LMFDB - Embedded newform 8015.2.a.l.1.56

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.56
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.39193 q^{2} -0.616339 q^{3} +3.72134 q^{4} -1.00000 q^{5} -1.47424 q^{6} -1.00000 q^{7} +4.11733 q^{8} -2.62013 q^{9} +O(q^{10})$	\(q+2.39193 q^{2} -0.616339 q^{3} +3.72134 q^{4} -1.00000 q^{5} -1.47424 q^{6} -1.00000 q^{7} +4.11733 q^{8} -2.62013 q^{9} -2.39193 q^{10} +0.550190 q^{11} -2.29361 q^{12} +3.12576 q^{13} -2.39193 q^{14} +0.616339 q^{15} +2.40569 q^{16} +2.92502 q^{17} -6.26717 q^{18} -7.49240 q^{19} -3.72134 q^{20} +0.616339 q^{21} +1.31602 q^{22} +5.91234 q^{23} -2.53767 q^{24} +1.00000 q^{25} +7.47660 q^{26} +3.46390 q^{27} -3.72134 q^{28} +3.14112 q^{29} +1.47424 q^{30} +1.69415 q^{31} -2.48041 q^{32} -0.339103 q^{33} +6.99644 q^{34} +1.00000 q^{35} -9.75038 q^{36} -0.900002 q^{37} -17.9213 q^{38} -1.92652 q^{39} -4.11733 q^{40} +4.84696 q^{41} +1.47424 q^{42} -7.55186 q^{43} +2.04744 q^{44} +2.62013 q^{45} +14.1419 q^{46} +9.22768 q^{47} -1.48272 q^{48} +1.00000 q^{49} +2.39193 q^{50} -1.80280 q^{51} +11.6320 q^{52} -0.956524 q^{53} +8.28542 q^{54} -0.550190 q^{55} -4.11733 q^{56} +4.61786 q^{57} +7.51336 q^{58} +10.7205 q^{59} +2.29361 q^{60} +8.86504 q^{61} +4.05230 q^{62} +2.62013 q^{63} -10.7443 q^{64} -3.12576 q^{65} -0.811112 q^{66} +0.505435 q^{67} +10.8850 q^{68} -3.64400 q^{69} +2.39193 q^{70} +7.84495 q^{71} -10.7879 q^{72} +7.74262 q^{73} -2.15274 q^{74} -0.616339 q^{75} -27.8818 q^{76} -0.550190 q^{77} -4.60812 q^{78} -0.0674259 q^{79} -2.40569 q^{80} +5.72544 q^{81} +11.5936 q^{82} -10.1691 q^{83} +2.29361 q^{84} -2.92502 q^{85} -18.0635 q^{86} -1.93600 q^{87} +2.26531 q^{88} +11.0915 q^{89} +6.26717 q^{90} -3.12576 q^{91} +22.0018 q^{92} -1.04417 q^{93} +22.0720 q^{94} +7.49240 q^{95} +1.52877 q^{96} -0.0409927 q^{97} +2.39193 q^{98} -1.44157 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.39193	1.69135	0.845676	−	0.533697i	$-0.179198\pi$
$2$	2.39193	1.69135	0.845676	+	0.533697i	$0.179198\pi$
$3$	−0.616339	−0.355843	−0.177922	−	0.984045i	$-0.556937\pi$
$3$	−0.616339	−0.355843	−0.177922	+	0.984045i	$0.556937\pi$
$4$	3.72134	1.86067
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.47424	−0.601856
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	4.11733	1.45570
$9$	−2.62013	−0.873376
$10$	−2.39193	−0.756395
$11$	0.550190	0.165888	0.0829442	−	0.996554i	$-0.473568\pi$
$11$	0.550190	0.165888	0.0829442	+	0.996554i	$0.473568\pi$
$12$	−2.29361	−0.662107
$13$	3.12576	0.866929	0.433464	−	0.901171i	$-0.357291\pi$
$13$	3.12576	0.866929	0.433464	+	0.901171i	$0.357291\pi$
$14$	−2.39193	−0.639271
$15$	0.616339	0.159138
$16$	2.40569	0.601423
$17$	2.92502	0.709421	0.354710	−	0.934976i	$-0.384579\pi$
$17$	2.92502	0.709421	0.354710	+	0.934976i	$0.384579\pi$
$18$	−6.26717	−1.47718
$19$	−7.49240	−1.71888	−0.859438	−	0.511241i	$-0.829186\pi$
$19$	−7.49240	−1.71888	−0.859438	+	0.511241i	$0.829186\pi$
$20$	−3.72134	−0.832117
$21$	0.616339	0.134496
$22$	1.31602	0.280576
$23$	5.91234	1.23281	0.616404	−	0.787430i	$-0.288589\pi$
$23$	5.91234	1.23281	0.616404	+	0.787430i	$0.288589\pi$
$24$	−2.53767	−0.517999
$25$	1.00000	0.200000
$26$	7.47660	1.46628
$27$	3.46390	0.666628
$28$	−3.72134	−0.703267
$29$	3.14112	0.583292	0.291646	−	0.956526i	$-0.405797\pi$
$29$	3.14112	0.583292	0.291646	+	0.956526i	$0.405797\pi$
$30$	1.47424	0.269158
$31$	1.69415	0.304279	0.152139	−	0.988359i	$-0.451384\pi$
$31$	1.69415	0.304279	0.152139	+	0.988359i	$0.451384\pi$
$32$	−2.48041	−0.438478
$33$	−0.339103	−0.0590303
$34$	6.99644	1.19988
$35$	1.00000	0.169031
$36$	−9.75038	−1.62506
$37$	−0.900002	−0.147959	−0.0739797	−	0.997260i	$-0.523570\pi$
$37$	−0.900002	−0.147959	−0.0739797	+	0.997260i	$0.523570\pi$
$38$	−17.9213	−2.90722
$39$	−1.92652	−0.308491
$40$	−4.11733	−0.651007
$41$	4.84696	0.756968	0.378484	−	0.925608i	$-0.376446\pi$
$41$	4.84696	0.756968	0.378484	+	0.925608i	$0.376446\pi$
$42$	1.47424	0.227480
$43$	−7.55186	−1.15165	−0.575824	−	0.817574i	$-0.695319\pi$
$43$	−7.55186	−1.15165	−0.575824	+	0.817574i	$0.695319\pi$
$44$	2.04744	0.308664
$45$	2.62013	0.390585
$46$	14.1419	2.08511
$47$	9.22768	1.34600	0.672998	−	0.739645i	$-0.265006\pi$
$47$	9.22768	1.34600	0.672998	+	0.739645i	$0.265006\pi$
$48$	−1.48272	−0.214012
$49$	1.00000	0.142857
$50$	2.39193	0.338270
$51$	−1.80280	−0.252443
$52$	11.6320	1.61307
$53$	−0.956524	−0.131389	−0.0656943	−	0.997840i	$-0.520926\pi$
$53$	−0.956524	−0.131389	−0.0656943	+	0.997840i	$0.520926\pi$
$54$	8.28542	1.12750
$55$	−0.550190	−0.0741876
$56$	−4.11733	−0.550201
$57$	4.61786	0.611650
$58$	7.51336	0.986552
$59$	10.7205	1.39570	0.697848	−	0.716246i	$-0.254141\pi$
$59$	10.7205	1.39570	0.697848	+	0.716246i	$0.254141\pi$
$60$	2.29361	0.296103
$61$	8.86504	1.13505	0.567526	−	0.823355i	$-0.307901\pi$
$61$	8.86504	1.13505	0.567526	+	0.823355i	$0.307901\pi$
$62$	4.05230	0.514642
$63$	2.62013	0.330105
$64$	−10.7443	−1.34304
$65$	−3.12576	−0.387702
$66$	−0.811112	−0.0998410
$67$	0.505435	0.0617487	0.0308743	−	0.999523i	$-0.490171\pi$
$67$	0.505435	0.0617487	0.0308743	+	0.999523i	$0.490171\pi$
$68$	10.8850	1.32000
$69$	−3.64400	−0.438686
$70$	2.39193	0.285891
$71$	7.84495	0.931025	0.465512	−	0.885041i	$-0.345870\pi$
$71$	7.84495	0.931025	0.465512	+	0.885041i	$0.345870\pi$
$72$	−10.7879	−1.27137
$73$	7.74262	0.906205	0.453103	−	0.891458i	$-0.350317\pi$
$73$	7.74262	0.906205	0.453103	+	0.891458i	$0.350317\pi$
$74$	−2.15274	−0.250251
$75$	−0.616339	−0.0711687
$76$	−27.8818	−3.19826
$77$	−0.550190	−0.0627000
$78$	−4.60812	−0.521766
$79$	−0.0674259	−0.00758601	−0.00379300	−	0.999993i	$-0.501207\pi$
$79$	−0.0674259	−0.00758601	−0.00379300	+	0.999993i	$0.501207\pi$
$80$	−2.40569	−0.268964
$81$	5.72544	0.636160
$82$	11.5936	1.28030
$83$	−10.1691	−1.11621	−0.558104	−	0.829771i	$-0.688471\pi$
$83$	−10.1691	−1.11621	−0.558104	+	0.829771i	$0.688471\pi$
$84$	2.29361	0.250253
$85$	−2.92502	−0.317263
$86$	−18.0635	−1.94784
$87$	−1.93600	−0.207561
$88$	2.26531	0.241483
$89$	11.0915	1.17570	0.587850	−	0.808970i	$-0.299975\pi$
$89$	11.0915	1.17570	0.587850	+	0.808970i	$0.299975\pi$
$90$	6.26717	0.660617
$91$	−3.12576	−0.327668
$92$	22.0018	2.29385
$93$	−1.04417	−0.108276
$94$	22.0720	2.27655
$95$	7.49240	0.768704
$96$	1.52877	0.156030
$97$	−0.0409927	−0.00416218	−0.00208109	−	0.999998i	$-0.500662\pi$
$97$	−0.0409927	−0.00416218	−0.00208109	+	0.999998i	$0.500662\pi$
$98$	2.39193	0.241622
$99$	−1.44157	−0.144883
$100$	3.72134	0.372134
$101$	−2.74522	−0.273160	−0.136580	−	0.990629i	$-0.543611\pi$
$101$	−2.74522	−0.273160	−0.136580	+	0.990629i	$0.543611\pi$
$102$	−4.31218	−0.426969
$103$	1.11173	0.109542	0.0547710	−	0.998499i	$-0.482557\pi$
$103$	1.11173	0.109542	0.0547710	+	0.998499i	$0.482557\pi$
$104$	12.8698	1.26198
$105$	−0.616339	−0.0601485
$106$	−2.28794	−0.222224
$107$	15.2749	1.47668	0.738339	−	0.674430i	$-0.235610\pi$
$107$	15.2749	1.47668	0.738339	+	0.674430i	$0.235610\pi$
$108$	12.8904	1.24038
$109$	10.2684	0.983538	0.491769	−	0.870726i	$-0.336350\pi$
$109$	10.2684	0.983538	0.491769	+	0.870726i	$0.336350\pi$
$110$	−1.31602	−0.125477
$111$	0.554706	0.0526504
$112$	−2.40569	−0.227316
$113$	14.2937	1.34464	0.672320	−	0.740261i	$-0.265298\pi$
$113$	14.2937	1.34464	0.672320	+	0.740261i	$0.265298\pi$
$114$	11.0456	1.03452
$115$	−5.91234	−0.551328
$116$	11.6892	1.08531
$117$	−8.18988	−0.757154
$118$	25.6428	2.36061
$119$	−2.92502	−0.268136
$120$	2.53767	0.231656
$121$	−10.6973	−0.972481
$122$	21.2046	1.91977
$123$	−2.98737	−0.269362
$124$	6.30452	0.566162
$125$	−1.00000	−0.0894427
$126$	6.26717	0.558323
$127$	−8.42042	−0.747191	−0.373596	−	0.927592i	$-0.621875\pi$
$127$	−8.42042	−0.747191	−0.373596	+	0.927592i	$0.621875\pi$
$128$	−20.7389	−1.83308
$129$	4.65450	0.409806
$130$	−7.47660	−0.655741
$131$	−0.747926	−0.0653466	−0.0326733	−	0.999466i	$-0.510402\pi$
$131$	−0.747926	−0.0653466	−0.0326733	+	0.999466i	$0.510402\pi$
$132$	−1.26192	−0.109836
$133$	7.49240	0.649674
$134$	1.20897	0.104439
$135$	−3.46390	−0.298125
$136$	12.0433	1.03270
$137$	−22.5558	−1.92707	−0.963536	−	0.267578i	$-0.913777\pi$
$137$	−22.5558	−1.92707	−0.963536	+	0.267578i	$0.913777\pi$
$138$	−8.71621	−0.741973
$139$	−12.9126	−1.09524	−0.547618	−	0.836729i	$-0.684465\pi$
$139$	−12.9126	−1.09524	−0.547618	+	0.836729i	$0.684465\pi$
$140$	3.72134	0.314511
$141$	−5.68737	−0.478963
$142$	18.7646	1.57469
$143$	1.71976	0.143813
$144$	−6.30321	−0.525268
$145$	−3.14112	−0.260856
$146$	18.5198	1.53271
$147$	−0.616339	−0.0508348
$148$	−3.34921	−0.275304
$149$	9.22538	0.755773	0.377886	−	0.925852i	$-0.376651\pi$
$149$	9.22538	0.755773	0.377886	+	0.925852i	$0.376651\pi$
$150$	−1.47424	−0.120371
$151$	1.41490	0.115143	0.0575715	−	0.998341i	$-0.481664\pi$
$151$	1.41490	0.115143	0.0575715	+	0.998341i	$0.481664\pi$
$152$	−30.8487	−2.50216
$153$	−7.66391	−0.619591
$154$	−1.31602	−0.106048
$155$	−1.69415	−0.136078
$156$	−7.16925	−0.574000
$157$	9.70918	0.774877	0.387438	−	0.921896i	$-0.373360\pi$
$157$	9.70918	0.774877	0.387438	+	0.921896i	$0.373360\pi$
$158$	−0.161278	−0.0128306
$159$	0.589543	0.0467538
$160$	2.48041	0.196093
$161$	−5.91234	−0.465958
$162$	13.6949	1.07597
$163$	−21.3032	−1.66859	−0.834297	−	0.551315i	$-0.814126\pi$
$163$	−21.3032	−1.66859	−0.834297	+	0.551315i	$0.814126\pi$
$164$	18.0372	1.40847
$165$	0.339103	0.0263992
$166$	−24.3239	−1.88790
$167$	23.0846	1.78634	0.893170	−	0.449720i	$-0.148476\pi$
$167$	23.0846	1.78634	0.893170	+	0.449720i	$0.148476\pi$
$168$	2.53767	0.195785
$169$	−3.22965	−0.248435
$170$	−6.99644	−0.536603
$171$	19.6310	1.50122
$172$	−28.1030	−2.14284
$173$	−2.64945	−0.201434	−0.100717	−	0.994915i	$-0.532114\pi$
$173$	−2.64945	−0.201434	−0.100717	+	0.994915i	$0.532114\pi$
$174$	−4.63077	−0.351058
$175$	−1.00000	−0.0755929
$176$	1.32359	0.0997691
$177$	−6.60749	−0.496649
$178$	26.5302	1.98852
$179$	−12.6460	−0.945206	−0.472603	−	0.881275i	$-0.656686\pi$
$179$	−12.6460	−0.945206	−0.472603	+	0.881275i	$0.656686\pi$
$180$	9.75038	0.726751
$181$	24.5138	1.82210	0.911049	−	0.412299i	$-0.135274\pi$
$181$	24.5138	1.82210	0.911049	+	0.412299i	$0.135274\pi$
$182$	−7.47660	−0.554202
$183$	−5.46387	−0.403901
$184$	24.3430	1.79459
$185$	0.900002	0.0661695
$186$	−2.49759	−0.183132
$187$	1.60931	0.117685
$188$	34.3393	2.50445
$189$	−3.46390	−0.251962
$190$	17.9213	1.30015
$191$	11.4174	0.826135	0.413068	−	0.910700i	$-0.364457\pi$
$191$	11.4174	0.826135	0.413068	+	0.910700i	$0.364457\pi$
$192$	6.62216	0.477913
$193$	22.5492	1.62313	0.811564	−	0.584264i	$-0.198617\pi$
$193$	22.5492	1.62313	0.811564	+	0.584264i	$0.198617\pi$
$194$	−0.0980518	−0.00703971
$195$	1.92652	0.137961
$196$	3.72134	0.265810
$197$	−2.24354	−0.159846	−0.0799229	−	0.996801i	$-0.525467\pi$
$197$	−2.24354	−0.159846	−0.0799229	+	0.996801i	$0.525467\pi$
$198$	−3.44813	−0.245048
$199$	12.2650	0.869442	0.434721	−	0.900565i	$-0.356847\pi$
$199$	12.2650	0.869442	0.434721	+	0.900565i	$0.356847\pi$
$200$	4.11733	0.291139
$201$	−0.311519	−0.0219729
$202$	−6.56638	−0.462009
$203$	−3.14112	−0.220464
$204$	−6.70883	−0.469712
$205$	−4.84696	−0.338526
$206$	2.65918	0.185274
$207$	−15.4911	−1.07670
$208$	7.51960	0.521391
$209$	−4.12224	−0.285142
$210$	−1.47424	−0.101732
$211$	7.55832	0.520336	0.260168	−	0.965563i	$-0.416222\pi$
$211$	7.55832	0.520336	0.260168	+	0.965563i	$0.416222\pi$
$212$	−3.55955	−0.244471
$213$	−4.83515	−0.331299
$214$	36.5365	2.49758
$215$	7.55186	0.515032
$216$	14.2620	0.970408
$217$	−1.69415	−0.115007
$218$	24.5614	1.66351
$219$	−4.77208	−0.322467
$220$	−2.04744	−0.138039
$221$	9.14289	0.615017
$222$	1.32682	0.0890503
$223$	1.94379	0.130166	0.0650830	−	0.997880i	$-0.479269\pi$
$223$	1.94379	0.130166	0.0650830	+	0.997880i	$0.479269\pi$
$224$	2.48041	0.165729
$225$	−2.62013	−0.174675
$226$	34.1896	2.27426
$227$	23.9843	1.59190	0.795948	−	0.605365i	$-0.206973\pi$
$227$	23.9843	1.59190	0.795948	+	0.605365i	$0.206973\pi$
$228$	17.1846	1.13808
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−14.1419	−0.932490
$231$	0.339103	0.0223114
$232$	12.9330	0.849096
$233$	3.91088	0.256210	0.128105	−	0.991761i	$-0.459110\pi$
$233$	3.91088	0.256210	0.128105	+	0.991761i	$0.459110\pi$
$234$	−19.5896	−1.28061
$235$	−9.22768	−0.601947
$236$	39.8948	2.59693
$237$	0.0415572	0.00269943
$238$	−6.99644	−0.453512
$239$	18.7411	1.21226	0.606129	−	0.795366i	$-0.292722\pi$
$239$	18.7411	1.21226	0.606129	+	0.795366i	$0.292722\pi$
$240$	1.48272	0.0957092
$241$	15.4978	0.998300	0.499150	−	0.866515i	$-0.333646\pi$
$241$	15.4978	0.998300	0.499150	+	0.866515i	$0.333646\pi$
$242$	−25.5872	−1.64481
$243$	−13.9205	−0.893002
$244$	32.9898	2.11196
$245$	−1.00000	−0.0638877
$246$	−7.14558	−0.455586
$247$	−23.4194	−1.49014
$248$	6.97538	0.442937
$249$	6.26763	0.397195
$250$	−2.39193	−0.151279
$251$	3.82419	0.241381	0.120690	−	0.992690i	$-0.461489\pi$
$251$	3.82419	0.241381	0.120690	+	0.992690i	$0.461489\pi$
$252$	9.75038	0.614216
$253$	3.25291	0.204509
$254$	−20.1411	−1.26376
$255$	1.80280	0.112896
$256$	−28.1174	−1.75734
$257$	−9.12482	−0.569191	−0.284595	−	0.958648i	$-0.591859\pi$
$257$	−9.12482	−0.569191	−0.284595	+	0.958648i	$0.591859\pi$
$258$	11.1333	0.693126
$259$	0.900002	0.0559234
$260$	−11.6320	−0.721386
$261$	−8.23014	−0.509433
$262$	−1.78899	−0.110524
$263$	−9.49212	−0.585309	−0.292655	−	0.956218i	$-0.594539\pi$
$263$	−9.49212	−0.585309	−0.292655	+	0.956218i	$0.594539\pi$
$264$	−1.39620	−0.0859301
$265$	0.956524	0.0587588
$266$	17.9213	1.09883
$267$	−6.83614	−0.418365
$268$	1.88089	0.114894
$269$	3.67972	0.224356	0.112178	−	0.993688i	$-0.464217\pi$
$269$	3.67972	0.224356	0.112178	+	0.993688i	$0.464217\pi$
$270$	−8.28542	−0.504234
$271$	−3.83658	−0.233056	−0.116528	−	0.993187i	$-0.537176\pi$
$271$	−3.83658	−0.233056	−0.116528	+	0.993187i	$0.537176\pi$
$272$	7.03668	0.426662
$273$	1.92652	0.116599
$274$	−53.9520	−3.25936
$275$	0.550190	0.0331777
$276$	−13.5606	−0.816251
$277$	−6.68087	−0.401415	−0.200707	−	0.979651i	$-0.564324\pi$
$277$	−6.68087	−0.401415	−0.200707	+	0.979651i	$0.564324\pi$
$278$	−30.8862	−1.85243
$279$	−4.43889	−0.265750
$280$	4.11733	0.246057
$281$	10.5174	0.627417	0.313709	−	0.949519i	$-0.398428\pi$
$281$	10.5174	0.627417	0.313709	+	0.949519i	$0.398428\pi$
$282$	−13.6038	−0.810095
$283$	−15.5762	−0.925906	−0.462953	−	0.886383i	$-0.653210\pi$
$283$	−15.5762	−0.925906	−0.462953	+	0.886383i	$0.653210\pi$
$284$	29.1937	1.73233
$285$	−4.61786	−0.273538
$286$	4.11355	0.243239
$287$	−4.84696	−0.286107
$288$	6.49898	0.382956
$289$	−8.44428	−0.496722
$290$	−7.51336	−0.441199
$291$	0.0252654	0.00148108
$292$	28.8129	1.68615
$293$	10.2836	0.600773	0.300386	−	0.953818i	$-0.402884\pi$
$293$	10.2836	0.600773	0.300386	+	0.953818i	$0.402884\pi$
$294$	−1.47424	−0.0859795
$295$	−10.7205	−0.624174
$296$	−3.70560	−0.215384
$297$	1.90580	0.110586
$298$	22.0665	1.27828
$299$	18.4805	1.06876
$300$	−2.29361	−0.132421
$301$	7.55186	0.435282
$302$	3.38435	0.194747
$303$	1.69199	0.0972020
$304$	−18.0244	−1.03377
$305$	−8.86504	−0.507611
$306$	−18.3316	−1.04795
$307$	−23.2532	−1.32713	−0.663566	−	0.748117i	$-0.730958\pi$
$307$	−23.2532	−1.32713	−0.663566	+	0.748117i	$0.730958\pi$
$308$	−2.04744	−0.116664
$309$	−0.685203	−0.0389798
$310$	−4.05230	−0.230155
$311$	5.59117	0.317046	0.158523	−	0.987355i	$-0.449327\pi$
$311$	5.59117	0.317046	0.158523	+	0.987355i	$0.449327\pi$
$312$	−7.93213	−0.449069
$313$	−28.2851	−1.59877	−0.799385	−	0.600819i	$-0.794841\pi$
$313$	−28.2851	−1.59877	−0.799385	+	0.600819i	$0.794841\pi$
$314$	23.2237	1.31059
$315$	−2.62013	−0.147627
$316$	−0.250915	−0.0141151
$317$	−19.4866	−1.09448	−0.547238	−	0.836977i	$-0.684321\pi$
$317$	−19.4866	−1.09448	−0.547238	+	0.836977i	$0.684321\pi$
$318$	1.41015	0.0790771
$319$	1.72821	0.0967614
$320$	10.7443	0.600627
$321$	−9.41450	−0.525466
$322$	−14.1419	−0.788098
$323$	−21.9154	−1.21941
$324$	21.3063	1.18368
$325$	3.12576	0.173386
$326$	−50.9558	−2.82218
$327$	−6.32884	−0.349986
$328$	19.9565	1.10191
$329$	−9.22768	−0.508738
$330$	0.811112	0.0446503
$331$	−30.8683	−1.69668	−0.848339	−	0.529453i	$-0.822397\pi$
$331$	−30.8683	−1.69668	−0.848339	+	0.529453i	$0.822397\pi$
$332$	−37.8428	−2.07689
$333$	2.35812	0.129224
$334$	55.2168	3.02133
$335$	−0.505435	−0.0276148
$336$	1.48272	0.0808890
$337$	−18.9961	−1.03478	−0.517391	−	0.855749i	$-0.673097\pi$
$337$	−18.9961	−1.03478	−0.517391	+	0.855749i	$0.673097\pi$
$338$	−7.72510	−0.420190
$339$	−8.80977	−0.478481
$340$	−10.8850	−0.590321
$341$	0.932105	0.0504763
$342$	46.9561	2.53910
$343$	−1.00000	−0.0539949
$344$	−31.0935	−1.67645
$345$	3.64400	0.196187
$346$	−6.33732	−0.340696
$347$	10.8780	0.583960	0.291980	−	0.956424i	$-0.405686\pi$
$347$	10.8780	0.583960	0.291980	+	0.956424i	$0.405686\pi$
$348$	−7.20450	−0.386202
$349$	−19.3947	−1.03817	−0.519086	−	0.854722i	$-0.673728\pi$
$349$	−19.3947	−1.03817	−0.519086	+	0.854722i	$0.673728\pi$
$350$	−2.39193	−0.127854
$351$	10.8273	0.577919
$352$	−1.36470	−0.0727385
$353$	23.8929	1.27169	0.635845	−	0.771817i	$-0.280652\pi$
$353$	23.8929	1.27169	0.635845	+	0.771817i	$0.280652\pi$
$354$	−15.8047	−0.840008
$355$	−7.84495	−0.416367
$356$	41.2753	2.18759
$357$	1.80280	0.0954143
$358$	−30.2484	−1.59868
$359$	−6.96980	−0.367852	−0.183926	−	0.982940i	$-0.558881\pi$
$359$	−6.96980	−0.367852	−0.183926	+	0.982940i	$0.558881\pi$
$360$	10.7879	0.568573
$361$	37.1361	1.95453
$362$	58.6354	3.08181
$363$	6.59315	0.346051
$364$	−11.6320	−0.609682
$365$	−7.74262	−0.405267
$366$	−13.0692	−0.683138
$367$	−35.2206	−1.83850	−0.919251	−	0.393673i	$-0.871204\pi$
$367$	−35.2206	−1.83850	−0.919251	+	0.393673i	$0.871204\pi$
$368$	14.2233	0.741439
$369$	−12.6996	−0.661117
$370$	2.15274	0.111916
$371$	0.956524	0.0496603
$372$	−3.88572	−0.201465
$373$	2.73361	0.141541	0.0707706	−	0.997493i	$-0.477454\pi$
$373$	2.73361	0.141541	0.0707706	+	0.997493i	$0.477454\pi$
$374$	3.84937	0.199046
$375$	0.616339	0.0318276
$376$	37.9934	1.95936
$377$	9.81839	0.505673
$378$	−8.28542	−0.426156
$379$	−10.9491	−0.562416	−0.281208	−	0.959647i	$-0.590735\pi$
$379$	−10.9491	−0.562416	−0.281208	+	0.959647i	$0.590735\pi$
$380$	27.8818	1.43031
$381$	5.18983	0.265883
$382$	27.3097	1.39728
$383$	20.4432	1.04460	0.522299	−	0.852763i	$-0.325075\pi$
$383$	20.4432	1.04460	0.522299	+	0.852763i	$0.325075\pi$
$384$	12.7822	0.652289
$385$	0.550190	0.0280403
$386$	53.9362	2.74528
$387$	19.7868	1.00582
$388$	−0.152548	−0.00774444
$389$	3.12924	0.158659	0.0793294	−	0.996848i	$-0.474722\pi$
$389$	3.12924	0.158659	0.0793294	+	0.996848i	$0.474722\pi$
$390$	4.60812	0.233341
$391$	17.2937	0.874579
$392$	4.11733	0.207956
$393$	0.460976	0.0232532
$394$	−5.36640	−0.270355
$395$	0.0674259	0.00339257
$396$	−5.36456	−0.269579
$397$	25.3923	1.27440	0.637201	−	0.770698i	$-0.280092\pi$
$397$	25.3923	1.27440	0.637201	+	0.770698i	$0.280092\pi$
$398$	29.3370	1.47053
$399$	−4.61786	−0.231182
$400$	2.40569	0.120285
$401$	−21.5201	−1.07466	−0.537331	−	0.843371i	$-0.680567\pi$
$401$	−21.5201	−1.07466	−0.537331	+	0.843371i	$0.680567\pi$
$402$	−0.745132	−0.0371638
$403$	5.29551	0.263788
$404$	−10.2159	−0.508260
$405$	−5.72544	−0.284500
$406$	−7.51336	−0.372882
$407$	−0.495172	−0.0245448
$408$	−7.42272	−0.367480
$409$	−2.02546	−0.100152	−0.0500762	−	0.998745i	$-0.515946\pi$
$409$	−2.02546	−0.100152	−0.0500762	+	0.998745i	$0.515946\pi$
$410$	−11.5936	−0.572567
$411$	13.9020	0.685736
$412$	4.13713	0.203822
$413$	−10.7205	−0.527524
$414$	−37.0536	−1.82109
$415$	10.1691	0.499183
$416$	−7.75315	−0.380129
$417$	7.95856	0.389732
$418$	−9.86013	−0.482275
$419$	−33.7393	−1.64827	−0.824137	−	0.566390i	$-0.808340\pi$
$419$	−33.7393	−1.64827	−0.824137	+	0.566390i	$0.808340\pi$
$420$	−2.29361	−0.111917
$421$	−34.9060	−1.70121	−0.850606	−	0.525803i	$-0.823765\pi$
$421$	−34.9060	−1.70121	−0.850606	+	0.525803i	$0.823765\pi$
$422$	18.0790	0.880072
$423$	−24.1777	−1.17556
$424$	−3.93832	−0.191262
$425$	2.92502	0.141884
$426$	−11.5653	−0.560343
$427$	−8.86504	−0.429009
$428$	56.8430	2.74761
$429$	−1.05995	−0.0511751
$430$	18.0635	0.871101
$431$	18.7058	0.901028	0.450514	−	0.892769i	$-0.351241\pi$
$431$	18.7058	0.901028	0.450514	+	0.892769i	$0.351241\pi$
$432$	8.33308	0.400925
$433$	3.18617	0.153117	0.0765587	−	0.997065i	$-0.475607\pi$
$433$	3.18617	0.153117	0.0765587	+	0.997065i	$0.475607\pi$
$434$	−4.05230	−0.194516
$435$	1.93600	0.0928239
$436$	38.2124	1.83004
$437$	−44.2976	−2.11904
$438$	−11.4145	−0.545405
$439$	27.2791	1.30196	0.650981	−	0.759094i	$-0.274358\pi$
$439$	27.2791	1.30196	0.650981	+	0.759094i	$0.274358\pi$
$440$	−2.26531	−0.107995
$441$	−2.62013	−0.124768
$442$	21.8692	1.04021
$443$	−34.8478	−1.65567	−0.827834	−	0.560974i	$-0.810427\pi$
$443$	−34.8478	−1.65567	−0.827834	+	0.560974i	$0.810427\pi$
$444$	2.06425	0.0979650
$445$	−11.0915	−0.525789
$446$	4.64942	0.220156
$447$	−5.68596	−0.268937
$448$	10.7443	0.507623
$449$	−17.2330	−0.813275	−0.406638	−	0.913590i	$-0.633299\pi$
$449$	−17.2330	−0.813275	−0.406638	+	0.913590i	$0.633299\pi$
$450$	−6.26717	−0.295437
$451$	2.66675	0.125572
$452$	53.1918	2.50193
$453$	−0.872059	−0.0409729
$454$	57.3689	2.69246
$455$	3.12576	0.146538
$456$	19.0132	0.890377
$457$	17.7944	0.832385	0.416192	−	0.909277i	$-0.363364\pi$
$457$	17.7944	0.832385	0.416192	+	0.909277i	$0.363364\pi$
$458$	2.39193	0.111768
$459$	10.1320	0.472920
$460$	−22.0018	−1.02584
$461$	−7.73559	−0.360282	−0.180141	−	0.983641i	$-0.557655\pi$
$461$	−7.73559	−0.360282	−0.180141	+	0.983641i	$0.557655\pi$
$462$	0.811112	0.0377364
$463$	26.9467	1.25232	0.626160	−	0.779695i	$-0.284626\pi$
$463$	26.9467	1.25232	0.626160	+	0.779695i	$0.284626\pi$
$464$	7.55657	0.350805
$465$	1.04417	0.0484223
$466$	9.35456	0.433342
$467$	27.5082	1.27293	0.636464	−	0.771307i	$-0.280396\pi$
$467$	27.5082	1.27293	0.636464	+	0.771307i	$0.280396\pi$
$468$	−30.4773	−1.40881
$469$	−0.505435	−0.0233388
$470$	−22.0720	−1.01810
$471$	−5.98414	−0.275735
$472$	44.1400	2.03171
$473$	−4.15496	−0.191045
$474$	0.0994020	0.00456569
$475$	−7.49240	−0.343775
$476$	−10.8850	−0.498912
$477$	2.50621	0.114752
$478$	44.8273	2.05035
$479$	24.6571	1.12661	0.563306	−	0.826248i	$-0.309529\pi$
$479$	24.6571	1.12661	0.563306	+	0.826248i	$0.309529\pi$
$480$	−1.52877	−0.0697786
$481$	−2.81319	−0.128270
$482$	37.0697	1.68848
$483$	3.64400	0.165808
$484$	−39.8083	−1.80947
$485$	0.0409927	0.00186138
$486$	−33.2969	−1.51038
$487$	−10.3641	−0.469644	−0.234822	−	0.972038i	$-0.575451\pi$
$487$	−10.3641	−0.469644	−0.234822	+	0.972038i	$0.575451\pi$
$488$	36.5003	1.65229
$489$	13.1300	0.593758
$490$	−2.39193	−0.108056
$491$	16.6841	0.752943	0.376471	−	0.926428i	$-0.377137\pi$
$491$	16.6841	0.752943	0.376471	+	0.926428i	$0.377137\pi$
$492$	−11.1170	−0.501194
$493$	9.18784	0.413800
$494$	−56.0177	−2.52035
$495$	1.44157	0.0647936
$496$	4.07561	0.183000
$497$	−7.84495	−0.351894
$498$	14.9918	0.671797
$499$	−20.9392	−0.937367	−0.468683	−	0.883366i	$-0.655271\pi$
$499$	−20.9392	−0.937367	−0.468683	+	0.883366i	$0.655271\pi$
$500$	−3.72134	−0.166423
$501$	−14.2279	−0.635657
$502$	9.14720	0.408259
$503$	11.2573	0.501937	0.250968	−	0.967995i	$-0.419251\pi$
$503$	11.2573	0.501937	0.250968	+	0.967995i	$0.419251\pi$
$504$	10.7879	0.480532
$505$	2.74522	0.122161
$506$	7.78074	0.345896
$507$	1.99056	0.0884038
$508$	−31.3352	−1.39028
$509$	−15.3245	−0.679245	−0.339623	−	0.940562i	$-0.610299\pi$
$509$	−15.3245	−0.679245	−0.339623	+	0.940562i	$0.610299\pi$
$510$	4.31218	0.190946
$511$	−7.74262	−0.342513
$512$	−25.7771	−1.13920
$513$	−25.9530	−1.14585
$514$	−21.8260	−0.962702
$515$	−1.11173	−0.0489887
$516$	17.3210	0.762514
$517$	5.07697	0.223285
$518$	2.15274	0.0945861
$519$	1.63296	0.0716791
$520$	−12.8698	−0.564376
$521$	13.9781	0.612394	0.306197	−	0.951968i	$-0.400943\pi$
$521$	13.9781	0.612394	0.306197	+	0.951968i	$0.400943\pi$
$522$	−19.6859	−0.861630
$523$	−43.8496	−1.91741	−0.958705	−	0.284402i	$-0.908205\pi$
$523$	−43.8496	−1.91741	−0.958705	+	0.284402i	$0.908205\pi$
$524$	−2.78329	−0.121588
$525$	0.616339	0.0268992
$526$	−22.7045	−0.989964
$527$	4.95542	0.215862
$528$	−0.815778	−0.0355022
$529$	11.9557	0.519815
$530$	2.28794	0.0993818
$531$	−28.0892	−1.21897
$532$	27.8818	1.20883
$533$	15.1504	0.656237
$534$	−16.3516	−0.707602
$535$	−15.2749	−0.660390
$536$	2.08104	0.0898873
$537$	7.79422	0.336345
$538$	8.80164	0.379465
$539$	0.550190	0.0236984
$540$	−12.8904	−0.554713
$541$	44.3227	1.90558	0.952791	−	0.303626i	$-0.0981972\pi$
$541$	44.3227	1.90558	0.952791	+	0.303626i	$0.0981972\pi$
$542$	−9.17684	−0.394179
$543$	−15.1088	−0.648381
$544$	−7.25523	−0.311066
$545$	−10.2684	−0.439852
$546$	4.60812	0.197209
$547$	30.3468	1.29754	0.648768	−	0.760986i	$-0.275285\pi$
$547$	30.3468	1.29754	0.648768	+	0.760986i	$0.275285\pi$
$548$	−83.9378	−3.58565
$549$	−23.2275	−0.991327
$550$	1.31602	0.0561151
$551$	−23.5346	−1.00261
$552$	−15.0036	−0.638594
$553$	0.0674259	0.00286724
$554$	−15.9802	−0.678934
$555$	−0.554706	−0.0235460
$556$	−48.0523	−2.03787
$557$	20.7732	0.880190	0.440095	−	0.897951i	$-0.354945\pi$
$557$	20.7732	0.880190	0.440095	+	0.897951i	$0.354945\pi$
$558$	−10.6175	−0.449476
$559$	−23.6053	−0.998396
$560$	2.40569	0.101659
$561$	−0.991883	−0.0418773
$562$	25.1570	1.06118
$563$	28.0941	1.18403	0.592013	−	0.805929i	$-0.298334\pi$
$563$	28.0941	1.18403	0.592013	+	0.805929i	$0.298334\pi$
$564$	−21.1647	−0.891193
$565$	−14.2937	−0.601341
$566$	−37.2571	−1.56603
$567$	−5.72544	−0.240446
$568$	32.3002	1.35529
$569$	−14.8752	−0.623603	−0.311801	−	0.950147i	$-0.600932\pi$
$569$	−14.8752	−0.623603	−0.311801	+	0.950147i	$0.600932\pi$
$570$	−11.0456	−0.462650
$571$	16.6643	0.697380	0.348690	−	0.937238i	$-0.386627\pi$
$571$	16.6643	0.697380	0.348690	+	0.937238i	$0.386627\pi$
$572$	6.39981	0.267589
$573$	−7.03700	−0.293975
$574$	−11.5936	−0.483907
$575$	5.91234	0.246562
$576$	28.1516	1.17298
$577$	23.0203	0.958349	0.479174	−	0.877720i	$-0.340936\pi$
$577$	23.0203	0.958349	0.479174	+	0.877720i	$0.340936\pi$
$578$	−20.1981	−0.840132
$579$	−13.8980	−0.577579
$580$	−11.6892	−0.485367
$581$	10.1691	0.421887
$582$	0.0604331	0.00250503
$583$	−0.526270	−0.0217959
$584$	31.8789	1.31916
$585$	8.18988	0.338610
$586$	24.5976	1.01612
$587$	−36.5714	−1.50946	−0.754731	−	0.656034i	$-0.772233\pi$
$587$	−36.5714	−1.50946	−0.754731	+	0.656034i	$0.772233\pi$
$588$	−2.29361	−0.0945867
$589$	−12.6933	−0.523017
$590$	−25.6428	−1.05570
$591$	1.38278	0.0568801
$592$	−2.16513	−0.0889861
$593$	20.7365	0.851547	0.425773	−	0.904830i	$-0.360002\pi$
$593$	20.7365	0.851547	0.425773	+	0.904830i	$0.360002\pi$
$594$	4.55855	0.187040
$595$	2.92502	0.119914
$596$	34.3308	1.40624
$597$	−7.55939	−0.309385
$598$	44.2042	1.80764
$599$	−28.7457	−1.17452	−0.587259	−	0.809399i	$-0.699793\pi$
$599$	−28.7457	−1.17452	−0.587259	+	0.809399i	$0.699793\pi$
$600$	−2.53767	−0.103600
$601$	16.6934	0.680938	0.340469	−	0.940256i	$-0.389414\pi$
$601$	16.6934	0.680938	0.340469	+	0.940256i	$0.389414\pi$
$602$	18.0635	0.736215
$603$	−1.32430	−0.0539298
$604$	5.26533	0.214243
$605$	10.6973	0.434907
$606$	4.04712	0.164403
$607$	−21.9168	−0.889574	−0.444787	−	0.895636i	$-0.646721\pi$
$607$	−21.9168	−0.889574	−0.444787	+	0.895636i	$0.646721\pi$
$608$	18.5842	0.753690
$609$	1.93600	0.0784505
$610$	−21.2046	−0.858548
$611$	28.8435	1.16688
$612$	−28.5200	−1.15285
$613$	−33.5060	−1.35329	−0.676647	−	0.736308i	$-0.736567\pi$
$613$	−33.5060	−1.35329	−0.676647	+	0.736308i	$0.736567\pi$
$614$	−55.6202	−2.24465
$615$	2.98737	0.120462
$616$	−2.26531	−0.0912720
$617$	16.8600	0.678760	0.339380	−	0.940649i	$-0.389783\pi$
$617$	16.8600	0.678760	0.339380	+	0.940649i	$0.389783\pi$
$618$	−1.63896	−0.0659286
$619$	−28.4173	−1.14219	−0.571094	−	0.820885i	$-0.693481\pi$
$619$	−28.4173	−1.14219	−0.571094	+	0.820885i	$0.693481\pi$
$620$	−6.30452	−0.253195
$621$	20.4798	0.821824
$622$	13.3737	0.536237
$623$	−11.0915	−0.444373
$624$	−4.63462	−0.185533
$625$	1.00000	0.0400000
$626$	−67.6561	−2.70408
$627$	2.54070	0.101466
$628$	36.1311	1.44179
$629$	−2.63252	−0.104965
$630$	−6.26717	−0.249690
$631$	21.9706	0.874636	0.437318	−	0.899307i	$-0.355928\pi$
$631$	21.9706	0.874636	0.437318	+	0.899307i	$0.355928\pi$
$632$	−0.277615	−0.0110429
$633$	−4.65849	−0.185158
$634$	−46.6106	−1.85114
$635$	8.42042	0.334154
$636$	2.19389	0.0869934
$637$	3.12576	0.123847
$638$	4.13377	0.163658
$639$	−20.5548	−0.813134
$640$	20.7389	0.819778
$641$	40.9895	1.61899	0.809493	−	0.587129i	$-0.199742\pi$
$641$	40.9895	1.61899	0.809493	+	0.587129i	$0.199742\pi$
$642$	−22.5188	−0.888748
$643$	−26.8360	−1.05831	−0.529155	−	0.848525i	$-0.677491\pi$
$643$	−26.8360	−1.05831	−0.529155	+	0.848525i	$0.677491\pi$
$644$	−22.0018	−0.866993
$645$	−4.65450	−0.183271
$646$	−52.4202	−2.06244
$647$	25.9958	1.02200	0.510999	−	0.859581i	$-0.329275\pi$
$647$	25.9958	1.02200	0.510999	+	0.859581i	$0.329275\pi$
$648$	23.5735	0.926056
$649$	5.89834	0.231530
$650$	7.47660	0.293256
$651$	1.04417	0.0409243
$652$	−79.2764	−3.10470
$653$	3.24324	0.126918	0.0634590	−	0.997984i	$-0.479787\pi$
$653$	3.24324	0.126918	0.0634590	+	0.997984i	$0.479787\pi$
$654$	−15.1382	−0.591949
$655$	0.747926	0.0292239
$656$	11.6603	0.455258
$657$	−20.2866	−0.791457
$658$	−22.0720	−0.860455
$659$	−7.65698	−0.298273	−0.149137	−	0.988817i	$-0.547649\pi$
$659$	−7.65698	−0.298273	−0.149137	+	0.988817i	$0.547649\pi$
$660$	1.26192	0.0491201
$661$	15.9221	0.619296	0.309648	−	0.950851i	$-0.399789\pi$
$661$	15.9221	0.619296	0.309648	+	0.950851i	$0.399789\pi$
$662$	−73.8350	−2.86968
$663$	−5.63512	−0.218850
$664$	−41.8697	−1.62486
$665$	−7.49240	−0.290543
$666$	5.64046	0.218563
$667$	18.5714	0.719087
$668$	85.9056	3.32379
$669$	−1.19803	−0.0463187
$670$	−1.20897	−0.0467064
$671$	4.87746	0.188292
$672$	−1.52877	−0.0589736
$673$	−32.5199	−1.25355	−0.626774	−	0.779201i	$-0.715625\pi$
$673$	−32.5199	−1.25355	−0.626774	+	0.779201i	$0.715625\pi$
$674$	−45.4373	−1.75018
$675$	3.46390	0.133326
$676$	−12.0186	−0.462255
$677$	3.77986	0.145272	0.0726359	−	0.997359i	$-0.476859\pi$
$677$	3.77986	0.145272	0.0726359	+	0.997359i	$0.476859\pi$
$678$	−21.0724	−0.809280
$679$	0.0409927	0.00157316
$680$	−12.0433	−0.461838
$681$	−14.7825	−0.566466
$682$	2.22953	0.0853732
$683$	−24.8965	−0.952639	−0.476319	−	0.879272i	$-0.658029\pi$
$683$	−24.8965	−0.952639	−0.476319	+	0.879272i	$0.658029\pi$
$684$	73.0538	2.79328
$685$	22.5558	0.861813
$686$	−2.39193	−0.0913244
$687$	−0.616339	−0.0235148
$688$	−18.1674	−0.692627
$689$	−2.98986	−0.113905
$690$	8.71621	0.331820
$691$	23.9413	0.910768	0.455384	−	0.890295i	$-0.349502\pi$
$691$	23.9413	0.910768	0.455384	+	0.890295i	$0.349502\pi$
$692$	−9.85952	−0.374803
$693$	1.44157	0.0547606
$694$	26.0194	0.987682
$695$	12.9126	0.489804
$696$	−7.97113	−0.302145
$697$	14.1774	0.537009
$698$	−46.3907	−1.75591
$699$	−2.41043	−0.0911708
$700$	−3.72134	−0.140653
$701$	−3.94347	−0.148943	−0.0744715	−	0.997223i	$-0.523727\pi$
$701$	−3.94347	−0.148943	−0.0744715	+	0.997223i	$0.523727\pi$
$702$	25.8982	0.977464
$703$	6.74318	0.254324
$704$	−5.91143	−0.222795
$705$	5.68737	0.214199
$706$	57.1501	2.15087
$707$	2.74522	0.103245
$708$	−24.5887	−0.924100
$709$	−47.3665	−1.77889	−0.889443	−	0.457046i	$-0.848907\pi$
$709$	−47.3665	−1.77889	−0.889443	+	0.457046i	$0.848907\pi$
$710$	−18.7646	−0.704223
$711$	0.176664	0.00662543
$712$	45.6675	1.71146
$713$	10.0164	0.375117
$714$	4.31218	0.161379
$715$	−1.71976	−0.0643153
$716$	−47.0601	−1.75872
$717$	−11.5508	−0.431374
$718$	−16.6713	−0.622167
$719$	−19.5578	−0.729384	−0.364692	−	0.931128i	$-0.618826\pi$
$719$	−19.5578	−0.729384	−0.364692	+	0.931128i	$0.618826\pi$
$720$	6.30321	0.234907
$721$	−1.11173	−0.0414030
$722$	88.8271	3.30580
$723$	−9.55189	−0.355239
$724$	91.2242	3.39032
$725$	3.14112	0.116658
$726$	15.7704	0.585294
$727$	−27.7183	−1.02802	−0.514008	−	0.857785i	$-0.671840\pi$
$727$	−27.7183	−1.02802	−0.514008	+	0.857785i	$0.671840\pi$
$728$	−12.8698	−0.476985
$729$	−8.59657	−0.318392
$730$	−18.5198	−0.685449
$731$	−22.0893	−0.817003
$732$	−20.3329	−0.751526
$733$	1.21768	0.0449759	0.0224879	−	0.999747i	$-0.492841\pi$
$733$	1.21768	0.0449759	0.0224879	+	0.999747i	$0.492841\pi$
$734$	−84.2453	−3.10955
$735$	0.616339	0.0227340
$736$	−14.6650	−0.540560
$737$	0.278085	0.0102434
$738$	−30.3767	−1.11818
$739$	−16.8351	−0.619289	−0.309645	−	0.950852i	$-0.600210\pi$
$739$	−16.8351	−0.619289	−0.309645	+	0.950852i	$0.600210\pi$
$740$	3.34921	0.123120
$741$	14.4343	0.530257
$742$	2.28794	0.0839929
$743$	−17.5584	−0.644157	−0.322078	−	0.946713i	$-0.604381\pi$
$743$	−17.5584	−0.644157	−0.322078	+	0.946713i	$0.604381\pi$
$744$	−4.29920	−0.157616
$745$	−9.22538	−0.337992
$746$	6.53862	0.239396
$747$	26.6444	0.974869
$748$	5.98881	0.218972
$749$	−15.2749	−0.558132
$750$	1.47424	0.0538317
$751$	−1.79226	−0.0654005	−0.0327002	−	0.999465i	$-0.510411\pi$
$751$	−1.79226	−0.0654005	−0.0327002	+	0.999465i	$0.510411\pi$
$752$	22.1989	0.809512
$753$	−2.35699	−0.0858937
$754$	23.4849	0.855270
$755$	−1.41490	−0.0514935
$756$	−12.8904	−0.468818
$757$	−10.0318	−0.364614	−0.182307	−	0.983242i	$-0.558356\pi$
$757$	−10.0318	−0.364614	−0.182307	+	0.983242i	$0.558356\pi$
$758$	−26.1894	−0.951243
$759$	−2.00489	−0.0727730
$760$	30.8487	1.11900
$761$	−22.4129	−0.812467	−0.406233	−	0.913769i	$-0.633158\pi$
$761$	−22.4129	−0.812467	−0.406233	+	0.913769i	$0.633158\pi$
$762$	12.4137	0.449702
$763$	−10.2684	−0.371743
$764$	42.4881	1.53716
$765$	7.66391	0.277089
$766$	48.8987	1.76678
$767$	33.5098	1.20997
$768$	17.3299	0.625338
$769$	−52.1271	−1.87975	−0.939876	−	0.341516i	$-0.889060\pi$
$769$	−52.1271	−1.87975	−0.939876	+	0.341516i	$0.889060\pi$
$770$	1.31602	0.0474260
$771$	5.62398	0.202543
$772$	83.9133	3.02011
$773$	−15.2613	−0.548910	−0.274455	−	0.961600i	$-0.588497\pi$
$773$	−15.2613	−0.548910	−0.274455	+	0.961600i	$0.588497\pi$
$774$	47.3287	1.70120
$775$	1.69415	0.0608557
$776$	−0.168780	−0.00605886
$777$	−0.554706	−0.0199000
$778$	7.48493	0.268348
$779$	−36.3154	−1.30113
$780$	7.16925	0.256700
$781$	4.31621	0.154446
$782$	41.3653	1.47922
$783$	10.8805	0.388839
$784$	2.40569	0.0859175
$785$	−9.70918	−0.346535
$786$	1.10262	0.0393293
$787$	−46.0429	−1.64125	−0.820626	−	0.571466i	$-0.806375\pi$
$787$	−46.0429	−1.64125	−0.820626	+	0.571466i	$0.806375\pi$
$788$	−8.34898	−0.297420
$789$	5.85036	0.208278
$790$	0.161278	0.00573802
$791$	−14.2937	−0.508226
$792$	−5.93540	−0.210905
$793$	27.7100	0.984010
$794$	60.7366	2.15546
$795$	−0.589543	−0.0209089
$796$	45.6422	1.61774
$797$	25.6399	0.908212	0.454106	−	0.890948i	$-0.349959\pi$
$797$	25.6399	0.908212	0.454106	+	0.890948i	$0.349959\pi$
$798$	−11.0456	−0.391010
$799$	26.9911	0.954877
$800$	−2.48041	−0.0876957
$801$	−29.0612	−1.02683
$802$	−51.4746	−1.81763
$803$	4.25991	0.150329
$804$	−1.15927	−0.0408842
$805$	5.91234	0.208383
$806$	12.6665	0.446158
$807$	−2.26795	−0.0798357
$808$	−11.3030	−0.397637
$809$	24.0710	0.846290	0.423145	−	0.906062i	$-0.360926\pi$
$809$	24.0710	0.846290	0.423145	+	0.906062i	$0.360926\pi$
$810$	−13.6949	−0.481189
$811$	24.2997	0.853279	0.426639	−	0.904422i	$-0.359697\pi$
$811$	24.2997	0.853279	0.426639	+	0.904422i	$0.359697\pi$
$812$	−11.6892	−0.410210
$813$	2.36463	0.0829313
$814$	−1.18442	−0.0415138
$815$	21.3032	0.746218
$816$	−4.33698	−0.151825
$817$	56.5816	1.97954
$818$	−4.84476	−0.169393
$819$	8.18988	0.286177
$820$	−18.0372	−0.629886
$821$	−34.0864	−1.18962	−0.594812	−	0.803865i	$-0.702773\pi$
$821$	−34.0864	−1.18962	−0.594812	+	0.803865i	$0.702773\pi$
$822$	33.2527	1.15982
$823$	23.5838	0.822080	0.411040	−	0.911617i	$-0.365166\pi$
$823$	23.5838	0.822080	0.411040	+	0.911617i	$0.365166\pi$
$824$	4.57736	0.159460
$825$	−0.339103	−0.0118061
$826$	−25.6428	−0.892228
$827$	−37.8637	−1.31665	−0.658324	−	0.752735i	$-0.728734\pi$
$827$	−37.8637	−1.31665	−0.658324	+	0.752735i	$0.728734\pi$
$828$	−57.6476	−2.00339
$829$	7.22183	0.250825	0.125412	−	0.992105i	$-0.459975\pi$
$829$	7.22183	0.250825	0.125412	+	0.992105i	$0.459975\pi$
$830$	24.3239	0.844295
$831$	4.11768	0.142841
$832$	−33.5842	−1.16432
$833$	2.92502	0.101346
$834$	19.0363	0.659174
$835$	−23.0846	−0.798875
$836$	−15.3403	−0.530554
$837$	5.86838	0.202841
$838$	−80.7022	−2.78781
$839$	1.18128	0.0407822	0.0203911	−	0.999792i	$-0.493509\pi$
$839$	1.18128	0.0407822	0.0203911	+	0.999792i	$0.493509\pi$
$840$	−2.53767	−0.0875579
$841$	−19.1333	−0.659770
$842$	−83.4927	−2.87735
$843$	−6.48230	−0.223262
$844$	28.1271	0.968174
$845$	3.22965	0.111103
$846$	−57.8314	−1.98828
$847$	10.6973	0.367563
$848$	−2.30110	−0.0790201
$849$	9.60019	0.329478
$850$	6.99644	0.239976
$851$	−5.32112	−0.182406
$852$	−17.9932	−0.616438
$853$	23.9614	0.820424	0.410212	−	0.911990i	$-0.365455\pi$
$853$	23.9614	0.820424	0.410212	+	0.911990i	$0.365455\pi$
$854$	−21.2046	−0.725606
$855$	−19.6310	−0.671368
$856$	62.8917	2.14959
$857$	44.5191	1.52074	0.760372	−	0.649488i	$-0.225017\pi$
$857$	44.5191	1.52074	0.760372	+	0.649488i	$0.225017\pi$
$858$	−2.53534	−0.0865550
$859$	21.3146	0.727244	0.363622	−	0.931547i	$-0.381540\pi$
$859$	21.3146	0.727244	0.363622	+	0.931547i	$0.381540\pi$
$860$	28.1030	0.958305
$861$	2.98737	0.101809
$862$	44.7431	1.52395
$863$	49.0682	1.67030	0.835150	−	0.550023i	$-0.185381\pi$
$863$	49.0682	1.67030	0.835150	+	0.550023i	$0.185381\pi$
$864$	−8.59189	−0.292302
$865$	2.64945	0.0900842
$866$	7.62110	0.258975
$867$	5.20454	0.176755
$868$	−6.30452	−0.213989
$869$	−0.0370971	−0.00125843
$870$	4.63077	0.156998
$871$	1.57987	0.0535317
$872$	42.2785	1.43173
$873$	0.107406	0.00363514
$874$	−105.957	−3.58405
$875$	1.00000	0.0338062
$876$	−17.7585	−0.600005
$877$	36.6965	1.23915	0.619577	−	0.784936i	$-0.287304\pi$
$877$	36.6965	1.23915	0.619577	+	0.784936i	$0.287304\pi$
$878$	65.2498	2.20208
$879$	−6.33817	−0.213781
$880$	−1.32359	−0.0446181
$881$	20.1719	0.679609	0.339804	−	0.940496i	$-0.389639\pi$
$881$	20.1719	0.679609	0.339804	+	0.940496i	$0.389639\pi$
$882$	−6.26717	−0.211026
$883$	36.3932	1.22473	0.612364	−	0.790576i	$-0.290219\pi$
$883$	36.3932	1.22473	0.612364	+	0.790576i	$0.290219\pi$
$884$	34.0238	1.14434
$885$	6.60749	0.222108
$886$	−83.3535	−2.80032
$887$	13.4073	0.450173	0.225087	−	0.974339i	$-0.427734\pi$
$887$	13.4073	0.450173	0.225087	+	0.974339i	$0.427734\pi$
$888$	2.28391	0.0766429
$889$	8.42042	0.282412
$890$	−26.5302	−0.889294
$891$	3.15008	0.105532
$892$	7.23351	0.242196
$893$	−69.1375	−2.31360
$894$	−13.6004	−0.454867
$895$	12.6460	0.422709
$896$	20.7389	0.692839
$897$	−11.3903	−0.380310
$898$	−41.2201	−1.37553
$899$	5.32154	0.177483
$900$	−9.75038	−0.325013
$901$	−2.79785	−0.0932098
$902$	6.37868	0.212387
$903$	−4.65450	−0.154892
$904$	58.8519	1.95739
$905$	−24.5138	−0.814867
$906$	−2.08591	−0.0692996
$907$	3.03808	0.100878	0.0504389	−	0.998727i	$-0.483938\pi$
$907$	3.03808	0.100878	0.0504389	+	0.998727i	$0.483938\pi$
$908$	89.2539	2.96199
$909$	7.19283	0.238571
$910$	7.47660	0.247847
$911$	−38.0329	−1.26008	−0.630042	−	0.776561i	$-0.716963\pi$
$911$	−38.0329	−1.26008	−0.630042	+	0.776561i	$0.716963\pi$
$912$	11.1091	0.367860
$913$	−5.59496	−0.185166
$914$	42.5629	1.40786
$915$	5.46387	0.180630
$916$	3.72134	0.122957
$917$	0.747926	0.0246987
$918$	24.2350	0.799874
$919$	6.74653	0.222547	0.111274	−	0.993790i	$-0.464507\pi$
$919$	6.74653	0.222547	0.111274	+	0.993790i	$0.464507\pi$
$920$	−24.3430	−0.802566
$921$	14.3319	0.472251
$922$	−18.5030	−0.609364
$923$	24.5214	0.807132
$924$	1.26192	0.0415141
$925$	−0.900002	−0.0295919
$926$	64.4547	2.11811
$927$	−2.91288	−0.0956714
$928$	−7.79127	−0.255761
$929$	−13.6534	−0.447952	−0.223976	−	0.974595i	$-0.571904\pi$
$929$	−13.6534	−0.447952	−0.223976	+	0.974595i	$0.571904\pi$
$930$	2.49759	0.0818991
$931$	−7.49240	−0.245554
$932$	14.5537	0.476723
$933$	−3.44606	−0.112819
$934$	65.7977	2.15297
$935$	−1.60931	−0.0526302
$936$	−33.7204	−1.10219
$937$	15.0556	0.491844	0.245922	−	0.969290i	$-0.420909\pi$
$937$	15.0556	0.491844	0.245922	+	0.969290i	$0.420909\pi$
$938$	−1.20897	−0.0394741
$939$	17.4332	0.568912
$940$	−34.3393	−1.12003
$941$	−15.7266	−0.512673	−0.256336	−	0.966588i	$-0.582515\pi$
$941$	−15.7266	−0.512673	−0.256336	+	0.966588i	$0.582515\pi$
$942$	−14.3137	−0.466364
$943$	28.6569	0.933196
$944$	25.7903	0.839403
$945$	3.46390	0.112681
$946$	−9.93837	−0.323124
$947$	−2.48662	−0.0808043	−0.0404021	−	0.999184i	$-0.512864\pi$
$947$	−2.48662	−0.0808043	−0.0404021	+	0.999184i	$0.512864\pi$
$948$	0.154648	0.00502275
$949$	24.2015	0.785615
$950$	−17.9213	−0.581444
$951$	12.0103	0.389462
$952$	−12.0433	−0.390324
$953$	−5.51985	−0.178806	−0.0894028	−	0.995996i	$-0.528496\pi$
$953$	−5.51985	−0.178806	−0.0894028	+	0.995996i	$0.528496\pi$
$954$	5.99469	0.194085
$955$	−11.4174	−0.369459
$956$	69.7418	2.25561
$957$	−1.06517	−0.0344319
$958$	58.9782	1.90550
$959$	22.5558	0.728365
$960$	−6.62216	−0.213729
$961$	−28.1298	−0.907414
$962$	−6.72895	−0.216950
$963$	−40.0221	−1.28969
$964$	57.6725	1.85751
$965$	−22.5492	−0.725885
$966$	8.71621	0.280439
$967$	40.2357	1.29389	0.646946	−	0.762535i	$-0.276046\pi$
$967$	40.2357	1.29389	0.646946	+	0.762535i	$0.276046\pi$
$968$	−44.0443	−1.41564
$969$	13.5073	0.433917
$970$	0.0980518	0.00314825
$971$	−19.9989	−0.641796	−0.320898	−	0.947114i	$-0.603985\pi$
$971$	−19.9989	−0.641796	−0.320898	+	0.947114i	$0.603985\pi$
$972$	−51.8030	−1.66158
$973$	12.9126	0.413960
$974$	−24.7903	−0.794333
$975$	−1.92652	−0.0616982
$976$	21.3265	0.682646
$977$	−38.7449	−1.23956	−0.619780	−	0.784776i	$-0.712778\pi$
$977$	−38.7449	−1.23956	−0.619780	+	0.784776i	$0.712778\pi$
$978$	31.4060	1.00425
$979$	6.10245	0.195035
$980$	−3.72134	−0.118874
$981$	−26.9046	−0.858998
$982$	39.9072	1.27349
$983$	−24.9431	−0.795562	−0.397781	−	0.917480i	$-0.630220\pi$
$983$	−24.9431	−0.795562	−0.397781	+	0.917480i	$0.630220\pi$
$984$	−12.3000	−0.392109
$985$	2.24354	0.0714852
$986$	21.9767	0.699880
$987$	5.68737	0.181031
$988$	−87.1516	−2.77266
$989$	−44.6491	−1.41976
$990$	3.44813	0.109589
$991$	40.9624	1.30121	0.650607	−	0.759414i	$-0.274514\pi$
$991$	40.9624	1.30121	0.650607	+	0.759414i	$0.274514\pi$
$992$	−4.20219	−0.133420
$993$	19.0254	0.603752
$994$	−18.7646	−0.595177
$995$	−12.2650	−0.388826
$996$	23.3240	0.739049
$997$	40.7070	1.28920	0.644602	−	0.764518i	$-0.277023\pi$
$997$	40.7070	1.28920	0.644602	+	0.764518i	$0.277023\pi$
$998$	−50.0851	−1.58542
$999$	−3.11752	−0.0986339

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.56	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.56	✓	62	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q+2.39193 q^{2} -0.616339 q^{3} +3.72134 q^{4} -1.00000 q^{5} -1.47424 q^{6} -1.00000 q^{7} +4.11733 q^{8} -2.62013 q^{9} +O(q^{10})\)	\(q+2.39193 q^{2} -0.616339 q^{3} +3.72134 q^{4} -1.00000 q^{5} -1.47424 q^{6} -1.00000 q^{7} +4.11733 q^{8} -2.62013 q^{9} -2.39193 q^{10} +0.550190 q^{11} -2.29361 q^{12} +3.12576 q^{13} -2.39193 q^{14} +0.616339 q^{15} +2.40569 q^{16} +2.92502 q^{17} -6.26717 q^{18} -7.49240 q^{19} -3.72134 q^{20} +0.616339 q^{21} +1.31602 q^{22} +5.91234 q^{23} -2.53767 q^{24} +1.00000 q^{25} +7.47660 q^{26} +3.46390 q^{27} -3.72134 q^{28} +3.14112 q^{29} +1.47424 q^{30} +1.69415 q^{31} -2.48041 q^{32} -0.339103 q^{33} +6.99644 q^{34} +1.00000 q^{35} -9.75038 q^{36} -0.900002 q^{37} -17.9213 q^{38} -1.92652 q^{39} -4.11733 q^{40} +4.84696 q^{41} +1.47424 q^{42} -7.55186 q^{43} +2.04744 q^{44} +2.62013 q^{45} +14.1419 q^{46} +9.22768 q^{47} -1.48272 q^{48} +1.00000 q^{49} +2.39193 q^{50} -1.80280 q^{51} +11.6320 q^{52} -0.956524 q^{53} +8.28542 q^{54} -0.550190 q^{55} -4.11733 q^{56} +4.61786 q^{57} +7.51336 q^{58} +10.7205 q^{59} +2.29361 q^{60} +8.86504 q^{61} +4.05230 q^{62} +2.62013 q^{63} -10.7443 q^{64} -3.12576 q^{65} -0.811112 q^{66} +0.505435 q^{67} +10.8850 q^{68} -3.64400 q^{69} +2.39193 q^{70} +7.84495 q^{71} -10.7879 q^{72} +7.74262 q^{73} -2.15274 q^{74} -0.616339 q^{75} -27.8818 q^{76} -0.550190 q^{77} -4.60812 q^{78} -0.0674259 q^{79} -2.40569 q^{80} +5.72544 q^{81} +11.5936 q^{82} -10.1691 q^{83} +2.29361 q^{84} -2.92502 q^{85} -18.0635 q^{86} -1.93600 q^{87} +2.26531 q^{88} +11.0915 q^{89} +6.26717 q^{90} -3.12576 q^{91} +22.0018 q^{92} -1.04417 q^{93} +22.0720 q^{94} +7.49240 q^{95} +1.52877 q^{96} -0.0409927 q^{97} +2.39193 q^{98} -1.44157 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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