LMFDB - Embedded newform 6026.2.a.g.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.293262 q^{3} +1.00000 q^{4} +2.91518 q^{5} -0.293262 q^{6} -1.20061 q^{7} +1.00000 q^{8} -2.91400 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.293262 q^{3} +1.00000 q^{4} +2.91518 q^{5} -0.293262 q^{6} -1.20061 q^{7} +1.00000 q^{8} -2.91400 q^{9} +2.91518 q^{10} +1.41331 q^{11} -0.293262 q^{12} -4.65392 q^{13} -1.20061 q^{14} -0.854912 q^{15} +1.00000 q^{16} -2.36797 q^{17} -2.91400 q^{18} -6.18126 q^{19} +2.91518 q^{20} +0.352095 q^{21} +1.41331 q^{22} -1.00000 q^{23} -0.293262 q^{24} +3.49827 q^{25} -4.65392 q^{26} +1.73435 q^{27} -1.20061 q^{28} +7.99068 q^{29} -0.854912 q^{30} +0.618029 q^{31} +1.00000 q^{32} -0.414470 q^{33} -2.36797 q^{34} -3.50000 q^{35} -2.91400 q^{36} -8.40404 q^{37} -6.18126 q^{38} +1.36482 q^{39} +2.91518 q^{40} +9.57225 q^{41} +0.352095 q^{42} +5.03707 q^{43} +1.41331 q^{44} -8.49482 q^{45} -1.00000 q^{46} +3.66057 q^{47} -0.293262 q^{48} -5.55853 q^{49} +3.49827 q^{50} +0.694437 q^{51} -4.65392 q^{52} -8.36372 q^{53} +1.73435 q^{54} +4.12004 q^{55} -1.20061 q^{56} +1.81273 q^{57} +7.99068 q^{58} -13.6531 q^{59} -0.854912 q^{60} -8.02282 q^{61} +0.618029 q^{62} +3.49859 q^{63} +1.00000 q^{64} -13.5670 q^{65} -0.414470 q^{66} -3.54042 q^{67} -2.36797 q^{68} +0.293262 q^{69} -3.50000 q^{70} -16.5616 q^{71} -2.91400 q^{72} +9.46231 q^{73} -8.40404 q^{74} -1.02591 q^{75} -6.18126 q^{76} -1.69684 q^{77} +1.36482 q^{78} -0.327709 q^{79} +2.91518 q^{80} +8.23337 q^{81} +9.57225 q^{82} -3.85948 q^{83} +0.352095 q^{84} -6.90306 q^{85} +5.03707 q^{86} -2.34336 q^{87} +1.41331 q^{88} -12.4247 q^{89} -8.49482 q^{90} +5.58756 q^{91} -1.00000 q^{92} -0.181245 q^{93} +3.66057 q^{94} -18.0195 q^{95} -0.293262 q^{96} -9.13312 q^{97} -5.55853 q^{98} -4.11837 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9} - 13 q^{10} - 4 q^{11} - 4 q^{13} - 18 q^{14} - 16 q^{15} + 21 q^{16} - 12 q^{17} + 7 q^{18} - 18 q^{19} - 13 q^{20} - 24 q^{21} - 4 q^{22} - 21 q^{23} + 2 q^{25} - 4 q^{26} - 9 q^{27} - 18 q^{28} - 16 q^{29} - 16 q^{30} - 7 q^{31} + 21 q^{32} - 15 q^{33} - 12 q^{34} + 7 q^{36} - 44 q^{37} - 18 q^{38} - 14 q^{39} - 13 q^{40} - 23 q^{41} - 24 q^{42} - 18 q^{43} - 4 q^{44} - 36 q^{45} - 21 q^{46} + 2 q^{47} - 13 q^{49} + 2 q^{50} - 26 q^{51} - 4 q^{52} - 39 q^{53} - 9 q^{54} - 32 q^{55} - 18 q^{56} - 22 q^{57} - 16 q^{58} - 27 q^{59} - 16 q^{60} - 34 q^{61} - 7 q^{62} - 28 q^{63} + 21 q^{64} - 25 q^{65} - 15 q^{66} - 19 q^{67} - 12 q^{68} - 24 q^{71} + 7 q^{72} - 8 q^{73} - 44 q^{74} + 50 q^{75} - 18 q^{76} - 16 q^{77} - 14 q^{78} - 27 q^{79} - 13 q^{80} + 33 q^{81} - 23 q^{82} + 7 q^{83} - 24 q^{84} - 22 q^{85} - 18 q^{86} - 15 q^{87} - 4 q^{88} - 12 q^{89} - 36 q^{90} - 20 q^{91} - 21 q^{92} - 43 q^{93} + 2 q^{94} - 14 q^{95} - 52 q^{97} - 13 q^{98} - 30 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9 - 13 * q^10 - 4 * q^11 - 4 * q^13 - 18 * q^14 - 16 * q^15 + 21 * q^16 - 12 * q^17 + 7 * q^18 - 18 * q^19 - 13 * q^20 - 24 * q^21 - 4 * q^22 - 21 * q^23 + 2 * q^25 - 4 * q^26 - 9 * q^27 - 18 * q^28 - 16 * q^29 - 16 * q^30 - 7 * q^31 + 21 * q^32 - 15 * q^33 - 12 * q^34 + 7 * q^36 - 44 * q^37 - 18 * q^38 - 14 * q^39 - 13 * q^40 - 23 * q^41 - 24 * q^42 - 18 * q^43 - 4 * q^44 - 36 * q^45 - 21 * q^46 + 2 * q^47 - 13 * q^49 + 2 * q^50 - 26 * q^51 - 4 * q^52 - 39 * q^53 - 9 * q^54 - 32 * q^55 - 18 * q^56 - 22 * q^57 - 16 * q^58 - 27 * q^59 - 16 * q^60 - 34 * q^61 - 7 * q^62 - 28 * q^63 + 21 * q^64 - 25 * q^65 - 15 * q^66 - 19 * q^67 - 12 * q^68 - 24 * q^71 + 7 * q^72 - 8 * q^73 - 44 * q^74 + 50 * q^75 - 18 * q^76 - 16 * q^77 - 14 * q^78 - 27 * q^79 - 13 * q^80 + 33 * q^81 - 23 * q^82 + 7 * q^83 - 24 * q^84 - 22 * q^85 - 18 * q^86 - 15 * q^87 - 4 * q^88 - 12 * q^89 - 36 * q^90 - 20 * q^91 - 21 * q^92 - 43 * q^93 + 2 * q^94 - 14 * q^95 - 52 * q^97 - 13 * q^98 - 30 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.293262	−0.169315	−0.0846575	−	0.996410i	$-0.526980\pi$
$3$	−0.293262	−0.169315	−0.0846575	+	0.996410i	$0.526980\pi$
$4$	1.00000	0.500000
$5$	2.91518	1.30371	0.651854	−	0.758345i	$-0.273992\pi$
$5$	2.91518	1.30371	0.651854	+	0.758345i	$0.273992\pi$
$6$	−0.293262	−0.119724
$7$	−1.20061	−0.453789	−0.226895	−	0.973919i	$-0.572857\pi$
$7$	−1.20061	−0.453789	−0.226895	+	0.973919i	$0.572857\pi$
$8$	1.00000	0.353553
$9$	−2.91400	−0.971332
$10$	2.91518	0.921861
$11$	1.41331	0.426128	0.213064	−	0.977038i	$-0.431656\pi$
$11$	1.41331	0.426128	0.213064	+	0.977038i	$0.431656\pi$
$12$	−0.293262	−0.0846575
$13$	−4.65392	−1.29077	−0.645383	−	0.763859i	$-0.723302\pi$
$13$	−4.65392	−1.29077	−0.645383	+	0.763859i	$0.723302\pi$
$14$	−1.20061	−0.320878
$15$	−0.854912	−0.220737
$16$	1.00000	0.250000
$17$	−2.36797	−0.574318	−0.287159	−	0.957883i	$-0.592711\pi$
$17$	−2.36797	−0.574318	−0.287159	+	0.957883i	$0.592711\pi$
$18$	−2.91400	−0.686836
$19$	−6.18126	−1.41808	−0.709040	−	0.705169i	$-0.750871\pi$
$19$	−6.18126	−1.41808	−0.709040	+	0.705169i	$0.750871\pi$
$20$	2.91518	0.651854
$21$	0.352095	0.0768334
$22$	1.41331	0.301318
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−0.293262	−0.0598619
$25$	3.49827	0.699654
$26$	−4.65392	−0.912709
$27$	1.73435	0.333776
$28$	−1.20061	−0.226895
$29$	7.99068	1.48383	0.741916	−	0.670493i	$-0.233917\pi$
$29$	7.99068	1.48383	0.741916	+	0.670493i	$0.233917\pi$
$30$	−0.854912	−0.156085
$31$	0.618029	0.111001	0.0555007	−	0.998459i	$-0.482325\pi$
$31$	0.618029	0.111001	0.0555007	+	0.998459i	$0.482325\pi$
$32$	1.00000	0.176777
$33$	−0.414470	−0.0721499
$34$	−2.36797	−0.406104
$35$	−3.50000	−0.591609
$36$	−2.91400	−0.485666
$37$	−8.40404	−1.38162	−0.690808	−	0.723038i	$-0.742745\pi$
$37$	−8.40404	−1.38162	−0.690808	+	0.723038i	$0.742745\pi$
$38$	−6.18126	−1.00273
$39$	1.36482	0.218546
$40$	2.91518	0.460930
$41$	9.57225	1.49493	0.747467	−	0.664299i	$-0.231270\pi$
$41$	9.57225	1.49493	0.747467	+	0.664299i	$0.231270\pi$
$42$	0.352095	0.0543294
$43$	5.03707	0.768146	0.384073	−	0.923303i	$-0.374521\pi$
$43$	5.03707	0.768146	0.384073	+	0.923303i	$0.374521\pi$
$44$	1.41331	0.213064
$45$	−8.49482	−1.26633
$46$	−1.00000	−0.147442
$47$	3.66057	0.533949	0.266975	−	0.963704i	$-0.413976\pi$
$47$	3.66057	0.533949	0.266975	+	0.963704i	$0.413976\pi$
$48$	−0.293262	−0.0423288
$49$	−5.55853	−0.794075
$50$	3.49827	0.494730
$51$	0.694437	0.0972406
$52$	−4.65392	−0.645383
$53$	−8.36372	−1.14885	−0.574423	−	0.818559i	$-0.694773\pi$
$53$	−8.36372	−1.14885	−0.574423	+	0.818559i	$0.694773\pi$
$54$	1.73435	0.236015
$55$	4.12004	0.555547
$56$	−1.20061	−0.160439
$57$	1.81273	0.240102
$58$	7.99068	1.04923
$59$	−13.6531	−1.77749	−0.888744	−	0.458404i	$-0.848421\pi$
$59$	−13.6531	−1.77749	−0.888744	+	0.458404i	$0.848421\pi$
$60$	−0.854912	−0.110369
$61$	−8.02282	−1.02722	−0.513609	−	0.858025i	$-0.671692\pi$
$61$	−8.02282	−1.02722	−0.513609	+	0.858025i	$0.671692\pi$
$62$	0.618029	0.0784898
$63$	3.49859	0.440780
$64$	1.00000	0.125000
$65$	−13.5670	−1.68278
$66$	−0.414470	−0.0510177
$67$	−3.54042	−0.432531	−0.216266	−	0.976335i	$-0.569388\pi$
$67$	−3.54042	−0.432531	−0.216266	+	0.976335i	$0.569388\pi$
$68$	−2.36797	−0.287159
$69$	0.293262	0.0353046
$70$	−3.50000	−0.418331
$71$	−16.5616	−1.96550	−0.982752	−	0.184929i	$-0.940794\pi$
$71$	−16.5616	−1.96550	−0.982752	+	0.184929i	$0.940794\pi$
$72$	−2.91400	−0.343418
$73$	9.46231	1.10748	0.553740	−	0.832690i	$-0.313200\pi$
$73$	9.46231	1.10748	0.553740	+	0.832690i	$0.313200\pi$
$74$	−8.40404	−0.976950
$75$	−1.02591	−0.118462
$76$	−6.18126	−0.709040
$77$	−1.69684	−0.193372
$78$	1.36482	0.154535
$79$	−0.327709	−0.0368701	−0.0184351	−	0.999830i	$-0.505868\pi$
$79$	−0.327709	−0.0368701	−0.0184351	+	0.999830i	$0.505868\pi$
$80$	2.91518	0.325927
$81$	8.23337	0.914819
$82$	9.57225	1.05708
$83$	−3.85948	−0.423633	−0.211817	−	0.977309i	$-0.567938\pi$
$83$	−3.85948	−0.423633	−0.211817	+	0.977309i	$0.567938\pi$
$84$	0.352095	0.0384167
$85$	−6.90306	−0.748742
$86$	5.03707	0.543161
$87$	−2.34336	−0.251235
$88$	1.41331	0.150659
$89$	−12.4247	−1.31702	−0.658508	−	0.752574i	$-0.728812\pi$
$89$	−12.4247	−1.31702	−0.658508	+	0.752574i	$0.728812\pi$
$90$	−8.49482	−0.895433
$91$	5.58756	0.585736
$92$	−1.00000	−0.104257
$93$	−0.181245	−0.0187942
$94$	3.66057	0.377559
$95$	−18.0195	−1.84876
$96$	−0.293262	−0.0299310
$97$	−9.13312	−0.927328	−0.463664	−	0.886011i	$-0.653466\pi$
$97$	−9.13312	−0.927328	−0.463664	+	0.886011i	$0.653466\pi$
$98$	−5.55853	−0.561496
$99$	−4.11837	−0.413912
$100$	3.49827	0.349827
$101$	6.83591	0.680199	0.340099	−	0.940390i	$-0.389539\pi$
$101$	6.83591	0.680199	0.340099	+	0.940390i	$0.389539\pi$
$102$	0.694437	0.0687595
$103$	−8.86600	−0.873592	−0.436796	−	0.899560i	$-0.643887\pi$
$103$	−8.86600	−0.873592	−0.436796	+	0.899560i	$0.643887\pi$
$104$	−4.65392	−0.456355
$105$	1.02642	0.100168
$106$	−8.36372	−0.812357
$107$	13.8868	1.34249	0.671243	−	0.741237i	$-0.265761\pi$
$107$	13.8868	1.34249	0.671243	+	0.741237i	$0.265761\pi$
$108$	1.73435	0.166888
$109$	−3.91458	−0.374949	−0.187474	−	0.982269i	$-0.560030\pi$
$109$	−3.91458	−0.374949	−0.187474	+	0.982269i	$0.560030\pi$
$110$	4.12004	0.392831
$111$	2.46459	0.233928
$112$	−1.20061	−0.113447
$113$	−12.1620	−1.14411	−0.572054	−	0.820216i	$-0.693853\pi$
$113$	−12.1620	−1.14411	−0.572054	+	0.820216i	$0.693853\pi$
$114$	1.81273	0.169778
$115$	−2.91518	−0.271842
$116$	7.99068	0.741916
$117$	13.5615	1.25376
$118$	−13.6531	−1.25687
$119$	2.84302	0.260619
$120$	−0.854912	−0.0780424
$121$	−9.00256	−0.818415
$122$	−8.02282	−0.726352
$123$	−2.80718	−0.253115
$124$	0.618029	0.0555007
$125$	−4.37781	−0.391563
$126$	3.49859	0.311679
$127$	4.12503	0.366037	0.183018	−	0.983109i	$-0.441413\pi$
$127$	4.12503	0.366037	0.183018	+	0.983109i	$0.441413\pi$
$128$	1.00000	0.0883883
$129$	−1.47718	−0.130059
$130$	−13.5670	−1.18991
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−0.414470	−0.0360750
$133$	7.42131	0.643509
$134$	−3.54042	−0.305846
$135$	5.05595	0.435147
$136$	−2.36797	−0.203052
$137$	4.66907	0.398906	0.199453	−	0.979907i	$-0.436084\pi$
$137$	4.66907	0.398906	0.199453	+	0.979907i	$0.436084\pi$
$138$	0.293262	0.0249641
$139$	−1.97951	−0.167900	−0.0839498	−	0.996470i	$-0.526754\pi$
$139$	−1.97951	−0.167900	−0.0839498	+	0.996470i	$0.526754\pi$
$140$	−3.50000	−0.295804
$141$	−1.07351	−0.0904056
$142$	−16.5616	−1.38982
$143$	−6.57742	−0.550032
$144$	−2.91400	−0.242833
$145$	23.2943	1.93448
$146$	9.46231	0.783106
$147$	1.63011	0.134449
$148$	−8.40404	−0.690808
$149$	−4.63128	−0.379409	−0.189705	−	0.981841i	$-0.560753\pi$
$149$	−4.63128	−0.379409	−0.189705	+	0.981841i	$0.560753\pi$
$150$	−1.02591	−0.0837652
$151$	0.890055	0.0724316	0.0362158	−	0.999344i	$-0.488470\pi$
$151$	0.890055	0.0724316	0.0362158	+	0.999344i	$0.488470\pi$
$152$	−6.18126	−0.501367
$153$	6.90026	0.557853
$154$	−1.69684	−0.136735
$155$	1.80167	0.144713
$156$	1.36482	0.109273
$157$	−3.68671	−0.294232	−0.147116	−	0.989119i	$-0.546999\pi$
$157$	−3.68671	−0.294232	−0.147116	+	0.989119i	$0.546999\pi$
$158$	−0.327709	−0.0260711
$159$	2.45276	0.194517
$160$	2.91518	0.230465
$161$	1.20061	0.0946216
$162$	8.23337	0.646875
$163$	23.4367	1.83571	0.917854	−	0.396919i	$-0.129921\pi$
$163$	23.4367	1.83571	0.917854	+	0.396919i	$0.129921\pi$
$164$	9.57225	0.747467
$165$	−1.20825	−0.0940624
$166$	−3.85948	−0.299554
$167$	−13.3323	−1.03168	−0.515842	−	0.856684i	$-0.672521\pi$
$167$	−13.3323	−1.03168	−0.515842	+	0.856684i	$0.672521\pi$
$168$	0.352095	0.0271647
$169$	8.65900	0.666077
$170$	−6.90306	−0.529441
$171$	18.0122	1.37743
$172$	5.03707	0.384073
$173$	−0.0637233	−0.00484479	−0.00242240	−	0.999997i	$-0.500771\pi$
$173$	−0.0637233	−0.00484479	−0.00242240	+	0.999997i	$0.500771\pi$
$174$	−2.34336	−0.177650
$175$	−4.20007	−0.317496
$176$	1.41331	0.106532
$177$	4.00395	0.300955
$178$	−12.4247	−0.931271
$179$	10.9013	0.814805	0.407403	−	0.913249i	$-0.366435\pi$
$179$	10.9013	0.814805	0.407403	+	0.913249i	$0.366435\pi$
$180$	−8.49482	−0.633167
$181$	3.72697	0.277023	0.138512	−	0.990361i	$-0.455768\pi$
$181$	3.72697	0.277023	0.138512	+	0.990361i	$0.455768\pi$
$182$	5.58756	0.414178
$183$	2.35279	0.173923
$184$	−1.00000	−0.0737210
$185$	−24.4993	−1.80122
$186$	−0.181245	−0.0132895
$187$	−3.34667	−0.244733
$188$	3.66057	0.266975
$189$	−2.08229	−0.151464
$190$	−18.0195	−1.30727
$191$	−21.3577	−1.54539	−0.772696	−	0.634777i	$-0.781092\pi$
$191$	−21.3577	−1.54539	−0.772696	+	0.634777i	$0.781092\pi$
$192$	−0.293262	−0.0211644
$193$	−23.2213	−1.67151	−0.835753	−	0.549105i	$-0.814969\pi$
$193$	−23.2213	−1.67151	−0.835753	+	0.549105i	$0.814969\pi$
$194$	−9.13312	−0.655720
$195$	3.97869	0.284920
$196$	−5.55853	−0.397038
$197$	−16.2479	−1.15762	−0.578809	−	0.815463i	$-0.696482\pi$
$197$	−16.2479	−1.15762	−0.578809	+	0.815463i	$0.696482\pi$
$198$	−4.11837	−0.292680
$199$	23.2740	1.64985	0.824924	−	0.565243i	$-0.191218\pi$
$199$	23.2740	1.64985	0.824924	+	0.565243i	$0.191218\pi$
$200$	3.49827	0.247365
$201$	1.03827	0.0732340
$202$	6.83591	0.480973
$203$	−9.59372	−0.673347
$204$	0.694437	0.0486203
$205$	27.9048	1.94896
$206$	−8.86600	−0.617723
$207$	2.91400	0.202537
$208$	−4.65392	−0.322691
$209$	−8.73603	−0.604284
$210$	1.02642	0.0708296
$211$	23.8909	1.64472	0.822359	−	0.568969i	$-0.192657\pi$
$211$	23.8909	1.64472	0.822359	+	0.568969i	$0.192657\pi$
$212$	−8.36372	−0.574423
$213$	4.85690	0.332789
$214$	13.8868	0.949281
$215$	14.6840	1.00144
$216$	1.73435	0.118008
$217$	−0.742015	−0.0503712
$218$	−3.91458	−0.265129
$219$	−2.77494	−0.187513
$220$	4.12004	0.277773
$221$	11.0204	0.741310
$222$	2.46459	0.165412
$223$	5.94441	0.398067	0.199033	−	0.979993i	$-0.436220\pi$
$223$	5.94441	0.398067	0.199033	+	0.979993i	$0.436220\pi$
$224$	−1.20061	−0.0802194
$225$	−10.1939	−0.679597
$226$	−12.1620	−0.809007
$227$	4.59029	0.304668	0.152334	−	0.988329i	$-0.451321\pi$
$227$	4.59029	0.304668	0.152334	+	0.988329i	$0.451321\pi$
$228$	1.81273	0.120051
$229$	2.33173	0.154085	0.0770426	−	0.997028i	$-0.475452\pi$
$229$	2.33173	0.154085	0.0770426	+	0.997028i	$0.475452\pi$
$230$	−2.91518	−0.192221
$231$	0.497618	0.0327409
$232$	7.99068	0.524614
$233$	10.9602	0.718028	0.359014	−	0.933332i	$-0.383113\pi$
$233$	10.9602	0.718028	0.359014	+	0.933332i	$0.383113\pi$
$234$	13.5615	0.886544
$235$	10.6712	0.696114
$236$	−13.6531	−0.888744
$237$	0.0961046	0.00624266
$238$	2.84302	0.184286
$239$	−13.4758	−0.871678	−0.435839	−	0.900025i	$-0.643548\pi$
$239$	−13.4758	−0.871678	−0.435839	+	0.900025i	$0.643548\pi$
$240$	−0.854912	−0.0551843
$241$	28.1083	1.81061	0.905307	−	0.424758i	$-0.139641\pi$
$241$	28.1083	1.81061	0.905307	+	0.424758i	$0.139641\pi$
$242$	−9.00256	−0.578707
$243$	−7.61759	−0.488669
$244$	−8.02282	−0.513609
$245$	−16.2041	−1.03524
$246$	−2.80718	−0.178979
$247$	28.7671	1.83041
$248$	0.618029	0.0392449
$249$	1.13184	0.0717274
$250$	−4.37781	−0.276877
$251$	−10.0873	−0.636703	−0.318352	−	0.947973i	$-0.603129\pi$
$251$	−10.0873	−0.636703	−0.318352	+	0.947973i	$0.603129\pi$
$252$	3.49859	0.220390
$253$	−1.41331	−0.0888539
$254$	4.12503	0.258827
$255$	2.02441	0.126773
$256$	1.00000	0.0625000
$257$	5.48759	0.342306	0.171153	−	0.985244i	$-0.445251\pi$
$257$	5.48759	0.342306	0.171153	+	0.985244i	$0.445251\pi$
$258$	−1.47718	−0.0919654
$259$	10.0900	0.626963
$260$	−13.5670	−0.841391
$261$	−23.2848	−1.44129
$262$	1.00000	0.0617802
$263$	−5.48073	−0.337956	−0.168978	−	0.985620i	$-0.554047\pi$
$263$	−5.48073	−0.337956	−0.168978	+	0.985620i	$0.554047\pi$
$264$	−0.414470	−0.0255088
$265$	−24.3818	−1.49776
$266$	7.42131	0.455030
$267$	3.64370	0.222991
$268$	−3.54042	−0.216266
$269$	20.9907	1.27983	0.639913	−	0.768448i	$-0.278970\pi$
$269$	20.9907	1.27983	0.639913	+	0.768448i	$0.278970\pi$
$270$	5.05595	0.307695
$271$	16.9950	1.03237	0.516187	−	0.856476i	$-0.327351\pi$
$271$	16.9950	1.03237	0.516187	+	0.856476i	$0.327351\pi$
$272$	−2.36797	−0.143579
$273$	−1.63862	−0.0991739
$274$	4.66907	0.282069
$275$	4.94413	0.298142
$276$	0.293262	0.0176523
$277$	7.32313	0.440004	0.220002	−	0.975499i	$-0.429394\pi$
$277$	7.32313	0.440004	0.220002	+	0.975499i	$0.429394\pi$
$278$	−1.97951	−0.118723
$279$	−1.80094	−0.107819
$280$	−3.50000	−0.209165
$281$	2.04822	0.122187	0.0610933	−	0.998132i	$-0.480541\pi$
$281$	2.04822	0.122187	0.0610933	+	0.998132i	$0.480541\pi$
$282$	−1.07351	−0.0639264
$283$	−0.872093	−0.0518405	−0.0259203	−	0.999664i	$-0.508252\pi$
$283$	−0.872093	−0.0518405	−0.0259203	+	0.999664i	$0.508252\pi$
$284$	−16.5616	−0.982752
$285$	5.28444	0.313023
$286$	−6.57742	−0.388931
$287$	−11.4926	−0.678385
$288$	−2.91400	−0.171709
$289$	−11.3927	−0.670159
$290$	23.2943	1.36789
$291$	2.67840	0.157011
$292$	9.46231	0.553740
$293$	20.2252	1.18157	0.590784	−	0.806830i	$-0.298819\pi$
$293$	20.2252	1.18157	0.590784	+	0.806830i	$0.298819\pi$
$294$	1.63011	0.0950697
$295$	−39.8014	−2.31732
$296$	−8.40404	−0.488475
$297$	2.45117	0.142231
$298$	−4.63128	−0.268283
$299$	4.65392	0.269143
$300$	−1.02591	−0.0592310
$301$	−6.04758	−0.348577
$302$	0.890055	0.0512169
$303$	−2.00471	−0.115168
$304$	−6.18126	−0.354520
$305$	−23.3880	−1.33919
$306$	6.90026	0.394462
$307$	0.440622	0.0251476	0.0125738	−	0.999921i	$-0.495998\pi$
$307$	0.440622	0.0251476	0.0125738	+	0.999921i	$0.495998\pi$
$308$	−1.69684	−0.0966862
$309$	2.60006	0.147912
$310$	1.80167	0.102328
$311$	13.0232	0.738478	0.369239	−	0.929335i	$-0.379618\pi$
$311$	13.0232	0.738478	0.369239	+	0.929335i	$0.379618\pi$
$312$	1.36482	0.0772677
$313$	−26.0102	−1.47019	−0.735093	−	0.677966i	$-0.762862\pi$
$313$	−26.0102	−1.47019	−0.735093	+	0.677966i	$0.762862\pi$
$314$	−3.68671	−0.208053
$315$	10.1990	0.574649
$316$	−0.327709	−0.0184351
$317$	12.1201	0.680731	0.340365	−	0.940293i	$-0.389449\pi$
$317$	12.1201	0.680731	0.340365	+	0.940293i	$0.389449\pi$
$318$	2.45276	0.137544
$319$	11.2933	0.632303
$320$	2.91518	0.162963
$321$	−4.07247	−0.227303
$322$	1.20061	0.0669076
$323$	14.6371	0.814428
$324$	8.23337	0.457410
$325$	−16.2807	−0.903089
$326$	23.4367	1.29804
$327$	1.14800	0.0634845
$328$	9.57225	0.528539
$329$	−4.39493	−0.242300
$330$	−1.20825	−0.0665122
$331$	−31.4814	−1.73037	−0.865187	−	0.501450i	$-0.832800\pi$
$331$	−31.4814	−1.73037	−0.865187	+	0.501450i	$0.832800\pi$
$332$	−3.85948	−0.211817
$333$	24.4894	1.34201
$334$	−13.3323	−0.729510
$335$	−10.3210	−0.563894
$336$	0.352095	0.0192083
$337$	−9.20104	−0.501213	−0.250606	−	0.968089i	$-0.580630\pi$
$337$	−9.20104	−0.501213	−0.250606	+	0.968089i	$0.580630\pi$
$338$	8.65900	0.470987
$339$	3.56667	0.193715
$340$	−6.90306	−0.374371
$341$	0.873466	0.0473008
$342$	18.0122	0.973987
$343$	15.0779	0.814132
$344$	5.03707	0.271581
$345$	0.854912	0.0460269
$346$	−0.0637233	−0.00342578
$347$	−18.8494	−1.01189	−0.505945	−	0.862566i	$-0.668856\pi$
$347$	−18.8494	−1.01189	−0.505945	+	0.862566i	$0.668856\pi$
$348$	−2.34336	−0.125618
$349$	−33.4051	−1.78814	−0.894068	−	0.447931i	$-0.852161\pi$
$349$	−33.4051	−1.78814	−0.894068	+	0.447931i	$0.852161\pi$
$350$	−4.20007	−0.224503
$351$	−8.07154	−0.430827
$352$	1.41331	0.0753295
$353$	28.6991	1.52750	0.763749	−	0.645513i	$-0.223356\pi$
$353$	28.6991	1.52750	0.763749	+	0.645513i	$0.223356\pi$
$354$	4.00395	0.212808
$355$	−48.2801	−2.56244
$356$	−12.4247	−0.658508
$357$	−0.833750	−0.0441268
$358$	10.9013	0.576154
$359$	−28.8931	−1.52492	−0.762458	−	0.647037i	$-0.776008\pi$
$359$	−28.8931	−1.52492	−0.762458	+	0.647037i	$0.776008\pi$
$360$	−8.49482	−0.447717
$361$	19.2080	1.01095
$362$	3.72697	0.195885
$363$	2.64011	0.138570
$364$	5.58756	0.292868
$365$	27.5843	1.44383
$366$	2.35279	0.122982
$367$	22.6159	1.18054	0.590270	−	0.807206i	$-0.299021\pi$
$367$	22.6159	1.18054	0.590270	+	0.807206i	$0.299021\pi$
$368$	−1.00000	−0.0521286
$369$	−27.8935	−1.45208
$370$	−24.4993	−1.27366
$371$	10.0416	0.521334
$372$	−0.181245	−0.00939710
$373$	−8.10731	−0.419781	−0.209890	−	0.977725i	$-0.567311\pi$
$373$	−8.10731	−0.419781	−0.209890	+	0.977725i	$0.567311\pi$
$374$	−3.34667	−0.173052
$375$	1.28385	0.0662976
$376$	3.66057	0.188779
$377$	−37.1880	−1.91528
$378$	−2.08229	−0.107101
$379$	−18.8717	−0.969372	−0.484686	−	0.874688i	$-0.661066\pi$
$379$	−18.8717	−0.969372	−0.484686	+	0.874688i	$0.661066\pi$
$380$	−18.0195	−0.924380
$381$	−1.20971	−0.0619756
$382$	−21.3577	−1.09276
$383$	17.7549	0.907232	0.453616	−	0.891197i	$-0.350134\pi$
$383$	17.7549	0.907232	0.453616	+	0.891197i	$0.350134\pi$
$384$	−0.293262	−0.0149655
$385$	−4.94658	−0.252101
$386$	−23.2213	−1.18193
$387$	−14.6780	−0.746125
$388$	−9.13312	−0.463664
$389$	−16.8965	−0.856687	−0.428344	−	0.903616i	$-0.640903\pi$
$389$	−16.8965	−0.856687	−0.428344	+	0.903616i	$0.640903\pi$
$390$	3.97869	0.201469
$391$	2.36797	0.119754
$392$	−5.55853	−0.280748
$393$	−0.293262	−0.0147931
$394$	−16.2479	−0.818559
$395$	−0.955330	−0.0480678
$396$	−4.11837	−0.206956
$397$	12.3550	0.620081	0.310040	−	0.950723i	$-0.399657\pi$
$397$	12.3550	0.620081	0.310040	+	0.950723i	$0.399657\pi$
$398$	23.2740	1.16662
$399$	−2.17639	−0.108956
$400$	3.49827	0.174913
$401$	−22.1350	−1.10537	−0.552683	−	0.833391i	$-0.686396\pi$
$401$	−22.1350	−1.10537	−0.552683	+	0.833391i	$0.686396\pi$
$402$	1.03827	0.0517843
$403$	−2.87626	−0.143277
$404$	6.83591	0.340099
$405$	24.0018	1.19266
$406$	−9.59372	−0.476128
$407$	−11.8775	−0.588746
$408$	0.694437	0.0343797
$409$	−1.35616	−0.0670580	−0.0335290	−	0.999438i	$-0.510675\pi$
$409$	−1.35616	−0.0670580	−0.0335290	+	0.999438i	$0.510675\pi$
$410$	27.9048	1.37812
$411$	−1.36926	−0.0675408
$412$	−8.86600	−0.436796
$413$	16.3921	0.806605
$414$	2.91400	0.143215
$415$	−11.2511	−0.552294
$416$	−4.65392	−0.228177
$417$	0.580514	0.0284279
$418$	−8.73603	−0.427293
$419$	−2.30180	−0.112450	−0.0562252	−	0.998418i	$-0.517906\pi$
$419$	−2.30180	−0.112450	−0.0562252	+	0.998418i	$0.517906\pi$
$420$	1.02642	0.0500841
$421$	3.16187	0.154100	0.0770502	−	0.997027i	$-0.475450\pi$
$421$	3.16187	0.154100	0.0770502	+	0.997027i	$0.475450\pi$
$422$	23.8909	1.16299
$423$	−10.6669	−0.518642
$424$	−8.36372	−0.406178
$425$	−8.28381	−0.401824
$426$	4.85690	0.235318
$427$	9.63231	0.466140
$428$	13.8868	0.671243
$429$	1.92891	0.0931287
$430$	14.6840	0.708124
$431$	35.8723	1.72791	0.863953	−	0.503572i	$-0.167981\pi$
$431$	35.8723	1.72791	0.863953	+	0.503572i	$0.167981\pi$
$432$	1.73435	0.0834440
$433$	19.5919	0.941527	0.470763	−	0.882260i	$-0.343979\pi$
$433$	19.5919	0.941527	0.470763	+	0.882260i	$0.343979\pi$
$434$	−0.742015	−0.0356178
$435$	−6.83133	−0.327537
$436$	−3.91458	−0.187474
$437$	6.18126	0.295690
$438$	−2.77494	−0.132592
$439$	9.55082	0.455836	0.227918	−	0.973680i	$-0.426808\pi$
$439$	9.55082	0.455836	0.227918	+	0.973680i	$0.426808\pi$
$440$	4.12004	0.196415
$441$	16.1975	0.771311
$442$	11.0204	0.524185
$443$	21.5470	1.02373	0.511864	−	0.859066i	$-0.328955\pi$
$443$	21.5470	1.02373	0.511864	+	0.859066i	$0.328955\pi$
$444$	2.46459	0.116964
$445$	−36.2203	−1.71700
$446$	5.94441	0.281476
$447$	1.35818	0.0642396
$448$	−1.20061	−0.0567237
$449$	−4.86826	−0.229747	−0.114874	−	0.993380i	$-0.536646\pi$
$449$	−4.86826	−0.229747	−0.114874	+	0.993380i	$0.536646\pi$
$450$	−10.1939	−0.480547
$451$	13.5285	0.637034
$452$	−12.1620	−0.572054
$453$	−0.261019	−0.0122638
$454$	4.59029	0.215433
$455$	16.2888	0.763628
$456$	1.81273	0.0848889
$457$	18.8015	0.879495	0.439747	−	0.898121i	$-0.355068\pi$
$457$	18.8015	0.879495	0.439747	+	0.898121i	$0.355068\pi$
$458$	2.33173	0.108955
$459$	−4.10690	−0.191694
$460$	−2.91518	−0.135921
$461$	−31.7904	−1.48063	−0.740313	−	0.672262i	$-0.765323\pi$
$461$	−31.7904	−1.48063	−0.740313	+	0.672262i	$0.765323\pi$
$462$	0.497618	0.0231513
$463$	34.7505	1.61499	0.807495	−	0.589874i	$-0.200823\pi$
$463$	34.7505	1.61499	0.807495	+	0.589874i	$0.200823\pi$
$464$	7.99068	0.370958
$465$	−0.528361	−0.0245021
$466$	10.9602	0.507723
$467$	33.6243	1.55595	0.777973	−	0.628297i	$-0.216248\pi$
$467$	33.6243	1.55595	0.777973	+	0.628297i	$0.216248\pi$
$468$	13.5615	0.626881
$469$	4.25068	0.196278
$470$	10.6712	0.492227
$471$	1.08117	0.0498178
$472$	−13.6531	−0.628437
$473$	7.11893	0.327329
$474$	0.0961046	0.00441423
$475$	−21.6237	−0.992165
$476$	2.84302	0.130310
$477$	24.3719	1.11591
$478$	−13.4758	−0.616369
$479$	2.34827	0.107295	0.0536476	−	0.998560i	$-0.482915\pi$
$479$	2.34827	0.107295	0.0536476	+	0.998560i	$0.482915\pi$
$480$	−0.854912	−0.0390212
$481$	39.1118	1.78334
$482$	28.1083	1.28030
$483$	−0.352095	−0.0160209
$484$	−9.00256	−0.409207
$485$	−26.6247	−1.20896
$486$	−7.61759	−0.345541
$487$	−11.7804	−0.533823	−0.266911	−	0.963721i	$-0.586003\pi$
$487$	−11.7804	−0.533823	−0.266911	+	0.963721i	$0.586003\pi$
$488$	−8.02282	−0.363176
$489$	−6.87311	−0.310813
$490$	−16.2041	−0.732027
$491$	−24.1672	−1.09065	−0.545325	−	0.838225i	$-0.683594\pi$
$491$	−24.1672	−1.09065	−0.545325	+	0.838225i	$0.683594\pi$
$492$	−2.80718	−0.126557
$493$	−18.9217	−0.852191
$494$	28.7671	1.29429
$495$	−12.0058	−0.539621
$496$	0.618029	0.0277503
$497$	19.8841	0.891925
$498$	1.13184	0.0507190
$499$	−16.9573	−0.759111	−0.379555	−	0.925169i	$-0.623923\pi$
$499$	−16.9573	−0.759111	−0.379555	+	0.925169i	$0.623923\pi$
$500$	−4.37781	−0.195782
$501$	3.90986	0.174680
$502$	−10.0873	−0.450217
$503$	−19.2465	−0.858160	−0.429080	−	0.903267i	$-0.641162\pi$
$503$	−19.2465	−0.858160	−0.429080	+	0.903267i	$0.641162\pi$
$504$	3.49859	0.155839
$505$	19.9279	0.886780
$506$	−1.41331	−0.0628292
$507$	−2.53936	−0.112777
$508$	4.12503	0.183018
$509$	−4.44531	−0.197035	−0.0985175	−	0.995135i	$-0.531410\pi$
$509$	−4.44531	−0.197035	−0.0985175	+	0.995135i	$0.531410\pi$
$510$	2.02441	0.0896423
$511$	−11.3606	−0.502562
$512$	1.00000	0.0441942
$513$	−10.7205	−0.473321
$514$	5.48759	0.242047
$515$	−25.8460	−1.13891
$516$	−1.47718	−0.0650293
$517$	5.17351	0.227531
$518$	10.0900	0.443330
$519$	0.0186876	0.000820296 0
$520$	−13.5670	−0.594953
$521$	19.3419	0.847383	0.423691	−	0.905807i	$-0.360734\pi$
$521$	19.3419	0.847383	0.423691	+	0.905807i	$0.360734\pi$
$522$	−23.2848	−1.01915
$523$	34.2453	1.49744	0.748721	−	0.662885i	$-0.230668\pi$
$523$	34.2453	1.49744	0.748721	+	0.662885i	$0.230668\pi$
$524$	1.00000	0.0436852
$525$	1.23172	0.0537568
$526$	−5.48073	−0.238971
$527$	−1.46348	−0.0637500
$528$	−0.414470	−0.0180375
$529$	1.00000	0.0434783
$530$	−24.3818	−1.05908
$531$	39.7852	1.72653
$532$	7.42131	0.321755
$533$	−44.5485	−1.92961
$534$	3.64370	0.157678
$535$	40.4825	1.75021
$536$	−3.54042	−0.152923
$537$	−3.19695	−0.137959
$538$	20.9907	0.904973
$539$	−7.85591	−0.338378
$540$	5.05595	0.217573
$541$	14.4019	0.619186	0.309593	−	0.950869i	$-0.399807\pi$
$541$	14.4019	0.619186	0.309593	+	0.950869i	$0.399807\pi$
$542$	16.9950	0.729998
$543$	−1.09298	−0.0469042
$544$	−2.36797	−0.101526
$545$	−11.4117	−0.488824
$546$	−1.63862	−0.0701265
$547$	34.6573	1.48184	0.740920	−	0.671594i	$-0.234390\pi$
$547$	34.6573	1.48184	0.740920	+	0.671594i	$0.234390\pi$
$548$	4.66907	0.199453
$549$	23.3785	0.997769
$550$	4.94413	0.210818
$551$	−49.3925	−2.10419
$552$	0.293262	0.0124821
$553$	0.393452	0.0167313
$554$	7.32313	0.311130
$555$	7.18472	0.304974
$556$	−1.97951	−0.0839498
$557$	17.4392	0.738923	0.369461	−	0.929246i	$-0.379542\pi$
$557$	17.4392	0.738923	0.369461	+	0.929246i	$0.379542\pi$
$558$	−1.80094	−0.0762397
$559$	−23.4421	−0.991497
$560$	−3.50000	−0.147902
$561$	0.981453	0.0414370
$562$	2.04822	0.0863989
$563$	−24.9191	−1.05021	−0.525106	−	0.851037i	$-0.675975\pi$
$563$	−24.9191	−1.05021	−0.525106	+	0.851037i	$0.675975\pi$
$564$	−1.07351	−0.0452028
$565$	−35.4545	−1.49158
$566$	−0.872093	−0.0366568
$567$	−9.88510	−0.415135
$568$	−16.5616	−0.694910
$569$	2.96078	0.124123	0.0620613	−	0.998072i	$-0.480233\pi$
$569$	2.96078	0.124123	0.0620613	+	0.998072i	$0.480233\pi$
$570$	5.28444	0.221341
$571$	30.6016	1.28064	0.640319	−	0.768109i	$-0.278802\pi$
$571$	30.6016	1.28064	0.640319	+	0.768109i	$0.278802\pi$
$572$	−6.57742	−0.275016
$573$	6.26342	0.261658
$574$	−11.4926	−0.479691
$575$	−3.49827	−0.145888
$576$	−2.91400	−0.121417
$577$	20.3199	0.845926	0.422963	−	0.906147i	$-0.360990\pi$
$577$	20.3199	0.845926	0.422963	+	0.906147i	$0.360990\pi$
$578$	−11.3927	−0.473874
$579$	6.80993	0.283011
$580$	23.2943	0.967241
$581$	4.63375	0.192240
$582$	2.67840	0.111023
$583$	−11.8205	−0.489556
$584$	9.46231	0.391553
$585$	39.5343	1.63454
$586$	20.2252	0.835494
$587$	18.7971	0.775840	0.387920	−	0.921693i	$-0.373194\pi$
$587$	18.7971	0.775840	0.387920	+	0.921693i	$0.373194\pi$
$588$	1.63011	0.0672244
$589$	−3.82020	−0.157409
$590$	−39.8014	−1.63860
$591$	4.76491	0.196002
$592$	−8.40404	−0.345404
$593$	−30.9631	−1.27150	−0.635751	−	0.771894i	$-0.719310\pi$
$593$	−30.9631	−1.27150	−0.635751	+	0.771894i	$0.719310\pi$
$594$	2.45117	0.100573
$595$	8.28791	0.339771
$596$	−4.63128	−0.189705
$597$	−6.82538	−0.279344
$598$	4.65392	0.190313
$599$	6.03783	0.246699	0.123350	−	0.992363i	$-0.460636\pi$
$599$	6.03783	0.246699	0.123350	+	0.992363i	$0.460636\pi$
$600$	−1.02591	−0.0418826
$601$	−1.19343	−0.0486809	−0.0243405	−	0.999704i	$-0.507749\pi$
$601$	−1.19343	−0.0486809	−0.0243405	+	0.999704i	$0.507749\pi$
$602$	−6.04758	−0.246481
$603$	10.3168	0.420132
$604$	0.890055	0.0362158
$605$	−26.2441	−1.06697
$606$	−2.00471	−0.0814360
$607$	38.0476	1.54431	0.772153	−	0.635437i	$-0.219180\pi$
$607$	38.0476	1.54431	0.772153	+	0.635437i	$0.219180\pi$
$608$	−6.18126	−0.250683
$609$	2.81348	0.114008
$610$	−23.3880	−0.946951
$611$	−17.0360	−0.689203
$612$	6.90026	0.278927
$613$	−38.1657	−1.54150	−0.770749	−	0.637139i	$-0.780118\pi$
$613$	−38.1657	−1.54150	−0.770749	+	0.637139i	$0.780118\pi$
$614$	0.440622	0.0177821
$615$	−8.18343	−0.329988
$616$	−1.69684	−0.0683675
$617$	27.1559	1.09325	0.546627	−	0.837376i	$-0.315911\pi$
$617$	27.1559	1.09325	0.546627	+	0.837376i	$0.315911\pi$
$618$	2.60006	0.104590
$619$	−39.6415	−1.59333	−0.796664	−	0.604423i	$-0.793404\pi$
$619$	−39.6415	−1.59333	−0.796664	+	0.604423i	$0.793404\pi$
$620$	1.80167	0.0723567
$621$	−1.73435	−0.0695971
$622$	13.0232	0.522183
$623$	14.9173	0.597648
$624$	1.36482	0.0546365
$625$	−30.2535	−1.21014
$626$	−26.0102	−1.03958
$627$	2.56195	0.102314
$628$	−3.68671	−0.147116
$629$	19.9005	0.793487
$630$	10.1990	0.406338
$631$	−35.3529	−1.40738	−0.703689	−	0.710508i	$-0.748465\pi$
$631$	−35.3529	−1.40738	−0.703689	+	0.710508i	$0.748465\pi$
$632$	−0.327709	−0.0130356
$633$	−7.00630	−0.278476
$634$	12.1201	0.481349
$635$	12.0252	0.477205
$636$	2.45276	0.0972584
$637$	25.8690	1.02497
$638$	11.2933	0.447105
$639$	48.2605	1.90916
$640$	2.91518	0.115233
$641$	−2.75085	−0.108652	−0.0543260	−	0.998523i	$-0.517301\pi$
$641$	−2.75085	−0.108652	−0.0543260	+	0.998523i	$0.517301\pi$
$642$	−4.07247	−0.160727
$643$	−11.7046	−0.461586	−0.230793	−	0.973003i	$-0.574132\pi$
$643$	−11.7046	−0.461586	−0.230793	+	0.973003i	$0.574132\pi$
$644$	1.20061	0.0473108
$645$	−4.30625	−0.169559
$646$	14.6371	0.575887
$647$	−26.1939	−1.02979	−0.514893	−	0.857254i	$-0.672168\pi$
$647$	−26.1939	−1.02979	−0.514893	+	0.857254i	$0.672168\pi$
$648$	8.23337	0.323437
$649$	−19.2961	−0.757438
$650$	−16.2807	−0.638581
$651$	0.217605	0.00852861
$652$	23.4367	0.917854
$653$	−19.3056	−0.755485	−0.377742	−	0.925911i	$-0.623300\pi$
$653$	−19.3056	−0.755485	−0.377742	+	0.925911i	$0.623300\pi$
$654$	1.14800	0.0448903
$655$	2.91518	0.113905
$656$	9.57225	0.373734
$657$	−27.5731	−1.07573
$658$	−4.39493	−0.171332
$659$	4.11612	0.160341	0.0801706	−	0.996781i	$-0.474453\pi$
$659$	4.11612	0.160341	0.0801706	+	0.996781i	$0.474453\pi$
$660$	−1.20825	−0.0470312
$661$	9.81026	0.381575	0.190787	−	0.981631i	$-0.438896\pi$
$661$	9.81026	0.381575	0.190787	+	0.981631i	$0.438896\pi$
$662$	−31.4814	−1.22356
$663$	−3.23186	−0.125515
$664$	−3.85948	−0.149777
$665$	21.6344	0.838948
$666$	24.4894	0.948943
$667$	−7.99068	−0.309400
$668$	−13.3323	−0.515842
$669$	−1.74327	−0.0673987
$670$	−10.3210	−0.398734
$671$	−11.3387	−0.437726
$672$	0.352095	0.0135823
$673$	−13.0082	−0.501430	−0.250715	−	0.968061i	$-0.580666\pi$
$673$	−13.0082	−0.501430	−0.250715	+	0.968061i	$0.580666\pi$
$674$	−9.20104	−0.354411
$675$	6.06723	0.233528
$676$	8.65900	0.333038
$677$	−21.5232	−0.827203	−0.413602	−	0.910458i	$-0.635729\pi$
$677$	−21.5232	−0.827203	−0.413602	+	0.910458i	$0.635729\pi$
$678$	3.56667	0.136977
$679$	10.9654	0.420812
$680$	−6.90306	−0.264720
$681$	−1.34616	−0.0515849
$682$	0.873466	0.0334467
$683$	22.2916	0.852963	0.426481	−	0.904496i	$-0.359753\pi$
$683$	22.2916	0.852963	0.426481	+	0.904496i	$0.359753\pi$
$684$	18.0122	0.688713
$685$	13.6112	0.520057
$686$	15.0779	0.575678
$687$	−0.683809	−0.0260889
$688$	5.03707	0.192037
$689$	38.9241	1.48289
$690$	0.854912	0.0325459
$691$	19.6027	0.745722	0.372861	−	0.927887i	$-0.378377\pi$
$691$	19.6027	0.745722	0.372861	+	0.927887i	$0.378377\pi$
$692$	−0.0637233	−0.00242240
$693$	4.94458	0.187829
$694$	−18.8494	−0.715514
$695$	−5.77062	−0.218892
$696$	−2.34336	−0.0888250
$697$	−22.6668	−0.858567
$698$	−33.4051	−1.26440
$699$	−3.21422	−0.121573
$700$	−4.20007	−0.158748
$701$	32.3061	1.22018	0.610091	−	0.792331i	$-0.291133\pi$
$701$	32.3061	1.22018	0.610091	+	0.792331i	$0.291133\pi$
$702$	−8.07154	−0.304641
$703$	51.9476	1.95924
$704$	1.41331	0.0532660
$705$	−3.12947	−0.117862
$706$	28.6991	1.08010
$707$	−8.20729	−0.308667
$708$	4.00395	0.150478
$709$	−49.3898	−1.85487	−0.927436	−	0.373981i	$-0.877992\pi$
$709$	−49.3898	−1.85487	−0.927436	+	0.373981i	$0.877992\pi$
$710$	−48.2801	−1.81192
$711$	0.954942	0.0358131
$712$	−12.4247	−0.465636
$713$	−0.618029	−0.0231454
$714$	−0.833750	−0.0312023
$715$	−19.1744	−0.717081
$716$	10.9013	0.407403
$717$	3.95195	0.147588
$718$	−28.8931	−1.07828
$719$	−12.1254	−0.452202	−0.226101	−	0.974104i	$-0.572598\pi$
$719$	−12.1254	−0.452202	−0.226101	+	0.974104i	$0.572598\pi$
$720$	−8.49482	−0.316583
$721$	10.6446	0.396427
$722$	19.2080	0.714848
$723$	−8.24310	−0.306564
$724$	3.72697	0.138512
$725$	27.9535	1.03817
$726$	2.64011	0.0979837
$727$	23.7848	0.882131	0.441066	−	0.897475i	$-0.354601\pi$
$727$	23.7848	0.882131	0.441066	+	0.897475i	$0.354601\pi$
$728$	5.58756	0.207089
$729$	−22.4662	−0.832080
$730$	27.5843	1.02094
$731$	−11.9276	−0.441160
$732$	2.35279	0.0869617
$733$	38.7968	1.43299	0.716496	−	0.697591i	$-0.245745\pi$
$733$	38.7968	1.43299	0.716496	+	0.697591i	$0.245745\pi$
$734$	22.6159	0.834768
$735$	4.75205	0.175282
$736$	−1.00000	−0.0368605
$737$	−5.00370	−0.184314
$738$	−27.8935	−1.02677
$739$	−46.8974	−1.72515	−0.862575	−	0.505929i	$-0.831150\pi$
$739$	−46.8974	−1.72515	−0.862575	+	0.505929i	$0.831150\pi$
$740$	−24.4993	−0.900612
$741$	−8.43631	−0.309916
$742$	10.0416	0.368639
$743$	17.0844	0.626764	0.313382	−	0.949627i	$-0.398538\pi$
$743$	17.0844	0.626764	0.313382	+	0.949627i	$0.398538\pi$
$744$	−0.181245	−0.00664475
$745$	−13.5010	−0.494638
$746$	−8.10731	−0.296830
$747$	11.2465	0.411489
$748$	−3.34667	−0.122366
$749$	−16.6727	−0.609206
$750$	1.28385	0.0468795
$751$	37.7584	1.37782	0.688912	−	0.724845i	$-0.258089\pi$
$751$	37.7584	1.37782	0.688912	+	0.724845i	$0.258089\pi$
$752$	3.66057	0.133487
$753$	2.95822	0.107803
$754$	−37.1880	−1.35431
$755$	2.59467	0.0944297
$756$	−2.08229	−0.0757320
$757$	−21.0488	−0.765031	−0.382516	−	0.923949i	$-0.624942\pi$
$757$	−21.0488	−0.765031	−0.382516	+	0.923949i	$0.624942\pi$
$758$	−18.8717	−0.685449
$759$	0.414470	0.0150443
$760$	−18.0195	−0.653636
$761$	−52.4942	−1.90291	−0.951457	−	0.307783i	$-0.900413\pi$
$761$	−52.4942	−1.90291	−0.951457	+	0.307783i	$0.900413\pi$
$762$	−1.20971	−0.0438233
$763$	4.69990	0.170148
$764$	−21.3577	−0.772696
$765$	20.1155	0.727278
$766$	17.7549	0.641510
$767$	63.5407	2.29432
$768$	−0.293262	−0.0105822
$769$	−48.6793	−1.75542	−0.877710	−	0.479193i	$-0.840929\pi$
$769$	−48.6793	−1.75542	−0.877710	+	0.479193i	$0.840929\pi$
$770$	−4.94658	−0.178262
$771$	−1.60930	−0.0579576
$772$	−23.2213	−0.835753
$773$	3.54652	0.127559	0.0637797	−	0.997964i	$-0.479684\pi$
$773$	3.54652	0.127559	0.0637797	+	0.997964i	$0.479684\pi$
$774$	−14.6780	−0.527590
$775$	2.16203	0.0776625
$776$	−9.13312	−0.327860
$777$	−2.95902	−0.106154
$778$	−16.8965	−0.605769
$779$	−59.1686	−2.11994
$780$	3.97869	0.142460
$781$	−23.4067	−0.837557
$782$	2.36797	0.0846785
$783$	13.8586	0.495268
$784$	−5.55853	−0.198519
$785$	−10.7474	−0.383592
$786$	−0.293262	−0.0104603
$787$	32.2335	1.14900	0.574500	−	0.818505i	$-0.305197\pi$
$787$	32.2335	1.14900	0.574500	+	0.818505i	$0.305197\pi$
$788$	−16.2479	−0.578809
$789$	1.60729	0.0572211
$790$	−0.955330	−0.0339891
$791$	14.6019	0.519184
$792$	−4.11837	−0.146340
$793$	37.3376	1.32590
$794$	12.3550	0.438463
$795$	7.15025	0.253593
$796$	23.2740	0.824924
$797$	−20.5028	−0.726246	−0.363123	−	0.931741i	$-0.618290\pi$
$797$	−20.5028	−0.726246	−0.363123	+	0.931741i	$0.618290\pi$
$798$	−2.17639	−0.0770434
$799$	−8.66813	−0.306656
$800$	3.49827	0.123683
$801$	36.2056	1.27926
$802$	−22.1350	−0.781612
$803$	13.3732	0.471928
$804$	1.03827	0.0366170
$805$	3.50000	0.123359
$806$	−2.87626	−0.101312
$807$	−6.15578	−0.216694
$808$	6.83591	0.240487
$809$	34.7961	1.22336	0.611682	−	0.791104i	$-0.290493\pi$
$809$	34.7961	1.22336	0.611682	+	0.791104i	$0.290493\pi$
$810$	24.0018	0.843336
$811$	−11.9892	−0.420998	−0.210499	−	0.977594i	$-0.567509\pi$
$811$	−11.9892	−0.420998	−0.210499	+	0.977594i	$0.567509\pi$
$812$	−9.59372	−0.336674
$813$	−4.98399	−0.174796
$814$	−11.8775	−0.416306
$815$	68.3223	2.39323
$816$	0.694437	0.0243102
$817$	−31.1355	−1.08929
$818$	−1.35616	−0.0474172
$819$	−16.2821	−0.568944
$820$	27.9048	0.974479
$821$	−38.5663	−1.34597	−0.672986	−	0.739655i	$-0.734989\pi$
$821$	−38.5663	−1.34597	−0.672986	+	0.739655i	$0.734989\pi$
$822$	−1.36926	−0.0477585
$823$	1.71288	0.0597073	0.0298536	−	0.999554i	$-0.490496\pi$
$823$	1.71288	0.0597073	0.0298536	+	0.999554i	$0.490496\pi$
$824$	−8.86600	−0.308862
$825$	−1.44993	−0.0504800
$826$	16.3921	0.570356
$827$	−40.8771	−1.42144	−0.710718	−	0.703477i	$-0.751630\pi$
$827$	−40.8771	−1.42144	−0.710718	+	0.703477i	$0.751630\pi$
$828$	2.91400	0.101268
$829$	50.7972	1.76426	0.882130	−	0.471005i	$-0.156109\pi$
$829$	50.7972	1.76426	0.882130	+	0.471005i	$0.156109\pi$
$830$	−11.2511	−0.390531
$831$	−2.14760	−0.0744993
$832$	−4.65392	−0.161346
$833$	13.1624	0.456051
$834$	0.580514	0.0201016
$835$	−38.8660	−1.34501
$836$	−8.73603	−0.302142
$837$	1.07188	0.0370496
$838$	−2.30180	−0.0795144
$839$	18.5231	0.639487	0.319743	−	0.947504i	$-0.396403\pi$
$839$	18.5231	0.639487	0.319743	+	0.947504i	$0.396403\pi$
$840$	1.02642	0.0354148
$841$	34.8509	1.20176
$842$	3.16187	0.108965
$843$	−0.600665	−0.0206880
$844$	23.8909	0.822359
$845$	25.2425	0.868369
$846$	−10.6669	−0.366735
$847$	10.8086	0.371388
$848$	−8.36372	−0.287211
$849$	0.255752	0.00877738
$850$	−8.28381	−0.284132
$851$	8.40404	0.288087
$852$	4.85690	0.166395
$853$	−50.3678	−1.72456	−0.862280	−	0.506433i	$-0.830964\pi$
$853$	−50.3678	−1.72456	−0.862280	+	0.506433i	$0.830964\pi$
$854$	9.63231	0.329611
$855$	52.5087	1.79576
$856$	13.8868	0.474640
$857$	−44.9011	−1.53379	−0.766896	−	0.641772i	$-0.778200\pi$
$857$	−44.9011	−1.53379	−0.766896	+	0.641772i	$0.778200\pi$
$858$	1.92891	0.0658519
$859$	28.7009	0.979262	0.489631	−	0.871930i	$-0.337131\pi$
$859$	28.7009	0.979262	0.489631	+	0.871930i	$0.337131\pi$
$860$	14.6840	0.500719
$861$	3.37034	0.114861
$862$	35.8723	1.22181
$863$	−5.20543	−0.177195	−0.0885974	−	0.996068i	$-0.528238\pi$
$863$	−5.20543	−0.177195	−0.0885974	+	0.996068i	$0.528238\pi$
$864$	1.73435	0.0590039
$865$	−0.185765	−0.00631619
$866$	19.5919	0.665760
$867$	3.34105	0.113468
$868$	−0.742015	−0.0251856
$869$	−0.463153	−0.0157114
$870$	−6.83133	−0.231604
$871$	16.4768	0.558297
$872$	−3.91458	−0.132564
$873$	26.6139	0.900744
$874$	6.18126	0.209084
$875$	5.25606	0.177687
$876$	−2.77494	−0.0937565
$877$	−18.2606	−0.616616	−0.308308	−	0.951287i	$-0.599763\pi$
$877$	−18.2606	−0.616616	−0.308308	+	0.951287i	$0.599763\pi$
$878$	9.55082	0.322325
$879$	−5.93128	−0.200057
$880$	4.12004	0.138887
$881$	−10.5087	−0.354048	−0.177024	−	0.984207i	$-0.556647\pi$
$881$	−10.5087	−0.354048	−0.177024	+	0.984207i	$0.556647\pi$
$882$	16.1975	0.545399
$883$	9.48995	0.319362	0.159681	−	0.987169i	$-0.448953\pi$
$883$	9.48995	0.319362	0.159681	+	0.987169i	$0.448953\pi$
$884$	11.0204	0.370655
$885$	11.6722	0.392358
$886$	21.5470	0.723886
$887$	15.6900	0.526820	0.263410	−	0.964684i	$-0.415153\pi$
$887$	15.6900	0.526820	0.263410	+	0.964684i	$0.415153\pi$
$888$	2.46459	0.0827062
$889$	−4.95256	−0.166104
$890$	−36.2203	−1.21411
$891$	11.6363	0.389830
$892$	5.94441	0.199033
$893$	−22.6269	−0.757182
$894$	1.35818	0.0454243
$895$	31.7794	1.06227
$896$	−1.20061	−0.0401097
$897$	−1.36482	−0.0455700
$898$	−4.86826	−0.162456
$899$	4.93847	0.164707
$900$	−10.1939	−0.339798
$901$	19.8051	0.659802
$902$	13.5285	0.450451
$903$	1.77353	0.0590192
$904$	−12.1620	−0.404503
$905$	10.8648	0.361158
$906$	−0.261019	−0.00867179
$907$	42.4683	1.41014	0.705068	−	0.709140i	$-0.250917\pi$
$907$	42.4683	1.41014	0.705068	+	0.709140i	$0.250917\pi$
$908$	4.59029	0.152334
$909$	−19.9198	−0.660699
$910$	16.2888	0.539967
$911$	−18.0385	−0.597643	−0.298822	−	0.954309i	$-0.596594\pi$
$911$	−18.0385	−0.597643	−0.298822	+	0.954309i	$0.596594\pi$
$912$	1.81273	0.0600255
$913$	−5.45463	−0.180522
$914$	18.8015	0.621897
$915$	6.85881	0.226745
$916$	2.33173	0.0770426
$917$	−1.20061	−0.0396478
$918$	−4.10690	−0.135548
$919$	53.9772	1.78054	0.890272	−	0.455428i	$-0.150514\pi$
$919$	53.9772	1.78054	0.890272	+	0.455428i	$0.150514\pi$
$920$	−2.91518	−0.0961106
$921$	−0.129218	−0.00425787
$922$	−31.7904	−1.04696
$923$	77.0765	2.53701
$924$	0.497618	0.0163704
$925$	−29.3996	−0.966653
$926$	34.7505	1.14197
$927$	25.8355	0.848549
$928$	7.99068	0.262307
$929$	−6.96775	−0.228605	−0.114302	−	0.993446i	$-0.536463\pi$
$929$	−6.96775	−0.228605	−0.114302	+	0.993446i	$0.536463\pi$
$930$	−0.528361	−0.0173256
$931$	34.3587	1.12606
$932$	10.9602	0.359014
$933$	−3.81921	−0.125035
$934$	33.6243	1.10022
$935$	−9.75615	−0.319060
$936$	13.5615	0.443272
$937$	−27.1324	−0.886377	−0.443189	−	0.896428i	$-0.646153\pi$
$937$	−27.1324	−0.886377	−0.443189	+	0.896428i	$0.646153\pi$
$938$	4.25068	0.138790
$939$	7.62782	0.248925
$940$	10.6712	0.348057
$941$	−17.9015	−0.583572	−0.291786	−	0.956484i	$-0.594250\pi$
$941$	−17.9015	−0.583572	−0.291786	+	0.956484i	$0.594250\pi$
$942$	1.08117	0.0352265
$943$	−9.57225	−0.311715
$944$	−13.6531	−0.444372
$945$	−6.07024	−0.197465
$946$	7.11893	0.231456
$947$	3.56926	0.115985	0.0579927	−	0.998317i	$-0.481530\pi$
$947$	3.56926	0.115985	0.0579927	+	0.998317i	$0.481530\pi$
$948$	0.0961046	0.00312133
$949$	−44.0369	−1.42950
$950$	−21.6237	−0.701566
$951$	−3.55436	−0.115258
$952$	2.84302	0.0921428
$953$	21.2129	0.687154	0.343577	−	0.939125i	$-0.388361\pi$
$953$	21.2129	0.687154	0.343577	+	0.939125i	$0.388361\pi$
$954$	24.3719	0.789068
$955$	−62.2616	−2.01474
$956$	−13.4758	−0.435839
$957$	−3.31189	−0.107058
$958$	2.34827	0.0758692
$959$	−5.60575	−0.181019
$960$	−0.854912	−0.0275922
$961$	−30.6180	−0.987679
$962$	39.1118	1.26101
$963$	−40.4660	−1.30400
$964$	28.1083	0.905307
$965$	−67.6943	−2.17916
$966$	−0.352095	−0.0113285
$967$	−31.7939	−1.02242	−0.511212	−	0.859455i	$-0.670803\pi$
$967$	−31.7939	−1.02242	−0.511212	+	0.859455i	$0.670803\pi$
$968$	−9.00256	−0.289353
$969$	−4.29250	−0.137895
$970$	−26.6247	−0.854867
$971$	−0.113576	−0.00364484	−0.00182242	−	0.999998i	$-0.500580\pi$
$971$	−0.113576	−0.00364484	−0.00182242	+	0.999998i	$0.500580\pi$
$972$	−7.61759	−0.244334
$973$	2.37662	0.0761910
$974$	−11.7804	−0.377470
$975$	4.77451	0.152907
$976$	−8.02282	−0.256804
$977$	15.3935	0.492483	0.246241	−	0.969209i	$-0.420804\pi$
$977$	15.3935	0.492483	0.246241	+	0.969209i	$0.420804\pi$
$978$	−6.87311	−0.219778
$979$	−17.5599	−0.561218
$980$	−16.2041	−0.517621
$981$	11.4071	0.364200
$982$	−24.1672	−0.771206
$983$	−28.0489	−0.894620	−0.447310	−	0.894379i	$-0.647618\pi$
$983$	−28.0489	−0.894620	−0.447310	+	0.894379i	$0.647618\pi$
$984$	−2.80718	−0.0894896
$985$	−47.3657	−1.50920
$986$	−18.9217	−0.602590
$987$	1.28887	0.0410251
$988$	28.7671	0.915204
$989$	−5.03707	−0.160170
$990$	−12.0058	−0.381569
$991$	58.8182	1.86842	0.934211	−	0.356720i	$-0.116105\pi$
$991$	58.8182	1.86842	0.934211	+	0.356720i	$0.116105\pi$
$992$	0.618029	0.0196225
$993$	9.23230	0.292978
$994$	19.8841	0.630686
$995$	67.8478	2.15092
$996$	1.13184	0.0358637
$997$	−49.0752	−1.55423	−0.777114	−	0.629360i	$-0.783317\pi$
$997$	−49.0752	−1.55423	−0.777114	+	0.629360i	$0.783317\pi$
$998$	−16.9573	−0.536772
$999$	−14.5756	−0.461151

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.g.1.9	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.g.1.9	✓	21	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.293262 q^{3} +1.00000 q^{4} +2.91518 q^{5} -0.293262 q^{6} -1.20061 q^{7} +1.00000 q^{8} -2.91400 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.293262 q^{3} +1.00000 q^{4} +2.91518 q^{5} -0.293262 q^{6} -1.20061 q^{7} +1.00000 q^{8} -2.91400 q^{9} +2.91518 q^{10} +1.41331 q^{11} -0.293262 q^{12} -4.65392 q^{13} -1.20061 q^{14} -0.854912 q^{15} +1.00000 q^{16} -2.36797 q^{17} -2.91400 q^{18} -6.18126 q^{19} +2.91518 q^{20} +0.352095 q^{21} +1.41331 q^{22} -1.00000 q^{23} -0.293262 q^{24} +3.49827 q^{25} -4.65392 q^{26} +1.73435 q^{27} -1.20061 q^{28} +7.99068 q^{29} -0.854912 q^{30} +0.618029 q^{31} +1.00000 q^{32} -0.414470 q^{33} -2.36797 q^{34} -3.50000 q^{35} -2.91400 q^{36} -8.40404 q^{37} -6.18126 q^{38} +1.36482 q^{39} +2.91518 q^{40} +9.57225 q^{41} +0.352095 q^{42} +5.03707 q^{43} +1.41331 q^{44} -8.49482 q^{45} -1.00000 q^{46} +3.66057 q^{47} -0.293262 q^{48} -5.55853 q^{49} +3.49827 q^{50} +0.694437 q^{51} -4.65392 q^{52} -8.36372 q^{53} +1.73435 q^{54} +4.12004 q^{55} -1.20061 q^{56} +1.81273 q^{57} +7.99068 q^{58} -13.6531 q^{59} -0.854912 q^{60} -8.02282 q^{61} +0.618029 q^{62} +3.49859 q^{63} +1.00000 q^{64} -13.5670 q^{65} -0.414470 q^{66} -3.54042 q^{67} -2.36797 q^{68} +0.293262 q^{69} -3.50000 q^{70} -16.5616 q^{71} -2.91400 q^{72} +9.46231 q^{73} -8.40404 q^{74} -1.02591 q^{75} -6.18126 q^{76} -1.69684 q^{77} +1.36482 q^{78} -0.327709 q^{79} +2.91518 q^{80} +8.23337 q^{81} +9.57225 q^{82} -3.85948 q^{83} +0.352095 q^{84} -6.90306 q^{85} +5.03707 q^{86} -2.34336 q^{87} +1.41331 q^{88} -12.4247 q^{89} -8.49482 q^{90} +5.58756 q^{91} -1.00000 q^{92} -0.181245 q^{93} +3.66057 q^{94} -18.0195 q^{95} -0.293262 q^{96} -9.13312 q^{97} -5.55853 q^{98} -4.11837 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9} - 13 q^{10} - 4 q^{11} - 4 q^{13} - 18 q^{14} - 16 q^{15} + 21 q^{16} - 12 q^{17} + 7 q^{18} - 18 q^{19} - 13 q^{20} - 24 q^{21} - 4 q^{22} - 21 q^{23} + 2 q^{25} - 4 q^{26} - 9 q^{27} - 18 q^{28} - 16 q^{29} - 16 q^{30} - 7 q^{31} + 21 q^{32} - 15 q^{33} - 12 q^{34} + 7 q^{36} - 44 q^{37} - 18 q^{38} - 14 q^{39} - 13 q^{40} - 23 q^{41} - 24 q^{42} - 18 q^{43} - 4 q^{44} - 36 q^{45} - 21 q^{46} + 2 q^{47} - 13 q^{49} + 2 q^{50} - 26 q^{51} - 4 q^{52} - 39 q^{53} - 9 q^{54} - 32 q^{55} - 18 q^{56} - 22 q^{57} - 16 q^{58} - 27 q^{59} - 16 q^{60} - 34 q^{61} - 7 q^{62} - 28 q^{63} + 21 q^{64} - 25 q^{65} - 15 q^{66} - 19 q^{67} - 12 q^{68} - 24 q^{71} + 7 q^{72} - 8 q^{73} - 44 q^{74} + 50 q^{75} - 18 q^{76} - 16 q^{77} - 14 q^{78} - 27 q^{79} - 13 q^{80} + 33 q^{81} - 23 q^{82} + 7 q^{83} - 24 q^{84} - 22 q^{85} - 18 q^{86} - 15 q^{87} - 4 q^{88} - 12 q^{89} - 36 q^{90} - 20 q^{91} - 21 q^{92} - 43 q^{93} + 2 q^{94} - 14 q^{95} - 52 q^{97} - 13 q^{98} - 30 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9 - 13 * q^10 - 4 * q^11 - 4 * q^13 - 18 * q^14 - 16 * q^15 + 21 * q^16 - 12 * q^17 + 7 * q^18 - 18 * q^19 - 13 * q^20 - 24 * q^21 - 4 * q^22 - 21 * q^23 + 2 * q^25 - 4 * q^26 - 9 * q^27 - 18 * q^28 - 16 * q^29 - 16 * q^30 - 7 * q^31 + 21 * q^32 - 15 * q^33 - 12 * q^34 + 7 * q^36 - 44 * q^37 - 18 * q^38 - 14 * q^39 - 13 * q^40 - 23 * q^41 - 24 * q^42 - 18 * q^43 - 4 * q^44 - 36 * q^45 - 21 * q^46 + 2 * q^47 - 13 * q^49 + 2 * q^50 - 26 * q^51 - 4 * q^52 - 39 * q^53 - 9 * q^54 - 32 * q^55 - 18 * q^56 - 22 * q^57 - 16 * q^58 - 27 * q^59 - 16 * q^60 - 34 * q^61 - 7 * q^62 - 28 * q^63 + 21 * q^64 - 25 * q^65 - 15 * q^66 - 19 * q^67 - 12 * q^68 - 24 * q^71 + 7 * q^72 - 8 * q^73 - 44 * q^74 + 50 * q^75 - 18 * q^76 - 16 * q^77 - 14 * q^78 - 27 * q^79 - 13 * q^80 + 33 * q^81 - 23 * q^82 + 7 * q^83 - 24 * q^84 - 22 * q^85 - 18 * q^86 - 15 * q^87 - 4 * q^88 - 12 * q^89 - 36 * q^90 - 20 * q^91 - 21 * q^92 - 43 * q^93 + 2 * q^94 - 14 * q^95 - 52 * q^97 - 13 * q^98 - 30 * q^99

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