LMFDB - Embedded newform 8043.2.a.s.1.20

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:	$0$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q-0.719015 q^{2} -1.00000 q^{3} -1.48302 q^{4} -1.74243 q^{5} +0.719015 q^{6} -1.00000 q^{7} +2.50434 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.719015 q^{2} -1.00000 q^{3} -1.48302 q^{4} -1.74243 q^{5} +0.719015 q^{6} -1.00000 q^{7} +2.50434 q^{8} +1.00000 q^{9} +1.25284 q^{10} -3.78984 q^{11} +1.48302 q^{12} +4.32458 q^{13} +0.719015 q^{14} +1.74243 q^{15} +1.16537 q^{16} -3.44007 q^{17} -0.719015 q^{18} -6.94115 q^{19} +2.58406 q^{20} +1.00000 q^{21} +2.72495 q^{22} +1.20533 q^{23} -2.50434 q^{24} -1.96392 q^{25} -3.10944 q^{26} -1.00000 q^{27} +1.48302 q^{28} +9.18950 q^{29} -1.25284 q^{30} -0.218376 q^{31} -5.84661 q^{32} +3.78984 q^{33} +2.47346 q^{34} +1.74243 q^{35} -1.48302 q^{36} -1.80979 q^{37} +4.99079 q^{38} -4.32458 q^{39} -4.36365 q^{40} -0.597921 q^{41} -0.719015 q^{42} -4.58056 q^{43} +5.62039 q^{44} -1.74243 q^{45} -0.866650 q^{46} -3.05751 q^{47} -1.16537 q^{48} +1.00000 q^{49} +1.41209 q^{50} +3.44007 q^{51} -6.41342 q^{52} +2.40782 q^{53} +0.719015 q^{54} +6.60354 q^{55} -2.50434 q^{56} +6.94115 q^{57} -6.60739 q^{58} -7.84594 q^{59} -2.58406 q^{60} +12.7090 q^{61} +0.157016 q^{62} -1.00000 q^{63} +1.87306 q^{64} -7.53530 q^{65} -2.72495 q^{66} +2.19566 q^{67} +5.10168 q^{68} -1.20533 q^{69} -1.25284 q^{70} -12.8251 q^{71} +2.50434 q^{72} -3.36098 q^{73} +1.30127 q^{74} +1.96392 q^{75} +10.2938 q^{76} +3.78984 q^{77} +3.10944 q^{78} -16.5996 q^{79} -2.03059 q^{80} +1.00000 q^{81} +0.429914 q^{82} -8.69870 q^{83} -1.48302 q^{84} +5.99409 q^{85} +3.29349 q^{86} -9.18950 q^{87} -9.49105 q^{88} +0.0226128 q^{89} +1.25284 q^{90} -4.32458 q^{91} -1.78752 q^{92} +0.218376 q^{93} +2.19840 q^{94} +12.0945 q^{95} +5.84661 q^{96} +3.32496 q^{97} -0.719015 q^{98} -3.78984 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9}+O(q^{10}) $ 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9} + 16 q^{10} - 31 q^{11} - 53 q^{12} + 42 q^{13} + q^{14} - 11 q^{15} + 59 q^{16} + 44 q^{17} - q^{18} + 11 q^{19} + 7 q^{20} + 50 q^{21} + 19 q^{22} - 16 q^{23} + 6 q^{24} + 71 q^{25} + q^{26} - 50 q^{27} - 53 q^{28} + 3 q^{29} - 16 q^{30} + 13 q^{31} - 23 q^{32} + 31 q^{33} + q^{34} - 11 q^{35} + 53 q^{36} + 53 q^{37} + 28 q^{38} - 42 q^{39} + 50 q^{40} + 23 q^{41} - q^{42} + 9 q^{43} - 78 q^{44} + 11 q^{45} - 8 q^{46} + 26 q^{47} - 59 q^{48} + 50 q^{49} - 38 q^{50} - 44 q^{51} + 86 q^{52} + 58 q^{53} + q^{54} + 28 q^{55} + 6 q^{56} - 11 q^{57} - 4 q^{58} + 7 q^{59} - 7 q^{60} + 51 q^{61} + 7 q^{62} - 50 q^{63} + 74 q^{64} - 14 q^{65} - 19 q^{66} + 23 q^{67} + 98 q^{68} + 16 q^{69} - 16 q^{70} - 75 q^{71} - 6 q^{72} + 34 q^{73} - 68 q^{74} - 71 q^{75} + 31 q^{76} + 31 q^{77} - q^{78} - 18 q^{79} - 21 q^{80} + 50 q^{81} + 31 q^{82} + 40 q^{83} + 53 q^{84} + 30 q^{85} - 15 q^{86} - 3 q^{87} + 70 q^{88} + 63 q^{89} + 16 q^{90} - 42 q^{91} - 38 q^{92} - 13 q^{93} + q^{94} - 77 q^{95} + 23 q^{96} + 77 q^{97} - q^{98} - 31 q^{99}+O(q^{100}) \) 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9 + 16 * q^10 - 31 * q^11 - 53 * q^12 + 42 * q^13 + q^14 - 11 * q^15 + 59 * q^16 + 44 * q^17 - q^18 + 11 * q^19 + 7 * q^20 + 50 * q^21 + 19 * q^22 - 16 * q^23 + 6 * q^24 + 71 * q^25 + q^26 - 50 * q^27 - 53 * q^28 + 3 * q^29 - 16 * q^30 + 13 * q^31 - 23 * q^32 + 31 * q^33 + q^34 - 11 * q^35 + 53 * q^36 + 53 * q^37 + 28 * q^38 - 42 * q^39 + 50 * q^40 + 23 * q^41 - q^42 + 9 * q^43 - 78 * q^44 + 11 * q^45 - 8 * q^46 + 26 * q^47 - 59 * q^48 + 50 * q^49 - 38 * q^50 - 44 * q^51 + 86 * q^52 + 58 * q^53 + q^54 + 28 * q^55 + 6 * q^56 - 11 * q^57 - 4 * q^58 + 7 * q^59 - 7 * q^60 + 51 * q^61 + 7 * q^62 - 50 * q^63 + 74 * q^64 - 14 * q^65 - 19 * q^66 + 23 * q^67 + 98 * q^68 + 16 * q^69 - 16 * q^70 - 75 * q^71 - 6 * q^72 + 34 * q^73 - 68 * q^74 - 71 * q^75 + 31 * q^76 + 31 * q^77 - q^78 - 18 * q^79 - 21 * q^80 + 50 * q^81 + 31 * q^82 + 40 * q^83 + 53 * q^84 + 30 * q^85 - 15 * q^86 - 3 * q^87 + 70 * q^88 + 63 * q^89 + 16 * q^90 - 42 * q^91 - 38 * q^92 - 13 * q^93 + q^94 - 77 * q^95 + 23 * q^96 + 77 * q^97 - 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 $

$2$	−0.719015	−0.508421	−0.254210	−	0.967149i	$-0.581816\pi$
$2$	−0.719015	−0.508421	−0.254210	+	0.967149i	$0.581816\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.48302	−0.741508
$5$	−1.74243	−0.779241	−0.389620	−	0.920976i	$-0.627394\pi$
$5$	−1.74243	−0.779241	−0.389620	+	0.920976i	$0.627394\pi$
$6$	0.719015	0.293537
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.50434	0.885419
$9$	1.00000	0.333333
$10$	1.25284	0.396182
$11$	−3.78984	−1.14268	−0.571340	−	0.820714i	$-0.693576\pi$
$11$	−3.78984	−1.14268	−0.571340	+	0.820714i	$0.693576\pi$
$12$	1.48302	0.428110
$13$	4.32458	1.19942	0.599711	−	0.800216i	$-0.295282\pi$
$13$	4.32458	1.19942	0.599711	+	0.800216i	$0.295282\pi$
$14$	0.719015	0.192165
$15$	1.74243	0.449895
$16$	1.16537	0.291343
$17$	−3.44007	−0.834339	−0.417169	−	0.908829i	$-0.636978\pi$
$17$	−3.44007	−0.834339	−0.417169	+	0.908829i	$0.636978\pi$
$18$	−0.719015	−0.169474
$19$	−6.94115	−1.59241	−0.796205	−	0.605028i	$-0.793162\pi$
$19$	−6.94115	−1.59241	−0.796205	+	0.605028i	$0.793162\pi$
$20$	2.58406	0.577813
$21$	1.00000	0.218218
$22$	2.72495	0.580962
$23$	1.20533	0.251329	0.125664	−	0.992073i	$-0.459894\pi$
$23$	1.20533	0.251329	0.125664	+	0.992073i	$0.459894\pi$
$24$	−2.50434	−0.511197
$25$	−1.96392	−0.392784
$26$	−3.10944	−0.609811
$27$	−1.00000	−0.192450
$28$	1.48302	0.280264
$29$	9.18950	1.70645	0.853224	−	0.521545i	$-0.174644\pi$
$29$	9.18950	1.70645	0.853224	+	0.521545i	$0.174644\pi$
$30$	−1.25284	−0.228736
$31$	−0.218376	−0.0392215	−0.0196107	−	0.999808i	$-0.506243\pi$
$31$	−0.218376	−0.0392215	−0.0196107	+	0.999808i	$0.506243\pi$
$32$	−5.84661	−1.03354
$33$	3.78984	0.659726
$34$	2.47346	0.424195
$35$	1.74243	0.294525
$36$	−1.48302	−0.247169
$37$	−1.80979	−0.297528	−0.148764	−	0.988873i	$-0.547530\pi$
$37$	−1.80979	−0.297528	−0.148764	+	0.988873i	$0.547530\pi$
$38$	4.99079	0.809614
$39$	−4.32458	−0.692487
$40$	−4.36365	−0.689954
$41$	−0.597921	−0.0933795	−0.0466898	−	0.998909i	$-0.514867\pi$
$41$	−0.597921	−0.0933795	−0.0466898	+	0.998909i	$0.514867\pi$
$42$	−0.719015	−0.110946
$43$	−4.58056	−0.698529	−0.349264	−	0.937024i	$-0.613569\pi$
$43$	−4.58056	−0.698529	−0.349264	+	0.937024i	$0.613569\pi$
$44$	5.62039	0.847306
$45$	−1.74243	−0.259747
$46$	−0.866650	−0.127781
$47$	−3.05751	−0.445984	−0.222992	−	0.974820i	$-0.571582\pi$
$47$	−3.05751	−0.445984	−0.222992	+	0.974820i	$0.571582\pi$
$48$	−1.16537	−0.168207
$49$	1.00000	0.142857
$50$	1.41209	0.199700
$51$	3.44007	0.481706
$52$	−6.41342	−0.889382
$53$	2.40782	0.330739	0.165370	−	0.986232i	$-0.447118\pi$
$53$	2.40782	0.330739	0.165370	+	0.986232i	$0.447118\pi$
$54$	0.719015	0.0978456
$55$	6.60354	0.890422
$56$	−2.50434	−0.334657
$57$	6.94115	0.919378
$58$	−6.60739	−0.867593
$59$	−7.84594	−1.02145	−0.510727	−	0.859743i	$-0.670624\pi$
$59$	−7.84594	−1.02145	−0.510727	+	0.859743i	$0.670624\pi$
$60$	−2.58406	−0.333601
$61$	12.7090	1.62722	0.813608	−	0.581414i	$-0.197500\pi$
$61$	12.7090	1.62722	0.813608	+	0.581414i	$0.197500\pi$
$62$	0.157016	0.0199410
$63$	−1.00000	−0.125988
$64$	1.87306	0.234132
$65$	−7.53530	−0.934639
$66$	−2.72495	−0.335418
$67$	2.19566	0.268242	0.134121	−	0.990965i	$-0.457179\pi$
$67$	2.19566	0.268242	0.134121	+	0.990965i	$0.457179\pi$
$68$	5.10168	0.618669
$69$	−1.20533	−0.145105
$70$	−1.25284	−0.149743
$71$	−12.8251	−1.52205	−0.761027	−	0.648720i	$-0.775305\pi$
$71$	−12.8251	−1.52205	−0.761027	+	0.648720i	$0.775305\pi$
$72$	2.50434	0.295140
$73$	−3.36098	−0.393373	−0.196687	−	0.980466i	$-0.563018\pi$
$73$	−3.36098	−0.393373	−0.196687	+	0.980466i	$0.563018\pi$
$74$	1.30127	0.151270
$75$	1.96392	0.226774
$76$	10.2938	1.18078
$77$	3.78984	0.431892
$78$	3.10944	0.352075
$79$	−16.5996	−1.86760	−0.933801	−	0.357792i	$-0.883530\pi$
$79$	−16.5996	−1.86760	−0.933801	+	0.357792i	$0.883530\pi$
$80$	−2.03059	−0.227026
$81$	1.00000	0.111111
$82$	0.429914	0.0474761
$83$	−8.69870	−0.954806	−0.477403	−	0.878684i	$-0.658422\pi$
$83$	−8.69870	−0.954806	−0.477403	+	0.878684i	$0.658422\pi$
$84$	−1.48302	−0.161810
$85$	5.99409	0.650151
$86$	3.29349	0.355147
$87$	−9.18950	−0.985218
$88$	−9.49105	−1.01175
$89$	0.0226128	0.00239695	0.00119847	−	0.999999i	$-0.499619\pi$
$89$	0.0226128	0.00239695	0.00119847	+	0.999999i	$0.499619\pi$
$90$	1.25284	0.132061
$91$	−4.32458	−0.453339
$92$	−1.78752	−0.186362
$93$	0.218376	0.0226445
$94$	2.19840	0.226747
$95$	12.0945	1.24087
$96$	5.84661	0.596717
$97$	3.32496	0.337599	0.168799	−	0.985650i	$-0.446011\pi$
$97$	3.32496	0.337599	0.168799	+	0.985650i	$0.446011\pi$
$98$	−0.719015	−0.0726315
$99$	−3.78984	−0.380893
$100$	2.91253	0.291253
$101$	−19.9692	−1.98701	−0.993503	−	0.113805i	$-0.963696\pi$
$101$	−19.9692	−1.98701	−0.993503	+	0.113805i	$0.963696\pi$
$102$	−2.47346	−0.244909
$103$	16.1522	1.59152	0.795760	−	0.605613i	$-0.207072\pi$
$103$	16.1522	1.59152	0.795760	+	0.605613i	$0.207072\pi$
$104$	10.8302	1.06199
$105$	−1.74243	−0.170044
$106$	−1.73126	−0.168155
$107$	−14.6274	−1.41408	−0.707042	−	0.707172i	$-0.749971\pi$
$107$	−14.6274	−1.41408	−0.707042	+	0.707172i	$0.749971\pi$
$108$	1.48302	0.142703
$109$	−0.202279	−0.0193749	−0.00968743	−	0.999953i	$-0.503084\pi$
$109$	−0.202279	−0.0193749	−0.00968743	+	0.999953i	$0.503084\pi$
$110$	−4.74805	−0.452709
$111$	1.80979	0.171778
$112$	−1.16537	−0.110117
$113$	5.40291	0.508263	0.254131	−	0.967170i	$-0.418210\pi$
$113$	5.40291	0.508263	0.254131	+	0.967170i	$0.418210\pi$
$114$	−4.99079	−0.467431
$115$	−2.10021	−0.195845
$116$	−13.6282	−1.26535
$117$	4.32458	0.399808
$118$	5.64135	0.519329
$119$	3.44007	0.315350
$120$	4.36365	0.398345
$121$	3.36287	0.305715
$122$	−9.13794	−0.827310
$123$	0.597921	0.0539127
$124$	0.323855	0.0290830
$125$	12.1342	1.08531
$126$	0.719015	0.0640550
$127$	−15.7426	−1.39693	−0.698465	−	0.715644i	$-0.746133\pi$
$127$	−15.7426	−1.39693	−0.698465	+	0.715644i	$0.746133\pi$
$128$	10.3465	0.914506
$129$	4.58056	0.403296
$130$	5.41800	0.475190
$131$	8.70722	0.760753	0.380377	−	0.924832i	$-0.375794\pi$
$131$	8.70722	0.760753	0.380377	+	0.924832i	$0.375794\pi$
$132$	−5.62039	−0.489192
$133$	6.94115	0.601874
$134$	−1.57871	−0.136380
$135$	1.74243	0.149965
$136$	−8.61511	−0.738740
$137$	−1.75603	−0.150028	−0.0750139	−	0.997182i	$-0.523900\pi$
$137$	−1.75603	−0.150028	−0.0750139	+	0.997182i	$0.523900\pi$
$138$	0.866650	0.0737742
$139$	1.33829	0.113512	0.0567561	−	0.998388i	$-0.481924\pi$
$139$	1.33829	0.113512	0.0567561	+	0.998388i	$0.481924\pi$
$140$	−2.58406	−0.218393
$141$	3.05751	0.257489
$142$	9.22142	0.773844
$143$	−16.3895	−1.37056
$144$	1.16537	0.0971144
$145$	−16.0121	−1.32973
$146$	2.41660	0.199999
$147$	−1.00000	−0.0824786
$148$	2.68395	0.220620
$149$	−10.5914	−0.867680	−0.433840	−	0.900990i	$-0.642842\pi$
$149$	−10.5914	−0.867680	−0.433840	+	0.900990i	$0.642842\pi$
$150$	−1.41209	−0.115297
$151$	−17.2214	−1.40146	−0.700728	−	0.713428i	$-0.747141\pi$
$151$	−17.2214	−1.40146	−0.700728	+	0.713428i	$0.747141\pi$
$152$	−17.3830	−1.40995
$153$	−3.44007	−0.278113
$154$	−2.72495	−0.219583
$155$	0.380506	0.0305630
$156$	6.41342	0.513485
$157$	−18.3677	−1.46590	−0.732951	−	0.680282i	$-0.761857\pi$
$157$	−18.3677	−1.46590	−0.732951	+	0.680282i	$0.761857\pi$
$158$	11.9354	0.949528
$159$	−2.40782	−0.190952
$160$	10.1873	0.805379
$161$	−1.20533	−0.0949933
$162$	−0.719015	−0.0564912
$163$	0.101128	0.00792097	0.00396048	−	0.999992i	$-0.498739\pi$
$163$	0.101128	0.00792097	0.00396048	+	0.999992i	$0.498739\pi$
$164$	0.886727	0.0692417
$165$	−6.60354	−0.514085
$166$	6.25450	0.485443
$167$	−21.4517	−1.65998	−0.829990	−	0.557778i	$-0.811654\pi$
$167$	−21.4517	−1.65998	−0.829990	+	0.557778i	$0.811654\pi$
$168$	2.50434	0.193214
$169$	5.70199	0.438615
$170$	−4.30985	−0.330550
$171$	−6.94115	−0.530803
$172$	6.79305	0.517965
$173$	0.210866	0.0160318	0.00801592	−	0.999968i	$-0.497448\pi$
$173$	0.210866	0.0160318	0.00801592	+	0.999968i	$0.497448\pi$
$174$	6.60739	0.500905
$175$	1.96392	0.148458
$176$	−4.41657	−0.332912
$177$	7.84594	0.589737
$178$	−0.0162589	−0.00121866
$179$	−0.906572	−0.0677604	−0.0338802	−	0.999426i	$-0.510786\pi$
$179$	−0.906572	−0.0677604	−0.0338802	+	0.999426i	$0.510786\pi$
$180$	2.58406	0.192604
$181$	17.6186	1.30958	0.654789	−	0.755812i	$-0.272757\pi$
$181$	17.6186	1.30958	0.654789	+	0.755812i	$0.272757\pi$
$182$	3.10944	0.230487
$183$	−12.7090	−0.939474
$184$	3.01856	0.222531
$185$	3.15345	0.231846
$186$	−0.157016	−0.0115129
$187$	13.0373	0.953382
$188$	4.53434	0.330701
$189$	1.00000	0.0727393
$190$	−8.69613	−0.630884
$191$	−6.51906	−0.471702	−0.235851	−	0.971789i	$-0.575788\pi$
$191$	−6.51906	−0.471702	−0.235851	+	0.971789i	$0.575788\pi$
$192$	−1.87306	−0.135176
$193$	−1.53377	−0.110403	−0.0552016	−	0.998475i	$-0.517580\pi$
$193$	−1.53377	−0.110403	−0.0552016	+	0.998475i	$0.517580\pi$
$194$	−2.39070	−0.171642
$195$	7.53530	0.539614
$196$	−1.48302	−0.105930
$197$	−12.0883	−0.861254	−0.430627	−	0.902530i	$-0.641708\pi$
$197$	−12.0883	−0.861254	−0.430627	+	0.902530i	$0.641708\pi$
$198$	2.72495	0.193654
$199$	27.2408	1.93105	0.965525	−	0.260311i	$-0.0838252\pi$
$199$	27.2408	1.93105	0.965525	+	0.260311i	$0.0838252\pi$
$200$	−4.91833	−0.347779
$201$	−2.19566	−0.154870
$202$	14.3581	1.01024
$203$	−9.18950	−0.644977
$204$	−5.10168	−0.357189
$205$	1.04184	0.0727651
$206$	−11.6137	−0.809161
$207$	1.20533	0.0837762
$208$	5.03975	0.349443
$209$	26.3058	1.81961
$210$	1.25284	0.0864540
$211$	−5.49010	−0.377954	−0.188977	−	0.981982i	$-0.560517\pi$
$211$	−5.49010	−0.377954	−0.188977	+	0.981982i	$0.560517\pi$
$212$	−3.57083	−0.245246
$213$	12.8251	0.878759
$214$	10.5173	0.718949
$215$	7.98133	0.544322
$216$	−2.50434	−0.170399
$217$	0.218376	0.0148243
$218$	0.145442	0.00985058
$219$	3.36098	0.227114
$220$	−9.79317	−0.660255
$221$	−14.8768	−1.00073
$222$	−1.30127	−0.0873355
$223$	11.4075	0.763903	0.381951	−	0.924182i	$-0.375252\pi$
$223$	11.4075	0.763903	0.381951	+	0.924182i	$0.375252\pi$
$224$	5.84661	0.390643
$225$	−1.96392	−0.130928
$226$	−3.88478	−0.258411
$227$	−15.3714	−1.02023	−0.510116	−	0.860105i	$-0.670398\pi$
$227$	−15.3714	−1.02023	−0.510116	+	0.860105i	$0.670398\pi$
$228$	−10.2938	−0.681726
$229$	−1.11073	−0.0733991	−0.0366995	−	0.999326i	$-0.511684\pi$
$229$	−1.11073	−0.0733991	−0.0366995	+	0.999326i	$0.511684\pi$
$230$	1.51008	0.0995718
$231$	−3.78984	−0.249353
$232$	23.0137	1.51092
$233$	−11.5373	−0.755837	−0.377918	−	0.925839i	$-0.623360\pi$
$233$	−11.5373	−0.755837	−0.377918	+	0.925839i	$0.623360\pi$
$234$	−3.10944	−0.203270
$235$	5.32751	0.347528
$236$	11.6357	0.757417
$237$	16.5996	1.07826
$238$	−2.47346	−0.160331
$239$	12.2631	0.793232	0.396616	−	0.917985i	$-0.370185\pi$
$239$	12.2631	0.793232	0.396616	+	0.917985i	$0.370185\pi$
$240$	2.03059	0.131074
$241$	−16.3762	−1.05489	−0.527443	−	0.849590i	$-0.676849\pi$
$241$	−16.3762	−1.05489	−0.527443	+	0.849590i	$0.676849\pi$
$242$	−2.41795	−0.155432
$243$	−1.00000	−0.0641500
$244$	−18.8476	−1.20659
$245$	−1.74243	−0.111320
$246$	−0.429914	−0.0274103
$247$	−30.0176	−1.90997
$248$	−0.546888	−0.0347274
$249$	8.69870	0.551257
$250$	−8.72466	−0.551796
$251$	−16.4332	−1.03725	−0.518626	−	0.855001i	$-0.673556\pi$
$251$	−16.4332	−1.03725	−0.518626	+	0.855001i	$0.673556\pi$
$252$	1.48302	0.0934213
$253$	−4.56800	−0.287188
$254$	11.3192	0.710228
$255$	−5.99409	−0.375365
$256$	−11.1854	−0.699086
$257$	26.8296	1.67359	0.836793	−	0.547519i	$-0.184428\pi$
$257$	26.8296	1.67359	0.836793	+	0.547519i	$0.184428\pi$
$258$	−3.29349	−0.205044
$259$	1.80979	0.112455
$260$	11.1750	0.693042
$261$	9.18950	0.568816
$262$	−6.26063	−0.386783
$263$	9.55741	0.589335	0.294668	−	0.955600i	$-0.404791\pi$
$263$	9.55741	0.589335	0.294668	+	0.955600i	$0.404791\pi$
$264$	9.49105	0.584134
$265$	−4.19546	−0.257725
$266$	−4.99079	−0.306005
$267$	−0.0226128	−0.00138388
$268$	−3.25620	−0.198904
$269$	−3.88085	−0.236619	−0.118310	−	0.992977i	$-0.537748\pi$
$269$	−3.88085	−0.236619	−0.118310	+	0.992977i	$0.537748\pi$
$270$	−1.25284	−0.0762453
$271$	−19.4715	−1.18281	−0.591404	−	0.806376i	$-0.701426\pi$
$271$	−19.4715	−1.18281	−0.591404	+	0.806376i	$0.701426\pi$
$272$	−4.00896	−0.243079
$273$	4.32458	0.261735
$274$	1.26261	0.0762772
$275$	7.44294	0.448826
$276$	1.78752	0.107596
$277$	12.0166	0.722007	0.361003	−	0.932565i	$-0.382434\pi$
$277$	12.0166	0.722007	0.361003	+	0.932565i	$0.382434\pi$
$278$	−0.962250	−0.0577119
$279$	−0.218376	−0.0130738
$280$	4.36365	0.260778
$281$	26.4307	1.57673	0.788363	−	0.615211i	$-0.210929\pi$
$281$	26.4307	1.57673	0.788363	+	0.615211i	$0.210929\pi$
$282$	−2.19840	−0.130913
$283$	−16.9567	−1.00797	−0.503987	−	0.863711i	$-0.668134\pi$
$283$	−16.9567	−1.00797	−0.503987	+	0.863711i	$0.668134\pi$
$284$	19.0198	1.12862
$285$	−12.0945	−0.716416
$286$	11.7843	0.696819
$287$	0.597921	0.0352941
$288$	−5.84661	−0.344515
$289$	−5.16593	−0.303879
$290$	11.5130	0.676064
$291$	−3.32496	−0.194913
$292$	4.98439	0.291690
$293$	−31.0464	−1.81375	−0.906876	−	0.421398i	$-0.861540\pi$
$293$	−31.0464	−1.81375	−0.906876	+	0.421398i	$0.861540\pi$
$294$	0.719015	0.0419338
$295$	13.6710	0.795959
$296$	−4.53234	−0.263437
$297$	3.78984	0.219909
$298$	7.61537	0.441146
$299$	5.21254	0.301449
$300$	−2.91253	−0.168155
$301$	4.58056	0.264019
$302$	12.3824	0.712529
$303$	19.9692	1.14720
$304$	−8.08902	−0.463937
$305$	−22.1445	−1.26799
$306$	2.47346	0.141398
$307$	34.3856	1.96249	0.981245	−	0.192764i	$-0.0617452\pi$
$307$	34.3856	1.96249	0.981245	+	0.192764i	$0.0617452\pi$
$308$	−5.62039	−0.320252
$309$	−16.1522	−0.918864
$310$	−0.273590	−0.0155388
$311$	29.4852	1.67195	0.835976	−	0.548766i	$-0.184902\pi$
$311$	29.4852	1.67195	0.835976	+	0.548766i	$0.184902\pi$
$312$	−10.8302	−0.613141
$313$	−6.00309	−0.339315	−0.169657	−	0.985503i	$-0.554266\pi$
$313$	−6.00309	−0.339315	−0.169657	+	0.985503i	$0.554266\pi$
$314$	13.2067	0.745295
$315$	1.74243	0.0981751
$316$	24.6175	1.38484
$317$	2.68404	0.150751	0.0753755	−	0.997155i	$-0.475984\pi$
$317$	2.68404	0.150751	0.0753755	+	0.997155i	$0.475984\pi$
$318$	1.73126	0.0970841
$319$	−34.8267	−1.94992
$320$	−3.26368	−0.182445
$321$	14.6274	0.816421
$322$	0.866650	0.0482965
$323$	23.8780	1.32861
$324$	−1.48302	−0.0823898
$325$	−8.49313	−0.471114
$326$	−0.0727127	−0.00402718
$327$	0.202279	0.0111861
$328$	−1.49740	−0.0826800
$329$	3.05751	0.168566
$330$	4.74805	0.261372
$331$	25.1640	1.38314	0.691570	−	0.722309i	$-0.256919\pi$
$331$	25.1640	1.38314	0.691570	+	0.722309i	$0.256919\pi$
$332$	12.9003	0.707997
$333$	−1.80979	−0.0991761
$334$	15.4241	0.843969
$335$	−3.82579	−0.209025
$336$	1.16537	0.0635763
$337$	16.3578	0.891068	0.445534	−	0.895265i	$-0.353014\pi$
$337$	16.3578	0.891068	0.445534	+	0.895265i	$0.353014\pi$
$338$	−4.09982	−0.223001
$339$	−5.40291	−0.293446
$340$	−8.88934	−0.482092
$341$	0.827609	0.0448175
$342$	4.99079	0.269871
$343$	−1.00000	−0.0539949
$344$	−11.4713	−0.618491
$345$	2.10021	0.113071
$346$	−0.151616	−0.00815092
$347$	−27.6783	−1.48585	−0.742926	−	0.669374i	$-0.766562\pi$
$347$	−27.6783	−1.48585	−0.742926	+	0.669374i	$0.766562\pi$
$348$	13.6282	0.730547
$349$	−22.2152	−1.18915	−0.594577	−	0.804039i	$-0.702680\pi$
$349$	−22.2152	−1.18915	−0.594577	+	0.804039i	$0.702680\pi$
$350$	−1.41209	−0.0754794
$351$	−4.32458	−0.230829
$352$	22.1577	1.18101
$353$	30.5666	1.62689	0.813447	−	0.581639i	$-0.197588\pi$
$353$	30.5666	1.62689	0.813447	+	0.581639i	$0.197588\pi$
$354$	−5.64135	−0.299834
$355$	22.3468	1.18605
$356$	−0.0335351	−0.00177736
$357$	−3.44007	−0.182068
$358$	0.651839	0.0344508
$359$	−3.55120	−0.187425	−0.0937127	−	0.995599i	$-0.529874\pi$
$359$	−3.55120	−0.187425	−0.0937127	+	0.995599i	$0.529874\pi$
$360$	−4.36365	−0.229985
$361$	29.1796	1.53577
$362$	−12.6680	−0.665817
$363$	−3.36287	−0.176505
$364$	6.41342	0.336155
$365$	5.85629	0.306532
$366$	9.13794	0.477648
$367$	20.8205	1.08682	0.543410	−	0.839467i	$-0.317133\pi$
$367$	20.8205	1.08682	0.543410	+	0.839467i	$0.317133\pi$
$368$	1.40466	0.0732228
$369$	−0.597921	−0.0311265
$370$	−2.26738	−0.117875
$371$	−2.40782	−0.125008
$372$	−0.323855	−0.0167911
$373$	1.81120	0.0937802	0.0468901	−	0.998900i	$-0.485069\pi$
$373$	1.81120	0.0937802	0.0468901	+	0.998900i	$0.485069\pi$
$374$	−9.37402	−0.484719
$375$	−12.1342	−0.626606
$376$	−7.65705	−0.394882
$377$	39.7407	2.04675
$378$	−0.719015	−0.0369822
$379$	12.0448	0.618700	0.309350	−	0.950948i	$-0.399889\pi$
$379$	12.0448	0.618700	0.309350	+	0.950948i	$0.399889\pi$
$380$	−17.9363	−0.920115
$381$	15.7426	0.806518
$382$	4.68730	0.239823
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	−10.3465	−0.527990
$385$	−6.60354	−0.336548
$386$	1.10280	0.0561313
$387$	−4.58056	−0.232843
$388$	−4.93097	−0.250332
$389$	34.6657	1.75762	0.878811	−	0.477171i	$-0.158338\pi$
$389$	34.6657	1.75762	0.878811	+	0.477171i	$0.158338\pi$
$390$	−5.41800	−0.274351
$391$	−4.14641	−0.209693
$392$	2.50434	0.126488
$393$	−8.70722	−0.439221
$394$	8.69166	0.437879
$395$	28.9237	1.45531
$396$	5.62039	0.282435
$397$	−5.89869	−0.296047	−0.148023	−	0.988984i	$-0.547291\pi$
$397$	−5.89869	−0.296047	−0.148023	+	0.988984i	$0.547291\pi$
$398$	−19.5866	−0.981786
$399$	−6.94115	−0.347492
$400$	−2.28870	−0.114435
$401$	−6.56339	−0.327760	−0.163880	−	0.986480i	$-0.552401\pi$
$401$	−6.56339	−0.327760	−0.163880	+	0.986480i	$0.552401\pi$
$402$	1.57871	0.0787390
$403$	−0.944384	−0.0470431
$404$	29.6146	1.47338
$405$	−1.74243	−0.0865823
$406$	6.60739	0.327919
$407$	6.85883	0.339979
$408$	8.61511	0.426511
$409$	36.2052	1.79023	0.895115	−	0.445835i	$-0.147093\pi$
$409$	36.2052	1.79023	0.895115	+	0.445835i	$0.147093\pi$
$410$	−0.749098	−0.0369953
$411$	1.75603	0.0866185
$412$	−23.9539	−1.18012
$413$	7.84594	0.386073
$414$	−0.866650	−0.0425935
$415$	15.1569	0.744023
$416$	−25.2841	−1.23966
$417$	−1.33829	−0.0655363
$418$	−18.9143	−0.925129
$419$	−27.6270	−1.34967	−0.674835	−	0.737969i	$-0.735785\pi$
$419$	−27.6270	−1.34967	−0.674835	+	0.737969i	$0.735785\pi$
$420$	2.58406	0.126089
$421$	21.9128	1.06796	0.533982	−	0.845496i	$-0.320695\pi$
$421$	21.9128	1.06796	0.533982	+	0.845496i	$0.320695\pi$
$422$	3.94747	0.192160
$423$	−3.05751	−0.148661
$424$	6.03000	0.292843
$425$	6.75602	0.327715
$426$	−9.22142	−0.446779
$427$	−12.7090	−0.615030
$428$	21.6927	1.04855
$429$	16.3895	0.791290
$430$	−5.73870	−0.276745
$431$	27.6752	1.33307	0.666533	−	0.745476i	$-0.267778\pi$
$431$	27.6752	1.33307	0.666533	+	0.745476i	$0.267778\pi$
$432$	−1.16537	−0.0560690
$433$	33.3649	1.60342	0.801708	−	0.597716i	$-0.203925\pi$
$433$	33.3649	1.60342	0.801708	+	0.597716i	$0.203925\pi$
$434$	−0.157016	−0.00753699
$435$	16.0121	0.767722
$436$	0.299984	0.0143666
$437$	−8.36637	−0.400218
$438$	−2.41660	−0.115470
$439$	8.22862	0.392731	0.196365	−	0.980531i	$-0.437086\pi$
$439$	8.22862	0.392731	0.196365	+	0.980531i	$0.437086\pi$
$440$	16.5375	0.788396
$441$	1.00000	0.0476190
$442$	10.6967	0.508789
$443$	25.1918	1.19690	0.598450	−	0.801160i	$-0.295783\pi$
$443$	25.1918	1.19690	0.598450	+	0.801160i	$0.295783\pi$
$444$	−2.68395	−0.127375
$445$	−0.0394013	−0.00186780
$446$	−8.20217	−0.388384
$447$	10.5914	0.500955
$448$	−1.87306	−0.0884936
$449$	27.5631	1.30078	0.650392	−	0.759599i	$-0.274605\pi$
$449$	27.5631	1.30078	0.650392	+	0.759599i	$0.274605\pi$
$450$	1.41209	0.0665665
$451$	2.26602	0.106703
$452$	−8.01260	−0.376881
$453$	17.2214	0.809131
$454$	11.0522	0.518707
$455$	7.53530	0.353260
$456$	17.3830	0.814035
$457$	−22.1702	−1.03708	−0.518539	−	0.855054i	$-0.673524\pi$
$457$	−22.1702	−1.03708	−0.518539	+	0.855054i	$0.673524\pi$
$458$	0.798632	0.0373176
$459$	3.44007	0.160569
$460$	3.11464	0.145221
$461$	−31.2254	−1.45431	−0.727156	−	0.686472i	$-0.759158\pi$
$461$	−31.2254	−1.45431	−0.727156	+	0.686472i	$0.759158\pi$
$462$	2.72495	0.126776
$463$	−35.7076	−1.65947	−0.829736	−	0.558156i	$-0.811509\pi$
$463$	−35.7076	−1.65947	−0.829736	+	0.558156i	$0.811509\pi$
$464$	10.7092	0.497162
$465$	−0.380506	−0.0176455
$466$	8.29553	0.384283
$467$	−28.8637	−1.33565	−0.667826	−	0.744317i	$-0.732775\pi$
$467$	−28.8637	−1.33565	−0.667826	+	0.744317i	$0.732775\pi$
$468$	−6.41342	−0.296461
$469$	−2.19566	−0.101386
$470$	−3.83056	−0.176691
$471$	18.3677	0.846338
$472$	−19.6489	−0.904415
$473$	17.3596	0.798194
$474$	−11.9354	−0.548210
$475$	13.6319	0.625473
$476$	−5.10168	−0.233835
$477$	2.40782	0.110246
$478$	−8.81733	−0.403295
$479$	23.0712	1.05415	0.527076	−	0.849818i	$-0.323288\pi$
$479$	23.0712	1.05415	0.527076	+	0.849818i	$0.323288\pi$
$480$	−10.1873	−0.464986
$481$	−7.82660	−0.356862
$482$	11.7748	0.536326
$483$	1.20533	0.0548444
$484$	−4.98719	−0.226690
$485$	−5.79353	−0.263071
$486$	0.719015	0.0326152
$487$	5.99656	0.271730	0.135865	−	0.990727i	$-0.456619\pi$
$487$	5.99656	0.271730	0.135865	+	0.990727i	$0.456619\pi$
$488$	31.8276	1.44077
$489$	−0.101128	−0.00457317
$490$	1.25284	0.0565974
$491$	−16.2236	−0.732163	−0.366081	−	0.930583i	$-0.619301\pi$
$491$	−16.2236	−0.732163	−0.366081	+	0.930583i	$0.619301\pi$
$492$	−0.886727	−0.0399767
$493$	−31.6125	−1.42376
$494$	21.5831	0.971069
$495$	6.60354	0.296807
$496$	−0.254489	−0.0114269
$497$	12.8251	0.575283
$498$	−6.25450	−0.280271
$499$	20.7905	0.930712	0.465356	−	0.885124i	$-0.345926\pi$
$499$	20.7905	0.930712	0.465356	+	0.885124i	$0.345926\pi$
$500$	−17.9952	−0.804769
$501$	21.4517	0.958390
$502$	11.8157	0.527360
$503$	9.68174	0.431687	0.215844	−	0.976428i	$-0.430750\pi$
$503$	9.68174	0.431687	0.215844	+	0.976428i	$0.430750\pi$
$504$	−2.50434	−0.111552
$505$	34.7950	1.54836
$506$	3.28446	0.146012
$507$	−5.70199	−0.253234
$508$	23.3465	1.03584
$509$	−6.87619	−0.304782	−0.152391	−	0.988320i	$-0.548697\pi$
$509$	−6.87619	−0.304782	−0.152391	+	0.988320i	$0.548697\pi$
$510$	4.30985	0.190843
$511$	3.36098	0.148681
$512$	−12.6505	−0.559076
$513$	6.94115	0.306459
$514$	−19.2909	−0.850886
$515$	−28.1441	−1.24018
$516$	−6.79305	−0.299047
$517$	11.5875	0.509616
$518$	−1.30127	−0.0571745
$519$	−0.210866	−0.00925598
$520$	−18.8710	−0.827547
$521$	8.08027	0.354003	0.177002	−	0.984211i	$-0.443360\pi$
$521$	8.08027	0.354003	0.177002	+	0.984211i	$0.443360\pi$
$522$	−6.60739	−0.289198
$523$	36.6728	1.60359	0.801794	−	0.597601i	$-0.203879\pi$
$523$	36.6728	1.60359	0.801794	+	0.597601i	$0.203879\pi$
$524$	−12.9130	−0.564105
$525$	−1.96392	−0.0857125
$526$	−6.87193	−0.299630
$527$	0.751228	0.0327240
$528$	4.41657	0.192207
$529$	−21.5472	−0.936834
$530$	3.01660	0.131033
$531$	−7.84594	−0.340485
$532$	−10.2938	−0.446295
$533$	−2.58576	−0.112002
$534$	0.0162589	0.000703593 0
$535$	25.4873	1.10191
$536$	5.49868	0.237507
$537$	0.906572	0.0391215
$538$	2.79039	0.120302
$539$	−3.78984	−0.163240
$540$	−2.58406	−0.111200
$541$	6.90404	0.296828	0.148414	−	0.988925i	$-0.452583\pi$
$541$	6.90404	0.296828	0.148414	+	0.988925i	$0.452583\pi$
$542$	14.0003	0.601364
$543$	−17.6186	−0.756085
$544$	20.1127	0.862326
$545$	0.352459	0.0150977
$546$	−3.10944	−0.133072
$547$	−17.2860	−0.739094	−0.369547	−	0.929212i	$-0.620487\pi$
$547$	−17.2860	−0.739094	−0.369547	+	0.929212i	$0.620487\pi$
$548$	2.60422	0.111247
$549$	12.7090	0.542405
$550$	−5.35159	−0.228193
$551$	−63.7857	−2.71736
$552$	−3.01856	−0.128478
$553$	16.5996	0.705887
$554$	−8.64011	−0.367083
$555$	−3.15345	−0.133856
$556$	−1.98470	−0.0841702
$557$	−22.5946	−0.957362	−0.478681	−	0.877989i	$-0.658885\pi$
$557$	−22.5946	−0.957362	−0.478681	+	0.877989i	$0.658885\pi$
$558$	0.157016	0.00664700
$559$	−19.8090	−0.837831
$560$	2.03059	0.0858079
$561$	−13.0373	−0.550435
$562$	−19.0041	−0.801640
$563$	6.61288	0.278700	0.139350	−	0.990243i	$-0.455499\pi$
$563$	6.61288	0.278700	0.139350	+	0.990243i	$0.455499\pi$
$564$	−4.53434	−0.190930
$565$	−9.41422	−0.396059
$566$	12.1922	0.512475
$567$	−1.00000	−0.0419961
$568$	−32.1184	−1.34766
$569$	−43.7184	−1.83277	−0.916385	−	0.400297i	$-0.868907\pi$
$569$	−43.7184	−1.83277	−0.916385	+	0.400297i	$0.868907\pi$
$570$	8.69613	0.364241
$571$	34.9116	1.46101	0.730503	−	0.682909i	$-0.239286\pi$
$571$	34.9116	1.46101	0.730503	+	0.682909i	$0.239286\pi$
$572$	24.3058	1.01628
$573$	6.51906	0.272337
$574$	−0.429914	−0.0179443
$575$	−2.36717	−0.0987179
$576$	1.87306	0.0780440
$577$	−9.29052	−0.386769	−0.193385	−	0.981123i	$-0.561947\pi$
$577$	−9.29052	−0.386769	−0.193385	+	0.981123i	$0.561947\pi$
$578$	3.71439	0.154498
$579$	1.53377	0.0637413
$580$	23.7462	0.986008
$581$	8.69870	0.360883
$582$	2.39070	0.0990977
$583$	−9.12523	−0.377929
$584$	−8.41706	−0.348300
$585$	−7.53530	−0.311546
$586$	22.3229	0.922149
$587$	6.98093	0.288134	0.144067	−	0.989568i	$-0.453982\pi$
$587$	6.98093	0.288134	0.144067	+	0.989568i	$0.453982\pi$
$588$	1.48302	0.0611586
$589$	1.51578	0.0624566
$590$	−9.82969	−0.404682
$591$	12.0883	0.497245
$592$	−2.10908	−0.0866828
$593$	−41.7551	−1.71468	−0.857339	−	0.514752i	$-0.827884\pi$
$593$	−41.7551	−1.71468	−0.857339	+	0.514752i	$0.827884\pi$
$594$	−2.72495	−0.111806
$595$	−5.99409	−0.245734
$596$	15.7072	0.643392
$597$	−27.2408	−1.11489
$598$	−3.74790	−0.153263
$599$	−4.58554	−0.187360	−0.0936800	−	0.995602i	$-0.529863\pi$
$599$	−4.58554	−0.187360	−0.0936800	+	0.995602i	$0.529863\pi$
$600$	4.91833	0.200790
$601$	37.3016	1.52156	0.760781	−	0.649009i	$-0.224816\pi$
$601$	37.3016	1.52156	0.760781	+	0.649009i	$0.224816\pi$
$602$	−3.29349	−0.134233
$603$	2.19566	0.0894141
$604$	25.5396	1.03919
$605$	−5.85958	−0.238226
$606$	−14.3581	−0.583259
$607$	16.9356	0.687393	0.343697	−	0.939081i	$-0.388321\pi$
$607$	16.9356	0.687393	0.343697	+	0.939081i	$0.388321\pi$
$608$	40.5822	1.64582
$609$	9.18950	0.372377
$610$	15.9223	0.644674
$611$	−13.2224	−0.534923
$612$	5.10168	0.206223
$613$	36.8405	1.48798	0.743988	−	0.668193i	$-0.232932\pi$
$613$	36.8405	1.48798	0.743988	+	0.668193i	$0.232932\pi$
$614$	−24.7238	−0.997771
$615$	−1.04184	−0.0420110
$616$	9.49105	0.382405
$617$	−9.24260	−0.372093	−0.186046	−	0.982541i	$-0.559568\pi$
$617$	−9.24260	−0.372093	−0.186046	+	0.982541i	$0.559568\pi$
$618$	11.6137	0.467170
$619$	30.4026	1.22198	0.610991	−	0.791638i	$-0.290771\pi$
$619$	30.4026	1.22198	0.610991	+	0.791638i	$0.290771\pi$
$620$	−0.564296	−0.0226627
$621$	−1.20533	−0.0483682
$622$	−21.2003	−0.850055
$623$	−0.0226128	−0.000905961 0
$624$	−5.03975	−0.201751
$625$	−11.3234	−0.452936
$626$	4.31631	0.172515
$627$	−26.3058	−1.05055
$628$	27.2396	1.08698
$629$	6.22581	0.248239
$630$	−1.25284	−0.0499142
$631$	39.4930	1.57219	0.786097	−	0.618104i	$-0.212099\pi$
$631$	39.4930	1.57219	0.786097	+	0.618104i	$0.212099\pi$
$632$	−41.5711	−1.65361
$633$	5.49010	0.218212
$634$	−1.92987	−0.0766449
$635$	27.4305	1.08854
$636$	3.57083	0.141593
$637$	4.32458	0.171346
$638$	25.0410	0.991381
$639$	−12.8251	−0.507352
$640$	−18.0280	−0.712620
$641$	−12.0848	−0.477320	−0.238660	−	0.971103i	$-0.576708\pi$
$641$	−12.0848	−0.477320	−0.238660	+	0.971103i	$0.576708\pi$
$642$	−10.5173	−0.415085
$643$	−17.7613	−0.700437	−0.350219	−	0.936668i	$-0.613893\pi$
$643$	−17.7613	−0.700437	−0.350219	+	0.936668i	$0.613893\pi$
$644$	1.78752	0.0704383
$645$	−7.98133	−0.314264
$646$	−17.1687	−0.675492
$647$	−31.4853	−1.23782	−0.618908	−	0.785464i	$-0.712424\pi$
$647$	−31.4853	−1.23782	−0.618908	+	0.785464i	$0.712424\pi$
$648$	2.50434	0.0983799
$649$	29.7348	1.16719
$650$	6.10669	0.239524
$651$	−0.218376	−0.00855883
$652$	−0.149975	−0.00587346
$653$	29.7449	1.16401	0.582005	−	0.813185i	$-0.302268\pi$
$653$	29.7449	1.16401	0.582005	+	0.813185i	$0.302268\pi$
$654$	−0.145442	−0.00568723
$655$	−15.1718	−0.592810
$656$	−0.696800	−0.0272055
$657$	−3.36098	−0.131124
$658$	−2.19840	−0.0857024
$659$	0.836125	0.0325708	0.0162854	−	0.999867i	$-0.494816\pi$
$659$	0.836125	0.0325708	0.0162854	+	0.999867i	$0.494816\pi$
$660$	9.79317	0.381199
$661$	−2.14102	−0.0832761	−0.0416381	−	0.999133i	$-0.513258\pi$
$661$	−2.14102	−0.0832761	−0.0416381	+	0.999133i	$0.513258\pi$
$662$	−18.0933	−0.703217
$663$	14.8768	0.577769
$664$	−21.7845	−0.845403
$665$	−12.0945	−0.469005
$666$	1.30127	0.0504232
$667$	11.0764	0.428879
$668$	31.8132	1.23089
$669$	−11.4075	−0.441039
$670$	2.75080	0.106273
$671$	−48.1649	−1.85939
$672$	−5.84661	−0.225538
$673$	−3.34408	−0.128905	−0.0644524	−	0.997921i	$-0.520530\pi$
$673$	−3.34408	−0.128905	−0.0644524	+	0.997921i	$0.520530\pi$
$674$	−11.7615	−0.453037
$675$	1.96392	0.0755914
$676$	−8.45615	−0.325236
$677$	40.4498	1.55461	0.777305	−	0.629124i	$-0.216586\pi$
$677$	40.4498	1.55461	0.777305	+	0.629124i	$0.216586\pi$
$678$	3.88478	0.149194
$679$	−3.32496	−0.127600
$680$	15.0113	0.575656
$681$	15.3714	0.589032
$682$	−0.595064	−0.0227862
$683$	36.4476	1.39463	0.697313	−	0.716766i	$-0.254379\pi$
$683$	36.4476	1.39463	0.697313	+	0.716766i	$0.254379\pi$
$684$	10.2938	0.393595
$685$	3.05977	0.116908
$686$	0.719015	0.0274521
$687$	1.11073	0.0423770
$688$	−5.33806	−0.203512
$689$	10.4128	0.396696
$690$	−1.51008	−0.0574878
$691$	44.4111	1.68948	0.844739	−	0.535179i	$-0.179756\pi$
$691$	44.4111	1.68948	0.844739	+	0.535179i	$0.179756\pi$
$692$	−0.312718	−0.0118877
$693$	3.78984	0.143964
$694$	19.9012	0.755437
$695$	−2.33188	−0.0884533
$696$	−23.0137	−0.872331
$697$	2.05689	0.0779102
$698$	15.9731	0.604590
$699$	11.5373	0.436383
$700$	−2.91253	−0.110083
$701$	−21.6583	−0.818021	−0.409011	−	0.912530i	$-0.634126\pi$
$701$	−21.6583	−0.818021	−0.409011	+	0.912530i	$0.634126\pi$
$702$	3.10944	0.117358
$703$	12.5621	0.473787
$704$	−7.09858	−0.267538
$705$	−5.32751	−0.200646
$706$	−21.9778	−0.827147
$707$	19.9692	0.751018
$708$	−11.6357	−0.437295
$709$	9.97311	0.374548	0.187274	−	0.982308i	$-0.440035\pi$
$709$	9.97311	0.374548	0.187274	+	0.982308i	$0.440035\pi$
$710$	−16.0677	−0.603011
$711$	−16.5996	−0.622534
$712$	0.0566301	0.00212230
$713$	−0.263215	−0.00985747
$714$	2.47346	0.0925670
$715$	28.5576	1.06799
$716$	1.34446	0.0502449
$717$	−12.2631	−0.457972
$718$	2.55337	0.0952910
$719$	−38.7783	−1.44619	−0.723094	−	0.690750i	$-0.757281\pi$
$719$	−38.7783	−1.44619	−0.723094	+	0.690750i	$0.757281\pi$
$720$	−2.03059	−0.0756754
$721$	−16.1522	−0.601538
$722$	−20.9806	−0.780816
$723$	16.3762	0.609039
$724$	−26.1286	−0.971063
$725$	−18.0475	−0.670266
$726$	2.41795	0.0897387
$727$	35.8586	1.32992	0.664960	−	0.746879i	$-0.268448\pi$
$727$	35.8586	1.32992	0.664960	+	0.746879i	$0.268448\pi$
$728$	−10.8302	−0.401395
$729$	1.00000	0.0370370
$730$	−4.21077	−0.155847
$731$	15.7574	0.582810
$732$	18.8476	0.696628
$733$	−25.6393	−0.947010	−0.473505	−	0.880791i	$-0.657011\pi$
$733$	−25.6393	−0.947010	−0.473505	+	0.880791i	$0.657011\pi$
$734$	−14.9703	−0.552562
$735$	1.74243	0.0642707
$736$	−7.04709	−0.259759
$737$	−8.32119	−0.306515
$738$	0.429914	0.0158254
$739$	4.19095	0.154167	0.0770833	−	0.997025i	$-0.475439\pi$
$739$	4.19095	0.154167	0.0770833	+	0.997025i	$0.475439\pi$
$740$	−4.67662	−0.171916
$741$	30.0176	1.10272
$742$	1.73126	0.0635565
$743$	−26.2751	−0.963941	−0.481970	−	0.876187i	$-0.660079\pi$
$743$	−26.2751	−0.963941	−0.481970	+	0.876187i	$0.660079\pi$
$744$	0.546888	0.0200499
$745$	18.4548	0.676131
$746$	−1.30228	−0.0476798
$747$	−8.69870	−0.318269
$748$	−19.3345	−0.706940
$749$	14.6274	0.534473
$750$	8.72466	0.318580
$751$	−31.6582	−1.15522	−0.577612	−	0.816312i	$-0.696015\pi$
$751$	−31.6582	−1.15522	−0.577612	+	0.816312i	$0.696015\pi$
$752$	−3.56314	−0.129934
$753$	16.4332	0.598858
$754$	−28.5742	−1.04061
$755$	30.0071	1.09207
$756$	−1.48302	−0.0539368
$757$	4.80424	0.174613	0.0873065	−	0.996181i	$-0.472174\pi$
$757$	4.80424	0.174613	0.0873065	+	0.996181i	$0.472174\pi$
$758$	−8.66040	−0.314560
$759$	4.56800	0.165808
$760$	30.2888	1.09869
$761$	−33.3500	−1.20894	−0.604469	−	0.796629i	$-0.706615\pi$
$761$	−33.3500	−1.20894	−0.604469	+	0.796629i	$0.706615\pi$
$762$	−11.3192	−0.410050
$763$	0.202279	0.00732301
$764$	9.66787	0.349771
$765$	5.99409	0.216717
$766$	−0.719015	−0.0259791
$767$	−33.9304	−1.22516
$768$	11.1854	0.403617
$769$	−51.2650	−1.84866	−0.924332	−	0.381590i	$-0.875377\pi$
$769$	−51.2650	−1.84866	−0.924332	+	0.381590i	$0.875377\pi$
$770$	4.74805	0.171108
$771$	−26.8296	−0.966246
$772$	2.27461	0.0818649
$773$	−7.02010	−0.252495	−0.126248	−	0.991999i	$-0.540293\pi$
$773$	−7.02010	−0.252495	−0.126248	+	0.991999i	$0.540293\pi$
$774$	3.29349	0.118382
$775$	0.428873	0.0154056
$776$	8.32684	0.298916
$777$	−1.80979	−0.0649260
$778$	−24.9252	−0.893611
$779$	4.15026	0.148698
$780$	−11.1750	−0.400128
$781$	48.6049	1.73922
$782$	2.98134	0.106612
$783$	−9.18950	−0.328406
$784$	1.16537	0.0416204
$785$	32.0045	1.14229
$786$	6.26063	0.223309
$787$	−9.46819	−0.337505	−0.168752	−	0.985658i	$-0.553974\pi$
$787$	−9.46819	−0.337505	−0.168752	+	0.985658i	$0.553974\pi$
$788$	17.9271	0.638627
$789$	−9.55741	−0.340253
$790$	−20.7966	−0.739911
$791$	−5.40291	−0.192105
$792$	−9.49105	−0.337250
$793$	54.9609	1.95172
$794$	4.24125	0.150516
$795$	4.19546	0.148798
$796$	−40.3986	−1.43189
$797$	−1.88946	−0.0669280	−0.0334640	−	0.999440i	$-0.510654\pi$
$797$	−1.88946	−0.0669280	−0.0334640	+	0.999440i	$0.510654\pi$
$798$	4.99079	0.176672
$799$	10.5180	0.372101
$800$	11.4823	0.405960
$801$	0.0226128	0.000798983 0
$802$	4.71918	0.166640
$803$	12.7376	0.449499
$804$	3.25620	0.114837
$805$	2.10021	0.0740226
$806$	0.679027	0.0239177
$807$	3.88085	0.136612
$808$	−50.0096	−1.75933
$809$	35.2755	1.24022	0.620110	−	0.784515i	$-0.287088\pi$
$809$	35.2755	1.24022	0.620110	+	0.784515i	$0.287088\pi$
$810$	1.25284	0.0440202
$811$	23.0294	0.808673	0.404337	−	0.914610i	$-0.367502\pi$
$811$	23.0294	0.808673	0.404337	+	0.914610i	$0.367502\pi$
$812$	13.6282	0.478256
$813$	19.4715	0.682894
$814$	−4.93160	−0.172853
$815$	−0.176209	−0.00617234
$816$	4.00896	0.140342
$817$	31.7944	1.11234
$818$	−26.0321	−0.910190
$819$	−4.32458	−0.151113
$820$	−1.54506	−0.0539559
$821$	3.08641	0.107716	0.0538582	−	0.998549i	$-0.482848\pi$
$821$	3.08641	0.107716	0.0538582	+	0.998549i	$0.482848\pi$
$822$	−1.26261	−0.0440387
$823$	7.88637	0.274901	0.137451	−	0.990509i	$-0.456109\pi$
$823$	7.88637	0.274901	0.137451	+	0.990509i	$0.456109\pi$
$824$	40.4505	1.40916
$825$	−7.44294	−0.259130
$826$	−5.64135	−0.196288
$827$	2.91988	0.101534	0.0507671	−	0.998711i	$-0.483833\pi$
$827$	2.91988	0.101534	0.0507671	+	0.998711i	$0.483833\pi$
$828$	−1.78752	−0.0621207
$829$	41.9014	1.45530	0.727648	−	0.685951i	$-0.240613\pi$
$829$	41.9014	1.45530	0.727648	+	0.685951i	$0.240613\pi$
$830$	−10.8981	−0.378277
$831$	−12.0166	−0.416851
$832$	8.10018	0.280823
$833$	−3.44007	−0.119191
$834$	0.962250	0.0333200
$835$	37.3782	1.29352
$836$	−39.0120	−1.34926
$837$	0.218376	0.00754818
$838$	19.8643	0.686200
$839$	47.5431	1.64137	0.820686	−	0.571380i	$-0.193592\pi$
$839$	47.5431	1.64137	0.820686	+	0.571380i	$0.193592\pi$
$840$	−4.36365	−0.150560
$841$	55.4470	1.91196
$842$	−15.7556	−0.542975
$843$	−26.4307	−0.910323
$844$	8.14191	0.280256
$845$	−9.93535	−0.341786
$846$	2.19840	0.0755824
$847$	−3.36287	−0.115550
$848$	2.80600	0.0963585
$849$	16.9567	0.581954
$850$	−4.85768	−0.166617
$851$	−2.18140	−0.0747774
$852$	−19.0198	−0.651607
$853$	−21.9681	−0.752172	−0.376086	−	0.926585i	$-0.622730\pi$
$853$	−21.9681	−0.752172	−0.376086	+	0.926585i	$0.622730\pi$
$854$	9.13794	0.312694
$855$	12.0945	0.413623
$856$	−36.6320	−1.25206
$857$	−35.3687	−1.20817	−0.604086	−	0.796919i	$-0.706462\pi$
$857$	−35.3687	−1.20817	−0.604086	+	0.796919i	$0.706462\pi$
$858$	−11.7843	−0.402308
$859$	32.9988	1.12590	0.562952	−	0.826490i	$-0.309666\pi$
$859$	32.9988	1.12590	0.562952	+	0.826490i	$0.309666\pi$
$860$	−11.8364	−0.403619
$861$	−0.597921	−0.0203771
$862$	−19.8989	−0.677758
$863$	10.0799	0.343125	0.171562	−	0.985173i	$-0.445118\pi$
$863$	10.0799	0.343125	0.171562	+	0.985173i	$0.445118\pi$
$864$	5.84661	0.198906
$865$	−0.367420	−0.0124927
$866$	−23.9899	−0.815210
$867$	5.16593	0.175444
$868$	−0.323855	−0.0109924
$869$	62.9098	2.13407
$870$	−11.5130	−0.390326
$871$	9.49530	0.321736
$872$	−0.506577	−0.0171549
$873$	3.32496	0.112533
$874$	6.01555	0.203479
$875$	−12.1342	−0.410210
$876$	−4.98439	−0.168407
$877$	−3.90256	−0.131780	−0.0658900	−	0.997827i	$-0.520989\pi$
$877$	−3.90256	−0.131780	−0.0658900	+	0.997827i	$0.520989\pi$
$878$	−5.91651	−0.199672
$879$	31.0464	1.04717
$880$	7.69559	0.259418
$881$	16.8467	0.567579	0.283789	−	0.958887i	$-0.408408\pi$
$881$	16.8467	0.567579	0.283789	+	0.958887i	$0.408408\pi$
$882$	−0.719015	−0.0242105
$883$	−28.7172	−0.966410	−0.483205	−	0.875507i	$-0.660527\pi$
$883$	−28.7172	−0.966410	−0.483205	+	0.875507i	$0.660527\pi$
$884$	22.0626	0.742046
$885$	−13.6710	−0.459547
$886$	−18.1133	−0.608529
$887$	−46.2234	−1.55203	−0.776015	−	0.630714i	$-0.782762\pi$
$887$	−46.2234	−1.55203	−0.776015	+	0.630714i	$0.782762\pi$
$888$	4.53234	0.152096
$889$	15.7426	0.527990
$890$	0.0283301	0.000949628 0
$891$	−3.78984	−0.126964
$892$	−16.9175	−0.566440
$893$	21.2226	0.710188
$894$	−7.61537	−0.254696
$895$	1.57964	0.0528016
$896$	−10.3465	−0.345651
$897$	−5.21254	−0.174042
$898$	−19.8183	−0.661346
$899$	−2.00677	−0.0669294
$900$	2.91253	0.0970843
$901$	−8.28305	−0.275948
$902$	−1.62931	−0.0542499
$903$	−4.58056	−0.152431
$904$	13.5307	0.450026
$905$	−30.6992	−1.02048
$906$	−12.3824	−0.411379
$907$	−8.07706	−0.268195	−0.134097	−	0.990968i	$-0.542813\pi$
$907$	−8.07706	−0.268195	−0.134097	+	0.990968i	$0.542813\pi$
$908$	22.7960	0.756511
$909$	−19.9692	−0.662335
$910$	−5.41800	−0.179605
$911$	−6.26542	−0.207583	−0.103791	−	0.994599i	$-0.533097\pi$
$911$	−6.26542	−0.207583	−0.103791	+	0.994599i	$0.533097\pi$
$912$	8.08902	0.267854
$913$	32.9666	1.09104
$914$	15.9407	0.527272
$915$	22.1445	0.732076
$916$	1.64723	0.0544260
$917$	−8.70722	−0.287538
$918$	−2.47346	−0.0816364
$919$	−35.4950	−1.17087	−0.585437	−	0.810718i	$-0.699077\pi$
$919$	−35.4950	−1.17087	−0.585437	+	0.810718i	$0.699077\pi$
$920$	−5.25964	−0.173405
$921$	−34.3856	−1.13304
$922$	22.4516	0.739403
$923$	−55.4630	−1.82559
$924$	5.62039	0.184897
$925$	3.55429	0.116864
$926$	25.6743	0.843710
$927$	16.1522	0.530506
$928$	−53.7274	−1.76369
$929$	16.7272	0.548801	0.274400	−	0.961616i	$-0.411521\pi$
$929$	16.7272	0.548801	0.274400	+	0.961616i	$0.411521\pi$
$930$	0.273590	0.00897135
$931$	−6.94115	−0.227487
$932$	17.1101	0.560459
$933$	−29.4852	−0.965302
$934$	20.7534	0.679073
$935$	−22.7166	−0.742914
$936$	10.8302	0.353997
$937$	53.7882	1.75718	0.878592	−	0.477572i	$-0.158483\pi$
$937$	53.7882	1.75718	0.878592	+	0.477572i	$0.158483\pi$
$938$	1.57871	0.0515468
$939$	6.00309	0.195903
$940$	−7.90079	−0.257695
$941$	23.1315	0.754065	0.377033	−	0.926200i	$-0.376944\pi$
$941$	23.1315	0.754065	0.377033	+	0.926200i	$0.376944\pi$
$942$	−13.2067	−0.430296
$943$	−0.720691	−0.0234689
$944$	−9.14344	−0.297594
$945$	−1.74243	−0.0566814
$946$	−12.4818	−0.405818
$947$	−29.7807	−0.967743	−0.483871	−	0.875139i	$-0.660770\pi$
$947$	−29.7807	−0.967743	−0.483871	+	0.875139i	$0.660770\pi$
$948$	−24.6175	−0.799539
$949$	−14.5348	−0.471821
$950$	−9.80153	−0.318004
$951$	−2.68404	−0.0870361
$952$	8.61511	0.279217
$953$	−35.2624	−1.14226	−0.571131	−	0.820859i	$-0.693495\pi$
$953$	−35.2624	−1.14226	−0.571131	+	0.820859i	$0.693495\pi$
$954$	−1.73126	−0.0560515
$955$	11.3590	0.367570
$956$	−18.1863	−0.588188
$957$	34.8267	1.12579
$958$	−16.5886	−0.535953
$959$	1.75603	0.0567052
$960$	3.26368	0.105335
$961$	−30.9523	−0.998462
$962$	5.62745	0.181436
$963$	−14.6274	−0.471361
$964$	24.2863	0.782208
$965$	2.67249	0.0860306
$966$	−0.866650	−0.0278840
$967$	−9.96769	−0.320539	−0.160270	−	0.987073i	$-0.551236\pi$
$967$	−9.96769	−0.320539	−0.160270	+	0.987073i	$0.551236\pi$
$968$	8.42178	0.270686
$969$	−23.8780	−0.767073
$970$	4.16564	0.133751
$971$	7.30296	0.234363	0.117182	−	0.993111i	$-0.462614\pi$
$971$	7.30296	0.234363	0.117182	+	0.993111i	$0.462614\pi$
$972$	1.48302	0.0475678
$973$	−1.33829	−0.0429036
$974$	−4.31162	−0.138153
$975$	8.49313	0.271998
$976$	14.8107	0.474078
$977$	−28.9365	−0.925761	−0.462881	−	0.886421i	$-0.653184\pi$
$977$	−28.9365	−0.925761	−0.462881	+	0.886421i	$0.653184\pi$
$978$	0.0727127	0.00232510
$979$	−0.0856987	−0.00273894
$980$	2.58406	0.0825448
$981$	−0.202279	−0.00645828
$982$	11.6650	0.372247
$983$	−21.8526	−0.696989	−0.348494	−	0.937311i	$-0.613307\pi$
$983$	−21.8526	−0.696989	−0.348494	+	0.937311i	$0.613307\pi$
$984$	1.49740	0.0477353
$985$	21.0630	0.671124
$986$	22.7299	0.723867
$987$	−3.05751	−0.0973216
$988$	44.5165	1.41626
$989$	−5.52108	−0.175560
$990$	−4.74805	−0.150903
$991$	−41.0263	−1.30324	−0.651621	−	0.758545i	$-0.725911\pi$
$991$	−41.0263	−1.30324	−0.651621	+	0.758545i	$0.725911\pi$
$992$	1.27676	0.0405371
$993$	−25.1640	−0.798557
$994$	−9.22142	−0.292486
$995$	−47.4653	−1.50475
$996$	−12.9003	−0.408762
$997$	−0.721999	−0.0228660	−0.0114330	−	0.999935i	$-0.503639\pi$
$997$	−0.721999	−0.0228660	−0.0114330	+	0.999935i	$0.503639\pi$
$998$	−14.9487	−0.473193
$999$	1.80979	0.0572593

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.s.1.20	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.s.1.20	✓	50	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)

\(f(q)\)	\(=\)	\(q-0.719015 q^{2} -1.00000 q^{3} -1.48302 q^{4} -1.74243 q^{5} +0.719015 q^{6} -1.00000 q^{7} +2.50434 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.719015 q^{2} -1.00000 q^{3} -1.48302 q^{4} -1.74243 q^{5} +0.719015 q^{6} -1.00000 q^{7} +2.50434 q^{8} +1.00000 q^{9} +1.25284 q^{10} -3.78984 q^{11} +1.48302 q^{12} +4.32458 q^{13} +0.719015 q^{14} +1.74243 q^{15} +1.16537 q^{16} -3.44007 q^{17} -0.719015 q^{18} -6.94115 q^{19} +2.58406 q^{20} +1.00000 q^{21} +2.72495 q^{22} +1.20533 q^{23} -2.50434 q^{24} -1.96392 q^{25} -3.10944 q^{26} -1.00000 q^{27} +1.48302 q^{28} +9.18950 q^{29} -1.25284 q^{30} -0.218376 q^{31} -5.84661 q^{32} +3.78984 q^{33} +2.47346 q^{34} +1.74243 q^{35} -1.48302 q^{36} -1.80979 q^{37} +4.99079 q^{38} -4.32458 q^{39} -4.36365 q^{40} -0.597921 q^{41} -0.719015 q^{42} -4.58056 q^{43} +5.62039 q^{44} -1.74243 q^{45} -0.866650 q^{46} -3.05751 q^{47} -1.16537 q^{48} +1.00000 q^{49} +1.41209 q^{50} +3.44007 q^{51} -6.41342 q^{52} +2.40782 q^{53} +0.719015 q^{54} +6.60354 q^{55} -2.50434 q^{56} +6.94115 q^{57} -6.60739 q^{58} -7.84594 q^{59} -2.58406 q^{60} +12.7090 q^{61} +0.157016 q^{62} -1.00000 q^{63} +1.87306 q^{64} -7.53530 q^{65} -2.72495 q^{66} +2.19566 q^{67} +5.10168 q^{68} -1.20533 q^{69} -1.25284 q^{70} -12.8251 q^{71} +2.50434 q^{72} -3.36098 q^{73} +1.30127 q^{74} +1.96392 q^{75} +10.2938 q^{76} +3.78984 q^{77} +3.10944 q^{78} -16.5996 q^{79} -2.03059 q^{80} +1.00000 q^{81} +0.429914 q^{82} -8.69870 q^{83} -1.48302 q^{84} +5.99409 q^{85} +3.29349 q^{86} -9.18950 q^{87} -9.49105 q^{88} +0.0226128 q^{89} +1.25284 q^{90} -4.32458 q^{91} -1.78752 q^{92} +0.218376 q^{93} +2.19840 q^{94} +12.0945 q^{95} +5.84661 q^{96} +3.32496 q^{97} -0.719015 q^{98} -3.78984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9}+O(q^{10}) \) 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9} + 16 q^{10} - 31 q^{11} - 53 q^{12} + 42 q^{13} + q^{14} - 11 q^{15} + 59 q^{16} + 44 q^{17} - q^{18} + 11 q^{19} + 7 q^{20} + 50 q^{21} + 19 q^{22} - 16 q^{23} + 6 q^{24} + 71 q^{25} + q^{26} - 50 q^{27} - 53 q^{28} + 3 q^{29} - 16 q^{30} + 13 q^{31} - 23 q^{32} + 31 q^{33} + q^{34} - 11 q^{35} + 53 q^{36} + 53 q^{37} + 28 q^{38} - 42 q^{39} + 50 q^{40} + 23 q^{41} - q^{42} + 9 q^{43} - 78 q^{44} + 11 q^{45} - 8 q^{46} + 26 q^{47} - 59 q^{48} + 50 q^{49} - 38 q^{50} - 44 q^{51} + 86 q^{52} + 58 q^{53} + q^{54} + 28 q^{55} + 6 q^{56} - 11 q^{57} - 4 q^{58} + 7 q^{59} - 7 q^{60} + 51 q^{61} + 7 q^{62} - 50 q^{63} + 74 q^{64} - 14 q^{65} - 19 q^{66} + 23 q^{67} + 98 q^{68} + 16 q^{69} - 16 q^{70} - 75 q^{71} - 6 q^{72} + 34 q^{73} - 68 q^{74} - 71 q^{75} + 31 q^{76} + 31 q^{77} - q^{78} - 18 q^{79} - 21 q^{80} + 50 q^{81} + 31 q^{82} + 40 q^{83} + 53 q^{84} + 30 q^{85} - 15 q^{86} - 3 q^{87} + 70 q^{88} + 63 q^{89} + 16 q^{90} - 42 q^{91} - 38 q^{92} - 13 q^{93} + q^{94} - 77 q^{95} + 23 q^{96} + 77 q^{97} - q^{98} - 31 q^{99}+O(q^{100}) \) 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9 + 16 * q^10 - 31 * q^11 - 53 * q^12 + 42 * q^13 + q^14 - 11 * q^15 + 59 * q^16 + 44 * q^17 - q^18 + 11 * q^19 + 7 * q^20 + 50 * q^21 + 19 * q^22 - 16 * q^23 + 6 * q^24 + 71 * q^25 + q^26 - 50 * q^27 - 53 * q^28 + 3 * q^29 - 16 * q^30 + 13 * q^31 - 23 * q^32 + 31 * q^33 + q^34 - 11 * q^35 + 53 * q^36 + 53 * q^37 + 28 * q^38 - 42 * q^39 + 50 * q^40 + 23 * q^41 - q^42 + 9 * q^43 - 78 * q^44 + 11 * q^45 - 8 * q^46 + 26 * q^47 - 59 * q^48 + 50 * q^49 - 38 * q^50 - 44 * q^51 + 86 * q^52 + 58 * q^53 + q^54 + 28 * q^55 + 6 * q^56 - 11 * q^57 - 4 * q^58 + 7 * q^59 - 7 * q^60 + 51 * q^61 + 7 * q^62 - 50 * q^63 + 74 * q^64 - 14 * q^65 - 19 * q^66 + 23 * q^67 + 98 * q^68 + 16 * q^69 - 16 * q^70 - 75 * q^71 - 6 * q^72 + 34 * q^73 - 68 * q^74 - 71 * q^75 + 31 * q^76 + 31 * q^77 - q^78 - 18 * q^79 - 21 * q^80 + 50 * q^81 + 31 * q^82 + 40 * q^83 + 53 * q^84 + 30 * q^85 - 15 * q^86 - 3 * q^87 + 70 * q^88 + 63 * q^89 + 16 * q^90 - 42 * q^91 - 38 * q^92 - 13 * q^93 + q^94 - 77 * q^95 + 23 * q^96 + 77 * q^97 - q^98 - 31 * q^99

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