LMFDB - Embedded newform 2006.2.a.n.1.2

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:	$1$
Dimension:	$3$
Coefficient field:	3.3.229.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 4x - 1 $ x^3 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.86081$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.46260 q^{3} +1.00000 q^{4} -1.46260 q^{5} -1.46260 q^{6} +4.72161 q^{7} -1.00000 q^{8} -0.860806 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.46260 q^{3} +1.00000 q^{4} -1.46260 q^{5} -1.46260 q^{6} +4.72161 q^{7} -1.00000 q^{8} -0.860806 q^{9} +1.46260 q^{10} -0.860806 q^{11} +1.46260 q^{12} -6.18421 q^{13} -4.72161 q^{14} -2.13919 q^{15} +1.00000 q^{16} -1.00000 q^{17} +0.860806 q^{18} -6.72161 q^{19} -1.46260 q^{20} +6.90582 q^{21} +0.860806 q^{22} +6.64681 q^{23} -1.46260 q^{24} -2.86081 q^{25} +6.18421 q^{26} -5.64681 q^{27} +4.72161 q^{28} +2.04502 q^{29} +2.13919 q^{30} -8.24860 q^{31} -1.00000 q^{32} -1.25901 q^{33} +1.00000 q^{34} -6.90582 q^{35} -0.860806 q^{36} -7.25901 q^{37} +6.72161 q^{38} -9.04502 q^{39} +1.46260 q^{40} -7.11982 q^{41} -6.90582 q^{42} -6.39821 q^{43} -0.860806 q^{44} +1.25901 q^{45} -6.64681 q^{46} +8.11982 q^{47} +1.46260 q^{48} +15.2936 q^{49} +2.86081 q^{50} -1.46260 q^{51} -6.18421 q^{52} -10.7562 q^{53} +5.64681 q^{54} +1.25901 q^{55} -4.72161 q^{56} -9.83102 q^{57} -2.04502 q^{58} -1.00000 q^{59} -2.13919 q^{60} +7.84143 q^{61} +8.24860 q^{62} -4.06439 q^{63} +1.00000 q^{64} +9.04502 q^{65} +1.25901 q^{66} +4.11982 q^{67} -1.00000 q^{68} +9.72161 q^{69} +6.90582 q^{70} +13.3234 q^{71} +0.860806 q^{72} +2.24860 q^{73} +7.25901 q^{74} -4.18421 q^{75} -6.72161 q^{76} -4.06439 q^{77} +9.04502 q^{78} -6.38780 q^{79} -1.46260 q^{80} -5.67660 q^{81} +7.11982 q^{82} +0.860806 q^{83} +6.90582 q^{84} +1.46260 q^{85} +6.39821 q^{86} +2.99104 q^{87} +0.860806 q^{88} -3.60179 q^{89} -1.25901 q^{90} -29.1994 q^{91} +6.64681 q^{92} -12.0644 q^{93} -8.11982 q^{94} +9.83102 q^{95} -1.46260 q^{96} +14.3040 q^{97} -15.2936 q^{98} +0.740987 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 2 q^{5} - 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 2 * q^5 - 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 2 q^{5} - 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} + 2 q^{10} + 3 q^{11} + 2 q^{12} - 5 q^{13} - 3 q^{14} - 12 q^{15} + 3 q^{16} - 3 q^{17} - 3 q^{18} - 9 q^{19} - 2 q^{20} - 4 q^{21} - 3 q^{22} + 4 q^{23} - 2 q^{24} - 3 q^{25} + 5 q^{26} - q^{27} + 3 q^{28} - 13 q^{29} + 12 q^{30} - 12 q^{31} - 3 q^{32} + 5 q^{33} + 3 q^{34} + 4 q^{35} + 3 q^{36} - 13 q^{37} + 9 q^{38} - 8 q^{39} + 2 q^{40} - 7 q^{41} + 4 q^{42} - 16 q^{43} + 3 q^{44} - 5 q^{45} - 4 q^{46} + 10 q^{47} + 2 q^{48} + 14 q^{49} + 3 q^{50} - 2 q^{51} - 5 q^{52} + 2 q^{53} + q^{54} - 5 q^{55} - 3 q^{56} + 13 q^{58} - 3 q^{59} - 12 q^{60} - 2 q^{61} + 12 q^{62} - 13 q^{63} + 3 q^{64} + 8 q^{65} - 5 q^{66} - 2 q^{67} - 3 q^{68} + 18 q^{69} - 4 q^{70} + 32 q^{71} - 3 q^{72} - 6 q^{73} + 13 q^{74} + q^{75} - 9 q^{76} - 13 q^{77} + 8 q^{78} - 12 q^{79} - 2 q^{80} - 25 q^{81} + 7 q^{82} - 3 q^{83} - 4 q^{84} + 2 q^{85} + 16 q^{86} - 7 q^{87} - 3 q^{88} - 14 q^{89} + 5 q^{90} - 31 q^{91} + 4 q^{92} - 37 q^{93} - 10 q^{94} - 2 q^{96} + 15 q^{97} - 14 q^{98} + 11 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 2 * q^5 - 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 + 2 * q^10 + 3 * q^11 + 2 * q^12 - 5 * q^13 - 3 * q^14 - 12 * q^15 + 3 * q^16 - 3 * q^17 - 3 * q^18 - 9 * q^19 - 2 * q^20 - 4 * q^21 - 3 * q^22 + 4 * q^23 - 2 * q^24 - 3 * q^25 + 5 * q^26 - q^27 + 3 * q^28 - 13 * q^29 + 12 * q^30 - 12 * q^31 - 3 * q^32 + 5 * q^33 + 3 * q^34 + 4 * q^35 + 3 * q^36 - 13 * q^37 + 9 * q^38 - 8 * q^39 + 2 * q^40 - 7 * q^41 + 4 * q^42 - 16 * q^43 + 3 * q^44 - 5 * q^45 - 4 * q^46 + 10 * q^47 + 2 * q^48 + 14 * q^49 + 3 * q^50 - 2 * q^51 - 5 * q^52 + 2 * q^53 + q^54 - 5 * q^55 - 3 * q^56 + 13 * q^58 - 3 * q^59 - 12 * q^60 - 2 * q^61 + 12 * q^62 - 13 * q^63 + 3 * q^64 + 8 * q^65 - 5 * q^66 - 2 * q^67 - 3 * q^68 + 18 * q^69 - 4 * q^70 + 32 * q^71 - 3 * q^72 - 6 * q^73 + 13 * q^74 + q^75 - 9 * q^76 - 13 * q^77 + 8 * q^78 - 12 * q^79 - 2 * q^80 - 25 * q^81 + 7 * q^82 - 3 * q^83 - 4 * q^84 + 2 * q^85 + 16 * q^86 - 7 * q^87 - 3 * q^88 - 14 * q^89 + 5 * q^90 - 31 * q^91 + 4 * q^92 - 37 * q^93 - 10 * q^94 - 2 * q^96 + 15 * q^97 - 14 * q^98 + 11 * 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
$3$	1.46260	0.844432	0.422216	−	0.906495i	$-0.361252\pi$
$3$	1.46260	0.844432	0.422216	+	0.906495i	$0.361252\pi$
$4$	1.00000	0.500000
$5$	−1.46260	−0.654094	−0.327047	−	0.945008i	$-0.606054\pi$
$5$	−1.46260	−0.654094	−0.327047	+	0.945008i	$0.606054\pi$
$6$	−1.46260	−0.597103
$7$	4.72161	1.78460	0.892301	−	0.451441i	$-0.149090\pi$
$7$	4.72161	1.78460	0.892301	+	0.451441i	$0.149090\pi$
$8$	−1.00000	−0.353553
$9$	−0.860806	−0.286935
$10$	1.46260	0.462514
$11$	−0.860806	−0.259543	−0.129771	−	0.991544i	$-0.541424\pi$
$11$	−0.860806	−0.259543	−0.129771	+	0.991544i	$0.541424\pi$
$12$	1.46260	0.422216
$13$	−6.18421	−1.71519	−0.857596	−	0.514325i	$-0.828043\pi$
$13$	−6.18421	−1.71519	−0.857596	+	0.514325i	$0.828043\pi$
$14$	−4.72161	−1.26190
$15$	−2.13919	−0.552338
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.860806	0.202894
$19$	−6.72161	−1.54204	−0.771022	−	0.636809i	$-0.780254\pi$
$19$	−6.72161	−1.54204	−0.771022	+	0.636809i	$0.780254\pi$
$20$	−1.46260	−0.327047
$21$	6.90582	1.50697
$22$	0.860806	0.183524
$23$	6.64681	1.38596	0.692978	−	0.720959i	$-0.256298\pi$
$23$	6.64681	1.38596	0.692978	+	0.720959i	$0.256298\pi$
$24$	−1.46260	−0.298552
$25$	−2.86081	−0.572161
$26$	6.18421	1.21282
$27$	−5.64681	−1.08673
$28$	4.72161	0.892301
$29$	2.04502	0.379750	0.189875	−	0.981808i	$-0.439192\pi$
$29$	2.04502	0.379750	0.189875	+	0.981808i	$0.439192\pi$
$30$	2.13919	0.390562
$31$	−8.24860	−1.48149	−0.740746	−	0.671785i	$-0.765528\pi$
$31$	−8.24860	−1.48149	−0.740746	+	0.671785i	$0.765528\pi$
$32$	−1.00000	−0.176777
$33$	−1.25901	−0.219166
$34$	1.00000	0.171499
$35$	−6.90582	−1.16730
$36$	−0.860806	−0.143468
$37$	−7.25901	−1.19337	−0.596687	−	0.802474i	$-0.703517\pi$
$37$	−7.25901	−1.19337	−0.596687	+	0.802474i	$0.703517\pi$
$38$	6.72161	1.09039
$39$	−9.04502	−1.44836
$40$	1.46260	0.231257
$41$	−7.11982	−1.11193	−0.555964	−	0.831206i	$-0.687651\pi$
$41$	−7.11982	−1.11193	−0.555964	+	0.831206i	$0.687651\pi$
$42$	−6.90582	−1.06559
$43$	−6.39821	−0.975717	−0.487859	−	0.872923i	$-0.662222\pi$
$43$	−6.39821	−0.975717	−0.487859	+	0.872923i	$0.662222\pi$
$44$	−0.860806	−0.129771
$45$	1.25901	0.187683
$46$	−6.64681	−0.980018
$47$	8.11982	1.18440	0.592199	−	0.805792i	$-0.298260\pi$
$47$	8.11982	1.18440	0.592199	+	0.805792i	$0.298260\pi$
$48$	1.46260	0.211108
$49$	15.2936	2.18480
$50$	2.86081	0.404579
$51$	−1.46260	−0.204805
$52$	−6.18421	−0.857596
$53$	−10.7562	−1.47748	−0.738740	−	0.673991i	$-0.764579\pi$
$53$	−10.7562	−1.47748	−0.738740	+	0.673991i	$0.764579\pi$
$54$	5.64681	0.768433
$55$	1.25901	0.169765
$56$	−4.72161	−0.630952
$57$	−9.83102	−1.30215
$58$	−2.04502	−0.268524
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−2.13919	−0.276169
$61$	7.84143	1.00399	0.501996	−	0.864870i	$-0.332599\pi$
$61$	7.84143	1.00399	0.501996	+	0.864870i	$0.332599\pi$
$62$	8.24860	1.04757
$63$	−4.06439	−0.512065
$64$	1.00000	0.125000
$65$	9.04502	1.12190
$66$	1.25901	0.154974
$67$	4.11982	0.503316	0.251658	−	0.967816i	$-0.419024\pi$
$67$	4.11982	0.503316	0.251658	+	0.967816i	$0.419024\pi$
$68$	−1.00000	−0.121268
$69$	9.72161	1.17034
$70$	6.90582	0.825404
$71$	13.3234	1.58120	0.790599	−	0.612335i	$-0.209770\pi$
$71$	13.3234	1.58120	0.790599	+	0.612335i	$0.209770\pi$
$72$	0.860806	0.101447
$73$	2.24860	0.263179	0.131589	−	0.991304i	$-0.457992\pi$
$73$	2.24860	0.263179	0.131589	+	0.991304i	$0.457992\pi$
$74$	7.25901	0.843843
$75$	−4.18421	−0.483151
$76$	−6.72161	−0.771022
$77$	−4.06439	−0.463180
$78$	9.04502	1.02415
$79$	−6.38780	−0.718683	−0.359342	−	0.933206i	$-0.616999\pi$
$79$	−6.38780	−0.718683	−0.359342	+	0.933206i	$0.616999\pi$
$80$	−1.46260	−0.163523
$81$	−5.67660	−0.630733
$82$	7.11982	0.786252
$83$	0.860806	0.0944857	0.0472429	−	0.998883i	$-0.484957\pi$
$83$	0.860806	0.0944857	0.0472429	+	0.998883i	$0.484957\pi$
$84$	6.90582	0.753487
$85$	1.46260	0.158641
$86$	6.39821	0.689936
$87$	2.99104	0.320673
$88$	0.860806	0.0917622
$89$	−3.60179	−0.381789	−0.190895	−	0.981611i	$-0.561139\pi$
$89$	−3.60179	−0.381789	−0.190895	+	0.981611i	$0.561139\pi$
$90$	−1.25901	−0.132712
$91$	−29.1994	−3.06093
$92$	6.64681	0.692978
$93$	−12.0644	−1.25102
$94$	−8.11982	−0.837495
$95$	9.83102	1.00864
$96$	−1.46260	−0.149276
$97$	14.3040	1.45235	0.726177	−	0.687508i	$-0.241295\pi$
$97$	14.3040	1.45235	0.726177	+	0.687508i	$0.241295\pi$
$98$	−15.2936	−1.54489
$99$	0.740987	0.0744720
$100$	−2.86081	−0.286081
$101$	19.1350	1.90401	0.952004	−	0.306085i	$-0.0990191\pi$
$101$	19.1350	1.90401	0.952004	+	0.306085i	$0.0990191\pi$
$102$	1.46260	0.144819
$103$	−11.9702	−1.17946	−0.589730	−	0.807600i	$-0.700766\pi$
$103$	−11.9702	−1.17946	−0.589730	+	0.807600i	$0.700766\pi$
$104$	6.18421	0.606412
$105$	−10.1004	−0.985702
$106$	10.7562	1.04474
$107$	−11.5180	−1.11349	−0.556745	−	0.830684i	$-0.687950\pi$
$107$	−11.5180	−1.11349	−0.556745	+	0.830684i	$0.687950\pi$
$108$	−5.64681	−0.543364
$109$	−3.47301	−0.332654	−0.166327	−	0.986071i	$-0.553191\pi$
$109$	−3.47301	−0.332654	−0.166327	+	0.986071i	$0.553191\pi$
$110$	−1.25901	−0.120042
$111$	−10.6170	−1.00772
$112$	4.72161	0.446150
$113$	13.1738	1.23929	0.619643	−	0.784884i	$-0.287277\pi$
$113$	13.1738	1.23929	0.619643	+	0.784884i	$0.287277\pi$
$114$	9.83102	0.920759
$115$	−9.72161	−0.906545
$116$	2.04502	0.189875
$117$	5.32340	0.492149
$118$	1.00000	0.0920575
$119$	−4.72161	−0.432829
$120$	2.13919	0.195281
$121$	−10.2590	−0.932638
$122$	−7.84143	−0.709930
$123$	−10.4134	−0.938948
$124$	−8.24860	−0.740746
$125$	11.4972	1.02834
$126$	4.06439	0.362085
$127$	−8.35319	−0.741226	−0.370613	−	0.928787i	$-0.620852\pi$
$127$	−8.35319	−0.741226	−0.370613	+	0.928787i	$0.620852\pi$
$128$	−1.00000	−0.0883883
$129$	−9.35801	−0.823927
$130$	−9.04502	−0.793300
$131$	−12.7756	−1.11621	−0.558104	−	0.829771i	$-0.688471\pi$
$131$	−12.7756	−1.11621	−0.558104	+	0.829771i	$0.688471\pi$
$132$	−1.25901	−0.109583
$133$	−31.7368	−2.75193
$134$	−4.11982	−0.355898
$135$	8.25901	0.710823
$136$	1.00000	0.0857493
$137$	0.537402	0.0459133	0.0229567	−	0.999736i	$-0.492692\pi$
$137$	0.537402	0.0459133	0.0229567	+	0.999736i	$0.492692\pi$
$138$	−9.72161	−0.827559
$139$	−13.6918	−1.16133	−0.580663	−	0.814144i	$-0.697206\pi$
$139$	−13.6918	−1.16133	−0.580663	+	0.814144i	$0.697206\pi$
$140$	−6.90582	−0.583648
$141$	11.8760	1.00014
$142$	−13.3234	−1.11808
$143$	5.32340	0.445165
$144$	−0.860806	−0.0717338
$145$	−2.99104	−0.248392
$146$	−2.24860	−0.186096
$147$	22.3684	1.84492
$148$	−7.25901	−0.596687
$149$	2.89541	0.237201	0.118601	−	0.992942i	$-0.462159\pi$
$149$	2.89541	0.237201	0.118601	+	0.992942i	$0.462159\pi$
$150$	4.18421	0.341639
$151$	9.20359	0.748977	0.374489	−	0.927232i	$-0.377818\pi$
$151$	9.20359	0.748977	0.374489	+	0.927232i	$0.377818\pi$
$152$	6.72161	0.545195
$153$	0.860806	0.0695920
$154$	4.06439	0.327518
$155$	12.0644	0.969035
$156$	−9.04502	−0.724181
$157$	7.47301	0.596411	0.298206	−	0.954502i	$-0.403612\pi$
$157$	7.47301	0.596411	0.298206	+	0.954502i	$0.403612\pi$
$158$	6.38780	0.508186
$159$	−15.7320	−1.24763
$160$	1.46260	0.115629
$161$	31.3836	2.47338
$162$	5.67660	0.445995
$163$	−18.6170	−1.45820	−0.729099	−	0.684408i	$-0.760061\pi$
$163$	−18.6170	−1.45820	−0.729099	+	0.684408i	$0.760061\pi$
$164$	−7.11982	−0.555964
$165$	1.84143	0.143355
$166$	−0.860806	−0.0668115
$167$	1.46260	0.113179	0.0565896	−	0.998398i	$-0.481977\pi$
$167$	1.46260	0.113179	0.0565896	+	0.998398i	$0.481977\pi$
$168$	−6.90582	−0.532796
$169$	25.2445	1.94188
$170$	−1.46260	−0.112176
$171$	5.78600	0.442467
$172$	−6.39821	−0.487859
$173$	−2.54781	−0.193707	−0.0968533	−	0.995299i	$-0.530878\pi$
$173$	−2.54781	−0.193707	−0.0968533	+	0.995299i	$0.530878\pi$
$174$	−2.99104	−0.226750
$175$	−13.5076	−1.02108
$176$	−0.860806	−0.0648857
$177$	−1.46260	−0.109936
$178$	3.60179	0.269966
$179$	18.5616	1.38736	0.693679	−	0.720284i	$-0.255989\pi$
$179$	18.5616	1.38736	0.693679	+	0.720284i	$0.255989\pi$
$180$	1.25901	0.0938413
$181$	12.2382	0.909657	0.454829	−	0.890579i	$-0.349700\pi$
$181$	12.2382	0.909657	0.454829	+	0.890579i	$0.349700\pi$
$182$	29.1994	2.16441
$183$	11.4689	0.847803
$184$	−6.64681	−0.490009
$185$	10.6170	0.780579
$186$	12.0644	0.884604
$187$	0.860806	0.0629484
$188$	8.11982	0.592199
$189$	−26.6620	−1.93938
$190$	−9.83102	−0.713217
$191$	−21.7562	−1.57422	−0.787112	−	0.616810i	$-0.788425\pi$
$191$	−21.7562	−1.57422	−0.787112	+	0.616810i	$0.788425\pi$
$192$	1.46260	0.105554
$193$	−10.9612	−0.789008	−0.394504	−	0.918894i	$-0.629084\pi$
$193$	−10.9612	−0.789008	−0.394504	+	0.918894i	$0.629084\pi$
$194$	−14.3040	−1.02697
$195$	13.2292	0.947365
$196$	15.2936	1.09240
$197$	−22.9211	−1.63306	−0.816529	−	0.577305i	$-0.804104\pi$
$197$	−22.9211	−1.63306	−0.816529	+	0.577305i	$0.804104\pi$
$198$	−0.740987	−0.0526596
$199$	−15.4924	−1.09823	−0.549113	−	0.835748i	$-0.685034\pi$
$199$	−15.4924	−1.09823	−0.549113	+	0.835748i	$0.685034\pi$
$200$	2.86081	0.202290
$201$	6.02564	0.425016
$202$	−19.1350	−1.34634
$203$	9.65577	0.677702
$204$	−1.46260	−0.102402
$205$	10.4134	0.727306
$206$	11.9702	0.834004
$207$	−5.72161	−0.397680
$208$	−6.18421	−0.428798
$209$	5.78600	0.400226
$210$	10.1004	0.696997
$211$	11.0152	0.758320	0.379160	−	0.925331i	$-0.376213\pi$
$211$	11.0152	0.758320	0.379160	+	0.925331i	$0.376213\pi$
$212$	−10.7562	−0.738740
$213$	19.4868	1.33521
$214$	11.5180	0.787356
$215$	9.35801	0.638211
$216$	5.64681	0.384217
$217$	−38.9467	−2.64387
$218$	3.47301	0.235222
$219$	3.28880	0.222237
$220$	1.25901	0.0848827
$221$	6.18421	0.415995
$222$	10.6170	0.712568
$223$	−13.7473	−0.920584	−0.460292	−	0.887768i	$-0.652255\pi$
$223$	−13.7473	−0.920584	−0.460292	+	0.887768i	$0.652255\pi$
$224$	−4.72161	−0.315476
$225$	2.46260	0.164173
$226$	−13.1738	−0.876308
$227$	6.37738	0.423282	0.211641	−	0.977347i	$-0.432119\pi$
$227$	6.37738	0.423282	0.211641	+	0.977347i	$0.432119\pi$
$228$	−9.83102	−0.651075
$229$	4.64681	0.307070	0.153535	−	0.988143i	$-0.450934\pi$
$229$	4.64681	0.307070	0.153535	+	0.988143i	$0.450934\pi$
$230$	9.72161	0.641024
$231$	−5.94457	−0.391124
$232$	−2.04502	−0.134262
$233$	−14.6814	−0.961811	−0.480906	−	0.876772i	$-0.659692\pi$
$233$	−14.6814	−0.961811	−0.480906	+	0.876772i	$0.659692\pi$
$234$	−5.32340	−0.348002
$235$	−11.8760	−0.774707
$236$	−1.00000	−0.0650945
$237$	−9.34278	−0.606879
$238$	4.72161	0.306057
$239$	13.4328	0.868896	0.434448	−	0.900697i	$-0.356943\pi$
$239$	13.4328	0.868896	0.434448	+	0.900697i	$0.356943\pi$
$240$	−2.13919	−0.138084
$241$	−0.168981	−0.0108850	−0.00544252	−	0.999985i	$-0.501732\pi$
$241$	−0.168981	−0.0108850	−0.00544252	+	0.999985i	$0.501732\pi$
$242$	10.2590	0.659474
$243$	8.63785	0.554118
$244$	7.84143	0.501996
$245$	−22.3684	−1.42907
$246$	10.4134	0.663936
$247$	41.5679	2.64490
$248$	8.24860	0.523787
$249$	1.25901	0.0797867
$250$	−11.4972	−0.727147
$251$	−16.8206	−1.06171	−0.530854	−	0.847464i	$-0.678129\pi$
$251$	−16.8206	−1.06171	−0.530854	+	0.847464i	$0.678129\pi$
$252$	−4.06439	−0.256033
$253$	−5.72161	−0.359715
$254$	8.35319	0.524126
$255$	2.13919	0.133962
$256$	1.00000	0.0625000
$257$	−0.452186	−0.0282066	−0.0141033	−	0.999901i	$-0.504489\pi$
$257$	−0.452186	−0.0282066	−0.0141033	+	0.999901i	$0.504489\pi$
$258$	9.35801	0.582604
$259$	−34.2742	−2.12970
$260$	9.04502	0.560948
$261$	−1.76036	−0.108964
$262$	12.7756	0.789279
$263$	2.90101	0.178884	0.0894418	−	0.995992i	$-0.471492\pi$
$263$	2.90101	0.178884	0.0894418	+	0.995992i	$0.471492\pi$
$264$	1.25901	0.0774869
$265$	15.7320	0.966411
$266$	31.7368	1.94591
$267$	−5.26798	−0.322395
$268$	4.11982	0.251658
$269$	−27.9017	−1.70120	−0.850598	−	0.525817i	$-0.823760\pi$
$269$	−27.9017	−1.70120	−0.850598	+	0.525817i	$0.823760\pi$
$270$	−8.25901	−0.502628
$271$	29.4495	1.78893	0.894465	−	0.447139i	$-0.147557\pi$
$271$	29.4495	1.78893	0.894465	+	0.447139i	$0.147557\pi$
$272$	−1.00000	−0.0606339
$273$	−42.7071	−2.58475
$274$	−0.537402	−0.0324656
$275$	2.46260	0.148500
$276$	9.72161	0.585172
$277$	8.62743	0.518372	0.259186	−	0.965827i	$-0.416546\pi$
$277$	8.62743	0.518372	0.259186	+	0.965827i	$0.416546\pi$
$278$	13.6918	0.821181
$279$	7.10044	0.425092
$280$	6.90582	0.412702
$281$	4.42240	0.263818	0.131909	−	0.991262i	$-0.457889\pi$
$281$	4.42240	0.263818	0.131909	+	0.991262i	$0.457889\pi$
$282$	−11.8760	−0.707208
$283$	−8.21400	−0.488271	−0.244136	−	0.969741i	$-0.578504\pi$
$283$	−8.21400	−0.488271	−0.244136	+	0.969741i	$0.578504\pi$
$284$	13.3234	0.790599
$285$	14.3788	0.851729
$286$	−5.32340	−0.314779
$287$	−33.6170	−1.98435
$288$	0.860806	0.0507235
$289$	1.00000	0.0588235
$290$	2.99104	0.175640
$291$	20.9211	1.22641
$292$	2.24860	0.131589
$293$	−11.4030	−0.666172	−0.333086	−	0.942896i	$-0.608090\pi$
$293$	−11.4030	−0.666172	−0.333086	+	0.942896i	$0.608090\pi$
$294$	−22.3684	−1.30455
$295$	1.46260	0.0851558
$296$	7.25901	0.421922
$297$	4.86081	0.282053
$298$	−2.89541	−0.167727
$299$	−41.1053	−2.37718
$300$	−4.18421	−0.241575
$301$	−30.2099	−1.74127
$302$	−9.20359	−0.529607
$303$	27.9869	1.60780
$304$	−6.72161	−0.385511
$305$	−11.4689	−0.656705
$306$	−0.860806	−0.0492090
$307$	−9.64681	−0.550572	−0.275286	−	0.961362i	$-0.588773\pi$
$307$	−9.64681	−0.550572	−0.275286	+	0.961362i	$0.588773\pi$
$308$	−4.06439	−0.231590
$309$	−17.5076	−0.995973
$310$	−12.0644	−0.685211
$311$	−19.4585	−1.10339	−0.551694	−	0.834047i	$-0.686018\pi$
$311$	−19.4585	−1.10339	−0.551694	+	0.834047i	$0.686018\pi$
$312$	9.04502	0.512073
$313$	−14.9854	−0.847027	−0.423514	−	0.905890i	$-0.639203\pi$
$313$	−14.9854	−0.847027	−0.423514	+	0.905890i	$0.639203\pi$
$314$	−7.47301	−0.421726
$315$	5.94457	0.334939
$316$	−6.38780	−0.359342
$317$	−2.73684	−0.153716	−0.0768581	−	0.997042i	$-0.524489\pi$
$317$	−2.73684	−0.153716	−0.0768581	+	0.997042i	$0.524489\pi$
$318$	15.7320	0.882208
$319$	−1.76036	−0.0985613
$320$	−1.46260	−0.0817617
$321$	−16.8462	−0.940266
$322$	−31.3836	−1.74894
$323$	6.72161	0.374000
$324$	−5.67660	−0.315366
$325$	17.6918	0.981366
$326$	18.6170	1.03110
$327$	−5.07962	−0.280904
$328$	7.11982	0.393126
$329$	38.3386	2.11368
$330$	−1.84143	−0.101367
$331$	6.32822	0.347830	0.173915	−	0.984761i	$-0.444358\pi$
$331$	6.32822	0.347830	0.173915	+	0.984761i	$0.444358\pi$
$332$	0.860806	0.0472429
$333$	6.24860	0.342421
$334$	−1.46260	−0.0800298
$335$	−6.02564	−0.329216
$336$	6.90582	0.376743
$337$	16.4972	0.898660	0.449330	−	0.893366i	$-0.351663\pi$
$337$	16.4972	0.898660	0.449330	+	0.893366i	$0.351663\pi$
$338$	−25.2445	−1.37312
$339$	19.2680	1.04649
$340$	1.46260	0.0793205
$341$	7.10044	0.384511
$342$	−5.78600	−0.312871
$343$	39.1592	2.11440
$344$	6.39821	0.344968
$345$	−14.2188	−0.765515
$346$	2.54781	0.136971
$347$	−9.38780	−0.503963	−0.251982	−	0.967732i	$-0.581082\pi$
$347$	−9.38780	−0.503963	−0.251982	+	0.967732i	$0.581082\pi$
$348$	2.99104	0.160336
$349$	−22.2694	−1.19206	−0.596028	−	0.802964i	$-0.703255\pi$
$349$	−22.2694	−1.19206	−0.596028	+	0.802964i	$0.703255\pi$
$350$	13.5076	0.722012
$351$	34.9211	1.86395
$352$	0.860806	0.0458811
$353$	15.3026	0.814474	0.407237	−	0.913322i	$-0.366492\pi$
$353$	15.3026	0.814474	0.407237	+	0.913322i	$0.366492\pi$
$354$	1.46260	0.0777362
$355$	−19.4868	−1.03425
$356$	−3.60179	−0.190895
$357$	−6.90582	−0.365495
$358$	−18.5616	−0.981011
$359$	22.8325	1.20505	0.602526	−	0.798099i	$-0.294161\pi$
$359$	22.8325	1.20505	0.602526	+	0.798099i	$0.294161\pi$
$360$	−1.25901	−0.0663558
$361$	26.1801	1.37790
$362$	−12.2382	−0.643225
$363$	−15.0048	−0.787549
$364$	−29.1994	−1.53047
$365$	−3.28880	−0.172144
$366$	−11.4689	−0.599487
$367$	22.2396	1.16090	0.580450	−	0.814296i	$-0.302877\pi$
$367$	22.2396	1.16090	0.580450	+	0.814296i	$0.302877\pi$
$368$	6.64681	0.346489
$369$	6.12878	0.319052
$370$	−10.6170	−0.551953
$371$	−50.7867	−2.63671
$372$	−12.0644	−0.625510
$373$	22.5526	1.16773	0.583865	−	0.811850i	$-0.301540\pi$
$373$	22.5526	1.16773	0.583865	+	0.811850i	$0.301540\pi$
$374$	−0.860806	−0.0445112
$375$	16.8158	0.868364
$376$	−8.11982	−0.418748
$377$	−12.6468	−0.651344
$378$	26.6620	1.37135
$379$	32.5422	1.67158	0.835791	−	0.549048i	$-0.185010\pi$
$379$	32.5422	1.67158	0.835791	+	0.549048i	$0.185010\pi$
$380$	9.83102	0.504321
$381$	−12.2174	−0.625915
$382$	21.7562	1.11314
$383$	8.15857	0.416883	0.208442	−	0.978035i	$-0.433161\pi$
$383$	8.15857	0.416883	0.208442	+	0.978035i	$0.433161\pi$
$384$	−1.46260	−0.0746379
$385$	5.94457	0.302963
$386$	10.9612	0.557913
$387$	5.50761	0.279968
$388$	14.3040	0.726177
$389$	22.4674	1.13914	0.569572	−	0.821942i	$-0.307109\pi$
$389$	22.4674	1.13914	0.569572	+	0.821942i	$0.307109\pi$
$390$	−13.2292	−0.669888
$391$	−6.64681	−0.336144
$392$	−15.2936	−0.772444
$393$	−18.6856	−0.942562
$394$	22.9211	1.15475
$395$	9.34278	0.470086
$396$	0.740987	0.0372360
$397$	6.15857	0.309090	0.154545	−	0.987986i	$-0.450609\pi$
$397$	6.15857	0.309090	0.154545	+	0.987986i	$0.450609\pi$
$398$	15.4924	0.776563
$399$	−46.4183	−2.32382
$400$	−2.86081	−0.143040
$401$	−9.45219	−0.472020	−0.236010	−	0.971751i	$-0.575840\pi$
$401$	−9.45219	−0.472020	−0.236010	+	0.971751i	$0.575840\pi$
$402$	−6.02564	−0.300532
$403$	51.0111	2.54104
$404$	19.1350	0.952004
$405$	8.30258	0.412559
$406$	−9.65577	−0.479208
$407$	6.24860	0.309732
$408$	1.46260	0.0724094
$409$	−1.59698	−0.0789654	−0.0394827	−	0.999220i	$-0.512571\pi$
$409$	−1.59698	−0.0789654	−0.0394827	+	0.999220i	$0.512571\pi$
$410$	−10.4134	−0.514283
$411$	0.786003	0.0387707
$412$	−11.9702	−0.589730
$413$	−4.72161	−0.232335
$414$	5.72161	0.281202
$415$	−1.25901	−0.0618025
$416$	6.18421	0.303206
$417$	−20.0256	−0.980660
$418$	−5.78600	−0.283003
$419$	−11.2847	−0.551291	−0.275646	−	0.961259i	$-0.588892\pi$
$419$	−11.2847	−0.551291	−0.275646	+	0.961259i	$0.588892\pi$
$420$	−10.1004	−0.492851
$421$	−28.1503	−1.37196	−0.685980	−	0.727620i	$-0.740626\pi$
$421$	−28.1503	−1.37196	−0.685980	+	0.727620i	$0.740626\pi$
$422$	−11.0152	−0.536213
$423$	−6.98959	−0.339845
$424$	10.7562	0.522368
$425$	2.86081	0.138769
$426$	−19.4868	−0.944138
$427$	37.0242	1.79173
$428$	−11.5180	−0.556745
$429$	7.78600	0.375912
$430$	−9.35801	−0.451283
$431$	−0.801232	−0.0385940	−0.0192970	−	0.999814i	$-0.506143\pi$
$431$	−0.801232	−0.0385940	−0.0192970	+	0.999814i	$0.506143\pi$
$432$	−5.64681	−0.271682
$433$	−28.1302	−1.35185	−0.675926	−	0.736969i	$-0.736256\pi$
$433$	−28.1302	−1.35185	−0.675926	+	0.736969i	$0.736256\pi$
$434$	38.9467	1.86950
$435$	−4.37469	−0.209750
$436$	−3.47301	−0.166327
$437$	−44.6773	−2.13720
$438$	−3.28880	−0.157145
$439$	−28.8358	−1.37626	−0.688130	−	0.725588i	$-0.741568\pi$
$439$	−28.8358	−1.37626	−0.688130	+	0.725588i	$0.741568\pi$
$440$	−1.25901	−0.0600211
$441$	−13.1648	−0.626897
$442$	−6.18421	−0.294153
$443$	31.8116	1.51142	0.755708	−	0.654908i	$-0.227293\pi$
$443$	31.8116	1.51142	0.755708	+	0.654908i	$0.227293\pi$
$444$	−10.6170	−0.503862
$445$	5.26798	0.249726
$446$	13.7473	0.650951
$447$	4.23482	0.200300
$448$	4.72161	0.223075
$449$	−0.935609	−0.0441541	−0.0220771	−	0.999756i	$-0.507028\pi$
$449$	−0.935609	−0.0441541	−0.0220771	+	0.999756i	$0.507028\pi$
$450$	−2.46260	−0.116088
$451$	6.12878	0.288593
$452$	13.1738	0.619643
$453$	13.4611	0.632460
$454$	−6.37738	−0.299305
$455$	42.7071	2.00214
$456$	9.83102	0.460380
$457$	17.6274	0.824577	0.412288	−	0.911053i	$-0.364730\pi$
$457$	17.6274	0.824577	0.412288	+	0.911053i	$0.364730\pi$
$458$	−4.64681	−0.217131
$459$	5.64681	0.263570
$460$	−9.72161	−0.453272
$461$	−23.6502	−1.10150	−0.550749	−	0.834671i	$-0.685658\pi$
$461$	−23.6502	−1.10150	−0.550749	+	0.834671i	$0.685658\pi$
$462$	5.94457	0.276567
$463$	−3.48679	−0.162045	−0.0810224	−	0.996712i	$-0.525819\pi$
$463$	−3.48679	−0.162045	−0.0810224	+	0.996712i	$0.525819\pi$
$464$	2.04502	0.0949375
$465$	17.6454	0.818284
$466$	14.6814	0.680103
$467$	12.0990	0.559875	0.279937	−	0.960018i	$-0.409686\pi$
$467$	12.0990	0.559875	0.279937	+	0.960018i	$0.409686\pi$
$468$	5.32340	0.246074
$469$	19.4522	0.898219
$470$	11.8760	0.547801
$471$	10.9300	0.503628
$472$	1.00000	0.0460287
$473$	5.50761	0.253240
$474$	9.34278	0.429128
$475$	19.2292	0.882297
$476$	−4.72161	−0.216415
$477$	9.25901	0.423941
$478$	−13.4328	−0.614402
$479$	12.9252	0.590567	0.295284	−	0.955410i	$-0.404586\pi$
$479$	12.9252	0.590567	0.295284	+	0.955410i	$0.404586\pi$
$480$	2.13919	0.0976404
$481$	44.8913	2.04687
$482$	0.168981	0.00769689
$483$	45.9017	2.08860
$484$	−10.2590	−0.466319
$485$	−20.9211	−0.949976
$486$	−8.63785	−0.391821
$487$	5.06024	0.229302	0.114651	−	0.993406i	$-0.463425\pi$
$487$	5.06024	0.229302	0.114651	+	0.993406i	$0.463425\pi$
$488$	−7.84143	−0.354965
$489$	−27.2292	−1.23135
$490$	22.3684	1.01050
$491$	30.9196	1.39538	0.697691	−	0.716399i	$-0.254211\pi$
$491$	30.9196	1.39538	0.697691	+	0.716399i	$0.254211\pi$
$492$	−10.4134	−0.469474
$493$	−2.04502	−0.0921029
$494$	−41.5679	−1.87023
$495$	−1.08377	−0.0487117
$496$	−8.24860	−0.370373
$497$	62.9079	2.82181
$498$	−1.25901	−0.0564177
$499$	−12.1738	−0.544974	−0.272487	−	0.962159i	$-0.587846\pi$
$499$	−12.1738	−0.544974	−0.272487	+	0.962159i	$0.587846\pi$
$500$	11.4972	0.514171
$501$	2.13919	0.0955721
$502$	16.8206	0.750740
$503$	−18.5020	−0.824964	−0.412482	−	0.910966i	$-0.635338\pi$
$503$	−18.5020	−0.824964	−0.412482	+	0.910966i	$0.635338\pi$
$504$	4.06439	0.181042
$505$	−27.9869	−1.24540
$506$	5.72161	0.254357
$507$	36.9225	1.63979
$508$	−8.35319	−0.370613
$509$	1.18276	0.0524250	0.0262125	−	0.999656i	$-0.491655\pi$
$509$	1.18276	0.0524250	0.0262125	+	0.999656i	$0.491655\pi$
$510$	−2.13919	−0.0947251
$511$	10.6170	0.469669
$512$	−1.00000	−0.0441942
$513$	37.9557	1.67578
$514$	0.452186	0.0199451
$515$	17.5076	0.771478
$516$	−9.35801	−0.411963
$517$	−6.98959	−0.307402
$518$	34.2742	1.50592
$519$	−3.72643	−0.163572
$520$	−9.04502	−0.396650
$521$	6.79641	0.297756	0.148878	−	0.988856i	$-0.452434\pi$
$521$	6.79641	0.297756	0.148878	+	0.988856i	$0.452434\pi$
$522$	1.76036	0.0770489
$523$	−16.4224	−0.718101	−0.359051	−	0.933318i	$-0.616899\pi$
$523$	−16.4224	−0.718101	−0.359051	+	0.933318i	$0.616899\pi$
$524$	−12.7756	−0.558104
$525$	−19.7562	−0.862232
$526$	−2.90101	−0.126490
$527$	8.24860	0.359315
$528$	−1.25901	−0.0547915
$529$	21.1801	0.920872
$530$	−15.7320	−0.683355
$531$	0.860806	0.0373558
$532$	−31.7368	−1.37597
$533$	44.0305	1.90717
$534$	5.26798	0.227968
$535$	16.8462	0.728327
$536$	−4.11982	−0.177949
$537$	27.1482	1.17153
$538$	27.9017	1.20293
$539$	−13.1648	−0.567050
$540$	8.25901	0.355411
$541$	−4.83998	−0.208087	−0.104044	−	0.994573i	$-0.533178\pi$
$541$	−4.83998	−0.208087	−0.104044	+	0.994573i	$0.533178\pi$
$542$	−29.4495	−1.26496
$543$	17.8996	0.768143
$544$	1.00000	0.0428746
$545$	5.07962	0.217587
$546$	42.7071	1.82769
$547$	−44.2355	−1.89137	−0.945687	−	0.325080i	$-0.894609\pi$
$547$	−44.2355	−1.89137	−0.945687	+	0.325080i	$0.894609\pi$
$548$	0.537402	0.0229567
$549$	−6.74995	−0.288081
$550$	−2.46260	−0.105006
$551$	−13.7458	−0.585591
$552$	−9.72161	−0.413779
$553$	−30.1607	−1.28256
$554$	−8.62743	−0.366545
$555$	15.5284	0.659146
$556$	−13.6918	−0.580663
$557$	−34.1559	−1.44723	−0.723615	−	0.690203i	$-0.757521\pi$
$557$	−34.1559	−1.44723	−0.723615	+	0.690203i	$0.757521\pi$
$558$	−7.10044	−0.300586
$559$	39.5679	1.67354
$560$	−6.90582	−0.291824
$561$	1.25901	0.0531556
$562$	−4.42240	−0.186548
$563$	10.6606	0.449290	0.224645	−	0.974441i	$-0.427878\pi$
$563$	10.6606	0.449290	0.224645	+	0.974441i	$0.427878\pi$
$564$	11.8760	0.500071
$565$	−19.2680	−0.810610
$566$	8.21400	0.345260
$567$	−26.8027	−1.12561
$568$	−13.3234	−0.559038
$569$	36.0602	1.51172	0.755862	−	0.654731i	$-0.227218\pi$
$569$	36.0602	1.51172	0.755862	+	0.654731i	$0.227218\pi$
$570$	−14.3788	−0.602263
$571$	40.9813	1.71501	0.857507	−	0.514472i	$-0.172012\pi$
$571$	40.9813	1.71501	0.857507	+	0.514472i	$0.172012\pi$
$572$	5.32340	0.222583
$573$	−31.8206	−1.32932
$574$	33.6170	1.40315
$575$	−19.0152	−0.792990
$576$	−0.860806	−0.0358669
$577$	−5.24860	−0.218502	−0.109251	−	0.994014i	$-0.534845\pi$
$577$	−5.24860	−0.218502	−0.109251	+	0.994014i	$0.534845\pi$
$578$	−1.00000	−0.0415945
$579$	−16.0319	−0.666263
$580$	−2.99104	−0.124196
$581$	4.06439	0.168619
$582$	−20.9211	−0.867205
$583$	9.25901	0.383469
$584$	−2.24860	−0.0930478
$585$	−7.78600	−0.321912
$586$	11.4030	0.471055
$587$	45.1171	1.86218	0.931091	−	0.364786i	$-0.118858\pi$
$587$	45.1171	1.86218	0.931091	+	0.364786i	$0.118858\pi$
$588$	22.3684	0.922458
$589$	55.4439	2.28453
$590$	−1.46260	−0.0602142
$591$	−33.5243	−1.37901
$592$	−7.25901	−0.298344
$593$	−3.58656	−0.147283	−0.0736413	−	0.997285i	$-0.523462\pi$
$593$	−3.58656	−0.147283	−0.0736413	+	0.997285i	$0.523462\pi$
$594$	−4.86081	−0.199441
$595$	6.90582	0.283111
$596$	2.89541	0.118601
$597$	−22.6591	−0.927377
$598$	41.1053	1.68092
$599$	−42.2847	−1.72770	−0.863852	−	0.503746i	$-0.831955\pi$
$599$	−42.2847	−1.72770	−0.863852	+	0.503746i	$0.831955\pi$
$600$	4.18421	0.170820
$601$	−5.79497	−0.236382	−0.118191	−	0.992991i	$-0.537709\pi$
$601$	−5.79497	−0.236382	−0.118191	+	0.992991i	$0.537709\pi$
$602$	30.2099	1.23126
$603$	−3.54636	−0.144419
$604$	9.20359	0.374489
$605$	15.0048	0.610033
$606$	−27.9869	−1.13689
$607$	44.6025	1.81036	0.905179	−	0.425030i	$-0.139737\pi$
$607$	44.6025	1.81036	0.905179	+	0.425030i	$0.139737\pi$
$608$	6.72161	0.272597
$609$	14.1225	0.572273
$610$	11.4689	0.464361
$611$	−50.2147	−2.03147
$612$	0.860806	0.0347960
$613$	26.0721	1.05304	0.526521	−	0.850162i	$-0.323496\pi$
$613$	26.0721	1.05304	0.526521	+	0.850162i	$0.323496\pi$
$614$	9.64681	0.389314
$615$	15.2307	0.614160
$616$	4.06439	0.163759
$617$	29.8477	1.20162	0.600812	−	0.799391i	$-0.294844\pi$
$617$	29.8477	1.20162	0.600812	+	0.799391i	$0.294844\pi$
$618$	17.5076	0.704260
$619$	20.5720	0.826859	0.413429	−	0.910536i	$-0.364331\pi$
$619$	20.5720	0.826859	0.413429	+	0.910536i	$0.364331\pi$
$620$	12.0644	0.484518
$621$	−37.5333	−1.50616
$622$	19.4585	0.780213
$623$	−17.0063	−0.681342
$624$	−9.04502	−0.362090
$625$	−2.51176	−0.100470
$626$	14.9854	0.598939
$627$	8.46260	0.337964
$628$	7.47301	0.298206
$629$	7.25901	0.289436
$630$	−5.94457	−0.236837
$631$	−4.52284	−0.180052	−0.0900258	−	0.995939i	$-0.528695\pi$
$631$	−4.52284	−0.180052	−0.0900258	+	0.995939i	$0.528695\pi$
$632$	6.38780	0.254093
$633$	16.1109	0.640349
$634$	2.73684	0.108694
$635$	12.2174	0.484831
$636$	−15.7320	−0.623815
$637$	−94.5789	−3.74735
$638$	1.76036	0.0696934
$639$	−11.4689	−0.453701
$640$	1.46260	0.0578143
$641$	5.19944	0.205365	0.102683	−	0.994714i	$-0.467257\pi$
$641$	5.19944	0.205365	0.102683	+	0.994714i	$0.467257\pi$
$642$	16.8462	0.664868
$643$	33.8269	1.33400	0.667001	−	0.745057i	$-0.267578\pi$
$643$	33.8269	1.33400	0.667001	+	0.745057i	$0.267578\pi$
$644$	31.3836	1.23669
$645$	13.6870	0.538925
$646$	−6.72161	−0.264458
$647$	−20.3324	−0.799348	−0.399674	−	0.916657i	$-0.630877\pi$
$647$	−20.3324	−0.799348	−0.399674	+	0.916657i	$0.630877\pi$
$648$	5.67660	0.222998
$649$	0.860806	0.0337896
$650$	−17.6918	−0.693930
$651$	−56.9634	−2.23257
$652$	−18.6170	−0.729099
$653$	47.9854	1.87782	0.938908	−	0.344169i	$-0.111839\pi$
$653$	47.9854	1.87782	0.938908	+	0.344169i	$0.111839\pi$
$654$	5.07962	0.198629
$655$	18.6856	0.730105
$656$	−7.11982	−0.277982
$657$	−1.93561	−0.0755153
$658$	−38.3386	−1.49460
$659$	11.8850	0.462974	0.231487	−	0.972838i	$-0.425641\pi$
$659$	11.8850	0.462974	0.231487	+	0.972838i	$0.425641\pi$
$660$	1.84143	0.0716776
$661$	−33.5180	−1.30370	−0.651850	−	0.758348i	$-0.726007\pi$
$661$	−33.5180	−1.30370	−0.651850	+	0.758348i	$0.726007\pi$
$662$	−6.32822	−0.245953
$663$	9.04502	0.351279
$664$	−0.860806	−0.0334057
$665$	46.4183	1.80002
$666$	−6.24860	−0.242128
$667$	13.5928	0.526316
$668$	1.46260	0.0565896
$669$	−20.1067	−0.777370
$670$	6.02564	0.232791
$671$	−6.74995	−0.260579
$672$	−6.90582	−0.266398
$673$	−24.4633	−0.942990	−0.471495	−	0.881869i	$-0.656285\pi$
$673$	−24.4633	−0.942990	−0.471495	+	0.881869i	$0.656285\pi$
$674$	−16.4972	−0.635448
$675$	16.1544	0.621784
$676$	25.2445	0.970941
$677$	−22.4674	−0.863493	−0.431746	−	0.901995i	$-0.642102\pi$
$677$	−22.4674	−0.863493	−0.431746	+	0.901995i	$0.642102\pi$
$678$	−19.2680	−0.739982
$679$	67.5381	2.59187
$680$	−1.46260	−0.0560881
$681$	9.32755	0.357433
$682$	−7.10044	−0.271890
$683$	−12.4190	−0.475201	−0.237601	−	0.971363i	$-0.576361\pi$
$683$	−12.4190	−0.475201	−0.237601	+	0.971363i	$0.576361\pi$
$684$	5.78600	0.221233
$685$	−0.786003	−0.0300316
$686$	−39.1592	−1.49511
$687$	6.79641	0.259299
$688$	−6.39821	−0.243929
$689$	66.5187	2.53416
$690$	14.2188	0.541301
$691$	18.5360	0.705141	0.352570	−	0.935785i	$-0.385308\pi$
$691$	18.5360	0.705141	0.352570	+	0.935785i	$0.385308\pi$
$692$	−2.54781	−0.0968533
$693$	3.49865	0.132903
$694$	9.38780	0.356356
$695$	20.0256	0.759616
$696$	−2.99104	−0.113375
$697$	7.11982	0.269682
$698$	22.2694	0.842910
$699$	−21.4730	−0.812184
$700$	−13.5076	−0.510540
$701$	−26.1336	−0.987052	−0.493526	−	0.869731i	$-0.664292\pi$
$701$	−26.1336	−0.987052	−0.493526	+	0.869731i	$0.664292\pi$
$702$	−34.9211	−1.31801
$703$	48.7923	1.84024
$704$	−0.860806	−0.0324428
$705$	−17.3699	−0.654187
$706$	−15.3026	−0.575920
$707$	90.3483	3.39790
$708$	−1.46260	−0.0549678
$709$	−21.0394	−0.790152	−0.395076	−	0.918648i	$-0.629282\pi$
$709$	−21.0394	−0.790152	−0.395076	+	0.918648i	$0.629282\pi$
$710$	19.4868	0.731326
$711$	5.49865	0.206216
$712$	3.60179	0.134983
$713$	−54.8269	−2.05328
$714$	6.90582	0.258444
$715$	−7.78600	−0.291180
$716$	18.5616	0.693679
$717$	19.6468	0.733724
$718$	−22.8325	−0.852100
$719$	−21.1350	−0.788204	−0.394102	−	0.919067i	$-0.628944\pi$
$719$	−21.1350	−0.788204	−0.394102	+	0.919067i	$0.628944\pi$
$720$	1.25901	0.0469207
$721$	−56.5187	−2.10487
$722$	−26.1801	−0.974321
$723$	−0.247152	−0.00919167
$724$	12.2382	0.454829
$725$	−5.85039	−0.217278
$726$	15.0048	0.556881
$727$	−1.51948	−0.0563542	−0.0281771	−	0.999603i	$-0.508970\pi$
$727$	−1.51948	−0.0563542	−0.0281771	+	0.999603i	$0.508970\pi$
$728$	29.1994	1.08220
$729$	29.6635	1.09865
$730$	3.28880	0.121724
$731$	6.39821	0.236646
$732$	11.4689	0.423901
$733$	−44.4882	−1.64321	−0.821605	−	0.570057i	$-0.806921\pi$
$733$	−44.4882	−1.64321	−0.821605	+	0.570057i	$0.806921\pi$
$734$	−22.2396	−0.820880
$735$	−32.7160	−1.20675
$736$	−6.64681	−0.245005
$737$	−3.54636	−0.130632
$738$	−6.12878	−0.225604
$739$	1.25420	0.0461364	0.0230682	−	0.999734i	$-0.492657\pi$
$739$	1.25420	0.0461364	0.0230682	+	0.999734i	$0.492657\pi$
$740$	10.6170	0.390289
$741$	60.7971	2.23344
$742$	50.7867	1.86444
$743$	−32.6773	−1.19881	−0.599406	−	0.800445i	$-0.704597\pi$
$743$	−32.6773	−1.19881	−0.599406	+	0.800445i	$0.704597\pi$
$744$	12.0644	0.442302
$745$	−4.23482	−0.155152
$746$	−22.5526	−0.825710
$747$	−0.740987	−0.0271113
$748$	0.860806	0.0314742
$749$	−54.3836	−1.98714
$750$	−16.8158	−0.614026
$751$	−4.48824	−0.163778	−0.0818891	−	0.996641i	$-0.526095\pi$
$751$	−4.48824	−0.163778	−0.0818891	+	0.996641i	$0.526095\pi$
$752$	8.11982	0.296099
$753$	−24.6018	−0.896539
$754$	12.6468	0.460570
$755$	−13.4611	−0.489901
$756$	−26.6620	−0.969689
$757$	40.8325	1.48408	0.742041	−	0.670355i	$-0.233858\pi$
$757$	40.8325	1.48408	0.742041	+	0.670355i	$0.233858\pi$
$758$	−32.5422	−1.18199
$759$	−8.36842	−0.303754
$760$	−9.83102	−0.356609
$761$	−19.8358	−0.719048	−0.359524	−	0.933136i	$-0.617061\pi$
$761$	−19.8358	−0.719048	−0.359524	+	0.933136i	$0.617061\pi$
$762$	12.2174	0.442588
$763$	−16.3982	−0.593655
$764$	−21.7562	−0.787112
$765$	−1.25901	−0.0455197
$766$	−8.15857	−0.294781
$767$	6.18421	0.223299
$768$	1.46260	0.0527770
$769$	11.7354	0.423189	0.211595	−	0.977358i	$-0.432134\pi$
$769$	11.7354	0.423189	0.211595	+	0.977358i	$0.432134\pi$
$770$	−5.94457	−0.214227
$771$	−0.661367	−0.0238185
$772$	−10.9612	−0.394504
$773$	5.79082	0.208281	0.104141	−	0.994563i	$-0.466791\pi$
$773$	5.79082	0.208281	0.104141	+	0.994563i	$0.466791\pi$
$774$	−5.50761	−0.197967
$775$	23.5976	0.847652
$776$	−14.3040	−0.513485
$777$	−50.1295	−1.79838
$778$	−22.4674	−0.805496
$779$	47.8567	1.71464
$780$	13.2292	0.473682
$781$	−11.4689	−0.410388
$782$	6.64681	0.237689
$783$	−11.5478	−0.412685
$784$	15.2936	0.546201
$785$	−10.9300	−0.390109
$786$	18.6856	0.666492
$787$	−35.8671	−1.27852	−0.639262	−	0.768989i	$-0.720760\pi$
$787$	−35.8671	−1.27852	−0.639262	+	0.768989i	$0.720760\pi$
$788$	−22.9211	−0.816529
$789$	4.24301	0.151055
$790$	−9.34278	−0.332401
$791$	62.2016	2.21163
$792$	−0.740987	−0.0263298
$793$	−48.4931	−1.72204
$794$	−6.15857	−0.218559
$795$	23.0096	0.816068
$796$	−15.4924	−0.549113
$797$	−30.5616	−1.08255	−0.541274	−	0.840847i	$-0.682058\pi$
$797$	−30.5616	−1.08255	−0.541274	+	0.840847i	$0.682058\pi$
$798$	46.4183	1.64319
$799$	−8.11982	−0.287259
$800$	2.86081	0.101145
$801$	3.10044	0.109549
$802$	9.45219	0.333768
$803$	−1.93561	−0.0683062
$804$	6.02564	0.212508
$805$	−45.9017	−1.61782
$806$	−51.0111	−1.79679
$807$	−40.8089	−1.43654
$808$	−19.1350	−0.673169
$809$	53.5243	1.88181	0.940907	−	0.338665i	$-0.109975\pi$
$809$	53.5243	1.88181	0.940907	+	0.338665i	$0.109975\pi$
$810$	−8.30258	−0.291723
$811$	−46.7071	−1.64011	−0.820053	−	0.572287i	$-0.806056\pi$
$811$	−46.7071	−1.64011	−0.820053	+	0.572287i	$0.806056\pi$
$812$	9.65577	0.338851
$813$	43.0728	1.51063
$814$	−6.24860	−0.219013
$815$	27.2292	0.953798
$816$	−1.46260	−0.0512012
$817$	43.0063	1.50460
$818$	1.59698	0.0558370
$819$	25.1350	0.878290
$820$	10.4134	0.363653
$821$	17.2459	0.601886	0.300943	−	0.953642i	$-0.402699\pi$
$821$	17.2459	0.601886	0.300943	+	0.953642i	$0.402699\pi$
$822$	−0.786003	−0.0274150
$823$	−17.9910	−0.627128	−0.313564	−	0.949567i	$-0.601523\pi$
$823$	−17.9910	−0.627128	−0.313564	+	0.949567i	$0.601523\pi$
$824$	11.9702	0.417002
$825$	3.60179	0.125398
$826$	4.72161	0.164286
$827$	−52.2611	−1.81730	−0.908649	−	0.417561i	$-0.862885\pi$
$827$	−52.2611	−1.81730	−0.908649	+	0.417561i	$0.862885\pi$
$828$	−5.72161	−0.198840
$829$	22.0844	0.767024	0.383512	−	0.923536i	$-0.374714\pi$
$829$	22.0844	0.767024	0.383512	+	0.923536i	$0.374714\pi$
$830$	1.25901	0.0437010
$831$	12.6185	0.437730
$832$	−6.18421	−0.214399
$833$	−15.2936	−0.529892
$834$	20.0256	0.693431
$835$	−2.13919	−0.0740299
$836$	5.78600	0.200113
$837$	46.5783	1.60998
$838$	11.2847	0.389822
$839$	8.32485	0.287406	0.143703	−	0.989621i	$-0.454099\pi$
$839$	8.32485	0.287406	0.143703	+	0.989621i	$0.454099\pi$
$840$	10.1004	0.348498
$841$	−24.8179	−0.855790
$842$	28.1503	0.970123
$843$	6.46819	0.222776
$844$	11.0152	0.379160
$845$	−36.9225	−1.27017
$846$	6.98959	0.240307
$847$	−48.4391	−1.66439
$848$	−10.7562	−0.369370
$849$	−12.0138	−0.412312
$850$	−2.86081	−0.0981248
$851$	−48.2493	−1.65396
$852$	19.4868	0.667606
$853$	15.6337	0.535288	0.267644	−	0.963518i	$-0.413755\pi$
$853$	15.6337	0.535288	0.267644	+	0.963518i	$0.413755\pi$
$854$	−37.0242	−1.26694
$855$	−8.46260	−0.289415
$856$	11.5180	0.393678
$857$	18.0208	0.615580	0.307790	−	0.951454i	$-0.400411\pi$
$857$	18.0208	0.615580	0.307790	+	0.951454i	$0.400411\pi$
$858$	−7.78600	−0.265810
$859$	−47.4689	−1.61962	−0.809808	−	0.586694i	$-0.800429\pi$
$859$	−47.4689	−1.61962	−0.809808	+	0.586694i	$0.800429\pi$
$860$	9.35801	0.319105
$861$	−49.1682	−1.67565
$862$	0.801232	0.0272901
$863$	−14.2445	−0.484887	−0.242443	−	0.970166i	$-0.577949\pi$
$863$	−14.2445	−0.484887	−0.242443	+	0.970166i	$0.577949\pi$
$864$	5.64681	0.192108
$865$	3.72643	0.126702
$866$	28.1302	0.955904
$867$	1.46260	0.0496724
$868$	−38.9467	−1.32194
$869$	5.49865	0.186529
$870$	4.37469	0.148316
$871$	−25.4778	−0.863283
$872$	3.47301	0.117611
$873$	−12.3130	−0.416732
$874$	44.6773	1.51123
$875$	54.2853	1.83518
$876$	3.28880	0.111118
$877$	14.8116	0.500154	0.250077	−	0.968226i	$-0.419544\pi$
$877$	14.8116	0.500154	0.250077	+	0.968226i	$0.419544\pi$
$878$	28.8358	0.973162
$879$	−16.6780	−0.562536
$880$	1.25901	0.0424413
$881$	−29.3241	−0.987953	−0.493977	−	0.869475i	$-0.664457\pi$
$881$	−29.3241	−0.987953	−0.493977	+	0.869475i	$0.664457\pi$
$882$	13.1648	0.443283
$883$	−6.82957	−0.229833	−0.114917	−	0.993375i	$-0.536660\pi$
$883$	−6.82957	−0.229833	−0.114917	+	0.993375i	$0.536660\pi$
$884$	6.18421	0.207997
$885$	2.13919	0.0719082
$886$	−31.8116	−1.06873
$887$	−12.1205	−0.406966	−0.203483	−	0.979078i	$-0.565226\pi$
$887$	−12.1205	−0.406966	−0.203483	+	0.979078i	$0.565226\pi$
$888$	10.6170	0.356284
$889$	−39.4405	−1.32279
$890$	−5.26798	−0.176583
$891$	4.88645	0.163702
$892$	−13.7473	−0.460292
$893$	−54.5783	−1.82639
$894$	−4.23482	−0.141634
$895$	−27.1482	−0.907463
$896$	−4.72161	−0.157738
$897$	−60.1205	−2.00736
$898$	0.935609	0.0312217
$899$	−16.8685	−0.562597
$900$	2.46260	0.0820866
$901$	10.7562	0.358341
$902$	−6.12878	−0.204066
$903$	−44.1849	−1.47038
$904$	−13.1738	−0.438154
$905$	−17.8996	−0.595001
$906$	−13.4611	−0.447217
$907$	29.5139	0.979992	0.489996	−	0.871725i	$-0.336998\pi$
$907$	29.5139	0.979992	0.489996	+	0.871725i	$0.336998\pi$
$908$	6.37738	0.211641
$909$	−16.4716	−0.546327
$910$	−42.7071	−1.41573
$911$	−29.0948	−0.963955	−0.481978	−	0.876184i	$-0.660081\pi$
$911$	−29.0948	−0.963955	−0.481978	+	0.876184i	$0.660081\pi$
$912$	−9.83102	−0.325538
$913$	−0.740987	−0.0245231
$914$	−17.6274	−0.583064
$915$	−16.7743	−0.554543
$916$	4.64681	0.153535
$917$	−60.3214	−1.99199
$918$	−5.64681	−0.186372
$919$	−52.2403	−1.72325	−0.861624	−	0.507546i	$-0.830553\pi$
$919$	−52.2403	−1.72325	−0.861624	+	0.507546i	$0.830553\pi$
$920$	9.72161	0.320512
$921$	−14.1094	−0.464921
$922$	23.6502	0.778877
$923$	−82.3947	−2.71206
$924$	−5.94457	−0.195562
$925$	20.7666	0.682803
$926$	3.48679	0.114583
$927$	10.3040	0.338429
$928$	−2.04502	−0.0671309
$929$	11.5630	0.379371	0.189686	−	0.981845i	$-0.439253\pi$
$929$	11.5630	0.379371	0.189686	+	0.981845i	$0.439253\pi$
$930$	−17.6454	−0.578614
$931$	−102.798	−3.36906
$932$	−14.6814	−0.480906
$933$	−28.4599	−0.931735
$934$	−12.0990	−0.395891
$935$	−1.25901	−0.0411741
$936$	−5.32340	−0.174001
$937$	−2.69327	−0.0879854	−0.0439927	−	0.999032i	$-0.514008\pi$
$937$	−2.69327	−0.0879854	−0.0439927	+	0.999032i	$0.514008\pi$
$938$	−19.4522	−0.635136
$939$	−21.9177	−0.715257
$940$	−11.8760	−0.387354
$941$	28.4495	0.927427	0.463713	−	0.885985i	$-0.346517\pi$
$941$	28.4495	0.927427	0.463713	+	0.885985i	$0.346517\pi$
$942$	−10.9300	−0.356119
$943$	−47.3241	−1.54108
$944$	−1.00000	−0.0325472
$945$	38.9959	1.26854
$946$	−5.50761	−0.179068
$947$	8.74725	0.284248	0.142124	−	0.989849i	$-0.454607\pi$
$947$	8.74725	0.284248	0.142124	+	0.989849i	$0.454607\pi$
$948$	−9.34278	−0.303439
$949$	−13.9058	−0.451402
$950$	−19.2292	−0.623878
$951$	−4.00290	−0.129803
$952$	4.72161	0.153028
$953$	−34.7071	−1.12427	−0.562136	−	0.827045i	$-0.690020\pi$
$953$	−34.7071	−1.12427	−0.562136	+	0.827045i	$0.690020\pi$
$954$	−9.25901	−0.299772
$955$	31.8206	1.02969
$956$	13.4328	0.434448
$957$	−2.57470	−0.0832283
$958$	−12.9252	−0.417594
$959$	2.53740	0.0819370
$960$	−2.13919	−0.0690422
$961$	37.0394	1.19482
$962$	−44.8913	−1.44735
$963$	9.91478	0.319499
$964$	−0.168981	−0.00544252
$965$	16.0319	0.516085
$966$	−45.9017	−1.47686
$967$	47.5589	1.52939	0.764696	−	0.644392i	$-0.222889\pi$
$967$	47.5589	1.52939	0.764696	+	0.644392i	$0.222889\pi$
$968$	10.2590	0.329737
$969$	9.83102	0.315818
$970$	20.9211	0.671734
$971$	24.0707	0.772464	0.386232	−	0.922402i	$-0.373776\pi$
$971$	24.0707	0.772464	0.386232	+	0.922402i	$0.373776\pi$
$972$	8.63785	0.277059
$973$	−64.6475	−2.07250
$974$	−5.06024	−0.162141
$975$	25.8760	0.828696
$976$	7.84143	0.250998
$977$	−12.1157	−0.387615	−0.193807	−	0.981040i	$-0.562084\pi$
$977$	−12.1157	−0.387615	−0.193807	+	0.981040i	$0.562084\pi$
$978$	27.2292	0.870695
$979$	3.10044	0.0990906
$980$	−22.3684	−0.714533
$981$	2.98959	0.0954502
$982$	−30.9196	−0.986684
$983$	6.42385	0.204889	0.102444	−	0.994739i	$-0.467334\pi$
$983$	6.42385	0.204889	0.102444	+	0.994739i	$0.467334\pi$
$984$	10.4134	0.331968
$985$	33.5243	1.06817
$986$	2.04502	0.0651266
$987$	56.0740	1.78486
$988$	41.5679	1.32245
$989$	−42.5277	−1.35230
$990$	1.08377	0.0344443
$991$	−19.3372	−0.614266	−0.307133	−	0.951667i	$-0.599370\pi$
$991$	−19.3372	−0.614266	−0.307133	+	0.951667i	$0.599370\pi$
$992$	8.24860	0.261893
$993$	9.25565	0.293719
$994$	−62.9079	−1.99532
$995$	22.6591	0.718343
$996$	1.25901	0.0398934
$997$	0.921830	0.0291946	0.0145973	−	0.999893i	$-0.495353\pi$
$997$	0.921830	0.0291946	0.0145973	+	0.999893i	$0.495353\pi$
$998$	12.1738	0.385355
$999$	40.9903	1.29687

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.n.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.n.1.2	✓	3	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.46260 q^{3} +1.00000 q^{4} -1.46260 q^{5} -1.46260 q^{6} +4.72161 q^{7} -1.00000 q^{8} -0.860806 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.46260 q^{3} +1.00000 q^{4} -1.46260 q^{5} -1.46260 q^{6} +4.72161 q^{7} -1.00000 q^{8} -0.860806 q^{9} +1.46260 q^{10} -0.860806 q^{11} +1.46260 q^{12} -6.18421 q^{13} -4.72161 q^{14} -2.13919 q^{15} +1.00000 q^{16} -1.00000 q^{17} +0.860806 q^{18} -6.72161 q^{19} -1.46260 q^{20} +6.90582 q^{21} +0.860806 q^{22} +6.64681 q^{23} -1.46260 q^{24} -2.86081 q^{25} +6.18421 q^{26} -5.64681 q^{27} +4.72161 q^{28} +2.04502 q^{29} +2.13919 q^{30} -8.24860 q^{31} -1.00000 q^{32} -1.25901 q^{33} +1.00000 q^{34} -6.90582 q^{35} -0.860806 q^{36} -7.25901 q^{37} +6.72161 q^{38} -9.04502 q^{39} +1.46260 q^{40} -7.11982 q^{41} -6.90582 q^{42} -6.39821 q^{43} -0.860806 q^{44} +1.25901 q^{45} -6.64681 q^{46} +8.11982 q^{47} +1.46260 q^{48} +15.2936 q^{49} +2.86081 q^{50} -1.46260 q^{51} -6.18421 q^{52} -10.7562 q^{53} +5.64681 q^{54} +1.25901 q^{55} -4.72161 q^{56} -9.83102 q^{57} -2.04502 q^{58} -1.00000 q^{59} -2.13919 q^{60} +7.84143 q^{61} +8.24860 q^{62} -4.06439 q^{63} +1.00000 q^{64} +9.04502 q^{65} +1.25901 q^{66} +4.11982 q^{67} -1.00000 q^{68} +9.72161 q^{69} +6.90582 q^{70} +13.3234 q^{71} +0.860806 q^{72} +2.24860 q^{73} +7.25901 q^{74} -4.18421 q^{75} -6.72161 q^{76} -4.06439 q^{77} +9.04502 q^{78} -6.38780 q^{79} -1.46260 q^{80} -5.67660 q^{81} +7.11982 q^{82} +0.860806 q^{83} +6.90582 q^{84} +1.46260 q^{85} +6.39821 q^{86} +2.99104 q^{87} +0.860806 q^{88} -3.60179 q^{89} -1.25901 q^{90} -29.1994 q^{91} +6.64681 q^{92} -12.0644 q^{93} -8.11982 q^{94} +9.83102 q^{95} -1.46260 q^{96} +14.3040 q^{97} -15.2936 q^{98} +0.740987 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 2 q^{5} - 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 2 * q^5 - 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 2 q^{5} - 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} + 2 q^{10} + 3 q^{11} + 2 q^{12} - 5 q^{13} - 3 q^{14} - 12 q^{15} + 3 q^{16} - 3 q^{17} - 3 q^{18} - 9 q^{19} - 2 q^{20} - 4 q^{21} - 3 q^{22} + 4 q^{23} - 2 q^{24} - 3 q^{25} + 5 q^{26} - q^{27} + 3 q^{28} - 13 q^{29} + 12 q^{30} - 12 q^{31} - 3 q^{32} + 5 q^{33} + 3 q^{34} + 4 q^{35} + 3 q^{36} - 13 q^{37} + 9 q^{38} - 8 q^{39} + 2 q^{40} - 7 q^{41} + 4 q^{42} - 16 q^{43} + 3 q^{44} - 5 q^{45} - 4 q^{46} + 10 q^{47} + 2 q^{48} + 14 q^{49} + 3 q^{50} - 2 q^{51} - 5 q^{52} + 2 q^{53} + q^{54} - 5 q^{55} - 3 q^{56} + 13 q^{58} - 3 q^{59} - 12 q^{60} - 2 q^{61} + 12 q^{62} - 13 q^{63} + 3 q^{64} + 8 q^{65} - 5 q^{66} - 2 q^{67} - 3 q^{68} + 18 q^{69} - 4 q^{70} + 32 q^{71} - 3 q^{72} - 6 q^{73} + 13 q^{74} + q^{75} - 9 q^{76} - 13 q^{77} + 8 q^{78} - 12 q^{79} - 2 q^{80} - 25 q^{81} + 7 q^{82} - 3 q^{83} - 4 q^{84} + 2 q^{85} + 16 q^{86} - 7 q^{87} - 3 q^{88} - 14 q^{89} + 5 q^{90} - 31 q^{91} + 4 q^{92} - 37 q^{93} - 10 q^{94} - 2 q^{96} + 15 q^{97} - 14 q^{98} + 11 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 2 * q^5 - 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 + 2 * q^10 + 3 * q^11 + 2 * q^12 - 5 * q^13 - 3 * q^14 - 12 * q^15 + 3 * q^16 - 3 * q^17 - 3 * q^18 - 9 * q^19 - 2 * q^20 - 4 * q^21 - 3 * q^22 + 4 * q^23 - 2 * q^24 - 3 * q^25 + 5 * q^26 - q^27 + 3 * q^28 - 13 * q^29 + 12 * q^30 - 12 * q^31 - 3 * q^32 + 5 * q^33 + 3 * q^34 + 4 * q^35 + 3 * q^36 - 13 * q^37 + 9 * q^38 - 8 * q^39 + 2 * q^40 - 7 * q^41 + 4 * q^42 - 16 * q^43 + 3 * q^44 - 5 * q^45 - 4 * q^46 + 10 * q^47 + 2 * q^48 + 14 * q^49 + 3 * q^50 - 2 * q^51 - 5 * q^52 + 2 * q^53 + q^54 - 5 * q^55 - 3 * q^56 + 13 * q^58 - 3 * q^59 - 12 * q^60 - 2 * q^61 + 12 * q^62 - 13 * q^63 + 3 * q^64 + 8 * q^65 - 5 * q^66 - 2 * q^67 - 3 * q^68 + 18 * q^69 - 4 * q^70 + 32 * q^71 - 3 * q^72 - 6 * q^73 + 13 * q^74 + q^75 - 9 * q^76 - 13 * q^77 + 8 * q^78 - 12 * q^79 - 2 * q^80 - 25 * q^81 + 7 * q^82 - 3 * q^83 - 4 * q^84 + 2 * q^85 + 16 * q^86 - 7 * q^87 - 3 * q^88 - 14 * q^89 + 5 * q^90 - 31 * q^91 + 4 * q^92 - 37 * q^93 - 10 * q^94 - 2 * q^96 + 15 * q^97 - 14 * q^98 + 11 * q^99

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