LMFDB - Embedded newform 6018.2.a.y.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0539719364$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 33x^{8} + 53x^{7} + 356x^{6} - 433x^{5} - 1296x^{4} + 1135x^{3} + 930x^{2} - 186x - 104 $ x^10 - 2x^9 - 33x^8 + 53x^7 + 356x^6 - 433x^5 - 1296x^4 + 1135x^3 + 930x^2 - 186*x - 104
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.390474$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.390474 q^{5} -1.00000 q^{6} -3.35881 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.390474 q^{5} -1.00000 q^{6} -3.35881 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.390474 q^{10} +2.35637 q^{11} +1.00000 q^{12} +0.685048 q^{13} +3.35881 q^{14} -0.390474 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -3.67853 q^{19} -0.390474 q^{20} -3.35881 q^{21} -2.35637 q^{22} +0.781785 q^{23} -1.00000 q^{24} -4.84753 q^{25} -0.685048 q^{26} +1.00000 q^{27} -3.35881 q^{28} +8.31225 q^{29} +0.390474 q^{30} +1.31598 q^{31} -1.00000 q^{32} +2.35637 q^{33} +1.00000 q^{34} +1.31153 q^{35} +1.00000 q^{36} +5.37239 q^{37} +3.67853 q^{38} +0.685048 q^{39} +0.390474 q^{40} +8.37739 q^{41} +3.35881 q^{42} -10.3167 q^{43} +2.35637 q^{44} -0.390474 q^{45} -0.781785 q^{46} -6.66378 q^{47} +1.00000 q^{48} +4.28163 q^{49} +4.84753 q^{50} -1.00000 q^{51} +0.685048 q^{52} -10.6247 q^{53} -1.00000 q^{54} -0.920103 q^{55} +3.35881 q^{56} -3.67853 q^{57} -8.31225 q^{58} +1.00000 q^{59} -0.390474 q^{60} +9.75950 q^{61} -1.31598 q^{62} -3.35881 q^{63} +1.00000 q^{64} -0.267494 q^{65} -2.35637 q^{66} +2.59031 q^{67} -1.00000 q^{68} +0.781785 q^{69} -1.31153 q^{70} -8.47670 q^{71} -1.00000 q^{72} -1.74201 q^{73} -5.37239 q^{74} -4.84753 q^{75} -3.67853 q^{76} -7.91462 q^{77} -0.685048 q^{78} +6.53184 q^{79} -0.390474 q^{80} +1.00000 q^{81} -8.37739 q^{82} -12.4462 q^{83} -3.35881 q^{84} +0.390474 q^{85} +10.3167 q^{86} +8.31225 q^{87} -2.35637 q^{88} +13.8950 q^{89} +0.390474 q^{90} -2.30095 q^{91} +0.781785 q^{92} +1.31598 q^{93} +6.66378 q^{94} +1.43637 q^{95} -1.00000 q^{96} -7.04743 q^{97} -4.28163 q^{98} +2.35637 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9} + 2 q^{10} - 3 q^{11} + 10 q^{12} - 10 q^{13} + 6 q^{14} - 2 q^{15} + 10 q^{16} - 10 q^{17} - 10 q^{18} + 8 q^{19} - 2 q^{20} - 6 q^{21} + 3 q^{22} - 9 q^{23} - 10 q^{24} + 20 q^{25} + 10 q^{26} + 10 q^{27} - 6 q^{28} - 24 q^{29} + 2 q^{30} - 7 q^{31} - 10 q^{32} - 3 q^{33} + 10 q^{34} - 22 q^{35} + 10 q^{36} - 4 q^{37} - 8 q^{38} - 10 q^{39} + 2 q^{40} - 9 q^{41} + 6 q^{42} - 11 q^{43} - 3 q^{44} - 2 q^{45} + 9 q^{46} - 18 q^{47} + 10 q^{48} + 6 q^{49} - 20 q^{50} - 10 q^{51} - 10 q^{52} - 9 q^{53} - 10 q^{54} + q^{55} + 6 q^{56} + 8 q^{57} + 24 q^{58} + 10 q^{59} - 2 q^{60} - 25 q^{61} + 7 q^{62} - 6 q^{63} + 10 q^{64} - 28 q^{65} + 3 q^{66} + 2 q^{67} - 10 q^{68} - 9 q^{69} + 22 q^{70} - 30 q^{71} - 10 q^{72} - 11 q^{73} + 4 q^{74} + 20 q^{75} + 8 q^{76} + 4 q^{77} + 10 q^{78} + 3 q^{79} - 2 q^{80} + 10 q^{81} + 9 q^{82} - q^{83} - 6 q^{84} + 2 q^{85} + 11 q^{86} - 24 q^{87} + 3 q^{88} - 14 q^{89} + 2 q^{90} - 13 q^{91} - 9 q^{92} - 7 q^{93} + 18 q^{94} - 35 q^{95} - 10 q^{96} - 10 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9 + 2 * q^10 - 3 * q^11 + 10 * q^12 - 10 * q^13 + 6 * q^14 - 2 * q^15 + 10 * q^16 - 10 * q^17 - 10 * q^18 + 8 * q^19 - 2 * q^20 - 6 * q^21 + 3 * q^22 - 9 * q^23 - 10 * q^24 + 20 * q^25 + 10 * q^26 + 10 * q^27 - 6 * q^28 - 24 * q^29 + 2 * q^30 - 7 * q^31 - 10 * q^32 - 3 * q^33 + 10 * q^34 - 22 * q^35 + 10 * q^36 - 4 * q^37 - 8 * q^38 - 10 * q^39 + 2 * q^40 - 9 * q^41 + 6 * q^42 - 11 * q^43 - 3 * q^44 - 2 * q^45 + 9 * q^46 - 18 * q^47 + 10 * q^48 + 6 * q^49 - 20 * q^50 - 10 * q^51 - 10 * q^52 - 9 * q^53 - 10 * q^54 + q^55 + 6 * q^56 + 8 * q^57 + 24 * q^58 + 10 * q^59 - 2 * q^60 - 25 * q^61 + 7 * q^62 - 6 * q^63 + 10 * q^64 - 28 * q^65 + 3 * q^66 + 2 * q^67 - 10 * q^68 - 9 * q^69 + 22 * q^70 - 30 * q^71 - 10 * q^72 - 11 * q^73 + 4 * q^74 + 20 * q^75 + 8 * q^76 + 4 * q^77 + 10 * q^78 + 3 * q^79 - 2 * q^80 + 10 * q^81 + 9 * q^82 - q^83 - 6 * q^84 + 2 * q^85 + 11 * q^86 - 24 * q^87 + 3 * q^88 - 14 * q^89 + 2 * q^90 - 13 * q^91 - 9 * q^92 - 7 * q^93 + 18 * q^94 - 35 * q^95 - 10 * q^96 - 10 * q^97 - 6 * q^98 - 3 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−0.390474	−0.174625	−0.0873126	−	0.996181i	$-0.527828\pi$
$5$	−0.390474	−0.174625	−0.0873126	+	0.996181i	$0.527828\pi$
$6$	−1.00000	−0.408248
$7$	−3.35881	−1.26951	−0.634756	−	0.772713i	$-0.718899\pi$
$7$	−3.35881	−1.26951	−0.634756	+	0.772713i	$0.718899\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.390474	0.123479
$11$	2.35637	0.710474	0.355237	−	0.934776i	$-0.384400\pi$
$11$	2.35637	0.710474	0.355237	+	0.934776i	$0.384400\pi$
$12$	1.00000	0.288675
$13$	0.685048	0.189998	0.0949991	−	0.995477i	$-0.469715\pi$
$13$	0.685048	0.189998	0.0949991	+	0.995477i	$0.469715\pi$
$14$	3.35881	0.897681
$15$	−0.390474	−0.100820
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	−3.67853	−0.843912	−0.421956	−	0.906616i	$-0.638656\pi$
$19$	−3.67853	−0.843912	−0.421956	+	0.906616i	$0.638656\pi$
$20$	−0.390474	−0.0873126
$21$	−3.35881	−0.732953
$22$	−2.35637	−0.502381
$23$	0.781785	0.163013	0.0815067	−	0.996673i	$-0.474027\pi$
$23$	0.781785	0.163013	0.0815067	+	0.996673i	$0.474027\pi$
$24$	−1.00000	−0.204124
$25$	−4.84753	−0.969506
$26$	−0.685048	−0.134349
$27$	1.00000	0.192450
$28$	−3.35881	−0.634756
$29$	8.31225	1.54355	0.771773	−	0.635898i	$-0.219370\pi$
$29$	8.31225	1.54355	0.771773	+	0.635898i	$0.219370\pi$
$30$	0.390474	0.0712905
$31$	1.31598	0.236357	0.118178	−	0.992992i	$-0.462295\pi$
$31$	1.31598	0.236357	0.118178	+	0.992992i	$0.462295\pi$
$32$	−1.00000	−0.176777
$33$	2.35637	0.410192
$34$	1.00000	0.171499
$35$	1.31153	0.221689
$36$	1.00000	0.166667
$37$	5.37239	0.883215	0.441608	−	0.897208i	$-0.354408\pi$
$37$	5.37239	0.883215	0.441608	+	0.897208i	$0.354408\pi$
$38$	3.67853	0.596736
$39$	0.685048	0.109696
$40$	0.390474	0.0617394
$41$	8.37739	1.30833	0.654164	−	0.756352i	$-0.273020\pi$
$41$	8.37739	1.30833	0.654164	+	0.756352i	$0.273020\pi$
$42$	3.35881	0.518276
$43$	−10.3167	−1.57328	−0.786641	−	0.617410i	$-0.788182\pi$
$43$	−10.3167	−1.57328	−0.786641	+	0.617410i	$0.788182\pi$
$44$	2.35637	0.355237
$45$	−0.390474	−0.0582084
$46$	−0.781785	−0.115268
$47$	−6.66378	−0.972013	−0.486006	−	0.873955i	$-0.661547\pi$
$47$	−6.66378	−0.972013	−0.486006	+	0.873955i	$0.661547\pi$
$48$	1.00000	0.144338
$49$	4.28163	0.611661
$50$	4.84753	0.685544
$51$	−1.00000	−0.140028
$52$	0.685048	0.0949991
$53$	−10.6247	−1.45942	−0.729709	−	0.683758i	$-0.760344\pi$
$53$	−10.6247	−1.45942	−0.729709	+	0.683758i	$0.760344\pi$
$54$	−1.00000	−0.136083
$55$	−0.920103	−0.124067
$56$	3.35881	0.448840
$57$	−3.67853	−0.487233
$58$	−8.31225	−1.09145
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−0.390474	−0.0504100
$61$	9.75950	1.24958	0.624788	−	0.780794i	$-0.285185\pi$
$61$	9.75950	1.24958	0.624788	+	0.780794i	$0.285185\pi$
$62$	−1.31598	−0.167130
$63$	−3.35881	−0.423171
$64$	1.00000	0.125000
$65$	−0.267494	−0.0331785
$66$	−2.35637	−0.290050
$67$	2.59031	0.316457	0.158228	−	0.987403i	$-0.449422\pi$
$67$	2.59031	0.316457	0.158228	+	0.987403i	$0.449422\pi$
$68$	−1.00000	−0.121268
$69$	0.781785	0.0941158
$70$	−1.31153	−0.156758
$71$	−8.47670	−1.00600	−0.503000	−	0.864287i	$-0.667770\pi$
$71$	−8.47670	−1.00600	−0.503000	+	0.864287i	$0.667770\pi$
$72$	−1.00000	−0.117851
$73$	−1.74201	−0.203887	−0.101943	−	0.994790i	$-0.532506\pi$
$73$	−1.74201	−0.203887	−0.101943	+	0.994790i	$0.532506\pi$
$74$	−5.37239	−0.624528
$75$	−4.84753	−0.559745
$76$	−3.67853	−0.421956
$77$	−7.91462	−0.901955
$78$	−0.685048	−0.0775665
$79$	6.53184	0.734889	0.367445	−	0.930045i	$-0.380233\pi$
$79$	6.53184	0.734889	0.367445	+	0.930045i	$0.380233\pi$
$80$	−0.390474	−0.0436563
$81$	1.00000	0.111111
$82$	−8.37739	−0.925128
$83$	−12.4462	−1.36614	−0.683072	−	0.730351i	$-0.739356\pi$
$83$	−12.4462	−1.36614	−0.683072	+	0.730351i	$0.739356\pi$
$84$	−3.35881	−0.366477
$85$	0.390474	0.0423528
$86$	10.3167	1.11248
$87$	8.31225	0.891167
$88$	−2.35637	−0.251190
$89$	13.8950	1.47286	0.736431	−	0.676512i	$-0.236510\pi$
$89$	13.8950	1.47286	0.736431	+	0.676512i	$0.236510\pi$
$90$	0.390474	0.0411596
$91$	−2.30095	−0.241205
$92$	0.781785	0.0815067
$93$	1.31598	0.136461
$94$	6.66378	0.687317
$95$	1.43637	0.147368
$96$	−1.00000	−0.102062
$97$	−7.04743	−0.715558	−0.357779	−	0.933806i	$-0.616466\pi$
$97$	−7.04743	−0.715558	−0.357779	+	0.933806i	$0.616466\pi$
$98$	−4.28163	−0.432510
$99$	2.35637	0.236825
$100$	−4.84753	−0.484753
$101$	−13.7367	−1.36685	−0.683425	−	0.730021i	$-0.739510\pi$
$101$	−13.7367	−1.36685	−0.683425	+	0.730021i	$0.739510\pi$
$102$	1.00000	0.0990148
$103$	0.551910	0.0543813	0.0271907	−	0.999630i	$-0.491344\pi$
$103$	0.551910	0.0543813	0.0271907	+	0.999630i	$0.491344\pi$
$104$	−0.685048	−0.0671745
$105$	1.31153	0.127992
$106$	10.6247	1.03196
$107$	−18.8801	−1.82521	−0.912604	−	0.408844i	$-0.865932\pi$
$107$	−18.8801	−1.82521	−0.912604	+	0.408844i	$0.865932\pi$
$108$	1.00000	0.0962250
$109$	7.11141	0.681149	0.340575	−	0.940218i	$-0.389378\pi$
$109$	7.11141	0.681149	0.340575	+	0.940218i	$0.389378\pi$
$110$	0.920103	0.0877284
$111$	5.37239	0.509925
$112$	−3.35881	−0.317378
$113$	1.30893	0.123134	0.0615671	−	0.998103i	$-0.480390\pi$
$113$	1.30893	0.123134	0.0615671	+	0.998103i	$0.480390\pi$
$114$	3.67853	0.344526
$115$	−0.305267	−0.0284663
$116$	8.31225	0.771773
$117$	0.685048	0.0633328
$118$	−1.00000	−0.0920575
$119$	3.35881	0.307902
$120$	0.390474	0.0356452
$121$	−5.44750	−0.495227
$122$	−9.75950	−0.883584
$123$	8.37739	0.755364
$124$	1.31598	0.118178
$125$	3.84520	0.343926
$126$	3.35881	0.299227
$127$	−11.3776	−1.00960	−0.504798	−	0.863238i	$-0.668433\pi$
$127$	−11.3776	−1.00960	−0.504798	+	0.863238i	$0.668433\pi$
$128$	−1.00000	−0.0883883
$129$	−10.3167	−0.908335
$130$	0.267494	0.0234607
$131$	0.282242	0.0246596	0.0123298	−	0.999924i	$-0.496075\pi$
$131$	0.282242	0.0246596	0.0123298	+	0.999924i	$0.496075\pi$
$132$	2.35637	0.205096
$133$	12.3555	1.07136
$134$	−2.59031	−0.223769
$135$	−0.390474	−0.0336066
$136$	1.00000	0.0857493
$137$	0.0466358	0.00398436	0.00199218	−	0.999998i	$-0.499366\pi$
$137$	0.0466358	0.00398436	0.00199218	+	0.999998i	$0.499366\pi$
$138$	−0.781785	−0.0665499
$139$	20.9833	1.77978	0.889892	−	0.456172i	$-0.150780\pi$
$139$	20.9833	1.77978	0.889892	+	0.456172i	$0.150780\pi$
$140$	1.31153	0.110844
$141$	−6.66378	−0.561192
$142$	8.47670	0.711349
$143$	1.61423	0.134989
$144$	1.00000	0.0833333
$145$	−3.24572	−0.269542
$146$	1.74201	0.144170
$147$	4.28163	0.353143
$148$	5.37239	0.441608
$149$	−12.3080	−1.00831	−0.504154	−	0.863614i	$-0.668196\pi$
$149$	−12.3080	−1.00831	−0.504154	+	0.863614i	$0.668196\pi$
$150$	4.84753	0.395799
$151$	2.58417	0.210297	0.105149	−	0.994457i	$-0.466468\pi$
$151$	2.58417	0.210297	0.105149	+	0.994457i	$0.466468\pi$
$152$	3.67853	0.298368
$153$	−1.00000	−0.0808452
$154$	7.91462	0.637779
$155$	−0.513856	−0.0412739
$156$	0.685048	0.0548478
$157$	10.8658	0.867188	0.433594	−	0.901108i	$-0.357245\pi$
$157$	10.8658	0.867188	0.433594	+	0.901108i	$0.357245\pi$
$158$	−6.53184	−0.519645
$159$	−10.6247	−0.842595
$160$	0.390474	0.0308697
$161$	−2.62587	−0.206948
$162$	−1.00000	−0.0785674
$163$	12.2002	0.955592	0.477796	−	0.878471i	$-0.341436\pi$
$163$	12.2002	0.955592	0.477796	+	0.878471i	$0.341436\pi$
$164$	8.37739	0.654164
$165$	−0.920103	−0.0716299
$166$	12.4462	0.966009
$167$	−20.5000	−1.58634	−0.793169	−	0.609002i	$-0.791570\pi$
$167$	−20.5000	−1.58634	−0.793169	+	0.609002i	$0.791570\pi$
$168$	3.35881	0.259138
$169$	−12.5307	−0.963901
$170$	−0.390474	−0.0299480
$171$	−3.67853	−0.281304
$172$	−10.3167	−0.786641
$173$	−3.83372	−0.291472	−0.145736	−	0.989324i	$-0.546555\pi$
$173$	−3.83372	−0.291472	−0.145736	+	0.989324i	$0.546555\pi$
$174$	−8.31225	−0.630150
$175$	16.2820	1.23080
$176$	2.35637	0.177618
$177$	1.00000	0.0751646
$178$	−13.8950	−1.04147
$179$	3.07926	0.230155	0.115078	−	0.993357i	$-0.463288\pi$
$179$	3.07926	0.230155	0.115078	+	0.993357i	$0.463288\pi$
$180$	−0.390474	−0.0291042
$181$	−2.08453	−0.154942	−0.0774711	−	0.996995i	$-0.524685\pi$
$181$	−2.08453	−0.154942	−0.0774711	+	0.996995i	$0.524685\pi$
$182$	2.30095	0.170558
$183$	9.75950	0.721443
$184$	−0.781785	−0.0576339
$185$	−2.09778	−0.154232
$186$	−1.31598	−0.0964923
$187$	−2.35637	−0.172315
$188$	−6.66378	−0.486006
$189$	−3.35881	−0.244318
$190$	−1.43637	−0.104205
$191$	−22.5823	−1.63400	−0.817000	−	0.576638i	$-0.804364\pi$
$191$	−22.5823	−1.63400	−0.817000	+	0.576638i	$0.804364\pi$
$192$	1.00000	0.0721688
$193$	−5.64059	−0.406018	−0.203009	−	0.979177i	$-0.565072\pi$
$193$	−5.64059	−0.406018	−0.203009	+	0.979177i	$0.565072\pi$
$194$	7.04743	0.505976
$195$	−0.267494	−0.0191556
$196$	4.28163	0.305831
$197$	−2.53408	−0.180546	−0.0902729	−	0.995917i	$-0.528774\pi$
$197$	−2.53408	−0.180546	−0.0902729	+	0.995917i	$0.528774\pi$
$198$	−2.35637	−0.167460
$199$	−11.1277	−0.788823	−0.394412	−	0.918934i	$-0.629052\pi$
$199$	−11.1277	−0.788823	−0.394412	+	0.918934i	$0.629052\pi$
$200$	4.84753	0.342772
$201$	2.59031	0.182706
$202$	13.7367	0.966509
$203$	−27.9193	−1.95955
$204$	−1.00000	−0.0700140
$205$	−3.27115	−0.228467
$206$	−0.551910	−0.0384534
$207$	0.781785	0.0543378
$208$	0.685048	0.0474996
$209$	−8.66799	−0.599577
$210$	−1.31153	−0.0905041
$211$	9.83568	0.677116	0.338558	−	0.940946i	$-0.390061\pi$
$211$	9.83568	0.677116	0.338558	+	0.940946i	$0.390061\pi$
$212$	−10.6247	−0.729709
$213$	−8.47670	−0.580814
$214$	18.8801	1.29062
$215$	4.02840	0.274735
$216$	−1.00000	−0.0680414
$217$	−4.42013	−0.300058
$218$	−7.11141	−0.481645
$219$	−1.74201	−0.117714
$220$	−0.920103	−0.0620333
$221$	−0.685048	−0.0460813
$222$	−5.37239	−0.360571
$223$	−21.9208	−1.46792	−0.733962	−	0.679190i	$-0.762331\pi$
$223$	−21.9208	−1.46792	−0.733962	+	0.679190i	$0.762331\pi$
$224$	3.35881	0.224420
$225$	−4.84753	−0.323169
$226$	−1.30893	−0.0870690
$227$	−1.81610	−0.120539	−0.0602694	−	0.998182i	$-0.519196\pi$
$227$	−1.81610	−0.120539	−0.0602694	+	0.998182i	$0.519196\pi$
$228$	−3.67853	−0.243616
$229$	−29.2910	−1.93561	−0.967803	−	0.251707i	$-0.919008\pi$
$229$	−29.2910	−1.93561	−0.967803	+	0.251707i	$0.919008\pi$
$230$	0.305267	0.0201287
$231$	−7.91462	−0.520744
$232$	−8.31225	−0.545726
$233$	−10.8801	−0.712781	−0.356391	−	0.934337i	$-0.615993\pi$
$233$	−10.8801	−0.712781	−0.356391	+	0.934337i	$0.615993\pi$
$234$	−0.685048	−0.0447830
$235$	2.60203	0.169738
$236$	1.00000	0.0650945
$237$	6.53184	0.424288
$238$	−3.35881	−0.217720
$239$	20.2309	1.30863	0.654315	−	0.756222i	$-0.272957\pi$
$239$	20.2309	1.30863	0.654315	+	0.756222i	$0.272957\pi$
$240$	−0.390474	−0.0252050
$241$	−20.1846	−1.30020	−0.650102	−	0.759847i	$-0.725274\pi$
$241$	−20.1846	−1.30020	−0.650102	+	0.759847i	$0.725274\pi$
$242$	5.44750	0.350178
$243$	1.00000	0.0641500
$244$	9.75950	0.624788
$245$	−1.67187	−0.106812
$246$	−8.37739	−0.534123
$247$	−2.51997	−0.160342
$248$	−1.31598	−0.0835648
$249$	−12.4462	−0.788743
$250$	−3.84520	−0.243192
$251$	−11.6280	−0.733952	−0.366976	−	0.930230i	$-0.619607\pi$
$251$	−11.6280	−0.733952	−0.366976	+	0.930230i	$0.619607\pi$
$252$	−3.35881	−0.211585
$253$	1.84218	0.115817
$254$	11.3776	0.713892
$255$	0.390474	0.0244524
$256$	1.00000	0.0625000
$257$	−1.34663	−0.0840003	−0.0420002	−	0.999118i	$-0.513373\pi$
$257$	−1.34663	−0.0840003	−0.0420002	+	0.999118i	$0.513373\pi$
$258$	10.3167	0.642290
$259$	−18.0449	−1.12125
$260$	−0.267494	−0.0165892
$261$	8.31225	0.514515
$262$	−0.282242	−0.0174370
$263$	0.769116	0.0474257	0.0237129	−	0.999719i	$-0.492451\pi$
$263$	0.769116	0.0474257	0.0237129	+	0.999719i	$0.492451\pi$
$264$	−2.35637	−0.145025
$265$	4.14868	0.254851
$266$	−12.3555	−0.757563
$267$	13.8950	0.850358
$268$	2.59031	0.158228
$269$	−7.52197	−0.458623	−0.229311	−	0.973353i	$-0.573647\pi$
$269$	−7.52197	−0.458623	−0.229311	+	0.973353i	$0.573647\pi$
$270$	0.390474	0.0237635
$271$	−17.7389	−1.07756	−0.538781	−	0.842446i	$-0.681115\pi$
$271$	−17.7389	−1.07756	−0.538781	+	0.842446i	$0.681115\pi$
$272$	−1.00000	−0.0606339
$273$	−2.30095	−0.139260
$274$	−0.0466358	−0.00281737
$275$	−11.4226	−0.688809
$276$	0.781785	0.0470579
$277$	−14.1232	−0.848579	−0.424290	−	0.905527i	$-0.639476\pi$
$277$	−14.1232	−0.848579	−0.424290	+	0.905527i	$0.639476\pi$
$278$	−20.9833	−1.25850
$279$	1.31598	0.0787857
$280$	−1.31153	−0.0783789
$281$	26.0999	1.55699	0.778494	−	0.627652i	$-0.215984\pi$
$281$	26.0999	1.55699	0.778494	+	0.627652i	$0.215984\pi$
$282$	6.66378	0.396823
$283$	18.6828	1.11057	0.555287	−	0.831659i	$-0.312608\pi$
$283$	18.6828	1.11057	0.555287	+	0.831659i	$0.312608\pi$
$284$	−8.47670	−0.503000
$285$	1.43637	0.0850831
$286$	−1.61423	−0.0954515
$287$	−28.1381	−1.66094
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	3.24572	0.190595
$291$	−7.04743	−0.413128
$292$	−1.74201	−0.101943
$293$	−20.5839	−1.20252	−0.601262	−	0.799052i	$-0.705335\pi$
$293$	−20.5839	−1.20252	−0.601262	+	0.799052i	$0.705335\pi$
$294$	−4.28163	−0.249710
$295$	−0.390474	−0.0227343
$296$	−5.37239	−0.312264
$297$	2.35637	0.136731
$298$	12.3080	0.712982
$299$	0.535560	0.0309723
$300$	−4.84753	−0.279872
$301$	34.6519	1.99730
$302$	−2.58417	−0.148702
$303$	−13.7367	−0.789151
$304$	−3.67853	−0.210978
$305$	−3.81083	−0.218208
$306$	1.00000	0.0571662
$307$	−23.4594	−1.33890	−0.669448	−	0.742859i	$-0.733469\pi$
$307$	−23.4594	−1.33890	−0.669448	+	0.742859i	$0.733469\pi$
$308$	−7.91462	−0.450978
$309$	0.551910	0.0313971
$310$	0.513856	0.0291851
$311$	−8.83544	−0.501012	−0.250506	−	0.968115i	$-0.580597\pi$
$311$	−8.83544	−0.501012	−0.250506	+	0.968115i	$0.580597\pi$
$312$	−0.685048	−0.0387832
$313$	0.602881	0.0340769	0.0170384	−	0.999855i	$-0.494576\pi$
$313$	0.602881	0.0340769	0.0170384	+	0.999855i	$0.494576\pi$
$314$	−10.8658	−0.613195
$315$	1.31153	0.0738963
$316$	6.53184	0.367445
$317$	5.39825	0.303196	0.151598	−	0.988442i	$-0.451558\pi$
$317$	5.39825	0.303196	0.151598	+	0.988442i	$0.451558\pi$
$318$	10.6247	0.595805
$319$	19.5868	1.09665
$320$	−0.390474	−0.0218282
$321$	−18.8801	−1.05378
$322$	2.62587	0.146334
$323$	3.67853	0.204679
$324$	1.00000	0.0555556
$325$	−3.32079	−0.184204
$326$	−12.2002	−0.675706
$327$	7.11141	0.393262
$328$	−8.37739	−0.462564
$329$	22.3824	1.23398
$330$	0.920103	0.0506500
$331$	−2.79767	−0.153774	−0.0768870	−	0.997040i	$-0.524498\pi$
$331$	−2.79767	−0.153774	−0.0768870	+	0.997040i	$0.524498\pi$
$332$	−12.4462	−0.683072
$333$	5.37239	0.294405
$334$	20.5000	1.12171
$335$	−1.01145	−0.0552613
$336$	−3.35881	−0.183238
$337$	−15.9599	−0.869392	−0.434696	−	0.900577i	$-0.643144\pi$
$337$	−15.9599	−0.869392	−0.434696	+	0.900577i	$0.643144\pi$
$338$	12.5307	0.681581
$339$	1.30893	0.0710915
$340$	0.390474	0.0211764
$341$	3.10094	0.167925
$342$	3.67853	0.198912
$343$	9.13050	0.493001
$344$	10.3167	0.556239
$345$	−0.305267	−0.0164350
$346$	3.83372	0.206102
$347$	−0.700838	−0.0376230	−0.0188115	−	0.999823i	$-0.505988\pi$
$347$	−0.700838	−0.0376230	−0.0188115	+	0.999823i	$0.505988\pi$
$348$	8.31225	0.445583
$349$	−7.79835	−0.417436	−0.208718	−	0.977976i	$-0.566929\pi$
$349$	−7.79835	−0.417436	−0.208718	+	0.977976i	$0.566929\pi$
$350$	−16.2820	−0.870307
$351$	0.685048	0.0365652
$352$	−2.35637	−0.125595
$353$	14.9809	0.797352	0.398676	−	0.917092i	$-0.369470\pi$
$353$	14.9809	0.797352	0.398676	+	0.917092i	$0.369470\pi$
$354$	−1.00000	−0.0531494
$355$	3.30993	0.175673
$356$	13.8950	0.736431
$357$	3.35881	0.177767
$358$	−3.07926	−0.162744
$359$	−10.5114	−0.554768	−0.277384	−	0.960759i	$-0.589467\pi$
$359$	−10.5114	−0.554768	−0.277384	+	0.960759i	$0.589467\pi$
$360$	0.390474	0.0205798
$361$	−5.46844	−0.287813
$362$	2.08453	0.109561
$363$	−5.44750	−0.285920
$364$	−2.30095	−0.120603
$365$	0.680210	0.0356038
$366$	−9.75950	−0.510137
$367$	33.0700	1.72624	0.863120	−	0.504998i	$-0.168507\pi$
$367$	33.0700	1.72624	0.863120	+	0.504998i	$0.168507\pi$
$368$	0.781785	0.0407533
$369$	8.37739	0.436110
$370$	2.09778	0.109058
$371$	35.6865	1.85275
$372$	1.31598	0.0682304
$373$	4.60191	0.238278	0.119139	−	0.992878i	$-0.461987\pi$
$373$	4.60191	0.238278	0.119139	+	0.992878i	$0.461987\pi$
$374$	2.35637	0.121845
$375$	3.84520	0.198565
$376$	6.66378	0.343658
$377$	5.69430	0.293271
$378$	3.35881	0.172759
$379$	12.2402	0.628738	0.314369	−	0.949301i	$-0.398207\pi$
$379$	12.2402	0.628738	0.314369	+	0.949301i	$0.398207\pi$
$380$	1.43637	0.0736842
$381$	−11.3776	−0.582890
$382$	22.5823	1.15541
$383$	28.0557	1.43358	0.716791	−	0.697288i	$-0.245610\pi$
$383$	28.0557	1.43358	0.716791	+	0.697288i	$0.245610\pi$
$384$	−1.00000	−0.0510310
$385$	3.09045	0.157504
$386$	5.64059	0.287098
$387$	−10.3167	−0.524427
$388$	−7.04743	−0.357779
$389$	−8.98330	−0.455471	−0.227736	−	0.973723i	$-0.573132\pi$
$389$	−8.98330	−0.455471	−0.227736	+	0.973723i	$0.573132\pi$
$390$	0.267494	0.0135451
$391$	−0.781785	−0.0395366
$392$	−4.28163	−0.216255
$393$	0.282242	0.0142372
$394$	2.53408	0.127665
$395$	−2.55051	−0.128330
$396$	2.35637	0.118412
$397$	20.7692	1.04238	0.521188	−	0.853442i	$-0.325489\pi$
$397$	20.7692	1.04238	0.521188	+	0.853442i	$0.325489\pi$
$398$	11.1277	0.557782
$399$	12.3555	0.618548
$400$	−4.84753	−0.242377
$401$	−5.46263	−0.272791	−0.136395	−	0.990654i	$-0.543552\pi$
$401$	−5.46263	−0.272791	−0.136395	+	0.990654i	$0.543552\pi$
$402$	−2.59031	−0.129193
$403$	0.901510	0.0449074
$404$	−13.7367	−0.683425
$405$	−0.390474	−0.0194028
$406$	27.9193	1.38561
$407$	12.6594	0.627501
$408$	1.00000	0.0495074
$409$	11.2104	0.554316	0.277158	−	0.960824i	$-0.410607\pi$
$409$	11.2104	0.554316	0.277158	+	0.960824i	$0.410607\pi$
$410$	3.27115	0.161551
$411$	0.0466358	0.00230037
$412$	0.551910	0.0271907
$413$	−3.35881	−0.165276
$414$	−0.781785	−0.0384226
$415$	4.85990	0.238563
$416$	−0.685048	−0.0335873
$417$	20.9833	1.02756
$418$	8.66799	0.423965
$419$	−21.9436	−1.07201	−0.536007	−	0.844213i	$-0.680068\pi$
$419$	−21.9436	−1.07201	−0.536007	+	0.844213i	$0.680068\pi$
$420$	1.31153	0.0639961
$421$	10.1086	0.492661	0.246331	−	0.969186i	$-0.420775\pi$
$421$	10.1086	0.492661	0.246331	+	0.969186i	$0.420775\pi$
$422$	−9.83568	−0.478793
$423$	−6.66378	−0.324004
$424$	10.6247	0.515982
$425$	4.84753	0.235140
$426$	8.47670	0.410697
$427$	−32.7804	−1.58635
$428$	−18.8801	−0.912604
$429$	1.61423	0.0779358
$430$	−4.02840	−0.194267
$431$	−33.3359	−1.60573	−0.802866	−	0.596160i	$-0.796692\pi$
$431$	−33.3359	−1.60573	−0.802866	+	0.596160i	$0.796692\pi$
$432$	1.00000	0.0481125
$433$	35.0553	1.68465	0.842326	−	0.538969i	$-0.181186\pi$
$433$	35.0553	1.68465	0.842326	+	0.538969i	$0.181186\pi$
$434$	4.42013	0.212173
$435$	−3.24572	−0.155620
$436$	7.11141	0.340575
$437$	−2.87582	−0.137569
$438$	1.74201	0.0832365
$439$	−17.3883	−0.829898	−0.414949	−	0.909845i	$-0.636201\pi$
$439$	−17.3883	−0.829898	−0.414949	+	0.909845i	$0.636201\pi$
$440$	0.920103	0.0438642
$441$	4.28163	0.203887
$442$	0.685048	0.0325844
$443$	−1.12088	−0.0532544	−0.0266272	−	0.999645i	$-0.508477\pi$
$443$	−1.12088	−0.0532544	−0.0266272	+	0.999645i	$0.508477\pi$
$444$	5.37239	0.254962
$445$	−5.42562	−0.257199
$446$	21.9208	1.03798
$447$	−12.3080	−0.582147
$448$	−3.35881	−0.158689
$449$	0.600108	0.0283208	0.0141604	−	0.999900i	$-0.495492\pi$
$449$	0.600108	0.0283208	0.0141604	+	0.999900i	$0.495492\pi$
$450$	4.84753	0.228515
$451$	19.7403	0.929533
$452$	1.30893	0.0615671
$453$	2.58417	0.121415
$454$	1.81610	0.0852338
$455$	0.898461	0.0421205
$456$	3.67853	0.172263
$457$	31.8113	1.48807	0.744035	−	0.668140i	$-0.232909\pi$
$457$	31.8113	1.48807	0.744035	+	0.668140i	$0.232909\pi$
$458$	29.2910	1.36868
$459$	−1.00000	−0.0466760
$460$	−0.305267	−0.0142331
$461$	−32.0305	−1.49181	−0.745905	−	0.666052i	$-0.767983\pi$
$461$	−32.0305	−1.49181	−0.745905	+	0.666052i	$0.767983\pi$
$462$	7.91462	0.368222
$463$	14.9623	0.695358	0.347679	−	0.937614i	$-0.386970\pi$
$463$	14.9623	0.695358	0.347679	+	0.937614i	$0.386970\pi$
$464$	8.31225	0.385887
$465$	−0.513856	−0.0238295
$466$	10.8801	0.504013
$467$	1.50103	0.0694594	0.0347297	−	0.999397i	$-0.488943\pi$
$467$	1.50103	0.0694594	0.0347297	+	0.999397i	$0.488943\pi$
$468$	0.685048	0.0316664
$469$	−8.70037	−0.401746
$470$	−2.60203	−0.120023
$471$	10.8658	0.500671
$472$	−1.00000	−0.0460287
$473$	−24.3100	−1.11778
$474$	−6.53184	−0.300017
$475$	17.8318	0.818178
$476$	3.35881	0.153951
$477$	−10.6247	−0.486473
$478$	−20.2309	−0.925342
$479$	−28.5285	−1.30350	−0.651751	−	0.758433i	$-0.725965\pi$
$479$	−28.5285	−1.30350	−0.651751	+	0.758433i	$0.725965\pi$
$480$	0.390474	0.0178226
$481$	3.68035	0.167809
$482$	20.1846	0.919383
$483$	−2.62587	−0.119481
$484$	−5.44750	−0.247614
$485$	2.75184	0.124955
$486$	−1.00000	−0.0453609
$487$	26.5758	1.20426	0.602132	−	0.798397i	$-0.294318\pi$
$487$	26.5758	1.20426	0.602132	+	0.798397i	$0.294318\pi$
$488$	−9.75950	−0.441792
$489$	12.2002	0.551711
$490$	1.67187	0.0755272
$491$	−37.4583	−1.69047	−0.845234	−	0.534396i	$-0.820539\pi$
$491$	−37.4583	−1.69047	−0.845234	+	0.534396i	$0.820539\pi$
$492$	8.37739	0.377682
$493$	−8.31225	−0.374365
$494$	2.51997	0.113379
$495$	−0.920103	−0.0413556
$496$	1.31598	0.0590892
$497$	28.4717	1.27713
$498$	12.4462	0.557726
$499$	−23.8331	−1.06692	−0.533459	−	0.845826i	$-0.679108\pi$
$499$	−23.8331	−1.06692	−0.533459	+	0.845826i	$0.679108\pi$
$500$	3.84520	0.171963
$501$	−20.5000	−0.915872
$502$	11.6280	0.518982
$503$	−10.9729	−0.489259	−0.244630	−	0.969617i	$-0.578666\pi$
$503$	−10.9729	−0.489259	−0.244630	+	0.969617i	$0.578666\pi$
$504$	3.35881	0.149613
$505$	5.36381	0.238687
$506$	−1.84218	−0.0818948
$507$	−12.5307	−0.556508
$508$	−11.3776	−0.504798
$509$	−26.0831	−1.15611	−0.578056	−	0.815997i	$-0.696189\pi$
$509$	−26.0831	−1.15611	−0.578056	+	0.815997i	$0.696189\pi$
$510$	−0.390474	−0.0172905
$511$	5.85109	0.258837
$512$	−1.00000	−0.0441942
$513$	−3.67853	−0.162411
$514$	1.34663	0.0593972
$515$	−0.215506	−0.00949635
$516$	−10.3167	−0.454168
$517$	−15.7024	−0.690589
$518$	18.0449	0.792845
$519$	−3.83372	−0.168281
$520$	0.267494	0.0117304
$521$	16.8697	0.739074	0.369537	−	0.929216i	$-0.379516\pi$
$521$	16.8697	0.739074	0.369537	+	0.929216i	$0.379516\pi$
$522$	−8.31225	−0.363817
$523$	−41.2616	−1.80424	−0.902122	−	0.431482i	$-0.857991\pi$
$523$	−41.2616	−1.80424	−0.902122	+	0.431482i	$0.857991\pi$
$524$	0.282242	0.0123298
$525$	16.2820	0.710603
$526$	−0.769116	−0.0335350
$527$	−1.31598	−0.0573250
$528$	2.35637	0.102548
$529$	−22.3888	−0.973427
$530$	−4.14868	−0.180207
$531$	1.00000	0.0433963
$532$	12.3555	0.535678
$533$	5.73892	0.248580
$534$	−13.8950	−0.601294
$535$	7.37219	0.318727
$536$	−2.59031	−0.111884
$537$	3.07926	0.132880
$538$	7.52197	0.324295
$539$	10.0891	0.434569
$540$	−0.390474	−0.0168033
$541$	−4.05774	−0.174456	−0.0872280	−	0.996188i	$-0.527801\pi$
$541$	−4.05774	−0.174456	−0.0872280	+	0.996188i	$0.527801\pi$
$542$	17.7389	0.761951
$543$	−2.08453	−0.0894559
$544$	1.00000	0.0428746
$545$	−2.77682	−0.118946
$546$	2.30095	0.0984716
$547$	29.1344	1.24570	0.622848	−	0.782343i	$-0.285975\pi$
$547$	29.1344	1.24570	0.622848	+	0.782343i	$0.285975\pi$
$548$	0.0466358	0.00199218
$549$	9.75950	0.416525
$550$	11.4226	0.487061
$551$	−30.5768	−1.30262
$552$	−0.781785	−0.0332750
$553$	−21.9392	−0.932951
$554$	14.1232	0.600036
$555$	−2.09778	−0.0890457
$556$	20.9833	0.889892
$557$	−4.04122	−0.171232	−0.0856160	−	0.996328i	$-0.527286\pi$
$557$	−4.04122	−0.171232	−0.0856160	+	0.996328i	$0.527286\pi$
$558$	−1.31598	−0.0557099
$559$	−7.06744	−0.298921
$560$	1.31153	0.0554222
$561$	−2.35637	−0.0994862
$562$	−26.0999	−1.10096
$563$	−33.7657	−1.42306	−0.711528	−	0.702658i	$-0.751996\pi$
$563$	−33.7657	−1.42306	−0.711528	+	0.702658i	$0.751996\pi$
$564$	−6.66378	−0.280596
$565$	−0.511104	−0.0215023
$566$	−18.6828	−0.785295
$567$	−3.35881	−0.141057
$568$	8.47670	0.355674
$569$	15.5895	0.653547	0.326773	−	0.945103i	$-0.394039\pi$
$569$	15.5895	0.653547	0.326773	+	0.945103i	$0.394039\pi$
$570$	−1.43637	−0.0601629
$571$	16.5360	0.692012	0.346006	−	0.938232i	$-0.387538\pi$
$571$	16.5360	0.692012	0.346006	+	0.938232i	$0.387538\pi$
$572$	1.61423	0.0674944
$573$	−22.5823	−0.943390
$574$	28.1381	1.17446
$575$	−3.78973	−0.158042
$576$	1.00000	0.0416667
$577$	10.1814	0.423858	0.211929	−	0.977285i	$-0.432025\pi$
$577$	10.1814	0.423858	0.211929	+	0.977285i	$0.432025\pi$
$578$	−1.00000	−0.0415945
$579$	−5.64059	−0.234415
$580$	−3.24572	−0.134771
$581$	41.8043	1.73434
$582$	7.04743	0.292125
$583$	−25.0358	−1.03688
$584$	1.74201	0.0720849
$585$	−0.267494	−0.0110595
$586$	20.5839	0.850312
$587$	35.2080	1.45319	0.726594	−	0.687067i	$-0.241102\pi$
$587$	35.2080	1.45319	0.726594	+	0.687067i	$0.241102\pi$
$588$	4.28163	0.176571
$589$	−4.84087	−0.199464
$590$	0.390474	0.0160756
$591$	−2.53408	−0.104238
$592$	5.37239	0.220804
$593$	3.33580	0.136985	0.0684925	−	0.997652i	$-0.478181\pi$
$593$	3.33580	0.136985	0.0684925	+	0.997652i	$0.478181\pi$
$594$	−2.35637	−0.0966832
$595$	−1.31153	−0.0537675
$596$	−12.3080	−0.504154
$597$	−11.1277	−0.455427
$598$	−0.535560	−0.0219007
$599$	−14.7873	−0.604194	−0.302097	−	0.953277i	$-0.597687\pi$
$599$	−14.7873	−0.604194	−0.302097	+	0.953277i	$0.597687\pi$
$600$	4.84753	0.197900
$601$	−5.93211	−0.241976	−0.120988	−	0.992654i	$-0.538606\pi$
$601$	−5.93211	−0.241976	−0.120988	+	0.992654i	$0.538606\pi$
$602$	−34.6519	−1.41231
$603$	2.59031	0.105486
$604$	2.58417	0.105149
$605$	2.12711	0.0864792
$606$	13.7367	0.558014
$607$	13.3278	0.540961	0.270480	−	0.962726i	$-0.412817\pi$
$607$	13.3278	0.540961	0.270480	+	0.962726i	$0.412817\pi$
$608$	3.67853	0.149184
$609$	−27.9193	−1.13135
$610$	3.81083	0.154296
$611$	−4.56501	−0.184681
$612$	−1.00000	−0.0404226
$613$	4.38886	0.177264	0.0886321	−	0.996064i	$-0.471750\pi$
$613$	4.38886	0.177264	0.0886321	+	0.996064i	$0.471750\pi$
$614$	23.4594	0.946743
$615$	−3.27115	−0.131906
$616$	7.91462	0.318889
$617$	18.3495	0.738724	0.369362	−	0.929286i	$-0.379576\pi$
$617$	18.3495	0.738724	0.369362	+	0.929286i	$0.379576\pi$
$618$	−0.551910	−0.0222011
$619$	−33.4890	−1.34603	−0.673017	−	0.739627i	$-0.735002\pi$
$619$	−33.4890	−1.34603	−0.673017	+	0.739627i	$0.735002\pi$
$620$	−0.513856	−0.0206370
$621$	0.781785	0.0313719
$622$	8.83544	0.354269
$623$	−46.6706	−1.86982
$624$	0.685048	0.0274239
$625$	22.7362	0.909448
$626$	−0.602881	−0.0240960
$627$	−8.66799	−0.346166
$628$	10.8658	0.433594
$629$	−5.37239	−0.214211
$630$	−1.31153	−0.0522526
$631$	29.0346	1.15585	0.577925	−	0.816090i	$-0.303863\pi$
$631$	29.0346	1.15585	0.577925	+	0.816090i	$0.303863\pi$
$632$	−6.53184	−0.259823
$633$	9.83568	0.390933
$634$	−5.39825	−0.214392
$635$	4.44264	0.176301
$636$	−10.6247	−0.421298
$637$	2.93312	0.116215
$638$	−19.5868	−0.775448
$639$	−8.47670	−0.335333
$640$	0.390474	0.0154348
$641$	−5.37687	−0.212374	−0.106187	−	0.994346i	$-0.533864\pi$
$641$	−5.37687	−0.212374	−0.106187	+	0.994346i	$0.533864\pi$
$642$	18.8801	0.745138
$643$	4.24720	0.167493	0.0837467	−	0.996487i	$-0.473311\pi$
$643$	4.24720	0.167493	0.0837467	+	0.996487i	$0.473311\pi$
$644$	−2.62587	−0.103474
$645$	4.02840	0.158618
$646$	−3.67853	−0.144730
$647$	0.797635	0.0313583	0.0156791	−	0.999877i	$-0.495009\pi$
$647$	0.797635	0.0313583	0.0156791	+	0.999877i	$0.495009\pi$
$648$	−1.00000	−0.0392837
$649$	2.35637	0.0924958
$650$	3.32079	0.130252
$651$	−4.42013	−0.173239
$652$	12.2002	0.477796
$653$	−28.2404	−1.10513	−0.552566	−	0.833469i	$-0.686351\pi$
$653$	−28.2404	−1.10513	−0.552566	+	0.833469i	$0.686351\pi$
$654$	−7.11141	−0.278078
$655$	−0.110208	−0.00430618
$656$	8.37739	0.327082
$657$	−1.74201	−0.0679623
$658$	−22.3824	−0.872557
$659$	5.77202	0.224846	0.112423	−	0.993660i	$-0.464139\pi$
$659$	5.77202	0.224846	0.112423	+	0.993660i	$0.464139\pi$
$660$	−0.920103	−0.0358150
$661$	4.54350	0.176722	0.0883608	−	0.996089i	$-0.471837\pi$
$661$	4.54350	0.176722	0.0883608	+	0.996089i	$0.471837\pi$
$662$	2.79767	0.108735
$663$	−0.685048	−0.0266051
$664$	12.4462	0.483005
$665$	−4.82450	−0.187086
$666$	−5.37239	−0.208176
$667$	6.49839	0.251619
$668$	−20.5000	−0.793169
$669$	−21.9208	−0.847507
$670$	1.01145	0.0390757
$671$	22.9970	0.887791
$672$	3.35881	0.129569
$673$	−21.7690	−0.839135	−0.419567	−	0.907724i	$-0.637818\pi$
$673$	−21.7690	−0.839135	−0.419567	+	0.907724i	$0.637818\pi$
$674$	15.9599	0.614753
$675$	−4.84753	−0.186582
$676$	−12.5307	−0.481950
$677$	−29.6370	−1.13904	−0.569522	−	0.821976i	$-0.692872\pi$
$677$	−29.6370	−1.13904	−0.569522	+	0.821976i	$0.692872\pi$
$678$	−1.30893	−0.0502693
$679$	23.6710	0.908410
$680$	−0.390474	−0.0149740
$681$	−1.81610	−0.0695931
$682$	−3.10094	−0.118741
$683$	−20.2350	−0.774271	−0.387136	−	0.922023i	$-0.626535\pi$
$683$	−20.2350	−0.774271	−0.387136	+	0.922023i	$0.626535\pi$
$684$	−3.67853	−0.140652
$685$	−0.0182100	−0.000695770 0
$686$	−9.13050	−0.348604
$687$	−29.2910	−1.11752
$688$	−10.3167	−0.393321
$689$	−7.27845	−0.277287
$690$	0.305267	0.0116213
$691$	−30.6767	−1.16700	−0.583498	−	0.812115i	$-0.698316\pi$
$691$	−30.6767	−1.16700	−0.583498	+	0.812115i	$0.698316\pi$
$692$	−3.83372	−0.145736
$693$	−7.91462	−0.300652
$694$	0.700838	0.0266034
$695$	−8.19345	−0.310795
$696$	−8.31225	−0.315075
$697$	−8.37739	−0.317316
$698$	7.79835	0.295172
$699$	−10.8801	−0.411525
$700$	16.2820	0.615400
$701$	−9.26671	−0.349999	−0.174999	−	0.984569i	$-0.555992\pi$
$701$	−9.26671	−0.349999	−0.174999	+	0.984569i	$0.555992\pi$
$702$	−0.685048	−0.0258555
$703$	−19.7625	−0.745356
$704$	2.35637	0.0888092
$705$	2.60203	0.0979983
$706$	−14.9809	−0.563813
$707$	46.1389	1.73523
$708$	1.00000	0.0375823
$709$	−24.3107	−0.913007	−0.456504	−	0.889722i	$-0.650898\pi$
$709$	−24.3107	−0.913007	−0.456504	+	0.889722i	$0.650898\pi$
$710$	−3.30993	−0.124219
$711$	6.53184	0.244963
$712$	−13.8950	−0.520736
$713$	1.02881	0.0385294
$714$	−3.35881	−0.125700
$715$	−0.630315	−0.0235724
$716$	3.07926	0.115078
$717$	20.2309	0.755538
$718$	10.5114	0.392280
$719$	−22.0954	−0.824018	−0.412009	−	0.911180i	$-0.635173\pi$
$719$	−22.0954	−0.824018	−0.412009	+	0.911180i	$0.635173\pi$
$720$	−0.390474	−0.0145521
$721$	−1.85376	−0.0690377
$722$	5.46844	0.203514
$723$	−20.1846	−0.750673
$724$	−2.08453	−0.0774711
$725$	−40.2939	−1.49648
$726$	5.44750	0.202176
$727$	−2.63841	−0.0978534	−0.0489267	−	0.998802i	$-0.515580\pi$
$727$	−2.63841	−0.0978534	−0.0489267	+	0.998802i	$0.515580\pi$
$728$	2.30095	0.0852789
$729$	1.00000	0.0370370
$730$	−0.680210	−0.0251757
$731$	10.3167	0.381577
$732$	9.75950	0.360722
$733$	18.3614	0.678192	0.339096	−	0.940752i	$-0.389879\pi$
$733$	18.3614	0.678192	0.339096	+	0.940752i	$0.389879\pi$
$734$	−33.0700	−1.22064
$735$	−1.67187	−0.0616677
$736$	−0.781785	−0.0288170
$737$	6.10374	0.224834
$738$	−8.37739	−0.308376
$739$	−28.6261	−1.05303	−0.526514	−	0.850167i	$-0.676501\pi$
$739$	−28.6261	−1.05303	−0.526514	+	0.850167i	$0.676501\pi$
$740$	−2.09778	−0.0771159
$741$	−2.51997	−0.0925734
$742$	−35.6865	−1.31009
$743$	−26.8109	−0.983597	−0.491799	−	0.870709i	$-0.663660\pi$
$743$	−26.8109	−0.983597	−0.491799	+	0.870709i	$0.663660\pi$
$744$	−1.31598	−0.0482462
$745$	4.80594	0.176076
$746$	−4.60191	−0.168488
$747$	−12.4462	−0.455381
$748$	−2.35637	−0.0861576
$749$	63.4147	2.31712
$750$	−3.84520	−0.140407
$751$	32.3426	1.18020	0.590098	−	0.807331i	$-0.299089\pi$
$751$	32.3426	1.18020	0.590098	+	0.807331i	$0.299089\pi$
$752$	−6.66378	−0.243003
$753$	−11.6280	−0.423747
$754$	−5.69430	−0.207374
$755$	−1.00905	−0.0367232
$756$	−3.35881	−0.122159
$757$	20.9702	0.762174	0.381087	−	0.924539i	$-0.375550\pi$
$757$	20.9702	0.762174	0.381087	+	0.924539i	$0.375550\pi$
$758$	−12.2402	−0.444585
$759$	1.84218	0.0668668
$760$	−1.43637	−0.0521026
$761$	35.6470	1.29220	0.646101	−	0.763252i	$-0.276398\pi$
$761$	35.6470	1.29220	0.646101	+	0.763252i	$0.276398\pi$
$762$	11.3776	0.412166
$763$	−23.8859	−0.864727
$764$	−22.5823	−0.817000
$765$	0.390474	0.0141176
$766$	−28.0557	−1.01370
$767$	0.685048	0.0247357
$768$	1.00000	0.0360844
$769$	11.7318	0.423059	0.211530	−	0.977372i	$-0.432156\pi$
$769$	11.7318	0.423059	0.211530	+	0.977372i	$0.432156\pi$
$770$	−3.09045	−0.111372
$771$	−1.34663	−0.0484976
$772$	−5.64059	−0.203009
$773$	−32.3128	−1.16221	−0.581106	−	0.813828i	$-0.697380\pi$
$773$	−32.3128	−1.16221	−0.581106	+	0.813828i	$0.697380\pi$
$774$	10.3167	0.370826
$775$	−6.37925	−0.229150
$776$	7.04743	0.252988
$777$	−18.0449	−0.647356
$778$	8.98330	0.322067
$779$	−30.8165	−1.10411
$780$	−0.267494	−0.00957781
$781$	−19.9743	−0.714736
$782$	0.781785	0.0279566
$783$	8.31225	0.297056
$784$	4.28163	0.152915
$785$	−4.24283	−0.151433
$786$	−0.282242	−0.0100672
$787$	22.3233	0.795739	0.397870	−	0.917442i	$-0.369750\pi$
$787$	22.3233	0.795739	0.397870	+	0.917442i	$0.369750\pi$
$788$	−2.53408	−0.0902729
$789$	0.769116	0.0273812
$790$	2.55051	0.0907432
$791$	−4.39646	−0.156320
$792$	−2.35637	−0.0837301
$793$	6.68573	0.237417
$794$	−20.7692	−0.737071
$795$	4.14868	0.147138
$796$	−11.1277	−0.394412
$797$	45.2982	1.60454	0.802272	−	0.596959i	$-0.203624\pi$
$797$	45.2982	1.60454	0.802272	+	0.596959i	$0.203624\pi$
$798$	−12.3555	−0.437379
$799$	6.66378	0.235748
$800$	4.84753	0.171386
$801$	13.8950	0.490954
$802$	5.46263	0.192892
$803$	−4.10483	−0.144856
$804$	2.59031	0.0913532
$805$	1.02533	0.0361383
$806$	−0.901510	−0.0317543
$807$	−7.52197	−0.264786
$808$	13.7367	0.483255
$809$	48.4476	1.70333	0.851663	−	0.524090i	$-0.175594\pi$
$809$	48.4476	1.70333	0.851663	+	0.524090i	$0.175594\pi$
$810$	0.390474	0.0137199
$811$	7.90687	0.277648	0.138824	−	0.990317i	$-0.455668\pi$
$811$	7.90687	0.277648	0.138824	+	0.990317i	$0.455668\pi$
$812$	−27.9193	−0.979776
$813$	−17.7389	−0.622130
$814$	−12.6594	−0.443710
$815$	−4.76385	−0.166871
$816$	−1.00000	−0.0350070
$817$	37.9503	1.32771
$818$	−11.2104	−0.391961
$819$	−2.30095	−0.0804017
$820$	−3.27115	−0.114234
$821$	20.2464	0.706603	0.353301	−	0.935510i	$-0.385059\pi$
$821$	20.2464	0.706603	0.353301	+	0.935510i	$0.385059\pi$
$822$	−0.0466358	−0.00162661
$823$	−18.8700	−0.657766	−0.328883	−	0.944371i	$-0.606672\pi$
$823$	−18.8700	−0.657766	−0.328883	+	0.944371i	$0.606672\pi$
$824$	−0.551910	−0.0192267
$825$	−11.4226	−0.397684
$826$	3.35881	0.116868
$827$	14.8640	0.516870	0.258435	−	0.966029i	$-0.416793\pi$
$827$	14.8640	0.516870	0.258435	+	0.966029i	$0.416793\pi$
$828$	0.781785	0.0271689
$829$	1.35670	0.0471201	0.0235600	−	0.999722i	$-0.492500\pi$
$829$	1.35670	0.0471201	0.0235600	+	0.999722i	$0.492500\pi$
$830$	−4.85990	−0.168690
$831$	−14.1232	−0.489927
$832$	0.685048	0.0237498
$833$	−4.28163	−0.148350
$834$	−20.9833	−0.726593
$835$	8.00471	0.277015
$836$	−8.66799	−0.299789
$837$	1.31598	0.0454869
$838$	21.9436	0.758029
$839$	31.1557	1.07561	0.537807	−	0.843068i	$-0.319253\pi$
$839$	31.1557	1.07561	0.537807	+	0.843068i	$0.319253\pi$
$840$	−1.31153	−0.0452521
$841$	40.0935	1.38254
$842$	−10.1086	−0.348364
$843$	26.0999	0.898928
$844$	9.83568	0.338558
$845$	4.89292	0.168321
$846$	6.66378	0.229106
$847$	18.2971	0.628697
$848$	−10.6247	−0.364854
$849$	18.6828	0.641191
$850$	−4.84753	−0.166269
$851$	4.20005	0.143976
$852$	−8.47670	−0.290407
$853$	3.50248	0.119923	0.0599614	−	0.998201i	$-0.480902\pi$
$853$	3.50248	0.119923	0.0599614	+	0.998201i	$0.480902\pi$
$854$	32.7804	1.12172
$855$	1.43637	0.0491228
$856$	18.8801	0.645309
$857$	−55.0691	−1.88112	−0.940562	−	0.339622i	$-0.889701\pi$
$857$	−55.0691	−1.88112	−0.940562	+	0.339622i	$0.889701\pi$
$858$	−1.61423	−0.0551089
$859$	40.1184	1.36882	0.684411	−	0.729097i	$-0.260059\pi$
$859$	40.1184	1.36882	0.684411	+	0.729097i	$0.260059\pi$
$860$	4.02840	0.137367
$861$	−28.1381	−0.958944
$862$	33.3359	1.13542
$863$	−31.1207	−1.05936	−0.529680	−	0.848197i	$-0.677688\pi$
$863$	−31.1207	−1.05936	−0.529680	+	0.848197i	$0.677688\pi$
$864$	−1.00000	−0.0340207
$865$	1.49697	0.0508984
$866$	−35.0553	−1.19123
$867$	1.00000	0.0339618
$868$	−4.42013	−0.150029
$869$	15.3915	0.522119
$870$	3.24572	0.110040
$871$	1.77449	0.0601262
$872$	−7.11141	−0.240823
$873$	−7.04743	−0.238519
$874$	2.87582	0.0972759
$875$	−12.9153	−0.436618
$876$	−1.74201	−0.0588571
$877$	−8.19548	−0.276742	−0.138371	−	0.990380i	$-0.544187\pi$
$877$	−8.19548	−0.276742	−0.138371	+	0.990380i	$0.544187\pi$
$878$	17.3883	0.586827
$879$	−20.5839	−0.694277
$880$	−0.920103	−0.0310167
$881$	13.5054	0.455007	0.227504	−	0.973777i	$-0.426944\pi$
$881$	13.5054	0.455007	0.227504	+	0.973777i	$0.426944\pi$
$882$	−4.28163	−0.144170
$883$	−51.6435	−1.73794	−0.868972	−	0.494862i	$-0.835219\pi$
$883$	−51.6435	−1.73794	−0.868972	+	0.494862i	$0.835219\pi$
$884$	−0.685048	−0.0230407
$885$	−0.390474	−0.0131256
$886$	1.12088	0.0376566
$887$	−34.5354	−1.15959	−0.579793	−	0.814764i	$-0.696867\pi$
$887$	−34.5354	−1.15959	−0.579793	+	0.814764i	$0.696867\pi$
$888$	−5.37239	−0.180286
$889$	38.2151	1.28169
$890$	5.42562	0.181867
$891$	2.35637	0.0789415
$892$	−21.9208	−0.733962
$893$	24.5129	0.820293
$894$	12.3080	0.411640
$895$	−1.20237	−0.0401909
$896$	3.35881	0.112210
$897$	0.535560	0.0178818
$898$	−0.600108	−0.0200258
$899$	10.9388	0.364828
$900$	−4.84753	−0.161584
$901$	10.6247	0.353961
$902$	−19.7403	−0.657279
$903$	34.6519	1.15314
$904$	−1.30893	−0.0435345
$905$	0.813956	0.0270568
$906$	−2.58417	−0.0858534
$907$	17.4107	0.578113	0.289057	−	0.957312i	$-0.406658\pi$
$907$	17.4107	0.578113	0.289057	+	0.957312i	$0.406658\pi$
$908$	−1.81610	−0.0602694
$909$	−13.7367	−0.455617
$910$	−0.898461	−0.0297837
$911$	27.3308	0.905509	0.452755	−	0.891635i	$-0.350441\pi$
$911$	27.3308	0.905509	0.452755	+	0.891635i	$0.350441\pi$
$912$	−3.67853	−0.121808
$913$	−29.3278	−0.970609
$914$	−31.8113	−1.05222
$915$	−3.81083	−0.125982
$916$	−29.2910	−0.967803
$917$	−0.947997	−0.0313056
$918$	1.00000	0.0330049
$919$	38.6059	1.27349	0.636745	−	0.771074i	$-0.280280\pi$
$919$	38.6059	1.27349	0.636745	+	0.771074i	$0.280280\pi$
$920$	0.305267	0.0100643
$921$	−23.4594	−0.773012
$922$	32.0305	1.05487
$923$	−5.80695	−0.191138
$924$	−7.91462	−0.260372
$925$	−26.0428	−0.856283
$926$	−14.9623	−0.491693
$927$	0.551910	0.0181271
$928$	−8.31225	−0.272863
$929$	7.84877	0.257510	0.128755	−	0.991676i	$-0.458902\pi$
$929$	7.84877	0.257510	0.128755	+	0.991676i	$0.458902\pi$
$930$	0.513856	0.0168500
$931$	−15.7501	−0.516188
$932$	−10.8801	−0.356391
$933$	−8.83544	−0.289259
$934$	−1.50103	−0.0491152
$935$	0.920103	0.0300906
$936$	−0.685048	−0.0223915
$937$	−50.9863	−1.66565	−0.832825	−	0.553536i	$-0.813278\pi$
$937$	−50.9863	−1.66565	−0.832825	+	0.553536i	$0.813278\pi$
$938$	8.70037	0.284077
$939$	0.602881	0.0196743
$940$	2.60203	0.0848690
$941$	−15.5477	−0.506841	−0.253421	−	0.967356i	$-0.581556\pi$
$941$	−15.5477	−0.506841	−0.253421	+	0.967356i	$0.581556\pi$
$942$	−10.8658	−0.354028
$943$	6.54932	0.213275
$944$	1.00000	0.0325472
$945$	1.31153	0.0426641
$946$	24.3100	0.790387
$947$	−23.6168	−0.767443	−0.383722	−	0.923449i	$-0.625358\pi$
$947$	−23.6168	−0.767443	−0.383722	+	0.923449i	$0.625358\pi$
$948$	6.53184	0.212144
$949$	−1.19336	−0.0387381
$950$	−17.8318	−0.578539
$951$	5.39825	0.175050
$952$	−3.35881	−0.108860
$953$	−6.81090	−0.220627	−0.110313	−	0.993897i	$-0.535185\pi$
$953$	−6.81090	−0.220627	−0.110313	+	0.993897i	$0.535185\pi$
$954$	10.6247	0.343988
$955$	8.81781	0.285338
$956$	20.2309	0.654315
$957$	19.5868	0.633151
$958$	28.5285	0.921715
$959$	−0.156641	−0.00505820
$960$	−0.390474	−0.0126025
$961$	−29.2682	−0.944135
$962$	−3.68035	−0.118659
$963$	−18.8801	−0.608403
$964$	−20.1846	−0.650102
$965$	2.20250	0.0709010
$966$	2.62587	0.0844860
$967$	−38.2372	−1.22963	−0.614813	−	0.788673i	$-0.710768\pi$
$967$	−38.2372	−1.22963	−0.614813	+	0.788673i	$0.710768\pi$
$968$	5.44750	0.175089
$969$	3.67853	0.118171
$970$	−2.75184	−0.0883562
$971$	1.76748	0.0567212	0.0283606	−	0.999598i	$-0.490971\pi$
$971$	1.76748	0.0567212	0.0283606	+	0.999598i	$0.490971\pi$
$972$	1.00000	0.0320750
$973$	−70.4791	−2.25946
$974$	−26.5758	−0.851543
$975$	−3.32079	−0.106350
$976$	9.75950	0.312394
$977$	−3.93823	−0.125995	−0.0629976	−	0.998014i	$-0.520066\pi$
$977$	−3.93823	−0.125995	−0.0629976	+	0.998014i	$0.520066\pi$
$978$	−12.2002	−0.390119
$979$	32.7417	1.04643
$980$	−1.67187	−0.0534058
$981$	7.11141	0.227050
$982$	37.4583	1.19534
$983$	33.9552	1.08300	0.541501	−	0.840700i	$-0.317856\pi$
$983$	33.9552	1.08300	0.541501	+	0.840700i	$0.317856\pi$
$984$	−8.37739	−0.267061
$985$	0.989493	0.0315279
$986$	8.31225	0.264716
$987$	22.3824	0.712440
$988$	−2.51997	−0.0801709
$989$	−8.06544	−0.256466
$990$	0.920103	0.0292428
$991$	23.6110	0.750029	0.375015	−	0.927019i	$-0.377638\pi$
$991$	23.6110	0.750029	0.375015	+	0.927019i	$0.377638\pi$
$992$	−1.31598	−0.0417824
$993$	−2.79767	−0.0887814
$994$	−28.4717	−0.903066
$995$	4.34508	0.137748
$996$	−12.4462	−0.394372
$997$	−16.6203	−0.526371	−0.263186	−	0.964745i	$-0.584773\pi$
$997$	−16.6203	−0.526371	−0.263186	+	0.964745i	$0.584773\pi$
$998$	23.8331	0.754424
$999$	5.37239	0.169975

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.y.1.5	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.y.1.5	✓	10	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.390474 q^{5} -1.00000 q^{6} -3.35881 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.390474 q^{5} -1.00000 q^{6} -3.35881 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.390474 q^{10} +2.35637 q^{11} +1.00000 q^{12} +0.685048 q^{13} +3.35881 q^{14} -0.390474 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -3.67853 q^{19} -0.390474 q^{20} -3.35881 q^{21} -2.35637 q^{22} +0.781785 q^{23} -1.00000 q^{24} -4.84753 q^{25} -0.685048 q^{26} +1.00000 q^{27} -3.35881 q^{28} +8.31225 q^{29} +0.390474 q^{30} +1.31598 q^{31} -1.00000 q^{32} +2.35637 q^{33} +1.00000 q^{34} +1.31153 q^{35} +1.00000 q^{36} +5.37239 q^{37} +3.67853 q^{38} +0.685048 q^{39} +0.390474 q^{40} +8.37739 q^{41} +3.35881 q^{42} -10.3167 q^{43} +2.35637 q^{44} -0.390474 q^{45} -0.781785 q^{46} -6.66378 q^{47} +1.00000 q^{48} +4.28163 q^{49} +4.84753 q^{50} -1.00000 q^{51} +0.685048 q^{52} -10.6247 q^{53} -1.00000 q^{54} -0.920103 q^{55} +3.35881 q^{56} -3.67853 q^{57} -8.31225 q^{58} +1.00000 q^{59} -0.390474 q^{60} +9.75950 q^{61} -1.31598 q^{62} -3.35881 q^{63} +1.00000 q^{64} -0.267494 q^{65} -2.35637 q^{66} +2.59031 q^{67} -1.00000 q^{68} +0.781785 q^{69} -1.31153 q^{70} -8.47670 q^{71} -1.00000 q^{72} -1.74201 q^{73} -5.37239 q^{74} -4.84753 q^{75} -3.67853 q^{76} -7.91462 q^{77} -0.685048 q^{78} +6.53184 q^{79} -0.390474 q^{80} +1.00000 q^{81} -8.37739 q^{82} -12.4462 q^{83} -3.35881 q^{84} +0.390474 q^{85} +10.3167 q^{86} +8.31225 q^{87} -2.35637 q^{88} +13.8950 q^{89} +0.390474 q^{90} -2.30095 q^{91} +0.781785 q^{92} +1.31598 q^{93} +6.66378 q^{94} +1.43637 q^{95} -1.00000 q^{96} -7.04743 q^{97} -4.28163 q^{98} +2.35637 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9} + 2 q^{10} - 3 q^{11} + 10 q^{12} - 10 q^{13} + 6 q^{14} - 2 q^{15} + 10 q^{16} - 10 q^{17} - 10 q^{18} + 8 q^{19} - 2 q^{20} - 6 q^{21} + 3 q^{22} - 9 q^{23} - 10 q^{24} + 20 q^{25} + 10 q^{26} + 10 q^{27} - 6 q^{28} - 24 q^{29} + 2 q^{30} - 7 q^{31} - 10 q^{32} - 3 q^{33} + 10 q^{34} - 22 q^{35} + 10 q^{36} - 4 q^{37} - 8 q^{38} - 10 q^{39} + 2 q^{40} - 9 q^{41} + 6 q^{42} - 11 q^{43} - 3 q^{44} - 2 q^{45} + 9 q^{46} - 18 q^{47} + 10 q^{48} + 6 q^{49} - 20 q^{50} - 10 q^{51} - 10 q^{52} - 9 q^{53} - 10 q^{54} + q^{55} + 6 q^{56} + 8 q^{57} + 24 q^{58} + 10 q^{59} - 2 q^{60} - 25 q^{61} + 7 q^{62} - 6 q^{63} + 10 q^{64} - 28 q^{65} + 3 q^{66} + 2 q^{67} - 10 q^{68} - 9 q^{69} + 22 q^{70} - 30 q^{71} - 10 q^{72} - 11 q^{73} + 4 q^{74} + 20 q^{75} + 8 q^{76} + 4 q^{77} + 10 q^{78} + 3 q^{79} - 2 q^{80} + 10 q^{81} + 9 q^{82} - q^{83} - 6 q^{84} + 2 q^{85} + 11 q^{86} - 24 q^{87} + 3 q^{88} - 14 q^{89} + 2 q^{90} - 13 q^{91} - 9 q^{92} - 7 q^{93} + 18 q^{94} - 35 q^{95} - 10 q^{96} - 10 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9 + 2 * q^10 - 3 * q^11 + 10 * q^12 - 10 * q^13 + 6 * q^14 - 2 * q^15 + 10 * q^16 - 10 * q^17 - 10 * q^18 + 8 * q^19 - 2 * q^20 - 6 * q^21 + 3 * q^22 - 9 * q^23 - 10 * q^24 + 20 * q^25 + 10 * q^26 + 10 * q^27 - 6 * q^28 - 24 * q^29 + 2 * q^30 - 7 * q^31 - 10 * q^32 - 3 * q^33 + 10 * q^34 - 22 * q^35 + 10 * q^36 - 4 * q^37 - 8 * q^38 - 10 * q^39 + 2 * q^40 - 9 * q^41 + 6 * q^42 - 11 * q^43 - 3 * q^44 - 2 * q^45 + 9 * q^46 - 18 * q^47 + 10 * q^48 + 6 * q^49 - 20 * q^50 - 10 * q^51 - 10 * q^52 - 9 * q^53 - 10 * q^54 + q^55 + 6 * q^56 + 8 * q^57 + 24 * q^58 + 10 * q^59 - 2 * q^60 - 25 * q^61 + 7 * q^62 - 6 * q^63 + 10 * q^64 - 28 * q^65 + 3 * q^66 + 2 * q^67 - 10 * q^68 - 9 * q^69 + 22 * q^70 - 30 * q^71 - 10 * q^72 - 11 * q^73 + 4 * q^74 + 20 * q^75 + 8 * q^76 + 4 * q^77 + 10 * q^78 + 3 * q^79 - 2 * q^80 + 10 * q^81 + 9 * q^82 - q^83 - 6 * q^84 + 2 * q^85 + 11 * q^86 - 24 * q^87 + 3 * q^88 - 14 * q^89 + 2 * q^90 - 13 * q^91 - 9 * q^92 - 7 * q^93 + 18 * q^94 - 35 * q^95 - 10 * q^96 - 10 * q^97 - 6 * q^98 - 3 * q^99

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