667i	$0.400631\pi$
$854$	65.9955	2.25832
$855$	5.06018	0.173055
$856$	−148.380	−5.07153
$857$	4.00012	0.136642	0.0683208	−	0.997663i	$-0.478236\pi$
$857$	4.00012	0.136642	0.0683208	+	0.997663i	$0.478236\pi$
$858$	−24.0415	−0.820762
$859$	1.71005	0.0583461	0.0291731	−	0.999574i	$-0.490713\pi$
$859$	1.71005	0.0583461	0.0291731	+	0.999574i	$0.490713\pi$
$860$	−17.6223	−0.600914
$861$	13.1324	0.447552
$862$	33.2702	1.13319
$863$	16.4565	0.560185	0.280093	−	0.959973i	$-0.409635\pi$
$863$	16.4565	0.560185	0.280093	+	0.959973i	$0.409635\pi$
$864$	−16.1391	−0.549062
$865$	16.3388	0.555536
$866$	−77.3186	−2.62739
$867$	−16.1350	−0.547972
$868$	−85.8334	−2.91337
$869$	−20.8925	−0.708729
$870$	−6.83656	−0.231781
$871$	−47.9990	−1.62638
$872$	94.5189	3.20081
$873$	10.5041	0.355511
$874$	−32.6846	−1.10557
$875$	−21.1962	−0.716564
$876$	−32.6089	−1.10175
$877$	−26.7159	−0.902131	−0.451066	−	0.892491i	$-0.648956\pi$
$877$	−26.7159	−0.902131	−0.451066	+	0.892491i	$0.648956\pi$
$878$	32.1628	1.08544
$879$	−1.90328	−0.0641961
$880$	−29.7972	−1.00446
$881$	20.3197	0.684587	0.342294	−	0.939593i	$-0.388796\pi$
$881$	20.3197	0.684587	0.342294	+	0.939593i	$0.388796\pi$
$882$	10.0112	0.337096
$883$	55.6977	1.87438	0.937189	−	0.348822i	$-0.113418\pi$
$883$	55.6977	1.87438	0.937189	+	0.348822i	$0.113418\pi$
$884$	27.5172	0.925504
$885$	−3.68904	−0.124006
$886$	19.8916	0.668270
$887$	58.7443	1.97244	0.986220	−	0.165441i	$-0.0529046\pi$
$887$	58.7443	1.97244	0.986220	+	0.165441i	$0.0529046\pi$
$888$	73.0546	2.45155
$889$	1.05459	0.0353699
$890$	48.7670	1.63467
$891$	−1.56831	−0.0525402
$892$	−144.516	−4.83876
$893$	14.5832	0.488009
$894$	55.2671	1.84841
$895$	−37.9653	−1.26904
$896$	−31.0537	−1.03743
$897$	−21.2340	−0.708982
$898$	−4.49381	−0.149960
$899$	−15.2871	−0.509853
$900$	−13.6295	−0.454315
$901$	−2.15174	−0.0716848
$902$	30.5354	1.01672
$903$	−4.00706	−0.133347
$904$	117.123	3.89546
$905$	−27.3317	−0.908537
$906$	−30.4748	−1.01246
$907$	−6.30206	−0.209256	−0.104628	−	0.994511i	$-0.533365\pi$
$907$	−6.30206	−0.209256	−0.104628	+	0.994511i	$0.533365\pi$
$908$	43.2893	1.43661
$909$	−0.448956	−0.0148909
$910$	42.5418	1.41025
$911$	32.2827	1.06958	0.534788	−	0.844987i	$-0.320392\pi$
$911$	32.2827	1.06958	0.534788	+	0.844987i	$0.320392\pi$
$912$	40.7016	1.34776
$913$	−22.1400	−0.732727
$914$	74.8036	2.47428
$915$	−20.9829	−0.693674
$916$	−7.81108	−0.258085
$917$	−33.8453	−1.11767
$918$	2.48988	0.0821782
$919$	−6.40229	−0.211192	−0.105596	−	0.994409i	$-0.533675\pi$
$919$	−6.40229	−0.211192	−0.105596	+	0.994409i	$0.533675\pi$
$920$	−48.3166	−1.59295
$921$	−27.6618	−0.911488
$922$	54.8578	1.80664
$923$	−68.4909	−2.25441
$924$	−14.6315	−0.481340
$925$	22.7312	0.747397
$926$	−80.1365	−2.63345
$927$	−4.48084	−0.147170
$928$	−26.8166	−0.880298
$929$	−49.1443	−1.61237	−0.806186	−	0.591662i	$-0.798472\pi$
$929$	−49.1443	−1.61237	−0.806186	+	0.591662i	$0.798472\pi$
$930$	37.8540	1.24128
$931$	−12.3124	−0.403521
$932$	85.6105	2.80427
$933$	−3.32329	−0.108800
$934$	−35.7457	−1.16963
$935$	2.24180	0.0733145
$936$	48.5456	1.58676
$937$	2.27974	0.0744759	0.0372379	−	0.999306i	$-0.488144\pi$
$937$	2.27974	0.0744759	0.0372379	+	0.999306i	$0.488144\pi$
$938$	−40.5194	−1.32301
$939$	−30.5188	−0.995945
$940$	35.1729	1.14721
$941$	−45.9548	−1.49808	−0.749041	−	0.662523i	$-0.769486\pi$
$941$	−45.9548	−1.49808	−0.749041	+	0.662523i	$0.769486\pi$
$942$	−5.51635	−0.179732
$943$	26.9696	0.878250
$944$	−29.6728	−0.965767
$945$	2.77514	0.0902754
$946$	−9.31717	−0.302927
$947$	7.25199	0.235658	0.117829	−	0.993034i	$-0.462407\pi$
$947$	7.25199	0.235658	0.117829	+	0.993034i	$0.462407\pi$
$948$	68.8304	2.23551
$949$	36.1395	1.17314
$950$	23.2507	0.754352
$951$	21.8763	0.709389
$952$	14.2375	0.461440
$953$	−21.7823	−0.705599	−0.352799	−	0.935699i	$-0.614770\pi$
$953$	−21.7823	−0.705599	−0.352799	+	0.935699i	$0.614770\pi$
$954$	−6.19351	−0.200522
$955$	−39.6654	−1.28354
$956$	−109.534	−3.54259
$957$	−2.60589	−0.0842365
$958$	2.86113	0.0924389
$959$	−19.3865	−0.626023
$960$	28.4042	0.916742
$961$	53.6445	1.73047
$962$	−132.098	−4.25900
$963$	17.5022	0.564001
$964$	−33.2967	−1.07241
$965$	15.2664	0.491442
$966$	−17.9251	−0.576731
$967$	3.30116	0.106158	0.0530791	−	0.998590i	$-0.483096\pi$
$967$	3.30116	0.106158	0.0530791	+	0.998590i	$0.483096\pi$
$968$	72.4038	2.32715
$969$	−3.06219	−0.0983716
$970$	−43.2188	−1.38767
$971$	33.0716	1.06132	0.530659	−	0.847586i	$-0.321945\pi$
$971$	33.0716	1.06132	0.530659	+	0.847586i	$0.321945\pi$
$972$	5.16680	0.165725
$973$	8.63295	0.276760
$974$	75.0586	2.40503
$975$	15.1051	0.483752
$976$	−168.776	−5.40240
$977$	23.0249	0.736633	0.368316	−	0.929701i	$-0.379934\pi$
$977$	23.0249	0.736633	0.368316	+	0.929701i	$0.379934\pi$
$978$	−46.7790	−1.49583
$979$	18.5885	0.594091
$980$	−29.6959	−0.948599
$981$	−11.1490	−0.355960
$982$	−28.4959	−0.909341
$983$	−15.8842	−0.506626	−0.253313	−	0.967384i	$-0.581520\pi$
$983$	−15.8842	−0.506626	−0.253313	+	0.967384i	$0.581520\pi$
$984$	−61.6584	−1.96560
$985$	−34.6218	−1.10314
$986$	4.13717	0.131754
$987$	7.99785	0.254574
$988$	−97.4104	−3.09904
$989$	−8.22915	−0.261672
$990$	6.45272	0.205081
$991$	−37.1559	−1.18030	−0.590149	−	0.807295i	$-0.700931\pi$
$991$	−37.1559	−1.18030	−0.590149	+	0.807295i	$0.700931\pi$
$992$	148.483	4.71435
$993$	−25.2174	−0.800250
$994$	−57.8180	−1.83388
$995$	−19.1154	−0.606000
$996$	72.9404	2.31120
$997$	−33.9688	−1.07580	−0.537901	−	0.843008i	$-0.680782\pi$
$997$	−33.9688	−1.07580	−0.537901	+	0.843008i	$0.680782\pi$
$998$	36.9421	1.16938
$999$	−8.61718	−0.272635

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.a.1.2	✓	95

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.a.1.2	✓	95	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:	\( N \)	\(=\)	\( 8049 = 3 \cdot 2683 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8049.a (trivial)

\(f(q)\)	\(=\)	\(q-2.67709 q^{2} +1.00000 q^{3} +5.16680 q^{4} +1.53691 q^{5} -2.67709 q^{6} +1.80566 q^{7} -8.47779 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.67709 q^{2} +1.00000 q^{3} +5.16680 q^{4} +1.53691 q^{5} -2.67709 q^{6} +1.80566 q^{7} -8.47779 q^{8} +1.00000 q^{9} -4.11445 q^{10} -1.56831 q^{11} +5.16680 q^{12} -5.72621 q^{13} -4.83390 q^{14} +1.53691 q^{15} +12.3622 q^{16} -0.930070 q^{17} -2.67709 q^{18} +3.29243 q^{19} +7.94092 q^{20} +1.80566 q^{21} +4.19849 q^{22} +3.70821 q^{23} -8.47779 q^{24} -2.63789 q^{25} +15.3296 q^{26} +1.00000 q^{27} +9.32947 q^{28} +1.66160 q^{29} -4.11445 q^{30} -9.20024 q^{31} -16.1391 q^{32} -1.56831 q^{33} +2.48988 q^{34} +2.77514 q^{35} +5.16680 q^{36} -8.61718 q^{37} -8.81412 q^{38} -5.72621 q^{39} -13.0296 q^{40} +7.27294 q^{41} -4.83390 q^{42} -2.21917 q^{43} -8.10311 q^{44} +1.53691 q^{45} -9.92720 q^{46} +4.42933 q^{47} +12.3622 q^{48} -3.73960 q^{49} +7.06187 q^{50} -0.930070 q^{51} -29.5862 q^{52} +2.31352 q^{53} -2.67709 q^{54} -2.41035 q^{55} -15.3080 q^{56} +3.29243 q^{57} -4.44824 q^{58} -2.40029 q^{59} +7.94092 q^{60} -13.6526 q^{61} +24.6299 q^{62} +1.80566 q^{63} +18.4813 q^{64} -8.80070 q^{65} +4.19849 q^{66} +8.38233 q^{67} -4.80548 q^{68} +3.70821 q^{69} -7.42930 q^{70} +11.9609 q^{71} -8.47779 q^{72} -6.31125 q^{73} +23.0689 q^{74} -2.63789 q^{75} +17.0113 q^{76} -2.83182 q^{77} +15.3296 q^{78} +13.3217 q^{79} +18.9996 q^{80} +1.00000 q^{81} -19.4703 q^{82} +14.1171 q^{83} +9.32947 q^{84} -1.42944 q^{85} +5.94091 q^{86} +1.66160 q^{87} +13.2958 q^{88} -11.8526 q^{89} -4.11445 q^{90} -10.3396 q^{91} +19.1596 q^{92} -9.20024 q^{93} -11.8577 q^{94} +5.06018 q^{95} -16.1391 q^{96} +10.5041 q^{97} +10.0112 q^{98} -1.56831 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 95 q - 9 q^{2} + 95 q^{3} + 65 q^{4} - 15 q^{5} - 9 q^{6} - 36 q^{7} - 27 q^{8} + 95 q^{9}+O(q^{10}) \) 95 * q - 9 * q^2 + 95 * q^3 + 65 * q^4 - 15 * q^5 - 9 * q^6 - 36 * q^7 - 27 * q^8 + 95 * q^9	\( 95 q - 9 q^{2} + 95 q^{3} + 65 q^{4} - 15 q^{5} - 9 q^{6} - 36 q^{7} - 27 q^{8} + 95 q^{9} - 36 q^{10} - 48 q^{11} + 65 q^{12} - 73 q^{13} - 17 q^{14} - 15 q^{15} + 13 q^{16} - 9 q^{17} - 9 q^{18} - 66 q^{19} - 35 q^{20} - 36 q^{21} - 37 q^{22} - 58 q^{23} - 27 q^{24} + 24 q^{25} - 25 q^{26} + 95 q^{27} - 75 q^{28} - 31 q^{29} - 36 q^{30} - 129 q^{31} - 53 q^{32} - 48 q^{33} - 61 q^{34} - 38 q^{35} + 65 q^{36} - 127 q^{37} + q^{38} - 73 q^{39} - 74 q^{40} - 31 q^{41} - 17 q^{42} - 62 q^{43} - 76 q^{44} - 15 q^{45} - 60 q^{46} - 75 q^{47} + 13 q^{48} + 5 q^{49} - 30 q^{50} - 9 q^{51} - 137 q^{52} - 28 q^{53} - 9 q^{54} - 117 q^{55} - 23 q^{56} - 66 q^{57} - 90 q^{58} - 60 q^{59} - 35 q^{60} - 96 q^{61} + 10 q^{62} - 36 q^{63} - 75 q^{64} - 28 q^{65} - 37 q^{66} - 116 q^{67} + 3 q^{68} - 58 q^{69} - 73 q^{70} - 144 q^{71} - 27 q^{72} - 121 q^{73} - 16 q^{74} + 24 q^{75} - 118 q^{76} - 3 q^{77} - 25 q^{78} - 135 q^{79} - 36 q^{80} + 95 q^{81} - 102 q^{82} - 21 q^{83} - 75 q^{84} - 129 q^{85} - 46 q^{86} - 31 q^{87} - 77 q^{88} - 63 q^{89} - 36 q^{90} - 123 q^{91} - 42 q^{92} - 129 q^{93} - 44 q^{94} - 80 q^{95} - 53 q^{96} - 144 q^{97} + 10 q^{98} - 48 q^{99}+O(q^{100}) \) 95 * q - 9 * q^2 + 95 * q^3 + 65 * q^4 - 15 * q^5 - 9 * q^6 - 36 * q^7 - 27 * q^8 + 95 * q^9 - 36 * q^10 - 48 * q^11 + 65 * q^12 - 73 * q^13 - 17 * q^14 - 15 * q^15 + 13 * q^16 - 9 * q^17 - 9 * q^18 - 66 * q^19 - 35 * q^20 - 36 * q^21 - 37 * q^22 - 58 * q^23 - 27 * q^24 + 24 * q^25 - 25 * q^26 + 95 * q^27 - 75 * q^28 - 31 * q^29 - 36 * q^30 - 129 * q^31 - 53 * q^32 - 48 * q^33 - 61 * q^34 - 38 * q^35 + 65 * q^36 - 127 * q^37 + q^38 - 73 * q^39 - 74 * q^40 - 31 * q^41 - 17 * q^42 - 62 * q^43 - 76 * q^44 - 15 * q^45 - 60 * q^46 - 75 * q^47 + 13 * q^48 + 5 * q^49 - 30 * q^50 - 9 * q^51 - 137 * q^52 - 28 * q^53 - 9 * q^54 - 117 * q^55 - 23 * q^56 - 66 * q^57 - 90 * q^58 - 60 * q^59 - 35 * q^60 - 96 * q^61 + 10 * q^62 - 36 * q^63 - 75 * q^64 - 28 * q^65 - 37 * q^66 - 116 * q^67 + 3 * q^68 - 58 * q^69 - 73 * q^70 - 144 * q^71 - 27 * q^72 - 121 * q^73 - 16 * q^74 + 24 * q^75 - 118 * q^76 - 3 * q^77 - 25 * q^78 - 135 * q^79 - 36 * q^80 + 95 * q^81 - 102 * q^82 - 21 * q^83 - 75 * q^84 - 129 * q^85 - 46 * q^86 - 31 * q^87 - 77 * q^88 - 63 * q^89 - 36 * q^90 - 123 * q^91 - 42 * q^92 - 129 * q^93 - 44 * q^94 - 80 * q^95 - 53 * q^96 - 144 * q^97 + 10 * q^98 - 48 * q^99

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