LMFDB - Embedded newform 2006.2.a.t.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2006,2,Mod(1,2006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2006, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2006 = 2 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2006.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:	$16.0179906455$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 13x^{6} + 24x^{5} + 50x^{4} - 50x^{3} - 62x^{2} + 28x + 24 $ x^8 - 3x^7 - 13x^6 + 24x^5 + 50x^4 - 50x^3 - 62x^2 + 28*x + 24
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-0.963332$ of defining polynomial
Character	$\chi$	$=$	2006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +3.31349 q^{3} +1.00000 q^{4} -2.70620 q^{5} +3.31349 q^{6} +2.77927 q^{7} +1.00000 q^{8} +7.97920 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.31349 q^{3} +1.00000 q^{4} -2.70620 q^{5} +3.31349 q^{6} +2.77927 q^{7} +1.00000 q^{8} +7.97920 q^{9} -2.70620 q^{10} -4.80310 q^{11} +3.31349 q^{12} +5.23749 q^{13} +2.77927 q^{14} -8.96696 q^{15} +1.00000 q^{16} -1.00000 q^{17} +7.97920 q^{18} +4.55215 q^{19} -2.70620 q^{20} +9.20907 q^{21} -4.80310 q^{22} -6.72413 q^{23} +3.31349 q^{24} +2.32352 q^{25} +5.23749 q^{26} +16.4985 q^{27} +2.77927 q^{28} +4.04168 q^{29} -8.96696 q^{30} -5.67363 q^{31} +1.00000 q^{32} -15.9150 q^{33} -1.00000 q^{34} -7.52125 q^{35} +7.97920 q^{36} -1.54452 q^{37} +4.55215 q^{38} +17.3544 q^{39} -2.70620 q^{40} +4.63066 q^{41} +9.20907 q^{42} +8.18798 q^{43} -4.80310 q^{44} -21.5933 q^{45} -6.72413 q^{46} +4.55826 q^{47} +3.31349 q^{48} +0.724327 q^{49} +2.32352 q^{50} -3.31349 q^{51} +5.23749 q^{52} -7.07511 q^{53} +16.4985 q^{54} +12.9981 q^{55} +2.77927 q^{56} +15.0835 q^{57} +4.04168 q^{58} -1.00000 q^{59} -8.96696 q^{60} -11.7494 q^{61} -5.67363 q^{62} +22.1763 q^{63} +1.00000 q^{64} -14.1737 q^{65} -15.9150 q^{66} +8.92603 q^{67} -1.00000 q^{68} -22.2803 q^{69} -7.52125 q^{70} +5.46707 q^{71} +7.97920 q^{72} -10.5757 q^{73} -1.54452 q^{74} +7.69895 q^{75} +4.55215 q^{76} -13.3491 q^{77} +17.3544 q^{78} -13.5689 q^{79} -2.70620 q^{80} +30.7300 q^{81} +4.63066 q^{82} -16.5278 q^{83} +9.20907 q^{84} +2.70620 q^{85} +8.18798 q^{86} +13.3921 q^{87} -4.80310 q^{88} -3.48939 q^{89} -21.5933 q^{90} +14.5564 q^{91} -6.72413 q^{92} -18.7995 q^{93} +4.55826 q^{94} -12.3190 q^{95} +3.31349 q^{96} +2.21934 q^{97} +0.724327 q^{98} -38.3248 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 5 q^{3} + 8 q^{4} - 5 q^{5} + 5 q^{6} + 8 q^{8} + 17 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 5 * q^3 + 8 * q^4 - 5 * q^5 + 5 * q^6 + 8 * q^8 + 17 * q^9	\( 8 q + 8 q^{2} + 5 q^{3} + 8 q^{4} - 5 q^{5} + 5 q^{6} + 8 q^{8} + 17 q^{9} - 5 q^{10} - 5 q^{11} + 5 q^{12} + q^{13} + 9 q^{15} + 8 q^{16} - 8 q^{17} + 17 q^{18} + 8 q^{19} - 5 q^{20} + 13 q^{21} - 5 q^{22} - 8 q^{23} + 5 q^{24} + 29 q^{25} + q^{26} + 44 q^{27} + 20 q^{29} + 9 q^{30} + 18 q^{31} + 8 q^{32} - 23 q^{33} - 8 q^{34} + 9 q^{35} + 17 q^{36} - 7 q^{37} + 8 q^{38} + 6 q^{39} - 5 q^{40} + 12 q^{41} + 13 q^{42} - 8 q^{43} - 5 q^{44} + 5 q^{45} - 8 q^{46} + 30 q^{47} + 5 q^{48} + 28 q^{49} + 29 q^{50} - 5 q^{51} + q^{52} - 5 q^{53} + 44 q^{54} + 23 q^{55} + 13 q^{57} + 20 q^{58} - 8 q^{59} + 9 q^{60} + 12 q^{61} + 18 q^{62} + 21 q^{63} + 8 q^{64} - 52 q^{65} - 23 q^{66} - 4 q^{67} - 8 q^{68} + 24 q^{69} + 9 q^{70} + 4 q^{71} + 17 q^{72} - 18 q^{73} - 7 q^{74} - 49 q^{75} + 8 q^{76} - 13 q^{77} + 6 q^{78} - 17 q^{79} - 5 q^{80} + 12 q^{81} + 12 q^{82} + 9 q^{83} + 13 q^{84} + 5 q^{85} - 8 q^{86} + 48 q^{87} - 5 q^{88} - 12 q^{89} + 5 q^{90} + 31 q^{91} - 8 q^{92} - 3 q^{93} + 30 q^{94} - 7 q^{95} + 5 q^{96} - 11 q^{97} + 28 q^{98} - 27 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 5 * q^3 + 8 * q^4 - 5 * q^5 + 5 * q^6 + 8 * q^8 + 17 * q^9 - 5 * q^10 - 5 * q^11 + 5 * q^12 + q^13 + 9 * q^15 + 8 * q^16 - 8 * q^17 + 17 * q^18 + 8 * q^19 - 5 * q^20 + 13 * q^21 - 5 * q^22 - 8 * q^23 + 5 * q^24 + 29 * q^25 + q^26 + 44 * q^27 + 20 * q^29 + 9 * q^30 + 18 * q^31 + 8 * q^32 - 23 * q^33 - 8 * q^34 + 9 * q^35 + 17 * q^36 - 7 * q^37 + 8 * q^38 + 6 * q^39 - 5 * q^40 + 12 * q^41 + 13 * q^42 - 8 * q^43 - 5 * q^44 + 5 * q^45 - 8 * q^46 + 30 * q^47 + 5 * q^48 + 28 * q^49 + 29 * q^50 - 5 * q^51 + q^52 - 5 * q^53 + 44 * q^54 + 23 * q^55 + 13 * q^57 + 20 * q^58 - 8 * q^59 + 9 * q^60 + 12 * q^61 + 18 * q^62 + 21 * q^63 + 8 * q^64 - 52 * q^65 - 23 * q^66 - 4 * q^67 - 8 * q^68 + 24 * q^69 + 9 * q^70 + 4 * q^71 + 17 * q^72 - 18 * q^73 - 7 * q^74 - 49 * q^75 + 8 * q^76 - 13 * q^77 + 6 * q^78 - 17 * q^79 - 5 * q^80 + 12 * q^81 + 12 * q^82 + 9 * q^83 + 13 * q^84 + 5 * q^85 - 8 * q^86 + 48 * q^87 - 5 * q^88 - 12 * q^89 + 5 * q^90 + 31 * q^91 - 8 * q^92 - 3 * q^93 + 30 * q^94 - 7 * q^95 + 5 * q^96 - 11 * q^97 + 28 * q^98 - 27 * 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
$3$	3.31349	1.91304	0.956521	−	0.291663i	$-0.0942084\pi$
$3$	3.31349	1.91304	0.956521	+	0.291663i	$0.0942084\pi$
$4$	1.00000	0.500000
$5$	−2.70620	−1.21025	−0.605125	−	0.796131i	$-0.706877\pi$
$5$	−2.70620	−1.21025	−0.605125	+	0.796131i	$0.706877\pi$
$6$	3.31349	1.35273
$7$	2.77927	1.05046	0.525232	−	0.850959i	$-0.323978\pi$
$7$	2.77927	1.05046	0.525232	+	0.850959i	$0.323978\pi$
$8$	1.00000	0.353553
$9$	7.97920	2.65973
$10$	−2.70620	−0.855776
$11$	−4.80310	−1.44819	−0.724094	−	0.689701i	$-0.757742\pi$
$11$	−4.80310	−1.44819	−0.724094	+	0.689701i	$0.757742\pi$
$12$	3.31349	0.956521
$13$	5.23749	1.45262	0.726310	−	0.687368i	$-0.241234\pi$
$13$	5.23749	1.45262	0.726310	+	0.687368i	$0.241234\pi$
$14$	2.77927	0.742790
$15$	−8.96696	−2.31526
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	7.97920	1.88071
$19$	4.55215	1.04433	0.522167	−	0.852843i	$-0.325124\pi$
$19$	4.55215	1.04433	0.522167	+	0.852843i	$0.325124\pi$
$20$	−2.70620	−0.605125
$21$	9.20907	2.00958
$22$	−4.80310	−1.02402
$23$	−6.72413	−1.40208	−0.701039	−	0.713123i	$-0.747280\pi$
$23$	−6.72413	−1.40208	−0.701039	+	0.713123i	$0.747280\pi$
$24$	3.31349	0.676363
$25$	2.32352	0.464704
$26$	5.23749	1.02716
$27$	16.4985	3.17514
$28$	2.77927	0.525232
$29$	4.04168	0.750522	0.375261	−	0.926919i	$-0.377553\pi$
$29$	4.04168	0.750522	0.375261	+	0.926919i	$0.377553\pi$
$30$	−8.96696	−1.63714
$31$	−5.67363	−1.01901	−0.509507	−	0.860466i	$-0.670172\pi$
$31$	−5.67363	−1.01901	−0.509507	+	0.860466i	$0.670172\pi$
$32$	1.00000	0.176777
$33$	−15.9150	−2.77045
$34$	−1.00000	−0.171499
$35$	−7.52125	−1.27132
$36$	7.97920	1.32987
$37$	−1.54452	−0.253918	−0.126959	−	0.991908i	$-0.540522\pi$
$37$	−1.54452	−0.253918	−0.126959	+	0.991908i	$0.540522\pi$
$38$	4.55215	0.738456
$39$	17.3544	2.77892
$40$	−2.70620	−0.427888
$41$	4.63066	0.723187	0.361594	−	0.932336i	$-0.382233\pi$
$41$	4.63066	0.723187	0.361594	+	0.932336i	$0.382233\pi$
$42$	9.20907	1.42099
$43$	8.18798	1.24866	0.624328	−	0.781162i	$-0.285373\pi$
$43$	8.18798	1.24866	0.624328	+	0.781162i	$0.285373\pi$
$44$	−4.80310	−0.724094
$45$	−21.5933	−3.21894
$46$	−6.72413	−0.991419
$47$	4.55826	0.664891	0.332446	−	0.943122i	$-0.392126\pi$
$47$	4.55826	0.664891	0.332446	+	0.943122i	$0.392126\pi$
$48$	3.31349	0.478261
$49$	0.724327	0.103475
$50$	2.32352	0.328595
$51$	−3.31349	−0.463981
$52$	5.23749	0.726310
$53$	−7.07511	−0.971841	−0.485921	−	0.874003i	$-0.661516\pi$
$53$	−7.07511	−0.971841	−0.485921	+	0.874003i	$0.661516\pi$
$54$	16.4985	2.24516
$55$	12.9981	1.75267
$56$	2.77927	0.371395
$57$	15.0835	1.99786
$58$	4.04168	0.530699
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−8.96696	−1.15763
$61$	−11.7494	−1.50436	−0.752181	−	0.658956i	$-0.770998\pi$
$61$	−11.7494	−1.50436	−0.752181	+	0.658956i	$0.770998\pi$
$62$	−5.67363	−0.720552
$63$	22.1763	2.79395
$64$	1.00000	0.125000
$65$	−14.1737	−1.75803
$66$	−15.9150	−1.95900
$67$	8.92603	1.09049	0.545244	−	0.838277i	$-0.316437\pi$
$67$	8.92603	1.09049	0.545244	+	0.838277i	$0.316437\pi$
$68$	−1.00000	−0.121268
$69$	−22.2803	−2.68224
$70$	−7.52125	−0.898962
$71$	5.46707	0.648822	0.324411	−	0.945916i	$-0.394834\pi$
$71$	5.46707	0.648822	0.324411	+	0.945916i	$0.394834\pi$
$72$	7.97920	0.940357
$73$	−10.5757	−1.23779	−0.618897	−	0.785472i	$-0.712420\pi$
$73$	−10.5757	−1.23779	−0.618897	+	0.785472i	$0.712420\pi$
$74$	−1.54452	−0.179547
$75$	7.69895	0.888998
$76$	4.55215	0.522167
$77$	−13.3491	−1.52127
$78$	17.3544	1.96499
$79$	−13.5689	−1.52662	−0.763311	−	0.646031i	$-0.776428\pi$
$79$	−13.5689	−1.52662	−0.763311	+	0.646031i	$0.776428\pi$
$80$	−2.70620	−0.302562
$81$	30.7300	3.41444
$82$	4.63066	0.511370
$83$	−16.5278	−1.81416	−0.907081	−	0.420957i	$-0.861694\pi$
$83$	−16.5278	−1.81416	−0.907081	+	0.420957i	$0.861694\pi$
$84$	9.20907	1.00479
$85$	2.70620	0.293529
$86$	8.18798	0.882933
$87$	13.3921	1.43578
$88$	−4.80310	−0.512012
$89$	−3.48939	−0.369875	−0.184938	−	0.982750i	$-0.559208\pi$
$89$	−3.48939	−0.369875	−0.184938	+	0.982750i	$0.559208\pi$
$90$	−21.5933	−2.27613
$91$	14.5564	1.52592
$92$	−6.72413	−0.701039
$93$	−18.7995	−1.94942
$94$	4.55826	0.470149
$95$	−12.3190	−1.26391
$96$	3.31349	0.338181
$97$	2.21934	0.225340	0.112670	−	0.993632i	$-0.464060\pi$
$97$	2.21934	0.225340	0.112670	+	0.993632i	$0.464060\pi$
$98$	0.724327	0.0731680
$99$	−38.3248	−3.85179
$100$	2.32352	0.232352
$101$	12.0778	1.20179	0.600895	−	0.799328i	$-0.294811\pi$
$101$	12.0778	1.20179	0.600895	+	0.799328i	$0.294811\pi$
$102$	−3.31349	−0.328084
$103$	7.26622	0.715962	0.357981	−	0.933729i	$-0.383465\pi$
$103$	7.26622	0.715962	0.357981	+	0.933729i	$0.383465\pi$
$104$	5.23749	0.513578
$105$	−24.9216	−2.43210
$106$	−7.07511	−0.687196
$107$	−12.1507	−1.17466	−0.587328	−	0.809349i	$-0.699820\pi$
$107$	−12.1507	−1.17466	−0.587328	+	0.809349i	$0.699820\pi$
$108$	16.4985	1.58757
$109$	0.308244	0.0295245	0.0147622	−	0.999891i	$-0.495301\pi$
$109$	0.308244	0.0295245	0.0147622	+	0.999891i	$0.495301\pi$
$110$	12.9981	1.23932
$111$	−5.11775	−0.485756
$112$	2.77927	0.262616
$113$	2.89087	0.271950	0.135975	−	0.990712i	$-0.456583\pi$
$113$	2.89087	0.271950	0.135975	+	0.990712i	$0.456583\pi$
$114$	15.0835	1.41270
$115$	18.1968	1.69686
$116$	4.04168	0.375261
$117$	41.7910	3.86358
$118$	−1.00000	−0.0920575
$119$	−2.77927	−0.254775
$120$	−8.96696	−0.818568
$121$	12.0697	1.09725
$122$	−11.7494	−1.06374
$123$	15.3436	1.38349
$124$	−5.67363	−0.509507
$125$	7.24310	0.647842
$126$	22.1763	1.97562
$127$	17.8166	1.58097	0.790484	−	0.612482i	$-0.209829\pi$
$127$	17.8166	1.58097	0.790484	+	0.612482i	$0.209829\pi$
$128$	1.00000	0.0883883
$129$	27.1308	2.38873
$130$	−14.1737	−1.24312
$131$	−6.18551	−0.540430	−0.270215	−	0.962800i	$-0.587095\pi$
$131$	−6.18551	−0.540430	−0.270215	+	0.962800i	$0.587095\pi$
$132$	−15.9150	−1.38522
$133$	12.6516	1.09704
$134$	8.92603	0.771092
$135$	−44.6482	−3.84271
$136$	−1.00000	−0.0857493
$137$	0.518562	0.0443038	0.0221519	−	0.999755i	$-0.492948\pi$
$137$	0.518562	0.0443038	0.0221519	+	0.999755i	$0.492948\pi$
$138$	−22.2803	−1.89663
$139$	8.21596	0.696868	0.348434	−	0.937333i	$-0.386714\pi$
$139$	8.21596	0.696868	0.348434	+	0.937333i	$0.386714\pi$
$140$	−7.52125	−0.635662
$141$	15.1037	1.27196
$142$	5.46707	0.458786
$143$	−25.1562	−2.10367
$144$	7.97920	0.664933
$145$	−10.9376	−0.908319
$146$	−10.5757	−0.875252
$147$	2.40005	0.197953
$148$	−1.54452	−0.126959
$149$	1.09633	0.0898151	0.0449075	−	0.998991i	$-0.485701\pi$
$149$	1.09633	0.0898151	0.0449075	+	0.998991i	$0.485701\pi$
$150$	7.69895	0.628616
$151$	−13.3241	−1.08430	−0.542148	−	0.840283i	$-0.682389\pi$
$151$	−13.3241	−1.08430	−0.542148	+	0.840283i	$0.682389\pi$
$152$	4.55215	0.369228
$153$	−7.97920	−0.645080
$154$	−13.3491	−1.07570
$155$	15.3540	1.23326
$156$	17.3544	1.38946
$157$	−24.4710	−1.95300	−0.976499	−	0.215522i	$-0.930855\pi$
$157$	−24.4710	−1.95300	−0.976499	+	0.215522i	$0.930855\pi$
$158$	−13.5689	−1.07948
$159$	−23.4433	−1.85917
$160$	−2.70620	−0.213944
$161$	−18.6882	−1.47283
$162$	30.7300	2.41438
$163$	−15.4619	−1.21107	−0.605535	−	0.795819i	$-0.707041\pi$
$163$	−15.4619	−1.21107	−0.605535	+	0.795819i	$0.707041\pi$
$164$	4.63066	0.361594
$165$	43.0692	3.35293
$166$	−16.5278	−1.28281
$167$	−16.6344	−1.28721	−0.643605	−	0.765358i	$-0.722562\pi$
$167$	−16.6344	−1.28721	−0.643605	+	0.765358i	$0.722562\pi$
$168$	9.20907	0.710495
$169$	14.4313	1.11010
$170$	2.70620	0.207556
$171$	36.3225	2.77765
$172$	8.18798	0.624328
$173$	−21.0308	−1.59894	−0.799472	−	0.600704i	$-0.794887\pi$
$173$	−21.0308	−1.59894	−0.799472	+	0.600704i	$0.794887\pi$
$174$	13.3921	1.01525
$175$	6.45768	0.488155
$176$	−4.80310	−0.362047
$177$	−3.31349	−0.249057
$178$	−3.48939	−0.261541
$179$	16.7584	1.25258	0.626292	−	0.779589i	$-0.284572\pi$
$179$	16.7584	1.25258	0.626292	+	0.779589i	$0.284572\pi$
$180$	−21.5933	−1.60947
$181$	18.3945	1.36726	0.683628	−	0.729831i	$-0.260401\pi$
$181$	18.3945	1.36726	0.683628	+	0.729831i	$0.260401\pi$
$182$	14.5564	1.07899
$183$	−38.9316	−2.87791
$184$	−6.72413	−0.495709
$185$	4.17979	0.307304
$186$	−18.7995	−1.37845
$187$	4.80310	0.351237
$188$	4.55826	0.332446
$189$	45.8537	3.33537
$190$	−12.3190	−0.893716
$191$	−17.9379	−1.29794	−0.648970	−	0.760814i	$-0.724800\pi$
$191$	−17.9379	−1.29794	−0.648970	+	0.760814i	$0.724800\pi$
$192$	3.31349	0.239130
$193$	−9.12580	−0.656890	−0.328445	−	0.944523i	$-0.606525\pi$
$193$	−9.12580	−0.656890	−0.328445	+	0.944523i	$0.606525\pi$
$194$	2.21934	0.159339
$195$	−46.9644	−3.36319
$196$	0.724327	0.0517376
$197$	−13.9604	−0.994635	−0.497317	−	0.867569i	$-0.665682\pi$
$197$	−13.9604	−0.994635	−0.497317	+	0.867569i	$0.665682\pi$
$198$	−38.3248	−2.72363
$199$	1.43132	0.101464	0.0507318	−	0.998712i	$-0.483845\pi$
$199$	1.43132	0.101464	0.0507318	+	0.998712i	$0.483845\pi$
$200$	2.32352	0.164298
$201$	29.5763	2.08615
$202$	12.0778	0.849794
$203$	11.2329	0.788396
$204$	−3.31349	−0.231990
$205$	−12.5315	−0.875237
$206$	7.26622	0.506261
$207$	−53.6532	−3.72915
$208$	5.23749	0.363155
$209$	−21.8644	−1.51239
$210$	−24.9216	−1.71975
$211$	6.70563	0.461634	0.230817	−	0.972997i	$-0.425860\pi$
$211$	6.70563	0.461634	0.230817	+	0.972997i	$0.425860\pi$
$212$	−7.07511	−0.485921
$213$	18.1151	1.24122
$214$	−12.1507	−0.830607
$215$	−22.1583	−1.51119
$216$	16.4985	1.12258
$217$	−15.7685	−1.07044
$218$	0.308244	0.0208769
$219$	−35.0425	−2.36795
$220$	12.9981	0.876334
$221$	−5.23749	−0.352312
$222$	−5.11775	−0.343481
$223$	4.80848	0.322000	0.161000	−	0.986954i	$-0.448528\pi$
$223$	4.80848	0.322000	0.161000	+	0.986954i	$0.448528\pi$
$224$	2.77927	0.185698
$225$	18.5398	1.23599
$226$	2.89087	0.192298
$227$	22.0951	1.46650	0.733252	−	0.679956i	$-0.238001\pi$
$227$	22.0951	1.46650	0.733252	+	0.679956i	$0.238001\pi$
$228$	15.0835	0.998929
$229$	−25.8732	−1.70975	−0.854873	−	0.518837i	$-0.826365\pi$
$229$	−25.8732	−1.70975	−0.854873	+	0.518837i	$0.826365\pi$
$230$	18.1968	1.19986
$231$	−44.2320	−2.91025
$232$	4.04168	0.265350
$233$	9.91008	0.649231	0.324615	−	0.945846i	$-0.394765\pi$
$233$	9.91008	0.649231	0.324615	+	0.945846i	$0.394765\pi$
$234$	41.7910	2.73196
$235$	−12.3356	−0.804684
$236$	−1.00000	−0.0650945
$237$	−44.9604	−2.92049
$238$	−2.77927	−0.180153
$239$	10.8608	0.702527	0.351264	−	0.936277i	$-0.385752\pi$
$239$	10.8608	0.702527	0.351264	+	0.936277i	$0.385752\pi$
$240$	−8.96696	−0.578815
$241$	−9.47695	−0.610464	−0.305232	−	0.952278i	$-0.598734\pi$
$241$	−9.47695	−0.610464	−0.305232	+	0.952278i	$0.598734\pi$
$242$	12.0697	0.775872
$243$	52.3279	3.35684
$244$	−11.7494	−0.752181
$245$	−1.96017	−0.125231
$246$	15.3436	0.978273
$247$	23.8419	1.51702
$248$	−5.67363	−0.360276
$249$	−54.7646	−3.47057
$250$	7.24310	0.458094
$251$	13.6641	0.862467	0.431234	−	0.902240i	$-0.358078\pi$
$251$	13.6641	0.862467	0.431234	+	0.902240i	$0.358078\pi$
$252$	22.1763	1.39698
$253$	32.2966	2.03047
$254$	17.8166	1.11791
$255$	8.96696	0.561533
$256$	1.00000	0.0625000
$257$	−11.5310	−0.719282	−0.359641	−	0.933091i	$-0.617101\pi$
$257$	−11.5310	−0.719282	−0.359641	+	0.933091i	$0.617101\pi$
$258$	27.1308	1.68909
$259$	−4.29264	−0.266732
$260$	−14.1737	−0.879016
$261$	32.2494	1.99619
$262$	−6.18551	−0.382142
$263$	−0.886939	−0.0546910	−0.0273455	−	0.999626i	$-0.508705\pi$
$263$	−0.886939	−0.0546910	−0.0273455	+	0.999626i	$0.508705\pi$
$264$	−15.9150	−0.979500
$265$	19.1467	1.17617
$266$	12.6516	0.775722
$267$	−11.5621	−0.707587
$268$	8.92603	0.545244
$269$	−3.50007	−0.213403	−0.106701	−	0.994291i	$-0.534029\pi$
$269$	−3.50007	−0.213403	−0.106701	+	0.994291i	$0.534029\pi$
$270$	−44.6482	−2.71721
$271$	−25.0603	−1.52231	−0.761153	−	0.648572i	$-0.775367\pi$
$271$	−25.0603	−1.52231	−0.761153	+	0.648572i	$0.775367\pi$
$272$	−1.00000	−0.0606339
$273$	48.2324	2.91916
$274$	0.518562	0.0313275
$275$	−11.1601	−0.672978
$276$	−22.2803	−1.34112
$277$	22.6011	1.35797	0.678984	−	0.734153i	$-0.262421\pi$
$277$	22.6011	1.35797	0.678984	+	0.734153i	$0.262421\pi$
$278$	8.21596	0.492760
$279$	−45.2710	−2.71030
$280$	−7.52125	−0.449481
$281$	16.2876	0.971634	0.485817	−	0.874060i	$-0.338522\pi$
$281$	16.2876	0.971634	0.485817	+	0.874060i	$0.338522\pi$
$282$	15.1037	0.899415
$283$	−23.6797	−1.40761	−0.703807	−	0.710391i	$-0.748518\pi$
$283$	−23.6797	−1.40761	−0.703807	+	0.710391i	$0.748518\pi$
$284$	5.46707	0.324411
$285$	−40.8189	−2.41791
$286$	−25.1562	−1.48752
$287$	12.8698	0.759682
$288$	7.97920	0.470179
$289$	1.00000	0.0588235
$290$	−10.9376	−0.642278
$291$	7.35375	0.431084
$292$	−10.5757	−0.618897
$293$	1.58524	0.0926108	0.0463054	−	0.998927i	$-0.485255\pi$
$293$	1.58524	0.0926108	0.0463054	+	0.998927i	$0.485255\pi$
$294$	2.40005	0.139974
$295$	2.70620	0.157561
$296$	−1.54452	−0.0897735
$297$	−79.2439	−4.59820
$298$	1.09633	0.0635089
$299$	−35.2176	−2.03669
$300$	7.69895	0.444499
$301$	22.7566	1.31167
$302$	−13.3241	−0.766713
$303$	40.0198	2.29907
$304$	4.55215	0.261084
$305$	31.7963	1.82065
$306$	−7.97920	−0.456140
$307$	−16.3949	−0.935704	−0.467852	−	0.883807i	$-0.654972\pi$
$307$	−16.3949	−0.935704	−0.467852	+	0.883807i	$0.654972\pi$
$308$	−13.3491	−0.760635
$309$	24.0765	1.36967
$310$	15.3540	0.872047
$311$	17.8671	1.01315	0.506574	−	0.862196i	$-0.330912\pi$
$311$	17.8671	1.01315	0.506574	+	0.862196i	$0.330912\pi$
$312$	17.3544	0.982497
$313$	29.5914	1.67261	0.836303	−	0.548267i	$-0.184712\pi$
$313$	29.5914	1.67261	0.836303	+	0.548267i	$0.184712\pi$
$314$	−24.4710	−1.38098
$315$	−60.0135	−3.38138
$316$	−13.5689	−0.763311
$317$	−6.93871	−0.389717	−0.194858	−	0.980831i	$-0.562425\pi$
$317$	−6.93871	−0.389717	−0.194858	+	0.980831i	$0.562425\pi$
$318$	−23.4433	−1.31463
$319$	−19.4126	−1.08690
$320$	−2.70620	−0.151281
$321$	−40.2613	−2.24717
$322$	−18.6882	−1.04145
$323$	−4.55215	−0.253288
$324$	30.7300	1.70722
$325$	12.1694	0.675037
$326$	−15.4619	−0.856356
$327$	1.02136	0.0564816
$328$	4.63066	0.255685
$329$	12.6686	0.698444
$330$	43.0692	2.37088
$331$	−3.93442	−0.216255	−0.108128	−	0.994137i	$-0.534485\pi$
$331$	−3.93442	−0.216255	−0.108128	+	0.994137i	$0.534485\pi$
$332$	−16.5278	−0.907081
$333$	−12.3240	−0.675353
$334$	−16.6344	−0.910195
$335$	−24.1556	−1.31976
$336$	9.20907	0.502396
$337$	1.20213	0.0654844	0.0327422	−	0.999464i	$-0.489576\pi$
$337$	1.20213	0.0654844	0.0327422	+	0.999464i	$0.489576\pi$
$338$	14.4313	0.784961
$339$	9.57885	0.520252
$340$	2.70620	0.146764
$341$	27.2510	1.47572
$342$	36.3225	1.96410
$343$	−17.4418	−0.941767
$344$	8.18798	0.441467
$345$	60.2950	3.24617
$346$	−21.0308	−1.13062
$347$	23.3113	1.25141	0.625707	−	0.780058i	$-0.284810\pi$
$347$	23.3113	1.25141	0.625707	+	0.780058i	$0.284810\pi$
$348$	13.3921	0.717890
$349$	−27.2181	−1.45695	−0.728476	−	0.685071i	$-0.759771\pi$
$349$	−27.2181	−1.45695	−0.728476	+	0.685071i	$0.759771\pi$
$350$	6.45768	0.345177
$351$	86.4108	4.61227
$352$	−4.80310	−0.256006
$353$	−2.39015	−0.127215	−0.0636074	−	0.997975i	$-0.520261\pi$
$353$	−2.39015	−0.127215	−0.0636074	+	0.997975i	$0.520261\pi$
$354$	−3.31349	−0.176110
$355$	−14.7950	−0.785236
$356$	−3.48939	−0.184938
$357$	−9.20907	−0.487395
$358$	16.7584	0.885711
$359$	−6.36929	−0.336158	−0.168079	−	0.985773i	$-0.553756\pi$
$359$	−6.36929	−0.336158	−0.168079	+	0.985773i	$0.553756\pi$
$360$	−21.5933	−1.13807
$361$	1.72207	0.0906354
$362$	18.3945	0.966795
$363$	39.9929	2.09908
$364$	14.5564	0.762962
$365$	28.6200	1.49804
$366$	−38.9316	−2.03499
$367$	22.9071	1.19574	0.597871	−	0.801592i	$-0.296014\pi$
$367$	22.9071	1.19574	0.597871	+	0.801592i	$0.296014\pi$
$368$	−6.72413	−0.350520
$369$	36.9489	1.92348
$370$	4.17979	0.217297
$371$	−19.6636	−1.02088
$372$	−18.7995	−0.974709
$373$	7.82461	0.405143	0.202571	−	0.979267i	$-0.435070\pi$
$373$	7.82461	0.405143	0.202571	+	0.979267i	$0.435070\pi$
$374$	4.80310	0.248362
$375$	23.9999	1.23935
$376$	4.55826	0.235074
$377$	21.1683	1.09022
$378$	45.8537	2.35846
$379$	29.7075	1.52597	0.762985	−	0.646416i	$-0.223733\pi$
$379$	29.7075	1.52597	0.762985	+	0.646416i	$0.223733\pi$
$380$	−12.3190	−0.631953
$381$	59.0351	3.02446
$382$	−17.9379	−0.917783
$383$	−15.4888	−0.791442	−0.395721	−	0.918371i	$-0.629505\pi$
$383$	−15.4888	−0.791442	−0.395721	+	0.918371i	$0.629505\pi$
$384$	3.31349	0.169091
$385$	36.1253	1.84112
$386$	−9.12580	−0.464491
$387$	65.3335	3.32109
$388$	2.21934	0.112670
$389$	−16.9127	−0.857509	−0.428755	−	0.903421i	$-0.641048\pi$
$389$	−16.9127	−0.857509	−0.428755	+	0.903421i	$0.641048\pi$
$390$	−46.9644	−2.37813
$391$	6.72413	0.340054
$392$	0.724327	0.0365840
$393$	−20.4956	−1.03387
$394$	−13.9604	−0.703313
$395$	36.7202	1.84759
$396$	−38.3248	−1.92590
$397$	6.43719	0.323073	0.161537	−	0.986867i	$-0.448355\pi$
$397$	6.43719	0.323073	0.161537	+	0.986867i	$0.448355\pi$
$398$	1.43132	0.0717456
$399$	41.9211	2.09868
$400$	2.32352	0.116176
$401$	25.0680	1.25183	0.625917	−	0.779890i	$-0.284725\pi$
$401$	25.0680	1.25183	0.625917	+	0.779890i	$0.284725\pi$
$402$	29.5763	1.47513
$403$	−29.7156	−1.48024
$404$	12.0778	0.600895
$405$	−83.1615	−4.13233
$406$	11.2329	0.557480
$407$	7.41849	0.367721
$408$	−3.31349	−0.164042
$409$	19.4295	0.960726	0.480363	−	0.877070i	$-0.340505\pi$
$409$	19.4295	0.960726	0.480363	+	0.877070i	$0.340505\pi$
$410$	−12.5315	−0.618886
$411$	1.71825	0.0847550
$412$	7.26622	0.357981
$413$	−2.77927	−0.136759
$414$	−53.6532	−2.63691
$415$	44.7275	2.19559
$416$	5.23749	0.256789
$417$	27.2235	1.33314
$418$	−21.8644	−1.06942
$419$	−13.1930	−0.644519	−0.322260	−	0.946651i	$-0.604442\pi$
$419$	−13.1930	−0.644519	−0.322260	+	0.946651i	$0.604442\pi$
$420$	−24.9216	−1.21605
$421$	−35.9713	−1.75313	−0.876566	−	0.481282i	$-0.840171\pi$
$421$	−35.9713	−1.75313	−0.876566	+	0.481282i	$0.840171\pi$
$422$	6.70563	0.326425
$423$	36.3713	1.76843
$424$	−7.07511	−0.343598
$425$	−2.32352	−0.112707
$426$	18.1151	0.877678
$427$	−32.6548	−1.58028
$428$	−12.1507	−0.587328
$429$	−83.3547	−4.02440
$430$	−22.1583	−1.06857
$431$	−26.7501	−1.28851	−0.644254	−	0.764812i	$-0.722832\pi$
$431$	−26.7501	−1.28851	−0.644254	+	0.764812i	$0.722832\pi$
$432$	16.4985	0.793784
$433$	19.2803	0.926550	0.463275	−	0.886214i	$-0.346674\pi$
$433$	19.2803	0.926550	0.463275	+	0.886214i	$0.346674\pi$
$434$	−15.7685	−0.756914
$435$	−36.2416	−1.73765
$436$	0.308244	0.0147622
$437$	−30.6093	−1.46424
$438$	−35.0425	−1.67439
$439$	19.7939	0.944711	0.472356	−	0.881408i	$-0.343404\pi$
$439$	19.7939	0.944711	0.472356	+	0.881408i	$0.343404\pi$
$440$	12.9981	0.619662
$441$	5.77954	0.275216
$442$	−5.23749	−0.249122
$443$	15.3959	0.731484	0.365742	−	0.930716i	$-0.380815\pi$
$443$	15.3959	0.731484	0.365742	+	0.930716i	$0.380815\pi$
$444$	−5.11775	−0.242878
$445$	9.44300	0.447641
$446$	4.80848	0.227688
$447$	3.63268	0.171820
$448$	2.77927	0.131308
$449$	24.6717	1.16433	0.582166	−	0.813070i	$-0.302205\pi$
$449$	24.6717	1.16433	0.582166	+	0.813070i	$0.302205\pi$
$450$	18.5398	0.873975
$451$	−22.2415	−1.04731
$452$	2.89087	0.135975
$453$	−44.1491	−2.07430
$454$	22.0951	1.03698
$455$	−39.3925	−1.84675
$456$	15.0835	0.706349
$457$	31.4621	1.47173	0.735867	−	0.677126i	$-0.236775\pi$
$457$	31.4621	1.47173	0.735867	+	0.677126i	$0.236775\pi$
$458$	−25.8732	−1.20897
$459$	−16.4985	−0.770084
$460$	18.1968	0.848432
$461$	−20.5614	−0.957641	−0.478821	−	0.877913i	$-0.658936\pi$
$461$	−20.5614	−0.957641	−0.478821	+	0.877913i	$0.658936\pi$
$462$	−44.2320	−2.05786
$463$	−15.6757	−0.728510	−0.364255	−	0.931299i	$-0.618676\pi$
$463$	−15.6757	−0.728510	−0.364255	+	0.931299i	$0.618676\pi$
$464$	4.04168	0.187630
$465$	50.8752	2.35928
$466$	9.91008	0.459076
$467$	25.0062	1.15715	0.578575	−	0.815629i	$-0.303609\pi$
$467$	25.0062	1.15715	0.578575	+	0.815629i	$0.303609\pi$
$468$	41.7910	1.93179
$469$	24.8078	1.14552
$470$	−12.3356	−0.568997
$471$	−81.0843	−3.73617
$472$	−1.00000	−0.0460287
$473$	−39.3277	−1.80829
$474$	−44.9604	−2.06510
$475$	10.5770	0.485306
$476$	−2.77927	−0.127388
$477$	−56.4537	−2.58484
$478$	10.8608	0.496762
$479$	31.4556	1.43724	0.718621	−	0.695402i	$-0.244774\pi$
$479$	31.4556	1.43724	0.718621	+	0.695402i	$0.244774\pi$
$480$	−8.96696	−0.409284
$481$	−8.08942	−0.368846
$482$	−9.47695	−0.431663
$483$	−61.9230	−2.81759
$484$	12.0697	0.548624
$485$	−6.00597	−0.272717
$486$	52.3279	2.37364
$487$	4.90262	0.222159	0.111080	−	0.993812i	$-0.464569\pi$
$487$	4.90262	0.222159	0.111080	+	0.993812i	$0.464569\pi$
$488$	−11.7494	−0.531872
$489$	−51.2328	−2.31683
$490$	−1.96017	−0.0885516
$491$	18.8991	0.852906	0.426453	−	0.904510i	$-0.359763\pi$
$491$	18.8991	0.852906	0.426453	+	0.904510i	$0.359763\pi$
$492$	15.3436	0.691744
$493$	−4.04168	−0.182028
$494$	23.8419	1.07270
$495$	103.715	4.66163
$496$	−5.67363	−0.254754
$497$	15.1944	0.681564
$498$	−54.7646	−2.45406
$499$	25.1827	1.12733	0.563667	−	0.826002i	$-0.309390\pi$
$499$	25.1827	1.12733	0.563667	+	0.826002i	$0.309390\pi$
$500$	7.24310	0.323921
$501$	−55.1179	−2.46249
$502$	13.6641	0.609856
$503$	−23.3585	−1.04150	−0.520752	−	0.853708i	$-0.674348\pi$
$503$	−23.3585	−1.04150	−0.520752	+	0.853708i	$0.674348\pi$
$504$	22.1763	0.987812
$505$	−32.6850	−1.45447
$506$	32.2966	1.43576
$507$	47.8180	2.12367
$508$	17.8166	0.790484
$509$	22.2889	0.987936	0.493968	−	0.869480i	$-0.335546\pi$
$509$	22.2889	0.987936	0.493968	+	0.869480i	$0.335546\pi$
$510$	8.96696	0.397064
$511$	−29.3927	−1.30026
$512$	1.00000	0.0441942
$513$	75.1037	3.31591
$514$	−11.5310	−0.508609
$515$	−19.6638	−0.866492
$516$	27.1308	1.19437
$517$	−21.8938	−0.962887
$518$	−4.29264	−0.188608
$519$	−69.6853	−3.05885
$520$	−14.1737	−0.621558
$521$	14.6776	0.643037	0.321518	−	0.946903i	$-0.395807\pi$
$521$	14.6776	0.643037	0.321518	+	0.946903i	$0.395807\pi$
$522$	32.2494	1.41152
$523$	39.4212	1.72377	0.861885	−	0.507103i	$-0.169284\pi$
$523$	39.4212	1.72377	0.861885	+	0.507103i	$0.169284\pi$
$524$	−6.18551	−0.270215
$525$	21.3974	0.933860
$526$	−0.886939	−0.0386724
$527$	5.67363	0.247147
$528$	−15.9150	−0.692611
$529$	22.2139	0.965823
$530$	19.1467	0.831678
$531$	−7.97920	−0.346268
$532$	12.6516	0.548518
$533$	24.2530	1.05052
$534$	−11.5621	−0.500339
$535$	32.8823	1.42163
$536$	8.92603	0.385546
$537$	55.5288	2.39625
$538$	−3.50007	−0.150899
$539$	−3.47901	−0.149852
$540$	−44.6482	−1.92135
$541$	33.3191	1.43250	0.716250	−	0.697843i	$-0.245857\pi$
$541$	33.3191	1.43250	0.716250	+	0.697843i	$0.245857\pi$
$542$	−25.0603	−1.07643
$543$	60.9501	2.61562
$544$	−1.00000	−0.0428746
$545$	−0.834171	−0.0357320
$546$	48.2324	2.06416
$547$	−37.6603	−1.61024	−0.805119	−	0.593113i	$-0.797899\pi$
$547$	−37.6603	−1.61024	−0.805119	+	0.593113i	$0.797899\pi$
$548$	0.518562	0.0221519
$549$	−93.7511	−4.00120
$550$	−11.1601	−0.475867
$551$	18.3984	0.783796
$552$	−22.2803	−0.948313
$553$	−37.7116	−1.60366
$554$	22.6011	0.960229
$555$	13.8497	0.587886
$556$	8.21596	0.348434
$557$	14.0903	0.597027	0.298514	−	0.954405i	$-0.403509\pi$
$557$	14.0903	0.597027	0.298514	+	0.954405i	$0.403509\pi$
$558$	−45.2710	−1.91647
$559$	42.8845	1.81382
$560$	−7.52125	−0.317831
$561$	15.9150	0.671932
$562$	16.2876	0.687049
$563$	21.9788	0.926298	0.463149	−	0.886280i	$-0.346720\pi$
$563$	21.9788	0.926298	0.463149	+	0.886280i	$0.346720\pi$
$564$	15.1037	0.635982
$565$	−7.82326	−0.329127
$566$	−23.6797	−0.995333
$567$	85.4068	3.58675
$568$	5.46707	0.229393
$569$	−32.3931	−1.35799	−0.678995	−	0.734143i	$-0.737584\pi$
$569$	−32.3931	−1.35799	−0.678995	+	0.734143i	$0.737584\pi$
$570$	−40.8189	−1.70972
$571$	−25.4080	−1.06329	−0.531646	−	0.846967i	$-0.678426\pi$
$571$	−25.4080	−1.06329	−0.531646	+	0.846967i	$0.678426\pi$
$572$	−25.1562	−1.05183
$573$	−59.4370	−2.48302
$574$	12.8698	0.537176
$575$	−15.6236	−0.651551
$576$	7.97920	0.332466
$577$	−12.3890	−0.515761	−0.257880	−	0.966177i	$-0.583024\pi$
$577$	−12.3890	−0.515761	−0.257880	+	0.966177i	$0.583024\pi$
$578$	1.00000	0.0415945
$579$	−30.2382	−1.25666
$580$	−10.9376	−0.454159
$581$	−45.9352	−1.90571
$582$	7.35375	0.304823
$583$	33.9824	1.40741
$584$	−10.5757	−0.437626
$585$	−113.095	−4.67589
$586$	1.58524	0.0654857
$587$	2.68519	0.110830	0.0554149	−	0.998463i	$-0.482352\pi$
$587$	2.68519	0.110830	0.0554149	+	0.998463i	$0.482352\pi$
$588$	2.40005	0.0989763
$589$	−25.8272	−1.06419
$590$	2.70620	0.111412
$591$	−46.2575	−1.90278
$592$	−1.54452	−0.0634795
$593$	5.07615	0.208453	0.104226	−	0.994554i	$-0.466763\pi$
$593$	5.07615	0.208453	0.104226	+	0.994554i	$0.466763\pi$
$594$	−79.2439	−3.25142
$595$	7.52125	0.308341
$596$	1.09633	0.0449075
$597$	4.74266	0.194104
$598$	−35.2176	−1.44015
$599$	−15.8710	−0.648471	−0.324236	−	0.945976i	$-0.605107\pi$
$599$	−15.8710	−0.648471	−0.324236	+	0.945976i	$0.605107\pi$
$600$	7.69895	0.314308
$601$	−31.2488	−1.27467	−0.637333	−	0.770589i	$-0.719962\pi$
$601$	−31.2488	−1.27467	−0.637333	+	0.770589i	$0.719962\pi$
$602$	22.7566	0.927490
$603$	71.2225	2.90041
$604$	−13.3241	−0.542148
$605$	−32.6631	−1.32794
$606$	40.0198	1.62569
$607$	15.6997	0.637230	0.318615	−	0.947884i	$-0.396782\pi$
$607$	15.6997	0.637230	0.318615	+	0.947884i	$0.396782\pi$
$608$	4.55215	0.184614
$609$	37.2201	1.50824
$610$	31.7963	1.28740
$611$	23.8739	0.965833
$612$	−7.97920	−0.322540
$613$	−0.814892	−0.0329132	−0.0164566	−	0.999865i	$-0.505239\pi$
$613$	−0.814892	−0.0329132	−0.0164566	+	0.999865i	$0.505239\pi$
$614$	−16.3949	−0.661643
$615$	−41.5229	−1.67436
$616$	−13.3491	−0.537850
$617$	14.6155	0.588396	0.294198	−	0.955744i	$-0.404947\pi$
$617$	14.6155	0.588396	0.294198	+	0.955744i	$0.404947\pi$
$618$	24.0765	0.968500
$619$	−18.6518	−0.749679	−0.374839	−	0.927090i	$-0.622302\pi$
$619$	−18.6518	−0.749679	−0.374839	+	0.927090i	$0.622302\pi$
$620$	15.3540	0.616631
$621$	−110.938	−4.45179
$622$	17.8671	0.716404
$623$	−9.69796	−0.388541
$624$	17.3544	0.694731
$625$	−31.2189	−1.24875
$626$	29.5914	1.18271
$627$	−72.4475	−2.89327
$628$	−24.4710	−0.976499
$629$	1.54452	0.0615841
$630$	−60.0135	−2.39100
$631$	−43.7524	−1.74176	−0.870879	−	0.491498i	$-0.836449\pi$
$631$	−43.7524	−1.74176	−0.870879	+	0.491498i	$0.836449\pi$
$632$	−13.5689	−0.539742
$633$	22.2190	0.883126
$634$	−6.93871	−0.275571
$635$	−48.2153	−1.91337
$636$	−23.4433	−0.929587
$637$	3.79366	0.150310
$638$	−19.4126	−0.768552
$639$	43.6228	1.72569
$640$	−2.70620	−0.106972
$641$	2.26929	0.0896316	0.0448158	−	0.998995i	$-0.485730\pi$
$641$	2.26929	0.0896316	0.0448158	+	0.998995i	$0.485730\pi$
$642$	−40.2613	−1.58899
$643$	24.4295	0.963407	0.481703	−	0.876334i	$-0.340018\pi$
$643$	24.4295	0.963407	0.481703	+	0.876334i	$0.340018\pi$
$644$	−18.6882	−0.736417
$645$	−73.4213	−2.89096
$646$	−4.55215	−0.179102
$647$	7.30369	0.287138	0.143569	−	0.989640i	$-0.454142\pi$
$647$	7.30369	0.287138	0.143569	+	0.989640i	$0.454142\pi$
$648$	30.7300	1.20719
$649$	4.80310	0.188538
$650$	12.1694	0.477323
$651$	−52.2488	−2.04779
$652$	−15.4619	−0.605535
$653$	15.3117	0.599192	0.299596	−	0.954066i	$-0.403148\pi$
$653$	15.3117	0.599192	0.299596	+	0.954066i	$0.403148\pi$
$654$	1.02136	0.0399385
$655$	16.7392	0.654056
$656$	4.63066	0.180797
$657$	−84.3857	−3.29220
$658$	12.6686	0.493875
$659$	−18.7914	−0.732010	−0.366005	−	0.930613i	$-0.619275\pi$
$659$	−18.7914	−0.732010	−0.366005	+	0.930613i	$0.619275\pi$
$660$	43.0692	1.67646
$661$	−0.971143	−0.0377731	−0.0188865	−	0.999822i	$-0.506012\pi$
$661$	−0.971143	−0.0377731	−0.0188865	+	0.999822i	$0.506012\pi$
$662$	−3.93442	−0.152915
$663$	−17.3544	−0.673988
$664$	−16.5278	−0.641403
$665$	−34.2379	−1.32769
$666$	−12.3240	−0.477547
$667$	−27.1768	−1.05229
$668$	−16.6344	−0.643605
$669$	15.9328	0.615999
$670$	−24.1556	−0.933213
$671$	56.4337	2.17860
$672$	9.20907	0.355247
$673$	41.5834	1.60292	0.801461	−	0.598047i	$-0.204056\pi$
$673$	41.5834	1.60292	0.801461	+	0.598047i	$0.204056\pi$
$674$	1.20213	0.0463045
$675$	38.3346	1.47550
$676$	14.4313	0.555051
$677$	34.1994	1.31439	0.657195	−	0.753720i	$-0.271743\pi$
$677$	34.1994	1.31439	0.657195	+	0.753720i	$0.271743\pi$
$678$	9.57885	0.367873
$679$	6.16813	0.236711
$680$	2.70620	0.103778
$681$	73.2119	2.80549
$682$	27.2510	1.04349
$683$	9.09733	0.348100	0.174050	−	0.984737i	$-0.444315\pi$
$683$	9.09733	0.348100	0.174050	+	0.984737i	$0.444315\pi$
$684$	36.3225	1.38883
$685$	−1.40333	−0.0536186
$686$	−17.4418	−0.665930
$687$	−85.7303	−3.27082
$688$	8.18798	0.312164
$689$	−37.0558	−1.41172
$690$	60.2950	2.29539
$691$	−16.9525	−0.644902	−0.322451	−	0.946586i	$-0.604507\pi$
$691$	−16.9525	−0.644902	−0.322451	+	0.946586i	$0.604507\pi$
$692$	−21.0308	−0.799472
$693$	−106.515	−4.04617
$694$	23.3113	0.884884
$695$	−22.2340	−0.843384
$696$	13.3921	0.507625
$697$	−4.63066	−0.175399
$698$	−27.2181	−1.03022
$699$	32.8369	1.24201
$700$	6.45768	0.244077
$701$	26.6355	1.00601	0.503004	−	0.864284i	$-0.332228\pi$
$701$	26.6355	1.00601	0.503004	+	0.864284i	$0.332228\pi$
$702$	86.4108	3.26136
$703$	−7.03090	−0.265175
$704$	−4.80310	−0.181023
$705$	−40.8738	−1.53939
$706$	−2.39015	−0.0899545
$707$	33.5675	1.26244
$708$	−3.31349	−0.124528
$709$	23.7582	0.892259	0.446130	−	0.894968i	$-0.352802\pi$
$709$	23.7582	0.892259	0.446130	+	0.894968i	$0.352802\pi$
$710$	−14.7950	−0.555246
$711$	−108.269	−4.06040
$712$	−3.48939	−0.130771
$713$	38.1502	1.42874
$714$	−9.20907	−0.344641
$715$	68.0777	2.54596
$716$	16.7584	0.626292
$717$	35.9871	1.34396
$718$	−6.36929	−0.237700
$719$	38.2464	1.42635	0.713175	−	0.700986i	$-0.247256\pi$
$719$	38.2464	1.42635	0.713175	+	0.700986i	$0.247256\pi$
$720$	−21.5933	−0.804735
$721$	20.1948	0.752092
$722$	1.72207	0.0640889
$723$	−31.4018	−1.16784
$724$	18.3945	0.683628
$725$	9.39092	0.348770
$726$	39.9929	1.48428
$727$	43.8318	1.62563	0.812816	−	0.582520i	$-0.197933\pi$
$727$	43.8318	1.62563	0.812816	+	0.582520i	$0.197933\pi$
$728$	14.5564	0.539496
$729$	81.1978	3.00733
$730$	28.6200	1.05927
$731$	−8.18798	−0.302844
$732$	−38.9316	−1.43895
$733$	−49.1241	−1.81444	−0.907220	−	0.420656i	$-0.861800\pi$
$733$	−49.1241	−1.81444	−0.907220	+	0.420656i	$0.861800\pi$
$734$	22.9071	0.845517
$735$	−6.49501	−0.239572
$736$	−6.72413	−0.247855
$737$	−42.8726	−1.57923
$738$	36.9489	1.36011
$739$	−32.5963	−1.19907	−0.599537	−	0.800347i	$-0.704648\pi$
$739$	−32.5963	−1.19907	−0.599537	+	0.800347i	$0.704648\pi$
$740$	4.17979	0.153652
$741$	78.9997	2.90213
$742$	−19.6636	−0.721874
$743$	24.1852	0.887268	0.443634	−	0.896208i	$-0.353689\pi$
$743$	24.1852	0.887268	0.443634	+	0.896208i	$0.353689\pi$
$744$	−18.7995	−0.689223
$745$	−2.96690	−0.108699
$746$	7.82461	0.286479
$747$	−131.879	−4.82518
$748$	4.80310	0.175619
$749$	−33.7701	−1.23393
$750$	23.9999	0.876353
$751$	14.8227	0.540886	0.270443	−	0.962736i	$-0.412830\pi$
$751$	14.8227	0.540886	0.270443	+	0.962736i	$0.412830\pi$
$752$	4.55826	0.166223
$753$	45.2757	1.64994
$754$	21.1683	0.770904
$755$	36.0576	1.31227
$756$	45.8537	1.66768
$757$	−37.4961	−1.36282	−0.681409	−	0.731903i	$-0.738632\pi$
$757$	−37.4961	−1.36282	−0.681409	+	0.731903i	$0.738632\pi$
$758$	29.7075	1.07902
$759$	107.015	3.88438
$760$	−12.3190	−0.446858
$761$	27.8254	1.00867	0.504335	−	0.863508i	$-0.331738\pi$
$761$	27.8254	1.00867	0.504335	+	0.863508i	$0.331738\pi$
$762$	59.0351	2.13862
$763$	0.856694	0.0310144
$764$	−17.9379	−0.648970
$765$	21.5933	0.780707
$766$	−15.4888	−0.559634
$767$	−5.23749	−0.189115
$768$	3.31349	0.119565
$769$	−7.97564	−0.287609	−0.143804	−	0.989606i	$-0.545934\pi$
$769$	−7.97564	−0.287609	−0.143804	+	0.989606i	$0.545934\pi$
$770$	36.1253	1.30187
$771$	−38.2077	−1.37602
$772$	−9.12580	−0.328445
$773$	−15.1752	−0.545816	−0.272908	−	0.962040i	$-0.587985\pi$
$773$	−15.1752	−0.545816	−0.272908	+	0.962040i	$0.587985\pi$
$774$	65.3335	2.34837
$775$	−13.1828	−0.473540
$776$	2.21934	0.0796696
$777$	−14.2236	−0.510269
$778$	−16.9127	−0.606351
$779$	21.0794	0.755249
$780$	−46.9644	−1.68159
$781$	−26.2589	−0.939616
$782$	6.72413	0.240454
$783$	66.6817	2.38301
$784$	0.724327	0.0258688
$785$	66.2234	2.36361
$786$	−20.4956	−0.731054
$787$	−2.37088	−0.0845129	−0.0422564	−	0.999107i	$-0.513455\pi$
$787$	−2.37088	−0.0845129	−0.0422564	+	0.999107i	$0.513455\pi$
$788$	−13.9604	−0.497317
$789$	−2.93886	−0.104626
$790$	36.7202	1.30645
$791$	8.03449	0.285674
$792$	−38.3248	−1.36181
$793$	−61.5376	−2.18527
$794$	6.43719	0.228447
$795$	63.4422	2.25006
$796$	1.43132	0.0507318
$797$	−2.49959	−0.0885399	−0.0442699	−	0.999020i	$-0.514096\pi$
$797$	−2.49959	−0.0885399	−0.0442699	+	0.999020i	$0.514096\pi$
$798$	41.9211	1.48399
$799$	−4.55826	−0.161260
$800$	2.32352	0.0821488
$801$	−27.8426	−0.983769
$802$	25.0680	0.885180
$803$	50.7961	1.79256
$804$	29.5763	1.04308
$805$	50.5739	1.78250
$806$	−29.7156	−1.04669
$807$	−11.5974	−0.408249
$808$	12.0778	0.424897
$809$	17.8354	0.627061	0.313530	−	0.949578i	$-0.398488\pi$
$809$	17.8354	0.627061	0.313530	+	0.949578i	$0.398488\pi$
$810$	−83.1615	−2.92200
$811$	32.6632	1.14696	0.573480	−	0.819219i	$-0.305593\pi$
$811$	32.6632	1.14696	0.573480	+	0.819219i	$0.305593\pi$
$812$	11.2329	0.394198
$813$	−83.0371	−2.91224
$814$	7.41849	0.260018
$815$	41.8430	1.46570
$816$	−3.31349	−0.115995
$817$	37.2729	1.30402
$818$	19.4295	0.679336
$819$	116.148	4.05855
$820$	−12.5315	−0.437618
$821$	−11.6576	−0.406852	−0.203426	−	0.979090i	$-0.565208\pi$
$821$	−11.6576	−0.406852	−0.203426	+	0.979090i	$0.565208\pi$
$822$	1.71825	0.0599308
$823$	16.7964	0.585486	0.292743	−	0.956191i	$-0.405432\pi$
$823$	16.7964	0.585486	0.292743	+	0.956191i	$0.405432\pi$
$824$	7.26622	0.253131
$825$	−36.9788	−1.28744
$826$	−2.77927	−0.0967031
$827$	11.4660	0.398710	0.199355	−	0.979927i	$-0.436115\pi$
$827$	11.4660	0.398710	0.199355	+	0.979927i	$0.436115\pi$
$828$	−53.6532	−1.86458
$829$	29.6499	1.02978	0.514892	−	0.857255i	$-0.327832\pi$
$829$	29.6499	1.02978	0.514892	+	0.857255i	$0.327832\pi$
$830$	44.7275	1.55251
$831$	74.8884	2.59785
$832$	5.23749	0.181577
$833$	−0.724327	−0.0250964
$834$	27.2235	0.942671
$835$	45.0161	1.55785
$836$	−21.8644	−0.756197
$837$	−93.6064	−3.23551
$838$	−13.1930	−0.455744
$839$	17.7833	0.613947	0.306973	−	0.951718i	$-0.400684\pi$
$839$	17.7833	0.613947	0.306973	+	0.951718i	$0.400684\pi$
$840$	−24.9216	−0.859876
$841$	−12.6648	−0.436717
$842$	−35.9713	−1.23965
$843$	53.9686	1.85878
$844$	6.70563	0.230817
$845$	−39.0541	−1.34350
$846$	36.3713	1.25047
$847$	33.5450	1.15262
$848$	−7.07511	−0.242960
$849$	−78.4625	−2.69283
$850$	−2.32352	−0.0796960
$851$	10.3856	0.356013
$852$	18.1151	0.620612
$853$	−31.7973	−1.08872	−0.544360	−	0.838852i	$-0.683227\pi$
$853$	−31.7973	−1.08872	−0.544360	+	0.838852i	$0.683227\pi$
$854$	−32.6548	−1.11743
$855$	−98.2959	−3.36165
$856$	−12.1507	−0.415304
$857$	−7.80779	−0.266709	−0.133354	−	0.991068i	$-0.542575\pi$
$857$	−7.80779	−0.266709	−0.133354	+	0.991068i	$0.542575\pi$
$858$	−83.3547	−2.84568
$859$	−34.2617	−1.16899	−0.584497	−	0.811396i	$-0.698708\pi$
$859$	−34.2617	−1.16899	−0.584497	+	0.811396i	$0.698708\pi$
$860$	−22.1583	−0.755593
$861$	42.6440	1.45330
$862$	−26.7501	−0.911112
$863$	−5.69444	−0.193841	−0.0969206	−	0.995292i	$-0.530899\pi$
$863$	−5.69444	−0.193841	−0.0969206	+	0.995292i	$0.530899\pi$
$864$	16.4985	0.561290
$865$	56.9136	1.93512
$866$	19.2803	0.655170
$867$	3.31349	0.112532
$868$	−15.7685	−0.535219
$869$	65.1728	2.21084
$870$	−36.2416	−1.22871
$871$	46.7500	1.58406
$872$	0.308244	0.0104385
$873$	17.7085	0.599343
$874$	−30.6093	−1.03537
$875$	20.1305	0.680535
$876$	−35.0425	−1.18398
$877$	−40.4438	−1.36569	−0.682845	−	0.730563i	$-0.739258\pi$
$877$	−40.4438	−1.36569	−0.682845	+	0.730563i	$0.739258\pi$
$878$	19.7939	0.668012
$879$	5.25268	0.177168
$880$	12.9981	0.438167
$881$	−26.9540	−0.908103	−0.454051	−	0.890976i	$-0.650022\pi$
$881$	−26.9540	−0.908103	−0.454051	+	0.890976i	$0.650022\pi$
$882$	5.77954	0.194607
$883$	3.96901	0.133568	0.0667839	−	0.997767i	$-0.478726\pi$
$883$	3.96901	0.133568	0.0667839	+	0.997767i	$0.478726\pi$
$884$	−5.23749	−0.176156
$885$	8.96696	0.301421
$886$	15.3959	0.517237
$887$	29.0018	0.973786	0.486893	−	0.873462i	$-0.338130\pi$
$887$	29.0018	0.973786	0.486893	+	0.873462i	$0.338130\pi$
$888$	−5.11775	−0.171741
$889$	49.5171	1.66075
$890$	9.44300	0.316530
$891$	−147.599	−4.94475
$892$	4.80848	0.161000
$893$	20.7499	0.694369
$894$	3.63268	0.121495
$895$	−45.3517	−1.51594
$896$	2.77927	0.0928488
$897$	−116.693	−3.89627
$898$	24.6717	0.823307
$899$	−22.9310	−0.764792
$900$	18.5398	0.617993
$901$	7.07511	0.235706
$902$	−22.2415	−0.740561
$903$	75.4037	2.50928
$904$	2.89087	0.0961488
$905$	−49.7793	−1.65472
$906$	−44.1491	−1.46675
$907$	−29.9448	−0.994302	−0.497151	−	0.867664i	$-0.665620\pi$
$907$	−29.9448	−0.994302	−0.497151	+	0.867664i	$0.665620\pi$
$908$	22.0951	0.733252
$909$	96.3714	3.19644
$910$	−39.3925	−1.30585
$911$	−31.8190	−1.05421	−0.527105	−	0.849800i	$-0.676722\pi$
$911$	−31.8190	−1.05421	−0.527105	+	0.849800i	$0.676722\pi$
$912$	15.0835	0.499464
$913$	79.3846	2.62725
$914$	31.4621	1.04067
$915$	105.357	3.48299
$916$	−25.8732	−0.854873
$917$	−17.1912	−0.567703
$918$	−16.4985	−0.544532
$919$	15.5525	0.513030	0.256515	−	0.966540i	$-0.417426\pi$
$919$	15.5525	0.513030	0.256515	+	0.966540i	$0.417426\pi$
$920$	18.1968	0.599932
$921$	−54.3242	−1.79004
$922$	−20.5614	−0.677155
$923$	28.6337	0.942491
$924$	−44.2320	−1.45513
$925$	−3.58872	−0.117997
$926$	−15.6757	−0.515135
$927$	57.9786	1.90427
$928$	4.04168	0.132675
$929$	−0.563389	−0.0184842	−0.00924209	−	0.999957i	$-0.502942\pi$
$929$	−0.563389	−0.0184842	−0.00924209	+	0.999957i	$0.502942\pi$
$930$	50.8752	1.66826
$931$	3.29724	0.108063
$932$	9.91008	0.324615
$933$	59.2023	1.93820
$934$	25.0062	0.818228
$935$	−12.9981	−0.425085
$936$	41.7910	1.36598
$937$	11.1404	0.363942	0.181971	−	0.983304i	$-0.441752\pi$
$937$	11.1404	0.363942	0.181971	+	0.983304i	$0.441752\pi$
$938$	24.8078	0.810004
$939$	98.0508	3.19977
$940$	−12.3356	−0.402342
$941$	−4.54739	−0.148241	−0.0741203	−	0.997249i	$-0.523615\pi$
$941$	−4.54739	−0.148241	−0.0741203	+	0.997249i	$0.523615\pi$
$942$	−81.0843	−2.64187
$943$	−31.1371	−1.01396
$944$	−1.00000	−0.0325472
$945$	−124.089	−4.03663
$946$	−39.3277	−1.27865
$947$	3.33037	0.108223	0.0541113	−	0.998535i	$-0.482767\pi$
$947$	3.33037	0.108223	0.0541113	+	0.998535i	$0.482767\pi$
$948$	−44.9604	−1.46025
$949$	−55.3902	−1.79804
$950$	10.5770	0.343163
$951$	−22.9913	−0.745545
$952$	−2.77927	−0.0900766
$953$	29.5502	0.957225	0.478612	−	0.878026i	$-0.341140\pi$
$953$	29.5502	0.957225	0.478612	+	0.878026i	$0.341140\pi$
$954$	−56.4537	−1.82776
$955$	48.5435	1.57083
$956$	10.8608	0.351264
$957$	−64.3234	−2.07928
$958$	31.4556	1.01628
$959$	1.44122	0.0465395
$960$	−8.96696	−0.289407
$961$	1.19009	0.0383900
$962$	−8.08942	−0.260813
$963$	−96.9531	−3.12427
$964$	−9.47695	−0.305232
$965$	24.6963	0.795000
$966$	−61.9230	−1.99234
$967$	−2.88520	−0.0927817	−0.0463908	−	0.998923i	$-0.514772\pi$
$967$	−2.88520	−0.0927817	−0.0463908	+	0.998923i	$0.514772\pi$
$968$	12.0697	0.387936
$969$	−15.0835	−0.484552
$970$	−6.00597	−0.192840
$971$	−23.9980	−0.770132	−0.385066	−	0.922889i	$-0.625821\pi$
$971$	−23.9980	−0.770132	−0.385066	+	0.922889i	$0.625821\pi$
$972$	52.3279	1.67842
$973$	22.8343	0.732035
$974$	4.90262	0.157090
$975$	40.3232	1.29138
$976$	−11.7494	−0.376091
$977$	43.6317	1.39590	0.697951	−	0.716146i	$-0.254095\pi$
$977$	43.6317	1.39590	0.697951	+	0.716146i	$0.254095\pi$
$978$	−51.2328	−1.63824
$979$	16.7599	0.535649
$980$	−1.96017	−0.0626154
$981$	2.45954	0.0785272
$982$	18.8991	0.603095
$983$	−6.33738	−0.202131	−0.101065	−	0.994880i	$-0.532225\pi$
$983$	−6.33738	−0.202131	−0.101065	+	0.994880i	$0.532225\pi$
$984$	15.3436	0.489137
$985$	37.7795	1.20376
$986$	−4.04168	−0.128713
$987$	41.9773	1.33615
$988$	23.8419	0.758510
$989$	−55.0571	−1.75071
$990$	103.715	3.29627
$991$	51.4676	1.63492	0.817461	−	0.575984i	$-0.195381\pi$
$991$	51.4676	1.63492	0.817461	+	0.575984i	$0.195381\pi$
$992$	−5.67363	−0.180138
$993$	−13.0366	−0.413705
$994$	15.1944	0.481939
$995$	−3.87344	−0.122796
$996$	−54.7646	−1.73528
$997$	23.1597	0.733475	0.366737	−	0.930325i	$-0.380475\pi$
$997$	23.1597	0.733475	0.366737	+	0.930325i	$0.380475\pi$
$998$	25.1827	0.797145
$999$	−25.4823	−0.806224

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.t.1.8	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.t.1.8	✓	8	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:	\( N \)	\(=\)	\( 2006 = 2 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.31349 q^{3} +1.00000 q^{4} -2.70620 q^{5} +3.31349 q^{6} +2.77927 q^{7} +1.00000 q^{8} +7.97920 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.31349 q^{3} +1.00000 q^{4} -2.70620 q^{5} +3.31349 q^{6} +2.77927 q^{7} +1.00000 q^{8} +7.97920 q^{9} -2.70620 q^{10} -4.80310 q^{11} +3.31349 q^{12} +5.23749 q^{13} +2.77927 q^{14} -8.96696 q^{15} +1.00000 q^{16} -1.00000 q^{17} +7.97920 q^{18} +4.55215 q^{19} -2.70620 q^{20} +9.20907 q^{21} -4.80310 q^{22} -6.72413 q^{23} +3.31349 q^{24} +2.32352 q^{25} +5.23749 q^{26} +16.4985 q^{27} +2.77927 q^{28} +4.04168 q^{29} -8.96696 q^{30} -5.67363 q^{31} +1.00000 q^{32} -15.9150 q^{33} -1.00000 q^{34} -7.52125 q^{35} +7.97920 q^{36} -1.54452 q^{37} +4.55215 q^{38} +17.3544 q^{39} -2.70620 q^{40} +4.63066 q^{41} +9.20907 q^{42} +8.18798 q^{43} -4.80310 q^{44} -21.5933 q^{45} -6.72413 q^{46} +4.55826 q^{47} +3.31349 q^{48} +0.724327 q^{49} +2.32352 q^{50} -3.31349 q^{51} +5.23749 q^{52} -7.07511 q^{53} +16.4985 q^{54} +12.9981 q^{55} +2.77927 q^{56} +15.0835 q^{57} +4.04168 q^{58} -1.00000 q^{59} -8.96696 q^{60} -11.7494 q^{61} -5.67363 q^{62} +22.1763 q^{63} +1.00000 q^{64} -14.1737 q^{65} -15.9150 q^{66} +8.92603 q^{67} -1.00000 q^{68} -22.2803 q^{69} -7.52125 q^{70} +5.46707 q^{71} +7.97920 q^{72} -10.5757 q^{73} -1.54452 q^{74} +7.69895 q^{75} +4.55215 q^{76} -13.3491 q^{77} +17.3544 q^{78} -13.5689 q^{79} -2.70620 q^{80} +30.7300 q^{81} +4.63066 q^{82} -16.5278 q^{83} +9.20907 q^{84} +2.70620 q^{85} +8.18798 q^{86} +13.3921 q^{87} -4.80310 q^{88} -3.48939 q^{89} -21.5933 q^{90} +14.5564 q^{91} -6.72413 q^{92} -18.7995 q^{93} +4.55826 q^{94} -12.3190 q^{95} +3.31349 q^{96} +2.21934 q^{97} +0.724327 q^{98} -38.3248 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 5 q^{3} + 8 q^{4} - 5 q^{5} + 5 q^{6} + 8 q^{8} + 17 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 5 * q^3 + 8 * q^4 - 5 * q^5 + 5 * q^6 + 8 * q^8 + 17 * q^9	\( 8 q + 8 q^{2} + 5 q^{3} + 8 q^{4} - 5 q^{5} + 5 q^{6} + 8 q^{8} + 17 q^{9} - 5 q^{10} - 5 q^{11} + 5 q^{12} + q^{13} + 9 q^{15} + 8 q^{16} - 8 q^{17} + 17 q^{18} + 8 q^{19} - 5 q^{20} + 13 q^{21} - 5 q^{22} - 8 q^{23} + 5 q^{24} + 29 q^{25} + q^{26} + 44 q^{27} + 20 q^{29} + 9 q^{30} + 18 q^{31} + 8 q^{32} - 23 q^{33} - 8 q^{34} + 9 q^{35} + 17 q^{36} - 7 q^{37} + 8 q^{38} + 6 q^{39} - 5 q^{40} + 12 q^{41} + 13 q^{42} - 8 q^{43} - 5 q^{44} + 5 q^{45} - 8 q^{46} + 30 q^{47} + 5 q^{48} + 28 q^{49} + 29 q^{50} - 5 q^{51} + q^{52} - 5 q^{53} + 44 q^{54} + 23 q^{55} + 13 q^{57} + 20 q^{58} - 8 q^{59} + 9 q^{60} + 12 q^{61} + 18 q^{62} + 21 q^{63} + 8 q^{64} - 52 q^{65} - 23 q^{66} - 4 q^{67} - 8 q^{68} + 24 q^{69} + 9 q^{70} + 4 q^{71} + 17 q^{72} - 18 q^{73} - 7 q^{74} - 49 q^{75} + 8 q^{76} - 13 q^{77} + 6 q^{78} - 17 q^{79} - 5 q^{80} + 12 q^{81} + 12 q^{82} + 9 q^{83} + 13 q^{84} + 5 q^{85} - 8 q^{86} + 48 q^{87} - 5 q^{88} - 12 q^{89} + 5 q^{90} + 31 q^{91} - 8 q^{92} - 3 q^{93} + 30 q^{94} - 7 q^{95} + 5 q^{96} - 11 q^{97} + 28 q^{98} - 27 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 5 * q^3 + 8 * q^4 - 5 * q^5 + 5 * q^6 + 8 * q^8 + 17 * q^9 - 5 * q^10 - 5 * q^11 + 5 * q^12 + q^13 + 9 * q^15 + 8 * q^16 - 8 * q^17 + 17 * q^18 + 8 * q^19 - 5 * q^20 + 13 * q^21 - 5 * q^22 - 8 * q^23 + 5 * q^24 + 29 * q^25 + q^26 + 44 * q^27 + 20 * q^29 + 9 * q^30 + 18 * q^31 + 8 * q^32 - 23 * q^33 - 8 * q^34 + 9 * q^35 + 17 * q^36 - 7 * q^37 + 8 * q^38 + 6 * q^39 - 5 * q^40 + 12 * q^41 + 13 * q^42 - 8 * q^43 - 5 * q^44 + 5 * q^45 - 8 * q^46 + 30 * q^47 + 5 * q^48 + 28 * q^49 + 29 * q^50 - 5 * q^51 + q^52 - 5 * q^53 + 44 * q^54 + 23 * q^55 + 13 * q^57 + 20 * q^58 - 8 * q^59 + 9 * q^60 + 12 * q^61 + 18 * q^62 + 21 * q^63 + 8 * q^64 - 52 * q^65 - 23 * q^66 - 4 * q^67 - 8 * q^68 + 24 * q^69 + 9 * q^70 + 4 * q^71 + 17 * q^72 - 18 * q^73 - 7 * q^74 - 49 * q^75 + 8 * q^76 - 13 * q^77 + 6 * q^78 - 17 * q^79 - 5 * q^80 + 12 * q^81 + 12 * q^82 + 9 * q^83 + 13 * q^84 + 5 * q^85 - 8 * q^86 + 48 * q^87 - 5 * q^88 - 12 * q^89 + 5 * q^90 + 31 * q^91 - 8 * q^92 - 3 * q^93 + 30 * q^94 - 7 * q^95 + 5 * q^96 - 11 * q^97 + 28 * q^98 - 27 * q^99

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