LMFDB - Embedded newform 8049.2.a.a.1.10

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			1.10
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)

$f(q)$	$=$	$q-2.40517 q^{2} +1.00000 q^{3} +3.78485 q^{4} +0.506302 q^{5} -2.40517 q^{6} -0.320355 q^{7} -4.29287 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.40517 q^{2} +1.00000 q^{3} +3.78485 q^{4} +0.506302 q^{5} -2.40517 q^{6} -0.320355 q^{7} -4.29287 q^{8} +1.00000 q^{9} -1.21774 q^{10} +1.60378 q^{11} +3.78485 q^{12} +3.06272 q^{13} +0.770508 q^{14} +0.506302 q^{15} +2.75538 q^{16} -2.58524 q^{17} -2.40517 q^{18} -4.64066 q^{19} +1.91628 q^{20} -0.320355 q^{21} -3.85737 q^{22} -5.29589 q^{23} -4.29287 q^{24} -4.74366 q^{25} -7.36637 q^{26} +1.00000 q^{27} -1.21249 q^{28} +2.15489 q^{29} -1.21774 q^{30} +4.88035 q^{31} +1.95857 q^{32} +1.60378 q^{33} +6.21796 q^{34} -0.162196 q^{35} +3.78485 q^{36} -0.412744 q^{37} +11.1616 q^{38} +3.06272 q^{39} -2.17349 q^{40} +6.53803 q^{41} +0.770508 q^{42} -11.7213 q^{43} +6.07006 q^{44} +0.506302 q^{45} +12.7375 q^{46} +9.52034 q^{47} +2.75538 q^{48} -6.89737 q^{49} +11.4093 q^{50} -2.58524 q^{51} +11.5919 q^{52} +5.97734 q^{53} -2.40517 q^{54} +0.811998 q^{55} +1.37524 q^{56} -4.64066 q^{57} -5.18288 q^{58} -6.40154 q^{59} +1.91628 q^{60} +3.52595 q^{61} -11.7381 q^{62} -0.320355 q^{63} -10.2215 q^{64} +1.55066 q^{65} -3.85737 q^{66} -3.33836 q^{67} -9.78476 q^{68} -5.29589 q^{69} +0.390110 q^{70} +5.49195 q^{71} -4.29287 q^{72} +8.12466 q^{73} +0.992721 q^{74} -4.74366 q^{75} -17.5642 q^{76} -0.513779 q^{77} -7.36637 q^{78} -9.78370 q^{79} +1.39506 q^{80} +1.00000 q^{81} -15.7251 q^{82} -2.32787 q^{83} -1.21249 q^{84} -1.30892 q^{85} +28.1917 q^{86} +2.15489 q^{87} -6.88481 q^{88} -1.70263 q^{89} -1.21774 q^{90} -0.981157 q^{91} -20.0441 q^{92} +4.88035 q^{93} -22.8980 q^{94} -2.34958 q^{95} +1.95857 q^{96} +4.04499 q^{97} +16.5894 q^{98} +1.60378 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.40517	−1.70071	−0.850356	−	0.526207i	$-0.823614\pi$
$2$	−2.40517	−1.70071	−0.850356	+	0.526207i	$0.823614\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.78485	1.89242
$5$	0.506302	0.226425	0.113213	−	0.993571i	$-0.463886\pi$
$5$	0.506302	0.226425	0.113213	+	0.993571i	$0.463886\pi$
$6$	−2.40517	−0.981907
$7$	−0.320355	−0.121083	−0.0605414	−	0.998166i	$-0.519283\pi$
$7$	−0.320355	−0.121083	−0.0605414	+	0.998166i	$0.519283\pi$
$8$	−4.29287	−1.51776
$9$	1.00000	0.333333
$10$	−1.21774	−0.385085
$11$	1.60378	0.483558	0.241779	−	0.970331i	$-0.422269\pi$
$11$	1.60378	0.483558	0.241779	+	0.970331i	$0.422269\pi$
$12$	3.78485	1.09259
$13$	3.06272	0.849446	0.424723	−	0.905323i	$-0.360372\pi$
$13$	3.06272	0.849446	0.424723	+	0.905323i	$0.360372\pi$
$14$	0.770508	0.205927
$15$	0.506302	0.130727
$16$	2.75538	0.688845
$17$	−2.58524	−0.627014	−0.313507	−	0.949586i	$-0.601504\pi$
$17$	−2.58524	−0.627014	−0.313507	+	0.949586i	$0.601504\pi$
$18$	−2.40517	−0.566904
$19$	−4.64066	−1.06464	−0.532320	−	0.846543i	$-0.678680\pi$
$19$	−4.64066	−1.06464	−0.532320	+	0.846543i	$0.678680\pi$
$20$	1.91628	0.428493
$21$	−0.320355	−0.0699072
$22$	−3.85737	−0.822393
$23$	−5.29589	−1.10427	−0.552135	−	0.833755i	$-0.686187\pi$
$23$	−5.29589	−1.10427	−0.552135	+	0.833755i	$0.686187\pi$
$24$	−4.29287	−0.876278
$25$	−4.74366	−0.948732
$26$	−7.36637	−1.44466
$27$	1.00000	0.192450
$28$	−1.21249	−0.229140
$29$	2.15489	0.400153	0.200077	−	0.979780i	$-0.435881\pi$
$29$	2.15489	0.400153	0.200077	+	0.979780i	$0.435881\pi$
$30$	−1.21774	−0.222329
$31$	4.88035	0.876537	0.438269	−	0.898844i	$-0.355592\pi$
$31$	4.88035	0.876537	0.438269	+	0.898844i	$0.355592\pi$
$32$	1.95857	0.346229
$33$	1.60378	0.279182
$34$	6.21796	1.06637
$35$	−0.162196	−0.0274162
$36$	3.78485	0.630808
$37$	−0.412744	−0.0678547	−0.0339274	−	0.999424i	$-0.510801\pi$
$37$	−0.412744	−0.0678547	−0.0339274	+	0.999424i	$0.510801\pi$
$38$	11.1616	1.81065
$39$	3.06272	0.490428
$40$	−2.17349	−0.343659
$41$	6.53803	1.02107	0.510534	−	0.859857i	$-0.329448\pi$
$41$	6.53803	1.02107	0.510534	+	0.859857i	$0.329448\pi$
$42$	0.770508	0.118892
$43$	−11.7213	−1.78748	−0.893741	−	0.448583i	$-0.851929\pi$
$43$	−11.7213	−1.78748	−0.893741	+	0.448583i	$0.851929\pi$
$44$	6.07006	0.915097
$45$	0.506302	0.0754751
$46$	12.7375	1.87804
$47$	9.52034	1.38868	0.694342	−	0.719645i	$-0.255696\pi$
$47$	9.52034	1.38868	0.694342	+	0.719645i	$0.255696\pi$
$48$	2.75538	0.397705
$49$	−6.89737	−0.985339
$50$	11.4093	1.61352
$51$	−2.58524	−0.362007
$52$	11.5919	1.60751
$53$	5.97734	0.821051	0.410525	−	0.911849i	$-0.365345\pi$
$53$	5.97734	0.821051	0.410525	+	0.911849i	$0.365345\pi$
$54$	−2.40517	−0.327302
$55$	0.811998	0.109490
$56$	1.37524	0.183774
$57$	−4.64066	−0.614671
$58$	−5.18288	−0.680546
$59$	−6.40154	−0.833409	−0.416705	−	0.909042i	$-0.636815\pi$
$59$	−6.40154	−0.833409	−0.416705	+	0.909042i	$0.636815\pi$
$60$	1.91628	0.247390
$61$	3.52595	0.451452	0.225726	−	0.974191i	$-0.427525\pi$
$61$	3.52595	0.451452	0.225726	+	0.974191i	$0.427525\pi$
$62$	−11.7381	−1.49074
$63$	−0.320355	−0.0403609
$64$	−10.2215	−1.27768
$65$	1.55066	0.192336
$66$	−3.85737	−0.474809
$67$	−3.33836	−0.407846	−0.203923	−	0.978987i	$-0.565369\pi$
$67$	−3.33836	−0.407846	−0.203923	+	0.978987i	$0.565369\pi$
$68$	−9.78476	−1.18658
$69$	−5.29589	−0.637550
$70$	0.390110	0.0466271
$71$	5.49195	0.651775	0.325887	−	0.945409i	$-0.394337\pi$
$71$	5.49195	0.651775	0.325887	+	0.945409i	$0.394337\pi$
$72$	−4.29287	−0.505919
$73$	8.12466	0.950920	0.475460	−	0.879737i	$-0.342282\pi$
$73$	8.12466	0.950920	0.475460	+	0.879737i	$0.342282\pi$
$74$	0.992721	0.115401
$75$	−4.74366	−0.547750
$76$	−17.5642	−2.01475
$77$	−0.513779	−0.0585505
$78$	−7.36637	−0.834077
$79$	−9.78370	−1.10075	−0.550376	−	0.834917i	$-0.685516\pi$
$79$	−9.78370	−1.10075	−0.550376	+	0.834917i	$0.685516\pi$
$80$	1.39506	0.155972
$81$	1.00000	0.111111
$82$	−15.7251	−1.73654
$83$	−2.32787	−0.255517	−0.127758	−	0.991805i	$-0.540778\pi$
$83$	−2.32787	−0.255517	−0.127758	+	0.991805i	$0.540778\pi$
$84$	−1.21249	−0.132294
$85$	−1.30892	−0.141972
$86$	28.1917	3.03999
$87$	2.15489	0.231029
$88$	−6.88481	−0.733924
$89$	−1.70263	−0.180479	−0.0902393	−	0.995920i	$-0.528763\pi$
$89$	−1.70263	−0.180479	−0.0902393	+	0.995920i	$0.528763\pi$
$90$	−1.21774	−0.128362
$91$	−0.981157	−0.102853
$92$	−20.0441	−2.08975
$93$	4.88035	0.506069
$94$	−22.8980	−2.36175
$95$	−2.34958	−0.241062
$96$	1.95857	0.199896
$97$	4.04499	0.410706	0.205353	−	0.978688i	$-0.434166\pi$
$97$	4.04499	0.410706	0.205353	+	0.978688i	$0.434166\pi$
$98$	16.5894	1.67578
$99$	1.60378	0.161186
$100$	−17.9540	−1.79540
$101$	−18.0917	−1.80019	−0.900097	−	0.435689i	$-0.856505\pi$
$101$	−18.0917	−1.80019	−0.900097	+	0.435689i	$0.856505\pi$
$102$	6.21796	0.615669
$103$	−8.98643	−0.885459	−0.442730	−	0.896655i	$-0.645990\pi$
$103$	−8.98643	−0.885459	−0.442730	+	0.896655i	$0.645990\pi$
$104$	−13.1478	−1.28925
$105$	−0.162196	−0.0158288
$106$	−14.3765	−1.39637
$107$	0.0453998	0.00438896	0.00219448	−	0.999998i	$-0.499301\pi$
$107$	0.0453998	0.00438896	0.00219448	+	0.999998i	$0.499301\pi$
$108$	3.78485	0.364197
$109$	−11.9725	−1.14676	−0.573379	−	0.819290i	$-0.694368\pi$
$109$	−11.9725	−1.14676	−0.573379	+	0.819290i	$0.694368\pi$
$110$	−1.95299	−0.186211
$111$	−0.412744	−0.0391760
$112$	−0.882700	−0.0834073
$113$	−5.78694	−0.544390	−0.272195	−	0.962242i	$-0.587750\pi$
$113$	−5.78694	−0.544390	−0.272195	+	0.962242i	$0.587750\pi$
$114$	11.1616	1.04538
$115$	−2.68132	−0.250035
$116$	8.15594	0.757260
$117$	3.06272	0.283149
$118$	15.3968	1.41739
$119$	0.828196	0.0759206
$120$	−2.17349	−0.198411
$121$	−8.42789	−0.766172
$122$	−8.48051	−0.767789
$123$	6.53803	0.589514
$124$	18.4714	1.65878
$125$	−4.93324	−0.441242
$126$	0.770508	0.0686423
$127$	4.03643	0.358175	0.179087	−	0.983833i	$-0.442685\pi$
$127$	4.03643	0.358175	0.179087	+	0.983833i	$0.442685\pi$
$128$	20.6672	1.82674
$129$	−11.7213	−1.03200
$130$	−3.72961	−0.327108
$131$	−6.90737	−0.603499	−0.301750	−	0.953387i	$-0.597571\pi$
$131$	−6.90737	−0.603499	−0.301750	+	0.953387i	$0.597571\pi$
$132$	6.07006	0.528331
$133$	1.48666	0.128910
$134$	8.02934	0.693629
$135$	0.506302	0.0435756
$136$	11.0981	0.951655
$137$	2.16696	0.185136	0.0925681	−	0.995706i	$-0.470492\pi$
$137$	2.16696	0.185136	0.0925681	+	0.995706i	$0.470492\pi$
$138$	12.7375	1.08429
$139$	16.9067	1.43401	0.717005	−	0.697068i	$-0.245512\pi$
$139$	16.9067	1.43401	0.717005	+	0.697068i	$0.245512\pi$
$140$	−0.613889	−0.0518831
$141$	9.52034	0.801757
$142$	−13.2091	−1.10848
$143$	4.91193	0.410756
$144$	2.75538	0.229615
$145$	1.09103	0.0906048
$146$	−19.5412	−1.61724
$147$	−6.89737	−0.568886
$148$	−1.56217	−0.128410
$149$	23.5066	1.92573	0.962866	−	0.269979i	$-0.0870167\pi$
$149$	23.5066	1.92573	0.962866	+	0.269979i	$0.0870167\pi$
$150$	11.4093	0.931566
$151$	−18.8511	−1.53408	−0.767042	−	0.641596i	$-0.778272\pi$
$151$	−18.8511	−1.53408	−0.767042	+	0.641596i	$0.778272\pi$
$152$	19.9217	1.61587
$153$	−2.58524	−0.209005
$154$	1.23573	0.0995776
$155$	2.47093	0.198470
$156$	11.5919	0.928097
$157$	−8.59866	−0.686248	−0.343124	−	0.939290i	$-0.611485\pi$
$157$	−8.59866	−0.686248	−0.343124	+	0.939290i	$0.611485\pi$
$158$	23.5315	1.87206
$159$	5.97734	0.474034
$160$	0.991628	0.0783951
$161$	1.69656	0.133708
$162$	−2.40517	−0.188968
$163$	0.707135	0.0553871	0.0276935	−	0.999616i	$-0.491184\pi$
$163$	0.707135	0.0553871	0.0276935	+	0.999616i	$0.491184\pi$
$164$	24.7454	1.93229
$165$	0.811998	0.0632139
$166$	5.59892	0.434561
$167$	−2.31418	−0.179077	−0.0895384	−	0.995983i	$-0.528539\pi$
$167$	−2.31418	−0.179077	−0.0895384	+	0.995983i	$0.528539\pi$
$168$	1.37524	0.106102
$169$	−3.61974	−0.278442
$170$	3.14817	0.241453
$171$	−4.64066	−0.354880
$172$	−44.3634	−3.38267
$173$	3.98310	0.302830	0.151415	−	0.988470i	$-0.451617\pi$
$173$	3.98310	0.302830	0.151415	+	0.988470i	$0.451617\pi$
$174$	−5.18288	−0.392913
$175$	1.51965	0.114875
$176$	4.41903	0.333097
$177$	−6.40154	−0.481169
$178$	4.09512	0.306942
$179$	−26.3761	−1.97144	−0.985720	−	0.168390i	$-0.946143\pi$
$179$	−26.3761	−1.97144	−0.985720	+	0.168390i	$0.946143\pi$
$180$	1.91628	0.142831
$181$	24.0967	1.79109	0.895546	−	0.444969i	$-0.146785\pi$
$181$	24.0967	1.79109	0.895546	+	0.444969i	$0.146785\pi$
$182$	2.35985	0.174924
$183$	3.52595	0.260646
$184$	22.7345	1.67601
$185$	−0.208973	−0.0153640
$186$	−11.7381	−0.860678
$187$	−4.14616	−0.303198
$188$	36.0330	2.62798
$189$	−0.320355	−0.0233024
$190$	5.65114	0.409977
$191$	−18.4439	−1.33455	−0.667277	−	0.744810i	$-0.732540\pi$
$191$	−18.4439	−1.33455	−0.667277	+	0.744810i	$0.732540\pi$
$192$	−10.2215	−0.737670
$193$	−5.11554	−0.368225	−0.184112	−	0.982905i	$-0.558941\pi$
$193$	−5.11554	−0.368225	−0.184112	+	0.982905i	$0.558941\pi$
$194$	−9.72888	−0.698493
$195$	1.55066	0.111045
$196$	−26.1055	−1.86468
$197$	7.37368	0.525353	0.262676	−	0.964884i	$-0.415395\pi$
$197$	7.37368	0.525353	0.262676	+	0.964884i	$0.415395\pi$
$198$	−3.85737	−0.274131
$199$	14.1377	1.00220	0.501098	−	0.865390i	$-0.332930\pi$
$199$	14.1377	1.00220	0.501098	+	0.865390i	$0.332930\pi$
$200$	20.3639	1.43994
$201$	−3.33836	−0.235470
$202$	43.5137	3.06161
$203$	−0.690330	−0.0484517
$204$	−9.78476	−0.685070
$205$	3.31022	0.231196
$206$	21.6139	1.50591
$207$	−5.29589	−0.368090
$208$	8.43896	0.585137
$209$	−7.44260	−0.514815
$210$	0.390110	0.0269202
$211$	−0.288697	−0.0198747	−0.00993736	−	0.999951i	$-0.503163\pi$
$211$	−0.288697	−0.0198747	−0.00993736	+	0.999951i	$0.503163\pi$
$212$	22.6233	1.55378
$213$	5.49195	0.376302
$214$	−0.109194	−0.00746436
$215$	−5.93452	−0.404731
$216$	−4.29287	−0.292093
$217$	−1.56344	−0.106134
$218$	28.7959	1.95031
$219$	8.12466	0.549014
$220$	3.07329	0.207201
$221$	−7.91788	−0.532614
$222$	0.992721	0.0666271
$223$	−22.8320	−1.52894	−0.764471	−	0.644658i	$-0.777000\pi$
$223$	−22.8320	−1.52894	−0.764471	+	0.644658i	$0.777000\pi$
$224$	−0.627437	−0.0419224
$225$	−4.74366	−0.316244
$226$	13.9186	0.925851
$227$	−18.2483	−1.21118	−0.605590	−	0.795777i	$-0.707063\pi$
$227$	−18.2483	−1.21118	−0.605590	+	0.795777i	$0.707063\pi$
$228$	−17.5642	−1.16322
$229$	−17.7883	−1.17548	−0.587740	−	0.809050i	$-0.699982\pi$
$229$	−17.7883	−1.17548	−0.587740	+	0.809050i	$0.699982\pi$
$230$	6.44904	0.425237
$231$	−0.513779	−0.0338042
$232$	−9.25066	−0.607336
$233$	7.87759	0.516078	0.258039	−	0.966134i	$-0.416924\pi$
$233$	7.87759	0.516078	0.258039	+	0.966134i	$0.416924\pi$
$234$	−7.36637	−0.481554
$235$	4.82017	0.314433
$236$	−24.2288	−1.57716
$237$	−9.78370	−0.635520
$238$	−1.99195	−0.129119
$239$	27.0484	1.74962	0.874808	−	0.484469i	$-0.160987\pi$
$239$	27.0484	1.74962	0.874808	+	0.484469i	$0.160987\pi$
$240$	1.39506	0.0900505
$241$	−14.1744	−0.913052	−0.456526	−	0.889710i	$-0.650906\pi$
$241$	−14.1744	−0.913052	−0.456526	+	0.889710i	$0.650906\pi$
$242$	20.2705	1.30304
$243$	1.00000	0.0641500
$244$	13.3452	0.854338
$245$	−3.49216	−0.223106
$246$	−15.7251	−1.00259
$247$	−14.2131	−0.904355
$248$	−20.9507	−1.33037
$249$	−2.32787	−0.147523
$250$	11.8653	0.750426
$251$	−4.33864	−0.273853	−0.136926	−	0.990581i	$-0.543722\pi$
$251$	−4.33864	−0.273853	−0.136926	+	0.990581i	$0.543722\pi$
$252$	−1.21249	−0.0763800
$253$	−8.49344	−0.533978
$254$	−9.70830	−0.609153
$255$	−1.30892	−0.0819675
$256$	−29.2653	−1.82908
$257$	15.1824	0.947050	0.473525	−	0.880780i	$-0.342981\pi$
$257$	15.1824	0.947050	0.473525	+	0.880780i	$0.342981\pi$
$258$	28.1917	1.75514
$259$	0.132225	0.00821604
$260$	5.86902	0.363981
$261$	2.15489	0.133384
$262$	16.6134	1.02638
$263$	8.39005	0.517352	0.258676	−	0.965964i	$-0.416714\pi$
$263$	8.39005	0.517352	0.258676	+	0.965964i	$0.416714\pi$
$264$	−6.88481	−0.423731
$265$	3.02634	0.185907
$266$	−3.57567	−0.219238
$267$	−1.70263	−0.104199
$268$	−12.6352	−0.771818
$269$	−29.1753	−1.77885	−0.889426	−	0.457079i	$-0.848896\pi$
$269$	−29.1753	−1.77885	−0.889426	+	0.457079i	$0.848896\pi$
$270$	−1.21774	−0.0741095
$271$	−1.00327	−0.0609441	−0.0304720	−	0.999536i	$-0.509701\pi$
$271$	−1.00327	−0.0609441	−0.0304720	+	0.999536i	$0.509701\pi$
$272$	−7.12334	−0.431916
$273$	−0.981157	−0.0593823
$274$	−5.21192	−0.314864
$275$	−7.60778	−0.458767
$276$	−20.0441	−1.20652
$277$	5.71864	0.343600	0.171800	−	0.985132i	$-0.445042\pi$
$277$	5.71864	0.343600	0.171800	+	0.985132i	$0.445042\pi$
$278$	−40.6636	−2.43884
$279$	4.88035	0.292179
$280$	0.696288	0.0416112
$281$	−25.8413	−1.54156	−0.770781	−	0.637100i	$-0.780134\pi$
$281$	−25.8413	−1.54156	−0.770781	+	0.637100i	$0.780134\pi$
$282$	−22.8980	−1.36356
$283$	−29.0782	−1.72852	−0.864260	−	0.503045i	$-0.832213\pi$
$283$	−29.0782	−1.72852	−0.864260	+	0.503045i	$0.832213\pi$
$284$	20.7862	1.23343
$285$	−2.34958	−0.139177
$286$	−11.8140	−0.698578
$287$	−2.09449	−0.123634
$288$	1.95857	0.115410
$289$	−10.3165	−0.606853
$290$	−2.62411	−0.154093
$291$	4.04499	0.237121
$292$	30.7506	1.79954
$293$	28.2249	1.64891	0.824457	−	0.565924i	$-0.191481\pi$
$293$	28.2249	1.64891	0.824457	+	0.565924i	$0.191481\pi$
$294$	16.5894	0.967511
$295$	−3.24111	−0.188705
$296$	1.77186	0.102987
$297$	1.60378	0.0930607
$298$	−56.5373	−3.27512
$299$	−16.2198	−0.938017
$300$	−17.9540	−1.03658
$301$	3.75498	0.216433
$302$	45.3402	2.60904
$303$	−18.0917	−1.03934
$304$	−12.7868	−0.733373
$305$	1.78520	0.102220
$306$	6.21796	0.355457
$307$	−20.0720	−1.14557	−0.572785	−	0.819706i	$-0.694137\pi$
$307$	−20.0720	−1.14557	−0.572785	+	0.819706i	$0.694137\pi$
$308$	−1.94457	−0.110802
$309$	−8.98643	−0.511220
$310$	−5.94302	−0.337541
$311$	−9.19778	−0.521558	−0.260779	−	0.965399i	$-0.583979\pi$
$311$	−9.19778	−0.521558	−0.260779	+	0.965399i	$0.583979\pi$
$312$	−13.1478	−0.744350
$313$	−23.2080	−1.31179	−0.655896	−	0.754852i	$-0.727709\pi$
$313$	−23.2080	−1.31179	−0.655896	+	0.754852i	$0.727709\pi$
$314$	20.6813	1.16711
$315$	−0.162196	−0.00913874
$316$	−37.0298	−2.08309
$317$	1.58655	0.0891093	0.0445546	−	0.999007i	$-0.485813\pi$
$317$	1.58655	0.0891093	0.0445546	+	0.999007i	$0.485813\pi$
$318$	−14.3765	−0.806195
$319$	3.45597	0.193497
$320$	−5.17515	−0.289300
$321$	0.0453998	0.00253397
$322$	−4.08053	−0.227399
$323$	11.9972	0.667545
$324$	3.78485	0.210269
$325$	−14.5285	−0.805896
$326$	−1.70078	−0.0941975
$327$	−11.9725	−0.662081
$328$	−28.0669	−1.54973
$329$	−3.04989	−0.168146
$330$	−1.95299	−0.107509
$331$	25.5490	1.40430	0.702150	−	0.712029i	$-0.252223\pi$
$331$	25.5490	1.40430	0.702150	+	0.712029i	$0.252223\pi$
$332$	−8.81063	−0.483546
$333$	−0.412744	−0.0226182
$334$	5.56600	0.304558
$335$	−1.69022	−0.0923467
$336$	−0.882700	−0.0481552
$337$	−8.25041	−0.449428	−0.224714	−	0.974425i	$-0.572145\pi$
$337$	−8.25041	−0.449428	−0.224714	+	0.974425i	$0.572145\pi$
$338$	8.70610	0.473550
$339$	−5.78694	−0.314304
$340$	−4.95405	−0.268671
$341$	7.82701	0.423856
$342$	11.1616	0.603550
$343$	4.45209	0.240390
$344$	50.3180	2.71296
$345$	−2.68132	−0.144358
$346$	−9.58004	−0.515026
$347$	21.9324	1.17739	0.588697	−	0.808354i	$-0.299641\pi$
$347$	21.9324	1.17739	0.588697	+	0.808354i	$0.299641\pi$
$348$	8.15594	0.437204
$349$	5.67913	0.303997	0.151998	−	0.988381i	$-0.451429\pi$
$349$	5.67913	0.303997	0.151998	+	0.988381i	$0.451429\pi$
$350$	−3.65503	−0.195369
$351$	3.06272	0.163476
$352$	3.14111	0.167422
$353$	19.3562	1.03023	0.515114	−	0.857122i	$-0.327750\pi$
$353$	19.3562	1.03023	0.515114	+	0.857122i	$0.327750\pi$
$354$	15.3968	0.818330
$355$	2.78059	0.147578
$356$	−6.44420	−0.341542
$357$	0.828196	0.0438328
$358$	63.4390	3.35285
$359$	−4.63567	−0.244661	−0.122331	−	0.992489i	$-0.539037\pi$
$359$	−4.63567	−0.244661	−0.122331	+	0.992489i	$0.539037\pi$
$360$	−2.17349	−0.114553
$361$	2.53575	0.133460
$362$	−57.9566	−3.04613
$363$	−8.42789	−0.442350
$364$	−3.71353	−0.194642
$365$	4.11354	0.215312
$366$	−8.48051	−0.443283
$367$	5.02655	0.262384	0.131192	−	0.991357i	$-0.458120\pi$
$367$	5.02655	0.262384	0.131192	+	0.991357i	$0.458120\pi$
$368$	−14.5922	−0.760671
$369$	6.53803	0.340356
$370$	0.502617	0.0261298
$371$	−1.91487	−0.0994151
$372$	18.4714	0.957697
$373$	26.9266	1.39420	0.697102	−	0.716972i	$-0.254472\pi$
$373$	26.9266	1.39420	0.697102	+	0.716972i	$0.254472\pi$
$374$	9.97223	0.515652
$375$	−4.93324	−0.254751
$376$	−40.8695	−2.10769
$377$	6.59983	0.339909
$378$	0.770508	0.0396307
$379$	3.08918	0.158681	0.0793404	−	0.996848i	$-0.474719\pi$
$379$	3.08918	0.158681	0.0793404	+	0.996848i	$0.474719\pi$
$380$	−8.89280	−0.456191
$381$	4.03643	0.206792
$382$	44.3608	2.26969
$383$	−9.43979	−0.482351	−0.241175	−	0.970482i	$-0.577533\pi$
$383$	−9.43979	−0.482351	−0.241175	+	0.970482i	$0.577533\pi$
$384$	20.6672	1.05467
$385$	−0.260127	−0.0132573
$386$	12.3038	0.626245
$387$	−11.7213	−0.595827
$388$	15.3097	0.777230
$389$	−14.2327	−0.721627	−0.360813	−	0.932638i	$-0.617501\pi$
$389$	−14.2327	−0.721627	−0.360813	+	0.932638i	$0.617501\pi$
$390$	−3.72961	−0.188856
$391$	13.6912	0.692392
$392$	29.6095	1.49551
$393$	−6.90737	−0.348431
$394$	−17.7350	−0.893475
$395$	−4.95351	−0.249238
$396$	6.07006	0.305032
$397$	15.5106	0.778453	0.389226	−	0.921142i	$-0.372742\pi$
$397$	15.5106	0.778453	0.389226	+	0.921142i	$0.372742\pi$
$398$	−34.0036	−1.70445
$399$	1.48666	0.0744260
$400$	−13.0706	−0.653529
$401$	2.48172	0.123931	0.0619655	−	0.998078i	$-0.480263\pi$
$401$	2.48172	0.123931	0.0619655	+	0.998078i	$0.480263\pi$
$402$	8.02934	0.400467
$403$	14.9472	0.744571
$404$	−68.4745	−3.40673
$405$	0.506302	0.0251584
$406$	1.66036	0.0824024
$407$	−0.661951	−0.0328117
$408$	11.0981	0.549438
$409$	−18.6357	−0.921477	−0.460738	−	0.887536i	$-0.652415\pi$
$409$	−18.6357	−0.921477	−0.460738	+	0.887536i	$0.652415\pi$
$410$	−7.96165	−0.393198
$411$	2.16696	0.106888
$412$	−34.0123	−1.67566
$413$	2.05076	0.100911
$414$	12.7375	0.626015
$415$	−1.17861	−0.0578555
$416$	5.99855	0.294103
$417$	16.9067	0.827926
$418$	17.9007	0.875553
$419$	10.7796	0.526616	0.263308	−	0.964712i	$-0.415187\pi$
$419$	10.7796	0.526616	0.263308	+	0.964712i	$0.415187\pi$
$420$	−0.613889	−0.0299547
$421$	0.613234	0.0298872	0.0149436	−	0.999888i	$-0.495243\pi$
$421$	0.613234	0.0298872	0.0149436	+	0.999888i	$0.495243\pi$
$422$	0.694366	0.0338012
$423$	9.52034	0.462895
$424$	−25.6599	−1.24616
$425$	12.2635	0.594868
$426$	−13.2091	−0.639982
$427$	−1.12956	−0.0546630
$428$	0.171831	0.00830577
$429$	4.91193	0.237150
$430$	14.2735	0.688332
$431$	6.73413	0.324371	0.162186	−	0.986760i	$-0.448146\pi$
$431$	6.73413	0.324371	0.162186	+	0.986760i	$0.448146\pi$
$432$	2.75538	0.132568
$433$	−2.51934	−0.121072	−0.0605359	−	0.998166i	$-0.519281\pi$
$433$	−2.51934	−0.121072	−0.0605359	+	0.998166i	$0.519281\pi$
$434$	3.76035	0.180503
$435$	1.09103	0.0523107
$436$	−45.3141	−2.17015
$437$	24.5764	1.17565
$438$	−19.5412	−0.933715
$439$	−8.38211	−0.400056	−0.200028	−	0.979790i	$-0.564103\pi$
$439$	−8.38211	−0.400056	−0.200028	+	0.979790i	$0.564103\pi$
$440$	−3.48580	−0.166179
$441$	−6.89737	−0.328446
$442$	19.0439	0.905824
$443$	6.53982	0.310716	0.155358	−	0.987858i	$-0.450347\pi$
$443$	6.53982	0.310716	0.155358	+	0.987858i	$0.450347\pi$
$444$	−1.56217	−0.0741375
$445$	−0.862046	−0.0408649
$446$	54.9148	2.60029
$447$	23.5066	1.11182
$448$	3.27449	0.154705
$449$	4.88805	0.230681	0.115341	−	0.993326i	$-0.463204\pi$
$449$	4.88805	0.230681	0.115341	+	0.993326i	$0.463204\pi$
$450$	11.4093	0.537840
$451$	10.4856	0.493746
$452$	−21.9027	−1.03022
$453$	−18.8511	−0.885704
$454$	43.8902	2.05987
$455$	−0.496762	−0.0232886
$456$	19.9217	0.932921
$457$	8.84476	0.413741	0.206870	−	0.978368i	$-0.433672\pi$
$457$	8.84476	0.413741	0.206870	+	0.978368i	$0.433672\pi$
$458$	42.7838	1.99916
$459$	−2.58524	−0.120669
$460$	−10.1484	−0.473171
$461$	−1.46185	−0.0680851	−0.0340426	−	0.999420i	$-0.510838\pi$
$461$	−1.46185	−0.0680851	−0.0340426	+	0.999420i	$0.510838\pi$
$462$	1.23573	0.0574912
$463$	−27.1667	−1.26254	−0.631272	−	0.775561i	$-0.717467\pi$
$463$	−27.1667	−1.26254	−0.631272	+	0.775561i	$0.717467\pi$
$464$	5.93755	0.275644
$465$	2.47093	0.114587
$466$	−18.9470	−0.877701
$467$	6.28872	0.291007	0.145504	−	0.989358i	$-0.453520\pi$
$467$	6.28872	0.291007	0.145504	+	0.989358i	$0.453520\pi$
$468$	11.5919	0.535837
$469$	1.06946	0.0493831
$470$	−11.5933	−0.534761
$471$	−8.59866	−0.396206
$472$	27.4809	1.26491
$473$	−18.7984	−0.864351
$474$	23.5315	1.08084
$475$	22.0137	1.01006
$476$	3.13460	0.143674
$477$	5.97734	0.273684
$478$	−65.0561	−2.97560
$479$	30.0599	1.37347	0.686736	−	0.726907i	$-0.259043\pi$
$479$	30.0599	1.37347	0.686736	+	0.726907i	$0.259043\pi$
$480$	0.991628	0.0452614
$481$	−1.26412	−0.0576389
$482$	34.0918	1.55284
$483$	1.69656	0.0771963
$484$	−31.8983	−1.44992
$485$	2.04799	0.0929943
$486$	−2.40517	−0.109101
$487$	−37.0714	−1.67987	−0.839933	−	0.542691i	$-0.817406\pi$
$487$	−37.0714	−1.67987	−0.839933	+	0.542691i	$0.817406\pi$
$488$	−15.1364	−0.685194
$489$	0.707135	0.0319777
$490$	8.39924	0.379439
$491$	−7.46208	−0.336759	−0.168380	−	0.985722i	$-0.553853\pi$
$491$	−7.46208	−0.336759	−0.168380	+	0.985722i	$0.553853\pi$
$492$	24.7454	1.11561
$493$	−5.57092	−0.250902
$494$	34.1848	1.53805
$495$	0.811998	0.0364966
$496$	13.4472	0.603799
$497$	−1.75937	−0.0789187
$498$	5.59892	0.250894
$499$	−22.0499	−0.987090	−0.493545	−	0.869720i	$-0.664299\pi$
$499$	−22.0499	−0.987090	−0.493545	+	0.869720i	$0.664299\pi$
$500$	−18.6716	−0.835018
$501$	−2.31418	−0.103390
$502$	10.4352	0.465745
$503$	7.42108	0.330890	0.165445	−	0.986219i	$-0.447094\pi$
$503$	7.42108	0.330890	0.165445	+	0.986219i	$0.447094\pi$
$504$	1.37524	0.0612581
$505$	−9.15989	−0.407610
$506$	20.4282	0.908143
$507$	−3.61974	−0.160758
$508$	15.2773	0.677819
$509$	35.7349	1.58392	0.791961	−	0.610572i	$-0.209060\pi$
$509$	35.7349	1.58392	0.791961	+	0.610572i	$0.209060\pi$
$510$	3.14817	0.139403
$511$	−2.60278	−0.115140
$512$	29.0536	1.28400
$513$	−4.64066	−0.204890
$514$	−36.5162	−1.61066
$515$	−4.54985	−0.200490
$516$	−44.3634	−1.95299
$517$	15.2685	0.671509
$518$	−0.318023	−0.0139731
$519$	3.98310	0.174839
$520$	−6.65679	−0.291920
$521$	26.3787	1.15567	0.577836	−	0.816153i	$-0.303897\pi$
$521$	26.3787	1.15567	0.577836	+	0.816153i	$0.303897\pi$
$522$	−5.18288	−0.226849
$523$	28.2996	1.23746	0.618728	−	0.785605i	$-0.287648\pi$
$523$	28.2996	1.23746	0.618728	+	0.785605i	$0.287648\pi$
$524$	−26.1433	−1.14208
$525$	1.51965	0.0663231
$526$	−20.1795	−0.879868
$527$	−12.6169	−0.549601
$528$	4.41903	0.192313
$529$	5.04644	0.219410
$530$	−7.27887	−0.316174
$531$	−6.40154	−0.277803
$532$	5.62678	0.243952
$533$	20.0242	0.867342
$534$	4.09512	0.177213
$535$	0.0229860	0.000993772 0
$536$	14.3311	0.619011
$537$	−26.3761	−1.13821
$538$	70.1717	3.02532
$539$	−11.0619	−0.476468
$540$	1.91628	0.0824635
$541$	22.4473	0.965083	0.482541	−	0.875873i	$-0.339714\pi$
$541$	22.4473	0.965083	0.482541	+	0.875873i	$0.339714\pi$
$542$	2.41303	0.103648
$543$	24.0967	1.03409
$544$	−5.06338	−0.217091
$545$	−6.06171	−0.259655
$546$	2.35985	0.100992
$547$	2.48576	0.106283	0.0531416	−	0.998587i	$-0.483077\pi$
$547$	2.48576	0.106283	0.0531416	+	0.998587i	$0.483077\pi$
$548$	8.20163	0.350356
$549$	3.52595	0.150484
$550$	18.2980	0.780230
$551$	−10.0001	−0.426020
$552$	22.7345	0.967646
$553$	3.13426	0.133282
$554$	−13.7543	−0.584364
$555$	−0.208973	−0.00887043
$556$	63.9894	2.71376
$557$	19.2263	0.814645	0.407322	−	0.913284i	$-0.366463\pi$
$557$	19.2263	0.814645	0.407322	+	0.913284i	$0.366463\pi$
$558$	−11.7381	−0.496913
$559$	−35.8991	−1.51837
$560$	−0.446913	−0.0188855
$561$	−4.14616	−0.175051
$562$	62.1527	2.62175
$563$	−10.8735	−0.458262	−0.229131	−	0.973396i	$-0.573588\pi$
$563$	−10.8735	−0.458262	−0.229131	+	0.973396i	$0.573588\pi$
$564$	36.0330	1.51726
$565$	−2.92994	−0.123264
$566$	69.9381	2.93972
$567$	−0.320355	−0.0134536
$568$	−23.5762	−0.989236
$569$	−35.1155	−1.47212	−0.736060	−	0.676917i	$-0.763316\pi$
$569$	−35.1155	−1.47212	−0.736060	+	0.676917i	$0.763316\pi$
$570$	5.65114	0.236700
$571$	−24.3624	−1.01954	−0.509768	−	0.860312i	$-0.670269\pi$
$571$	−24.3624	−1.01954	−0.509768	+	0.860312i	$0.670269\pi$
$572$	18.5909	0.777325
$573$	−18.4439	−0.770505
$574$	5.03760	0.210266
$575$	25.1219	1.04765
$576$	−10.2215	−0.425894
$577$	−36.0995	−1.50284	−0.751420	−	0.659824i	$-0.770631\pi$
$577$	−36.0995	−1.50284	−0.751420	+	0.659824i	$0.770631\pi$
$578$	24.8130	1.03208
$579$	−5.11554	−0.212595
$580$	4.12937	0.171463
$581$	0.745744	0.0309387
$582$	−9.72888	−0.403275
$583$	9.58634	0.397025
$584$	−34.8781	−1.44327
$585$	1.55066	0.0641120
$586$	−67.8856	−2.80433
$587$	−9.70848	−0.400712	−0.200356	−	0.979723i	$-0.564210\pi$
$587$	−9.70848	−0.400712	−0.200356	+	0.979723i	$0.564210\pi$
$588$	−26.1055	−1.07657
$589$	−22.6481	−0.933197
$590$	7.79543	0.320933
$591$	7.37368	0.303313
$592$	−1.13727	−0.0467414
$593$	5.82306	0.239125	0.119562	−	0.992827i	$-0.461851\pi$
$593$	5.82306	0.239125	0.119562	+	0.992827i	$0.461851\pi$
$594$	−3.85737	−0.158270
$595$	0.419318	0.0171903
$596$	88.9688	3.64430
$597$	14.1377	0.578618
$598$	39.0115	1.59530
$599$	39.7956	1.62601	0.813003	−	0.582259i	$-0.197831\pi$
$599$	39.7956	1.62601	0.813003	+	0.582259i	$0.197831\pi$
$600$	20.3639	0.831352
$601$	−27.8187	−1.13475	−0.567374	−	0.823460i	$-0.692041\pi$
$601$	−27.8187	−1.13475	−0.567374	+	0.823460i	$0.692041\pi$
$602$	−9.03136	−0.368091
$603$	−3.33836	−0.135949
$604$	−71.3487	−2.90314
$605$	−4.26706	−0.173481
$606$	43.5137	1.76762
$607$	24.9123	1.01116	0.505579	−	0.862780i	$-0.331279\pi$
$607$	24.9123	1.01116	0.505579	+	0.862780i	$0.331279\pi$
$608$	−9.08905	−0.368610
$609$	−0.690330	−0.0279736
$610$	−4.29370	−0.173847
$611$	29.1581	1.17961
$612$	−9.78476	−0.395526
$613$	−39.6088	−1.59978	−0.799892	−	0.600144i	$-0.795110\pi$
$613$	−39.6088	−1.59978	−0.799892	+	0.600144i	$0.795110\pi$
$614$	48.2766	1.94829
$615$	3.31022	0.133481
$616$	2.20558	0.0888655
$617$	23.4714	0.944923	0.472462	−	0.881351i	$-0.343366\pi$
$617$	23.4714	0.944923	0.472462	+	0.881351i	$0.343366\pi$
$618$	21.6139	0.869439
$619$	0.197832	0.00795155	0.00397577	−	0.999992i	$-0.498734\pi$
$619$	0.197832	0.00795155	0.00397577	+	0.999992i	$0.498734\pi$
$620$	9.35211	0.375590
$621$	−5.29589	−0.212517
$622$	22.1222	0.887020
$623$	0.545446	0.0218528
$624$	8.43896	0.337829
$625$	21.2206	0.848823
$626$	55.8191	2.23098
$627$	−7.44260	−0.297229
$628$	−32.5446	−1.29867
$629$	1.06705	0.0425459
$630$	0.390110	0.0155424
$631$	41.7781	1.66316	0.831580	−	0.555405i	$-0.187437\pi$
$631$	41.7781	1.66316	0.831580	+	0.555405i	$0.187437\pi$
$632$	42.0001	1.67067
$633$	−0.288697	−0.0114747
$634$	−3.81591	−0.151549
$635$	2.04365	0.0810999
$636$	22.6233	0.897073
$637$	−21.1247	−0.836992
$638$	−8.31220	−0.329083
$639$	5.49195	0.217258
$640$	10.4639	0.413620
$641$	−36.0241	−1.42287	−0.711434	−	0.702753i	$-0.751954\pi$
$641$	−36.0241	−1.42287	−0.711434	+	0.702753i	$0.751954\pi$
$642$	−0.109194	−0.00430955
$643$	−25.2638	−0.996309	−0.498154	−	0.867088i	$-0.665989\pi$
$643$	−25.2638	−0.996309	−0.498154	+	0.867088i	$0.665989\pi$
$644$	6.42124	0.253032
$645$	−5.93452	−0.233672
$646$	−28.8554	−1.13530
$647$	−30.0269	−1.18048	−0.590240	−	0.807228i	$-0.700967\pi$
$647$	−30.0269	−1.18048	−0.590240	+	0.807228i	$0.700967\pi$
$648$	−4.29287	−0.168640
$649$	−10.2667	−0.403002
$650$	34.9435	1.37060
$651$	−1.56344	−0.0612762
$652$	2.67640	0.104816
$653$	−34.4762	−1.34916	−0.674579	−	0.738203i	$-0.735675\pi$
$653$	−34.4762	−1.34916	−0.674579	+	0.738203i	$0.735675\pi$
$654$	28.7959	1.12601
$655$	−3.49722	−0.136648
$656$	18.0148	0.703358
$657$	8.12466	0.316973
$658$	7.33550	0.285968
$659$	−30.9039	−1.20385	−0.601923	−	0.798554i	$-0.705599\pi$
$659$	−30.9039	−1.20385	−0.601923	+	0.798554i	$0.705599\pi$
$660$	3.07329	0.119628
$661$	−26.4938	−1.03049	−0.515244	−	0.857043i	$-0.672299\pi$
$661$	−26.4938	−1.03049	−0.515244	+	0.857043i	$0.672299\pi$
$662$	−61.4497	−2.38831
$663$	−7.91788	−0.307505
$664$	9.99323	0.387812
$665$	0.752699	0.0291884
$666$	0.992721	0.0384671
$667$	−11.4121	−0.441877
$668$	−8.75883	−0.338889
$669$	−22.8320	−0.882735
$670$	4.06527	0.157055
$671$	5.65485	0.218303
$672$	−0.627437	−0.0242039
$673$	12.1908	0.469922	0.234961	−	0.972005i	$-0.424504\pi$
$673$	12.1908	0.469922	0.234961	+	0.972005i	$0.424504\pi$
$674$	19.8436	0.764348
$675$	−4.74366	−0.182583
$676$	−13.7002	−0.526930
$677$	−33.6386	−1.29284	−0.646419	−	0.762983i	$-0.723734\pi$
$677$	−33.6386	−1.29284	−0.646419	+	0.762983i	$0.723734\pi$
$678$	13.9186	0.534540
$679$	−1.29583	−0.0497294
$680$	5.61900	0.215479
$681$	−18.2483	−0.699275
$682$	−18.8253	−0.720858
$683$	8.07160	0.308851	0.154426	−	0.988004i	$-0.450647\pi$
$683$	8.07160	0.308851	0.154426	+	0.988004i	$0.450647\pi$
$684$	−17.5642	−0.671584
$685$	1.09714	0.0419195
$686$	−10.7080	−0.408835
$687$	−17.7883	−0.678664
$688$	−32.2967	−1.23130
$689$	18.3069	0.697438
$690$	6.44904	0.245511
$691$	7.60767	0.289410	0.144705	−	0.989475i	$-0.453777\pi$
$691$	7.60767	0.289410	0.144705	+	0.989475i	$0.453777\pi$
$692$	15.0754	0.573082
$693$	−0.513779	−0.0195168
$694$	−52.7512	−2.00241
$695$	8.55992	0.324696
$696$	−9.25066	−0.350645
$697$	−16.9024	−0.640224
$698$	−13.6593	−0.517011
$699$	7.87759	0.297958
$700$	5.75166	0.217392
$701$	30.5276	1.15301	0.576505	−	0.817093i	$-0.304416\pi$
$701$	30.5276	1.15301	0.576505	+	0.817093i	$0.304416\pi$
$702$	−7.36637	−0.278026
$703$	1.91541	0.0722409
$704$	−16.3930	−0.617833
$705$	4.82017	0.181538
$706$	−46.5550	−1.75212
$707$	5.79577	0.217973
$708$	−24.2288	−0.910576
$709$	9.17085	0.344419	0.172209	−	0.985060i	$-0.444909\pi$
$709$	9.17085	0.344419	0.172209	+	0.985060i	$0.444909\pi$
$710$	−6.68779	−0.250988
$711$	−9.78370	−0.366917
$712$	7.30917	0.273923
$713$	−25.8458	−0.967933
$714$	−1.99195	−0.0745470
$715$	2.48692	0.0930056
$716$	−99.8295	−3.73080
$717$	27.0484	1.01014
$718$	11.1496	0.416099
$719$	−50.4374	−1.88100	−0.940498	−	0.339799i	$-0.889641\pi$
$719$	−50.4374	−1.88100	−0.940498	+	0.339799i	$0.889641\pi$
$720$	1.39506	0.0519907
$721$	2.87885	0.107214
$722$	−6.09890	−0.226978
$723$	−14.1744	−0.527151
$724$	91.2023	3.38951
$725$	−10.2221	−0.379638
$726$	20.2705	0.752309
$727$	−21.9535	−0.814212	−0.407106	−	0.913381i	$-0.633462\pi$
$727$	−21.9535	−0.814212	−0.407106	+	0.913381i	$0.633462\pi$
$728$	4.21198	0.156106
$729$	1.00000	0.0370370
$730$	−9.89376	−0.366185
$731$	30.3024	1.12078
$732$	13.3452	0.493252
$733$	−2.45033	−0.0905048	−0.0452524	−	0.998976i	$-0.514409\pi$
$733$	−2.45033	−0.0905048	−0.0452524	+	0.998976i	$0.514409\pi$
$734$	−12.0897	−0.446239
$735$	−3.49216	−0.128810
$736$	−10.3724	−0.382330
$737$	−5.35400	−0.197217
$738$	−15.7251	−0.578848
$739$	−33.7259	−1.24063	−0.620314	−	0.784353i	$-0.712995\pi$
$739$	−33.7259	−1.24063	−0.620314	+	0.784353i	$0.712995\pi$
$740$	−0.790933	−0.0290753
$741$	−14.2131	−0.522129
$742$	4.60559	0.169076
$743$	−2.18958	−0.0803279	−0.0401639	−	0.999193i	$-0.512788\pi$
$743$	−2.18958	−0.0803279	−0.0401639	+	0.999193i	$0.512788\pi$
$744$	−20.9507	−0.768090
$745$	11.9014	0.436035
$746$	−64.7630	−2.37114
$747$	−2.32787	−0.0851722
$748$	−15.6926	−0.573778
$749$	−0.0145440	−0.000531427 0
$750$	11.8653	0.433259
$751$	34.4917	1.25862	0.629310	−	0.777155i	$-0.283338\pi$
$751$	34.4917	1.25862	0.629310	+	0.777155i	$0.283338\pi$
$752$	26.2322	0.956588
$753$	−4.33864	−0.158109
$754$	−15.8737	−0.578087
$755$	−9.54438	−0.347356
$756$	−1.21249	−0.0440980
$757$	46.9537	1.70656	0.853280	−	0.521453i	$-0.174610\pi$
$757$	46.9537	1.70656	0.853280	+	0.521453i	$0.174610\pi$
$758$	−7.43002	−0.269870
$759$	−8.49344	−0.308292
$760$	10.0864	0.365873
$761$	−8.94201	−0.324148	−0.162074	−	0.986779i	$-0.551818\pi$
$761$	−8.94201	−0.324148	−0.162074	+	0.986779i	$0.551818\pi$
$762$	−9.70830	−0.351694
$763$	3.83545	0.138853
$764$	−69.8074	−2.52554
$765$	−1.30892	−0.0473240
$766$	22.7043	0.820340
$767$	−19.6061	−0.707936
$768$	−29.2653	−1.05602
$769$	−21.9587	−0.791852	−0.395926	−	0.918282i	$-0.629576\pi$
$769$	−21.9587	−0.791852	−0.395926	+	0.918282i	$0.629576\pi$
$770$	0.625651	0.0225469
$771$	15.1824	0.546780
$772$	−19.3616	−0.696838
$773$	−44.1693	−1.58866	−0.794330	−	0.607486i	$-0.792178\pi$
$773$	−44.1693	−1.58866	−0.794330	+	0.607486i	$0.792178\pi$
$774$	28.1917	1.01333
$775$	−23.1507	−0.831599
$776$	−17.3646	−0.623352
$777$	0.132225	0.00474353
$778$	34.2321	1.22728
$779$	−30.3408	−1.08707
$780$	5.86902	0.210145
$781$	8.80788	0.315171
$782$	−32.9296	−1.17756
$783$	2.15489	0.0770095
$784$	−19.0049	−0.678746
$785$	−4.35353	−0.155384
$786$	16.6134	0.592580
$787$	−10.9062	−0.388766	−0.194383	−	0.980926i	$-0.562270\pi$
$787$	−10.9062	−0.388766	−0.194383	+	0.980926i	$0.562270\pi$
$788$	27.9083	0.994191
$789$	8.39005	0.298694
$790$	11.9140	0.423883
$791$	1.85387	0.0659162
$792$	−6.88481	−0.244641
$793$	10.7990	0.383484
$794$	−37.3056	−1.32392
$795$	3.02634	0.107333
$796$	53.5091	1.89658
$797$	17.6917	0.626671	0.313336	−	0.949642i	$-0.398553\pi$
$797$	17.6917	0.626671	0.313336	+	0.949642i	$0.398553\pi$
$798$	−3.57567	−0.126577
$799$	−24.6124	−0.870724
$800$	−9.29078	−0.328479
$801$	−1.70263	−0.0601595
$802$	−5.96896	−0.210771
$803$	13.0302	0.459825
$804$	−12.6352	−0.445609
$805$	0.858974	0.0302749
$806$	−35.9505	−1.26630
$807$	−29.1753	−1.02702
$808$	77.6654	2.73226
$809$	−27.1129	−0.953237	−0.476619	−	0.879110i	$-0.658138\pi$
$809$	−27.1129	−0.953237	−0.476619	+	0.879110i	$0.658138\pi$
$810$	−1.21774	−0.0427872
$811$	4.58860	0.161128	0.0805638	−	0.996749i	$-0.474328\pi$
$811$	4.58860	0.161128	0.0805638	+	0.996749i	$0.474328\pi$
$812$	−2.61279	−0.0916911
$813$	−1.00327	−0.0351861
$814$	1.59211	0.0558033
$815$	0.358024	0.0125410
$816$	−7.12334	−0.249367
$817$	54.3946	1.90303
$818$	44.8221	1.56717
$819$	−0.981157	−0.0342844
$820$	12.5287	0.437521
$821$	36.5010	1.27389	0.636947	−	0.770907i	$-0.280197\pi$
$821$	36.5010	1.27389	0.636947	+	0.770907i	$0.280197\pi$
$822$	−5.21192	−0.181787
$823$	49.5710	1.72794	0.863969	−	0.503545i	$-0.167971\pi$
$823$	49.5710	1.72794	0.863969	+	0.503545i	$0.167971\pi$
$824$	38.5775	1.34391
$825$	−7.60778	−0.264869
$826$	−4.93244	−0.171621
$827$	−17.5347	−0.609742	−0.304871	−	0.952394i	$-0.598613\pi$
$827$	−17.5347	−0.609742	−0.304871	+	0.952394i	$0.598613\pi$
$828$	−20.0441	−0.696582
$829$	−10.8890	−0.378190	−0.189095	−	0.981959i	$-0.560555\pi$
$829$	−10.8890	−0.378190	−0.189095	+	0.981959i	$0.560555\pi$
$830$	2.83475	0.0983955
$831$	5.71864	0.198377
$832$	−31.3055	−1.08532
$833$	17.8314	0.617821
$834$	−40.6636	−1.40806
$835$	−1.17168	−0.0405475
$836$	−28.1691	−0.974249
$837$	4.88035	0.168690
$838$	−25.9267	−0.895622
$839$	−37.5471	−1.29627	−0.648135	−	0.761525i	$-0.724451\pi$
$839$	−37.5471	−1.29627	−0.648135	+	0.761525i	$0.724451\pi$
$840$	0.696288	0.0240242
$841$	−24.3564	−0.839877
$842$	−1.47493	−0.0508296
$843$	−25.8413	−0.890021
$844$	−1.09267	−0.0376114
$845$	−1.83269	−0.0630463
$846$	−22.8980	−0.787251
$847$	2.69992	0.0927702
$848$	16.4698	0.565577
$849$	−29.0782	−0.997962
$850$	−29.4959	−1.01170
$851$	2.18585	0.0749299
$852$	20.7862	0.712123
$853$	−32.9838	−1.12934	−0.564671	−	0.825316i	$-0.690997\pi$
$853$	−32.9838	−1.12934	−0.564671	+	0.825316i	$0.690997\pi$
$854$	2.71677	0.0929661
$855$	−2.34958	−0.0803539
$856$	−0.194895	−0.00666138
$857$	−23.3760	−0.798508	−0.399254	−	0.916840i	$-0.630731\pi$
$857$	−23.3760	−0.798508	−0.399254	+	0.916840i	$0.630731\pi$
$858$	−11.8140	−0.403324
$859$	−24.6506	−0.841068	−0.420534	−	0.907277i	$-0.638157\pi$
$859$	−24.6506	−0.841068	−0.420534	+	0.907277i	$0.638157\pi$
$860$	−22.4613	−0.765923
$861$	−2.09449	−0.0713800
$862$	−16.1967	−0.551663
$863$	−40.3013	−1.37187	−0.685936	−	0.727662i	$-0.740607\pi$
$863$	−40.3013	−1.37187	−0.685936	+	0.727662i	$0.740607\pi$
$864$	1.95857	0.0666319
$865$	2.01665	0.0685683
$866$	6.05944	0.205908
$867$	−10.3165	−0.350367
$868$	−5.91740	−0.200850
$869$	−15.6909	−0.532277
$870$	−2.62411	−0.0889655
$871$	−10.2245	−0.346443
$872$	51.3964	1.74050
$873$	4.04499	0.136902
$874$	−59.1105	−1.99944
$875$	1.58039	0.0534268
$876$	30.7506	1.03897
$877$	52.0484	1.75755	0.878775	−	0.477237i	$-0.158362\pi$
$877$	52.0484	1.75755	0.878775	+	0.477237i	$0.158362\pi$
$878$	20.1604	0.680381
$879$	28.2249	0.952001
$880$	2.23736	0.0754215
$881$	18.4129	0.620345	0.310173	−	0.950680i	$-0.399613\pi$
$881$	18.4129	0.620345	0.310173	+	0.950680i	$0.399613\pi$
$882$	16.5894	0.558593
$883$	−36.3349	−1.22277	−0.611383	−	0.791335i	$-0.709386\pi$
$883$	−36.3349	−1.22277	−0.611383	+	0.791335i	$0.709386\pi$
$884$	−29.9680	−1.00793
$885$	−3.24111	−0.108949
$886$	−15.7294	−0.528439
$887$	14.8852	0.499797	0.249899	−	0.968272i	$-0.419603\pi$
$887$	14.8852	0.499797	0.249899	+	0.968272i	$0.419603\pi$
$888$	1.77186	0.0594596
$889$	−1.29309	−0.0433688
$890$	2.07337	0.0694995
$891$	1.60378	0.0537286
$892$	−86.4156	−2.89341
$893$	−44.1807	−1.47845
$894$	−56.5373	−1.89089
$895$	−13.3543	−0.446384
$896$	−6.62084	−0.221187
$897$	−16.2198	−0.541564
$898$	−11.7566	−0.392322
$899$	10.5166	0.350749
$900$	−17.9540	−0.598468
$901$	−15.4529	−0.514810
$902$	−25.2196	−0.839720
$903$	3.75498	0.124958
$904$	24.8426	0.826252
$905$	12.2002	0.405549
$906$	45.3402	1.50633
$907$	50.2562	1.66873	0.834364	−	0.551213i	$-0.185835\pi$
$907$	50.2562	1.66873	0.834364	+	0.551213i	$0.185835\pi$
$908$	−69.0669	−2.29207
$909$	−18.0917	−0.600065
$910$	1.19480	0.0396072
$911$	−1.60916	−0.0533139	−0.0266570	−	0.999645i	$-0.508486\pi$
$911$	−1.60916	−0.0533139	−0.0266570	+	0.999645i	$0.508486\pi$
$912$	−12.7868	−0.423413
$913$	−3.73339	−0.123557
$914$	−21.2732	−0.703654
$915$	1.78520	0.0590168
$916$	−67.3258	−2.22451
$917$	2.21281	0.0730734
$918$	6.21796	0.205223
$919$	51.9961	1.71519	0.857597	−	0.514322i	$-0.171956\pi$
$919$	51.9961	1.71519	0.857597	+	0.514322i	$0.171956\pi$
$920$	11.5106	0.379492
$921$	−20.0720	−0.661395
$922$	3.51600	0.115793
$923$	16.8203	0.553647
$924$	−1.94457	−0.0639718
$925$	1.95792	0.0643759
$926$	65.3406	2.14723
$927$	−8.98643	−0.295153
$928$	4.22050	0.138545
$929$	−43.0279	−1.41170	−0.705850	−	0.708361i	$-0.749435\pi$
$929$	−43.0279	−1.41170	−0.705850	+	0.708361i	$0.749435\pi$
$930$	−5.94302	−0.194879
$931$	32.0084	1.04903
$932$	29.8155	0.976639
$933$	−9.19778	−0.301122
$934$	−15.1254	−0.494920
$935$	−2.09921	−0.0686516
$936$	−13.1478	−0.429751
$937$	43.8607	1.43287	0.716434	−	0.697655i	$-0.245773\pi$
$937$	43.8607	1.43287	0.716434	+	0.697655i	$0.245773\pi$
$938$	−2.57224	−0.0839865
$939$	−23.2080	−0.757363
$940$	18.2436	0.595041
$941$	−3.14604	−0.102558	−0.0512791	−	0.998684i	$-0.516330\pi$
$941$	−3.14604	−0.102558	−0.0512791	+	0.998684i	$0.516330\pi$
$942$	20.6813	0.673832
$943$	−34.6247	−1.12753
$944$	−17.6387	−0.574090
$945$	−0.162196	−0.00527625
$946$	45.2133	1.47001
$947$	−7.30346	−0.237330	−0.118665	−	0.992934i	$-0.537862\pi$
$947$	−7.30346	−0.237330	−0.118665	+	0.992934i	$0.537862\pi$
$948$	−37.0298	−1.20267
$949$	24.8836	0.807755
$950$	−52.9467	−1.71782
$951$	1.58655	0.0514473
$952$	−3.55533	−0.115229
$953$	6.37426	0.206483	0.103241	−	0.994656i	$-0.467079\pi$
$953$	6.37426	0.206483	0.103241	+	0.994656i	$0.467079\pi$
$954$	−14.3765	−0.465457
$955$	−9.33820	−0.302177
$956$	102.374	3.31102
$957$	3.45597	0.111716
$958$	−72.2992	−2.33588
$959$	−0.694197	−0.0224168
$960$	−5.17515	−0.167027
$961$	−7.18215	−0.231682
$962$	3.04043	0.0980273
$963$	0.0453998	0.00146299
$964$	−53.6479	−1.72788
$965$	−2.59001	−0.0833754
$966$	−4.08053	−0.131289
$967$	−25.7047	−0.826607	−0.413304	−	0.910593i	$-0.635625\pi$
$967$	−25.7047	−0.826607	−0.413304	+	0.910593i	$0.635625\pi$
$968$	36.1798	1.16286
$969$	11.9972	0.385407
$970$	−4.92576	−0.158157
$971$	−6.47133	−0.207675	−0.103837	−	0.994594i	$-0.533112\pi$
$971$	−6.47133	−0.207675	−0.103837	+	0.994594i	$0.533112\pi$
$972$	3.78485	0.121399
$973$	−5.41615	−0.173634
$974$	89.1630	2.85697
$975$	−14.5285	−0.465284
$976$	9.71534	0.310980
$977$	27.8172	0.889952	0.444976	−	0.895543i	$-0.353212\pi$
$977$	27.8172	0.889952	0.444976	+	0.895543i	$0.353212\pi$
$978$	−1.70078	−0.0543849
$979$	−2.73065	−0.0872718
$980$	−13.2173	−0.422211
$981$	−11.9725	−0.382253
$982$	17.9476	0.572730
$983$	−27.0702	−0.863405	−0.431703	−	0.902016i	$-0.642087\pi$
$983$	−27.0702	−0.863405	−0.431703	+	0.902016i	$0.642087\pi$
$984$	−28.0669	−0.894739
$985$	3.73331	0.118953
$986$	13.3990	0.426712
$987$	−3.04989	−0.0970789
$988$	−53.7942	−1.71142
$989$	62.0747	1.97386
$990$	−1.95299	−0.0620702
$991$	−2.98951	−0.0949649	−0.0474825	−	0.998872i	$-0.515120\pi$
$991$	−2.98951	−0.0949649	−0.0474825	+	0.998872i	$0.515120\pi$
$992$	9.55851	0.303483
$993$	25.5490	0.810773
$994$	4.23159	0.134218
$995$	7.15796	0.226923
$996$	−8.81063	−0.279175
$997$	28.4347	0.900535	0.450267	−	0.892894i	$-0.351329\pi$
$997$	28.4347	0.900535	0.450267	+	0.892894i	$0.351329\pi$
$998$	53.0338	1.67876
$999$	−0.412744	−0.0130587

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.a.1.10	✓	95

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.a.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-2.40517 q^{2} +1.00000 q^{3} +3.78485 q^{4} +0.506302 q^{5} -2.40517 q^{6} -0.320355 q^{7} -4.29287 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.40517 q^{2} +1.00000 q^{3} +3.78485 q^{4} +0.506302 q^{5} -2.40517 q^{6} -0.320355 q^{7} -4.29287 q^{8} +1.00000 q^{9} -1.21774 q^{10} +1.60378 q^{11} +3.78485 q^{12} +3.06272 q^{13} +0.770508 q^{14} +0.506302 q^{15} +2.75538 q^{16} -2.58524 q^{17} -2.40517 q^{18} -4.64066 q^{19} +1.91628 q^{20} -0.320355 q^{21} -3.85737 q^{22} -5.29589 q^{23} -4.29287 q^{24} -4.74366 q^{25} -7.36637 q^{26} +1.00000 q^{27} -1.21249 q^{28} +2.15489 q^{29} -1.21774 q^{30} +4.88035 q^{31} +1.95857 q^{32} +1.60378 q^{33} +6.21796 q^{34} -0.162196 q^{35} +3.78485 q^{36} -0.412744 q^{37} +11.1616 q^{38} +3.06272 q^{39} -2.17349 q^{40} +6.53803 q^{41} +0.770508 q^{42} -11.7213 q^{43} +6.07006 q^{44} +0.506302 q^{45} +12.7375 q^{46} +9.52034 q^{47} +2.75538 q^{48} -6.89737 q^{49} +11.4093 q^{50} -2.58524 q^{51} +11.5919 q^{52} +5.97734 q^{53} -2.40517 q^{54} +0.811998 q^{55} +1.37524 q^{56} -4.64066 q^{57} -5.18288 q^{58} -6.40154 q^{59} +1.91628 q^{60} +3.52595 q^{61} -11.7381 q^{62} -0.320355 q^{63} -10.2215 q^{64} +1.55066 q^{65} -3.85737 q^{66} -3.33836 q^{67} -9.78476 q^{68} -5.29589 q^{69} +0.390110 q^{70} +5.49195 q^{71} -4.29287 q^{72} +8.12466 q^{73} +0.992721 q^{74} -4.74366 q^{75} -17.5642 q^{76} -0.513779 q^{77} -7.36637 q^{78} -9.78370 q^{79} +1.39506 q^{80} +1.00000 q^{81} -15.7251 q^{82} -2.32787 q^{83} -1.21249 q^{84} -1.30892 q^{85} +28.1917 q^{86} +2.15489 q^{87} -6.88481 q^{88} -1.70263 q^{89} -1.21774 q^{90} -0.981157 q^{91} -20.0441 q^{92} +4.88035 q^{93} -22.8980 q^{94} -2.34958 q^{95} +1.95857 q^{96} +4.04499 q^{97} +16.5894 q^{98} +1.60378 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 95 q - 9 q^{2} + 95 q^{3} + 65 q^{4} - 15 q^{5} - 9 q^{6} - 36 q^{7} - 27 q^{8} + 95 q^{9}+O(q^{10}) \) 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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