LMFDB - Embedded newform 8043.2.a.r.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$1$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.696464 q^{2} -1.00000 q^{3} -1.51494 q^{4} +1.11267 q^{5} +0.696464 q^{6} -1.00000 q^{7} +2.44803 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.696464 q^{2} -1.00000 q^{3} -1.51494 q^{4} +1.11267 q^{5} +0.696464 q^{6} -1.00000 q^{7} +2.44803 q^{8} +1.00000 q^{9} -0.774934 q^{10} -0.517817 q^{11} +1.51494 q^{12} +1.28800 q^{13} +0.696464 q^{14} -1.11267 q^{15} +1.32492 q^{16} +2.15443 q^{17} -0.696464 q^{18} +7.72841 q^{19} -1.68563 q^{20} +1.00000 q^{21} +0.360641 q^{22} +1.19809 q^{23} -2.44803 q^{24} -3.76197 q^{25} -0.897044 q^{26} -1.00000 q^{27} +1.51494 q^{28} -4.87233 q^{29} +0.774934 q^{30} -7.13189 q^{31} -5.81881 q^{32} +0.517817 q^{33} -1.50048 q^{34} -1.11267 q^{35} -1.51494 q^{36} -2.35077 q^{37} -5.38256 q^{38} -1.28800 q^{39} +2.72385 q^{40} -1.23960 q^{41} -0.696464 q^{42} -10.3349 q^{43} +0.784461 q^{44} +1.11267 q^{45} -0.834427 q^{46} +5.59120 q^{47} -1.32492 q^{48} +1.00000 q^{49} +2.62007 q^{50} -2.15443 q^{51} -1.95124 q^{52} -10.7367 q^{53} +0.696464 q^{54} -0.576160 q^{55} -2.44803 q^{56} -7.72841 q^{57} +3.39340 q^{58} +13.5172 q^{59} +1.68563 q^{60} -4.05097 q^{61} +4.96710 q^{62} -1.00000 q^{63} +1.40276 q^{64} +1.43312 q^{65} -0.360641 q^{66} -2.88644 q^{67} -3.26383 q^{68} -1.19809 q^{69} +0.774934 q^{70} -10.2865 q^{71} +2.44803 q^{72} +13.2213 q^{73} +1.63722 q^{74} +3.76197 q^{75} -11.7081 q^{76} +0.517817 q^{77} +0.897044 q^{78} +5.67647 q^{79} +1.47419 q^{80} +1.00000 q^{81} +0.863334 q^{82} -0.398539 q^{83} -1.51494 q^{84} +2.39717 q^{85} +7.19791 q^{86} +4.87233 q^{87} -1.26763 q^{88} +2.32090 q^{89} -0.774934 q^{90} -1.28800 q^{91} -1.81504 q^{92} +7.13189 q^{93} -3.89406 q^{94} +8.59917 q^{95} +5.81881 q^{96} +18.1281 q^{97} -0.696464 q^{98} -0.517817 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9	\( 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9} - 10 q^{10} + 31 q^{11} - 45 q^{12} - 32 q^{13} - 3 q^{14} + 9 q^{15} + 43 q^{16} - 36 q^{17} + 3 q^{18} - 13 q^{19} - 19 q^{20} + 46 q^{21} - 13 q^{22} + 24 q^{23} - 6 q^{24} + 35 q^{25} - 11 q^{26} - 46 q^{27} - 45 q^{28} + 11 q^{29} + 10 q^{30} - 23 q^{31} + 5 q^{32} - 31 q^{33} - 35 q^{34} + 9 q^{35} + 45 q^{36} - 37 q^{37} - 32 q^{38} + 32 q^{39} - 28 q^{40} - 27 q^{41} + 3 q^{42} - 7 q^{43} + 46 q^{44} - 9 q^{45} + 16 q^{46} - 18 q^{47} - 43 q^{48} + 46 q^{49} + 10 q^{50} + 36 q^{51} - 62 q^{52} - 62 q^{53} - 3 q^{54} - 28 q^{55} - 6 q^{56} + 13 q^{57} - 36 q^{58} - 3 q^{59} + 19 q^{60} - 31 q^{61} - 41 q^{62} - 46 q^{63} + 42 q^{64} + 2 q^{65} + 13 q^{66} - 9 q^{67} - 70 q^{68} - 24 q^{69} + 10 q^{70} + 77 q^{71} + 6 q^{72} - 38 q^{73} + 14 q^{74} - 35 q^{75} - 41 q^{76} - 31 q^{77} + 11 q^{78} + 8 q^{79} - 59 q^{80} + 46 q^{81} - 53 q^{82} - 38 q^{83} + 45 q^{84} - 26 q^{85} + 37 q^{86} - 11 q^{87} - 26 q^{88} - 39 q^{89} - 10 q^{90} + 32 q^{91} + 2 q^{92} + 23 q^{93} - 55 q^{94} + 35 q^{95} - 5 q^{96} - 61 q^{97} + 3 q^{98} + 31 q^{99}+O(q^{100}) \) 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9 - 10 * q^10 + 31 * q^11 - 45 * q^12 - 32 * q^13 - 3 * q^14 + 9 * q^15 + 43 * q^16 - 36 * q^17 + 3 * q^18 - 13 * q^19 - 19 * q^20 + 46 * q^21 - 13 * q^22 + 24 * q^23 - 6 * q^24 + 35 * q^25 - 11 * q^26 - 46 * q^27 - 45 * q^28 + 11 * q^29 + 10 * q^30 - 23 * q^31 + 5 * q^32 - 31 * q^33 - 35 * q^34 + 9 * q^35 + 45 * q^36 - 37 * q^37 - 32 * q^38 + 32 * q^39 - 28 * q^40 - 27 * q^41 + 3 * q^42 - 7 * q^43 + 46 * q^44 - 9 * q^45 + 16 * q^46 - 18 * q^47 - 43 * q^48 + 46 * q^49 + 10 * q^50 + 36 * q^51 - 62 * q^52 - 62 * q^53 - 3 * q^54 - 28 * q^55 - 6 * q^56 + 13 * q^57 - 36 * q^58 - 3 * q^59 + 19 * q^60 - 31 * q^61 - 41 * q^62 - 46 * q^63 + 42 * q^64 + 2 * q^65 + 13 * q^66 - 9 * q^67 - 70 * q^68 - 24 * q^69 + 10 * q^70 + 77 * q^71 + 6 * q^72 - 38 * q^73 + 14 * q^74 - 35 * q^75 - 41 * q^76 - 31 * q^77 + 11 * q^78 + 8 * q^79 - 59 * q^80 + 46 * q^81 - 53 * q^82 - 38 * q^83 + 45 * q^84 - 26 * q^85 + 37 * q^86 - 11 * q^87 - 26 * q^88 - 39 * q^89 - 10 * q^90 + 32 * q^91 + 2 * q^92 + 23 * q^93 - 55 * q^94 + 35 * q^95 - 5 * q^96 - 61 * q^97 + 3 * q^98 + 31 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.696464	−0.492474	−0.246237	−	0.969210i	$-0.579194\pi$
$2$	−0.696464	−0.492474	−0.246237	+	0.969210i	$0.579194\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.51494	−0.757469
$5$	1.11267	0.497601	0.248801	−	0.968555i	$-0.419964\pi$
$5$	1.11267	0.497601	0.248801	+	0.968555i	$0.419964\pi$
$6$	0.696464	0.284330
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.44803	0.865508
$9$	1.00000	0.333333
$10$	−0.774934	−0.245056
$11$	−0.517817	−0.156128	−0.0780639	−	0.996948i	$-0.524874\pi$
$11$	−0.517817	−0.156128	−0.0780639	+	0.996948i	$0.524874\pi$
$12$	1.51494	0.437325
$13$	1.28800	0.357226	0.178613	−	0.983919i	$-0.442839\pi$
$13$	1.28800	0.357226	0.178613	+	0.983919i	$0.442839\pi$
$14$	0.696464	0.186138
$15$	−1.11267	−0.287290
$16$	1.32492	0.331229
$17$	2.15443	0.522527	0.261263	−	0.965268i	$-0.415861\pi$
$17$	2.15443	0.522527	0.261263	+	0.965268i	$0.415861\pi$
$18$	−0.696464	−0.164158
$19$	7.72841	1.77302	0.886510	−	0.462710i	$-0.153123\pi$
$19$	7.72841	1.77302	0.886510	+	0.462710i	$0.153123\pi$
$20$	−1.68563	−0.376918
$21$	1.00000	0.218218
$22$	0.360641	0.0768889
$23$	1.19809	0.249819	0.124910	−	0.992168i	$-0.460136\pi$
$23$	1.19809	0.249819	0.124910	+	0.992168i	$0.460136\pi$
$24$	−2.44803	−0.499701
$25$	−3.76197	−0.752393
$26$	−0.897044	−0.175925
$27$	−1.00000	−0.192450
$28$	1.51494	0.286296
$29$	−4.87233	−0.904770	−0.452385	−	0.891823i	$-0.649427\pi$
$29$	−4.87233	−0.904770	−0.452385	+	0.891823i	$0.649427\pi$
$30$	0.774934	0.141483
$31$	−7.13189	−1.28093	−0.640463	−	0.767989i	$-0.721257\pi$
$31$	−7.13189	−1.28093	−0.640463	+	0.767989i	$0.721257\pi$
$32$	−5.81881	−1.02863
$33$	0.517817	0.0901404
$34$	−1.50048	−0.257331
$35$	−1.11267	−0.188076
$36$	−1.51494	−0.252490
$37$	−2.35077	−0.386464	−0.193232	−	0.981153i	$-0.561897\pi$
$37$	−2.35077	−0.386464	−0.193232	+	0.981153i	$0.561897\pi$
$38$	−5.38256	−0.873166
$39$	−1.28800	−0.206245
$40$	2.72385	0.430678
$41$	−1.23960	−0.193592	−0.0967962	−	0.995304i	$-0.530860\pi$
$41$	−1.23960	−0.193592	−0.0967962	+	0.995304i	$0.530860\pi$
$42$	−0.696464	−0.107467
$43$	−10.3349	−1.57606	−0.788032	−	0.615634i	$-0.788900\pi$
$43$	−10.3349	−1.57606	−0.788032	+	0.615634i	$0.788900\pi$
$44$	0.784461	0.118262
$45$	1.11267	0.165867
$46$	−0.834427	−0.123030
$47$	5.59120	0.815560	0.407780	−	0.913080i	$-0.366303\pi$
$47$	5.59120	0.815560	0.407780	+	0.913080i	$0.366303\pi$
$48$	−1.32492	−0.191235
$49$	1.00000	0.142857
$50$	2.62007	0.370534
$51$	−2.15443	−0.301681
$52$	−1.95124	−0.270588
$53$	−10.7367	−1.47480	−0.737398	−	0.675458i	$-0.763946\pi$
$53$	−10.7367	−1.47480	−0.737398	+	0.675458i	$0.763946\pi$
$54$	0.696464	0.0947767
$55$	−0.576160	−0.0776894
$56$	−2.44803	−0.327131
$57$	−7.72841	−1.02365
$58$	3.39340	0.445576
$59$	13.5172	1.75979	0.879895	−	0.475169i	$-0.157613\pi$
$59$	13.5172	1.75979	0.879895	+	0.475169i	$0.157613\pi$
$60$	1.68563	0.217613
$61$	−4.05097	−0.518674	−0.259337	−	0.965787i	$-0.583504\pi$
$61$	−4.05097	−0.518674	−0.259337	+	0.965787i	$0.583504\pi$
$62$	4.96710	0.630822
$63$	−1.00000	−0.125988
$64$	1.40276	0.175345
$65$	1.43312	0.177756
$66$	−0.360641	−0.0443918
$67$	−2.88644	−0.352635	−0.176317	−	0.984333i	$-0.556418\pi$
$67$	−2.88644	−0.352635	−0.176317	+	0.984333i	$0.556418\pi$
$68$	−3.26383	−0.395798
$69$	−1.19809	−0.144233
$70$	0.774934	0.0926223
$71$	−10.2865	−1.22078	−0.610391	−	0.792100i	$-0.708988\pi$
$71$	−10.2865	−1.22078	−0.610391	+	0.792100i	$0.708988\pi$
$72$	2.44803	0.288503
$73$	13.2213	1.54744	0.773721	−	0.633527i	$-0.218393\pi$
$73$	13.2213	1.54744	0.773721	+	0.633527i	$0.218393\pi$
$74$	1.63722	0.190324
$75$	3.76197	0.434394
$76$	−11.7081	−1.34301
$77$	0.517817	0.0590108
$78$	0.897044	0.101570
$79$	5.67647	0.638653	0.319326	−	0.947645i	$-0.396543\pi$
$79$	5.67647	0.638653	0.319326	+	0.947645i	$0.396543\pi$
$80$	1.47419	0.164820
$81$	1.00000	0.111111
$82$	0.863334	0.0953392
$83$	−0.398539	−0.0437453	−0.0218727	−	0.999761i	$-0.506963\pi$
$83$	−0.398539	−0.0437453	−0.0218727	+	0.999761i	$0.506963\pi$
$84$	−1.51494	−0.165293
$85$	2.39717	0.260010
$86$	7.19791	0.776171
$87$	4.87233	0.522369
$88$	−1.26763	−0.135130
$89$	2.32090	0.246015	0.123007	−	0.992406i	$-0.460746\pi$
$89$	2.32090	0.246015	0.123007	+	0.992406i	$0.460746\pi$
$90$	−0.774934	−0.0816852
$91$	−1.28800	−0.135019
$92$	−1.81504	−0.189231
$93$	7.13189	0.739542
$94$	−3.89406	−0.401642
$95$	8.59917	0.882256
$96$	5.81881	0.593880
$97$	18.1281	1.84063	0.920317	−	0.391173i	$-0.127931\pi$
$97$	18.1281	1.84063	0.920317	+	0.391173i	$0.127931\pi$
$98$	−0.696464	−0.0703534
$99$	−0.517817	−0.0520426
$100$	5.69915	0.569915
$101$	−8.35917	−0.831769	−0.415884	−	0.909417i	$-0.636528\pi$
$101$	−8.35917	−0.831769	−0.415884	+	0.909417i	$0.636528\pi$
$102$	1.50048	0.148570
$103$	4.51896	0.445267	0.222633	−	0.974902i	$-0.428535\pi$
$103$	4.51896	0.445267	0.222633	+	0.974902i	$0.428535\pi$
$104$	3.15305	0.309182
$105$	1.11267	0.108585
$106$	7.47771	0.726299
$107$	−3.54301	−0.342515	−0.171258	−	0.985226i	$-0.554783\pi$
$107$	−3.54301	−0.342515	−0.171258	+	0.985226i	$0.554783\pi$
$108$	1.51494	0.145775
$109$	9.00608	0.862626	0.431313	−	0.902202i	$-0.358050\pi$
$109$	9.00608	0.862626	0.431313	+	0.902202i	$0.358050\pi$
$110$	0.401274	0.0382600
$111$	2.35077	0.223125
$112$	−1.32492	−0.125193
$113$	−4.13340	−0.388838	−0.194419	−	0.980919i	$-0.562282\pi$
$113$	−4.13340	−0.388838	−0.194419	+	0.980919i	$0.562282\pi$
$114$	5.38256	0.504123
$115$	1.33308	0.124310
$116$	7.38129	0.685335
$117$	1.28800	0.119075
$118$	−9.41424	−0.866651
$119$	−2.15443	−0.197496
$120$	−2.72385	−0.248652
$121$	−10.7319	−0.975624
$122$	2.82135	0.255433
$123$	1.23960	0.111771
$124$	10.8044	0.970261
$125$	−9.74918	−0.871993
$126$	0.696464	0.0620459
$127$	−12.0436	−1.06870	−0.534349	−	0.845264i	$-0.679443\pi$
$127$	−12.0436	−1.06870	−0.534349	+	0.845264i	$0.679443\pi$
$128$	10.6606	0.942277
$129$	10.3349	0.909941
$130$	−0.998113	−0.0875403
$131$	−8.38519	−0.732618	−0.366309	−	0.930493i	$-0.619379\pi$
$131$	−8.38519	−0.732618	−0.366309	+	0.930493i	$0.619379\pi$
$132$	−0.784461	−0.0682786
$133$	−7.72841	−0.670138
$134$	2.01030	0.173663
$135$	−1.11267	−0.0957634
$136$	5.27411	0.452251
$137$	7.80087	0.666473	0.333237	−	0.942843i	$-0.391859\pi$
$137$	7.80087	0.666473	0.333237	+	0.942843i	$0.391859\pi$
$138$	0.834427	0.0710312
$139$	10.8346	0.918975	0.459488	−	0.888184i	$-0.348033\pi$
$139$	10.8346	0.918975	0.459488	+	0.888184i	$0.348033\pi$
$140$	1.68563	0.142461
$141$	−5.59120	−0.470864
$142$	7.16416	0.601203
$143$	−0.666948	−0.0557730
$144$	1.32492	0.110410
$145$	−5.42130	−0.450214
$146$	−9.20819	−0.762075
$147$	−1.00000	−0.0824786
$148$	3.56127	0.292735
$149$	9.43196	0.772696	0.386348	−	0.922353i	$-0.373736\pi$
$149$	9.43196	0.772696	0.386348	+	0.922353i	$0.373736\pi$
$150$	−2.62007	−0.213928
$151$	−6.95164	−0.565717	−0.282858	−	0.959162i	$-0.591283\pi$
$151$	−6.95164	−0.565717	−0.282858	+	0.959162i	$0.591283\pi$
$152$	18.9194	1.53456
$153$	2.15443	0.174176
$154$	−0.360641	−0.0290613
$155$	−7.93544	−0.637390
$156$	1.95124	0.156224
$157$	−13.5316	−1.07994	−0.539968	−	0.841685i	$-0.681564\pi$
$157$	−13.5316	−1.07994	−0.539968	+	0.841685i	$0.681564\pi$
$158$	−3.95345	−0.314520
$159$	10.7367	0.851474
$160$	−6.47441	−0.511847
$161$	−1.19809	−0.0944229
$162$	−0.696464	−0.0547193
$163$	−1.23630	−0.0968347	−0.0484173	−	0.998827i	$-0.515418\pi$
$163$	−1.23630	−0.0968347	−0.0484173	+	0.998827i	$0.515418\pi$
$164$	1.87791	0.146640
$165$	0.576160	0.0448540
$166$	0.277568	0.0215434
$167$	14.6736	1.13547	0.567737	−	0.823210i	$-0.307819\pi$
$167$	14.6736	1.13547	0.567737	+	0.823210i	$0.307819\pi$
$168$	2.44803	0.188869
$169$	−11.3411	−0.872389
$170$	−1.66954	−0.128048
$171$	7.72841	0.591006
$172$	15.6568	1.19382
$173$	4.62082	0.351314	0.175657	−	0.984451i	$-0.443795\pi$
$173$	4.62082	0.351314	0.175657	+	0.984451i	$0.443795\pi$
$174$	−3.39340	−0.257253
$175$	3.76197	0.284378
$176$	−0.686064	−0.0517140
$177$	−13.5172	−1.01601
$178$	−1.61642	−0.121156
$179$	7.07320	0.528676	0.264338	−	0.964430i	$-0.414847\pi$
$179$	7.07320	0.528676	0.264338	+	0.964430i	$0.414847\pi$
$180$	−1.68563	−0.125639
$181$	15.3647	1.14205	0.571025	−	0.820933i	$-0.306546\pi$
$181$	15.3647	1.14205	0.571025	+	0.820933i	$0.306546\pi$
$182$	0.897044	0.0664933
$183$	4.05097	0.299456
$184$	2.93296	0.216221
$185$	−2.61563	−0.192305
$186$	−4.96710	−0.364206
$187$	−1.11560	−0.0815809
$188$	−8.47032	−0.617762
$189$	1.00000	0.0727393
$190$	−5.98901	−0.434488
$191$	−2.82875	−0.204681	−0.102341	−	0.994749i	$-0.532633\pi$
$191$	−2.82875	−0.204681	−0.102341	+	0.994749i	$0.532633\pi$
$192$	−1.40276	−0.101235
$193$	13.0007	0.935814	0.467907	−	0.883778i	$-0.345008\pi$
$193$	13.0007	0.935814	0.467907	+	0.883778i	$0.345008\pi$
$194$	−12.6256	−0.906465
$195$	−1.43312	−0.102628
$196$	−1.51494	−0.108210
$197$	−22.5086	−1.60367	−0.801836	−	0.597545i	$-0.796143\pi$
$197$	−22.5086	−1.60367	−0.801836	+	0.597545i	$0.796143\pi$
$198$	0.360641	0.0256296
$199$	−13.5007	−0.957036	−0.478518	−	0.878078i	$-0.658826\pi$
$199$	−13.5007	−0.957036	−0.478518	+	0.878078i	$0.658826\pi$
$200$	−9.20939	−0.651202
$201$	2.88644	0.203594
$202$	5.82186	0.409625
$203$	4.87233	0.341971
$204$	3.26383	0.228514
$205$	−1.37926	−0.0963318
$206$	−3.14729	−0.219282
$207$	1.19809	0.0832732
$208$	1.70649	0.118324
$209$	−4.00191	−0.276818
$210$	−0.774934	−0.0534755
$211$	9.30714	0.640730	0.320365	−	0.947294i	$-0.396194\pi$
$211$	9.30714	0.640730	0.320365	+	0.947294i	$0.396194\pi$
$212$	16.2654	1.11711
$213$	10.2865	0.704819
$214$	2.46757	0.168680
$215$	−11.4994	−0.784251
$216$	−2.44803	−0.166567
$217$	7.13189	0.484144
$218$	−6.27241	−0.424821
$219$	−13.2213	−0.893416
$220$	0.872846	0.0588473
$221$	2.77490	0.186660
$222$	−1.63722	−0.109883
$223$	−15.9841	−1.07037	−0.535186	−	0.844734i	$-0.679759\pi$
$223$	−15.9841	−1.07037	−0.535186	+	0.844734i	$0.679759\pi$
$224$	5.81881	0.388786
$225$	−3.76197	−0.250798
$226$	2.87876	0.191492
$227$	−25.6410	−1.70185	−0.850926	−	0.525286i	$-0.823958\pi$
$227$	−25.6410	−1.70185	−0.850926	+	0.525286i	$0.823958\pi$
$228$	11.7081	0.775386
$229$	−5.23018	−0.345620	−0.172810	−	0.984955i	$-0.555285\pi$
$229$	−5.23018	−0.345620	−0.172810	+	0.984955i	$0.555285\pi$
$230$	−0.928442	−0.0612197
$231$	−0.517817	−0.0340699
$232$	−11.9276	−0.783085
$233$	−10.5768	−0.692907	−0.346454	−	0.938067i	$-0.612614\pi$
$233$	−10.5768	−0.692907	−0.346454	+	0.938067i	$0.612614\pi$
$234$	−0.897044	−0.0586416
$235$	6.22116	0.405824
$236$	−20.4777	−1.33299
$237$	−5.67647	−0.368726
$238$	1.50048	0.0972619
$239$	−22.1433	−1.43233	−0.716167	−	0.697929i	$-0.754105\pi$
$239$	−22.1433	−1.43233	−0.716167	+	0.697929i	$0.754105\pi$
$240$	−1.47419	−0.0951588
$241$	8.27401	0.532976	0.266488	−	0.963838i	$-0.414137\pi$
$241$	8.27401	0.532976	0.266488	+	0.963838i	$0.414137\pi$
$242$	7.47435	0.480470
$243$	−1.00000	−0.0641500
$244$	6.13697	0.392879
$245$	1.11267	0.0710859
$246$	−0.863334	−0.0550441
$247$	9.95418	0.633369
$248$	−17.4591	−1.10865
$249$	0.398539	0.0252564
$250$	6.78995	0.429434
$251$	−8.26858	−0.521908	−0.260954	−	0.965351i	$-0.584037\pi$
$251$	−8.26858	−0.521908	−0.260954	+	0.965351i	$0.584037\pi$
$252$	1.51494	0.0954322
$253$	−0.620393	−0.0390038
$254$	8.38794	0.526306
$255$	−2.39717	−0.150117
$256$	−10.2303	−0.639392
$257$	−12.2789	−0.765934	−0.382967	−	0.923762i	$-0.625098\pi$
$257$	−12.2789	−0.765934	−0.382967	+	0.923762i	$0.625098\pi$
$258$	−7.19791	−0.448122
$259$	2.35077	0.146070
$260$	−2.17108	−0.134645
$261$	−4.87233	−0.301590
$262$	5.83998	0.360795
$263$	−9.13225	−0.563119	−0.281559	−	0.959544i	$-0.590852\pi$
$263$	−9.13225	−0.563119	−0.281559	+	0.959544i	$0.590852\pi$
$264$	1.26763	0.0780173
$265$	−11.9464	−0.733860
$266$	5.38256	0.330026
$267$	−2.32090	−0.142037
$268$	4.37278	0.267110
$269$	10.5708	0.644514	0.322257	−	0.946652i	$-0.395558\pi$
$269$	10.5708	0.644514	0.322257	+	0.946652i	$0.395558\pi$
$270$	0.774934	0.0471610
$271$	8.79106	0.534019	0.267010	−	0.963694i	$-0.413964\pi$
$271$	8.79106	0.534019	0.267010	+	0.963694i	$0.413964\pi$
$272$	2.85444	0.173076
$273$	1.28800	0.0779532
$274$	−5.43302	−0.328221
$275$	1.94801	0.117469
$276$	1.81504	0.109252
$277$	−16.3758	−0.983929	−0.491964	−	0.870615i	$-0.663721\pi$
$277$	−16.3758	−0.983929	−0.491964	+	0.870615i	$0.663721\pi$
$278$	−7.54588	−0.452572
$279$	−7.13189	−0.426975
$280$	−2.72385	−0.162781
$281$	6.13822	0.366175	0.183088	−	0.983097i	$-0.441391\pi$
$281$	6.13822	0.366175	0.183088	+	0.983097i	$0.441391\pi$
$282$	3.89406	0.231888
$283$	−2.53453	−0.150662	−0.0753310	−	0.997159i	$-0.524001\pi$
$283$	−2.53453	−0.150662	−0.0753310	+	0.997159i	$0.524001\pi$
$284$	15.5834	0.924705
$285$	−8.59917	−0.509371
$286$	0.464505	0.0274667
$287$	1.23960	0.0731710
$288$	−5.81881	−0.342877
$289$	−12.3584	−0.726966
$290$	3.77574	0.221719
$291$	−18.1281	−1.06269
$292$	−20.0295	−1.17214
$293$	−9.71459	−0.567532	−0.283766	−	0.958894i	$-0.591584\pi$
$293$	−9.71459	−0.567532	−0.283766	+	0.958894i	$0.591584\pi$
$294$	0.696464	0.0406186
$295$	15.0402	0.875673
$296$	−5.75474	−0.334488
$297$	0.517817	0.0300468
$298$	−6.56902	−0.380533
$299$	1.54314	0.0892421
$300$	−5.69915	−0.329040
$301$	10.3349	0.595696
$302$	4.84157	0.278601
$303$	8.35917	0.480222
$304$	10.2395	0.587275
$305$	−4.50739	−0.258093
$306$	−1.50048	−0.0857769
$307$	30.4409	1.73736	0.868678	−	0.495377i	$-0.164970\pi$
$307$	30.4409	1.73736	0.868678	+	0.495377i	$0.164970\pi$
$308$	−0.784461	−0.0446988
$309$	−4.51896	−0.257075
$310$	5.52674	0.313898
$311$	32.5176	1.84390	0.921951	−	0.387306i	$-0.126594\pi$
$311$	32.5176	1.84390	0.921951	+	0.387306i	$0.126594\pi$
$312$	−3.15305	−0.178506
$313$	0.467236	0.0264097	0.0132049	−	0.999913i	$-0.495797\pi$
$313$	0.467236	0.0264097	0.0132049	+	0.999913i	$0.495797\pi$
$314$	9.42424	0.531841
$315$	−1.11267	−0.0626918
$316$	−8.59950	−0.483760
$317$	3.82777	0.214989	0.107494	−	0.994206i	$-0.465717\pi$
$317$	3.82777	0.214989	0.107494	+	0.994206i	$0.465717\pi$
$318$	−7.47771	−0.419329
$319$	2.52298	0.141260
$320$	1.56080	0.0872516
$321$	3.54301	0.197751
$322$	0.834427	0.0465008
$323$	16.6503	0.926450
$324$	−1.51494	−0.0841633
$325$	−4.84540	−0.268775
$326$	0.861039	0.0476886
$327$	−9.00608	−0.498037
$328$	−3.03456	−0.167556
$329$	−5.59120	−0.308253
$330$	−0.401274	−0.0220894
$331$	−16.6589	−0.915654	−0.457827	−	0.889041i	$-0.651372\pi$
$331$	−16.6589	−0.915654	−0.457827	+	0.889041i	$0.651372\pi$
$332$	0.603762	0.0331357
$333$	−2.35077	−0.128821
$334$	−10.2196	−0.559191
$335$	−3.21165	−0.175471
$336$	1.32492	0.0722801
$337$	25.9938	1.41597	0.707985	−	0.706227i	$-0.249604\pi$
$337$	25.9938	1.41597	0.707985	+	0.706227i	$0.249604\pi$
$338$	7.89864	0.429629
$339$	4.13340	0.224496
$340$	−3.63157	−0.196949
$341$	3.69302	0.199988
$342$	−5.38256	−0.291055
$343$	−1.00000	−0.0539949
$344$	−25.3002	−1.36410
$345$	−1.33308	−0.0717707
$346$	−3.21823	−0.173013
$347$	1.64036	0.0880589	0.0440294	−	0.999030i	$-0.485980\pi$
$347$	1.64036	0.0880589	0.0440294	+	0.999030i	$0.485980\pi$
$348$	−7.38129	−0.395678
$349$	−34.2428	−1.83298	−0.916489	−	0.400061i	$-0.868989\pi$
$349$	−34.2428	−1.83298	−0.916489	+	0.400061i	$0.868989\pi$
$350$	−2.62007	−0.140049
$351$	−1.28800	−0.0687482
$352$	3.01308	0.160598
$353$	13.2020	0.702669	0.351335	−	0.936250i	$-0.385728\pi$
$353$	13.2020	0.702669	0.351335	+	0.936250i	$0.385728\pi$
$354$	9.41424	0.500361
$355$	−11.4455	−0.607462
$356$	−3.51602	−0.186349
$357$	2.15443	0.114025
$358$	−4.92623	−0.260359
$359$	36.0540	1.90286	0.951428	−	0.307872i	$-0.0996168\pi$
$359$	36.0540	1.90286	0.951428	+	0.307872i	$0.0996168\pi$
$360$	2.72385	0.143559
$361$	40.7284	2.14360
$362$	−10.7010	−0.562430
$363$	10.7319	0.563277
$364$	1.95124	0.102273
$365$	14.7110	0.770009
$366$	−2.82135	−0.147474
$367$	−23.3681	−1.21981	−0.609904	−	0.792476i	$-0.708792\pi$
$367$	−23.3681	−1.21981	−0.609904	+	0.792476i	$0.708792\pi$
$368$	1.58737	0.0827474
$369$	−1.23960	−0.0645308
$370$	1.82169	0.0947052
$371$	10.7367	0.557421
$372$	−10.8044	−0.560181
$373$	−15.8900	−0.822751	−0.411376	−	0.911466i	$-0.634952\pi$
$373$	−15.8900	−0.822751	−0.411376	+	0.911466i	$0.634952\pi$
$374$	0.776976	0.0401765
$375$	9.74918	0.503445
$376$	13.6874	0.705874
$377$	−6.27556	−0.323208
$378$	−0.696464	−0.0358222
$379$	−3.44250	−0.176829	−0.0884146	−	0.996084i	$-0.528180\pi$
$379$	−3.44250	−0.176829	−0.0884146	+	0.996084i	$0.528180\pi$
$380$	−13.0272	−0.668282
$381$	12.0436	0.617014
$382$	1.97012	0.100800
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	−10.6606	−0.544024
$385$	0.576160	0.0293638
$386$	−9.05454	−0.460864
$387$	−10.3349	−0.525355
$388$	−27.4630	−1.39422
$389$	−25.6018	−1.29806	−0.649032	−	0.760761i	$-0.724826\pi$
$389$	−25.6018	−1.29806	−0.649032	+	0.760761i	$0.724826\pi$
$390$	0.998113	0.0505414
$391$	2.58121	0.130537
$392$	2.44803	0.123644
$393$	8.38519	0.422977
$394$	15.6764	0.789767
$395$	6.31604	0.317794
$396$	0.784461	0.0394207
$397$	−9.99072	−0.501420	−0.250710	−	0.968062i	$-0.580664\pi$
$397$	−9.99072	−0.501420	−0.250710	+	0.968062i	$0.580664\pi$
$398$	9.40272	0.471316
$399$	7.72841	0.386905
$400$	−4.98429	−0.249214
$401$	−16.3779	−0.817875	−0.408938	−	0.912562i	$-0.634101\pi$
$401$	−16.3779	−0.817875	−0.408938	+	0.912562i	$0.634101\pi$
$402$	−2.01030	−0.100265
$403$	−9.18586	−0.457580
$404$	12.6636	0.630039
$405$	1.11267	0.0552890
$406$	−3.39340	−0.168412
$407$	1.21727	0.0603378
$408$	−5.27411	−0.261107
$409$	1.28873	0.0637236	0.0318618	−	0.999492i	$-0.489856\pi$
$409$	1.28873	0.0637236	0.0318618	+	0.999492i	$0.489856\pi$
$410$	0.960605	0.0474409
$411$	−7.80087	−0.384789
$412$	−6.84595	−0.337276
$413$	−13.5172	−0.665138
$414$	−0.834427	−0.0410099
$415$	−0.443442	−0.0217677
$416$	−7.49461	−0.367454
$417$	−10.8346	−0.530571
$418$	2.78718	0.136325
$419$	35.3167	1.72533	0.862667	−	0.505773i	$-0.168793\pi$
$419$	35.3167	1.72533	0.862667	+	0.505773i	$0.168793\pi$
$420$	−1.68563	−0.0822502
$421$	27.7739	1.35362	0.676809	−	0.736158i	$-0.263362\pi$
$421$	27.7739	1.35362	0.676809	+	0.736158i	$0.263362\pi$
$422$	−6.48209	−0.315543
$423$	5.59120	0.271853
$424$	−26.2837	−1.27645
$425$	−8.10490	−0.393145
$426$	−7.16416	−0.347105
$427$	4.05097	0.196040
$428$	5.36744	0.259445
$429$	0.666948	0.0322005
$430$	8.00890	0.386223
$431$	33.9054	1.63316	0.816582	−	0.577229i	$-0.195866\pi$
$431$	33.9054	1.63316	0.816582	+	0.577229i	$0.195866\pi$
$432$	−1.32492	−0.0637450
$433$	12.1272	0.582795	0.291398	−	0.956602i	$-0.405880\pi$
$433$	12.1272	0.582795	0.291398	+	0.956602i	$0.405880\pi$
$434$	−4.96710	−0.238428
$435$	5.42130	0.259931
$436$	−13.6437	−0.653413
$437$	9.25935	0.442935
$438$	9.20819	0.439984
$439$	−41.6973	−1.99010	−0.995051	−	0.0993649i	$-0.968319\pi$
$439$	−41.6973	−1.99010	−0.995051	+	0.0993649i	$0.968319\pi$
$440$	−1.41045	−0.0672408
$441$	1.00000	0.0476190
$442$	−1.93262	−0.0919253
$443$	0.256802	0.0122010	0.00610051	−	0.999981i	$-0.498058\pi$
$443$	0.256802	0.0122010	0.00610051	+	0.999981i	$0.498058\pi$
$444$	−3.56127	−0.169010
$445$	2.58239	0.122417
$446$	11.1323	0.527131
$447$	−9.43196	−0.446116
$448$	−1.40276	−0.0662740
$449$	−41.0643	−1.93795	−0.968973	−	0.247167i	$-0.920500\pi$
$449$	−41.0643	−1.93795	−0.968973	+	0.247167i	$0.920500\pi$
$450$	2.62007	0.123511
$451$	0.641884	0.0302252
$452$	6.26185	0.294533
$453$	6.95164	0.326617
$454$	17.8580	0.838118
$455$	−1.43312	−0.0671855
$456$	−18.9194	−0.885980
$457$	−19.5370	−0.913903	−0.456951	−	0.889492i	$-0.651059\pi$
$457$	−19.5370	−0.913903	−0.456951	+	0.889492i	$0.651059\pi$
$458$	3.64263	0.170209
$459$	−2.15443	−0.100560
$460$	−2.01954	−0.0941613
$461$	−32.2152	−1.50041	−0.750206	−	0.661204i	$-0.770046\pi$
$461$	−32.2152	−1.50041	−0.750206	+	0.661204i	$0.770046\pi$
$462$	0.360641	0.0167785
$463$	−12.4328	−0.577801	−0.288901	−	0.957359i	$-0.593290\pi$
$463$	−12.4328	−0.577801	−0.288901	+	0.957359i	$0.593290\pi$
$464$	−6.45543	−0.299686
$465$	7.93544	0.367997
$466$	7.36633	0.341239
$467$	0.712744	0.0329818	0.0164909	−	0.999864i	$-0.494751\pi$
$467$	0.712744	0.0329818	0.0164909	+	0.999864i	$0.494751\pi$
$468$	−1.95124	−0.0901960
$469$	2.88644	0.133283
$470$	−4.33281	−0.199858
$471$	13.5316	0.623502
$472$	33.0905	1.52311
$473$	5.35161	0.246067
$474$	3.95345	0.181588
$475$	−29.0740	−1.33401
$476$	3.26383	0.149598
$477$	−10.7367	−0.491599
$478$	15.4220	0.705387
$479$	−13.8987	−0.635046	−0.317523	−	0.948251i	$-0.602851\pi$
$479$	−13.8987	−0.635046	−0.317523	+	0.948251i	$0.602851\pi$
$480$	6.47441	0.295515
$481$	−3.02779	−0.138055
$482$	−5.76255	−0.262477
$483$	1.19809	0.0545151
$484$	16.2581	0.739005
$485$	20.1706	0.915902
$486$	0.696464	0.0315922
$487$	−38.1800	−1.73010	−0.865051	−	0.501683i	$-0.832714\pi$
$487$	−38.1800	−1.73010	−0.865051	+	0.501683i	$0.832714\pi$
$488$	−9.91688	−0.448916
$489$	1.23630	0.0559075
$490$	−0.774934	−0.0350079
$491$	19.8907	0.897654	0.448827	−	0.893619i	$-0.351842\pi$
$491$	19.8907	0.897654	0.448827	+	0.893619i	$0.351842\pi$
$492$	−1.87791	−0.0846628
$493$	−10.4971	−0.472766
$494$	−6.93272	−0.311918
$495$	−0.576160	−0.0258965
$496$	−9.44915	−0.424280
$497$	10.2865	0.461412
$498$	−0.277568	−0.0124381
$499$	−14.1149	−0.631868	−0.315934	−	0.948781i	$-0.602318\pi$
$499$	−14.1149	−0.631868	−0.315934	+	0.948781i	$0.602318\pi$
$500$	14.7694	0.660508
$501$	−14.6736	−0.655566
$502$	5.75876	0.257026
$503$	9.67635	0.431447	0.215724	−	0.976454i	$-0.430789\pi$
$503$	9.67635	0.431447	0.215724	+	0.976454i	$0.430789\pi$
$504$	−2.44803	−0.109044
$505$	−9.30100	−0.413889
$506$	0.432081	0.0192083
$507$	11.3411	0.503674
$508$	18.2453	0.809506
$509$	10.0446	0.445218	0.222609	−	0.974908i	$-0.428543\pi$
$509$	10.0446	0.445218	0.222609	+	0.974908i	$0.428543\pi$
$510$	1.66954	0.0739286
$511$	−13.2213	−0.584878
$512$	−14.1963	−0.627393
$513$	−7.72841	−0.341218
$514$	8.55177	0.377203
$515$	5.02811	0.221565
$516$	−15.6568	−0.689252
$517$	−2.89522	−0.127332
$518$	−1.63722	−0.0719355
$519$	−4.62082	−0.202831
$520$	3.50831	0.153849
$521$	3.40722	0.149273	0.0746366	−	0.997211i	$-0.476220\pi$
$521$	3.40722	0.149273	0.0746366	+	0.997211i	$0.476220\pi$
$522$	3.39340	0.148525
$523$	−15.5946	−0.681905	−0.340953	−	0.940080i	$-0.610750\pi$
$523$	−15.5946	−0.681905	−0.340953	+	0.940080i	$0.610750\pi$
$524$	12.7031	0.554935
$525$	−3.76197	−0.164186
$526$	6.36028	0.277321
$527$	−15.3652	−0.669317
$528$	0.686064	0.0298571
$529$	−21.5646	−0.937590
$530$	8.32022	0.361407
$531$	13.5172	0.586596
$532$	11.7081	0.507609
$533$	−1.59660	−0.0691563
$534$	1.61642	0.0699494
$535$	−3.94220	−0.170436
$536$	−7.06608	−0.305208
$537$	−7.07320	−0.305231
$538$	−7.36219	−0.317406
$539$	−0.517817	−0.0223040
$540$	1.68563	0.0725378
$541$	−16.7657	−0.720812	−0.360406	−	0.932795i	$-0.617362\pi$
$541$	−16.7657	−0.720812	−0.360406	+	0.932795i	$0.617362\pi$
$542$	−6.12266	−0.262991
$543$	−15.3647	−0.659363
$544$	−12.5362	−0.537486
$545$	10.0208	0.429244
$546$	−0.897044	−0.0383899
$547$	−14.3443	−0.613320	−0.306660	−	0.951819i	$-0.599211\pi$
$547$	−14.3443	−0.613320	−0.306660	+	0.951819i	$0.599211\pi$
$548$	−11.8178	−0.504833
$549$	−4.05097	−0.172891
$550$	−1.35672	−0.0578507
$551$	−37.6554	−1.60417
$552$	−2.93296	−0.124835
$553$	−5.67647	−0.241388
$554$	11.4052	0.484560
$555$	2.61563	0.111027
$556$	−16.4137	−0.696096
$557$	−4.08744	−0.173190	−0.0865952	−	0.996244i	$-0.527599\pi$
$557$	−4.08744	−0.173190	−0.0865952	+	0.996244i	$0.527599\pi$
$558$	4.96710	0.210274
$559$	−13.3114	−0.563012
$560$	−1.47419	−0.0622961
$561$	1.11560	0.0471008
$562$	−4.27505	−0.180332
$563$	21.0760	0.888247	0.444124	−	0.895966i	$-0.353515\pi$
$563$	21.0760	0.888247	0.444124	+	0.895966i	$0.353515\pi$
$564$	8.47032	0.356665
$565$	−4.59911	−0.193486
$566$	1.76521	0.0741972
$567$	−1.00000	−0.0419961
$568$	−25.1816	−1.05660
$569$	−10.0431	−0.421029	−0.210514	−	0.977591i	$-0.567514\pi$
$569$	−10.0431	−0.421029	−0.210514	+	0.977591i	$0.567514\pi$
$570$	5.98901	0.250852
$571$	9.71102	0.406394	0.203197	−	0.979138i	$-0.434867\pi$
$571$	9.71102	0.406394	0.203197	+	0.979138i	$0.434867\pi$
$572$	1.01038	0.0422463
$573$	2.82875	0.118173
$574$	−0.863334	−0.0360348
$575$	−4.50718	−0.187962
$576$	1.40276	0.0584482
$577$	−10.1694	−0.423358	−0.211679	−	0.977339i	$-0.567893\pi$
$577$	−10.1694	−0.423358	−0.211679	+	0.977339i	$0.567893\pi$
$578$	8.60719	0.358012
$579$	−13.0007	−0.540292
$580$	8.21293	0.341024
$581$	0.398539	0.0165342
$582$	12.6256	0.523348
$583$	5.55964	0.230257
$584$	32.3662	1.33932
$585$	1.43312	0.0592521
$586$	6.76586	0.279495
$587$	37.9095	1.56469	0.782345	−	0.622845i	$-0.214023\pi$
$587$	37.9095	1.56469	0.782345	+	0.622845i	$0.214023\pi$
$588$	1.51494	0.0624750
$589$	−55.1182	−2.27111
$590$	−10.4749	−0.431246
$591$	22.5086	0.925880
$592$	−3.11457	−0.128008
$593$	10.7092	0.439772	0.219886	−	0.975526i	$-0.429431\pi$
$593$	10.7092	0.439772	0.219886	+	0.975526i	$0.429431\pi$
$594$	−0.360641	−0.0147973
$595$	−2.39717	−0.0982745
$596$	−14.2888	−0.585294
$597$	13.5007	0.552545
$598$	−1.07474	−0.0439494
$599$	−39.7452	−1.62395	−0.811973	−	0.583695i	$-0.801606\pi$
$599$	−39.7452	−1.62395	−0.811973	+	0.583695i	$0.801606\pi$
$600$	9.20939	0.375972
$601$	−29.3693	−1.19800	−0.599000	−	0.800749i	$-0.704435\pi$
$601$	−29.3693	−1.19800	−0.599000	+	0.800749i	$0.704435\pi$
$602$	−7.19791	−0.293365
$603$	−2.88644	−0.117545
$604$	10.5313	0.428513
$605$	−11.9410	−0.485472
$606$	−5.82186	−0.236497
$607$	2.52502	0.102487	0.0512436	−	0.998686i	$-0.483681\pi$
$607$	2.52502	0.102487	0.0512436	+	0.998686i	$0.483681\pi$
$608$	−44.9702	−1.82378
$609$	−4.87233	−0.197437
$610$	3.13923	0.127104
$611$	7.20145	0.291339
$612$	−3.26383	−0.131933
$613$	−47.7612	−1.92906	−0.964528	−	0.263980i	$-0.914965\pi$
$613$	−47.7612	−1.92906	−0.964528	+	0.263980i	$0.914965\pi$
$614$	−21.2010	−0.855603
$615$	1.37926	0.0556172
$616$	1.26763	0.0510743
$617$	−27.6173	−1.11183	−0.555915	−	0.831239i	$-0.687632\pi$
$617$	−27.6173	−1.11183	−0.555915	+	0.831239i	$0.687632\pi$
$618$	3.14729	0.126603
$619$	−25.2287	−1.01403	−0.507013	−	0.861939i	$-0.669250\pi$
$619$	−25.2287	−1.01403	−0.507013	+	0.861939i	$0.669250\pi$
$620$	12.0217	0.482803
$621$	−1.19809	−0.0480778
$622$	−22.6473	−0.908074
$623$	−2.32090	−0.0929849
$624$	−1.70649	−0.0683142
$625$	7.96221	0.318489
$626$	−0.325413	−0.0130061
$627$	4.00191	0.159821
$628$	20.4995	0.818019
$629$	−5.06457	−0.201938
$630$	0.774934	0.0308741
$631$	−4.03392	−0.160588	−0.0802938	−	0.996771i	$-0.525586\pi$
$631$	−4.03392	−0.160588	−0.0802938	+	0.996771i	$0.525586\pi$
$632$	13.8961	0.552759
$633$	−9.30714	−0.369926
$634$	−2.66590	−0.105876
$635$	−13.4006	−0.531786
$636$	−16.2654	−0.644965
$637$	1.28800	0.0510323
$638$	−1.75716	−0.0695667
$639$	−10.2865	−0.406927
$640$	11.8618	0.468878
$641$	38.5692	1.52339	0.761696	−	0.647934i	$-0.224367\pi$
$641$	38.5692	1.52339	0.761696	+	0.647934i	$0.224367\pi$
$642$	−2.46757	−0.0973874
$643$	14.5992	0.575736	0.287868	−	0.957670i	$-0.407054\pi$
$643$	14.5992	0.575736	0.287868	+	0.957670i	$0.407054\pi$
$644$	1.81504	0.0715224
$645$	11.4994	0.452788
$646$	−11.5964	−0.456252
$647$	24.1653	0.950036	0.475018	−	0.879976i	$-0.342442\pi$
$647$	24.1653	0.950036	0.475018	+	0.879976i	$0.342442\pi$
$648$	2.44803	0.0961676
$649$	−6.99944	−0.274752
$650$	3.37465	0.132365
$651$	−7.13189	−0.279521
$652$	1.87292	0.0733493
$653$	−17.8175	−0.697251	−0.348626	−	0.937262i	$-0.613351\pi$
$653$	−17.8175	−0.697251	−0.348626	+	0.937262i	$0.613351\pi$
$654$	6.27241	0.245271
$655$	−9.32995	−0.364551
$656$	−1.64236	−0.0641234
$657$	13.2213	0.515814
$658$	3.89406	0.151806
$659$	17.8831	0.696627	0.348313	−	0.937378i	$-0.386754\pi$
$659$	17.8831	0.696627	0.348313	+	0.937378i	$0.386754\pi$
$660$	−0.872846	−0.0339755
$661$	−32.6775	−1.27101	−0.635504	−	0.772098i	$-0.719208\pi$
$661$	−32.6775	−1.27101	−0.635504	+	0.772098i	$0.719208\pi$
$662$	11.6023	0.450936
$663$	−2.77490	−0.107768
$664$	−0.975633	−0.0378619
$665$	−8.59917	−0.333462
$666$	1.63722	0.0634412
$667$	−5.83750	−0.226029
$668$	−22.2295	−0.860086
$669$	15.9841	0.617980
$670$	2.23680	0.0864151
$671$	2.09766	0.0809793
$672$	−5.81881	−0.224465
$673$	−37.7199	−1.45400	−0.726998	−	0.686639i	$-0.759085\pi$
$673$	−37.7199	−1.45400	−0.726998	+	0.686639i	$0.759085\pi$
$674$	−18.1037	−0.697329
$675$	3.76197	0.144798
$676$	17.1810	0.660808
$677$	0.409744	0.0157477	0.00787387	−	0.999969i	$-0.497494\pi$
$677$	0.409744	0.0157477	0.00787387	+	0.999969i	$0.497494\pi$
$678$	−2.87876	−0.110558
$679$	−18.1281	−0.695694
$680$	5.86834	0.225041
$681$	25.6410	0.982564
$682$	−2.57205	−0.0984889
$683$	25.6524	0.981561	0.490781	−	0.871283i	$-0.336712\pi$
$683$	25.6524	0.981561	0.490781	+	0.871283i	$0.336712\pi$
$684$	−11.7081	−0.447669
$685$	8.67979	0.331638
$686$	0.696464	0.0265911
$687$	5.23018	0.199544
$688$	−13.6929	−0.522038
$689$	−13.8288	−0.526836
$690$	0.928442	0.0353452
$691$	−17.5424	−0.667344	−0.333672	−	0.942689i	$-0.608288\pi$
$691$	−17.5424	−0.667344	−0.333672	+	0.942689i	$0.608288\pi$
$692$	−7.00026	−0.266110
$693$	0.517817	0.0196703
$694$	−1.14245	−0.0433667
$695$	12.0553	0.457283
$696$	11.9276	0.452115
$697$	−2.67063	−0.101157
$698$	23.8489	0.902694
$699$	10.5768	0.400050
$700$	−5.69915	−0.215408
$701$	−1.67619	−0.0633087	−0.0316544	−	0.999499i	$-0.510078\pi$
$701$	−1.67619	−0.0633087	−0.0316544	+	0.999499i	$0.510078\pi$
$702$	0.897044	0.0338567
$703$	−18.1677	−0.685208
$704$	−0.726371	−0.0273762
$705$	−6.22116	−0.234302
$706$	−9.19468	−0.346046
$707$	8.35917	0.314379
$708$	20.4777	0.769600
$709$	−3.68482	−0.138386	−0.0691932	−	0.997603i	$-0.522042\pi$
$709$	−3.68482	−0.138386	−0.0691932	+	0.997603i	$0.522042\pi$
$710$	7.97135	0.299159
$711$	5.67647	0.212884
$712$	5.68162	0.212928
$713$	−8.54466	−0.320000
$714$	−1.50048	−0.0561542
$715$	−0.742092	−0.0277527
$716$	−10.7155	−0.400456
$717$	22.1433	0.826958
$718$	−25.1103	−0.937107
$719$	0.969285	0.0361482	0.0180741	−	0.999837i	$-0.494247\pi$
$719$	0.969285	0.0361482	0.0180741	+	0.999837i	$0.494247\pi$
$720$	1.47419	0.0549400
$721$	−4.51896	−0.168295
$722$	−28.3658	−1.05567
$723$	−8.27401	−0.307714
$724$	−23.2766	−0.865068
$725$	18.3296	0.680742
$726$	−7.47435	−0.277399
$727$	7.27097	0.269665	0.134833	−	0.990868i	$-0.456950\pi$
$727$	7.27097	0.269665	0.134833	+	0.990868i	$0.456950\pi$
$728$	−3.15305	−0.116860
$729$	1.00000	0.0370370
$730$	−10.2457	−0.379209
$731$	−22.2659	−0.823535
$732$	−6.13697	−0.226829
$733$	−25.9520	−0.958558	−0.479279	−	0.877663i	$-0.659102\pi$
$733$	−25.9520	−0.958558	−0.479279	+	0.877663i	$0.659102\pi$
$734$	16.2751	0.600723
$735$	−1.11267	−0.0410414
$736$	−6.97147	−0.256972
$737$	1.49465	0.0550561
$738$	0.863334	0.0317797
$739$	22.7083	0.835339	0.417670	−	0.908599i	$-0.362847\pi$
$739$	22.7083	0.835339	0.417670	+	0.908599i	$0.362847\pi$
$740$	3.96252	0.145665
$741$	−9.95418	−0.365676
$742$	−7.47771	−0.274515
$743$	−12.2150	−0.448124	−0.224062	−	0.974575i	$-0.571932\pi$
$743$	−12.2150	−0.448124	−0.224062	+	0.974575i	$0.571932\pi$
$744$	17.4591	0.640080
$745$	10.4947	0.384495
$746$	11.0668	0.405184
$747$	−0.398539	−0.0145818
$748$	1.69007	0.0617950
$749$	3.54301	0.129459
$750$	−6.78995	−0.247934
$751$	45.7940	1.67105	0.835524	−	0.549455i	$-0.185164\pi$
$751$	45.7940	1.67105	0.835524	+	0.549455i	$0.185164\pi$
$752$	7.40787	0.270137
$753$	8.26858	0.301324
$754$	4.37070	0.159171
$755$	−7.73488	−0.281501
$756$	−1.51494	−0.0550978
$757$	−2.06741	−0.0751412	−0.0375706	−	0.999294i	$-0.511962\pi$
$757$	−2.06741	−0.0751412	−0.0375706	+	0.999294i	$0.511962\pi$
$758$	2.39757	0.0870838
$759$	0.620393	0.0225188
$760$	21.0510	0.763600
$761$	31.6529	1.14742	0.573709	−	0.819059i	$-0.305504\pi$
$761$	31.6529	1.14742	0.573709	+	0.819059i	$0.305504\pi$
$762$	−8.38794	−0.303863
$763$	−9.00608	−0.326042
$764$	4.28538	0.155040
$765$	2.39717	0.0866699
$766$	0.696464	0.0251643
$767$	17.4101	0.628643
$768$	10.2303	0.369153
$769$	−38.7556	−1.39756	−0.698781	−	0.715336i	$-0.746274\pi$
$769$	−38.7556	−1.39756	−0.698781	+	0.715336i	$0.746274\pi$
$770$	−0.401274	−0.0144609
$771$	12.2789	0.442212
$772$	−19.6953	−0.708850
$773$	−27.4444	−0.987106	−0.493553	−	0.869716i	$-0.664302\pi$
$773$	−27.4444	−0.987106	−0.493553	+	0.869716i	$0.664302\pi$
$774$	7.19791	0.258724
$775$	26.8299	0.963759
$776$	44.3782	1.59308
$777$	−2.35077	−0.0843334
$778$	17.8307	0.639263
$779$	−9.58011	−0.343243
$780$	2.17108	0.0777373
$781$	5.32652	0.190598
$782$	−1.79772	−0.0642862
$783$	4.87233	0.174123
$784$	1.32492	0.0473184
$785$	−15.0562	−0.537377
$786$	−5.83998	−0.208305
$787$	−2.82977	−0.100870	−0.0504352	−	0.998727i	$-0.516061\pi$
$787$	−2.82977	−0.100870	−0.0504352	+	0.998727i	$0.516061\pi$
$788$	34.0991	1.21473
$789$	9.13225	0.325117
$790$	−4.39889	−0.156505
$791$	4.13340	0.146967
$792$	−1.26763	−0.0450433
$793$	−5.21764	−0.185284
$794$	6.95817	0.246936
$795$	11.9464	0.423694
$796$	20.4527	0.724926
$797$	−11.2596	−0.398834	−0.199417	−	0.979915i	$-0.563905\pi$
$797$	−11.2596	−0.398834	−0.199417	+	0.979915i	$0.563905\pi$
$798$	−5.38256	−0.190540
$799$	12.0459	0.426152
$800$	21.8902	0.773934
$801$	2.32090	0.0820049
$802$	11.4066	0.402782
$803$	−6.84624	−0.241599
$804$	−4.37278	−0.154216
$805$	−1.33308	−0.0469849
$806$	6.39762	0.225346
$807$	−10.5708	−0.372110
$808$	−20.4635	−0.719903
$809$	−2.47152	−0.0868940	−0.0434470	−	0.999056i	$-0.513834\pi$
$809$	−2.47152	−0.0868940	−0.0434470	+	0.999056i	$0.513834\pi$
$810$	−0.774934	−0.0272284
$811$	−0.973888	−0.0341978	−0.0170989	−	0.999854i	$-0.505443\pi$
$811$	−0.973888	−0.0341978	−0.0170989	+	0.999854i	$0.505443\pi$
$812$	−7.38129	−0.259032
$813$	−8.79106	−0.308316
$814$	−0.847783	−0.0297148
$815$	−1.37560	−0.0481850
$816$	−2.85444	−0.0999254
$817$	−79.8727	−2.79439
$818$	−0.897554	−0.0313822
$819$	−1.28800	−0.0450063
$820$	2.08950	0.0729684
$821$	1.74280	0.0608241	0.0304121	−	0.999537i	$-0.490318\pi$
$821$	1.74280	0.0608241	0.0304121	+	0.999537i	$0.490318\pi$
$822$	5.43302	0.189498
$823$	44.5926	1.55440	0.777200	−	0.629253i	$-0.216639\pi$
$823$	44.5926	1.55440	0.777200	+	0.629253i	$0.216639\pi$
$824$	11.0625	0.385382
$825$	−1.94801	−0.0678210
$826$	9.41424	0.327563
$827$	−49.5809	−1.72410	−0.862048	−	0.506826i	$-0.830819\pi$
$827$	−49.5809	−1.72410	−0.862048	+	0.506826i	$0.830819\pi$
$828$	−1.81504	−0.0630769
$829$	−50.1490	−1.74175	−0.870873	−	0.491508i	$-0.836446\pi$
$829$	−50.1490	−1.74175	−0.870873	+	0.491508i	$0.836446\pi$
$830$	0.308841	0.0107200
$831$	16.3758	0.568072
$832$	1.80675	0.0626377
$833$	2.15443	0.0746467
$834$	7.54588	0.261292
$835$	16.3268	0.565013
$836$	6.06264	0.209681
$837$	7.13189	0.246514
$838$	−24.5968	−0.849682
$839$	−35.5999	−1.22904	−0.614522	−	0.788900i	$-0.710651\pi$
$839$	−35.5999	−1.22904	−0.614522	+	0.788900i	$0.710651\pi$
$840$	2.72385	0.0939816
$841$	−5.26037	−0.181392
$842$	−19.3435	−0.666622
$843$	−6.13822	−0.211411
$844$	−14.0998	−0.485333
$845$	−12.6189	−0.434102
$846$	−3.89406	−0.133881
$847$	10.7319	0.368751
$848$	−14.2252	−0.488495
$849$	2.53453	0.0869848
$850$	5.64477	0.193614
$851$	−2.81644	−0.0965462
$852$	−15.5834	−0.533878
$853$	−26.9584	−0.923038	−0.461519	−	0.887130i	$-0.652695\pi$
$853$	−26.9584	−0.923038	−0.461519	+	0.887130i	$0.652695\pi$
$854$	−2.82135	−0.0965447
$855$	8.59917	0.294085
$856$	−8.67337	−0.296450
$857$	24.3689	0.832426	0.416213	−	0.909267i	$-0.363357\pi$
$857$	24.3689	0.832426	0.416213	+	0.909267i	$0.363357\pi$
$858$	−0.464505	−0.0158579
$859$	2.39413	0.0816865	0.0408432	−	0.999166i	$-0.486996\pi$
$859$	2.39413	0.0816865	0.0408432	+	0.999166i	$0.486996\pi$
$860$	17.4209	0.594046
$861$	−1.23960	−0.0422453
$862$	−23.6139	−0.804291
$863$	−4.87626	−0.165990	−0.0829950	−	0.996550i	$-0.526449\pi$
$863$	−4.87626	−0.165990	−0.0829950	+	0.996550i	$0.526449\pi$
$864$	5.81881	0.197960
$865$	5.14145	0.174814
$866$	−8.44614	−0.287012
$867$	12.3584	0.419714
$868$	−10.8044	−0.366724
$869$	−2.93937	−0.0997114
$870$	−3.77574	−0.128009
$871$	−3.71773	−0.125970
$872$	22.0471	0.746610
$873$	18.1281	0.613545
$874$	−6.44880	−0.218134
$875$	9.74918	0.329582
$876$	20.0295	0.676735
$877$	−12.0049	−0.405375	−0.202688	−	0.979243i	$-0.564968\pi$
$877$	−12.0049	−0.405375	−0.202688	+	0.979243i	$0.564968\pi$
$878$	29.0406	0.980074
$879$	9.71459	0.327665
$880$	−0.763363	−0.0257330
$881$	−24.2447	−0.816824	−0.408412	−	0.912798i	$-0.633917\pi$
$881$	−24.2447	−0.816824	−0.408412	+	0.912798i	$0.633917\pi$
$882$	−0.696464	−0.0234511
$883$	−19.3749	−0.652018	−0.326009	−	0.945367i	$-0.605704\pi$
$883$	−19.3749	−0.652018	−0.326009	+	0.945367i	$0.605704\pi$
$884$	−4.20381	−0.141389
$885$	−15.0402	−0.505570
$886$	−0.178853	−0.00600868
$887$	7.98138	0.267988	0.133994	−	0.990982i	$-0.457220\pi$
$887$	7.98138	0.267988	0.133994	+	0.990982i	$0.457220\pi$
$888$	5.75474	0.193117
$889$	12.0436	0.403930
$890$	−1.79854	−0.0602873
$891$	−0.517817	−0.0173475
$892$	24.2149	0.810774
$893$	43.2111	1.44600
$894$	6.56902	0.219701
$895$	7.87014	0.263070
$896$	−10.6606	−0.356147
$897$	−1.54314	−0.0515239
$898$	28.5998	0.954388
$899$	34.7489	1.15894
$900$	5.69915	0.189972
$901$	−23.1315	−0.770620
$902$	−0.447049	−0.0148851
$903$	−10.3349	−0.343925
$904$	−10.1187	−0.336542
$905$	17.0958	0.568285
$906$	−4.84157	−0.160850
$907$	−14.0444	−0.466338	−0.233169	−	0.972436i	$-0.574910\pi$
$907$	−14.0444	−0.466338	−0.233169	+	0.972436i	$0.574910\pi$
$908$	38.8445	1.28910
$909$	−8.35917	−0.277256
$910$	0.998113	0.0330871
$911$	23.6337	0.783019	0.391509	−	0.920174i	$-0.371953\pi$
$911$	23.6337	0.783019	0.391509	+	0.920174i	$0.371953\pi$
$912$	−10.2395	−0.339064
$913$	0.206370	0.00682986
$914$	13.6068	0.450073
$915$	4.50739	0.149010
$916$	7.92340	0.261796
$917$	8.38519	0.276904
$918$	1.50048	0.0495233
$919$	48.9041	1.61320	0.806599	−	0.591099i	$-0.201306\pi$
$919$	48.9041	1.61320	0.806599	+	0.591099i	$0.201306\pi$
$920$	3.26342	0.107592
$921$	−30.4409	−1.00306
$922$	22.4367	0.738914
$923$	−13.2490	−0.436095
$924$	0.784461	0.0258069
$925$	8.84351	0.290773
$926$	8.65899	0.284552
$927$	4.51896	0.148422
$928$	28.3512	0.930673
$929$	−27.0538	−0.887606	−0.443803	−	0.896124i	$-0.646371\pi$
$929$	−27.0538	−0.887606	−0.443803	+	0.896124i	$0.646371\pi$
$930$	−5.52674	−0.181229
$931$	7.72841	0.253288
$932$	16.0232	0.524856
$933$	−32.5176	−1.06458
$934$	−0.496400	−0.0162427
$935$	−1.24130	−0.0405948
$936$	3.15305	0.103061
$937$	60.6169	1.98027	0.990135	−	0.140119i	$-0.0447484\pi$
$937$	60.6169	1.98027	0.990135	+	0.140119i	$0.0447484\pi$
$938$	−2.01030	−0.0656386
$939$	−0.467236	−0.0152477
$940$	−9.42467	−0.307399
$941$	6.41093	0.208990	0.104495	−	0.994525i	$-0.466677\pi$
$941$	6.41093	0.208990	0.104495	+	0.994525i	$0.466677\pi$
$942$	−9.42424	−0.307058
$943$	−1.48515	−0.0483631
$944$	17.9091	0.582893
$945$	1.11267	0.0361952
$946$	−3.72720	−0.121182
$947$	25.2657	0.821025	0.410513	−	0.911855i	$-0.365350\pi$
$947$	25.2657	0.821025	0.410513	+	0.911855i	$0.365350\pi$
$948$	8.59950	0.279299
$949$	17.0291	0.552787
$950$	20.2490	0.656964
$951$	−3.82777	−0.124124
$952$	−5.27411	−0.170935
$953$	−21.8194	−0.706801	−0.353401	−	0.935472i	$-0.614975\pi$
$953$	−21.8194	−0.706801	−0.353401	+	0.935472i	$0.614975\pi$
$954$	7.47771	0.242100
$955$	−3.14747	−0.101850
$956$	33.5458	1.08495
$957$	−2.52298	−0.0815563
$958$	9.67991	0.312744
$959$	−7.80087	−0.251903
$960$	−1.56080	−0.0503748
$961$	19.8638	0.640769
$962$	2.10874	0.0679886
$963$	−3.54301	−0.114172
$964$	−12.5346	−0.403713
$965$	14.4655	0.465662
$966$	−0.834427	−0.0268473
$967$	−12.6496	−0.406784	−0.203392	−	0.979097i	$-0.565197\pi$
$967$	−12.6496	−0.406784	−0.203392	+	0.979097i	$0.565197\pi$
$968$	−26.2719	−0.844411
$969$	−16.6503	−0.534886
$970$	−14.0481	−0.451058
$971$	−23.3844	−0.750443	−0.375221	−	0.926935i	$-0.622433\pi$
$971$	−23.3844	−0.750443	−0.375221	+	0.926935i	$0.622433\pi$
$972$	1.51494	0.0485917
$973$	−10.8346	−0.347340
$974$	26.5910	0.852031
$975$	4.84540	0.155177
$976$	−5.36719	−0.171800
$977$	−25.1876	−0.805823	−0.402912	−	0.915239i	$-0.632002\pi$
$977$	−25.1876	−0.805823	−0.402912	+	0.915239i	$0.632002\pi$
$978$	−0.861039	−0.0275330
$979$	−1.20180	−0.0384097
$980$	−1.68563	−0.0538454
$981$	9.00608	0.287542
$982$	−13.8531	−0.442072
$983$	2.05536	0.0655558	0.0327779	−	0.999463i	$-0.489565\pi$
$983$	2.05536	0.0655558	0.0327779	+	0.999463i	$0.489565\pi$
$984$	3.03456	0.0967384
$985$	−25.0446	−0.797989
$986$	7.31086	0.232825
$987$	5.59120	0.177970
$988$	−15.0800	−0.479758
$989$	−12.3822	−0.393731
$990$	0.401274	0.0127533
$991$	−41.7710	−1.32690	−0.663451	−	0.748220i	$-0.730909\pi$
$991$	−41.7710	−1.32690	−0.663451	+	0.748220i	$0.730909\pi$
$992$	41.4991	1.31760
$993$	16.6589	0.528653
$994$	−7.16416	−0.227233
$995$	−15.0218	−0.476222
$996$	−0.603762	−0.0191309
$997$	17.1640	0.543588	0.271794	−	0.962355i	$-0.412383\pi$
$997$	17.1640	0.543588	0.271794	+	0.962355i	$0.412383\pi$
$998$	9.83048	0.311179
$999$	2.35077	0.0743750

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.r.1.17	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.r.1.17	✓	46	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-0.696464 q^{2} -1.00000 q^{3} -1.51494 q^{4} +1.11267 q^{5} +0.696464 q^{6} -1.00000 q^{7} +2.44803 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.696464 q^{2} -1.00000 q^{3} -1.51494 q^{4} +1.11267 q^{5} +0.696464 q^{6} -1.00000 q^{7} +2.44803 q^{8} +1.00000 q^{9} -0.774934 q^{10} -0.517817 q^{11} +1.51494 q^{12} +1.28800 q^{13} +0.696464 q^{14} -1.11267 q^{15} +1.32492 q^{16} +2.15443 q^{17} -0.696464 q^{18} +7.72841 q^{19} -1.68563 q^{20} +1.00000 q^{21} +0.360641 q^{22} +1.19809 q^{23} -2.44803 q^{24} -3.76197 q^{25} -0.897044 q^{26} -1.00000 q^{27} +1.51494 q^{28} -4.87233 q^{29} +0.774934 q^{30} -7.13189 q^{31} -5.81881 q^{32} +0.517817 q^{33} -1.50048 q^{34} -1.11267 q^{35} -1.51494 q^{36} -2.35077 q^{37} -5.38256 q^{38} -1.28800 q^{39} +2.72385 q^{40} -1.23960 q^{41} -0.696464 q^{42} -10.3349 q^{43} +0.784461 q^{44} +1.11267 q^{45} -0.834427 q^{46} +5.59120 q^{47} -1.32492 q^{48} +1.00000 q^{49} +2.62007 q^{50} -2.15443 q^{51} -1.95124 q^{52} -10.7367 q^{53} +0.696464 q^{54} -0.576160 q^{55} -2.44803 q^{56} -7.72841 q^{57} +3.39340 q^{58} +13.5172 q^{59} +1.68563 q^{60} -4.05097 q^{61} +4.96710 q^{62} -1.00000 q^{63} +1.40276 q^{64} +1.43312 q^{65} -0.360641 q^{66} -2.88644 q^{67} -3.26383 q^{68} -1.19809 q^{69} +0.774934 q^{70} -10.2865 q^{71} +2.44803 q^{72} +13.2213 q^{73} +1.63722 q^{74} +3.76197 q^{75} -11.7081 q^{76} +0.517817 q^{77} +0.897044 q^{78} +5.67647 q^{79} +1.47419 q^{80} +1.00000 q^{81} +0.863334 q^{82} -0.398539 q^{83} -1.51494 q^{84} +2.39717 q^{85} +7.19791 q^{86} +4.87233 q^{87} -1.26763 q^{88} +2.32090 q^{89} -0.774934 q^{90} -1.28800 q^{91} -1.81504 q^{92} +7.13189 q^{93} -3.89406 q^{94} +8.59917 q^{95} +5.81881 q^{96} +18.1281 q^{97} -0.696464 q^{98} -0.517817 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9	\( 46 q + 3 q^{2} - 46 q^{3} + 45 q^{4} - 9 q^{5} - 3 q^{6} - 46 q^{7} + 6 q^{8} + 46 q^{9} - 10 q^{10} + 31 q^{11} - 45 q^{12} - 32 q^{13} - 3 q^{14} + 9 q^{15} + 43 q^{16} - 36 q^{17} + 3 q^{18} - 13 q^{19} - 19 q^{20} + 46 q^{21} - 13 q^{22} + 24 q^{23} - 6 q^{24} + 35 q^{25} - 11 q^{26} - 46 q^{27} - 45 q^{28} + 11 q^{29} + 10 q^{30} - 23 q^{31} + 5 q^{32} - 31 q^{33} - 35 q^{34} + 9 q^{35} + 45 q^{36} - 37 q^{37} - 32 q^{38} + 32 q^{39} - 28 q^{40} - 27 q^{41} + 3 q^{42} - 7 q^{43} + 46 q^{44} - 9 q^{45} + 16 q^{46} - 18 q^{47} - 43 q^{48} + 46 q^{49} + 10 q^{50} + 36 q^{51} - 62 q^{52} - 62 q^{53} - 3 q^{54} - 28 q^{55} - 6 q^{56} + 13 q^{57} - 36 q^{58} - 3 q^{59} + 19 q^{60} - 31 q^{61} - 41 q^{62} - 46 q^{63} + 42 q^{64} + 2 q^{65} + 13 q^{66} - 9 q^{67} - 70 q^{68} - 24 q^{69} + 10 q^{70} + 77 q^{71} + 6 q^{72} - 38 q^{73} + 14 q^{74} - 35 q^{75} - 41 q^{76} - 31 q^{77} + 11 q^{78} + 8 q^{79} - 59 q^{80} + 46 q^{81} - 53 q^{82} - 38 q^{83} + 45 q^{84} - 26 q^{85} + 37 q^{86} - 11 q^{87} - 26 q^{88} - 39 q^{89} - 10 q^{90} + 32 q^{91} + 2 q^{92} + 23 q^{93} - 55 q^{94} + 35 q^{95} - 5 q^{96} - 61 q^{97} + 3 q^{98} + 31 q^{99}+O(q^{100}) \) 46 * q + 3 * q^2 - 46 * q^3 + 45 * q^4 - 9 * q^5 - 3 * q^6 - 46 * q^7 + 6 * q^8 + 46 * q^9 - 10 * q^10 + 31 * q^11 - 45 * q^12 - 32 * q^13 - 3 * q^14 + 9 * q^15 + 43 * q^16 - 36 * q^17 + 3 * q^18 - 13 * q^19 - 19 * q^20 + 46 * q^21 - 13 * q^22 + 24 * q^23 - 6 * q^24 + 35 * q^25 - 11 * q^26 - 46 * q^27 - 45 * q^28 + 11 * q^29 + 10 * q^30 - 23 * q^31 + 5 * q^32 - 31 * q^33 - 35 * q^34 + 9 * q^35 + 45 * q^36 - 37 * q^37 - 32 * q^38 + 32 * q^39 - 28 * q^40 - 27 * q^41 + 3 * q^42 - 7 * q^43 + 46 * q^44 - 9 * q^45 + 16 * q^46 - 18 * q^47 - 43 * q^48 + 46 * q^49 + 10 * q^50 + 36 * q^51 - 62 * q^52 - 62 * q^53 - 3 * q^54 - 28 * q^55 - 6 * q^56 + 13 * q^57 - 36 * q^58 - 3 * q^59 + 19 * q^60 - 31 * q^61 - 41 * q^62 - 46 * q^63 + 42 * q^64 + 2 * q^65 + 13 * q^66 - 9 * q^67 - 70 * q^68 - 24 * q^69 + 10 * q^70 + 77 * q^71 + 6 * q^72 - 38 * q^73 + 14 * q^74 - 35 * q^75 - 41 * q^76 - 31 * q^77 + 11 * q^78 + 8 * q^79 - 59 * q^80 + 46 * q^81 - 53 * q^82 - 38 * q^83 + 45 * q^84 - 26 * q^85 + 37 * q^86 - 11 * q^87 - 26 * q^88 - 39 * q^89 - 10 * q^90 + 32 * q^91 + 2 * q^92 + 23 * q^93 - 55 * q^94 + 35 * q^95 - 5 * q^96 - 61 * q^97 + 3 * q^98 + 31 * q^99

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