LMFDB - Embedded newform 6005.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, 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("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$1$
Dimension:	$88$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70073 q^{2} -2.65354 q^{3} +5.29393 q^{4} +1.00000 q^{5} +7.16648 q^{6} -4.13839 q^{7} -8.89601 q^{8} +4.04126 q^{9} +O(q^{10})$	\(q-2.70073 q^{2} -2.65354 q^{3} +5.29393 q^{4} +1.00000 q^{5} +7.16648 q^{6} -4.13839 q^{7} -8.89601 q^{8} +4.04126 q^{9} -2.70073 q^{10} +2.42320 q^{11} -14.0476 q^{12} +0.338091 q^{13} +11.1767 q^{14} -2.65354 q^{15} +13.4378 q^{16} +2.08464 q^{17} -10.9144 q^{18} -0.244072 q^{19} +5.29393 q^{20} +10.9814 q^{21} -6.54441 q^{22} -0.722117 q^{23} +23.6059 q^{24} +1.00000 q^{25} -0.913093 q^{26} -2.76303 q^{27} -21.9083 q^{28} -3.58302 q^{29} +7.16648 q^{30} -3.98088 q^{31} -18.4999 q^{32} -6.43006 q^{33} -5.63006 q^{34} -4.13839 q^{35} +21.3942 q^{36} -0.583149 q^{37} +0.659172 q^{38} -0.897138 q^{39} -8.89601 q^{40} -8.61041 q^{41} -29.6577 q^{42} +7.24639 q^{43} +12.8283 q^{44} +4.04126 q^{45} +1.95024 q^{46} +6.16658 q^{47} -35.6578 q^{48} +10.1262 q^{49} -2.70073 q^{50} -5.53168 q^{51} +1.78983 q^{52} -2.30580 q^{53} +7.46220 q^{54} +2.42320 q^{55} +36.8151 q^{56} +0.647654 q^{57} +9.67676 q^{58} -5.87759 q^{59} -14.0476 q^{60} +5.81180 q^{61} +10.7513 q^{62} -16.7243 q^{63} +23.0876 q^{64} +0.338091 q^{65} +17.3658 q^{66} -4.62811 q^{67} +11.0360 q^{68} +1.91616 q^{69} +11.1767 q^{70} +2.22998 q^{71} -35.9511 q^{72} +9.63834 q^{73} +1.57493 q^{74} -2.65354 q^{75} -1.29210 q^{76} -10.0281 q^{77} +2.42293 q^{78} -3.57066 q^{79} +13.4378 q^{80} -4.79198 q^{81} +23.2544 q^{82} -12.1067 q^{83} +58.1346 q^{84} +2.08464 q^{85} -19.5705 q^{86} +9.50768 q^{87} -21.5568 q^{88} +6.55838 q^{89} -10.9144 q^{90} -1.39915 q^{91} -3.82284 q^{92} +10.5634 q^{93} -16.6543 q^{94} -0.244072 q^{95} +49.0903 q^{96} -3.77646 q^{97} -27.3482 q^{98} +9.79280 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9}+O(q^{10}) $ 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9} - 14 q^{10} - 26 q^{11} - 64 q^{12} - 31 q^{13} - 17 q^{14} - 34 q^{15} + 34 q^{16} - 31 q^{17} - 42 q^{18} - 56 q^{19} + 66 q^{20} - q^{21} - 49 q^{22} - 74 q^{23} - 3 q^{24} + 88 q^{25} - q^{26} - 130 q^{27} - 57 q^{28} - 6 q^{29} - q^{30} - 37 q^{31} - 87 q^{32} - 43 q^{33} - 35 q^{34} - 35 q^{35} + 53 q^{36} - 67 q^{37} - 40 q^{38} - 21 q^{39} - 39 q^{40} + 2 q^{41} - 15 q^{42} - 136 q^{43} - 15 q^{44} + 72 q^{45} - 16 q^{46} - 139 q^{47} - 71 q^{48} + 41 q^{49} - 14 q^{50} - 71 q^{51} - 71 q^{52} - 75 q^{53} + 26 q^{54} - 26 q^{55} - 22 q^{56} - 34 q^{57} - 65 q^{58} - 41 q^{59} - 64 q^{60} - 11 q^{61} - 30 q^{62} - 114 q^{63} - 33 q^{64} - 31 q^{65} + 24 q^{66} - 209 q^{67} - 42 q^{68} - 22 q^{69} - 17 q^{70} - 43 q^{71} - 80 q^{72} - 50 q^{73} + 9 q^{74} - 34 q^{75} - 62 q^{76} - 49 q^{77} - 19 q^{78} - 77 q^{79} + 34 q^{80} + 72 q^{81} - 107 q^{82} - 113 q^{83} + 19 q^{84} - 31 q^{85} + 14 q^{86} - 87 q^{87} - 107 q^{88} - 5 q^{89} - 42 q^{90} - 159 q^{91} - 100 q^{92} - 82 q^{93} - 31 q^{94} - 56 q^{95} + 58 q^{96} - 105 q^{97} - 29 q^{98} - 68 q^{99}+O(q^{100}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9 - 14 * q^10 - 26 * q^11 - 64 * q^12 - 31 * q^13 - 17 * q^14 - 34 * q^15 + 34 * q^16 - 31 * q^17 - 42 * q^18 - 56 * q^19 + 66 * q^20 - q^21 - 49 * q^22 - 74 * q^23 - 3 * q^24 + 88 * q^25 - q^26 - 130 * q^27 - 57 * q^28 - 6 * q^29 - q^30 - 37 * q^31 - 87 * q^32 - 43 * q^33 - 35 * q^34 - 35 * q^35 + 53 * q^36 - 67 * q^37 - 40 * q^38 - 21 * q^39 - 39 * q^40 + 2 * q^41 - 15 * q^42 - 136 * q^43 - 15 * q^44 + 72 * q^45 - 16 * q^46 - 139 * q^47 - 71 * q^48 + 41 * q^49 - 14 * q^50 - 71 * q^51 - 71 * q^52 - 75 * q^53 + 26 * q^54 - 26 * q^55 - 22 * q^56 - 34 * q^57 - 65 * q^58 - 41 * q^59 - 64 * q^60 - 11 * q^61 - 30 * q^62 - 114 * q^63 - 33 * q^64 - 31 * q^65 + 24 * q^66 - 209 * q^67 - 42 * q^68 - 22 * q^69 - 17 * q^70 - 43 * q^71 - 80 * q^72 - 50 * q^73 + 9 * q^74 - 34 * q^75 - 62 * q^76 - 49 * q^77 - 19 * q^78 - 77 * q^79 + 34 * q^80 + 72 * q^81 - 107 * q^82 - 113 * q^83 + 19 * q^84 - 31 * q^85 + 14 * q^86 - 87 * q^87 - 107 * q^88 - 5 * q^89 - 42 * q^90 - 159 * q^91 - 100 * q^92 - 82 * q^93 - 31 * q^94 - 56 * q^95 + 58 * q^96 - 105 * q^97 - 29 * q^98 - 68 * 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 $

$2$	−2.70073	−1.90970	−0.954851	−	0.297084i	$-0.903986\pi$
$2$	−2.70073	−1.90970	−0.954851	+	0.297084i	$0.903986\pi$
$3$	−2.65354	−1.53202	−0.766010	−	0.642828i	$-0.777761\pi$
$3$	−2.65354	−1.53202	−0.766010	+	0.642828i	$0.777761\pi$
$4$	5.29393	2.64697
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	7.16648	2.92570
$7$	−4.13839	−1.56416	−0.782081	−	0.623176i	$-0.785842\pi$
$7$	−4.13839	−1.56416	−0.782081	+	0.623176i	$0.785842\pi$
$8$	−8.89601	−3.14521
$9$	4.04126	1.34709
$10$	−2.70073	−0.854045
$11$	2.42320	0.730623	0.365311	−	0.930885i	$-0.380963\pi$
$11$	2.42320	0.730623	0.365311	+	0.930885i	$0.380963\pi$
$12$	−14.0476	−4.05521
$13$	0.338091	0.0937697	0.0468848	−	0.998900i	$-0.485071\pi$
$13$	0.338091	0.0937697	0.0468848	+	0.998900i	$0.485071\pi$
$14$	11.1767	2.98709
$15$	−2.65354	−0.685141
$16$	13.4378	3.35946
$17$	2.08464	0.505601	0.252800	−	0.967518i	$-0.418648\pi$
$17$	2.08464	0.505601	0.252800	+	0.967518i	$0.418648\pi$
$18$	−10.9144	−2.57254
$19$	−0.244072	−0.0559940	−0.0279970	−	0.999608i	$-0.508913\pi$
$19$	−0.244072	−0.0559940	−0.0279970	+	0.999608i	$0.508913\pi$
$20$	5.29393	1.18376
$21$	10.9814	2.39633
$22$	−6.54441	−1.39527
$23$	−0.722117	−0.150572	−0.0752859	−	0.997162i	$-0.523987\pi$
$23$	−0.722117	−0.150572	−0.0752859	+	0.997162i	$0.523987\pi$
$24$	23.6059	4.81853
$25$	1.00000	0.200000
$26$	−0.913093	−0.179072
$27$	−2.76303	−0.531746
$28$	−21.9083	−4.14029
$29$	−3.58302	−0.665350	−0.332675	−	0.943042i	$-0.607951\pi$
$29$	−3.58302	−0.665350	−0.332675	+	0.943042i	$0.607951\pi$
$30$	7.16648	1.30841
$31$	−3.98088	−0.714988	−0.357494	−	0.933916i	$-0.616369\pi$
$31$	−3.98088	−0.714988	−0.357494	+	0.933916i	$0.616369\pi$
$32$	−18.4999	−3.27036
$33$	−6.43006	−1.11933
$34$	−5.63006	−0.965547
$35$	−4.13839	−0.699515
$36$	21.3942	3.56569
$37$	−0.583149	−0.0958690	−0.0479345	−	0.998850i	$-0.515264\pi$
$37$	−0.583149	−0.0958690	−0.0479345	+	0.998850i	$0.515264\pi$
$38$	0.659172	0.106932
$39$	−0.897138	−0.143657
$40$	−8.89601	−1.40658
$41$	−8.61041	−1.34472	−0.672360	−	0.740224i	$-0.734719\pi$
$41$	−8.61041	−1.34472	−0.672360	+	0.740224i	$0.734719\pi$
$42$	−29.6577	−4.57628
$43$	7.24639	1.10506	0.552532	−	0.833492i	$-0.313662\pi$
$43$	7.24639	1.10506	0.552532	+	0.833492i	$0.313662\pi$
$44$	12.8283	1.93393
$45$	4.04126	0.602436
$46$	1.95024	0.287547
$47$	6.16658	0.899488	0.449744	−	0.893157i	$-0.351515\pi$
$47$	6.16658	0.899488	0.449744	+	0.893157i	$0.351515\pi$
$48$	−35.6578	−5.14676
$49$	10.1262	1.44661
$50$	−2.70073	−0.381941
$51$	−5.53168	−0.774591
$52$	1.78983	0.248205
$53$	−2.30580	−0.316726	−0.158363	−	0.987381i	$-0.550622\pi$
$53$	−2.30580	−0.316726	−0.158363	+	0.987381i	$0.550622\pi$
$54$	7.46220	1.01548
$55$	2.42320	0.326744
$56$	36.8151	4.91963
$57$	0.647654	0.0857839
$58$	9.67676	1.27062
$59$	−5.87759	−0.765197	−0.382598	−	0.923915i	$-0.624971\pi$
$59$	−5.87759	−0.765197	−0.382598	+	0.923915i	$0.624971\pi$
$60$	−14.0476	−1.81354
$61$	5.81180	0.744125	0.372063	−	0.928208i	$-0.378651\pi$
$61$	5.81180	0.744125	0.372063	+	0.928208i	$0.378651\pi$
$62$	10.7513	1.36541
$63$	−16.7243	−2.10706
$64$	23.0876	2.88595
$65$	0.338091	0.0419351
$66$	17.3658	2.13759
$67$	−4.62811	−0.565414	−0.282707	−	0.959206i	$-0.591232\pi$
$67$	−4.62811	−0.565414	−0.282707	+	0.959206i	$0.591232\pi$
$68$	11.0360	1.33831
$69$	1.91616	0.230679
$70$	11.1767	1.33587
$71$	2.22998	0.264649	0.132325	−	0.991206i	$-0.457756\pi$
$71$	2.22998	0.264649	0.132325	+	0.991206i	$0.457756\pi$
$72$	−35.9511	−4.23688
$73$	9.63834	1.12808	0.564041	−	0.825747i	$-0.309246\pi$
$73$	9.63834	1.12808	0.564041	+	0.825747i	$0.309246\pi$
$74$	1.57493	0.183081
$75$	−2.65354	−0.306404
$76$	−1.29210	−0.148214
$77$	−10.0281	−1.14281
$78$	2.42293	0.274342
$79$	−3.57066	−0.401730	−0.200865	−	0.979619i	$-0.564375\pi$
$79$	−3.57066	−0.401730	−0.200865	+	0.979619i	$0.564375\pi$
$80$	13.4378	1.50240
$81$	−4.79198	−0.532442
$82$	23.2544	2.56802
$83$	−12.1067	−1.32888	−0.664440	−	0.747341i	$-0.731330\pi$
$83$	−12.1067	−1.32888	−0.664440	+	0.747341i	$0.731330\pi$
$84$	58.1346	6.34300
$85$	2.08464	0.226111
$86$	−19.5705	−2.11034
$87$	9.50768	1.01933
$88$	−21.5568	−2.29797
$89$	6.55838	0.695186	0.347593	−	0.937645i	$-0.386999\pi$
$89$	6.55838	0.695186	0.347593	+	0.937645i	$0.386999\pi$
$90$	−10.9144	−1.15047
$91$	−1.39915	−0.146671
$92$	−3.82284	−0.398558
$93$	10.5634	1.09538
$94$	−16.6543	−1.71776
$95$	−0.244072	−0.0250413
$96$	49.0903	5.01025
$97$	−3.77646	−0.383442	−0.191721	−	0.981450i	$-0.561407\pi$
$97$	−3.77646	−0.383442	−0.191721	+	0.981450i	$0.561407\pi$
$98$	−27.3482	−2.76259
$99$	9.79280	0.984213
$100$	5.29393	0.529393
$101$	14.8526	1.47789	0.738945	−	0.673766i	$-0.235325\pi$
$101$	14.8526	1.47789	0.738945	+	0.673766i	$0.235325\pi$
$102$	14.9396	1.47924
$103$	−6.32104	−0.622830	−0.311415	−	0.950274i	$-0.600803\pi$
$103$	−6.32104	−0.622830	−0.311415	+	0.950274i	$0.600803\pi$
$104$	−3.00766	−0.294926
$105$	10.9814	1.07167
$106$	6.22733	0.604852
$107$	−9.57376	−0.925531	−0.462765	−	0.886481i	$-0.653143\pi$
$107$	−9.57376	−0.925531	−0.462765	+	0.886481i	$0.653143\pi$
$108$	−14.6273	−1.40751
$109$	3.06559	0.293630	0.146815	−	0.989164i	$-0.453098\pi$
$109$	3.06559	0.293630	0.146815	+	0.989164i	$0.453098\pi$
$110$	−6.54441	−0.623985
$111$	1.54741	0.146873
$112$	−55.6110	−5.25474
$113$	4.26903	0.401596	0.200798	−	0.979633i	$-0.435646\pi$
$113$	4.26903	0.401596	0.200798	+	0.979633i	$0.435646\pi$
$114$	−1.74914	−0.163822
$115$	−0.722117	−0.0673378
$116$	−18.9683	−1.76116
$117$	1.36632	0.126316
$118$	15.8738	1.46130
$119$	−8.62706	−0.790842
$120$	23.6059	2.15491
$121$	−5.12809	−0.466190
$122$	−15.6961	−1.42106
$123$	22.8480	2.06014
$124$	−21.0745	−1.89255
$125$	1.00000	0.0894427
$126$	45.1678	4.02387
$127$	−3.95276	−0.350750	−0.175375	−	0.984502i	$-0.556114\pi$
$127$	−3.95276	−0.350750	−0.175375	+	0.984502i	$0.556114\pi$
$128$	−25.3534	−2.24095
$129$	−19.2286	−1.69298
$130$	−0.913093	−0.0800835
$131$	13.7359	1.20011	0.600055	−	0.799959i	$-0.295145\pi$
$131$	13.7359	1.20011	0.600055	+	0.799959i	$0.295145\pi$
$132$	−34.0403	−2.96283
$133$	1.01006	0.0875837
$134$	12.4993	1.07977
$135$	−2.76303	−0.237804
$136$	−18.5450	−1.59022
$137$	−0.275807	−0.0235638	−0.0117819	−	0.999931i	$-0.503750\pi$
$137$	−0.275807	−0.0235638	−0.0117819	+	0.999931i	$0.503750\pi$
$138$	−5.17504	−0.440529
$139$	−8.98672	−0.762243	−0.381122	−	0.924525i	$-0.624462\pi$
$139$	−8.98672	−0.762243	−0.381122	+	0.924525i	$0.624462\pi$
$140$	−21.9083	−1.85159
$141$	−16.3633	−1.37803
$142$	−6.02256	−0.505402
$143$	0.819264	0.0685103
$144$	54.3059	4.52549
$145$	−3.58302	−0.297554
$146$	−26.0305	−2.15430
$147$	−26.8704	−2.21623
$148$	−3.08715	−0.253762
$149$	14.6913	1.20356	0.601781	−	0.798661i	$-0.294458\pi$
$149$	14.6913	1.20356	0.601781	+	0.798661i	$0.294458\pi$
$150$	7.16648	0.585141
$151$	−13.5859	−1.10560	−0.552802	−	0.833313i	$-0.686441\pi$
$151$	−13.5859	−1.10560	−0.552802	+	0.833313i	$0.686441\pi$
$152$	2.17127	0.176113
$153$	8.42460	0.681088
$154$	27.0833	2.18243
$155$	−3.98088	−0.319752
$156$	−4.74939	−0.380255
$157$	−5.82357	−0.464772	−0.232386	−	0.972624i	$-0.574653\pi$
$157$	−5.82357	−0.464772	−0.232386	+	0.972624i	$0.574653\pi$
$158$	9.64337	0.767186
$159$	6.11852	0.485230
$160$	−18.4999	−1.46255
$161$	2.98840	0.235519
$162$	12.9418	1.01681
$163$	−12.7649	−0.999823	−0.499911	−	0.866077i	$-0.666634\pi$
$163$	−12.7649	−0.999823	−0.499911	+	0.866077i	$0.666634\pi$
$164$	−45.5829	−3.55943
$165$	−6.43006	−0.500579
$166$	32.6968	2.53777
$167$	16.3785	1.26741	0.633704	−	0.773576i	$-0.281534\pi$
$167$	16.3785	1.26741	0.633704	+	0.773576i	$0.281534\pi$
$168$	−97.6903	−7.53697
$169$	−12.8857	−0.991207
$170$	−5.63006	−0.431806
$171$	−0.986359	−0.0754288
$172$	38.3619	2.92507
$173$	−12.5783	−0.956311	−0.478155	−	0.878275i	$-0.658694\pi$
$173$	−12.5783	−0.956311	−0.478155	+	0.878275i	$0.658694\pi$
$174$	−25.6776	−1.94662
$175$	−4.13839	−0.312833
$176$	32.5626	2.45450
$177$	15.5964	1.17230
$178$	−17.7124	−1.32760
$179$	2.28581	0.170850	0.0854248	−	0.996345i	$-0.472775\pi$
$179$	2.28581	0.170850	0.0854248	+	0.996345i	$0.472775\pi$
$180$	21.3942	1.59463
$181$	4.46907	0.332183	0.166092	−	0.986110i	$-0.446885\pi$
$181$	4.46907	0.332183	0.166092	+	0.986110i	$0.446885\pi$
$182$	3.77873	0.280098
$183$	−15.4218	−1.14002
$184$	6.42396	0.473581
$185$	−0.583149	−0.0428739
$186$	−28.5289	−2.09184
$187$	5.05151	0.369403
$188$	32.6454	2.38091
$189$	11.4345	0.831737
$190$	0.659172	0.0478214
$191$	13.8104	0.999287	0.499644	−	0.866231i	$-0.333464\pi$
$191$	13.8104	0.999287	0.499644	+	0.866231i	$0.333464\pi$
$192$	−61.2638	−4.42133
$193$	20.4326	1.47077	0.735385	−	0.677650i	$-0.237002\pi$
$193$	20.4326	1.47077	0.735385	+	0.677650i	$0.237002\pi$
$194$	10.1992	0.732260
$195$	−0.897138	−0.0642454
$196$	53.6076	3.82912
$197$	26.0487	1.85589	0.927945	−	0.372717i	$-0.121574\pi$
$197$	26.0487	1.85589	0.927945	+	0.372717i	$0.121574\pi$
$198$	−26.4477	−1.87955
$199$	−13.8529	−0.982006	−0.491003	−	0.871158i	$-0.663370\pi$
$199$	−13.8529	−0.982006	−0.491003	+	0.871158i	$0.663370\pi$
$200$	−8.89601	−0.629043
$201$	12.2809	0.866226
$202$	−40.1128	−2.82233
$203$	14.8279	1.04072
$204$	−29.2843	−2.05031
$205$	−8.61041	−0.601377
$206$	17.0714	1.18942
$207$	−2.91827	−0.202833
$208$	4.54322	0.315015
$209$	−0.591436	−0.0409105
$210$	−29.6577	−2.04657
$211$	−8.29855	−0.571296	−0.285648	−	0.958335i	$-0.592209\pi$
$211$	−8.29855	−0.571296	−0.285648	+	0.958335i	$0.592209\pi$
$212$	−12.2067	−0.838362
$213$	−5.91733	−0.405449
$214$	25.8561	1.76749
$215$	7.24639	0.494200
$216$	24.5800	1.67245
$217$	16.4744	1.11836
$218$	−8.27931	−0.560746
$219$	−25.5757	−1.72825
$220$	12.8283	0.864881
$221$	0.704800	0.0474100
$222$	−4.17912	−0.280484
$223$	7.47748	0.500729	0.250365	−	0.968152i	$-0.419449\pi$
$223$	7.47748	0.500729	0.250365	+	0.968152i	$0.419449\pi$
$224$	76.5599	5.11537
$225$	4.04126	0.269418
$226$	−11.5295	−0.766930
$227$	21.0513	1.39723	0.698613	−	0.715499i	$-0.253801\pi$
$227$	21.0513	1.39723	0.698613	+	0.715499i	$0.253801\pi$
$228$	3.42864	0.227067
$229$	14.1858	0.937425	0.468712	−	0.883351i	$-0.344718\pi$
$229$	14.1858	0.937425	0.468712	+	0.883351i	$0.344718\pi$
$230$	1.95024	0.128595
$231$	26.6101	1.75081
$232$	31.8746	2.09267
$233$	20.5239	1.34456	0.672282	−	0.740295i	$-0.265314\pi$
$233$	20.5239	1.34456	0.672282	+	0.740295i	$0.265314\pi$
$234$	−3.69005	−0.241226
$235$	6.16658	0.402263
$236$	−31.1156	−2.02545
$237$	9.47488	0.615459
$238$	23.2994	1.51027
$239$	−6.77192	−0.438039	−0.219019	−	0.975720i	$-0.570286\pi$
$239$	−6.77192	−0.438039	−0.219019	+	0.975720i	$0.570286\pi$
$240$	−35.6578	−2.30170
$241$	24.7962	1.59726	0.798631	−	0.601821i	$-0.205558\pi$
$241$	24.7962	1.59726	0.798631	+	0.601821i	$0.205558\pi$
$242$	13.8496	0.890285
$243$	21.0048	1.34746
$244$	30.7673	1.96967
$245$	10.1262	0.646942
$246$	−61.7063	−3.93425
$247$	−0.0825186	−0.00525053
$248$	35.4140	2.24879
$249$	32.1255	2.03587
$250$	−2.70073	−0.170809
$251$	10.2568	0.647404	0.323702	−	0.946159i	$-0.395073\pi$
$251$	10.2568	0.647404	0.323702	+	0.946159i	$0.395073\pi$
$252$	−88.5373	−5.57733
$253$	−1.74984	−0.110011
$254$	10.6753	0.669829
$255$	−5.53168	−0.346407
$256$	22.2976	1.39360
$257$	−10.5872	−0.660409	−0.330204	−	0.943909i	$-0.607118\pi$
$257$	−10.5872	−0.660409	−0.330204	+	0.943909i	$0.607118\pi$
$258$	51.9311	3.23309
$259$	2.41329	0.149955
$260$	1.78983	0.111001
$261$	−14.4799	−0.896285
$262$	−37.0969	−2.29185
$263$	8.47700	0.522714	0.261357	−	0.965242i	$-0.415830\pi$
$263$	8.47700	0.522714	0.261357	+	0.965242i	$0.415830\pi$
$264$	57.2019	3.52053
$265$	−2.30580	−0.141644
$266$	−2.72791	−0.167259
$267$	−17.4029	−1.06504
$268$	−24.5009	−1.49663
$269$	−18.6464	−1.13689	−0.568447	−	0.822720i	$-0.692456\pi$
$269$	−18.6464	−1.13689	−0.568447	+	0.822720i	$0.692456\pi$
$270$	7.46220	0.454135
$271$	4.07528	0.247555	0.123778	−	0.992310i	$-0.460499\pi$
$271$	4.07528	0.247555	0.123778	+	0.992310i	$0.460499\pi$
$272$	28.0131	1.69854
$273$	3.71270	0.224703
$274$	0.744880	0.0449998
$275$	2.42320	0.146125
$276$	10.1440	0.610600
$277$	10.5180	0.631967	0.315984	−	0.948765i	$-0.397666\pi$
$277$	10.5180	0.631967	0.315984	+	0.948765i	$0.397666\pi$
$278$	24.2707	1.45566
$279$	−16.0878	−0.963151
$280$	36.8151	2.20012
$281$	19.3058	1.15169	0.575843	−	0.817560i	$-0.304674\pi$
$281$	19.3058	1.15169	0.575843	+	0.817560i	$0.304674\pi$
$282$	44.1927	2.63164
$283$	−11.7160	−0.696445	−0.348222	−	0.937412i	$-0.613215\pi$
$283$	−11.7160	−0.696445	−0.348222	+	0.937412i	$0.613215\pi$
$284$	11.8053	0.700518
$285$	0.647654	0.0383637
$286$	−2.21261	−0.130834
$287$	35.6332	2.10336
$288$	−74.7631	−4.40546
$289$	−12.6543	−0.744368
$290$	9.67676	0.568239
$291$	10.0210	0.587441
$292$	51.0247	2.98599
$293$	13.4051	0.783135	0.391567	−	0.920149i	$-0.371933\pi$
$293$	13.4051	0.783135	0.391567	+	0.920149i	$0.371933\pi$
$294$	72.5695	4.23234
$295$	−5.87759	−0.342206
$296$	5.18770	0.301529
$297$	−6.69538	−0.388506
$298$	−39.6773	−2.29845
$299$	−0.244142	−0.0141191
$300$	−14.0476	−0.811041
$301$	−29.9884	−1.72850
$302$	36.6918	2.11138
$303$	−39.4119	−2.26416
$304$	−3.27980	−0.188109
$305$	5.81180	0.332783
$306$	−22.7525	−1.30068
$307$	−8.83823	−0.504424	−0.252212	−	0.967672i	$-0.581158\pi$
$307$	−8.83823	−0.504424	−0.252212	+	0.967672i	$0.581158\pi$
$308$	−53.0883	−3.02499
$309$	16.7731	0.954189
$310$	10.7513	0.610632
$311$	−32.2401	−1.82817	−0.914084	−	0.405525i	$-0.867089\pi$
$311$	−32.2401	−1.82817	−0.914084	+	0.405525i	$0.867089\pi$
$312$	7.98095	0.451832
$313$	−2.46823	−0.139513	−0.0697563	−	0.997564i	$-0.522222\pi$
$313$	−2.46823	−0.139513	−0.0697563	+	0.997564i	$0.522222\pi$
$314$	15.7279	0.887576
$315$	−16.7243	−0.942308
$316$	−18.9028	−1.06337
$317$	14.1725	0.796005	0.398002	−	0.917384i	$-0.369704\pi$
$317$	14.1725	0.796005	0.398002	+	0.917384i	$0.369704\pi$
$318$	−16.5245	−0.926646
$319$	−8.68238	−0.486120
$320$	23.0876	1.29064
$321$	25.4043	1.41793
$322$	−8.07085	−0.449771
$323$	−0.508803	−0.0283106
$324$	−25.3684	−1.40936
$325$	0.338091	0.0187539
$326$	34.4745	1.90936
$327$	−8.13465	−0.449847
$328$	76.5983	4.22943
$329$	−25.5197	−1.40695
$330$	17.3658	0.955958
$331$	−18.7261	−1.02928	−0.514640	−	0.857406i	$-0.672075\pi$
$331$	−18.7261	−1.02928	−0.514640	+	0.857406i	$0.672075\pi$
$332$	−64.0919	−3.51750
$333$	−2.35666	−0.129144
$334$	−44.2339	−2.42037
$335$	−4.62811	−0.252861
$336$	147.566	8.05038
$337$	−3.66231	−0.199499	−0.0997494	−	0.995013i	$-0.531804\pi$
$337$	−3.66231	−0.199499	−0.0997494	+	0.995013i	$0.531804\pi$
$338$	34.8008	1.89291
$339$	−11.3280	−0.615254
$340$	11.0360	0.598509
$341$	−9.64648	−0.522386
$342$	2.66389	0.144047
$343$	−12.9376	−0.698564
$344$	−64.4640	−3.47566
$345$	1.91616	0.103163
$346$	33.9706	1.82627
$347$	21.2815	1.14245	0.571225	−	0.820794i	$-0.306468\pi$
$347$	21.2815	1.14245	0.571225	+	0.820794i	$0.306468\pi$
$348$	50.3330	2.69813
$349$	5.75221	0.307909	0.153954	−	0.988078i	$-0.450799\pi$
$349$	5.75221	0.307909	0.153954	+	0.988078i	$0.450799\pi$
$350$	11.1767	0.597417
$351$	−0.934157	−0.0498616
$352$	−44.8291	−2.38940
$353$	3.37050	0.179394	0.0896968	−	0.995969i	$-0.471410\pi$
$353$	3.37050	0.179394	0.0896968	+	0.995969i	$0.471410\pi$
$354$	−42.1216	−2.23874
$355$	2.22998	0.118355
$356$	34.7196	1.84013
$357$	22.8922	1.21159
$358$	−6.17336	−0.326272
$359$	8.34643	0.440507	0.220254	−	0.975443i	$-0.429311\pi$
$359$	8.34643	0.440507	0.220254	+	0.975443i	$0.429311\pi$
$360$	−35.9511	−1.89479
$361$	−18.9404	−0.996865
$362$	−12.0697	−0.634372
$363$	13.6076	0.714213
$364$	−7.40702	−0.388233
$365$	9.63834	0.504494
$366$	41.6502	2.17709
$367$	−18.5183	−0.966647	−0.483323	−	0.875442i	$-0.660570\pi$
$367$	−18.5183	−0.966647	−0.483323	+	0.875442i	$0.660570\pi$
$368$	−9.70369	−0.505840
$369$	−34.7969	−1.81146
$370$	1.57493	0.0818765
$371$	9.54228	0.495411
$372$	55.9220	2.89942
$373$	16.9535	0.877819	0.438910	−	0.898531i	$-0.355365\pi$
$373$	16.9535	0.877819	0.438910	+	0.898531i	$0.355365\pi$
$374$	−13.6428	−0.705451
$375$	−2.65354	−0.137028
$376$	−54.8580	−2.82908
$377$	−1.21139	−0.0623896
$378$	−30.8814	−1.58837
$379$	29.2295	1.50142	0.750711	−	0.660631i	$-0.229711\pi$
$379$	29.2295	1.50142	0.750711	+	0.660631i	$0.229711\pi$
$380$	−1.29210	−0.0662833
$381$	10.4888	0.537357
$382$	−37.2982	−1.90834
$383$	28.8901	1.47622	0.738108	−	0.674683i	$-0.235720\pi$
$383$	28.8901	1.47622	0.738108	+	0.674683i	$0.235720\pi$
$384$	67.2763	3.43318
$385$	−10.0281	−0.511082
$386$	−55.1828	−2.80873
$387$	29.2846	1.48862
$388$	−19.9923	−1.01496
$389$	8.54267	0.433130	0.216565	−	0.976268i	$-0.430515\pi$
$389$	8.54267	0.433130	0.216565	+	0.976268i	$0.430515\pi$
$390$	2.42293	0.122690
$391$	−1.50536	−0.0761292
$392$	−90.0831	−4.54989
$393$	−36.4487	−1.83859
$394$	−70.3503	−3.54420
$395$	−3.57066	−0.179659
$396$	51.8424	2.60518
$397$	−1.73812	−0.0872339	−0.0436170	−	0.999048i	$-0.513888\pi$
$397$	−1.73812	−0.0872339	−0.0436170	+	0.999048i	$0.513888\pi$
$398$	37.4129	1.87534
$399$	−2.68024	−0.134180
$400$	13.4378	0.671892
$401$	8.42194	0.420572	0.210286	−	0.977640i	$-0.432561\pi$
$401$	8.42194	0.420572	0.210286	+	0.977640i	$0.432561\pi$
$402$	−33.1673	−1.65423
$403$	−1.34590	−0.0670441
$404$	78.6286	3.91192
$405$	−4.79198	−0.238115
$406$	−40.0462	−1.98746
$407$	−1.41309	−0.0700441
$408$	49.2099	2.43625
$409$	−2.42547	−0.119932	−0.0599659	−	0.998200i	$-0.519099\pi$
$409$	−2.42547	−0.119932	−0.0599659	+	0.998200i	$0.519099\pi$
$410$	23.2544	1.14845
$411$	0.731864	0.0361002
$412$	−33.4631	−1.64861
$413$	24.3237	1.19689
$414$	7.88144	0.387352
$415$	−12.1067	−0.594294
$416$	−6.25467	−0.306660
$417$	23.8466	1.16777
$418$	1.59731	0.0781268
$419$	10.2527	0.500878	0.250439	−	0.968132i	$-0.419425\pi$
$419$	10.2527	0.500878	0.250439	+	0.968132i	$0.419425\pi$
$420$	58.1346	2.83668
$421$	−27.5403	−1.34223	−0.671115	−	0.741353i	$-0.734184\pi$
$421$	−27.5403	−1.34223	−0.671115	+	0.741353i	$0.734184\pi$
$422$	22.4121	1.09101
$423$	24.9208	1.21169
$424$	20.5124	0.996170
$425$	2.08464	0.101120
$426$	15.9811	0.774286
$427$	−24.0515	−1.16393
$428$	−50.6828	−2.44985
$429$	−2.17395	−0.104959
$430$	−19.5705	−0.943775
$431$	2.51314	0.121054	0.0605269	−	0.998167i	$-0.480722\pi$
$431$	2.51314	0.121054	0.0605269	+	0.998167i	$0.480722\pi$
$432$	−37.1292	−1.78638
$433$	−29.0296	−1.39507	−0.697536	−	0.716550i	$-0.745720\pi$
$433$	−29.0296	−1.39507	−0.697536	+	0.716550i	$0.745720\pi$
$434$	−44.4929	−2.13573
$435$	9.50768	0.455858
$436$	16.2290	0.777228
$437$	0.176249	0.00843111
$438$	69.0730	3.30044
$439$	−14.9347	−0.712796	−0.356398	−	0.934334i	$-0.615995\pi$
$439$	−14.9347	−0.712796	−0.356398	+	0.934334i	$0.615995\pi$
$440$	−21.5568	−1.02768
$441$	40.9228	1.94870
$442$	−1.90347	−0.0905390
$443$	−24.0148	−1.14098	−0.570490	−	0.821305i	$-0.693247\pi$
$443$	−24.0148	−1.14098	−0.570490	+	0.821305i	$0.693247\pi$
$444$	8.19186	0.388769
$445$	6.55838	0.310897
$446$	−20.1946	−0.956244
$447$	−38.9840	−1.84388
$448$	−95.5454	−4.51410
$449$	8.67803	0.409541	0.204771	−	0.978810i	$-0.434355\pi$
$449$	8.67803	0.409541	0.204771	+	0.978810i	$0.434355\pi$
$450$	−10.9144	−0.514507
$451$	−20.8648	−0.982483
$452$	22.5999	1.06301
$453$	36.0507	1.69381
$454$	−56.8540	−2.66829
$455$	−1.39915	−0.0655933
$456$	−5.76154	−0.269809
$457$	0.710095	0.0332168	0.0166084	−	0.999862i	$-0.494713\pi$
$457$	0.710095	0.0332168	0.0166084	+	0.999862i	$0.494713\pi$
$458$	−38.3120	−1.79020
$459$	−5.75994	−0.268851
$460$	−3.82284	−0.178241
$461$	−5.03235	−0.234380	−0.117190	−	0.993110i	$-0.537389\pi$
$461$	−5.03235	−0.234380	−0.117190	+	0.993110i	$0.537389\pi$
$462$	−71.8665	−3.34353
$463$	9.75999	0.453585	0.226793	−	0.973943i	$-0.427176\pi$
$463$	9.75999	0.453585	0.226793	+	0.973943i	$0.427176\pi$
$464$	−48.1480	−2.23522
$465$	10.5634	0.489867
$466$	−55.4294	−2.56772
$467$	−11.2836	−0.522144	−0.261072	−	0.965319i	$-0.584076\pi$
$467$	−11.2836	−0.522144	−0.261072	+	0.965319i	$0.584076\pi$
$468$	7.23318	0.334354
$469$	19.1529	0.884400
$470$	−16.6543	−0.768203
$471$	15.4531	0.712040
$472$	52.2871	2.40671
$473$	17.5595	0.807385
$474$	−25.5891	−1.17534
$475$	−0.244072	−0.0111988
$476$	−45.6711	−2.09333
$477$	−9.31834	−0.426657
$478$	18.2891	0.836524
$479$	−35.6376	−1.62832	−0.814162	−	0.580637i	$-0.802803\pi$
$479$	−35.6376	−1.62832	−0.814162	+	0.580637i	$0.802803\pi$
$480$	49.0903	2.24065
$481$	−0.197157	−0.00898961
$482$	−66.9677	−3.05030
$483$	−7.92983	−0.360820
$484$	−27.1478	−1.23399
$485$	−3.77646	−0.171480
$486$	−56.7282	−2.57325
$487$	−34.6321	−1.56933	−0.784665	−	0.619920i	$-0.787165\pi$
$487$	−34.6321	−1.56933	−0.784665	+	0.619920i	$0.787165\pi$
$488$	−51.7019	−2.34043
$489$	33.8721	1.53175
$490$	−27.3482	−1.23547
$491$	0.624045	0.0281627	0.0140814	−	0.999901i	$-0.495518\pi$
$491$	0.624045	0.0281627	0.0140814	+	0.999901i	$0.495518\pi$
$492$	120.956	5.45312
$493$	−7.46932	−0.336401
$494$	0.222860	0.0100270
$495$	9.79280	0.440153
$496$	−53.4945	−2.40197
$497$	−9.22850	−0.413955
$498$	−86.7623	−3.88791
$499$	16.4819	0.737830	0.368915	−	0.929463i	$-0.379729\pi$
$499$	16.4819	0.737830	0.368915	+	0.929463i	$0.379729\pi$
$500$	5.29393	0.236752
$501$	−43.4610	−1.94170
$502$	−27.7008	−1.23635
$503$	−38.2430	−1.70517	−0.852586	−	0.522587i	$-0.824967\pi$
$503$	−38.2430	−1.70517	−0.852586	+	0.522587i	$0.824967\pi$
$504$	148.780	6.62717
$505$	14.8526	0.660932
$506$	4.72583	0.210089
$507$	34.1927	1.51855
$508$	−20.9256	−0.928424
$509$	−0.173868	−0.00770656	−0.00385328	−	0.999993i	$-0.501227\pi$
$509$	−0.173868	−0.00770656	−0.00385328	+	0.999993i	$0.501227\pi$
$510$	14.9396	0.661535
$511$	−39.8872	−1.76450
$512$	−9.51278	−0.420409
$513$	0.674379	0.0297745
$514$	28.5930	1.26118
$515$	−6.32104	−0.278538
$516$	−101.795	−4.48126
$517$	14.9429	0.657187
$518$	−6.51765	−0.286369
$519$	33.3770	1.46509
$520$	−3.00766	−0.131895
$521$	2.03929	0.0893428	0.0446714	−	0.999002i	$-0.485776\pi$
$521$	2.03929	0.0893428	0.0446714	+	0.999002i	$0.485776\pi$
$522$	39.1063	1.71164
$523$	−28.0079	−1.22470	−0.612350	−	0.790587i	$-0.709776\pi$
$523$	−28.0079	−1.22470	−0.612350	+	0.790587i	$0.709776\pi$
$524$	72.7168	3.17665
$525$	10.9814	0.479266
$526$	−22.8941	−0.998229
$527$	−8.29872	−0.361498
$528$	−86.4061	−3.76034
$529$	−22.4785	−0.977328
$530$	6.22733	0.270498
$531$	−23.7529	−1.03079
$532$	5.34721	0.231831
$533$	−2.91110	−0.126094
$534$	47.0005	2.03391
$535$	−9.57376	−0.413910
$536$	41.1717	1.77835
$537$	−6.06549	−0.261745
$538$	50.3590	2.17113
$539$	24.5379	1.05692
$540$	−14.6273	−0.629459
$541$	29.9668	1.28837	0.644187	−	0.764868i	$-0.277196\pi$
$541$	29.9668	1.28837	0.644187	+	0.764868i	$0.277196\pi$
$542$	−11.0062	−0.472757
$543$	−11.8589	−0.508912
$544$	−38.5658	−1.65349
$545$	3.06559	0.131315
$546$	−10.0270	−0.429116
$547$	−44.8145	−1.91613	−0.958064	−	0.286553i	$-0.907491\pi$
$547$	−44.8145	−1.91613	−0.958064	+	0.286553i	$0.907491\pi$
$548$	−1.46010	−0.0623725
$549$	23.4870	1.00240
$550$	−6.54441	−0.279055
$551$	0.874515	0.0372556
$552$	−17.0462	−0.725535
$553$	14.7768	0.628372
$554$	−28.4063	−1.20687
$555$	1.54741	0.0656838
$556$	−47.5751	−2.01763
$557$	40.6179	1.72104	0.860518	−	0.509420i	$-0.170140\pi$
$557$	40.6179	1.72104	0.860518	+	0.509420i	$0.170140\pi$
$558$	43.4487	1.83933
$559$	2.44994	0.103621
$560$	−55.6110	−2.34999
$561$	−13.4044	−0.565934
$562$	−52.1396	−2.19938
$563$	43.0402	1.81393	0.906964	−	0.421207i	$-0.138394\pi$
$563$	43.0402	1.81393	0.906964	+	0.421207i	$0.138394\pi$
$564$	−86.6259	−3.64761
$565$	4.26903	0.179599
$566$	31.6418	1.33000
$567$	19.8311	0.832827
$568$	−19.8379	−0.832379
$569$	−17.8521	−0.748400	−0.374200	−	0.927348i	$-0.622083\pi$
$569$	−17.8521	−0.748400	−0.374200	+	0.927348i	$0.622083\pi$
$570$	−1.74914	−0.0732633
$571$	17.6452	0.738428	0.369214	−	0.929344i	$-0.379627\pi$
$571$	17.6452	0.738428	0.369214	+	0.929344i	$0.379627\pi$
$572$	4.33712	0.181344
$573$	−36.6465	−1.53093
$574$	−96.2355	−4.01679
$575$	−0.722117	−0.0301144
$576$	93.3030	3.88763
$577$	−15.8109	−0.658218	−0.329109	−	0.944292i	$-0.606748\pi$
$577$	−15.8109	−0.658218	−0.329109	+	0.944292i	$0.606748\pi$
$578$	34.1757	1.42152
$579$	−54.2186	−2.25325
$580$	−18.9683	−0.787614
$581$	50.1021	2.07859
$582$	−27.0640	−1.12184
$583$	−5.58741	−0.231407
$584$	−85.7428	−3.54806
$585$	1.36632	0.0564902
$586$	−36.2036	−1.49555
$587$	27.2892	1.12634	0.563172	−	0.826340i	$-0.309581\pi$
$587$	27.2892	1.12634	0.563172	+	0.826340i	$0.309581\pi$
$588$	−142.250	−5.86628
$589$	0.971622	0.0400350
$590$	15.8738	0.653513
$591$	−69.1211	−2.84326
$592$	−7.83626	−0.322068
$593$	−42.1273	−1.72996	−0.864981	−	0.501805i	$-0.832669\pi$
$593$	−42.1273	−1.72996	−0.864981	+	0.501805i	$0.832669\pi$
$594$	18.0824	0.741930
$595$	−8.62706	−0.353675
$596$	77.7750	3.18579
$597$	36.7592	1.50445
$598$	0.659360	0.0269632
$599$	−44.0344	−1.79920	−0.899599	−	0.436717i	$-0.856141\pi$
$599$	−44.0344	−1.79920	−0.899599	+	0.436717i	$0.856141\pi$
$600$	23.6059	0.963707
$601$	−1.06136	−0.0432936	−0.0216468	−	0.999766i	$-0.506891\pi$
$601$	−1.06136	−0.0432936	−0.0216468	+	0.999766i	$0.506891\pi$
$602$	80.9904	3.30092
$603$	−18.7034	−0.761662
$604$	−71.9228	−2.92650
$605$	−5.12809	−0.208487
$606$	106.441	4.32387
$607$	30.8345	1.25153	0.625767	−	0.780010i	$-0.284786\pi$
$607$	30.8345	1.25153	0.625767	+	0.780010i	$0.284786\pi$
$608$	4.51532	0.183120
$609$	−39.3464	−1.59440
$610$	−15.6961	−0.635517
$611$	2.08487	0.0843447
$612$	44.5992	1.80282
$613$	24.2762	0.980506	0.490253	−	0.871580i	$-0.336904\pi$
$613$	24.2762	0.980506	0.490253	+	0.871580i	$0.336904\pi$
$614$	23.8696	0.963300
$615$	22.8480	0.921322
$616$	89.2105	3.59439
$617$	19.4809	0.784270	0.392135	−	0.919908i	$-0.371737\pi$
$617$	19.4809	0.784270	0.392135	+	0.919908i	$0.371737\pi$
$618$	−45.2996	−1.82222
$619$	14.7356	0.592276	0.296138	−	0.955145i	$-0.404301\pi$
$619$	14.7356	0.592276	0.296138	+	0.955145i	$0.404301\pi$
$620$	−21.0745	−0.846373
$621$	1.99523	0.0800659
$622$	87.0717	3.49126
$623$	−27.1411	−1.08738
$624$	−12.0556	−0.482610
$625$	1.00000	0.0400000
$626$	6.66601	0.266427
$627$	1.56940	0.0626757
$628$	−30.8296	−1.23023
$629$	−1.21566	−0.0484714
$630$	45.1678	1.79953
$631$	0.229325	0.00912929	0.00456465	−	0.999990i	$-0.498547\pi$
$631$	0.229325	0.00912929	0.00456465	+	0.999990i	$0.498547\pi$
$632$	31.7646	1.26353
$633$	22.0205	0.875237
$634$	−38.2760	−1.52013
$635$	−3.95276	−0.156860
$636$	32.3910	1.28439
$637$	3.42359	0.135648
$638$	23.4487	0.928344
$639$	9.01192	0.356506
$640$	−25.3534	−1.00218
$641$	12.8806	0.508752	0.254376	−	0.967105i	$-0.418130\pi$
$641$	12.8806	0.508752	0.254376	+	0.967105i	$0.418130\pi$
$642$	−68.6102	−2.70783
$643$	−27.0154	−1.06538	−0.532691	−	0.846310i	$-0.678819\pi$
$643$	−27.0154	−1.06538	−0.532691	+	0.846310i	$0.678819\pi$
$644$	15.8204	0.623410
$645$	−19.2286	−0.757124
$646$	1.37414	0.0540648
$647$	−43.6806	−1.71726	−0.858631	−	0.512595i	$-0.828684\pi$
$647$	−43.6806	−1.71726	−0.858631	+	0.512595i	$0.828684\pi$
$648$	42.6295	1.67465
$649$	−14.2426	−0.559070
$650$	−0.913093	−0.0358144
$651$	−43.7155	−1.71335
$652$	−67.5764	−2.64650
$653$	−49.4475	−1.93503	−0.967515	−	0.252813i	$-0.918644\pi$
$653$	−49.4475	−1.93503	−0.967515	+	0.252813i	$0.918644\pi$
$654$	21.9695	0.859074
$655$	13.7359	0.536705
$656$	−115.705	−4.51753
$657$	38.9511	1.51963
$658$	68.9217	2.68685
$659$	−15.7307	−0.612783	−0.306391	−	0.951906i	$-0.599122\pi$
$659$	−15.7307	−0.612783	−0.306391	+	0.951906i	$0.599122\pi$
$660$	−34.0403	−1.32502
$661$	24.3217	0.946006	0.473003	−	0.881061i	$-0.343170\pi$
$661$	24.3217	0.946006	0.473003	+	0.881061i	$0.343170\pi$
$662$	50.5741	1.96562
$663$	−1.87021	−0.0726331
$664$	107.701	4.17962
$665$	1.01006	0.0391686
$666$	6.36469	0.246627
$667$	2.58736	0.100183
$668$	86.7068	3.35478
$669$	−19.8418	−0.767128
$670$	12.4993	0.482889
$671$	14.0832	0.543675
$672$	−203.154	−7.83685
$673$	24.3069	0.936962	0.468481	−	0.883474i	$-0.344802\pi$
$673$	24.3069	0.936962	0.468481	+	0.883474i	$0.344802\pi$
$674$	9.89090	0.380983
$675$	−2.76303	−0.106349
$676$	−68.2160	−2.62369
$677$	−13.6113	−0.523126	−0.261563	−	0.965186i	$-0.584238\pi$
$677$	−13.6113	−0.523126	−0.261563	+	0.965186i	$0.584238\pi$
$678$	30.5939	1.17495
$679$	15.6285	0.599765
$680$	−18.5450	−0.711169
$681$	−55.8605	−2.14058
$682$	26.0525	0.997603
$683$	−34.0447	−1.30268	−0.651342	−	0.758785i	$-0.725793\pi$
$683$	−34.0447	−1.30268	−0.651342	+	0.758785i	$0.725793\pi$
$684$	−5.22172	−0.199657
$685$	−0.275807	−0.0105380
$686$	34.9409	1.33405
$687$	−37.6426	−1.43615
$688$	97.3758	3.71242
$689$	−0.779570	−0.0296993
$690$	−5.17504	−0.197010
$691$	15.3988	0.585799	0.292899	−	0.956143i	$-0.405380\pi$
$691$	15.3988	0.585799	0.292899	+	0.956143i	$0.405380\pi$
$692$	−66.5887	−2.53132
$693$	−40.5264	−1.53947
$694$	−57.4755	−2.18174
$695$	−8.98672	−0.340886
$696$	−84.5804	−3.20601
$697$	−17.9496	−0.679891
$698$	−15.5352	−0.588014
$699$	−54.4609	−2.05990
$700$	−21.9083	−0.828057
$701$	−28.8384	−1.08921	−0.544606	−	0.838692i	$-0.683321\pi$
$701$	−28.8384	−1.08921	−0.544606	+	0.838692i	$0.683321\pi$
$702$	2.52290	0.0952209
$703$	0.142330	0.00536809
$704$	55.9459	2.10854
$705$	−16.3633	−0.616276
$706$	−9.10281	−0.342589
$707$	−61.4658	−2.31166
$708$	82.5663	3.10303
$709$	−1.30103	−0.0488613	−0.0244307	−	0.999702i	$-0.507777\pi$
$709$	−1.30103	−0.0488613	−0.0244307	+	0.999702i	$0.507777\pi$
$710$	−6.02256	−0.226023
$711$	−14.4300	−0.541166
$712$	−58.3434	−2.18651
$713$	2.87466	0.107657
$714$	−61.8257	−2.31377
$715$	0.819264	0.0306387
$716$	12.1009	0.452233
$717$	17.9695	0.671085
$718$	−22.5414	−0.841238
$719$	8.76005	0.326695	0.163347	−	0.986569i	$-0.447771\pi$
$719$	8.76005	0.326695	0.163347	+	0.986569i	$0.447771\pi$
$720$	54.3059	2.02386
$721$	26.1589	0.974208
$722$	51.1529	1.90372
$723$	−65.7976	−2.44704
$724$	23.6590	0.879278
$725$	−3.58302	−0.133070
$726$	−36.7504	−1.36394
$727$	−18.4132	−0.682908	−0.341454	−	0.939899i	$-0.610919\pi$
$727$	−18.4132	−0.682908	−0.341454	+	0.939899i	$0.610919\pi$
$728$	12.4469	0.461312
$729$	−41.3611	−1.53189
$730$	−26.0305	−0.963433
$731$	15.1061	0.558721
$732$	−81.6422	−3.01758
$733$	−3.09501	−0.114317	−0.0571583	−	0.998365i	$-0.518204\pi$
$733$	−3.09501	−0.114317	−0.0571583	+	0.998365i	$0.518204\pi$
$734$	50.0129	1.84601
$735$	−26.8704	−0.991128
$736$	13.3591	0.492424
$737$	−11.2149	−0.413104
$738$	93.9770	3.45934
$739$	−38.8941	−1.43074	−0.715371	−	0.698745i	$-0.753742\pi$
$739$	−38.8941	−1.43074	−0.715371	+	0.698745i	$0.753742\pi$
$740$	−3.08715	−0.113486
$741$	0.218966	0.00804393
$742$	−25.7711	−0.946087
$743$	−50.6105	−1.85672	−0.928359	−	0.371684i	$-0.878781\pi$
$743$	−50.6105	−1.85672	−0.928359	+	0.371684i	$0.878781\pi$
$744$	−93.9723	−3.44519
$745$	14.6913	0.538249
$746$	−45.7868	−1.67637
$747$	−48.9263	−1.79012
$748$	26.7424	0.977798
$749$	39.6199	1.44768
$750$	7.16648	0.261683
$751$	−2.54850	−0.0929960	−0.0464980	−	0.998918i	$-0.514806\pi$
$751$	−2.54850	−0.0929960	−0.0464980	+	0.998918i	$0.514806\pi$
$752$	82.8655	3.02179
$753$	−27.2168	−0.991836
$754$	3.27163	0.119146
$755$	−13.5859	−0.494441
$756$	60.5334	2.20158
$757$	−37.6034	−1.36672	−0.683359	−	0.730082i	$-0.739482\pi$
$757$	−37.6034	−1.36672	−0.683359	+	0.730082i	$0.739482\pi$
$758$	−78.9411	−2.86727
$759$	4.64325	0.168539
$760$	2.17127	0.0787601
$761$	32.6360	1.18305	0.591526	−	0.806286i	$-0.298526\pi$
$761$	32.6360	1.18305	0.591526	+	0.806286i	$0.298526\pi$
$762$	−28.3274	−1.02619
$763$	−12.6866	−0.459285
$764$	73.1114	2.64508
$765$	8.42460	0.304592
$766$	−78.0243	−2.81913
$767$	−1.98716	−0.0717523
$768$	−59.1675	−2.13502
$769$	24.5621	0.885731	0.442866	−	0.896588i	$-0.353962\pi$
$769$	24.5621	0.885731	0.442866	+	0.896588i	$0.353962\pi$
$770$	27.0833	0.976014
$771$	28.0934	1.01176
$772$	108.169	3.89307
$773$	−41.8161	−1.50402	−0.752010	−	0.659152i	$-0.770915\pi$
$773$	−41.8161	−1.50402	−0.752010	+	0.659152i	$0.770915\pi$
$774$	−79.0896	−2.84282
$775$	−3.98088	−0.142998
$776$	33.5954	1.20601
$777$	−6.40377	−0.229734
$778$	−23.0714	−0.827151
$779$	2.10156	0.0752962
$780$	−4.74939	−0.170055
$781$	5.40368	0.193359
$782$	4.06556	0.145384
$783$	9.89999	0.353797
$784$	136.075	4.85981
$785$	−5.82357	−0.207852
$786$	98.4380	3.51117
$787$	−28.5285	−1.01693	−0.508466	−	0.861082i	$-0.669787\pi$
$787$	−28.5285	−1.01693	−0.508466	+	0.861082i	$0.669787\pi$
$788$	137.900	4.91248
$789$	−22.4940	−0.800809
$790$	9.64337	0.343096
$791$	−17.6669	−0.628162
$792$	−87.1168	−3.09556
$793$	1.96492	0.0697764
$794$	4.69420	0.166591
$795$	6.11852	0.217002
$796$	−73.3363	−2.59934
$797$	−31.4416	−1.11372	−0.556859	−	0.830607i	$-0.687994\pi$
$797$	−31.4416	−1.11372	−0.556859	+	0.830607i	$0.687994\pi$
$798$	7.23861	0.256244
$799$	12.8551	0.454782
$800$	−18.4999	−0.654071
$801$	26.5041	0.936477
$802$	−22.7454	−0.803167
$803$	23.3556	0.824203
$804$	65.0141	2.29287
$805$	2.98840	0.105327
$806$	3.63491	0.128034
$807$	49.4790	1.74174
$808$	−132.129	−4.64828
$809$	−17.6730	−0.621348	−0.310674	−	0.950516i	$-0.600555\pi$
$809$	−17.6730	−0.621348	−0.310674	+	0.950516i	$0.600555\pi$
$810$	12.9418	0.454730
$811$	28.8683	1.01370	0.506852	−	0.862033i	$-0.330809\pi$
$811$	28.8683	1.01370	0.506852	+	0.862033i	$0.330809\pi$
$812$	78.4980	2.75474
$813$	−10.8139	−0.379260
$814$	3.81636	0.133763
$815$	−12.7649	−0.447134
$816$	−74.3339	−2.60221
$817$	−1.76864	−0.0618769
$818$	6.55053	0.229034
$819$	−5.65434	−0.197579
$820$	−45.5829	−1.59182
$821$	−33.1403	−1.15660	−0.578302	−	0.815822i	$-0.696285\pi$
$821$	−33.1403	−1.15660	−0.578302	+	0.815822i	$0.696285\pi$
$822$	−1.97657	−0.0689407
$823$	28.4769	0.992643	0.496321	−	0.868139i	$-0.334684\pi$
$823$	28.4769	0.992643	0.496321	+	0.868139i	$0.334684\pi$
$824$	56.2320	1.95894
$825$	−6.43006	−0.223866
$826$	−65.6918	−2.28571
$827$	−25.1888	−0.875900	−0.437950	−	0.898999i	$-0.644295\pi$
$827$	−25.1888	−0.875900	−0.437950	+	0.898999i	$0.644295\pi$
$828$	−15.4491	−0.536893
$829$	0.427700	0.0148546	0.00742731	−	0.999972i	$-0.497636\pi$
$829$	0.427700	0.0148546	0.00742731	+	0.999972i	$0.497636\pi$
$830$	32.6968	1.13492
$831$	−27.9100	−0.968187
$832$	7.80572	0.270614
$833$	21.1096	0.731405
$834$	−64.4032	−2.23010
$835$	16.3785	0.566802
$836$	−3.13102	−0.108289
$837$	10.9993	0.380192
$838$	−27.6898	−0.956528
$839$	29.5626	1.02061	0.510307	−	0.859992i	$-0.329532\pi$
$839$	29.5626	1.02061	0.510307	+	0.859992i	$0.329532\pi$
$840$	−97.6903	−3.37064
$841$	−16.1620	−0.557310
$842$	74.3788	2.56326
$843$	−51.2286	−1.76441
$844$	−43.9320	−1.51220
$845$	−12.8857	−0.443281
$846$	−67.3042	−2.31397
$847$	21.2220	0.729198
$848$	−30.9849	−1.06403
$849$	31.0889	1.06697
$850$	−5.63006	−0.193109
$851$	0.421102	0.0144352
$852$	−31.3259	−1.07321
$853$	50.0005	1.71198	0.855992	−	0.516990i	$-0.172947\pi$
$853$	50.0005	1.71198	0.855992	+	0.516990i	$0.172947\pi$
$854$	64.9565	2.22277
$855$	−0.986359	−0.0337328
$856$	85.1683	2.91099
$857$	−23.6595	−0.808194	−0.404097	−	0.914716i	$-0.632414\pi$
$857$	−23.6595	−0.808194	−0.404097	+	0.914716i	$0.632414\pi$
$858$	5.87124	0.200441
$859$	−34.3358	−1.17152	−0.585762	−	0.810483i	$-0.699205\pi$
$859$	−34.3358	−1.17152	−0.585762	+	0.810483i	$0.699205\pi$
$860$	38.3619	1.30813
$861$	−94.5540	−3.22239
$862$	−6.78732	−0.231177
$863$	−5.74368	−0.195517	−0.0977586	−	0.995210i	$-0.531167\pi$
$863$	−5.74368	−0.195517	−0.0977586	+	0.995210i	$0.531167\pi$
$864$	51.1159	1.73900
$865$	−12.5783	−0.427675
$866$	78.4010	2.66417
$867$	33.5786	1.14039
$868$	87.2145	2.96025
$869$	−8.65242	−0.293513
$870$	−25.6776	−0.870554
$871$	−1.56472	−0.0530187
$872$	−27.2715	−0.923529
$873$	−15.2617	−0.516529
$874$	−0.475999	−0.0161009
$875$	−4.13839	−0.139903
$876$	−135.396	−4.57461
$877$	−23.4920	−0.793269	−0.396635	−	0.917977i	$-0.629822\pi$
$877$	−23.4920	−0.793269	−0.396635	+	0.917977i	$0.629822\pi$
$878$	40.3347	1.36123
$879$	−35.5710	−1.19978
$880$	32.5626	1.09769
$881$	26.5664	0.895045	0.447523	−	0.894273i	$-0.352306\pi$
$881$	26.5664	0.895045	0.447523	+	0.894273i	$0.352306\pi$
$882$	−110.521	−3.72145
$883$	−22.5811	−0.759914	−0.379957	−	0.925004i	$-0.624061\pi$
$883$	−22.5811	−0.759914	−0.379957	+	0.925004i	$0.624061\pi$
$884$	3.73116	0.125493
$885$	15.5964	0.524267
$886$	64.8575	2.17893
$887$	−8.30346	−0.278803	−0.139401	−	0.990236i	$-0.544518\pi$
$887$	−8.30346	−0.278803	−0.139401	+	0.990236i	$0.544518\pi$
$888$	−13.7657	−0.461948
$889$	16.3580	0.548631
$890$	−17.7124	−0.593721
$891$	−11.6119	−0.389015
$892$	39.5853	1.32541
$893$	−1.50509	−0.0503659
$894$	105.285	3.52127
$895$	2.28581	0.0764063
$896$	104.922	3.50521
$897$	0.647839	0.0216307
$898$	−23.4370	−0.782103
$899$	14.2636	0.475717
$900$	21.3942	0.713139
$901$	−4.80677	−0.160137
$902$	56.3500	1.87625
$903$	79.5752	2.64810
$904$	−37.9773	−1.26311
$905$	4.46907	0.148557
$906$	−97.3631	−3.23467
$907$	8.60944	0.285872	0.142936	−	0.989732i	$-0.454346\pi$
$907$	8.60944	0.285872	0.142936	+	0.989732i	$0.454346\pi$
$908$	111.444	3.69841
$909$	60.0233	1.99085
$910$	3.77873	0.125264
$911$	7.61852	0.252413	0.126206	−	0.992004i	$-0.459720\pi$
$911$	7.61852	0.252413	0.126206	+	0.992004i	$0.459720\pi$
$912$	8.70308	0.288188
$913$	−29.3369	−0.970911
$914$	−1.91777	−0.0634343
$915$	−15.4218	−0.509830
$916$	75.0987	2.48133
$917$	−56.8444	−1.87717
$918$	15.5560	0.513425
$919$	−6.83501	−0.225466	−0.112733	−	0.993625i	$-0.535960\pi$
$919$	−6.83501	−0.225466	−0.112733	+	0.993625i	$0.535960\pi$
$920$	6.42396	0.211792
$921$	23.4526	0.772788
$922$	13.5910	0.447596
$923$	0.753936	0.0248161
$924$	140.872	4.63434
$925$	−0.583149	−0.0191738
$926$	−26.3591	−0.866213
$927$	−25.5450	−0.839007
$928$	66.2856	2.17593
$929$	−60.3132	−1.97881	−0.989406	−	0.145177i	$-0.953625\pi$
$929$	−60.3132	−1.97881	−0.989406	+	0.145177i	$0.953625\pi$
$930$	−28.5289	−0.935500
$931$	−2.47153	−0.0810012
$932$	108.652	3.55902
$933$	85.5503	2.80079
$934$	30.4740	0.997139
$935$	5.05151	0.165202
$936$	−12.1548	−0.397291
$937$	−27.0810	−0.884699	−0.442349	−	0.896843i	$-0.645855\pi$
$937$	−27.0810	−0.884699	−0.442349	+	0.896843i	$0.645855\pi$
$938$	−51.7268	−1.68894
$939$	6.54954	0.213736
$940$	32.6454	1.06478
$941$	58.5281	1.90796	0.953981	−	0.299868i	$-0.0969425\pi$
$941$	58.5281	1.90796	0.953981	+	0.299868i	$0.0969425\pi$
$942$	−41.7345	−1.35978
$943$	6.21772	0.202477
$944$	−78.9821	−2.57065
$945$	11.4345	0.371964
$946$	−47.4233	−1.54187
$947$	−55.2043	−1.79390	−0.896950	−	0.442132i	$-0.854222\pi$
$947$	−55.2043	−1.79390	−0.896950	+	0.442132i	$0.854222\pi$
$948$	50.1593	1.62910
$949$	3.25864	0.105780
$950$	0.659172	0.0213864
$951$	−37.6072	−1.21950
$952$	76.7464	2.48737
$953$	58.3696	1.89078	0.945388	−	0.325946i	$-0.105683\pi$
$953$	58.3696	1.89078	0.945388	+	0.325946i	$0.105683\pi$
$954$	25.1663	0.814789
$955$	13.8104	0.446895
$956$	−35.8501	−1.15947
$957$	23.0390	0.744746
$958$	96.2475	3.10962
$959$	1.14140	0.0368576
$960$	−61.2638	−1.97728
$961$	−15.1526	−0.488793
$962$	0.532469	0.0171675
$963$	−38.6901	−1.24677
$964$	131.269	4.22790
$965$	20.4326	0.657748
$966$	21.4163	0.689059
$967$	−47.6892	−1.53358	−0.766791	−	0.641897i	$-0.778148\pi$
$967$	−47.6892	−1.53358	−0.766791	+	0.641897i	$0.778148\pi$
$968$	45.6196	1.46627
$969$	1.35013	0.0433724
$970$	10.1992	0.327476
$971$	40.4923	1.29946	0.649730	−	0.760165i	$-0.274882\pi$
$971$	40.4923	1.29946	0.649730	+	0.760165i	$0.274882\pi$
$972$	111.198	3.56668
$973$	37.1905	1.19227
$974$	93.5319	2.99695
$975$	−0.897138	−0.0287314
$976$	78.0981	2.49986
$977$	14.4327	0.461743	0.230871	−	0.972984i	$-0.425842\pi$
$977$	14.4327	0.461743	0.230871	+	0.972984i	$0.425842\pi$
$978$	−91.4793	−2.92519
$979$	15.8923	0.507919
$980$	53.6076	1.71243
$981$	12.3888	0.395545
$982$	−1.68537	−0.0537825
$983$	28.9185	0.922357	0.461178	−	0.887308i	$-0.347427\pi$
$983$	28.9185	0.922357	0.461178	+	0.887308i	$0.347427\pi$
$984$	−203.256	−6.47958
$985$	26.0487	0.829979
$986$	20.1726	0.642426
$987$	67.7175	2.15547
$988$	−0.436848	−0.0138980
$989$	−5.23274	−0.166391
$990$	−26.4477	−0.840562
$991$	−38.7109	−1.22969	−0.614846	−	0.788648i	$-0.710782\pi$
$991$	−38.7109	−1.22969	−0.614846	+	0.788648i	$0.710782\pi$
$992$	73.6460	2.33826
$993$	49.6905	1.57688
$994$	24.9237	0.790531
$995$	−13.8529	−0.439167
$996$	170.070	5.38889
$997$	−11.1352	−0.352654	−0.176327	−	0.984332i	$-0.556422\pi$
$997$	−11.1352	−0.352654	−0.176327	+	0.984332i	$0.556422\pi$
$998$	−44.5131	−1.40904
$999$	1.61126	0.0509779

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.e.1.2	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.e.1.2	✓	88	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.70073 q^{2} -2.65354 q^{3} +5.29393 q^{4} +1.00000 q^{5} +7.16648 q^{6} -4.13839 q^{7} -8.89601 q^{8} +4.04126 q^{9} +O(q^{10})\)	\(q-2.70073 q^{2} -2.65354 q^{3} +5.29393 q^{4} +1.00000 q^{5} +7.16648 q^{6} -4.13839 q^{7} -8.89601 q^{8} +4.04126 q^{9} -2.70073 q^{10} +2.42320 q^{11} -14.0476 q^{12} +0.338091 q^{13} +11.1767 q^{14} -2.65354 q^{15} +13.4378 q^{16} +2.08464 q^{17} -10.9144 q^{18} -0.244072 q^{19} +5.29393 q^{20} +10.9814 q^{21} -6.54441 q^{22} -0.722117 q^{23} +23.6059 q^{24} +1.00000 q^{25} -0.913093 q^{26} -2.76303 q^{27} -21.9083 q^{28} -3.58302 q^{29} +7.16648 q^{30} -3.98088 q^{31} -18.4999 q^{32} -6.43006 q^{33} -5.63006 q^{34} -4.13839 q^{35} +21.3942 q^{36} -0.583149 q^{37} +0.659172 q^{38} -0.897138 q^{39} -8.89601 q^{40} -8.61041 q^{41} -29.6577 q^{42} +7.24639 q^{43} +12.8283 q^{44} +4.04126 q^{45} +1.95024 q^{46} +6.16658 q^{47} -35.6578 q^{48} +10.1262 q^{49} -2.70073 q^{50} -5.53168 q^{51} +1.78983 q^{52} -2.30580 q^{53} +7.46220 q^{54} +2.42320 q^{55} +36.8151 q^{56} +0.647654 q^{57} +9.67676 q^{58} -5.87759 q^{59} -14.0476 q^{60} +5.81180 q^{61} +10.7513 q^{62} -16.7243 q^{63} +23.0876 q^{64} +0.338091 q^{65} +17.3658 q^{66} -4.62811 q^{67} +11.0360 q^{68} +1.91616 q^{69} +11.1767 q^{70} +2.22998 q^{71} -35.9511 q^{72} +9.63834 q^{73} +1.57493 q^{74} -2.65354 q^{75} -1.29210 q^{76} -10.0281 q^{77} +2.42293 q^{78} -3.57066 q^{79} +13.4378 q^{80} -4.79198 q^{81} +23.2544 q^{82} -12.1067 q^{83} +58.1346 q^{84} +2.08464 q^{85} -19.5705 q^{86} +9.50768 q^{87} -21.5568 q^{88} +6.55838 q^{89} -10.9144 q^{90} -1.39915 q^{91} -3.82284 q^{92} +10.5634 q^{93} -16.6543 q^{94} -0.244072 q^{95} +49.0903 q^{96} -3.77646 q^{97} -27.3482 q^{98} +9.79280 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9}+O(q^{10}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9} - 14 q^{10} - 26 q^{11} - 64 q^{12} - 31 q^{13} - 17 q^{14} - 34 q^{15} + 34 q^{16} - 31 q^{17} - 42 q^{18} - 56 q^{19} + 66 q^{20} - q^{21} - 49 q^{22} - 74 q^{23} - 3 q^{24} + 88 q^{25} - q^{26} - 130 q^{27} - 57 q^{28} - 6 q^{29} - q^{30} - 37 q^{31} - 87 q^{32} - 43 q^{33} - 35 q^{34} - 35 q^{35} + 53 q^{36} - 67 q^{37} - 40 q^{38} - 21 q^{39} - 39 q^{40} + 2 q^{41} - 15 q^{42} - 136 q^{43} - 15 q^{44} + 72 q^{45} - 16 q^{46} - 139 q^{47} - 71 q^{48} + 41 q^{49} - 14 q^{50} - 71 q^{51} - 71 q^{52} - 75 q^{53} + 26 q^{54} - 26 q^{55} - 22 q^{56} - 34 q^{57} - 65 q^{58} - 41 q^{59} - 64 q^{60} - 11 q^{61} - 30 q^{62} - 114 q^{63} - 33 q^{64} - 31 q^{65} + 24 q^{66} - 209 q^{67} - 42 q^{68} - 22 q^{69} - 17 q^{70} - 43 q^{71} - 80 q^{72} - 50 q^{73} + 9 q^{74} - 34 q^{75} - 62 q^{76} - 49 q^{77} - 19 q^{78} - 77 q^{79} + 34 q^{80} + 72 q^{81} - 107 q^{82} - 113 q^{83} + 19 q^{84} - 31 q^{85} + 14 q^{86} - 87 q^{87} - 107 q^{88} - 5 q^{89} - 42 q^{90} - 159 q^{91} - 100 q^{92} - 82 q^{93} - 31 q^{94} - 56 q^{95} + 58 q^{96} - 105 q^{97} - 29 q^{98} - 68 q^{99}+O(q^{100}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9 - 14 * q^10 - 26 * q^11 - 64 * q^12 - 31 * q^13 - 17 * q^14 - 34 * q^15 + 34 * q^16 - 31 * q^17 - 42 * q^18 - 56 * q^19 + 66 * q^20 - q^21 - 49 * q^22 - 74 * q^23 - 3 * q^24 + 88 * q^25 - q^26 - 130 * q^27 - 57 * q^28 - 6 * q^29 - q^30 - 37 * q^31 - 87 * q^32 - 43 * q^33 - 35 * q^34 - 35 * q^35 + 53 * q^36 - 67 * q^37 - 40 * q^38 - 21 * q^39 - 39 * q^40 + 2 * q^41 - 15 * q^42 - 136 * q^43 - 15 * q^44 + 72 * q^45 - 16 * q^46 - 139 * q^47 - 71 * q^48 + 41 * q^49 - 14 * q^50 - 71 * q^51 - 71 * q^52 - 75 * q^53 + 26 * q^54 - 26 * q^55 - 22 * q^56 - 34 * q^57 - 65 * q^58 - 41 * q^59 - 64 * q^60 - 11 * q^61 - 30 * q^62 - 114 * q^63 - 33 * q^64 - 31 * q^65 + 24 * q^66 - 209 * q^67 - 42 * q^68 - 22 * q^69 - 17 * q^70 - 43 * q^71 - 80 * q^72 - 50 * q^73 + 9 * q^74 - 34 * q^75 - 62 * q^76 - 49 * q^77 - 19 * q^78 - 77 * q^79 + 34 * q^80 + 72 * q^81 - 107 * q^82 - 113 * q^83 + 19 * q^84 - 31 * q^85 + 14 * q^86 - 87 * q^87 - 107 * q^88 - 5 * q^89 - 42 * q^90 - 159 * q^91 - 100 * q^92 - 82 * q^93 - 31 * q^94 - 56 * q^95 + 58 * q^96 - 105 * q^97 - 29 * q^98 - 68 * q^99

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