LMFDB - Embedded newform 8049.2.a.a.1.13

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			1.13
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)

$f(q)$	$=$	$q-2.21332 q^{2} +1.00000 q^{3} +2.89880 q^{4} -0.906600 q^{5} -2.21332 q^{6} -0.601026 q^{7} -1.98934 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.21332 q^{2} +1.00000 q^{3} +2.89880 q^{4} -0.906600 q^{5} -2.21332 q^{6} -0.601026 q^{7} -1.98934 q^{8} +1.00000 q^{9} +2.00660 q^{10} +3.61819 q^{11} +2.89880 q^{12} +1.22188 q^{13} +1.33027 q^{14} -0.906600 q^{15} -1.39455 q^{16} -4.81739 q^{17} -2.21332 q^{18} +4.88486 q^{19} -2.62805 q^{20} -0.601026 q^{21} -8.00823 q^{22} +3.46196 q^{23} -1.98934 q^{24} -4.17808 q^{25} -2.70443 q^{26} +1.00000 q^{27} -1.74226 q^{28} -3.25721 q^{29} +2.00660 q^{30} -8.27225 q^{31} +7.06527 q^{32} +3.61819 q^{33} +10.6625 q^{34} +0.544890 q^{35} +2.89880 q^{36} +4.59647 q^{37} -10.8118 q^{38} +1.22188 q^{39} +1.80353 q^{40} +9.42540 q^{41} +1.33027 q^{42} -2.02744 q^{43} +10.4884 q^{44} -0.906600 q^{45} -7.66244 q^{46} -8.37762 q^{47} -1.39455 q^{48} -6.63877 q^{49} +9.24744 q^{50} -4.81739 q^{51} +3.54200 q^{52} -3.62379 q^{53} -2.21332 q^{54} -3.28025 q^{55} +1.19565 q^{56} +4.88486 q^{57} +7.20926 q^{58} +10.6391 q^{59} -2.62805 q^{60} -14.1008 q^{61} +18.3092 q^{62} -0.601026 q^{63} -12.8486 q^{64} -1.10776 q^{65} -8.00823 q^{66} +12.2684 q^{67} -13.9647 q^{68} +3.46196 q^{69} -1.20602 q^{70} -6.88258 q^{71} -1.98934 q^{72} -8.06566 q^{73} -10.1735 q^{74} -4.17808 q^{75} +14.1602 q^{76} -2.17463 q^{77} -2.70443 q^{78} +5.26745 q^{79} +1.26430 q^{80} +1.00000 q^{81} -20.8615 q^{82} +11.4413 q^{83} -1.74226 q^{84} +4.36745 q^{85} +4.48737 q^{86} -3.25721 q^{87} -7.19782 q^{88} -3.30103 q^{89} +2.00660 q^{90} -0.734385 q^{91} +10.0355 q^{92} -8.27225 q^{93} +18.5424 q^{94} -4.42861 q^{95} +7.06527 q^{96} -10.7482 q^{97} +14.6937 q^{98} +3.61819 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.21332	−1.56506	−0.782528	−	0.622615i	$-0.786070\pi$
$2$	−2.21332	−1.56506	−0.782528	+	0.622615i	$0.786070\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.89880	1.44940
$5$	−0.906600	−0.405444	−0.202722	−	0.979236i	$-0.564979\pi$
$5$	−0.906600	−0.405444	−0.202722	+	0.979236i	$0.564979\pi$
$6$	−2.21332	−0.903586
$7$	−0.601026	−0.227167	−0.113583	−	0.993528i	$-0.536233\pi$
$7$	−0.601026	−0.227167	−0.113583	+	0.993528i	$0.536233\pi$
$8$	−1.98934	−0.703338
$9$	1.00000	0.333333
$10$	2.00660	0.634542
$11$	3.61819	1.09093	0.545463	−	0.838135i	$-0.316354\pi$
$11$	3.61819	1.09093	0.545463	+	0.838135i	$0.316354\pi$
$12$	2.89880	0.836812
$13$	1.22188	0.338890	0.169445	−	0.985540i	$-0.445803\pi$
$13$	1.22188	0.338890	0.169445	+	0.985540i	$0.445803\pi$
$14$	1.33027	0.355529
$15$	−0.906600	−0.234083
$16$	−1.39455	−0.348638
$17$	−4.81739	−1.16839	−0.584195	−	0.811613i	$-0.698590\pi$
$17$	−4.81739	−1.16839	−0.584195	+	0.811613i	$0.698590\pi$
$18$	−2.21332	−0.521685
$19$	4.88486	1.12066	0.560332	−	0.828268i	$-0.310674\pi$
$19$	4.88486	1.12066	0.560332	+	0.828268i	$0.310674\pi$
$20$	−2.62805	−0.587651
$21$	−0.601026	−0.131155
$22$	−8.00823	−1.70736
$23$	3.46196	0.721868	0.360934	−	0.932591i	$-0.382458\pi$
$23$	3.46196	0.721868	0.360934	+	0.932591i	$0.382458\pi$
$24$	−1.98934	−0.406072
$25$	−4.17808	−0.835615
$26$	−2.70443	−0.530381
$27$	1.00000	0.192450
$28$	−1.74226	−0.329256
$29$	−3.25721	−0.604849	−0.302424	−	0.953173i	$-0.597796\pi$
$29$	−3.25721	−0.604849	−0.302424	+	0.953173i	$0.597796\pi$
$30$	2.00660	0.366353
$31$	−8.27225	−1.48574	−0.742870	−	0.669436i	$-0.766536\pi$
$31$	−8.27225	−1.48574	−0.742870	+	0.669436i	$0.766536\pi$
$32$	7.06527	1.24898
$33$	3.61819	0.629847
$34$	10.6625	1.82860
$35$	0.544890	0.0921033
$36$	2.89880	0.483134
$37$	4.59647	0.755656	0.377828	−	0.925876i	$-0.376671\pi$
$37$	4.59647	0.755656	0.377828	+	0.925876i	$0.376671\pi$
$38$	−10.8118	−1.75390
$39$	1.22188	0.195658
$40$	1.80353	0.285164
$41$	9.42540	1.47200	0.736000	−	0.676982i	$-0.236712\pi$
$41$	9.42540	1.47200	0.736000	+	0.676982i	$0.236712\pi$
$42$	1.33027	0.205265
$43$	−2.02744	−0.309181	−0.154591	−	0.987979i	$-0.549406\pi$
$43$	−2.02744	−0.309181	−0.154591	+	0.987979i	$0.549406\pi$
$44$	10.4884	1.58119
$45$	−0.906600	−0.135148
$46$	−7.66244	−1.12976
$47$	−8.37762	−1.22200	−0.611001	−	0.791630i	$-0.709233\pi$
$47$	−8.37762	−1.22200	−0.611001	+	0.791630i	$0.709233\pi$
$48$	−1.39455	−0.201286
$49$	−6.63877	−0.948395
$50$	9.24744	1.30779
$51$	−4.81739	−0.674570
$52$	3.54200	0.491187
$53$	−3.62379	−0.497766	−0.248883	−	0.968534i	$-0.580064\pi$
$53$	−3.62379	−0.497766	−0.248883	+	0.968534i	$0.580064\pi$
$54$	−2.21332	−0.301195
$55$	−3.28025	−0.442309
$56$	1.19565	0.159775
$57$	4.88486	0.647016
$58$	7.20926	0.946622
$59$	10.6391	1.38510	0.692548	−	0.721372i	$-0.256488\pi$
$59$	10.6391	1.38510	0.692548	+	0.721372i	$0.256488\pi$
$60$	−2.62805	−0.339280
$61$	−14.1008	−1.80543	−0.902713	−	0.430243i	$-0.858428\pi$
$61$	−14.1008	−1.80543	−0.902713	+	0.430243i	$0.858428\pi$
$62$	18.3092	2.32527
$63$	−0.601026	−0.0757222
$64$	−12.8486	−1.60608
$65$	−1.10776	−0.137401
$66$	−8.00823	−0.985746
$67$	12.2684	1.49883	0.749414	−	0.662101i	$-0.230335\pi$
$67$	12.2684	1.49883	0.749414	+	0.662101i	$0.230335\pi$
$68$	−13.9647	−1.69346
$69$	3.46196	0.416771
$70$	−1.20602	−0.144147
$71$	−6.88258	−0.816812	−0.408406	−	0.912800i	$-0.633915\pi$
$71$	−6.88258	−0.816812	−0.408406	+	0.912800i	$0.633915\pi$
$72$	−1.98934	−0.234446
$73$	−8.06566	−0.944014	−0.472007	−	0.881595i	$-0.656470\pi$
$73$	−8.06566	−0.944014	−0.472007	+	0.881595i	$0.656470\pi$
$74$	−10.1735	−1.18264
$75$	−4.17808	−0.482443
$76$	14.1602	1.62429
$77$	−2.17463	−0.247822
$78$	−2.70443	−0.306216
$79$	5.26745	0.592634	0.296317	−	0.955090i	$-0.404241\pi$
$79$	5.26745	0.592634	0.296317	+	0.955090i	$0.404241\pi$
$80$	1.26430	0.141353
$81$	1.00000	0.111111
$82$	−20.8615	−2.30376
$83$	11.4413	1.25584	0.627922	−	0.778276i	$-0.283906\pi$
$83$	11.4413	1.25584	0.627922	+	0.778276i	$0.283906\pi$
$84$	−1.74226	−0.190096
$85$	4.36745	0.473716
$86$	4.48737	0.483886
$87$	−3.25721	−0.349209
$88$	−7.19782	−0.767290
$89$	−3.30103	−0.349908	−0.174954	−	0.984577i	$-0.555978\pi$
$89$	−3.30103	−0.349908	−0.174954	+	0.984577i	$0.555978\pi$
$90$	2.00660	0.211514
$91$	−0.734385	−0.0769844
$92$	10.0355	1.04628
$93$	−8.27225	−0.857792
$94$	18.5424	1.91250
$95$	−4.42861	−0.454366
$96$	7.06527	0.721096
$97$	−10.7482	−1.09131	−0.545656	−	0.838009i	$-0.683719\pi$
$97$	−10.7482	−1.09131	−0.545656	+	0.838009i	$0.683719\pi$
$98$	14.6937	1.48429
$99$	3.61819	0.363642
$100$	−12.1114	−1.21114
$101$	−18.7291	−1.86361	−0.931805	−	0.362959i	$-0.881767\pi$
$101$	−18.7291	−1.86361	−0.931805	+	0.362959i	$0.881767\pi$
$102$	10.6625	1.05574
$103$	−12.6413	−1.24559	−0.622794	−	0.782386i	$-0.714003\pi$
$103$	−12.6413	−1.24559	−0.622794	+	0.782386i	$0.714003\pi$
$104$	−2.43074	−0.238354
$105$	0.544890	0.0531759
$106$	8.02063	0.779032
$107$	−17.5743	−1.69898	−0.849488	−	0.527608i	$-0.823089\pi$
$107$	−17.5743	−1.69898	−0.849488	+	0.527608i	$0.823089\pi$
$108$	2.89880	0.278937
$109$	−6.24719	−0.598372	−0.299186	−	0.954195i	$-0.596715\pi$
$109$	−6.24719	−0.598372	−0.299186	+	0.954195i	$0.596715\pi$
$110$	7.26026	0.692239
$111$	4.59647	0.436278
$112$	0.838162	0.0791989
$113$	−3.65814	−0.344129	−0.172065	−	0.985086i	$-0.555044\pi$
$113$	−3.65814	−0.344129	−0.172065	+	0.985086i	$0.555044\pi$
$114$	−10.8118	−1.01262
$115$	−3.13861	−0.292677
$116$	−9.44200	−0.876668
$117$	1.22188	0.112963
$118$	−23.5478	−2.16775
$119$	2.89538	0.265419
$120$	1.80353	0.164639
$121$	2.09133	0.190121
$122$	31.2097	2.82559
$123$	9.42540	0.849860
$124$	−23.9796	−2.15343
$125$	8.32084	0.744239
$126$	1.33027	0.118510
$127$	−8.27174	−0.733999	−0.366999	−	0.930221i	$-0.619615\pi$
$127$	−8.27174	−0.733999	−0.366999	+	0.930221i	$0.619615\pi$
$128$	14.3076	1.26463
$129$	−2.02744	−0.178506
$130$	2.45183	0.215040
$131$	8.81038	0.769766	0.384883	−	0.922965i	$-0.374242\pi$
$131$	8.81038	0.769766	0.384883	+	0.922965i	$0.374242\pi$
$132$	10.4884	0.912900
$133$	−2.93593	−0.254577
$134$	−27.1540	−2.34575
$135$	−0.906600	−0.0780277
$136$	9.58343	0.821772
$137$	22.6312	1.93351	0.966756	−	0.255701i	$-0.0823063\pi$
$137$	22.6312	1.93351	0.966756	+	0.255701i	$0.0823063\pi$
$138$	−7.66244	−0.652270
$139$	4.67572	0.396590	0.198295	−	0.980142i	$-0.436460\pi$
$139$	4.67572	0.396590	0.198295	+	0.980142i	$0.436460\pi$
$140$	1.57953	0.133495
$141$	−8.37762	−0.705523
$142$	15.2334	1.27836
$143$	4.42101	0.369704
$144$	−1.39455	−0.116213
$145$	2.95298	0.245232
$146$	17.8519	1.47743
$147$	−6.63877	−0.547556
$148$	13.3243	1.09525
$149$	−5.08039	−0.416202	−0.208101	−	0.978107i	$-0.566728\pi$
$149$	−5.08039	−0.416202	−0.208101	+	0.978107i	$0.566728\pi$
$150$	9.24744	0.755050
$151$	−2.19120	−0.178317	−0.0891585	−	0.996017i	$-0.528418\pi$
$151$	−2.19120	−0.178317	−0.0891585	+	0.996017i	$0.528418\pi$
$152$	−9.71765	−0.788205
$153$	−4.81739	−0.389463
$154$	4.81316	0.387856
$155$	7.49962	0.602384
$156$	3.54200	0.283587
$157$	8.55033	0.682390	0.341195	−	0.939992i	$-0.389168\pi$
$157$	8.55033	0.682390	0.341195	+	0.939992i	$0.389168\pi$
$158$	−11.6586	−0.927506
$159$	−3.62379	−0.287386
$160$	−6.40537	−0.506389
$161$	−2.08073	−0.163984
$162$	−2.21332	−0.173895
$163$	2.24298	0.175683	0.0878417	−	0.996134i	$-0.472003\pi$
$163$	2.24298	0.175683	0.0878417	+	0.996134i	$0.472003\pi$
$164$	27.3224	2.13352
$165$	−3.28025	−0.255367
$166$	−25.3233	−1.96547
$167$	11.3389	0.877430	0.438715	−	0.898626i	$-0.355434\pi$
$167$	11.3389	0.877430	0.438715	+	0.898626i	$0.355434\pi$
$168$	1.19565	0.0922461
$169$	−11.5070	−0.885154
$170$	−9.66658	−0.741393
$171$	4.88486	0.373555
$172$	−5.87714	−0.448127
$173$	7.94625	0.604142	0.302071	−	0.953285i	$-0.402322\pi$
$173$	7.94625	0.604142	0.302071	+	0.953285i	$0.402322\pi$
$174$	7.20926	0.546532
$175$	2.51113	0.189824
$176$	−5.04576	−0.380338
$177$	10.6391	0.799685
$178$	7.30624	0.547626
$179$	18.4787	1.38116	0.690580	−	0.723256i	$-0.257355\pi$
$179$	18.4787	1.38116	0.690580	+	0.723256i	$0.257355\pi$
$180$	−2.62805	−0.195884
$181$	−4.35105	−0.323411	−0.161705	−	0.986839i	$-0.551699\pi$
$181$	−4.35105	−0.323411	−0.161705	+	0.986839i	$0.551699\pi$
$182$	1.62543	0.120485
$183$	−14.1008	−1.04236
$184$	−6.88701	−0.507717
$185$	−4.16716	−0.306376
$186$	18.3092	1.34249
$187$	−17.4303	−1.27463
$188$	−24.2851	−1.77117
$189$	−0.601026	−0.0437182
$190$	9.80196	0.711109
$191$	−3.35386	−0.242677	−0.121339	−	0.992611i	$-0.538719\pi$
$191$	−3.35386	−0.242677	−0.121339	+	0.992611i	$0.538719\pi$
$192$	−12.8486	−0.927270
$193$	4.81414	0.346529	0.173265	−	0.984875i	$-0.444568\pi$
$193$	4.81414	0.346529	0.173265	+	0.984875i	$0.444568\pi$
$194$	23.7892	1.70796
$195$	−1.10776	−0.0793283
$196$	−19.2445	−1.37461
$197$	14.6644	1.04480	0.522398	−	0.852702i	$-0.325037\pi$
$197$	14.6644	1.04480	0.522398	+	0.852702i	$0.325037\pi$
$198$	−8.00823	−0.569120
$199$	8.50493	0.602899	0.301449	−	0.953482i	$-0.402530\pi$
$199$	8.50493	0.602899	0.301449	+	0.953482i	$0.402530\pi$
$200$	8.31161	0.587720
$201$	12.2684	0.865349
$202$	41.4535	2.91665
$203$	1.95767	0.137401
$204$	−13.9647	−0.977722
$205$	−8.54506	−0.596813
$206$	27.9794	1.94942
$207$	3.46196	0.240623
$208$	−1.70398	−0.118150
$209$	17.6744	1.22256
$210$	−1.20602	−0.0832232
$211$	−17.3367	−1.19351	−0.596755	−	0.802424i	$-0.703544\pi$
$211$	−17.3367	−1.19351	−0.596755	+	0.802424i	$0.703544\pi$
$212$	−10.5047	−0.721463
$213$	−6.88258	−0.471587
$214$	38.8977	2.65899
$215$	1.83807	0.125356
$216$	−1.98934	−0.135357
$217$	4.97184	0.337510
$218$	13.8271	0.936486
$219$	−8.06566	−0.545027
$220$	−9.50881	−0.641084
$221$	−5.88630	−0.395955
$222$	−10.1735	−0.682800
$223$	20.9759	1.40465	0.702326	−	0.711856i	$-0.252145\pi$
$223$	20.9759	1.40465	0.702326	+	0.711856i	$0.252145\pi$
$224$	−4.24642	−0.283726
$225$	−4.17808	−0.278538
$226$	8.09665	0.538581
$227$	−5.97204	−0.396379	−0.198189	−	0.980164i	$-0.563506\pi$
$227$	−5.97204	−0.396379	−0.198189	+	0.980164i	$0.563506\pi$
$228$	14.1602	0.937785
$229$	−9.81332	−0.648483	−0.324241	−	0.945974i	$-0.605109\pi$
$229$	−9.81332	−0.648483	−0.324241	+	0.945974i	$0.605109\pi$
$230$	6.94676	0.458056
$231$	−2.17463	−0.143080
$232$	6.47969	0.425413
$233$	−24.7120	−1.61894	−0.809470	−	0.587161i	$-0.800245\pi$
$233$	−24.7120	−1.61894	−0.809470	+	0.587161i	$0.800245\pi$
$234$	−2.70443	−0.176794
$235$	7.59515	0.495453
$236$	30.8407	2.00756
$237$	5.26745	0.342157
$238$	−6.40842	−0.415396
$239$	13.7832	0.891558	0.445779	−	0.895143i	$-0.352927\pi$
$239$	13.7832	0.891558	0.445779	+	0.895143i	$0.352927\pi$
$240$	1.26430	0.0816102
$241$	−22.8960	−1.47486	−0.737430	−	0.675424i	$-0.763961\pi$
$241$	−22.8960	−1.47486	−0.737430	+	0.675424i	$0.763961\pi$
$242$	−4.62878	−0.297550
$243$	1.00000	0.0641500
$244$	−40.8755	−2.61679
$245$	6.01870	0.384521
$246$	−20.8615	−1.33008
$247$	5.96873	0.379781
$248$	16.4563	1.04498
$249$	11.4413	0.725062
$250$	−18.4167	−1.16478
$251$	−17.0523	−1.07633	−0.538166	−	0.842839i	$-0.680883\pi$
$251$	−17.0523	−1.07633	−0.538166	+	0.842839i	$0.680883\pi$
$252$	−1.74226	−0.109752
$253$	12.5260	0.787505
$254$	18.3080	1.14875
$255$	4.36745	0.273500
$256$	−5.97017	−0.373136
$257$	−5.72754	−0.357274	−0.178637	−	0.983915i	$-0.557169\pi$
$257$	−5.72754	−0.357274	−0.178637	+	0.983915i	$0.557169\pi$
$258$	4.48737	0.279372
$259$	−2.76260	−0.171660
$260$	−3.21118	−0.199149
$261$	−3.25721	−0.201616
$262$	−19.5002	−1.20473
$263$	−4.86697	−0.300110	−0.150055	−	0.988678i	$-0.547945\pi$
$263$	−4.86697	−0.300110	−0.150055	+	0.988678i	$0.547945\pi$
$264$	−7.19782	−0.442995
$265$	3.28533	0.201816
$266$	6.49816	0.398428
$267$	−3.30103	−0.202020
$268$	35.5638	2.17240
$269$	−25.4835	−1.55376	−0.776879	−	0.629650i	$-0.783198\pi$
$269$	−25.4835	−1.55376	−0.776879	+	0.629650i	$0.783198\pi$
$270$	2.00660	0.122118
$271$	7.45632	0.452939	0.226470	−	0.974018i	$-0.427282\pi$
$271$	7.45632	0.452939	0.226470	+	0.974018i	$0.427282\pi$
$272$	6.71810	0.407345
$273$	−0.734385	−0.0444470
$274$	−50.0901	−3.02605
$275$	−15.1171	−0.911595
$276$	10.0355	0.604068
$277$	−4.08810	−0.245630	−0.122815	−	0.992430i	$-0.539192\pi$
$277$	−4.08810	−0.245630	−0.122815	+	0.992430i	$0.539192\pi$
$278$	−10.3489	−0.620685
$279$	−8.27225	−0.495247
$280$	−1.08397	−0.0647797
$281$	6.68982	0.399081	0.199541	−	0.979890i	$-0.436055\pi$
$281$	6.68982	0.399081	0.199541	+	0.979890i	$0.436055\pi$
$282$	18.5424	1.10418
$283$	−17.5779	−1.04490	−0.522448	−	0.852671i	$-0.674981\pi$
$283$	−17.5779	−1.04490	−0.522448	+	0.852671i	$0.674981\pi$
$284$	−19.9512	−1.18389
$285$	−4.42861	−0.262328
$286$	−9.78514	−0.578607
$287$	−5.66491	−0.334389
$288$	7.06527	0.416325
$289$	6.20728	0.365134
$290$	−6.53591	−0.383802
$291$	−10.7482	−0.630069
$292$	−23.3807	−1.36825
$293$	−23.4512	−1.37003	−0.685017	−	0.728527i	$-0.740205\pi$
$293$	−23.4512	−1.37003	−0.685017	+	0.728527i	$0.740205\pi$
$294$	14.6937	0.856956
$295$	−9.64542	−0.561578
$296$	−9.14395	−0.531481
$297$	3.61819	0.209949
$298$	11.2445	0.651379
$299$	4.23011	0.244634
$300$	−12.1114	−0.699253
$301$	1.21854	0.0702356
$302$	4.84982	0.279076
$303$	−18.7291	−1.07596
$304$	−6.81219	−0.390706
$305$	12.7838	0.731999
$306$	10.6625	0.609532
$307$	16.2766	0.928954	0.464477	−	0.885585i	$-0.346242\pi$
$307$	16.2766	0.928954	0.464477	+	0.885585i	$0.346242\pi$
$308$	−6.30382	−0.359194
$309$	−12.6413	−0.719141
$310$	−16.5991	−0.942765
$311$	4.28800	0.243150	0.121575	−	0.992582i	$-0.461205\pi$
$311$	4.28800	0.243150	0.121575	+	0.992582i	$0.461205\pi$
$312$	−2.43074	−0.137614
$313$	10.8317	0.612245	0.306122	−	0.951992i	$-0.400968\pi$
$313$	10.8317	0.612245	0.306122	+	0.951992i	$0.400968\pi$
$314$	−18.9246	−1.06798
$315$	0.544890	0.0307011
$316$	15.2693	0.858964
$317$	14.9430	0.839284	0.419642	−	0.907690i	$-0.362156\pi$
$317$	14.9430	0.839284	0.419642	+	0.907690i	$0.362156\pi$
$318$	8.02063	0.449775
$319$	−11.7852	−0.659845
$320$	11.6486	0.651175
$321$	−17.5743	−0.980904
$322$	4.60533	0.256645
$323$	−23.5323	−1.30937
$324$	2.89880	0.161045
$325$	−5.10513	−0.283181
$326$	−4.96443	−0.274954
$327$	−6.24719	−0.345470
$328$	−18.7503	−1.03531
$329$	5.03517	0.277598
$330$	7.26026	0.399664
$331$	11.2968	0.620926	0.310463	−	0.950585i	$-0.399516\pi$
$331$	11.2968	0.620926	0.310463	+	0.950585i	$0.399516\pi$
$332$	33.1660	1.82022
$333$	4.59647	0.251885
$334$	−25.0967	−1.37323
$335$	−11.1226	−0.607691
$336$	0.838162	0.0457255
$337$	3.14434	0.171283	0.0856417	−	0.996326i	$-0.472706\pi$
$337$	3.14434	0.171283	0.0856417	+	0.996326i	$0.472706\pi$
$338$	25.4687	1.38532
$339$	−3.65814	−0.198683
$340$	12.6604	0.686605
$341$	−29.9306	−1.62083
$342$	−10.8118	−0.584634
$343$	8.19726	0.442610
$344$	4.03326	0.217459
$345$	−3.13861	−0.168977
$346$	−17.5876	−0.945517
$347$	−24.8885	−1.33609	−0.668043	−	0.744122i	$-0.732868\pi$
$347$	−24.8885	−1.33609	−0.668043	+	0.744122i	$0.732868\pi$
$348$	−9.44200	−0.506145
$349$	−17.4200	−0.932473	−0.466236	−	0.884660i	$-0.654390\pi$
$349$	−17.4200	−0.932473	−0.466236	+	0.884660i	$0.654390\pi$
$350$	−5.55795	−0.297085
$351$	1.22188	0.0652194
$352$	25.5635	1.36254
$353$	28.0319	1.49199	0.745994	−	0.665953i	$-0.231975\pi$
$353$	28.0319	1.49199	0.745994	+	0.665953i	$0.231975\pi$
$354$	−23.5478	−1.25155
$355$	6.23975	0.331171
$356$	−9.56902	−0.507157
$357$	2.89538	0.153240
$358$	−40.8993	−2.16159
$359$	27.1572	1.43330	0.716650	−	0.697433i	$-0.245675\pi$
$359$	27.1572	1.43330	0.716650	+	0.697433i	$0.245675\pi$
$360$	1.80353	0.0950546
$361$	4.86186	0.255888
$362$	9.63028	0.506156
$363$	2.09133	0.109766
$364$	−2.12884	−0.111581
$365$	7.31232	0.382744
$366$	31.2097	1.63136
$367$	−3.14066	−0.163941	−0.0819706	−	0.996635i	$-0.526121\pi$
$367$	−3.14066	−0.163941	−0.0819706	+	0.996635i	$0.526121\pi$
$368$	−4.82788	−0.251671
$369$	9.42540	0.490667
$370$	9.22328	0.479495
$371$	2.17800	0.113076
$372$	−23.9796	−1.24328
$373$	−20.2267	−1.04730	−0.523649	−	0.851934i	$-0.675430\pi$
$373$	−20.2267	−1.04730	−0.523649	+	0.851934i	$0.675430\pi$
$374$	38.5788	1.99486
$375$	8.32084	0.429686
$376$	16.6659	0.859479
$377$	−3.97993	−0.204977
$378$	1.33027	0.0684215
$379$	−14.1721	−0.727972	−0.363986	−	0.931404i	$-0.618584\pi$
$379$	−14.1721	−0.727972	−0.363986	+	0.931404i	$0.618584\pi$
$380$	−12.8377	−0.658559
$381$	−8.27174	−0.423774
$382$	7.42318	0.379803
$383$	15.1517	0.774216	0.387108	−	0.922034i	$-0.373474\pi$
$383$	15.1517	0.774216	0.387108	+	0.922034i	$0.373474\pi$
$384$	14.3076	0.730134
$385$	1.97152	0.100478
$386$	−10.6553	−0.542338
$387$	−2.02744	−0.103060
$388$	−31.1568	−1.58175
$389$	−34.3608	−1.74216	−0.871080	−	0.491141i	$-0.836580\pi$
$389$	−34.3608	−1.74216	−0.871080	+	0.491141i	$0.836580\pi$
$390$	2.45183	0.124153
$391$	−16.6776	−0.843423
$392$	13.2068	0.667042
$393$	8.81038	0.444425
$394$	−32.4571	−1.63517
$395$	−4.77547	−0.240280
$396$	10.4884	0.527063
$397$	−19.0772	−0.957455	−0.478728	−	0.877964i	$-0.658902\pi$
$397$	−19.0772	−0.957455	−0.478728	+	0.877964i	$0.658902\pi$
$398$	−18.8242	−0.943570
$399$	−2.93593	−0.146980
$400$	5.82654	0.291327
$401$	34.3770	1.71670	0.858352	−	0.513061i	$-0.171488\pi$
$401$	34.3770	1.71670	0.858352	+	0.513061i	$0.171488\pi$
$402$	−27.1540	−1.35432
$403$	−10.1077	−0.503502
$404$	−54.2918	−2.70112
$405$	−0.906600	−0.0450493
$406$	−4.33295	−0.215041
$407$	16.6309	0.824365
$408$	9.58343	0.474451
$409$	−19.7124	−0.974715	−0.487357	−	0.873203i	$-0.662039\pi$
$409$	−19.7124	−0.974715	−0.487357	+	0.873203i	$0.662039\pi$
$410$	18.9130	0.934046
$411$	22.6312	1.11631
$412$	−36.6447	−1.80536
$413$	−6.39439	−0.314647
$414$	−7.66244	−0.376588
$415$	−10.3727	−0.509174
$416$	8.63295	0.423265
$417$	4.67572	0.228971
$418$	−39.1191	−1.91338
$419$	19.0723	0.931743	0.465872	−	0.884852i	$-0.345741\pi$
$419$	19.0723	0.931743	0.465872	+	0.884852i	$0.345741\pi$
$420$	1.57953	0.0770731
$421$	−29.1217	−1.41930	−0.709651	−	0.704553i	$-0.751148\pi$
$421$	−29.1217	−1.41930	−0.709651	+	0.704553i	$0.751148\pi$
$422$	38.3718	1.86791
$423$	−8.37762	−0.407334
$424$	7.20896	0.350098
$425$	20.1274	0.976324
$426$	15.2334	0.738060
$427$	8.47497	0.410133
$428$	−50.9445	−2.46250
$429$	4.42101	0.213449
$430$	−4.06825	−0.196188
$431$	−14.0459	−0.676567	−0.338283	−	0.941044i	$-0.609846\pi$
$431$	−14.0459	−0.676567	−0.338283	+	0.941044i	$0.609846\pi$
$432$	−1.39455	−0.0670954
$433$	28.5524	1.37214	0.686070	−	0.727536i	$-0.259334\pi$
$433$	28.5524	1.37214	0.686070	+	0.727536i	$0.259334\pi$
$434$	−11.0043	−0.528223
$435$	2.95298	0.141585
$436$	−18.1094	−0.867281
$437$	16.9112	0.808972
$438$	17.8519	0.852997
$439$	22.9863	1.09708	0.548538	−	0.836125i	$-0.315185\pi$
$439$	22.9863	1.09708	0.548538	+	0.836125i	$0.315185\pi$
$440$	6.52554	0.311093
$441$	−6.63877	−0.316132
$442$	13.0283	0.619692
$443$	9.58743	0.455512	0.227756	−	0.973718i	$-0.426861\pi$
$443$	9.58743	0.455512	0.227756	+	0.973718i	$0.426861\pi$
$444$	13.3243	0.632342
$445$	2.99271	0.141868
$446$	−46.4265	−2.19836
$447$	−5.08039	−0.240294
$448$	7.72237	0.364848
$449$	−21.1143	−0.996446	−0.498223	−	0.867049i	$-0.666014\pi$
$449$	−21.1143	−0.996446	−0.498223	+	0.867049i	$0.666014\pi$
$450$	9.24744	0.435928
$451$	34.1029	1.60584
$452$	−10.6042	−0.498781
$453$	−2.19120	−0.102951
$454$	13.2181	0.620355
$455$	0.665793	0.0312129
$456$	−9.71765	−0.455070
$457$	−19.7026	−0.921650	−0.460825	−	0.887491i	$-0.652446\pi$
$457$	−19.7026	−0.921650	−0.460825	+	0.887491i	$0.652446\pi$
$458$	21.7201	1.01491
$459$	−4.81739	−0.224857
$460$	−9.09821	−0.424206
$461$	−0.710873	−0.0331086	−0.0165543	−	0.999863i	$-0.505270\pi$
$461$	−0.710873	−0.0331086	−0.0165543	+	0.999863i	$0.505270\pi$
$462$	4.81316	0.223929
$463$	−36.4326	−1.69317	−0.846583	−	0.532256i	$-0.821344\pi$
$463$	−36.4326	−1.69317	−0.846583	+	0.532256i	$0.821344\pi$
$464$	4.54235	0.210873
$465$	7.49962	0.347786
$466$	54.6958	2.53373
$467$	34.9446	1.61704	0.808522	−	0.588466i	$-0.200268\pi$
$467$	34.9446	1.61704	0.808522	+	0.588466i	$0.200268\pi$
$468$	3.54200	0.163729
$469$	−7.37366	−0.340484
$470$	−16.8105	−0.775411
$471$	8.55033	0.393978
$472$	−21.1648	−0.974190
$473$	−7.33566	−0.337294
$474$	−11.6586	−0.535496
$475$	−20.4093	−0.936444
$476$	8.39314	0.384699
$477$	−3.62379	−0.165922
$478$	−30.5066	−1.39534
$479$	2.92477	0.133636	0.0668180	−	0.997765i	$-0.478715\pi$
$479$	2.92477	0.133636	0.0668180	+	0.997765i	$0.478715\pi$
$480$	−6.40537	−0.292364
$481$	5.61636	0.256084
$482$	50.6762	2.30824
$483$	−2.08073	−0.0946764
$484$	6.06234	0.275561
$485$	9.74429	0.442466
$486$	−2.21332	−0.100398
$487$	−3.57587	−0.162038	−0.0810190	−	0.996713i	$-0.525817\pi$
$487$	−3.57587	−0.162038	−0.0810190	+	0.996713i	$0.525817\pi$
$488$	28.0513	1.26982
$489$	2.24298	0.101431
$490$	−13.3213	−0.601797
$491$	35.4972	1.60197	0.800984	−	0.598685i	$-0.204310\pi$
$491$	35.4972	1.60197	0.800984	+	0.598685i	$0.204310\pi$
$492$	27.3224	1.23179
$493$	15.6913	0.706699
$494$	−13.2107	−0.594379
$495$	−3.28025	−0.147436
$496$	11.5361	0.517985
$497$	4.13661	0.185552
$498$	−25.3233	−1.13476
$499$	−14.2852	−0.639492	−0.319746	−	0.947503i	$-0.603598\pi$
$499$	−14.2852	−0.639492	−0.319746	+	0.947503i	$0.603598\pi$
$500$	24.1205	1.07870
$501$	11.3389	0.506585
$502$	37.7423	1.68452
$503$	30.6461	1.36644	0.683220	−	0.730212i	$-0.260579\pi$
$503$	30.6461	1.36644	0.683220	+	0.730212i	$0.260579\pi$
$504$	1.19565	0.0532583
$505$	16.9798	0.755589
$506$	−27.7242	−1.23249
$507$	−11.5070	−0.511044
$508$	−23.9781	−1.06386
$509$	−28.7761	−1.27548	−0.637738	−	0.770253i	$-0.720130\pi$
$509$	−28.7761	−1.27548	−0.637738	+	0.770253i	$0.720130\pi$
$510$	−9.66658	−0.428043
$511$	4.84767	0.214448
$512$	−15.4014	−0.680650
$513$	4.88486	0.215672
$514$	12.6769	0.559154
$515$	11.4606	0.505016
$516$	−5.87714	−0.258726
$517$	−30.3118	−1.33311
$518$	6.11453	0.268657
$519$	7.94625	0.348802
$520$	2.20371	0.0966391
$521$	34.3719	1.50586	0.752931	−	0.658100i	$-0.228640\pi$
$521$	34.3719	1.50586	0.752931	+	0.658100i	$0.228640\pi$
$522$	7.20926	0.315541
$523$	19.6621	0.859762	0.429881	−	0.902885i	$-0.358555\pi$
$523$	19.6621	0.859762	0.429881	+	0.902885i	$0.358555\pi$
$524$	25.5395	1.11570
$525$	2.51113	0.109595
$526$	10.7722	0.469689
$527$	39.8507	1.73592
$528$	−5.04576	−0.219588
$529$	−11.0148	−0.478906
$530$	−7.27150	−0.315854
$531$	10.6391	0.461698
$532$	−8.51068	−0.368985
$533$	11.5167	0.498846
$534$	7.30624	0.316172
$535$	15.9329	0.688839
$536$	−24.4061	−1.05418
$537$	18.4787	0.797413
$538$	56.4033	2.43172
$539$	−24.0203	−1.03463
$540$	−2.62805	−0.113093
$541$	26.6403	1.14535	0.572677	−	0.819781i	$-0.305905\pi$
$541$	26.6403	1.14535	0.572677	+	0.819781i	$0.305905\pi$
$542$	−16.5033	−0.708875
$543$	−4.35105	−0.186721
$544$	−34.0362	−1.45929
$545$	5.66370	0.242606
$546$	1.62543	0.0695620
$547$	−0.0974146	−0.00416515	−0.00208257	−	0.999998i	$-0.500663\pi$
$547$	−0.0974146	−0.00416515	−0.00208257	+	0.999998i	$0.500663\pi$
$548$	65.6033	2.80243
$549$	−14.1008	−0.601809
$550$	33.4590	1.42670
$551$	−15.9110	−0.677832
$552$	−6.88701	−0.293131
$553$	−3.16588	−0.134627
$554$	9.04828	0.384425
$555$	−4.16716	−0.176886
$556$	13.5540	0.574818
$557$	−5.12574	−0.217184	−0.108592	−	0.994086i	$-0.534634\pi$
$557$	−5.12574	−0.217184	−0.108592	+	0.994086i	$0.534634\pi$
$558$	18.3092	0.775089
$559$	−2.47729	−0.104778
$560$	−0.759878	−0.0321107
$561$	−17.4303	−0.735906
$562$	−14.8067	−0.624585
$563$	−32.9098	−1.38698	−0.693492	−	0.720464i	$-0.743929\pi$
$563$	−32.9098	−1.38698	−0.693492	+	0.720464i	$0.743929\pi$
$564$	−24.2851	−1.02259
$565$	3.31647	0.139525
$566$	38.9055	1.63532
$567$	−0.601026	−0.0252407
$568$	13.6918	0.574495
$569$	16.2123	0.679654	0.339827	−	0.940488i	$-0.389632\pi$
$569$	16.2123	0.679654	0.339827	+	0.940488i	$0.389632\pi$
$570$	9.80196	0.410559
$571$	−1.39857	−0.0585284	−0.0292642	−	0.999572i	$-0.509316\pi$
$571$	−1.39857	−0.0585284	−0.0292642	+	0.999572i	$0.509316\pi$
$572$	12.8156	0.535849
$573$	−3.35386	−0.140110
$574$	12.5383	0.523338
$575$	−14.4643	−0.603204
$576$	−12.8486	−0.535360
$577$	−24.4869	−1.01940	−0.509702	−	0.860351i	$-0.670244\pi$
$577$	−24.4869	−1.01940	−0.509702	+	0.860351i	$0.670244\pi$
$578$	−13.7387	−0.571456
$579$	4.81414	0.200069
$580$	8.56012	0.355440
$581$	−6.87651	−0.285286
$582$	23.7892	0.986094
$583$	−13.1116	−0.543027
$584$	16.0453	0.663961
$585$	−1.10776	−0.0458002
$586$	51.9051	2.14418
$587$	−1.69437	−0.0699341	−0.0349671	−	0.999388i	$-0.511133\pi$
$587$	−1.69437	−0.0699341	−0.0349671	+	0.999388i	$0.511133\pi$
$588$	−19.2445	−0.793629
$589$	−40.4088	−1.66501
$590$	21.3484	0.878901
$591$	14.6644	0.603214
$592$	−6.41002	−0.263450
$593$	14.4932	0.595164	0.297582	−	0.954696i	$-0.403820\pi$
$593$	14.4932	0.595164	0.297582	+	0.954696i	$0.403820\pi$
$594$	−8.00823	−0.328582
$595$	−2.62495	−0.107613
$596$	−14.7270	−0.603243
$597$	8.50493	0.348084
$598$	−9.36261	−0.382866
$599$	−34.9980	−1.42998	−0.714990	−	0.699135i	$-0.753569\pi$
$599$	−34.9980	−1.42998	−0.714990	+	0.699135i	$0.753569\pi$
$600$	8.31161	0.339320
$601$	−29.5865	−1.20686	−0.603429	−	0.797417i	$-0.706199\pi$
$601$	−29.5865	−1.20686	−0.603429	+	0.797417i	$0.706199\pi$
$602$	−2.69703	−0.109923
$603$	12.2684	0.499609
$604$	−6.35184	−0.258453
$605$	−1.89600	−0.0770832
$606$	41.4535	1.68393
$607$	−1.03688	−0.0420857	−0.0210429	−	0.999779i	$-0.506699\pi$
$607$	−1.03688	−0.0420857	−0.0210429	+	0.999779i	$0.506699\pi$
$608$	34.5129	1.39968
$609$	1.95767	0.0793287
$610$	−28.2947	−1.14562
$611$	−10.2365	−0.414124
$612$	−13.9647	−0.564488
$613$	−21.6405	−0.874053	−0.437027	−	0.899449i	$-0.643968\pi$
$613$	−21.6405	−0.874053	−0.437027	+	0.899449i	$0.643968\pi$
$614$	−36.0254	−1.45387
$615$	−8.54506	−0.344570
$616$	4.32608	0.174303
$617$	25.6071	1.03090	0.515452	−	0.856918i	$-0.327624\pi$
$617$	25.6071	1.03090	0.515452	+	0.856918i	$0.327624\pi$
$618$	27.9794	1.12550
$619$	20.3149	0.816523	0.408262	−	0.912865i	$-0.366135\pi$
$619$	20.3149	0.816523	0.408262	+	0.912865i	$0.366135\pi$
$620$	21.7399	0.873096
$621$	3.46196	0.138924
$622$	−9.49074	−0.380544
$623$	1.98400	0.0794874
$624$	−1.70398	−0.0682138
$625$	13.3467	0.533868
$626$	−23.9741	−0.958198
$627$	17.6744	0.705846
$628$	24.7857	0.989057
$629$	−22.1430	−0.882900
$630$	−1.20602	−0.0480489
$631$	−26.9032	−1.07100	−0.535501	−	0.844535i	$-0.679877\pi$
$631$	−26.9032	−1.07100	−0.535501	+	0.844535i	$0.679877\pi$
$632$	−10.4787	−0.416822
$633$	−17.3367	−0.689073
$634$	−33.0738	−1.31353
$635$	7.49916	0.297595
$636$	−10.5047	−0.416537
$637$	−8.11181	−0.321401
$638$	26.0845	1.03270
$639$	−6.88258	−0.272271
$640$	−12.9713	−0.512736
$641$	−26.7737	−1.05750	−0.528748	−	0.848779i	$-0.677338\pi$
$641$	−26.7737	−1.05750	−0.528748	+	0.848779i	$0.677338\pi$
$642$	38.8977	1.53517
$643$	21.8118	0.860174	0.430087	−	0.902787i	$-0.358483\pi$
$643$	21.8118	0.860174	0.430087	+	0.902787i	$0.358483\pi$
$644$	−6.03162	−0.237679
$645$	1.83807	0.0723741
$646$	52.0846	2.04924
$647$	−36.7138	−1.44337	−0.721684	−	0.692222i	$-0.756632\pi$
$647$	−36.7138	−1.44337	−0.721684	+	0.692222i	$0.756632\pi$
$648$	−1.98934	−0.0781486
$649$	38.4944	1.51104
$650$	11.2993	0.443195
$651$	4.97184	0.194862
$652$	6.50194	0.254636
$653$	−20.2740	−0.793384	−0.396692	−	0.917952i	$-0.629842\pi$
$653$	−20.2740	−0.793384	−0.396692	+	0.917952i	$0.629842\pi$
$654$	13.8271	0.540681
$655$	−7.98749	−0.312097
$656$	−13.1442	−0.513195
$657$	−8.06566	−0.314671
$658$	−11.1445	−0.434456
$659$	16.4965	0.642611	0.321306	−	0.946976i	$-0.395878\pi$
$659$	16.4965	0.642611	0.321306	+	0.946976i	$0.395878\pi$
$660$	−9.50881	−0.370130
$661$	−11.8160	−0.459590	−0.229795	−	0.973239i	$-0.573806\pi$
$661$	−11.8160	−0.459590	−0.229795	+	0.973239i	$0.573806\pi$
$662$	−25.0034	−0.971785
$663$	−5.88630	−0.228605
$664$	−22.7606	−0.883282
$665$	2.66171	0.103217
$666$	−10.1735	−0.394214
$667$	−11.2763	−0.436621
$668$	32.8692	1.27175
$669$	20.9759	0.810976
$670$	24.6178	0.951070
$671$	−51.0195	−1.96959
$672$	−4.24642	−0.163809
$673$	−8.39606	−0.323644	−0.161822	−	0.986820i	$-0.551737\pi$
$673$	−8.39606	−0.323644	−0.161822	+	0.986820i	$0.551737\pi$
$674$	−6.95945	−0.268068
$675$	−4.17808	−0.160814
$676$	−33.3565	−1.28294
$677$	−24.6486	−0.947324	−0.473662	−	0.880707i	$-0.657068\pi$
$677$	−24.6486	−0.947324	−0.473662	+	0.880707i	$0.657068\pi$
$678$	8.09665	0.310950
$679$	6.45994	0.247910
$680$	−8.68834	−0.333182
$681$	−5.97204	−0.228849
$682$	66.2461	2.53669
$683$	−24.6138	−0.941822	−0.470911	−	0.882181i	$-0.656075\pi$
$683$	−24.6138	−0.941822	−0.470911	+	0.882181i	$0.656075\pi$
$684$	14.1602	0.541430
$685$	−20.5174	−0.783930
$686$	−18.1432	−0.692710
$687$	−9.81332	−0.374402
$688$	2.82736	0.107792
$689$	−4.42786	−0.168688
$690$	6.94676	0.264459
$691$	−26.9165	−1.02395	−0.511977	−	0.858999i	$-0.671087\pi$
$691$	−26.9165	−1.02395	−0.511977	+	0.858999i	$0.671087\pi$
$692$	23.0346	0.875644
$693$	−2.17463	−0.0826074
$694$	55.0864	2.09105
$695$	−4.23901	−0.160795
$696$	6.47969	0.245612
$697$	−45.4059	−1.71987
$698$	38.5562	1.45937
$699$	−24.7120	−0.934695
$700$	7.27928	0.275131
$701$	−49.5118	−1.87004	−0.935018	−	0.354601i	$-0.884617\pi$
$701$	−49.5118	−1.87004	−0.935018	+	0.354601i	$0.884617\pi$
$702$	−2.70443	−0.102072
$703$	22.4531	0.846836
$704$	−46.4888	−1.75211
$705$	7.59515	0.286050
$706$	−62.0437	−2.33504
$707$	11.2567	0.423350
$708$	30.8407	1.15906
$709$	−23.8673	−0.896357	−0.448178	−	0.893944i	$-0.647927\pi$
$709$	−23.8673	−0.896357	−0.448178	+	0.893944i	$0.647927\pi$
$710$	−13.8106	−0.518302
$711$	5.26745	0.197545
$712$	6.56686	0.246104
$713$	−28.6382	−1.07251
$714$	−6.40842	−0.239829
$715$	−4.00809	−0.149894
$716$	53.5660	2.00185
$717$	13.7832	0.514741
$718$	−60.1076	−2.24319
$719$	2.62453	0.0978786	0.0489393	−	0.998802i	$-0.484416\pi$
$719$	2.62453	0.0978786	0.0489393	+	0.998802i	$0.484416\pi$
$720$	1.26430	0.0471177
$721$	7.59778	0.282956
$722$	−10.7609	−0.400478
$723$	−22.8960	−0.851511
$724$	−12.6128	−0.468752
$725$	13.6089	0.505421
$726$	−4.62878	−0.171790
$727$	37.4891	1.39039	0.695197	−	0.718819i	$-0.255317\pi$
$727$	37.4891	1.39039	0.695197	+	0.718819i	$0.255317\pi$
$728$	1.46094	0.0541461
$729$	1.00000	0.0370370
$730$	−16.1845	−0.599017
$731$	9.76696	0.361244
$732$	−40.8755	−1.51080
$733$	32.3446	1.19467	0.597337	−	0.801990i	$-0.296226\pi$
$733$	32.3446	1.19467	0.597337	+	0.801990i	$0.296226\pi$
$734$	6.95130	0.256577
$735$	6.01870	0.222003
$736$	24.4597	0.901596
$737$	44.3896	1.63511
$738$	−20.8615	−0.767921
$739$	2.72940	0.100403	0.0502013	−	0.998739i	$-0.484014\pi$
$739$	2.72940	0.100403	0.0502013	+	0.998739i	$0.484014\pi$
$740$	−12.0798	−0.444061
$741$	5.96873	0.219267
$742$	−4.82061	−0.176970
$743$	−8.76960	−0.321726	−0.160863	−	0.986977i	$-0.551428\pi$
$743$	−8.76960	−0.321726	−0.160863	+	0.986977i	$0.551428\pi$
$744$	16.4563	0.603318
$745$	4.60588	0.168746
$746$	44.7682	1.63908
$747$	11.4413	0.418615
$748$	−50.5269	−1.84745
$749$	10.5626	0.385951
$750$	−18.4167	−0.672483
$751$	−30.0530	−1.09665	−0.548325	−	0.836265i	$-0.684734\pi$
$751$	−30.0530	−1.09665	−0.548325	+	0.836265i	$0.684734\pi$
$752$	11.6830	0.426036
$753$	−17.0523	−0.621421
$754$	8.80888	0.320800
$755$	1.98654	0.0722975
$756$	−1.74226	−0.0633653
$757$	22.5823	0.820768	0.410384	−	0.911913i	$-0.365395\pi$
$757$	22.5823	0.820768	0.410384	+	0.911913i	$0.365395\pi$
$758$	31.3675	1.13932
$759$	12.5260	0.454666
$760$	8.81002	0.319573
$761$	−18.0150	−0.653043	−0.326521	−	0.945190i	$-0.605876\pi$
$761$	−18.0150	−0.653043	−0.326521	+	0.945190i	$0.605876\pi$
$762$	18.3080	0.663231
$763$	3.75473	0.135930
$764$	−9.72218	−0.351736
$765$	4.36745	0.157905
$766$	−33.5356	−1.21169
$767$	12.9998	0.469394
$768$	−5.97017	−0.215430
$769$	−11.0278	−0.397671	−0.198836	−	0.980033i	$-0.563716\pi$
$769$	−11.0278	−0.397671	−0.198836	+	0.980033i	$0.563716\pi$
$770$	−4.36361	−0.157254
$771$	−5.72754	−0.206272
$772$	13.9552	0.502260
$773$	−34.1093	−1.22683	−0.613414	−	0.789762i	$-0.710204\pi$
$773$	−34.1093	−1.22683	−0.613414	+	0.789762i	$0.710204\pi$
$774$	4.48737	0.161295
$775$	34.5621	1.24151
$776$	21.3818	0.767561
$777$	−2.76260	−0.0991078
$778$	76.0515	2.72658
$779$	46.0418	1.64962
$780$	−3.21118	−0.114979
$781$	−24.9025	−0.891082
$782$	36.9130	1.32001
$783$	−3.25721	−0.116403
$784$	9.25810	0.330647
$785$	−7.75173	−0.276671
$786$	−19.5002	−0.695550
$787$	6.82036	0.243120	0.121560	−	0.992584i	$-0.461210\pi$
$787$	6.82036	0.243120	0.121560	+	0.992584i	$0.461210\pi$
$788$	42.5092	1.51433
$789$	−4.86697	−0.173269
$790$	10.5697	0.376051
$791$	2.19864	0.0781746
$792$	−7.19782	−0.255763
$793$	−17.2296	−0.611841
$794$	42.2239	1.49847
$795$	3.28533	0.116519
$796$	24.6541	0.873842
$797$	−7.20817	−0.255326	−0.127663	−	0.991818i	$-0.540748\pi$
$797$	−7.20817	−0.255326	−0.127663	+	0.991818i	$0.540748\pi$
$798$	6.49816	0.230033
$799$	40.3583	1.42777
$800$	−29.5193	−1.04366
$801$	−3.30103	−0.116636
$802$	−76.0874	−2.68674
$803$	−29.1831	−1.02985
$804$	35.5638	1.25424
$805$	1.88639	0.0664864
$806$	22.3717	0.788009
$807$	−25.4835	−0.897062
$808$	37.2584	1.31075
$809$	−40.3795	−1.41967	−0.709834	−	0.704369i	$-0.751230\pi$
$809$	−40.3795	−1.41967	−0.709834	+	0.704369i	$0.751230\pi$
$810$	2.00660	0.0705047
$811$	−8.46340	−0.297190	−0.148595	−	0.988898i	$-0.547475\pi$
$811$	−8.46340	−0.297190	−0.148595	+	0.988898i	$0.547475\pi$
$812$	5.67489	0.199150
$813$	7.45632	0.261505
$814$	−36.8096	−1.29018
$815$	−2.03348	−0.0712298
$816$	6.71810	0.235181
$817$	−9.90374	−0.346488
$818$	43.6299	1.52548
$819$	−0.734385	−0.0256615
$820$	−24.7704	−0.865022
$821$	−29.8027	−1.04012	−0.520060	−	0.854130i	$-0.674091\pi$
$821$	−29.8027	−1.04012	−0.520060	+	0.854130i	$0.674091\pi$
$822$	−50.0901	−1.74709
$823$	1.44259	0.0502854	0.0251427	−	0.999684i	$-0.491996\pi$
$823$	1.44259	0.0502854	0.0251427	+	0.999684i	$0.491996\pi$
$824$	25.1479	0.876069
$825$	−15.1171	−0.526310
$826$	14.1529	0.492441
$827$	−18.8288	−0.654743	−0.327372	−	0.944896i	$-0.606163\pi$
$827$	−18.8288	−0.654743	−0.327372	+	0.944896i	$0.606163\pi$
$828$	10.0355	0.348759
$829$	−26.6587	−0.925896	−0.462948	−	0.886385i	$-0.653208\pi$
$829$	−26.6587	−0.925896	−0.462948	+	0.886385i	$0.653208\pi$
$830$	22.9581	0.796886
$831$	−4.08810	−0.141814
$832$	−15.6995	−0.544284
$833$	31.9816	1.10810
$834$	−10.3489	−0.358353
$835$	−10.2798	−0.355749
$836$	51.2345	1.77198
$837$	−8.27225	−0.285931
$838$	−42.2132	−1.45823
$839$	−25.5165	−0.880926	−0.440463	−	0.897771i	$-0.645186\pi$
$839$	−25.5165	−0.880926	−0.440463	+	0.897771i	$0.645186\pi$
$840$	−1.08397	−0.0374006
$841$	−18.3906	−0.634158
$842$	64.4557	2.22129
$843$	6.68982	0.230410
$844$	−50.2557	−1.72987
$845$	10.4322	0.358880
$846$	18.5424	0.637500
$847$	−1.25694	−0.0431891
$848$	5.05357	0.173540
$849$	−17.5779	−0.603271
$850$	−44.5485	−1.52800
$851$	15.9128	0.545484
$852$	−19.9512	−0.683518
$853$	28.8214	0.986824	0.493412	−	0.869796i	$-0.335749\pi$
$853$	28.8214	0.986824	0.493412	+	0.869796i	$0.335749\pi$
$854$	−18.7579	−0.641881
$855$	−4.42861	−0.151455
$856$	34.9613	1.19495
$857$	7.71856	0.263661	0.131831	−	0.991272i	$-0.457915\pi$
$857$	7.71856	0.263661	0.131831	+	0.991272i	$0.457915\pi$
$858$	−9.78514	−0.334059
$859$	1.19722	0.0408488	0.0204244	−	0.999791i	$-0.493498\pi$
$859$	1.19722	0.0408488	0.0204244	+	0.999791i	$0.493498\pi$
$860$	5.32821	0.181690
$861$	−5.66491	−0.193060
$862$	31.0881	1.05887
$863$	−6.76305	−0.230217	−0.115108	−	0.993353i	$-0.536722\pi$
$863$	−6.76305	−0.230217	−0.115108	+	0.993353i	$0.536722\pi$
$864$	7.06527	0.240365
$865$	−7.20407	−0.244946
$866$	−63.1956	−2.14748
$867$	6.20728	0.210810
$868$	14.4124	0.489188
$869$	19.0586	0.646520
$870$	−6.53591	−0.221588
$871$	14.9906	0.507938
$872$	12.4278	0.420858
$873$	−10.7482	−0.363771
$874$	−37.4299	−1.26609
$875$	−5.00105	−0.169066
$876$	−23.3807	−0.789962
$877$	−7.63148	−0.257697	−0.128848	−	0.991664i	$-0.541128\pi$
$877$	−7.63148	−0.257697	−0.128848	+	0.991664i	$0.541128\pi$
$878$	−50.8761	−1.71699
$879$	−23.4512	−0.790989
$880$	4.57448	0.154206
$881$	17.9641	0.605226	0.302613	−	0.953113i	$-0.402141\pi$
$881$	17.9641	0.605226	0.302613	+	0.953113i	$0.402141\pi$
$882$	14.6937	0.494764
$883$	3.85695	0.129797	0.0648983	−	0.997892i	$-0.479328\pi$
$883$	3.85695	0.129797	0.0648983	+	0.997892i	$0.479328\pi$
$884$	−17.0632	−0.573898
$885$	−9.64542	−0.324227
$886$	−21.2201	−0.712902
$887$	50.1914	1.68526	0.842631	−	0.538491i	$-0.181005\pi$
$887$	50.1914	1.68526	0.842631	+	0.538491i	$0.181005\pi$
$888$	−9.14395	−0.306851
$889$	4.97154	0.166740
$890$	−6.62383	−0.222031
$891$	3.61819	0.121214
$892$	60.8050	2.03590
$893$	−40.9235	−1.36945
$894$	11.2445	0.376074
$895$	−16.7527	−0.559983
$896$	−8.59927	−0.287281
$897$	4.23011	0.141239
$898$	46.7328	1.55949
$899$	26.9444	0.898647
$900$	−12.1114	−0.403714
$901$	17.4572	0.581585
$902$	−75.4808	−2.51324
$903$	1.21854	0.0405506
$904$	7.27729	0.242039
$905$	3.94466	0.131125
$906$	4.84982	0.161125
$907$	−16.4822	−0.547283	−0.273641	−	0.961832i	$-0.588228\pi$
$907$	−16.4822	−0.547283	−0.273641	+	0.961832i	$0.588228\pi$
$908$	−17.3118	−0.574511
$909$	−18.7291	−0.621203
$910$	−1.47362	−0.0488499
$911$	4.12044	0.136516	0.0682582	−	0.997668i	$-0.478256\pi$
$911$	4.12044	0.136516	0.0682582	+	0.997668i	$0.478256\pi$
$912$	−6.81219	−0.225574
$913$	41.3968	1.37003
$914$	43.6083	1.44243
$915$	12.7838	0.422620
$916$	−28.4469	−0.939911
$917$	−5.29527	−0.174865
$918$	10.6625	0.351913
$919$	11.0257	0.363705	0.181852	−	0.983326i	$-0.441791\pi$
$919$	11.0257	0.363705	0.181852	+	0.983326i	$0.441791\pi$
$920$	6.24376	0.205851
$921$	16.2766	0.536332
$922$	1.57339	0.0518169
$923$	−8.40972	−0.276809
$924$	−6.30382	−0.207381
$925$	−19.2044	−0.631437
$926$	80.6371	2.64990
$927$	−12.6413	−0.415196
$928$	−23.0131	−0.755441
$929$	17.0842	0.560516	0.280258	−	0.959925i	$-0.409580\pi$
$929$	17.0842	0.560516	0.280258	+	0.959925i	$0.409580\pi$
$930$	−16.5991	−0.544305
$931$	−32.4295	−1.06283
$932$	−71.6353	−2.34649
$933$	4.28800	0.140383
$934$	−77.3437	−2.53076
$935$	15.8023	0.516790
$936$	−2.43074	−0.0794513
$937$	−38.2371	−1.24915	−0.624575	−	0.780965i	$-0.714728\pi$
$937$	−38.2371	−1.24915	−0.624575	+	0.780965i	$0.714728\pi$
$938$	16.3203	0.532876
$939$	10.8317	0.353480
$940$	22.0168	0.718110
$941$	27.5672	0.898665	0.449332	−	0.893365i	$-0.351662\pi$
$941$	27.5672	0.898665	0.449332	+	0.893365i	$0.351662\pi$
$942$	−18.9246	−0.616598
$943$	32.6303	1.06259
$944$	−14.8368	−0.482897
$945$	0.544890	0.0177253
$946$	16.2362	0.527884
$947$	−10.9362	−0.355378	−0.177689	−	0.984087i	$-0.556862\pi$
$947$	−10.9362	−0.355378	−0.177689	+	0.984087i	$0.556862\pi$
$948$	15.2693	0.495923
$949$	−9.85530	−0.319917
$950$	45.1724	1.46559
$951$	14.9430	0.484561
$952$	−5.75990	−0.186679
$953$	−46.7681	−1.51497	−0.757484	−	0.652854i	$-0.773572\pi$
$953$	−46.7681	−1.51497	−0.757484	+	0.652854i	$0.773572\pi$
$954$	8.02063	0.259677
$955$	3.04061	0.0983919
$956$	39.9546	1.29223
$957$	−11.7852	−0.380962
$958$	−6.47345	−0.209148
$959$	−13.6019	−0.439229
$960$	11.6486	0.375956
$961$	37.4301	1.20742
$962$	−12.4308	−0.400786
$963$	−17.5743	−0.566325
$964$	−66.3709	−2.13766
$965$	−4.36450	−0.140498
$966$	4.60533	0.148174
$967$	21.5630	0.693419	0.346709	−	0.937973i	$-0.387299\pi$
$967$	21.5630	0.693419	0.346709	+	0.937973i	$0.387299\pi$
$968$	−4.16036	−0.133719
$969$	−23.5323	−0.755966
$970$	−21.5673	−0.692483
$971$	−37.5445	−1.20486	−0.602430	−	0.798171i	$-0.705801\pi$
$971$	−37.5445	−1.20486	−0.602430	+	0.798171i	$0.705801\pi$
$972$	2.89880	0.0929791
$973$	−2.81023	−0.0900920
$974$	7.91455	0.253599
$975$	−5.10513	−0.163495
$976$	19.6643	0.629440
$977$	−15.7619	−0.504269	−0.252135	−	0.967692i	$-0.581133\pi$
$977$	−15.7619	−0.504269	−0.252135	+	0.967692i	$0.581133\pi$
$978$	−4.96443	−0.158745
$979$	−11.9438	−0.381724
$980$	17.4470	0.557325
$981$	−6.24719	−0.199457
$982$	−78.5669	−2.50717
$983$	−48.6538	−1.55181	−0.775907	−	0.630847i	$-0.782708\pi$
$983$	−48.6538	−1.55181	−0.775907	+	0.630847i	$0.782708\pi$
$984$	−18.7503	−0.597738
$985$	−13.2948	−0.423606
$986$	−34.7298	−1.10602
$987$	5.03517	0.160271
$988$	17.3022	0.550456
$989$	−7.01890	−0.223188
$990$	7.26026	0.230746
$991$	−36.5769	−1.16190	−0.580952	−	0.813938i	$-0.697320\pi$
$991$	−36.5769	−1.16190	−0.580952	+	0.813938i	$0.697320\pi$
$992$	−58.4457	−1.85565
$993$	11.2968	0.358492
$994$	−9.15567	−0.290400
$995$	−7.71057	−0.244442
$996$	33.1660	1.05091
$997$	10.6477	0.337215	0.168608	−	0.985683i	$-0.446073\pi$
$997$	10.6477	0.337215	0.168608	+	0.985683i	$0.446073\pi$
$998$	31.6177	1.00084
$999$	4.59647	0.145426

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.a.1.13	✓	95

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.a.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-2.21332 q^{2} +1.00000 q^{3} +2.89880 q^{4} -0.906600 q^{5} -2.21332 q^{6} -0.601026 q^{7} -1.98934 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.21332 q^{2} +1.00000 q^{3} +2.89880 q^{4} -0.906600 q^{5} -2.21332 q^{6} -0.601026 q^{7} -1.98934 q^{8} +1.00000 q^{9} +2.00660 q^{10} +3.61819 q^{11} +2.89880 q^{12} +1.22188 q^{13} +1.33027 q^{14} -0.906600 q^{15} -1.39455 q^{16} -4.81739 q^{17} -2.21332 q^{18} +4.88486 q^{19} -2.62805 q^{20} -0.601026 q^{21} -8.00823 q^{22} +3.46196 q^{23} -1.98934 q^{24} -4.17808 q^{25} -2.70443 q^{26} +1.00000 q^{27} -1.74226 q^{28} -3.25721 q^{29} +2.00660 q^{30} -8.27225 q^{31} +7.06527 q^{32} +3.61819 q^{33} +10.6625 q^{34} +0.544890 q^{35} +2.89880 q^{36} +4.59647 q^{37} -10.8118 q^{38} +1.22188 q^{39} +1.80353 q^{40} +9.42540 q^{41} +1.33027 q^{42} -2.02744 q^{43} +10.4884 q^{44} -0.906600 q^{45} -7.66244 q^{46} -8.37762 q^{47} -1.39455 q^{48} -6.63877 q^{49} +9.24744 q^{50} -4.81739 q^{51} +3.54200 q^{52} -3.62379 q^{53} -2.21332 q^{54} -3.28025 q^{55} +1.19565 q^{56} +4.88486 q^{57} +7.20926 q^{58} +10.6391 q^{59} -2.62805 q^{60} -14.1008 q^{61} +18.3092 q^{62} -0.601026 q^{63} -12.8486 q^{64} -1.10776 q^{65} -8.00823 q^{66} +12.2684 q^{67} -13.9647 q^{68} +3.46196 q^{69} -1.20602 q^{70} -6.88258 q^{71} -1.98934 q^{72} -8.06566 q^{73} -10.1735 q^{74} -4.17808 q^{75} +14.1602 q^{76} -2.17463 q^{77} -2.70443 q^{78} +5.26745 q^{79} +1.26430 q^{80} +1.00000 q^{81} -20.8615 q^{82} +11.4413 q^{83} -1.74226 q^{84} +4.36745 q^{85} +4.48737 q^{86} -3.25721 q^{87} -7.19782 q^{88} -3.30103 q^{89} +2.00660 q^{90} -0.734385 q^{91} +10.0355 q^{92} -8.27225 q^{93} +18.5424 q^{94} -4.42861 q^{95} +7.06527 q^{96} -10.7482 q^{97} +14.6937 q^{98} +3.61819 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 95 q - 9 q^{2} + 95 q^{3} + 65 q^{4} - 15 q^{5} - 9 q^{6} - 36 q^{7} - 27 q^{8} + 95 q^{9}+O(q^{10}) \) 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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