LMFDB - Embedded newform 8018.2.a.d.1.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.21
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.920583 q^{3} +1.00000 q^{4} -2.78284 q^{5} +0.920583 q^{6} -0.210139 q^{7} +1.00000 q^{8} -2.15253 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.920583 q^{3} +1.00000 q^{4} -2.78284 q^{5} +0.920583 q^{6} -0.210139 q^{7} +1.00000 q^{8} -2.15253 q^{9} -2.78284 q^{10} +5.28306 q^{11} +0.920583 q^{12} +1.36696 q^{13} -0.210139 q^{14} -2.56183 q^{15} +1.00000 q^{16} -3.62564 q^{17} -2.15253 q^{18} +1.00000 q^{19} -2.78284 q^{20} -0.193451 q^{21} +5.28306 q^{22} -4.33287 q^{23} +0.920583 q^{24} +2.74418 q^{25} +1.36696 q^{26} -4.74333 q^{27} -0.210139 q^{28} -9.10294 q^{29} -2.56183 q^{30} +5.99383 q^{31} +1.00000 q^{32} +4.86350 q^{33} -3.62564 q^{34} +0.584783 q^{35} -2.15253 q^{36} +0.893226 q^{37} +1.00000 q^{38} +1.25840 q^{39} -2.78284 q^{40} +2.52152 q^{41} -0.193451 q^{42} +3.37270 q^{43} +5.28306 q^{44} +5.99013 q^{45} -4.33287 q^{46} -7.73406 q^{47} +0.920583 q^{48} -6.95584 q^{49} +2.74418 q^{50} -3.33771 q^{51} +1.36696 q^{52} +7.53598 q^{53} -4.74333 q^{54} -14.7019 q^{55} -0.210139 q^{56} +0.920583 q^{57} -9.10294 q^{58} +13.8888 q^{59} -2.56183 q^{60} -8.16379 q^{61} +5.99383 q^{62} +0.452330 q^{63} +1.00000 q^{64} -3.80403 q^{65} +4.86350 q^{66} -1.47985 q^{67} -3.62564 q^{68} -3.98877 q^{69} +0.584783 q^{70} +7.74681 q^{71} -2.15253 q^{72} -9.00274 q^{73} +0.893226 q^{74} +2.52625 q^{75} +1.00000 q^{76} -1.11018 q^{77} +1.25840 q^{78} -10.1313 q^{79} -2.78284 q^{80} +2.09095 q^{81} +2.52152 q^{82} -7.51146 q^{83} -0.193451 q^{84} +10.0896 q^{85} +3.37270 q^{86} -8.38002 q^{87} +5.28306 q^{88} -8.00293 q^{89} +5.99013 q^{90} -0.287252 q^{91} -4.33287 q^{92} +5.51782 q^{93} -7.73406 q^{94} -2.78284 q^{95} +0.920583 q^{96} -7.56976 q^{97} -6.95584 q^{98} -11.3719 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) $ 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * 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
$3$	0.920583	0.531499	0.265749	−	0.964042i	$-0.414381\pi$
$3$	0.920583	0.531499	0.265749	+	0.964042i	$0.414381\pi$
$4$	1.00000	0.500000
$5$	−2.78284	−1.24452	−0.622261	−	0.782810i	$-0.713786\pi$
$5$	−2.78284	−1.24452	−0.622261	+	0.782810i	$0.713786\pi$
$6$	0.920583	0.375827
$7$	−0.210139	−0.0794251	−0.0397126	−	0.999211i	$-0.512644\pi$
$7$	−0.210139	−0.0794251	−0.0397126	+	0.999211i	$0.512644\pi$
$8$	1.00000	0.353553
$9$	−2.15253	−0.717509
$10$	−2.78284	−0.880010
$11$	5.28306	1.59290	0.796451	−	0.604703i	$-0.206708\pi$
$11$	5.28306	1.59290	0.796451	+	0.604703i	$0.206708\pi$
$12$	0.920583	0.265749
$13$	1.36696	0.379127	0.189563	−	0.981868i	$-0.439293\pi$
$13$	1.36696	0.379127	0.189563	+	0.981868i	$0.439293\pi$
$14$	−0.210139	−0.0561621
$15$	−2.56183	−0.661462
$16$	1.00000	0.250000
$17$	−3.62564	−0.879348	−0.439674	−	0.898158i	$-0.644906\pi$
$17$	−3.62564	−0.879348	−0.439674	+	0.898158i	$0.644906\pi$
$18$	−2.15253	−0.507355
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−2.78284	−0.622261
$21$	−0.193451	−0.0422144
$22$	5.28306	1.12635
$23$	−4.33287	−0.903465	−0.451733	−	0.892153i	$-0.649194\pi$
$23$	−4.33287	−0.903465	−0.451733	+	0.892153i	$0.649194\pi$
$24$	0.920583	0.187913
$25$	2.74418	0.548837
$26$	1.36696	0.268083
$27$	−4.74333	−0.912854
$28$	−0.210139	−0.0397126
$29$	−9.10294	−1.69037	−0.845187	−	0.534471i	$-0.820511\pi$
$29$	−9.10294	−1.69037	−0.845187	+	0.534471i	$0.820511\pi$
$30$	−2.56183	−0.467725
$31$	5.99383	1.07652	0.538262	−	0.842778i	$-0.319081\pi$
$31$	5.99383	1.07652	0.538262	+	0.842778i	$0.319081\pi$
$32$	1.00000	0.176777
$33$	4.86350	0.846626
$34$	−3.62564	−0.621793
$35$	0.584783	0.0988464
$36$	−2.15253	−0.358754
$37$	0.893226	0.146845	0.0734227	−	0.997301i	$-0.476608\pi$
$37$	0.893226	0.146845	0.0734227	+	0.997301i	$0.476608\pi$
$38$	1.00000	0.162221
$39$	1.25840	0.201505
$40$	−2.78284	−0.440005
$41$	2.52152	0.393795	0.196897	−	0.980424i	$-0.436913\pi$
$41$	2.52152	0.393795	0.196897	+	0.980424i	$0.436913\pi$
$42$	−0.193451	−0.0298501
$43$	3.37270	0.514333	0.257166	−	0.966367i	$-0.417211\pi$
$43$	3.37270	0.514333	0.257166	+	0.966367i	$0.417211\pi$
$44$	5.28306	0.796451
$45$	5.99013	0.892956
$46$	−4.33287	−0.638847
$47$	−7.73406	−1.12813	−0.564064	−	0.825731i	$-0.690763\pi$
$47$	−7.73406	−1.12813	−0.564064	+	0.825731i	$0.690763\pi$
$48$	0.920583	0.132875
$49$	−6.95584	−0.993692
$50$	2.74418	0.388086
$51$	−3.33771	−0.467372
$52$	1.36696	0.189563
$53$	7.53598	1.03515	0.517573	−	0.855639i	$-0.326836\pi$
$53$	7.53598	1.03515	0.517573	+	0.855639i	$0.326836\pi$
$54$	−4.74333	−0.645485
$55$	−14.7019	−1.98240
$56$	−0.210139	−0.0280810
$57$	0.920583	0.121934
$58$	−9.10294	−1.19528
$59$	13.8888	1.80817	0.904084	−	0.427354i	$-0.140554\pi$
$59$	13.8888	1.80817	0.904084	+	0.427354i	$0.140554\pi$
$60$	−2.56183	−0.330731
$61$	−8.16379	−1.04527	−0.522633	−	0.852558i	$-0.675050\pi$
$61$	−8.16379	−1.04527	−0.522633	+	0.852558i	$0.675050\pi$
$62$	5.99383	0.761217
$63$	0.452330	0.0569882
$64$	1.00000	0.125000
$65$	−3.80403	−0.471832
$66$	4.86350	0.598655
$67$	−1.47985	−0.180793	−0.0903965	−	0.995906i	$-0.528813\pi$
$67$	−1.47985	−0.180793	−0.0903965	+	0.995906i	$0.528813\pi$
$68$	−3.62564	−0.439674
$69$	−3.98877	−0.480191
$70$	0.584783	0.0698949
$71$	7.74681	0.919377	0.459688	−	0.888080i	$-0.347961\pi$
$71$	7.74681	0.919377	0.459688	+	0.888080i	$0.347961\pi$
$72$	−2.15253	−0.253678
$73$	−9.00274	−1.05369	−0.526846	−	0.849961i	$-0.676625\pi$
$73$	−9.00274	−1.05369	−0.526846	+	0.849961i	$0.676625\pi$
$74$	0.893226	0.103835
$75$	2.52625	0.291706
$76$	1.00000	0.114708
$77$	−1.11018	−0.126516
$78$	1.25840	0.142486
$79$	−10.1313	−1.13986	−0.569932	−	0.821692i	$-0.693031\pi$
$79$	−10.1313	−1.13986	−0.569932	+	0.821692i	$0.693031\pi$
$80$	−2.78284	−0.311131
$81$	2.09095	0.232328
$82$	2.52152	0.278455
$83$	−7.51146	−0.824490	−0.412245	−	0.911073i	$-0.635255\pi$
$83$	−7.51146	−0.824490	−0.412245	+	0.911073i	$0.635255\pi$
$84$	−0.193451	−0.0211072
$85$	10.0896	1.09437
$86$	3.37270	0.363688
$87$	−8.38002	−0.898432
$88$	5.28306	0.563176
$89$	−8.00293	−0.848309	−0.424154	−	0.905590i	$-0.639429\pi$
$89$	−8.00293	−0.848309	−0.424154	+	0.905590i	$0.639429\pi$
$90$	5.99013	0.631415
$91$	−0.287252	−0.0301122
$92$	−4.33287	−0.451733
$93$	5.51782	0.572171
$94$	−7.73406	−0.797707
$95$	−2.78284	−0.285513
$96$	0.920583	0.0939566
$97$	−7.56976	−0.768593	−0.384296	−	0.923210i	$-0.625556\pi$
$97$	−7.56976	−0.768593	−0.384296	+	0.923210i	$0.625556\pi$
$98$	−6.95584	−0.702646
$99$	−11.3719	−1.14292
$100$	2.74418	0.274418
$101$	10.0862	1.00362	0.501808	−	0.864979i	$-0.332668\pi$
$101$	10.0862	1.00362	0.501808	+	0.864979i	$0.332668\pi$
$102$	−3.33771	−0.330482
$103$	−3.81644	−0.376045	−0.188023	−	0.982165i	$-0.560208\pi$
$103$	−3.81644	−0.376045	−0.188023	+	0.982165i	$0.560208\pi$
$104$	1.36696	0.134042
$105$	0.538341	0.0525367
$106$	7.53598	0.731959
$107$	−13.4102	−1.29641	−0.648205	−	0.761466i	$-0.724480\pi$
$107$	−13.4102	−1.29641	−0.648205	+	0.761466i	$0.724480\pi$
$108$	−4.74333	−0.456427
$109$	−4.29741	−0.411617	−0.205808	−	0.978592i	$-0.565982\pi$
$109$	−4.29741	−0.411617	−0.205808	+	0.978592i	$0.565982\pi$
$110$	−14.7019	−1.40177
$111$	0.822289	0.0780482
$112$	−0.210139	−0.0198563
$113$	−8.36830	−0.787223	−0.393612	−	0.919277i	$-0.628774\pi$
$113$	−8.36830	−0.787223	−0.393612	+	0.919277i	$0.628774\pi$
$114$	0.920583	0.0862205
$115$	12.0577	1.12438
$116$	−9.10294	−0.845187
$117$	−2.94242	−0.272027
$118$	13.8888	1.27857
$119$	0.761890	0.0698423
$120$	−2.56183	−0.233862
$121$	16.9107	1.53734
$122$	−8.16379	−0.739115
$123$	2.32127	0.209301
$124$	5.99383	0.538262
$125$	6.27757	0.561483
$126$	0.452330	0.0402968
$127$	−12.7646	−1.13267	−0.566336	−	0.824175i	$-0.691639\pi$
$127$	−12.7646	−1.13267	−0.566336	+	0.824175i	$0.691639\pi$
$128$	1.00000	0.0883883
$129$	3.10485	0.273367
$130$	−3.80403	−0.333635
$131$	−5.05284	−0.441469	−0.220734	−	0.975334i	$-0.570845\pi$
$131$	−5.05284	−0.441469	−0.220734	+	0.975334i	$0.570845\pi$
$132$	4.86350	0.423313
$133$	−0.210139	−0.0182214
$134$	−1.47985	−0.127840
$135$	13.1999	1.13607
$136$	−3.62564	−0.310896
$137$	−12.7542	−1.08967	−0.544833	−	0.838545i	$-0.683407\pi$
$137$	−12.7542	−1.08967	−0.544833	+	0.838545i	$0.683407\pi$
$138$	−3.98877	−0.339546
$139$	−15.7163	−1.33304	−0.666518	−	0.745489i	$-0.732216\pi$
$139$	−15.7163	−1.33304	−0.666518	+	0.745489i	$0.732216\pi$
$140$	0.584783	0.0494232
$141$	−7.11985	−0.599599
$142$	7.74681	0.650098
$143$	7.22173	0.603912
$144$	−2.15253	−0.179377
$145$	25.3320	2.10371
$146$	−9.00274	−0.745072
$147$	−6.40343	−0.528146
$148$	0.893226	0.0734227
$149$	−2.72234	−0.223022	−0.111511	−	0.993763i	$-0.535569\pi$
$149$	−2.72234	−0.223022	−0.111511	+	0.993763i	$0.535569\pi$
$150$	2.52625	0.206267
$151$	−10.8713	−0.884693	−0.442346	−	0.896844i	$-0.645854\pi$
$151$	−10.8713	−0.884693	−0.442346	+	0.896844i	$0.645854\pi$
$152$	1.00000	0.0811107
$153$	7.80429	0.630940
$154$	−1.11018	−0.0894607
$155$	−16.6799	−1.33976
$156$	1.25840	0.100753
$157$	−6.56184	−0.523692	−0.261846	−	0.965110i	$-0.584331\pi$
$157$	−6.56184	−0.523692	−0.261846	+	0.965110i	$0.584331\pi$
$158$	−10.1313	−0.806006
$159$	6.93750	0.550179
$160$	−2.78284	−0.220003
$161$	0.910505	0.0717579
$162$	2.09095	0.164281
$163$	−7.12159	−0.557806	−0.278903	−	0.960319i	$-0.589971\pi$
$163$	−7.12159	−0.557806	−0.278903	+	0.960319i	$0.589971\pi$
$164$	2.52152	0.196897
$165$	−13.5343	−1.05365
$166$	−7.51146	−0.583002
$167$	9.20063	0.711966	0.355983	−	0.934492i	$-0.384146\pi$
$167$	9.20063	0.711966	0.355983	+	0.934492i	$0.384146\pi$
$168$	−0.193451	−0.0149250
$169$	−11.1314	−0.856263
$170$	10.0896	0.773835
$171$	−2.15253	−0.164608
$172$	3.37270	0.257166
$173$	1.25029	0.0950574	0.0475287	−	0.998870i	$-0.484865\pi$
$173$	1.25029	0.0950574	0.0475287	+	0.998870i	$0.484865\pi$
$174$	−8.38002	−0.635287
$175$	−0.576660	−0.0435914
$176$	5.28306	0.398226
$177$	12.7858	0.961040
$178$	−8.00293	−0.599845
$179$	−3.00713	−0.224763	−0.112382	−	0.993665i	$-0.535848\pi$
$179$	−3.00713	−0.224763	−0.112382	+	0.993665i	$0.535848\pi$
$180$	5.99013	0.446478
$181$	14.7493	1.09630	0.548152	−	0.836379i	$-0.315332\pi$
$181$	14.7493	1.09630	0.548152	+	0.836379i	$0.315332\pi$
$182$	−0.287252	−0.0212925
$183$	−7.51545	−0.555558
$184$	−4.33287	−0.319423
$185$	−2.48570	−0.182752
$186$	5.51782	0.404586
$187$	−19.1545	−1.40072
$188$	−7.73406	−0.564064
$189$	0.996759	0.0725036
$190$	−2.78284	−0.201888
$191$	16.9298	1.22500	0.612500	−	0.790471i	$-0.290164\pi$
$191$	16.9298	1.22500	0.612500	+	0.790471i	$0.290164\pi$
$192$	0.920583	0.0664374
$193$	4.08409	0.293980	0.146990	−	0.989138i	$-0.453042\pi$
$193$	4.08409	0.293980	0.146990	+	0.989138i	$0.453042\pi$
$194$	−7.56976	−0.543477
$195$	−3.50192	−0.250778
$196$	−6.95584	−0.496846
$197$	25.9699	1.85028	0.925140	−	0.379627i	$-0.123948\pi$
$197$	25.9699	1.85028	0.925140	+	0.379627i	$0.123948\pi$
$198$	−11.3719	−0.808168
$199$	7.12209	0.504872	0.252436	−	0.967614i	$-0.418768\pi$
$199$	7.12209	0.504872	0.252436	+	0.967614i	$0.418768\pi$
$200$	2.74418	0.194043
$201$	−1.36233	−0.0960913
$202$	10.0862	0.709664
$203$	1.91288	0.134258
$204$	−3.33771	−0.233686
$205$	−7.01697	−0.490086
$206$	−3.81644	−0.265904
$207$	9.32661	0.648244
$208$	1.36696	0.0947817
$209$	5.28306	0.365437
$210$	0.538341	0.0371491
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	7.53598	0.517573
$213$	7.13158	0.488648
$214$	−13.4102	−0.916701
$215$	−9.38569	−0.640099
$216$	−4.74333	−0.322743
$217$	−1.25954	−0.0855031
$218$	−4.29741	−0.291057
$219$	−8.28777	−0.560036
$220$	−14.7019	−0.991202
$221$	−4.95611	−0.333384
$222$	0.822289	0.0551884
$223$	−24.6189	−1.64860	−0.824301	−	0.566152i	$-0.808432\pi$
$223$	−24.6189	−1.64860	−0.824301	+	0.566152i	$0.808432\pi$
$224$	−0.210139	−0.0140405
$225$	−5.90693	−0.393795
$226$	−8.36830	−0.556651
$227$	−6.08178	−0.403662	−0.201831	−	0.979420i	$-0.564689\pi$
$227$	−6.08178	−0.403662	−0.201831	+	0.979420i	$0.564689\pi$
$228$	0.920583	0.0609671
$229$	16.5489	1.09358	0.546792	−	0.837269i	$-0.315849\pi$
$229$	16.5489	1.09358	0.546792	+	0.837269i	$0.315849\pi$
$230$	12.0577	0.795059
$231$	−1.02201	−0.0672434
$232$	−9.10294	−0.597638
$233$	−28.1077	−1.84139	−0.920697	−	0.390278i	$-0.872379\pi$
$233$	−28.1077	−1.84139	−0.920697	+	0.390278i	$0.872379\pi$
$234$	−2.94242	−0.192352
$235$	21.5226	1.40398
$236$	13.8888	0.904084
$237$	−9.32674	−0.605837
$238$	0.761890	0.0493860
$239$	10.7076	0.692618	0.346309	−	0.938120i	$-0.387435\pi$
$239$	10.7076	0.692618	0.346309	+	0.938120i	$0.387435\pi$
$240$	−2.56183	−0.165366
$241$	−30.1530	−1.94233	−0.971164	−	0.238412i	$-0.923373\pi$
$241$	−30.1530	−1.94233	−0.971164	+	0.238412i	$0.923373\pi$
$242$	16.9107	1.08706
$243$	16.1549	1.03634
$244$	−8.16379	−0.522633
$245$	19.3570	1.23667
$246$	2.32127	0.147998
$247$	1.36696	0.0869776
$248$	5.99383	0.380609
$249$	−6.91492	−0.438215
$250$	6.27757	0.397028
$251$	22.2443	1.40405	0.702023	−	0.712154i	$-0.252280\pi$
$251$	22.2443	1.40405	0.702023	+	0.712154i	$0.252280\pi$
$252$	0.452330	0.0284941
$253$	−22.8908	−1.43913
$254$	−12.7646	−0.800920
$255$	9.28829	0.581655
$256$	1.00000	0.0625000
$257$	−1.68749	−0.105262	−0.0526312	−	0.998614i	$-0.516761\pi$
$257$	−1.68749	−0.105262	−0.0526312	+	0.998614i	$0.516761\pi$
$258$	3.10485	0.193300
$259$	−0.187702	−0.0116632
$260$	−3.80403	−0.235916
$261$	19.5943	1.21286
$262$	−5.05284	−0.312166
$263$	6.53091	0.402713	0.201356	−	0.979518i	$-0.435465\pi$
$263$	6.53091	0.402713	0.201356	+	0.979518i	$0.435465\pi$
$264$	4.86350	0.299327
$265$	−20.9714	−1.28826
$266$	−0.210139	−0.0128845
$267$	−7.36736	−0.450875
$268$	−1.47985	−0.0903965
$269$	7.46192	0.454961	0.227481	−	0.973783i	$-0.426951\pi$
$269$	7.46192	0.454961	0.227481	+	0.973783i	$0.426951\pi$
$270$	13.1999	0.803321
$271$	−14.6115	−0.887584	−0.443792	−	0.896130i	$-0.646367\pi$
$271$	−14.6115	−0.887584	−0.443792	+	0.896130i	$0.646367\pi$
$272$	−3.62564	−0.219837
$273$	−0.264439	−0.0160046
$274$	−12.7542	−0.770510
$275$	14.4977	0.874243
$276$	−3.98877	−0.240095
$277$	−11.2142	−0.673794	−0.336897	−	0.941542i	$-0.609377\pi$
$277$	−11.2142	−0.673794	−0.336897	+	0.941542i	$0.609377\pi$
$278$	−15.7163	−0.942599
$279$	−12.9019	−0.772415
$280$	0.584783	0.0349475
$281$	0.448578	0.0267599	0.0133799	−	0.999910i	$-0.495741\pi$
$281$	0.448578	0.0267599	0.0133799	+	0.999910i	$0.495741\pi$
$282$	−7.11985	−0.423981
$283$	9.30656	0.553218	0.276609	−	0.960983i	$-0.410789\pi$
$283$	9.30656	0.553218	0.276609	+	0.960983i	$0.410789\pi$
$284$	7.74681	0.459688
$285$	−2.56183	−0.151750
$286$	7.22173	0.427030
$287$	−0.529869	−0.0312772
$288$	−2.15253	−0.126839
$289$	−3.85471	−0.226748
$290$	25.3320	1.48755
$291$	−6.96860	−0.408506
$292$	−9.00274	−0.526846
$293$	9.99734	0.584051	0.292025	−	0.956411i	$-0.405671\pi$
$293$	9.99734	0.584051	0.292025	+	0.956411i	$0.405671\pi$
$294$	−6.40343	−0.373456
$295$	−38.6503	−2.25031
$296$	0.893226	0.0519177
$297$	−25.0593	−1.45409
$298$	−2.72234	−0.157701
$299$	−5.92286	−0.342528
$300$	2.52625	0.145853
$301$	−0.708737	−0.0408509
$302$	−10.8713	−0.625572
$303$	9.28520	0.533421
$304$	1.00000	0.0573539
$305$	22.7185	1.30086
$306$	7.80429	0.446142
$307$	−6.10808	−0.348606	−0.174303	−	0.984692i	$-0.555767\pi$
$307$	−6.10808	−0.348606	−0.174303	+	0.984692i	$0.555767\pi$
$308$	−1.11018	−0.0632582
$309$	−3.51335	−0.199868
$310$	−16.6799	−0.947352
$311$	−3.62033	−0.205290	−0.102645	−	0.994718i	$-0.532731\pi$
$311$	−3.62033	−0.205290	−0.102645	+	0.994718i	$0.532731\pi$
$312$	1.25840	0.0712429
$313$	−15.1305	−0.855229	−0.427614	−	0.903961i	$-0.640646\pi$
$313$	−15.1305	−0.855229	−0.427614	+	0.903961i	$0.640646\pi$
$314$	−6.56184	−0.370306
$315$	−1.25876	−0.0709232
$316$	−10.1313	−0.569932
$317$	−31.2100	−1.75293	−0.876465	−	0.481466i	$-0.840105\pi$
$317$	−31.2100	−1.75293	−0.876465	+	0.481466i	$0.840105\pi$
$318$	6.93750	0.389035
$319$	−48.0914	−2.69260
$320$	−2.78284	−0.155565
$321$	−12.3452	−0.689041
$322$	0.910505	0.0507405
$323$	−3.62564	−0.201736
$324$	2.09095	0.116164
$325$	3.75119	0.208079
$326$	−7.12159	−0.394428
$327$	−3.95612	−0.218774
$328$	2.52152	0.139227
$329$	1.62523	0.0896018
$330$	−13.5343	−0.745040
$331$	−9.54983	−0.524906	−0.262453	−	0.964945i	$-0.584532\pi$
$331$	−9.54983	−0.524906	−0.262453	+	0.964945i	$0.584532\pi$
$332$	−7.51146	−0.412245
$333$	−1.92269	−0.105363
$334$	9.20063	0.503436
$335$	4.11820	0.225001
$336$	−0.193451	−0.0105536
$337$	28.2185	1.53716	0.768580	−	0.639754i	$-0.220964\pi$
$337$	28.2185	1.53716	0.768580	+	0.639754i	$0.220964\pi$
$338$	−11.1314	−0.605469
$339$	−7.70371	−0.418408
$340$	10.0896	0.547184
$341$	31.6658	1.71480
$342$	−2.15253	−0.116395
$343$	2.93267	0.158349
$344$	3.37270	0.181844
$345$	11.1001	0.597608
$346$	1.25029	0.0672157
$347$	−6.22085	−0.333953	−0.166976	−	0.985961i	$-0.553400\pi$
$347$	−6.22085	−0.333953	−0.166976	+	0.985961i	$0.553400\pi$
$348$	−8.38002	−0.449216
$349$	−8.53659	−0.456953	−0.228477	−	0.973549i	$-0.573374\pi$
$349$	−8.53659	−0.456953	−0.228477	+	0.973549i	$0.573374\pi$
$350$	−0.576660	−0.0308238
$351$	−6.48394	−0.346087
$352$	5.28306	0.281588
$353$	15.8426	0.843219	0.421609	−	0.906778i	$-0.361465\pi$
$353$	15.8426	0.843219	0.421609	+	0.906778i	$0.361465\pi$
$354$	12.7858	0.679558
$355$	−21.5581	−1.14419
$356$	−8.00293	−0.424154
$357$	0.701383	0.0371211
$358$	−3.00713	−0.158932
$359$	−11.5340	−0.608740	−0.304370	−	0.952554i	$-0.598446\pi$
$359$	−11.5340	−0.608740	−0.304370	+	0.952554i	$0.598446\pi$
$360$	5.99013	0.315708
$361$	1.00000	0.0526316
$362$	14.7493	0.775203
$363$	15.5677	0.817094
$364$	−0.287252	−0.0150561
$365$	25.0532	1.31134
$366$	−7.51545	−0.392839
$367$	−15.4782	−0.807958	−0.403979	−	0.914768i	$-0.632373\pi$
$367$	−15.4782	−0.807958	−0.403979	+	0.914768i	$0.632373\pi$
$368$	−4.33287	−0.225866
$369$	−5.42763	−0.282551
$370$	−2.48570	−0.129225
$371$	−1.58360	−0.0822166
$372$	5.51782	0.286086
$373$	25.1439	1.30190	0.650951	−	0.759120i	$-0.274370\pi$
$373$	25.1439	1.30190	0.650951	+	0.759120i	$0.274370\pi$
$374$	−19.1545	−0.990455
$375$	5.77903	0.298428
$376$	−7.73406	−0.398854
$377$	−12.4434	−0.640866
$378$	0.996759	0.0512678
$379$	−35.1738	−1.80676	−0.903379	−	0.428842i	$-0.858922\pi$
$379$	−35.1738	−1.80676	−0.903379	+	0.428842i	$0.858922\pi$
$380$	−2.78284	−0.142757
$381$	−11.7508	−0.602014
$382$	16.9298	0.866206
$383$	−12.2088	−0.623841	−0.311921	−	0.950108i	$-0.600972\pi$
$383$	−12.2088	−0.623841	−0.311921	+	0.950108i	$0.600972\pi$
$384$	0.920583	0.0469783
$385$	3.08944	0.157453
$386$	4.08409	0.207875
$387$	−7.25984	−0.369038
$388$	−7.56976	−0.384296
$389$	35.0586	1.77754	0.888771	−	0.458351i	$-0.151560\pi$
$389$	35.0586	1.77754	0.888771	+	0.458351i	$0.151560\pi$
$390$	−3.50192	−0.177327
$391$	15.7094	0.794460
$392$	−6.95584	−0.351323
$393$	−4.65156	−0.234640
$394$	25.9699	1.30835
$395$	28.1939	1.41859
$396$	−11.3719	−0.571461
$397$	14.1263	0.708977	0.354489	−	0.935060i	$-0.384655\pi$
$397$	14.1263	0.708977	0.354489	+	0.935060i	$0.384655\pi$
$398$	7.12209	0.356998
$399$	−0.193451	−0.00968464
$400$	2.74418	0.137209
$401$	−18.8546	−0.941552	−0.470776	−	0.882253i	$-0.656026\pi$
$401$	−18.8546	−0.941552	−0.470776	+	0.882253i	$0.656026\pi$
$402$	−1.36233	−0.0679468
$403$	8.19333	0.408139
$404$	10.0862	0.501808
$405$	−5.81878	−0.289137
$406$	1.91288	0.0949349
$407$	4.71896	0.233910
$408$	−3.33771	−0.165241
$409$	17.7308	0.876732	0.438366	−	0.898797i	$-0.355557\pi$
$409$	17.7308	0.876732	0.438366	+	0.898797i	$0.355557\pi$
$410$	−7.01697	−0.346543
$411$	−11.7413	−0.579156
$412$	−3.81644	−0.188023
$413$	−2.91858	−0.143614
$414$	9.32661	0.458378
$415$	20.9032	1.02610
$416$	1.36696	0.0670208
$417$	−14.4681	−0.708507
$418$	5.28306	0.258403
$419$	−35.7529	−1.74665	−0.873323	−	0.487142i	$-0.838039\pi$
$419$	−35.7529	−1.74665	−0.873323	+	0.487142i	$0.838039\pi$
$420$	0.538341	0.0262684
$421$	−9.62961	−0.469318	−0.234659	−	0.972078i	$-0.575397\pi$
$421$	−9.62961	−0.469318	−0.234659	+	0.972078i	$0.575397\pi$
$422$	−1.00000	−0.0486792
$423$	16.6478	0.809442
$424$	7.53598	0.365980
$425$	−9.94943	−0.482618
$426$	7.13158	0.345526
$427$	1.71553	0.0830204
$428$	−13.4102	−0.648205
$429$	6.64821	0.320978
$430$	−9.38569	−0.452618
$431$	14.5384	0.700292	0.350146	−	0.936695i	$-0.386132\pi$
$431$	14.5384	0.700292	0.350146	+	0.936695i	$0.386132\pi$
$432$	−4.74333	−0.228214
$433$	3.57498	0.171803	0.0859013	−	0.996304i	$-0.472623\pi$
$433$	3.57498	0.171803	0.0859013	+	0.996304i	$0.472623\pi$
$434$	−1.25954	−0.0604598
$435$	23.3202	1.11812
$436$	−4.29741	−0.205808
$437$	−4.33287	−0.207269
$438$	−8.28777	−0.396005
$439$	−28.2146	−1.34661	−0.673304	−	0.739366i	$-0.735125\pi$
$439$	−28.2146	−1.34661	−0.673304	+	0.739366i	$0.735125\pi$
$440$	−14.7019	−0.700885
$441$	14.9726	0.712983
$442$	−4.95611	−0.235738
$443$	−15.2253	−0.723374	−0.361687	−	0.932300i	$-0.617799\pi$
$443$	−15.2253	−0.723374	−0.361687	+	0.932300i	$0.617799\pi$
$444$	0.822289	0.0390241
$445$	22.2708	1.05574
$446$	−24.6189	−1.16574
$447$	−2.50614	−0.118536
$448$	−0.210139	−0.00992814
$449$	−37.6624	−1.77740	−0.888699	−	0.458491i	$-0.848390\pi$
$449$	−37.6624	−1.77740	−0.888699	+	0.458491i	$0.848390\pi$
$450$	−5.90693	−0.278455
$451$	13.3213	0.627277
$452$	−8.36830	−0.393612
$453$	−10.0079	−0.470213
$454$	−6.08178	−0.285432
$455$	0.799375	0.0374753
$456$	0.920583	0.0431103
$457$	18.4048	0.860940	0.430470	−	0.902605i	$-0.358348\pi$
$457$	18.4048	0.860940	0.430470	+	0.902605i	$0.358348\pi$
$458$	16.5489	0.773280
$459$	17.1976	0.802716
$460$	12.0577	0.562192
$461$	32.7869	1.52704	0.763518	−	0.645786i	$-0.223470\pi$
$461$	32.7869	1.52704	0.763518	+	0.645786i	$0.223470\pi$
$462$	−1.02201	−0.0475482
$463$	−38.7330	−1.80007	−0.900037	−	0.435814i	$-0.856461\pi$
$463$	−38.7330	−1.80007	−0.900037	+	0.435814i	$0.856461\pi$
$464$	−9.10294	−0.422594
$465$	−15.3552	−0.712080
$466$	−28.1077	−1.30206
$467$	−37.2327	−1.72293	−0.861463	−	0.507821i	$-0.830451\pi$
$467$	−37.2327	−1.72293	−0.861463	+	0.507821i	$0.830451\pi$
$468$	−2.94242	−0.136013
$469$	0.310975	0.0143595
$470$	21.5226	0.992765
$471$	−6.04072	−0.278342
$472$	13.8888	0.639284
$473$	17.8182	0.819282
$474$	−9.32674	−0.428391
$475$	2.74418	0.125912
$476$	0.761890	0.0349212
$477$	−16.2214	−0.742727
$478$	10.7076	0.489755
$479$	16.2088	0.740601	0.370300	−	0.928912i	$-0.379255\pi$
$479$	16.2088	0.740601	0.370300	+	0.928912i	$0.379255\pi$
$480$	−2.56183	−0.116931
$481$	1.22100	0.0556730
$482$	−30.1530	−1.37343
$483$	0.838196	0.0381392
$484$	16.9107	0.768669
$485$	21.0654	0.956531
$486$	16.1549	0.732800
$487$	17.2527	0.781792	0.390896	−	0.920435i	$-0.372165\pi$
$487$	17.2527	0.781792	0.390896	+	0.920435i	$0.372165\pi$
$488$	−8.16379	−0.369558
$489$	−6.55602	−0.296473
$490$	19.3570	0.874459
$491$	−4.11029	−0.185495	−0.0927475	−	0.995690i	$-0.529565\pi$
$491$	−4.11029	−0.185495	−0.0927475	+	0.995690i	$0.529565\pi$
$492$	2.32127	0.104651
$493$	33.0040	1.48643
$494$	1.36696	0.0615025
$495$	31.6462	1.42239
$496$	5.99383	0.269131
$497$	−1.62791	−0.0730216
$498$	−6.91492	−0.309865
$499$	6.70895	0.300334	0.150167	−	0.988661i	$-0.452019\pi$
$499$	6.70895	0.300334	0.150167	+	0.988661i	$0.452019\pi$
$500$	6.27757	0.280741
$501$	8.46994	0.378409
$502$	22.2443	0.992810
$503$	6.19770	0.276342	0.138171	−	0.990408i	$-0.455878\pi$
$503$	6.19770	0.276342	0.138171	+	0.990408i	$0.455878\pi$
$504$	0.452330	0.0201484
$505$	−28.0683	−1.24902
$506$	−22.8908	−1.01762
$507$	−10.2474	−0.455103
$508$	−12.7646	−0.566336
$509$	44.3361	1.96516	0.982582	−	0.185831i	$-0.0594975\pi$
$509$	44.3361	1.96516	0.982582	+	0.185831i	$0.0594975\pi$
$510$	9.28829	0.411293
$511$	1.89183	0.0836896
$512$	1.00000	0.0441942
$513$	−4.74333	−0.209423
$514$	−1.68749	−0.0744318
$515$	10.6205	0.467997
$516$	3.10485	0.136684
$517$	−40.8595	−1.79700
$518$	−0.187702	−0.00824714
$519$	1.15099	0.0505229
$520$	−3.80403	−0.166818
$521$	−31.0168	−1.35887	−0.679435	−	0.733736i	$-0.737775\pi$
$521$	−31.0168	−1.35887	−0.679435	+	0.733736i	$0.737775\pi$
$522$	19.5943	0.857620
$523$	0.430500	0.0188244	0.00941221	−	0.999956i	$-0.497004\pi$
$523$	0.430500	0.0188244	0.00941221	+	0.999956i	$0.497004\pi$
$524$	−5.05284	−0.220734
$525$	−0.530864	−0.0231688
$526$	6.53091	0.284761
$527$	−21.7315	−0.946639
$528$	4.86350	0.211656
$529$	−4.22625	−0.183750
$530$	−20.9714	−0.910940
$531$	−29.8960	−1.29738
$532$	−0.210139	−0.00911069
$533$	3.44681	0.149298
$534$	−7.36736	−0.318817
$535$	37.3183	1.61341
$536$	−1.47985	−0.0639200
$537$	−2.76831	−0.119461
$538$	7.46192	0.321706
$539$	−36.7481	−1.58285
$540$	13.1999	0.568034
$541$	9.71877	0.417843	0.208921	−	0.977932i	$-0.433005\pi$
$541$	9.71877	0.417843	0.208921	+	0.977932i	$0.433005\pi$
$542$	−14.6115	−0.627617
$543$	13.5779	0.582684
$544$	−3.62564	−0.155448
$545$	11.9590	0.512266
$546$	−0.264439	−0.0113170
$547$	−38.5774	−1.64945	−0.824726	−	0.565533i	$-0.808671\pi$
$547$	−38.5774	−1.64945	−0.824726	+	0.565533i	$0.808671\pi$
$548$	−12.7542	−0.544833
$549$	17.5728	0.749988
$550$	14.4977	0.618183
$551$	−9.10294	−0.387798
$552$	−3.98877	−0.169773
$553$	2.12899	0.0905339
$554$	−11.2142	−0.476444
$555$	−2.28830	−0.0971327
$556$	−15.7163	−0.666518
$557$	−5.79760	−0.245652	−0.122826	−	0.992428i	$-0.539196\pi$
$557$	−5.79760	−0.245652	−0.122826	+	0.992428i	$0.539196\pi$
$558$	−12.9019	−0.546180
$559$	4.61035	0.194997
$560$	0.584783	0.0247116
$561$	−17.6333	−0.744479
$562$	0.448578	0.0189221
$563$	43.1840	1.81999	0.909995	−	0.414620i	$-0.136085\pi$
$563$	43.1840	1.81999	0.909995	+	0.414620i	$0.136085\pi$
$564$	−7.11985	−0.299800
$565$	23.2876	0.979717
$566$	9.30656	0.391184
$567$	−0.439391	−0.0184527
$568$	7.74681	0.325049
$569$	11.9421	0.500639	0.250320	−	0.968163i	$-0.419464\pi$
$569$	11.9421	0.500639	0.250320	+	0.968163i	$0.419464\pi$
$570$	−2.56183	−0.107303
$571$	19.1210	0.800187	0.400094	−	0.916474i	$-0.368978\pi$
$571$	19.1210	0.800187	0.400094	+	0.916474i	$0.368978\pi$
$572$	7.22173	0.301956
$573$	15.5853	0.651086
$574$	−0.529869	−0.0221163
$575$	−11.8902	−0.495855
$576$	−2.15253	−0.0896886
$577$	15.3782	0.640202	0.320101	−	0.947383i	$-0.396283\pi$
$577$	15.3782	0.640202	0.320101	+	0.947383i	$0.396283\pi$
$578$	−3.85471	−0.160335
$579$	3.75975	0.156250
$580$	25.3320	1.05185
$581$	1.57845	0.0654852
$582$	−6.96860	−0.288858
$583$	39.8130	1.64889
$584$	−9.00274	−0.372536
$585$	8.18827	0.338543
$586$	9.99734	0.412986
$587$	21.5145	0.888000	0.444000	−	0.896027i	$-0.353559\pi$
$587$	21.5145	0.888000	0.444000	+	0.896027i	$0.353559\pi$
$588$	−6.40343	−0.264073
$589$	5.99383	0.246972
$590$	−38.6503	−1.59121
$591$	23.9075	0.983422
$592$	0.893226	0.0367114
$593$	−23.4412	−0.962613	−0.481307	−	0.876552i	$-0.659838\pi$
$593$	−23.4412	−0.962613	−0.481307	+	0.876552i	$0.659838\pi$
$594$	−25.0593	−1.02820
$595$	−2.12021	−0.0869203
$596$	−2.72234	−0.111511
$597$	6.55648	0.268339
$598$	−5.92286	−0.242204
$599$	6.02915	0.246344	0.123172	−	0.992385i	$-0.460693\pi$
$599$	6.02915	0.246344	0.123172	+	0.992385i	$0.460693\pi$
$600$	2.52625	0.103134
$601$	31.5265	1.28599	0.642996	−	0.765869i	$-0.277691\pi$
$601$	31.5265	1.28599	0.642996	+	0.765869i	$0.277691\pi$
$602$	−0.708737	−0.0288860
$603$	3.18543	0.129721
$604$	−10.8713	−0.442346
$605$	−47.0598	−1.91325
$606$	9.28520	0.377186
$607$	36.5276	1.48261	0.741305	−	0.671168i	$-0.234207\pi$
$607$	36.5276	1.48261	0.741305	+	0.671168i	$0.234207\pi$
$608$	1.00000	0.0405554
$609$	1.76097	0.0713581
$610$	22.7185	0.919845
$611$	−10.5722	−0.427704
$612$	7.80429	0.315470
$613$	−3.35193	−0.135383	−0.0676915	−	0.997706i	$-0.521563\pi$
$613$	−3.35193	−0.135383	−0.0676915	+	0.997706i	$0.521563\pi$
$614$	−6.10808	−0.246502
$615$	−6.45970	−0.260480
$616$	−1.11018	−0.0447303
$617$	−39.6270	−1.59532	−0.797661	−	0.603106i	$-0.793929\pi$
$617$	−39.6270	−1.59532	−0.797661	+	0.603106i	$0.793929\pi$
$618$	−3.51335	−0.141328
$619$	19.5531	0.785905	0.392953	−	0.919559i	$-0.371454\pi$
$619$	19.5531	0.785905	0.392953	+	0.919559i	$0.371454\pi$
$620$	−16.6799	−0.669879
$621$	20.5522	0.824732
$622$	−3.62033	−0.145162
$623$	1.68173	0.0673770
$624$	1.25840	0.0503764
$625$	−31.1904	−1.24761
$626$	−15.1305	−0.604738
$627$	4.86350	0.194229
$628$	−6.56184	−0.261846
$629$	−3.23852	−0.129128
$630$	−1.25876	−0.0501502
$631$	−31.6186	−1.25872	−0.629358	−	0.777115i	$-0.716682\pi$
$631$	−31.6186	−1.25872	−0.629358	+	0.777115i	$0.716682\pi$
$632$	−10.1313	−0.403003
$633$	−0.920583	−0.0365899
$634$	−31.2100	−1.23951
$635$	35.5217	1.40964
$636$	6.93750	0.275090
$637$	−9.50836	−0.376735
$638$	−48.0914	−1.90396
$639$	−16.6752	−0.659661
$640$	−2.78284	−0.110001
$641$	50.3062	1.98698	0.993489	−	0.113932i	$-0.0363445\pi$
$641$	50.3062	1.98698	0.993489	+	0.113932i	$0.0363445\pi$
$642$	−12.3452	−0.487225
$643$	24.3898	0.961840	0.480920	−	0.876765i	$-0.340303\pi$
$643$	24.3898	0.961840	0.480920	+	0.876765i	$0.340303\pi$
$644$	0.910505	0.0358789
$645$	−8.64031	−0.340212
$646$	−3.62564	−0.142649
$647$	28.8446	1.13400	0.566999	−	0.823718i	$-0.308104\pi$
$647$	28.8446	1.13400	0.566999	+	0.823718i	$0.308104\pi$
$648$	2.09095	0.0821403
$649$	73.3754	2.88024
$650$	3.75119	0.147134
$651$	−1.15951	−0.0454448
$652$	−7.12159	−0.278903
$653$	9.56986	0.374497	0.187249	−	0.982313i	$-0.440043\pi$
$653$	9.56986	0.374497	0.187249	+	0.982313i	$0.440043\pi$
$654$	−3.95612	−0.154697
$655$	14.0612	0.549418
$656$	2.52152	0.0984487
$657$	19.3786	0.756033
$658$	1.62523	0.0633580
$659$	−9.86484	−0.384280	−0.192140	−	0.981368i	$-0.561543\pi$
$659$	−9.86484	−0.384280	−0.192140	+	0.981368i	$0.561543\pi$
$660$	−13.5343	−0.526823
$661$	−14.9021	−0.579625	−0.289812	−	0.957083i	$-0.593593\pi$
$661$	−14.9021	−0.579625	−0.289812	+	0.957083i	$0.593593\pi$
$662$	−9.54983	−0.371165
$663$	−4.56251	−0.177193
$664$	−7.51146	−0.291501
$665$	0.584783	0.0226769
$666$	−1.92269	−0.0745028
$667$	39.4419	1.52719
$668$	9.20063	0.355983
$669$	−22.6637	−0.876230
$670$	4.11820	0.159100
$671$	−43.1298	−1.66501
$672$	−0.193451	−0.00746252
$673$	37.4947	1.44531	0.722657	−	0.691207i	$-0.242921\pi$
$673$	37.4947	1.44531	0.722657	+	0.691207i	$0.242921\pi$
$674$	28.2185	1.08694
$675$	−13.0166	−0.501008
$676$	−11.1314	−0.428131
$677$	25.9029	0.995530	0.497765	−	0.867312i	$-0.334154\pi$
$677$	25.9029	0.995530	0.497765	+	0.867312i	$0.334154\pi$
$678$	−7.70371	−0.295859
$679$	1.59070	0.0610456
$680$	10.0896	0.386918
$681$	−5.59878	−0.214546
$682$	31.6658	1.21254
$683$	−6.75293	−0.258394	−0.129197	−	0.991619i	$-0.541240\pi$
$683$	−6.75293	−0.258394	−0.129197	+	0.991619i	$0.541240\pi$
$684$	−2.15253	−0.0823039
$685$	35.4929	1.35611
$686$	2.93267	0.111970
$687$	15.2347	0.581238
$688$	3.37270	0.128583
$689$	10.3014	0.392452
$690$	11.1001	0.422573
$691$	31.6304	1.20328	0.601639	−	0.798768i	$-0.294515\pi$
$691$	31.6304	1.20328	0.601639	+	0.798768i	$0.294515\pi$
$692$	1.25029	0.0475287
$693$	2.38969	0.0907767
$694$	−6.22085	−0.236140
$695$	43.7358	1.65899
$696$	−8.38002	−0.317644
$697$	−9.14212	−0.346282
$698$	−8.53659	−0.323115
$699$	−25.8754	−0.978699
$700$	−0.576660	−0.0217957
$701$	23.9395	0.904182	0.452091	−	0.891972i	$-0.350678\pi$
$701$	23.9395	0.904182	0.452091	+	0.891972i	$0.350678\pi$
$702$	−6.48394	−0.244721
$703$	0.893226	0.0336886
$704$	5.28306	0.199113
$705$	19.8134	0.746215
$706$	15.8426	0.596246
$707$	−2.11951	−0.0797124
$708$	12.7858	0.480520
$709$	−40.7370	−1.52991	−0.764955	−	0.644084i	$-0.777239\pi$
$709$	−40.7370	−1.52991	−0.764955	+	0.644084i	$0.777239\pi$
$710$	−21.5581	−0.809061
$711$	21.8080	0.817863
$712$	−8.00293	−0.299922
$713$	−25.9705	−0.972602
$714$	0.701383	0.0262486
$715$	−20.0969	−0.751582
$716$	−3.00713	−0.112382
$717$	9.85725	0.368126
$718$	−11.5340	−0.430445
$719$	−24.2995	−0.906217	−0.453108	−	0.891455i	$-0.649685\pi$
$719$	−24.2995	−0.906217	−0.453108	+	0.891455i	$0.649685\pi$
$720$	5.99013	0.223239
$721$	0.801984	0.0298675
$722$	1.00000	0.0372161
$723$	−27.7584	−1.03235
$724$	14.7493	0.548152
$725$	−24.9801	−0.927739
$726$	15.5677	0.577772
$727$	−49.9602	−1.85292	−0.926461	−	0.376391i	$-0.877165\pi$
$727$	−49.9602	−1.85292	−0.926461	+	0.376391i	$0.877165\pi$
$728$	−0.287252	−0.0106463
$729$	8.59906	0.318484
$730$	25.0532	0.927259
$731$	−12.2282	−0.452277
$732$	−7.51545	−0.277779
$733$	49.7372	1.83708	0.918542	−	0.395323i	$-0.129367\pi$
$733$	49.7372	1.83708	0.918542	+	0.395323i	$0.129367\pi$
$734$	−15.4782	−0.571313
$735$	17.8197	0.657290
$736$	−4.33287	−0.159712
$737$	−7.81816	−0.287986
$738$	−5.42763	−0.199794
$739$	37.4829	1.37883	0.689415	−	0.724367i	$-0.257868\pi$
$739$	37.4829	1.37883	0.689415	+	0.724367i	$0.257868\pi$
$740$	−2.48570	−0.0913762
$741$	1.25840	0.0462285
$742$	−1.58360	−0.0581359
$743$	−47.8123	−1.75406	−0.877031	−	0.480433i	$-0.840480\pi$
$743$	−47.8123	−1.75406	−0.877031	+	0.480433i	$0.840480\pi$
$744$	5.51782	0.202293
$745$	7.57582	0.277557
$746$	25.1439	0.920584
$747$	16.1686	0.591579
$748$	−19.1545	−0.700358
$749$	2.81800	0.102968
$750$	5.77903	0.211020
$751$	−1.95914	−0.0714900	−0.0357450	−	0.999361i	$-0.511380\pi$
$751$	−1.95914	−0.0714900	−0.0357450	+	0.999361i	$0.511380\pi$
$752$	−7.73406	−0.282032
$753$	20.4777	0.746249
$754$	−12.4434	−0.453161
$755$	30.2530	1.10102
$756$	0.996759	0.0362518
$757$	40.0226	1.45464	0.727322	−	0.686296i	$-0.240764\pi$
$757$	40.0226	1.45464	0.727322	+	0.686296i	$0.240764\pi$
$758$	−35.1738	−1.27757
$759$	−21.0729	−0.764897
$760$	−2.78284	−0.100944
$761$	26.6441	0.965847	0.482924	−	0.875663i	$-0.339575\pi$
$761$	26.6441	0.965847	0.482924	+	0.875663i	$0.339575\pi$
$762$	−11.7508	−0.425688
$763$	0.903053	0.0326927
$764$	16.9298	0.612500
$765$	−21.7181	−0.785219
$766$	−12.2088	−0.441122
$767$	18.9854	0.685525
$768$	0.920583	0.0332187
$769$	20.0941	0.724611	0.362305	−	0.932059i	$-0.381990\pi$
$769$	20.0941	0.724611	0.362305	+	0.932059i	$0.381990\pi$
$770$	3.08944	0.111336
$771$	−1.55347	−0.0559469
$772$	4.08409	0.146990
$773$	−3.25430	−0.117049	−0.0585245	−	0.998286i	$-0.518640\pi$
$773$	−3.25430	−0.117049	−0.0585245	+	0.998286i	$0.518640\pi$
$774$	−7.25984	−0.260949
$775$	16.4482	0.590836
$776$	−7.56976	−0.271739
$777$	−0.172795	−0.00619899
$778$	35.0586	1.25691
$779$	2.52152	0.0903427
$780$	−3.50192	−0.125389
$781$	40.9268	1.46448
$782$	15.7094	0.561768
$783$	43.1783	1.54307
$784$	−6.95584	−0.248423
$785$	18.2605	0.651747
$786$	−4.65156	−0.165916
$787$	0.937857	0.0334310	0.0167155	−	0.999860i	$-0.494679\pi$
$787$	0.937857	0.0334310	0.0167155	+	0.999860i	$0.494679\pi$
$788$	25.9699	0.925140
$789$	6.01224	0.214042
$790$	28.1939	1.00309
$791$	1.75851	0.0625253
$792$	−11.3719	−0.404084
$793$	−11.1596	−0.396288
$794$	14.1263	0.501323
$795$	−19.3059	−0.684710
$796$	7.12209	0.252436
$797$	−30.8638	−1.09325	−0.546625	−	0.837377i	$-0.684088\pi$
$797$	−30.8638	−1.09325	−0.546625	+	0.837377i	$0.684088\pi$
$798$	−0.193451	−0.00684808
$799$	28.0409	0.992017
$800$	2.74418	0.0970215
$801$	17.2265	0.608669
$802$	−18.8546	−0.665777
$803$	−47.5620	−1.67843
$804$	−1.36233	−0.0480457
$805$	−2.53379	−0.0893043
$806$	8.19333	0.288598
$807$	6.86932	0.241811
$808$	10.0862	0.354832
$809$	34.7670	1.22234	0.611171	−	0.791498i	$-0.290699\pi$
$809$	34.7670	1.22234	0.611171	+	0.791498i	$0.290699\pi$
$810$	−5.81878	−0.204451
$811$	4.03805	0.141795	0.0708976	−	0.997484i	$-0.477414\pi$
$811$	4.03805	0.141795	0.0708976	+	0.997484i	$0.477414\pi$
$812$	1.91288	0.0671291
$813$	−13.4511	−0.471750
$814$	4.71896	0.165400
$815$	19.8182	0.694202
$816$	−3.33771	−0.116843
$817$	3.37270	0.117996
$818$	17.7308	0.619943
$819$	0.618317	0.0216058
$820$	−7.01697	−0.245043
$821$	−9.09441	−0.317397	−0.158699	−	0.987327i	$-0.550730\pi$
$821$	−9.09441	−0.317397	−0.158699	+	0.987327i	$0.550730\pi$
$822$	−11.7413	−0.409525
$823$	28.1437	0.981029	0.490515	−	0.871433i	$-0.336809\pi$
$823$	28.1437	0.981029	0.490515	+	0.871433i	$0.336809\pi$
$824$	−3.81644	−0.132952
$825$	13.3463	0.464659
$826$	−2.91858	−0.101550
$827$	10.3482	0.359842	0.179921	−	0.983681i	$-0.442416\pi$
$827$	10.3482	0.359842	0.179921	+	0.983681i	$0.442416\pi$
$828$	9.32661	0.324122
$829$	6.07363	0.210946	0.105473	−	0.994422i	$-0.466364\pi$
$829$	6.07363	0.210946	0.105473	+	0.994422i	$0.466364\pi$
$830$	20.9032	0.725559
$831$	−10.3236	−0.358121
$832$	1.36696	0.0473908
$833$	25.2194	0.873800
$834$	−14.4681	−0.500990
$835$	−25.6038	−0.886058
$836$	5.28306	0.182718
$837$	−28.4307	−0.982709
$838$	−35.7529	−1.23506
$839$	27.0665	0.934440	0.467220	−	0.884141i	$-0.345256\pi$
$839$	27.0665	0.934440	0.467220	+	0.884141i	$0.345256\pi$
$840$	0.538341	0.0185745
$841$	53.8636	1.85737
$842$	−9.62961	−0.331858
$843$	0.412953	0.0142229
$844$	−1.00000	−0.0344214
$845$	30.9769	1.06564
$846$	16.6478	0.572362
$847$	−3.55360	−0.122103
$848$	7.53598	0.258787
$849$	8.56747	0.294035
$850$	−9.94943	−0.341263
$851$	−3.87023	−0.132670
$852$	7.13158	0.244324
$853$	−35.6376	−1.22021	−0.610104	−	0.792322i	$-0.708872\pi$
$853$	−35.6376	−1.22021	−0.610104	+	0.792322i	$0.708872\pi$
$854$	1.71553	0.0587043
$855$	5.99013	0.204858
$856$	−13.4102	−0.458350
$857$	8.22368	0.280916	0.140458	−	0.990087i	$-0.455143\pi$
$857$	8.22368	0.280916	0.140458	+	0.990087i	$0.455143\pi$
$858$	6.64821	0.226966
$859$	23.8543	0.813899	0.406949	−	0.913451i	$-0.366593\pi$
$859$	23.8543	0.813899	0.406949	+	0.913451i	$0.366593\pi$
$860$	−9.38569	−0.320049
$861$	−0.487789	−0.0166238
$862$	14.5384	0.495181
$863$	20.7074	0.704889	0.352444	−	0.935833i	$-0.385351\pi$
$863$	20.7074	0.704889	0.352444	+	0.935833i	$0.385351\pi$
$864$	−4.74333	−0.161371
$865$	−3.47934	−0.118301
$866$	3.57498	0.121483
$867$	−3.54858	−0.120516
$868$	−1.25954	−0.0427515
$869$	−53.5245	−1.81569
$870$	23.3202	0.790630
$871$	−2.02290	−0.0685435
$872$	−4.29741	−0.145529
$873$	16.2941	0.551472
$874$	−4.33287	−0.146561
$875$	−1.31916	−0.0445959
$876$	−8.28777	−0.280018
$877$	−40.7465	−1.37591	−0.687957	−	0.725752i	$-0.741492\pi$
$877$	−40.7465	−1.37591	−0.687957	+	0.725752i	$0.741492\pi$
$878$	−28.2146	−0.952195
$879$	9.20338	0.310422
$880$	−14.7019	−0.495601
$881$	−18.6646	−0.628827	−0.314413	−	0.949286i	$-0.601808\pi$
$881$	−18.6646	−0.628827	−0.314413	+	0.949286i	$0.601808\pi$
$882$	14.9726	0.504155
$883$	−19.7581	−0.664913	−0.332457	−	0.943119i	$-0.607878\pi$
$883$	−19.7581	−0.664913	−0.332457	+	0.943119i	$0.607878\pi$
$884$	−4.95611	−0.166692
$885$	−35.5808	−1.19604
$886$	−15.2253	−0.511503
$887$	9.60576	0.322530	0.161265	−	0.986911i	$-0.448443\pi$
$887$	9.60576	0.322530	0.161265	+	0.986911i	$0.448443\pi$
$888$	0.822289	0.0275942
$889$	2.68233	0.0899626
$890$	22.2708	0.746521
$891$	11.0466	0.370076
$892$	−24.6189	−0.824301
$893$	−7.73406	−0.258810
$894$	−2.50614	−0.0838178
$895$	8.36835	0.279723
$896$	−0.210139	−0.00702026
$897$	−5.45248	−0.182053
$898$	−37.6624	−1.25681
$899$	−54.5615	−1.81973
$900$	−5.90693	−0.196898
$901$	−27.3228	−0.910254
$902$	13.3213	0.443552
$903$	−0.652452	−0.0217122
$904$	−8.36830	−0.278325
$905$	−41.0448	−1.36437
$906$	−10.0079	−0.332491
$907$	36.4294	1.20962	0.604809	−	0.796370i	$-0.293249\pi$
$907$	36.4294	1.20962	0.604809	+	0.796370i	$0.293249\pi$
$908$	−6.08178	−0.201831
$909$	−21.7109	−0.720104
$910$	0.799375	0.0264990
$911$	55.1342	1.82668	0.913339	−	0.407200i	$-0.133495\pi$
$911$	55.1342	1.82668	0.913339	+	0.407200i	$0.133495\pi$
$912$	0.920583	0.0304836
$913$	−39.6835	−1.31333
$914$	18.4048	0.608777
$915$	20.9143	0.691405
$916$	16.5489	0.546792
$917$	1.06180	0.0350637
$918$	17.1976	0.567606
$919$	−17.0118	−0.561168	−0.280584	−	0.959829i	$-0.590528\pi$
$919$	−17.0118	−0.561168	−0.280584	+	0.959829i	$0.590528\pi$
$920$	12.0577	0.397529
$921$	−5.62299	−0.185284
$922$	32.7869	1.07978
$923$	10.5896	0.348560
$924$	−1.02201	−0.0336217
$925$	2.45118	0.0805941
$926$	−38.7330	−1.27284
$927$	8.21500	0.269816
$928$	−9.10294	−0.298819
$929$	−28.0209	−0.919335	−0.459668	−	0.888091i	$-0.652031\pi$
$929$	−28.0209	−0.919335	−0.459668	+	0.888091i	$0.652031\pi$
$930$	−15.3552	−0.503517
$931$	−6.95584	−0.227968
$932$	−28.1077	−0.920697
$933$	−3.33282	−0.109112
$934$	−37.2327	−1.21829
$935$	53.3038	1.74322
$936$	−2.94242	−0.0961760
$937$	−36.2072	−1.18284	−0.591419	−	0.806365i	$-0.701432\pi$
$937$	−36.2072	−1.18284	−0.591419	+	0.806365i	$0.701432\pi$
$938$	0.310975	0.0101537
$939$	−13.9289	−0.454553
$940$	21.5226	0.701991
$941$	22.7655	0.742133	0.371066	−	0.928606i	$-0.378992\pi$
$941$	22.7655	0.742133	0.371066	+	0.928606i	$0.378992\pi$
$942$	−6.04072	−0.196817
$943$	−10.9254	−0.355780
$944$	13.8888	0.452042
$945$	−2.77382	−0.0902323
$946$	17.8182	0.579320
$947$	53.0454	1.72375	0.861873	−	0.507125i	$-0.169292\pi$
$947$	53.0454	1.72375	0.861873	+	0.507125i	$0.169292\pi$
$948$	−9.32674	−0.302918
$949$	−12.3064	−0.399482
$950$	2.74418	0.0890331
$951$	−28.7314	−0.931680
$952$	0.761890	0.0246930
$953$	36.1757	1.17185	0.585923	−	0.810367i	$-0.300732\pi$
$953$	36.1757	1.17185	0.585923	+	0.810367i	$0.300732\pi$
$954$	−16.2214	−0.525187
$955$	−47.1130	−1.52454
$956$	10.7076	0.346309
$957$	−44.2721	−1.43111
$958$	16.2088	0.523684
$959$	2.68016	0.0865468
$960$	−2.56183	−0.0826828
$961$	4.92601	0.158904
$962$	1.22100	0.0393668
$963$	28.8658	0.930186
$964$	−30.1530	−0.971164
$965$	−11.3654	−0.365864
$966$	0.838196	0.0269685
$967$	13.9065	0.447204	0.223602	−	0.974681i	$-0.428218\pi$
$967$	13.9065	0.447204	0.223602	+	0.974681i	$0.428218\pi$
$968$	16.9107	0.543531
$969$	−3.33771	−0.107223
$970$	21.0654	0.676370
$971$	59.2010	1.89985	0.949926	−	0.312476i	$-0.101159\pi$
$971$	59.2010	1.89985	0.949926	+	0.312476i	$0.101159\pi$
$972$	16.1549	0.518168
$973$	3.30260	0.105877
$974$	17.2527	0.552811
$975$	3.45328	0.110594
$976$	−8.16379	−0.261317
$977$	−19.7035	−0.630372	−0.315186	−	0.949030i	$-0.602067\pi$
$977$	−19.7035	−0.630372	−0.315186	+	0.949030i	$0.602067\pi$
$978$	−6.55602	−0.209638
$979$	−42.2800	−1.35127
$980$	19.3570	0.618336
$981$	9.25028	0.295339
$982$	−4.11029	−0.131165
$983$	1.34608	0.0429332	0.0214666	−	0.999770i	$-0.493166\pi$
$983$	1.34608	0.0429332	0.0214666	+	0.999770i	$0.493166\pi$
$984$	2.32127	0.0739992
$985$	−72.2700	−2.30271
$986$	33.0040	1.05106
$987$	1.49616	0.0476232
$988$	1.36696	0.0434888
$989$	−14.6135	−0.464682
$990$	31.6462	1.00578
$991$	6.69984	0.212827	0.106414	−	0.994322i	$-0.466063\pi$
$991$	6.69984	0.212827	0.106414	+	0.994322i	$0.466063\pi$
$992$	5.99383	0.190304
$993$	−8.79141	−0.278987
$994$	−1.62791	−0.0516341
$995$	−19.8196	−0.628324
$996$	−6.91492	−0.219108
$997$	−0.406802	−0.0128835	−0.00644177	−	0.999979i	$-0.502050\pi$
$997$	−0.406802	−0.0128835	−0.00644177	+	0.999979i	$0.502050\pi$
$998$	6.70895	0.212368
$999$	−4.23686	−0.134048

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.d.1.21	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.d.1.21	✓	30	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.920583 q^{3} +1.00000 q^{4} -2.78284 q^{5} +0.920583 q^{6} -0.210139 q^{7} +1.00000 q^{8} -2.15253 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.920583 q^{3} +1.00000 q^{4} -2.78284 q^{5} +0.920583 q^{6} -0.210139 q^{7} +1.00000 q^{8} -2.15253 q^{9} -2.78284 q^{10} +5.28306 q^{11} +0.920583 q^{12} +1.36696 q^{13} -0.210139 q^{14} -2.56183 q^{15} +1.00000 q^{16} -3.62564 q^{17} -2.15253 q^{18} +1.00000 q^{19} -2.78284 q^{20} -0.193451 q^{21} +5.28306 q^{22} -4.33287 q^{23} +0.920583 q^{24} +2.74418 q^{25} +1.36696 q^{26} -4.74333 q^{27} -0.210139 q^{28} -9.10294 q^{29} -2.56183 q^{30} +5.99383 q^{31} +1.00000 q^{32} +4.86350 q^{33} -3.62564 q^{34} +0.584783 q^{35} -2.15253 q^{36} +0.893226 q^{37} +1.00000 q^{38} +1.25840 q^{39} -2.78284 q^{40} +2.52152 q^{41} -0.193451 q^{42} +3.37270 q^{43} +5.28306 q^{44} +5.99013 q^{45} -4.33287 q^{46} -7.73406 q^{47} +0.920583 q^{48} -6.95584 q^{49} +2.74418 q^{50} -3.33771 q^{51} +1.36696 q^{52} +7.53598 q^{53} -4.74333 q^{54} -14.7019 q^{55} -0.210139 q^{56} +0.920583 q^{57} -9.10294 q^{58} +13.8888 q^{59} -2.56183 q^{60} -8.16379 q^{61} +5.99383 q^{62} +0.452330 q^{63} +1.00000 q^{64} -3.80403 q^{65} +4.86350 q^{66} -1.47985 q^{67} -3.62564 q^{68} -3.98877 q^{69} +0.584783 q^{70} +7.74681 q^{71} -2.15253 q^{72} -9.00274 q^{73} +0.893226 q^{74} +2.52625 q^{75} +1.00000 q^{76} -1.11018 q^{77} +1.25840 q^{78} -10.1313 q^{79} -2.78284 q^{80} +2.09095 q^{81} +2.52152 q^{82} -7.51146 q^{83} -0.193451 q^{84} +10.0896 q^{85} +3.37270 q^{86} -8.38002 q^{87} +5.28306 q^{88} -8.00293 q^{89} +5.99013 q^{90} -0.287252 q^{91} -4.33287 q^{92} +5.51782 q^{93} -7.73406 q^{94} -2.78284 q^{95} +0.920583 q^{96} -7.56976 q^{97} -6.95584 q^{98} -11.3719 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * q^99

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