LMFDB - Embedded newform 2006.2.a.u.1.7

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:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 23x^{7} + 18x^{6} + 185x^{5} - 91x^{4} - 615x^{3} + 126x^{2} + 668x - 44 $ x^9 - x^8 - 23x^7 + 18x^6 + 185x^5 - 91x^4 - 615x^3 + 126x^2 + 668*x - 44
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-1.94466$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.94466 q^{3} +1.00000 q^{4} +4.05667 q^{5} -1.94466 q^{6} -2.97242 q^{7} -1.00000 q^{8} +0.781710 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.94466 q^{3} +1.00000 q^{4} +4.05667 q^{5} -1.94466 q^{6} -2.97242 q^{7} -1.00000 q^{8} +0.781710 q^{9} -4.05667 q^{10} -0.141416 q^{11} +1.94466 q^{12} +1.83078 q^{13} +2.97242 q^{14} +7.88885 q^{15} +1.00000 q^{16} +1.00000 q^{17} -0.781710 q^{18} +5.45325 q^{19} +4.05667 q^{20} -5.78036 q^{21} +0.141416 q^{22} -5.75850 q^{23} -1.94466 q^{24} +11.4566 q^{25} -1.83078 q^{26} -4.31382 q^{27} -2.97242 q^{28} +8.77949 q^{29} -7.88885 q^{30} -8.78000 q^{31} -1.00000 q^{32} -0.275007 q^{33} -1.00000 q^{34} -12.0581 q^{35} +0.781710 q^{36} +4.09285 q^{37} -5.45325 q^{38} +3.56026 q^{39} -4.05667 q^{40} +8.36372 q^{41} +5.78036 q^{42} +9.04794 q^{43} -0.141416 q^{44} +3.17114 q^{45} +5.75850 q^{46} +6.19574 q^{47} +1.94466 q^{48} +1.83530 q^{49} -11.4566 q^{50} +1.94466 q^{51} +1.83078 q^{52} +10.9972 q^{53} +4.31382 q^{54} -0.573678 q^{55} +2.97242 q^{56} +10.6047 q^{57} -8.77949 q^{58} -1.00000 q^{59} +7.88885 q^{60} +4.66652 q^{61} +8.78000 q^{62} -2.32357 q^{63} +1.00000 q^{64} +7.42689 q^{65} +0.275007 q^{66} +2.61009 q^{67} +1.00000 q^{68} -11.1983 q^{69} +12.0581 q^{70} +13.7301 q^{71} -0.781710 q^{72} -12.5132 q^{73} -4.09285 q^{74} +22.2792 q^{75} +5.45325 q^{76} +0.420348 q^{77} -3.56026 q^{78} -11.1344 q^{79} +4.05667 q^{80} -10.7341 q^{81} -8.36372 q^{82} -11.5836 q^{83} -5.78036 q^{84} +4.05667 q^{85} -9.04794 q^{86} +17.0731 q^{87} +0.141416 q^{88} -7.08263 q^{89} -3.17114 q^{90} -5.44186 q^{91} -5.75850 q^{92} -17.0741 q^{93} -6.19574 q^{94} +22.1220 q^{95} -1.94466 q^{96} +5.13089 q^{97} -1.83530 q^{98} -0.110546 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - q^{3} + 9 q^{4} + 7 q^{5} + q^{6} - 9 q^{8} + 20 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - q^3 + 9 * q^4 + 7 * q^5 + q^6 - 9 * q^8 + 20 * q^9	\( 9 q - 9 q^{2} - q^{3} + 9 q^{4} + 7 q^{5} + q^{6} - 9 q^{8} + 20 q^{9} - 7 q^{10} + 5 q^{11} - q^{12} + 25 q^{13} - 5 q^{15} + 9 q^{16} + 9 q^{17} - 20 q^{18} + 14 q^{19} + 7 q^{20} - 7 q^{21} - 5 q^{22} + 2 q^{23} + q^{24} + 20 q^{25} - 25 q^{26} - 10 q^{27} + 18 q^{29} + 5 q^{30} + 6 q^{31} - 9 q^{32} - 9 q^{33} - 9 q^{34} - 17 q^{35} + 20 q^{36} + 11 q^{37} - 14 q^{38} - 8 q^{39} - 7 q^{40} + 18 q^{41} + 7 q^{42} - 10 q^{43} + 5 q^{44} + 27 q^{45} - 2 q^{46} - 20 q^{47} - q^{48} + 13 q^{49} - 20 q^{50} - q^{51} + 25 q^{52} - 7 q^{53} + 10 q^{54} + 29 q^{55} + 17 q^{57} - 18 q^{58} - 9 q^{59} - 5 q^{60} + 30 q^{61} - 6 q^{62} - 47 q^{63} + 9 q^{64} + 8 q^{65} + 9 q^{66} + 6 q^{67} + 9 q^{68} + 20 q^{69} + 17 q^{70} + 30 q^{71} - 20 q^{72} - 11 q^{74} - 7 q^{75} + 14 q^{76} - 3 q^{77} + 8 q^{78} + 29 q^{79} + 7 q^{80} - 3 q^{81} - 18 q^{82} + 9 q^{83} - 7 q^{84} + 7 q^{85} + 10 q^{86} + 44 q^{87} - 5 q^{88} + 8 q^{89} - 27 q^{90} + 13 q^{91} + 2 q^{92} + 7 q^{93} + 20 q^{94} + 27 q^{95} + q^{96} - 13 q^{97} - 13 q^{98} - 19 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - q^3 + 9 * q^4 + 7 * q^5 + q^6 - 9 * q^8 + 20 * q^9 - 7 * q^10 + 5 * q^11 - q^12 + 25 * q^13 - 5 * q^15 + 9 * q^16 + 9 * q^17 - 20 * q^18 + 14 * q^19 + 7 * q^20 - 7 * q^21 - 5 * q^22 + 2 * q^23 + q^24 + 20 * q^25 - 25 * q^26 - 10 * q^27 + 18 * q^29 + 5 * q^30 + 6 * q^31 - 9 * q^32 - 9 * q^33 - 9 * q^34 - 17 * q^35 + 20 * q^36 + 11 * q^37 - 14 * q^38 - 8 * q^39 - 7 * q^40 + 18 * q^41 + 7 * q^42 - 10 * q^43 + 5 * q^44 + 27 * q^45 - 2 * q^46 - 20 * q^47 - q^48 + 13 * q^49 - 20 * q^50 - q^51 + 25 * q^52 - 7 * q^53 + 10 * q^54 + 29 * q^55 + 17 * q^57 - 18 * q^58 - 9 * q^59 - 5 * q^60 + 30 * q^61 - 6 * q^62 - 47 * q^63 + 9 * q^64 + 8 * q^65 + 9 * q^66 + 6 * q^67 + 9 * q^68 + 20 * q^69 + 17 * q^70 + 30 * q^71 - 20 * q^72 - 11 * q^74 - 7 * q^75 + 14 * q^76 - 3 * q^77 + 8 * q^78 + 29 * q^79 + 7 * q^80 - 3 * q^81 - 18 * q^82 + 9 * q^83 - 7 * q^84 + 7 * q^85 + 10 * q^86 + 44 * q^87 - 5 * q^88 + 8 * q^89 - 27 * q^90 + 13 * q^91 + 2 * q^92 + 7 * q^93 + 20 * q^94 + 27 * q^95 + q^96 - 13 * q^97 - 13 * q^98 - 19 * 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
$3$	1.94466	1.12275	0.561376	−	0.827561i	$-0.310272\pi$
$3$	1.94466	1.12275	0.561376	+	0.827561i	$0.310272\pi$
$4$	1.00000	0.500000
$5$	4.05667	1.81420	0.907099	−	0.420917i	$-0.138292\pi$
$5$	4.05667	1.81420	0.907099	+	0.420917i	$0.138292\pi$
$6$	−1.94466	−0.793905
$7$	−2.97242	−1.12347	−0.561735	−	0.827317i	$-0.689866\pi$
$7$	−2.97242	−1.12347	−0.561735	+	0.827317i	$0.689866\pi$
$8$	−1.00000	−0.353553
$9$	0.781710	0.260570
$10$	−4.05667	−1.28283
$11$	−0.141416	−0.0426386	−0.0213193	−	0.999773i	$-0.506787\pi$
$11$	−0.141416	−0.0426386	−0.0213193	+	0.999773i	$0.506787\pi$
$12$	1.94466	0.561376
$13$	1.83078	0.507768	0.253884	−	0.967235i	$-0.418292\pi$
$13$	1.83078	0.507768	0.253884	+	0.967235i	$0.418292\pi$
$14$	2.97242	0.794413
$15$	7.88885	2.03689
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.781710	−0.184251
$19$	5.45325	1.25106	0.625531	−	0.780199i	$-0.284882\pi$
$19$	5.45325	1.25106	0.625531	+	0.780199i	$0.284882\pi$
$20$	4.05667	0.907099
$21$	−5.78036	−1.26138
$22$	0.141416	0.0301500
$23$	−5.75850	−1.20073	−0.600365	−	0.799726i	$-0.704978\pi$
$23$	−5.75850	−1.20073	−0.600365	+	0.799726i	$0.704978\pi$
$24$	−1.94466	−0.396952
$25$	11.4566	2.29131
$26$	−1.83078	−0.359046
$27$	−4.31382	−0.830196
$28$	−2.97242	−0.561735
$29$	8.77949	1.63031	0.815155	−	0.579243i	$-0.196652\pi$
$29$	8.77949	1.63031	0.815155	+	0.579243i	$0.196652\pi$
$30$	−7.88885	−1.44030
$31$	−8.78000	−1.57693	−0.788467	−	0.615077i	$-0.789125\pi$
$31$	−8.78000	−1.57693	−0.788467	+	0.615077i	$0.789125\pi$
$32$	−1.00000	−0.176777
$33$	−0.275007	−0.0478725
$34$	−1.00000	−0.171499
$35$	−12.0581	−2.03820
$36$	0.781710	0.130285
$37$	4.09285	0.672860	0.336430	−	0.941708i	$-0.390780\pi$
$37$	4.09285	0.672860	0.336430	+	0.941708i	$0.390780\pi$
$38$	−5.45325	−0.884634
$39$	3.56026	0.570097
$40$	−4.05667	−0.641416
$41$	8.36372	1.30619	0.653097	−	0.757274i	$-0.273469\pi$
$41$	8.36372	1.30619	0.653097	+	0.757274i	$0.273469\pi$
$42$	5.78036	0.891929
$43$	9.04794	1.37980	0.689899	−	0.723905i	$-0.257655\pi$
$43$	9.04794	1.37980	0.689899	+	0.723905i	$0.257655\pi$
$44$	−0.141416	−0.0213193
$45$	3.17114	0.472726
$46$	5.75850	0.849044
$47$	6.19574	0.903741	0.451870	−	0.892084i	$-0.350757\pi$
$47$	6.19574	0.903741	0.451870	+	0.892084i	$0.350757\pi$
$48$	1.94466	0.280688
$49$	1.83530	0.262186
$50$	−11.4566	−1.62020
$51$	1.94466	0.272307
$52$	1.83078	0.253884
$53$	10.9972	1.51059	0.755294	−	0.655387i	$-0.227494\pi$
$53$	10.9972	1.51059	0.755294	+	0.655387i	$0.227494\pi$
$54$	4.31382	0.587037
$55$	−0.573678	−0.0773548
$56$	2.97242	0.397207
$57$	10.6047	1.40463
$58$	−8.77949	−1.15280
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	7.88885	1.01845
$61$	4.66652	0.597486	0.298743	−	0.954334i	$-0.403433\pi$
$61$	4.66652	0.597486	0.298743	+	0.954334i	$0.403433\pi$
$62$	8.78000	1.11506
$63$	−2.32357	−0.292743
$64$	1.00000	0.125000
$65$	7.42689	0.921192
$66$	0.275007	0.0338510
$67$	2.61009	0.318873	0.159437	−	0.987208i	$-0.449032\pi$
$67$	2.61009	0.318873	0.159437	+	0.987208i	$0.449032\pi$
$68$	1.00000	0.121268
$69$	−11.1983	−1.34812
$70$	12.0581	1.44122
$71$	13.7301	1.62946	0.814730	−	0.579840i	$-0.196885\pi$
$71$	13.7301	1.62946	0.814730	+	0.579840i	$0.196885\pi$
$72$	−0.781710	−0.0921254
$73$	−12.5132	−1.46456	−0.732282	−	0.681001i	$-0.761545\pi$
$73$	−12.5132	−1.46456	−0.732282	+	0.681001i	$0.761545\pi$
$74$	−4.09285	−0.475784
$75$	22.2792	2.57258
$76$	5.45325	0.625531
$77$	0.420348	0.0479032
$78$	−3.56026	−0.403120
$79$	−11.1344	−1.25271	−0.626357	−	0.779536i	$-0.715455\pi$
$79$	−11.1344	−1.25271	−0.626357	+	0.779536i	$0.715455\pi$
$80$	4.05667	0.453550
$81$	−10.7341	−1.19267
$82$	−8.36372	−0.923619
$83$	−11.5836	−1.27146	−0.635731	−	0.771911i	$-0.719301\pi$
$83$	−11.5836	−1.27146	−0.635731	+	0.771911i	$0.719301\pi$
$84$	−5.78036	−0.630689
$85$	4.05667	0.440008
$86$	−9.04794	−0.975665
$87$	17.0731	1.83043
$88$	0.141416	0.0150750
$89$	−7.08263	−0.750757	−0.375378	−	0.926872i	$-0.622487\pi$
$89$	−7.08263	−0.750757	−0.375378	+	0.926872i	$0.622487\pi$
$90$	−3.17114	−0.334267
$91$	−5.44186	−0.570462
$92$	−5.75850	−0.600365
$93$	−17.0741	−1.77050
$94$	−6.19574	−0.639041
$95$	22.1220	2.26967
$96$	−1.94466	−0.198476
$97$	5.13089	0.520963	0.260481	−	0.965479i	$-0.416119\pi$
$97$	5.13089	0.520963	0.260481	+	0.965479i	$0.416119\pi$
$98$	−1.83530	−0.185393
$99$	−0.110546	−0.0111103
$100$	11.4566	1.14566
$101$	1.94083	0.193120	0.0965599	−	0.995327i	$-0.469216\pi$
$101$	1.94083	0.193120	0.0965599	+	0.995327i	$0.469216\pi$
$102$	−1.94466	−0.192550
$103$	−1.08215	−0.106627	−0.0533136	−	0.998578i	$-0.516978\pi$
$103$	−1.08215	−0.106627	−0.0533136	+	0.998578i	$0.516978\pi$
$104$	−1.83078	−0.179523
$105$	−23.4490	−2.28839
$106$	−10.9972	−1.06815
$107$	−4.43839	−0.429076	−0.214538	−	0.976716i	$-0.568825\pi$
$107$	−4.43839	−0.429076	−0.214538	+	0.976716i	$0.568825\pi$
$108$	−4.31382	−0.415098
$109$	1.45933	0.139779	0.0698893	−	0.997555i	$-0.477735\pi$
$109$	1.45933	0.139779	0.0698893	+	0.997555i	$0.477735\pi$
$110$	0.573678	0.0546981
$111$	7.95921	0.755455
$112$	−2.97242	−0.280868
$113$	−12.5668	−1.18218	−0.591092	−	0.806604i	$-0.701303\pi$
$113$	−12.5668	−1.18218	−0.591092	+	0.806604i	$0.701303\pi$
$114$	−10.6047	−0.993224
$115$	−23.3603	−2.17836
$116$	8.77949	0.815155
$117$	1.43114	0.132309
$118$	1.00000	0.0920575
$119$	−2.97242	−0.272482
$120$	−7.88885	−0.720150
$121$	−10.9800	−0.998182
$122$	−4.66652	−0.422487
$123$	16.2646	1.46653
$124$	−8.78000	−0.788467
$125$	26.1922	2.34270
$126$	2.32357	0.207000
$127$	−19.6351	−1.74233	−0.871165	−	0.490990i	$-0.836635\pi$
$127$	−19.6351	−1.74233	−0.871165	+	0.490990i	$0.836635\pi$
$128$	−1.00000	−0.0883883
$129$	17.5952	1.54917
$130$	−7.42689	−0.651381
$131$	11.1062	0.970354	0.485177	−	0.874416i	$-0.338755\pi$
$131$	11.1062	0.970354	0.485177	+	0.874416i	$0.338755\pi$
$132$	−0.275007	−0.0239362
$133$	−16.2094	−1.40553
$134$	−2.61009	−0.225477
$135$	−17.4998	−1.50614
$136$	−1.00000	−0.0857493
$137$	−12.2695	−1.04826	−0.524128	−	0.851640i	$-0.675609\pi$
$137$	−12.2695	−1.04826	−0.524128	+	0.851640i	$0.675609\pi$
$138$	11.1983	0.953266
$139$	19.5384	1.65722	0.828612	−	0.559823i	$-0.189131\pi$
$139$	19.5384	1.65722	0.828612	+	0.559823i	$0.189131\pi$
$140$	−12.0581	−1.01910
$141$	12.0486	1.01468
$142$	−13.7301	−1.15220
$143$	−0.258902	−0.0216505
$144$	0.781710	0.0651425
$145$	35.6155	2.95771
$146$	12.5132	1.03560
$147$	3.56904	0.294369
$148$	4.09285	0.336430
$149$	−10.2295	−0.838030	−0.419015	−	0.907979i	$-0.637625\pi$
$149$	−10.2295	−0.838030	−0.419015	+	0.907979i	$0.637625\pi$
$150$	−22.2792	−1.81909
$151$	−1.34945	−0.109817	−0.0549083	−	0.998491i	$-0.517487\pi$
$151$	−1.34945	−0.109817	−0.0549083	+	0.998491i	$0.517487\pi$
$152$	−5.45325	−0.442317
$153$	0.781710	0.0631975
$154$	−0.420348	−0.0338726
$155$	−35.6175	−2.86087
$156$	3.56026	0.285049
$157$	17.1263	1.36683	0.683415	−	0.730030i	$-0.260494\pi$
$157$	17.1263	1.36683	0.683415	+	0.730030i	$0.260494\pi$
$158$	11.1344	0.885803
$159$	21.3859	1.69601
$160$	−4.05667	−0.320708
$161$	17.1167	1.34898
$162$	10.7341	0.843347
$163$	−17.4868	−1.36967	−0.684837	−	0.728696i	$-0.740127\pi$
$163$	−17.4868	−1.36967	−0.684837	+	0.728696i	$0.740127\pi$
$164$	8.36372	0.653097
$165$	−1.11561	−0.0868502
$166$	11.5836	0.899060
$167$	0.203018	0.0157100	0.00785502	−	0.999969i	$-0.497500\pi$
$167$	0.203018	0.0157100	0.00785502	+	0.999969i	$0.497500\pi$
$168$	5.78036	0.445964
$169$	−9.64823	−0.742172
$170$	−4.05667	−0.311132
$171$	4.26286	0.325989
$172$	9.04794	0.689899
$173$	−26.0647	−1.98166	−0.990830	−	0.135117i	$-0.956859\pi$
$173$	−26.0647	−1.98166	−0.990830	+	0.135117i	$0.956859\pi$
$174$	−17.0731	−1.29431
$175$	−34.0538	−2.57422
$176$	−0.141416	−0.0106596
$177$	−1.94466	−0.146170
$178$	7.08263	0.530865
$179$	−19.8663	−1.48487	−0.742437	−	0.669915i	$-0.766330\pi$
$179$	−19.8663	−1.48487	−0.742437	+	0.669915i	$0.766330\pi$
$180$	3.17114	0.236363
$181$	11.5385	0.857651	0.428825	−	0.903387i	$-0.358928\pi$
$181$	11.5385	0.857651	0.428825	+	0.903387i	$0.358928\pi$
$182$	5.44186	0.403378
$183$	9.07480	0.670829
$184$	5.75850	0.424522
$185$	16.6033	1.22070
$186$	17.0741	1.25194
$187$	−0.141416	−0.0103414
$188$	6.19574	0.451870
$189$	12.8225	0.932700
$190$	−22.1220	−1.60490
$191$	8.29517	0.600218	0.300109	−	0.953905i	$-0.402977\pi$
$191$	8.29517	0.600218	0.300109	+	0.953905i	$0.402977\pi$
$192$	1.94466	0.140344
$193$	−12.8710	−0.926475	−0.463238	−	0.886234i	$-0.653312\pi$
$193$	−12.8710	−0.926475	−0.463238	+	0.886234i	$0.653312\pi$
$194$	−5.13089	−0.368376
$195$	14.4428	1.03427
$196$	1.83530	0.131093
$197$	16.3738	1.16659	0.583293	−	0.812262i	$-0.301764\pi$
$197$	16.3738	1.16659	0.583293	+	0.812262i	$0.301764\pi$
$198$	0.110546	0.00785619
$199$	−8.85051	−0.627396	−0.313698	−	0.949523i	$-0.601568\pi$
$199$	−8.85051	−0.627396	−0.313698	+	0.949523i	$0.601568\pi$
$200$	−11.4566	−0.810102
$201$	5.07574	0.358015
$202$	−1.94083	−0.136556
$203$	−26.0964	−1.83161
$204$	1.94466	0.136154
$205$	33.9289	2.36969
$206$	1.08215	0.0753968
$207$	−4.50148	−0.312874
$208$	1.83078	0.126942
$209$	−0.771178	−0.0533435
$210$	23.4490	1.61814
$211$	15.5470	1.07030	0.535150	−	0.844757i	$-0.320255\pi$
$211$	15.5470	1.07030	0.535150	+	0.844757i	$0.320255\pi$
$212$	10.9972	0.755294
$213$	26.7004	1.82948
$214$	4.43839	0.303402
$215$	36.7045	2.50323
$216$	4.31382	0.293519
$217$	26.0979	1.77164
$218$	−1.45933	−0.0988384
$219$	−24.3340	−1.64434
$220$	−0.573678	−0.0386774
$221$	1.83078	0.123152
$222$	−7.95921	−0.534187
$223$	−2.17188	−0.145440	−0.0727198	−	0.997352i	$-0.523168\pi$
$223$	−2.17188	−0.145440	−0.0727198	+	0.997352i	$0.523168\pi$
$224$	2.97242	0.198603
$225$	8.95572	0.597048
$226$	12.5668	0.835930
$227$	8.14015	0.540281	0.270141	−	0.962821i	$-0.412930\pi$
$227$	8.14015	0.540281	0.270141	+	0.962821i	$0.412930\pi$
$228$	10.6047	0.702315
$229$	−20.8636	−1.37870	−0.689352	−	0.724426i	$-0.742105\pi$
$229$	−20.8636	−1.37870	−0.689352	+	0.724426i	$0.742105\pi$
$230$	23.3603	1.54033
$231$	0.817436	0.0537833
$232$	−8.77949	−0.576402
$233$	3.64486	0.238783	0.119391	−	0.992847i	$-0.461906\pi$
$233$	3.64486	0.238783	0.119391	+	0.992847i	$0.461906\pi$
$234$	−1.43114	−0.0935567
$235$	25.1341	1.63957
$236$	−1.00000	−0.0650945
$237$	−21.6526	−1.40649
$238$	2.97242	0.192674
$239$	12.0956	0.782398	0.391199	−	0.920306i	$-0.372060\pi$
$239$	12.0956	0.782398	0.391199	+	0.920306i	$0.372060\pi$
$240$	7.88885	0.509223
$241$	24.0737	1.55072	0.775361	−	0.631518i	$-0.217568\pi$
$241$	24.0737	1.55072	0.775361	+	0.631518i	$0.217568\pi$
$242$	10.9800	0.705821
$243$	−7.93264	−0.508879
$244$	4.66652	0.298743
$245$	7.44520	0.475656
$246$	−16.2646	−1.03699
$247$	9.98372	0.635249
$248$	8.78000	0.557530
$249$	−22.5261	−1.42754
$250$	−26.1922	−1.65654
$251$	−20.4738	−1.29230	−0.646148	−	0.763213i	$-0.723621\pi$
$251$	−20.4738	−1.29230	−0.646148	+	0.763213i	$0.723621\pi$
$252$	−2.32357	−0.146371
$253$	0.814345	0.0511974
$254$	19.6351	1.23201
$255$	7.88885	0.494019
$256$	1.00000	0.0625000
$257$	−14.7902	−0.922584	−0.461292	−	0.887248i	$-0.652614\pi$
$257$	−14.7902	−0.922584	−0.461292	+	0.887248i	$0.652614\pi$
$258$	−17.5952	−1.09543
$259$	−12.1657	−0.755939
$260$	7.42689	0.460596
$261$	6.86301	0.424810
$262$	−11.1062	−0.686144
$263$	−12.0829	−0.745067	−0.372533	−	0.928019i	$-0.621511\pi$
$263$	−12.0829	−0.745067	−0.372533	+	0.928019i	$0.621511\pi$
$264$	0.275007	0.0169255
$265$	44.6122	2.74050
$266$	16.2094	0.993860
$267$	−13.7733	−0.842913
$268$	2.61009	0.159437
$269$	−20.7360	−1.26430	−0.632149	−	0.774847i	$-0.717827\pi$
$269$	−20.7360	−1.26430	−0.632149	+	0.774847i	$0.717827\pi$
$270$	17.4998	1.06500
$271$	−18.2907	−1.11108	−0.555540	−	0.831490i	$-0.687488\pi$
$271$	−18.2907	−1.11108	−0.555540	+	0.831490i	$0.687488\pi$
$272$	1.00000	0.0606339
$273$	−10.5826	−0.640487
$274$	12.2695	0.741229
$275$	−1.62014	−0.0976983
$276$	−11.1983	−0.674061
$277$	−8.44933	−0.507671	−0.253836	−	0.967247i	$-0.581692\pi$
$277$	−8.44933	−0.507671	−0.253836	+	0.967247i	$0.581692\pi$
$278$	−19.5384	−1.17183
$279$	−6.86341	−0.410902
$280$	12.0581	0.720612
$281$	−0.364052	−0.0217175	−0.0108588	−	0.999941i	$-0.503457\pi$
$281$	−0.364052	−0.0217175	−0.0108588	+	0.999941i	$0.503457\pi$
$282$	−12.0486	−0.717484
$283$	30.2044	1.79547	0.897733	−	0.440540i	$-0.145213\pi$
$283$	30.2044	1.79547	0.897733	+	0.440540i	$0.145213\pi$
$284$	13.7301	0.814730
$285$	43.0199	2.54828
$286$	0.258902	0.0153092
$287$	−24.8605	−1.46747
$288$	−0.781710	−0.0460627
$289$	1.00000	0.0588235
$290$	−35.6155	−2.09141
$291$	9.97784	0.584911
$292$	−12.5132	−0.732282
$293$	−20.6232	−1.20482	−0.602411	−	0.798186i	$-0.705793\pi$
$293$	−20.6232	−1.20482	−0.602411	+	0.798186i	$0.705793\pi$
$294$	−3.56904	−0.208150
$295$	−4.05667	−0.236188
$296$	−4.09285	−0.237892
$297$	0.610044	0.0353984
$298$	10.2295	0.592577
$299$	−10.5426	−0.609692
$300$	22.2792	1.28629
$301$	−26.8943	−1.55016
$302$	1.34945	0.0776521
$303$	3.77426	0.216825
$304$	5.45325	0.312765
$305$	18.9305	1.08396
$306$	−0.781710	−0.0446874
$307$	−0.934463	−0.0533326	−0.0266663	−	0.999644i	$-0.508489\pi$
$307$	−0.934463	−0.0533326	−0.0266663	+	0.999644i	$0.508489\pi$
$308$	0.420348	0.0239516
$309$	−2.10441	−0.119716
$310$	35.6175	2.02294
$311$	−31.0280	−1.75944	−0.879718	−	0.475496i	$-0.842269\pi$
$311$	−31.0280	−1.75944	−0.879718	+	0.475496i	$0.842269\pi$
$312$	−3.56026	−0.201560
$313$	−4.97533	−0.281222	−0.140611	−	0.990065i	$-0.544907\pi$
$313$	−4.97533	−0.281222	−0.140611	+	0.990065i	$0.544907\pi$
$314$	−17.1263	−0.966495
$315$	−9.42597	−0.531093
$316$	−11.1344	−0.626357
$317$	−18.4137	−1.03422	−0.517110	−	0.855919i	$-0.672992\pi$
$317$	−18.4137	−1.03422	−0.517110	+	0.855919i	$0.672992\pi$
$318$	−21.3859	−1.19926
$319$	−1.24156	−0.0695141
$320$	4.05667	0.226775
$321$	−8.63118	−0.481745
$322$	−17.1167	−0.953876
$323$	5.45325	0.303427
$324$	−10.7341	−0.596337
$325$	20.9745	1.16346
$326$	17.4868	0.968506
$327$	2.83791	0.156937
$328$	−8.36372	−0.461809
$329$	−18.4163	−1.01533
$330$	1.11561	0.0614123
$331$	−27.2260	−1.49648	−0.748239	−	0.663429i	$-0.769100\pi$
$331$	−27.2260	−1.49648	−0.748239	+	0.663429i	$0.769100\pi$
$332$	−11.5836	−0.635731
$333$	3.19942	0.175327
$334$	−0.203018	−0.0111087
$335$	10.5883	0.578499
$336$	−5.78036	−0.315344
$337$	18.4297	1.00393	0.501965	−	0.864888i	$-0.332611\pi$
$337$	18.4297	1.00393	0.501965	+	0.864888i	$0.332611\pi$
$338$	9.64823	0.524795
$339$	−24.4382	−1.32730
$340$	4.05667	0.220004
$341$	1.24163	0.0672382
$342$	−4.26286	−0.230509
$343$	15.3517	0.828913
$344$	−9.04794	−0.487832
$345$	−45.4279	−2.44576
$346$	26.0647	1.40124
$347$	18.0626	0.969652	0.484826	−	0.874611i	$-0.338883\pi$
$347$	18.0626	0.969652	0.484826	+	0.874611i	$0.338883\pi$
$348$	17.0731	0.915216
$349$	17.8881	0.957527	0.478764	−	0.877944i	$-0.341085\pi$
$349$	17.8881	0.957527	0.478764	+	0.877944i	$0.341085\pi$
$350$	34.0538	1.82025
$351$	−7.89768	−0.421547
$352$	0.141416	0.00753750
$353$	−1.31492	−0.0699860	−0.0349930	−	0.999388i	$-0.511141\pi$
$353$	−1.31492	−0.0699860	−0.0349930	+	0.999388i	$0.511141\pi$
$354$	1.94466	0.103358
$355$	55.6984	2.95616
$356$	−7.08263	−0.375378
$357$	−5.78036	−0.305929
$358$	19.8663	1.04997
$359$	25.0475	1.32196	0.660979	−	0.750404i	$-0.270141\pi$
$359$	25.0475	1.32196	0.660979	+	0.750404i	$0.270141\pi$
$360$	−3.17114	−0.167134
$361$	10.7380	0.565155
$362$	−11.5385	−0.606450
$363$	−21.3524	−1.12071
$364$	−5.44186	−0.285231
$365$	−50.7621	−2.65701
$366$	−9.07480	−0.474347
$367$	5.86779	0.306296	0.153148	−	0.988203i	$-0.451059\pi$
$367$	5.86779	0.306296	0.153148	+	0.988203i	$0.451059\pi$
$368$	−5.75850	−0.300183
$369$	6.53800	0.340355
$370$	−16.6033	−0.863167
$371$	−32.6885	−1.69710
$372$	−17.0741	−0.885252
$373$	29.5524	1.53017	0.765083	−	0.643931i	$-0.222698\pi$
$373$	29.5524	1.53017	0.765083	+	0.643931i	$0.222698\pi$
$374$	0.141416	0.00731245
$375$	50.9349	2.63027
$376$	−6.19574	−0.319521
$377$	16.0733	0.827819
$378$	−12.8225	−0.659519
$379$	−0.462266	−0.0237450	−0.0118725	−	0.999930i	$-0.503779\pi$
$379$	−0.462266	−0.0237450	−0.0118725	+	0.999930i	$0.503779\pi$
$380$	22.1220	1.13484
$381$	−38.1836	−1.95620
$382$	−8.29517	−0.424418
$383$	16.0427	0.819743	0.409871	−	0.912143i	$-0.365574\pi$
$383$	16.0427	0.819743	0.409871	+	0.912143i	$0.365574\pi$
$384$	−1.94466	−0.0992381
$385$	1.70522	0.0869058
$386$	12.8710	0.655117
$387$	7.07287	0.359534
$388$	5.13089	0.260481
$389$	33.0592	1.67617	0.838084	−	0.545542i	$-0.183676\pi$
$389$	33.0592	1.67617	0.838084	+	0.545542i	$0.183676\pi$
$390$	−14.4428	−0.731339
$391$	−5.75850	−0.291220
$392$	−1.83530	−0.0926966
$393$	21.5978	1.08947
$394$	−16.3738	−0.824900
$395$	−45.1684	−2.27267
$396$	−0.110546	−0.00555516
$397$	−12.8771	−0.646281	−0.323141	−	0.946351i	$-0.604739\pi$
$397$	−12.8771	−0.646281	−0.323141	+	0.946351i	$0.604739\pi$
$398$	8.85051	0.443636
$399$	−31.5217	−1.57806
$400$	11.4566	0.572829
$401$	−5.48346	−0.273831	−0.136915	−	0.990583i	$-0.543719\pi$
$401$	−5.48346	−0.273831	−0.136915	+	0.990583i	$0.543719\pi$
$402$	−5.07574	−0.253155
$403$	−16.0743	−0.800717
$404$	1.94083	0.0965599
$405$	−43.5445	−2.16375
$406$	26.0964	1.29514
$407$	−0.578795	−0.0286898
$408$	−1.94466	−0.0962751
$409$	32.9686	1.63019	0.815097	−	0.579324i	$-0.196684\pi$
$409$	32.9686	1.63019	0.815097	+	0.579324i	$0.196684\pi$
$410$	−33.9289	−1.67563
$411$	−23.8601	−1.17693
$412$	−1.08215	−0.0533136
$413$	2.97242	0.146263
$414$	4.50148	0.221235
$415$	−46.9907	−2.30668
$416$	−1.83078	−0.0897616
$417$	37.9956	1.86065
$418$	0.771178	0.0377195
$419$	4.90911	0.239826	0.119913	−	0.992784i	$-0.461739\pi$
$419$	4.90911	0.239826	0.119913	+	0.992784i	$0.461739\pi$
$420$	−23.4490	−1.14419
$421$	−7.14928	−0.348434	−0.174217	−	0.984707i	$-0.555739\pi$
$421$	−7.14928	−0.348434	−0.174217	+	0.984707i	$0.555739\pi$
$422$	−15.5470	−0.756816
$423$	4.84327	0.235488
$424$	−10.9972	−0.534073
$425$	11.4566	0.555725
$426$	−26.7004	−1.29364
$427$	−13.8709	−0.671258
$428$	−4.43839	−0.214538
$429$	−0.503477	−0.0243081
$430$	−36.7045	−1.77005
$431$	12.7884	0.615994	0.307997	−	0.951387i	$-0.400341\pi$
$431$	12.7884	0.615994	0.307997	+	0.951387i	$0.400341\pi$
$432$	−4.31382	−0.207549
$433$	−14.7143	−0.707125	−0.353562	−	0.935411i	$-0.615030\pi$
$433$	−14.7143	−0.707125	−0.353562	+	0.935411i	$0.615030\pi$
$434$	−26.0979	−1.25274
$435$	69.2601	3.32077
$436$	1.45933	0.0698893
$437$	−31.4025	−1.50219
$438$	24.3340	1.16272
$439$	39.7914	1.89914	0.949571	−	0.313553i	$-0.101519\pi$
$439$	39.7914	1.89914	0.949571	+	0.313553i	$0.101519\pi$
$440$	0.573678	0.0273490
$441$	1.43467	0.0683177
$442$	−1.83078	−0.0870815
$443$	−2.60018	−0.123539	−0.0617693	−	0.998090i	$-0.519674\pi$
$443$	−2.60018	−0.123539	−0.0617693	+	0.998090i	$0.519674\pi$
$444$	7.95921	0.377727
$445$	−28.7319	−1.36202
$446$	2.17188	0.102841
$447$	−19.8928	−0.940899
$448$	−2.97242	−0.140434
$449$	−10.6023	−0.500353	−0.250176	−	0.968200i	$-0.580489\pi$
$449$	−10.6023	−0.500353	−0.250176	+	0.968200i	$0.580489\pi$
$450$	−8.95572	−0.422177
$451$	−1.18277	−0.0556942
$452$	−12.5668	−0.591092
$453$	−2.62422	−0.123297
$454$	−8.14015	−0.382036
$455$	−22.0758	−1.03493
$456$	−10.6047	−0.496612
$457$	−24.4822	−1.14523	−0.572614	−	0.819825i	$-0.694071\pi$
$457$	−24.4822	−1.14523	−0.572614	+	0.819825i	$0.694071\pi$
$458$	20.8636	0.974891
$459$	−4.31382	−0.201352
$460$	−23.3603	−1.08918
$461$	7.11791	0.331514	0.165757	−	0.986167i	$-0.446993\pi$
$461$	7.11791	0.331514	0.165757	+	0.986167i	$0.446993\pi$
$462$	−0.817436	−0.0380306
$463$	15.1579	0.704450	0.352225	−	0.935915i	$-0.385425\pi$
$463$	15.1579	0.704450	0.352225	+	0.935915i	$0.385425\pi$
$464$	8.77949	0.407578
$465$	−69.2641	−3.21205
$466$	−3.64486	−0.168845
$467$	11.3661	0.525959	0.262979	−	0.964801i	$-0.415295\pi$
$467$	11.3661	0.525959	0.262979	+	0.964801i	$0.415295\pi$
$468$	1.43114	0.0661546
$469$	−7.75829	−0.358244
$470$	−25.1341	−1.15935
$471$	33.3049	1.53461
$472$	1.00000	0.0460287
$473$	−1.27953	−0.0588326
$474$	21.6526	0.994536
$475$	62.4756	2.86658
$476$	−2.97242	−0.136241
$477$	8.59665	0.393614
$478$	−12.0956	−0.553239
$479$	−15.3707	−0.702307	−0.351153	−	0.936318i	$-0.614210\pi$
$479$	−15.3707	−0.702307	−0.351153	+	0.936318i	$0.614210\pi$
$480$	−7.88885	−0.360075
$481$	7.49312	0.341657
$482$	−24.0737	−1.09653
$483$	33.2862	1.51457
$484$	−10.9800	−0.499091
$485$	20.8143	0.945129
$486$	7.93264	0.359832
$487$	3.04291	0.137887	0.0689436	−	0.997621i	$-0.478037\pi$
$487$	3.04291	0.137887	0.0689436	+	0.997621i	$0.478037\pi$
$488$	−4.66652	−0.211243
$489$	−34.0060	−1.53780
$490$	−7.44520	−0.336340
$491$	13.5899	0.613302	0.306651	−	0.951822i	$-0.400792\pi$
$491$	13.5899	0.613302	0.306651	+	0.951822i	$0.400792\pi$
$492$	16.2646	0.733265
$493$	8.77949	0.395408
$494$	−9.98372	−0.449189
$495$	−0.448450	−0.0201563
$496$	−8.78000	−0.394233
$497$	−40.8116	−1.83065
$498$	22.5261	1.00942
$499$	13.4836	0.603609	0.301805	−	0.953370i	$-0.402411\pi$
$499$	13.4836	0.603609	0.301805	+	0.953370i	$0.402411\pi$
$500$	26.1922	1.17135
$501$	0.394802	0.0176385
$502$	20.4738	0.913791
$503$	−32.5457	−1.45114	−0.725571	−	0.688147i	$-0.758424\pi$
$503$	−32.5457	−1.45114	−0.725571	+	0.688147i	$0.758424\pi$
$504$	2.32357	0.103500
$505$	7.87331	0.350358
$506$	−0.814345	−0.0362020
$507$	−18.7625	−0.833274
$508$	−19.6351	−0.871165
$509$	−30.2286	−1.33986	−0.669930	−	0.742425i	$-0.733676\pi$
$509$	−30.2286	−1.33986	−0.669930	+	0.742425i	$0.733676\pi$
$510$	−7.88885	−0.349324
$511$	37.1947	1.64539
$512$	−1.00000	−0.0441942
$513$	−23.5244	−1.03863
$514$	14.7902	0.652366
$515$	−4.38992	−0.193443
$516$	17.5952	0.774585
$517$	−0.876177	−0.0385342
$518$	12.1657	0.534529
$519$	−50.6870	−2.22491
$520$	−7.42689	−0.325690
$521$	−13.5533	−0.593782	−0.296891	−	0.954911i	$-0.595950\pi$
$521$	−13.5533	−0.593782	−0.296891	+	0.954911i	$0.595950\pi$
$522$	−6.86301	−0.300386
$523$	−21.0687	−0.921271	−0.460636	−	0.887589i	$-0.652379\pi$
$523$	−21.0687	−0.921271	−0.460636	+	0.887589i	$0.652379\pi$
$524$	11.1062	0.485177
$525$	−66.2231	−2.89021
$526$	12.0829	0.526842
$527$	−8.78000	−0.382463
$528$	−0.275007	−0.0119681
$529$	10.1603	0.441753
$530$	−44.6122	−1.93783
$531$	−0.781710	−0.0339233
$532$	−16.2094	−0.702765
$533$	15.3122	0.663244
$534$	13.7733	0.596030
$535$	−18.0051	−0.778428
$536$	−2.61009	−0.112739
$537$	−38.6332	−1.66714
$538$	20.7360	0.893994
$539$	−0.259541	−0.0111792
$540$	−17.4998	−0.753070
$541$	35.5859	1.52996	0.764978	−	0.644056i	$-0.222750\pi$
$541$	35.5859	1.52996	0.764978	+	0.644056i	$0.222750\pi$
$542$	18.2907	0.785652
$543$	22.4385	0.962928
$544$	−1.00000	−0.0428746
$545$	5.92003	0.253586
$546$	10.5826	0.452893
$547$	2.40681	0.102908	0.0514540	−	0.998675i	$-0.483614\pi$
$547$	2.40681	0.102908	0.0514540	+	0.998675i	$0.483614\pi$
$548$	−12.2695	−0.524128
$549$	3.64786	0.155687
$550$	1.62014	0.0690832
$551$	47.8768	2.03962
$552$	11.1983	0.476633
$553$	33.0960	1.40739
$554$	8.44933	0.358978
$555$	32.2879	1.37054
$556$	19.5384	0.828612
$557$	−35.0374	−1.48458	−0.742292	−	0.670077i	$-0.766261\pi$
$557$	−35.0374	−1.48458	−0.742292	+	0.670077i	$0.766261\pi$
$558$	6.86341	0.290551
$559$	16.5648	0.700618
$560$	−12.0581	−0.509549
$561$	−0.275007	−0.0116108
$562$	0.364052	0.0153566
$563$	−8.73500	−0.368136	−0.184068	−	0.982913i	$-0.558927\pi$
$563$	−8.73500	−0.368136	−0.184068	+	0.982913i	$0.558927\pi$
$564$	12.0486	0.507338
$565$	−50.9793	−2.14472
$566$	−30.2044	−1.26959
$567$	31.9062	1.33993
$568$	−13.7301	−0.576101
$569$	−6.80971	−0.285478	−0.142739	−	0.989760i	$-0.545591\pi$
$569$	−6.80971	−0.285478	−0.142739	+	0.989760i	$0.545591\pi$
$570$	−43.0199	−1.80191
$571$	−16.8869	−0.706695	−0.353347	−	0.935492i	$-0.614957\pi$
$571$	−16.8869	−0.706695	−0.353347	+	0.935492i	$0.614957\pi$
$572$	−0.258902	−0.0108252
$573$	16.1313	0.673895
$574$	24.8605	1.03766
$575$	−65.9727	−2.75125
$576$	0.781710	0.0325712
$577$	34.1087	1.41996	0.709982	−	0.704220i	$-0.248703\pi$
$577$	34.1087	1.41996	0.709982	+	0.704220i	$0.248703\pi$
$578$	−1.00000	−0.0415945
$579$	−25.0298	−1.04020
$580$	35.6155	1.47885
$581$	34.4313	1.42845
$582$	−9.97784	−0.413595
$583$	−1.55519	−0.0644093
$584$	12.5132	0.517802
$585$	5.80567	0.240035
$586$	20.6232	0.851938
$587$	−33.3100	−1.37485	−0.687426	−	0.726255i	$-0.741259\pi$
$587$	−33.3100	−1.37485	−0.687426	+	0.726255i	$0.741259\pi$
$588$	3.56904	0.147185
$589$	−47.8795	−1.97284
$590$	4.05667	0.167010
$591$	31.8415	1.30979
$592$	4.09285	0.168215
$593$	−3.61386	−0.148403	−0.0742016	−	0.997243i	$-0.523641\pi$
$593$	−3.61386	−0.148403	−0.0742016	+	0.997243i	$0.523641\pi$
$594$	−0.610044	−0.0250304
$595$	−12.0581	−0.494336
$596$	−10.2295	−0.419015
$597$	−17.2112	−0.704409
$598$	10.5426	0.431118
$599$	−21.8651	−0.893385	−0.446692	−	0.894688i	$-0.647398\pi$
$599$	−21.8651	−0.893385	−0.446692	+	0.894688i	$0.647398\pi$
$600$	−22.2792	−0.909543
$601$	−4.04348	−0.164937	−0.0824684	−	0.996594i	$-0.526280\pi$
$601$	−4.04348	−0.164937	−0.0824684	+	0.996594i	$0.526280\pi$
$602$	26.8943	1.09613
$603$	2.04033	0.0830887
$604$	−1.34945	−0.0549083
$605$	−44.5422	−1.81090
$606$	−3.77426	−0.153319
$607$	19.3918	0.787089	0.393545	−	0.919306i	$-0.371249\pi$
$607$	19.3918	0.787089	0.393545	+	0.919306i	$0.371249\pi$
$608$	−5.45325	−0.221159
$609$	−50.7486	−2.05644
$610$	−18.9305	−0.766475
$611$	11.3431	0.458891
$612$	0.781710	0.0315988
$613$	−40.5152	−1.63639	−0.818197	−	0.574938i	$-0.805026\pi$
$613$	−40.5152	−1.63639	−0.818197	+	0.574938i	$0.805026\pi$
$614$	0.934463	0.0377119
$615$	65.9802	2.66058
$616$	−0.420348	−0.0169363
$617$	−32.7610	−1.31891	−0.659454	−	0.751745i	$-0.729213\pi$
$617$	−32.7610	−1.31891	−0.659454	+	0.751745i	$0.729213\pi$
$618$	2.10441	0.0846518
$619$	13.5200	0.543414	0.271707	−	0.962380i	$-0.412412\pi$
$619$	13.5200	0.543414	0.271707	+	0.962380i	$0.412412\pi$
$620$	−35.6175	−1.43044
$621$	24.8412	0.996841
$622$	31.0280	1.24411
$623$	21.0526	0.843453
$624$	3.56026	0.142524
$625$	48.9702	1.95881
$626$	4.97533	0.198854
$627$	−1.49968	−0.0598914
$628$	17.1263	0.683415
$629$	4.09285	0.163193
$630$	9.42597	0.375540
$631$	20.7026	0.824156	0.412078	−	0.911149i	$-0.364803\pi$
$631$	20.7026	0.824156	0.412078	+	0.911149i	$0.364803\pi$
$632$	11.1344	0.442901
$633$	30.2337	1.20168
$634$	18.4137	0.731303
$635$	−79.6530	−3.16093
$636$	21.3859	0.848007
$637$	3.36004	0.133129
$638$	1.24156	0.0491539
$639$	10.7329	0.424589
$640$	−4.05667	−0.160354
$641$	12.2157	0.482493	0.241246	−	0.970464i	$-0.422444\pi$
$641$	12.2157	0.482493	0.241246	+	0.970464i	$0.422444\pi$
$642$	8.63118	0.340645
$643$	3.73807	0.147415	0.0737076	−	0.997280i	$-0.476517\pi$
$643$	3.73807	0.147415	0.0737076	+	0.997280i	$0.476517\pi$
$644$	17.1167	0.674492
$645$	71.3779	2.81050
$646$	−5.45325	−0.214555
$647$	14.4008	0.566155	0.283078	−	0.959097i	$-0.408645\pi$
$647$	14.4008	0.566155	0.283078	+	0.959097i	$0.408645\pi$
$648$	10.7341	0.421674
$649$	0.141416	0.00555107
$650$	−20.9745	−0.822688
$651$	50.7515	1.98911
$652$	−17.4868	−0.684837
$653$	−22.3384	−0.874170	−0.437085	−	0.899420i	$-0.643989\pi$
$653$	−22.3384	−0.874170	−0.437085	+	0.899420i	$0.643989\pi$
$654$	−2.83791	−0.110971
$655$	45.0542	1.76041
$656$	8.36372	0.326548
$657$	−9.78173	−0.381621
$658$	18.4163	0.717944
$659$	−20.5310	−0.799772	−0.399886	−	0.916565i	$-0.630950\pi$
$659$	−20.5310	−0.799772	−0.399886	+	0.916565i	$0.630950\pi$
$660$	−1.11561	−0.0434251
$661$	−28.7509	−1.11828	−0.559140	−	0.829073i	$-0.688869\pi$
$661$	−28.7509	−1.11828	−0.559140	+	0.829073i	$0.688869\pi$
$662$	27.2260	1.05817
$663$	3.56026	0.138269
$664$	11.5836	0.449530
$665$	−65.7561	−2.54991
$666$	−3.19942	−0.123975
$667$	−50.5567	−1.95756
$668$	0.203018	0.00785502
$669$	−4.22357	−0.163293
$670$	−10.5883	−0.409060
$671$	−0.659921	−0.0254760
$672$	5.78036	0.222982
$673$	−13.4555	−0.518672	−0.259336	−	0.965787i	$-0.583504\pi$
$673$	−13.4555	−0.518672	−0.259336	+	0.965787i	$0.583504\pi$
$674$	−18.4297	−0.709886
$675$	−49.4216	−1.90224
$676$	−9.64823	−0.371086
$677$	48.8250	1.87650	0.938249	−	0.345961i	$-0.112447\pi$
$677$	48.8250	1.87650	0.938249	+	0.345961i	$0.112447\pi$
$678$	24.4382	0.938542
$679$	−15.2512	−0.585286
$680$	−4.05667	−0.155566
$681$	15.8298	0.606601
$682$	−1.24163	−0.0475446
$683$	−35.4369	−1.35595	−0.677977	−	0.735083i	$-0.737143\pi$
$683$	−35.4369	−1.35595	−0.677977	+	0.735083i	$0.737143\pi$
$684$	4.26286	0.162995
$685$	−49.7734	−1.90174
$686$	−15.3517	−0.586130
$687$	−40.5726	−1.54794
$688$	9.04794	0.344950
$689$	20.1336	0.767028
$690$	45.4279	1.72941
$691$	−3.09603	−0.117779	−0.0588893	−	0.998265i	$-0.518756\pi$
$691$	−3.09603	−0.117779	−0.0588893	+	0.998265i	$0.518756\pi$
$692$	−26.0647	−0.990830
$693$	0.328591	0.0124821
$694$	−18.0626	−0.685647
$695$	79.2608	3.00653
$696$	−17.0731	−0.647156
$697$	8.36372	0.316799
$698$	−17.8881	−0.677074
$699$	7.08802	0.268094
$700$	−34.0538	−1.28711
$701$	−39.1326	−1.47802	−0.739008	−	0.673696i	$-0.764706\pi$
$701$	−39.1326	−1.47802	−0.739008	+	0.673696i	$0.764706\pi$
$702$	7.89768	0.298079
$703$	22.3193	0.841790
$704$	−0.141416	−0.00532982
$705$	48.8772	1.84082
$706$	1.31492	0.0494876
$707$	−5.76897	−0.216964
$708$	−1.94466	−0.0730849
$709$	16.9443	0.636356	0.318178	−	0.948031i	$-0.396929\pi$
$709$	16.9443	0.636356	0.318178	+	0.948031i	$0.396929\pi$
$710$	−55.6984	−2.09032
$711$	−8.70384	−0.326420
$712$	7.08263	0.265433
$713$	50.5596	1.89347
$714$	5.78036	0.216324
$715$	−1.05028	−0.0392783
$716$	−19.8663	−0.742437
$717$	23.5218	0.878439
$718$	−25.0475	−0.934766
$719$	−38.3867	−1.43158	−0.715790	−	0.698315i	$-0.753933\pi$
$719$	−38.3867	−1.43158	−0.715790	+	0.698315i	$0.753933\pi$
$720$	3.17114	0.118181
$721$	3.21660	0.119792
$722$	−10.7380	−0.399625
$723$	46.8152	1.74107
$724$	11.5385	0.428825
$725$	100.583	3.73555
$726$	21.3524	0.792462
$727$	17.6106	0.653140	0.326570	−	0.945173i	$-0.394107\pi$
$727$	17.6106	0.653140	0.326570	+	0.945173i	$0.394107\pi$
$728$	5.44186	0.201689
$729$	16.7759	0.621328
$730$	50.7621	1.87879
$731$	9.04794	0.334650
$732$	9.07480	0.335414
$733$	29.6781	1.09618	0.548092	−	0.836418i	$-0.315354\pi$
$733$	29.6781	1.09618	0.548092	+	0.836418i	$0.315354\pi$
$734$	−5.86779	−0.216584
$735$	14.4784	0.534044
$736$	5.75850	0.212261
$737$	−0.369109	−0.0135963
$738$	−6.53800	−0.240667
$739$	−32.8681	−1.20907	−0.604537	−	0.796577i	$-0.706642\pi$
$739$	−32.8681	−1.20907	−0.604537	+	0.796577i	$0.706642\pi$
$740$	16.6033	0.610351
$741$	19.4150	0.713227
$742$	32.6885	1.20003
$743$	20.1254	0.738330	0.369165	−	0.929364i	$-0.379644\pi$
$743$	20.1254	0.738330	0.369165	+	0.929364i	$0.379644\pi$
$744$	17.0741	0.625968
$745$	−41.4975	−1.52035
$746$	−29.5524	−1.08199
$747$	−9.05499	−0.331305
$748$	−0.141416	−0.00517068
$749$	13.1928	0.482054
$750$	−50.9349	−1.85988
$751$	1.65626	0.0604377	0.0302188	−	0.999543i	$-0.490380\pi$
$751$	1.65626	0.0604377	0.0302188	+	0.999543i	$0.490380\pi$
$752$	6.19574	0.225935
$753$	−39.8146	−1.45093
$754$	−16.0733	−0.585357
$755$	−5.47427	−0.199229
$756$	12.8225	0.466350
$757$	−11.5811	−0.420923	−0.210462	−	0.977602i	$-0.567497\pi$
$757$	−11.5811	−0.420923	−0.210462	+	0.977602i	$0.567497\pi$
$758$	0.462266	0.0167903
$759$	1.58362	0.0574819
$760$	−22.1220	−0.802451
$761$	30.9773	1.12293	0.561463	−	0.827502i	$-0.310239\pi$
$761$	30.9773	1.12293	0.561463	+	0.827502i	$0.310239\pi$
$762$	38.1836	1.38324
$763$	−4.33775	−0.157037
$764$	8.29517	0.300109
$765$	3.17114	0.114653
$766$	−16.0427	−0.579646
$767$	−1.83078	−0.0661058
$768$	1.94466	0.0701719
$769$	−14.6641	−0.528801	−0.264400	−	0.964413i	$-0.585174\pi$
$769$	−14.6641	−0.528801	−0.264400	+	0.964413i	$0.585174\pi$
$770$	−1.70522	−0.0614517
$771$	−28.7618	−1.03583
$772$	−12.8710	−0.463238
$773$	16.8763	0.606998	0.303499	−	0.952832i	$-0.401845\pi$
$773$	16.8763	0.606998	0.303499	+	0.952832i	$0.401845\pi$
$774$	−7.07287	−0.254229
$775$	−100.589	−3.61325
$776$	−5.13089	−0.184188
$777$	−23.6581	−0.848731
$778$	−33.0592	−1.18523
$779$	45.6095	1.63413
$780$	14.4428	0.517135
$781$	−1.94165	−0.0694779
$782$	5.75850	0.205924
$783$	−37.8732	−1.35348
$784$	1.83530	0.0655464
$785$	69.4759	2.47970
$786$	−21.5978	−0.770369
$787$	−25.5155	−0.909528	−0.454764	−	0.890612i	$-0.650276\pi$
$787$	−25.5155	−0.909528	−0.454764	+	0.890612i	$0.650276\pi$
$788$	16.3738	0.583293
$789$	−23.4972	−0.836524
$790$	45.1684	1.60702
$791$	37.3538	1.32815
$792$	0.110546	0.00392809
$793$	8.54339	0.303385
$794$	12.8771	0.456990
$795$	86.7556	3.07690
$796$	−8.85051	−0.313698
$797$	−19.9949	−0.708257	−0.354128	−	0.935197i	$-0.615222\pi$
$797$	−19.9949	−0.708257	−0.354128	+	0.935197i	$0.615222\pi$
$798$	31.5217	1.11586
$799$	6.19574	0.219189
$800$	−11.4566	−0.405051
$801$	−5.53656	−0.195625
$802$	5.48346	0.193628
$803$	1.76957	0.0624469
$804$	5.07574	0.179008
$805$	69.4368	2.44733
$806$	16.0743	0.566192
$807$	−40.3246	−1.41949
$808$	−1.94083	−0.0682782
$809$	14.1407	0.497160	0.248580	−	0.968611i	$-0.420036\pi$
$809$	14.1407	0.497160	0.248580	+	0.968611i	$0.420036\pi$
$810$	43.5445	1.53000
$811$	−34.6552	−1.21691	−0.608454	−	0.793589i	$-0.708210\pi$
$811$	−34.6552	−1.21691	−0.608454	+	0.793589i	$0.708210\pi$
$812$	−26.0964	−0.915803
$813$	−35.5692	−1.24747
$814$	0.578795	0.0202868
$815$	−70.9383	−2.48486
$816$	1.94466	0.0680768
$817$	49.3407	1.72621
$818$	−32.9686	−1.15272
$819$	−4.25396	−0.148645
$820$	33.9289	1.18485
$821$	35.1448	1.22656	0.613282	−	0.789864i	$-0.289849\pi$
$821$	35.1448	1.22656	0.613282	+	0.789864i	$0.289849\pi$
$822$	23.8601	0.832215
$823$	21.3325	0.743603	0.371802	−	0.928312i	$-0.378740\pi$
$823$	21.3325	0.743603	0.371802	+	0.928312i	$0.378740\pi$
$824$	1.08215	0.0376984
$825$	−3.15063	−0.109691
$826$	−2.97242	−0.103424
$827$	−51.5550	−1.79274	−0.896371	−	0.443304i	$-0.853806\pi$
$827$	−51.5550	−1.79274	−0.896371	+	0.443304i	$0.853806\pi$
$828$	−4.50148	−0.156437
$829$	15.5678	0.540693	0.270347	−	0.962763i	$-0.412862\pi$
$829$	15.5678	0.540693	0.270347	+	0.962763i	$0.412862\pi$
$830$	46.9907	1.63107
$831$	−16.4311	−0.569988
$832$	1.83078	0.0634710
$833$	1.83530	0.0635893
$834$	−37.9956	−1.31568
$835$	0.823579	0.0285011
$836$	−0.771178	−0.0266717
$837$	37.8754	1.30916
$838$	−4.90911	−0.169582
$839$	−42.4196	−1.46449	−0.732243	−	0.681043i	$-0.761526\pi$
$839$	−42.4196	−1.46449	−0.732243	+	0.681043i	$0.761526\pi$
$840$	23.4490	0.809068
$841$	48.0794	1.65791
$842$	7.14928	0.246380
$843$	−0.707959	−0.0243834
$844$	15.5470	0.535150
$845$	−39.1397	−1.34645
$846$	−4.84327	−0.166515
$847$	32.6372	1.12143
$848$	10.9972	0.377647
$849$	58.7374	2.01586
$850$	−11.4566	−0.392957
$851$	−23.5687	−0.807924
$852$	26.7004	0.914739
$853$	7.82572	0.267948	0.133974	−	0.990985i	$-0.457226\pi$
$853$	7.82572	0.267948	0.133974	+	0.990985i	$0.457226\pi$
$854$	13.8709	0.474651
$855$	17.2930	0.591409
$856$	4.43839	0.151701
$857$	−16.8396	−0.575231	−0.287616	−	0.957746i	$-0.592863\pi$
$857$	−16.8396	−0.575231	−0.287616	+	0.957746i	$0.592863\pi$
$858$	0.503477	0.0171884
$859$	−16.7652	−0.572021	−0.286010	−	0.958227i	$-0.592329\pi$
$859$	−16.7652	−0.572021	−0.286010	+	0.958227i	$0.592329\pi$
$860$	36.7045	1.25161
$861$	−48.3453	−1.64760
$862$	−12.7884	−0.435574
$863$	11.3553	0.386538	0.193269	−	0.981146i	$-0.438091\pi$
$863$	11.3553	0.386538	0.193269	+	0.981146i	$0.438091\pi$
$864$	4.31382	0.146759
$865$	−105.736	−3.59512
$866$	14.7143	0.500013
$867$	1.94466	0.0660442
$868$	26.0979	0.885819
$869$	1.57458	0.0534139
$870$	−69.2601	−2.34814
$871$	4.77851	0.161914
$872$	−1.45933	−0.0494192
$873$	4.01087	0.135747
$874$	31.4025	1.06221
$875$	−77.8543	−2.63195
$876$	−24.3340	−0.822171
$877$	14.8779	0.502392	0.251196	−	0.967936i	$-0.419176\pi$
$877$	14.8779	0.502392	0.251196	+	0.967936i	$0.419176\pi$
$878$	−39.7914	−1.34290
$879$	−40.1052	−1.35272
$880$	−0.573678	−0.0193387
$881$	26.1475	0.880931	0.440465	−	0.897770i	$-0.354813\pi$
$881$	26.1475	0.880931	0.440465	+	0.897770i	$0.354813\pi$
$882$	−1.43467	−0.0483079
$883$	−47.3483	−1.59340	−0.796698	−	0.604378i	$-0.793422\pi$
$883$	−47.3483	−1.59340	−0.796698	+	0.604378i	$0.793422\pi$
$884$	1.83078	0.0615759
$885$	−7.88885	−0.265181
$886$	2.60018	0.0873549
$887$	−28.9130	−0.970804	−0.485402	−	0.874291i	$-0.661327\pi$
$887$	−28.9130	−0.970804	−0.485402	+	0.874291i	$0.661327\pi$
$888$	−7.95921	−0.267094
$889$	58.3637	1.95746
$890$	28.7319	0.963095
$891$	1.51797	0.0508539
$892$	−2.17188	−0.0727198
$893$	33.7869	1.13064
$894$	19.8928	0.665316
$895$	−80.5909	−2.69386
$896$	2.97242	0.0993017
$897$	−20.5017	−0.684533
$898$	10.6023	0.353803
$899$	−77.0839	−2.57089
$900$	8.95572	0.298524
$901$	10.9972	0.366371
$902$	1.18277	0.0393818
$903$	−52.3004	−1.74045
$904$	12.5668	0.417965
$905$	46.8079	1.55595
$906$	2.62422	0.0871839
$907$	34.5617	1.14760	0.573801	−	0.818995i	$-0.305468\pi$
$907$	34.5617	1.14760	0.573801	+	0.818995i	$0.305468\pi$
$908$	8.14015	0.270141
$909$	1.51717	0.0503212
$910$	22.0758	0.731807
$911$	18.3559	0.608159	0.304080	−	0.952647i	$-0.401651\pi$
$911$	18.3559	0.608159	0.304080	+	0.952647i	$0.401651\pi$
$912$	10.6047	0.351158
$913$	1.63810	0.0542133
$914$	24.4822	0.809798
$915$	36.8135	1.21702
$916$	−20.8636	−0.689352
$917$	−33.0123	−1.09016
$918$	4.31382	0.142377
$919$	11.3586	0.374687	0.187344	−	0.982294i	$-0.440012\pi$
$919$	11.3586	0.374687	0.187344	+	0.982294i	$0.440012\pi$
$920$	23.3603	0.770167
$921$	−1.81721	−0.0598792
$922$	−7.11791	−0.234416
$923$	25.1368	0.827388
$924$	0.817436	0.0268917
$925$	46.8900	1.54173
$926$	−15.1579	−0.498121
$927$	−0.845925	−0.0277838
$928$	−8.77949	−0.288201
$929$	−31.6711	−1.03910	−0.519548	−	0.854441i	$-0.673900\pi$
$929$	−31.6711	−1.03910	−0.519548	+	0.854441i	$0.673900\pi$
$930$	69.2641	2.27126
$931$	10.0083	0.328010
$932$	3.64486	0.119391
$933$	−60.3389	−1.97541
$934$	−11.3661	−0.371909
$935$	−0.573678	−0.0187613
$936$	−1.43114	−0.0467783
$937$	−37.6771	−1.23086	−0.615429	−	0.788193i	$-0.711017\pi$
$937$	−37.6771	−1.23086	−0.615429	+	0.788193i	$0.711017\pi$
$938$	7.75829	0.253317
$939$	−9.67533	−0.315743
$940$	25.1341	0.819783
$941$	−8.09015	−0.263731	−0.131866	−	0.991268i	$-0.542097\pi$
$941$	−8.09015	−0.263731	−0.131866	+	0.991268i	$0.542097\pi$
$942$	−33.3049	−1.08513
$943$	−48.1625	−1.56839
$944$	−1.00000	−0.0325472
$945$	52.0167	1.69210
$946$	1.27953	0.0416010
$947$	−27.0054	−0.877559	−0.438779	−	0.898595i	$-0.644589\pi$
$947$	−27.0054	−0.877559	−0.438779	+	0.898595i	$0.644589\pi$
$948$	−21.6526	−0.703243
$949$	−22.9090	−0.743659
$950$	−62.4756	−2.02698
$951$	−35.8085	−1.16117
$952$	2.97242	0.0963368
$953$	6.22817	0.201750	0.100875	−	0.994899i	$-0.467836\pi$
$953$	6.22817	0.201750	0.100875	+	0.994899i	$0.467836\pi$
$954$	−8.59665	−0.278327
$955$	33.6508	1.08891
$956$	12.0956	0.391199
$957$	−2.41442	−0.0780470
$958$	15.3707	0.496606
$959$	36.4702	1.17768
$960$	7.88885	0.254612
$961$	46.0883	1.48672
$962$	−7.49312	−0.241588
$963$	−3.46954	−0.111804
$964$	24.0737	0.775361
$965$	−52.2134	−1.68081
$966$	−33.2862	−1.07097
$967$	41.2048	1.32506	0.662529	−	0.749036i	$-0.269483\pi$
$967$	41.2048	1.32506	0.662529	+	0.749036i	$0.269483\pi$
$968$	10.9800	0.352911
$969$	10.6047	0.340673
$970$	−20.8143	−0.668307
$971$	39.9166	1.28098	0.640492	−	0.767965i	$-0.278730\pi$
$971$	39.9166	1.28098	0.640492	+	0.767965i	$0.278730\pi$
$972$	−7.93264	−0.254440
$973$	−58.0763	−1.86184
$974$	−3.04291	−0.0975010
$975$	40.7883	1.30627
$976$	4.66652	0.149372
$977$	43.2812	1.38469	0.692343	−	0.721568i	$-0.256578\pi$
$977$	43.2812	1.38469	0.692343	+	0.721568i	$0.256578\pi$
$978$	34.0060	1.08739
$979$	1.00160	0.0320112
$980$	7.44520	0.237828
$981$	1.14077	0.0364221
$982$	−13.5899	−0.433670
$983$	−9.46365	−0.301843	−0.150922	−	0.988546i	$-0.548224\pi$
$983$	−9.46365	−0.301843	−0.150922	+	0.988546i	$0.548224\pi$
$984$	−16.2646	−0.518497
$985$	66.4231	2.11642
$986$	−8.77949	−0.279596
$987$	−35.8136	−1.13996
$988$	9.98372	0.317625
$989$	−52.1026	−1.65677
$990$	0.448450	0.0142527
$991$	17.7177	0.562821	0.281410	−	0.959588i	$-0.409198\pi$
$991$	17.7177	0.562821	0.281410	+	0.959588i	$0.409198\pi$
$992$	8.78000	0.278765
$993$	−52.9454	−1.68017
$994$	40.8116	1.29447
$995$	−35.9036	−1.13822
$996$	−22.5261	−0.713768
$997$	2.81538	0.0891640	0.0445820	−	0.999006i	$-0.485804\pi$
$997$	2.81538	0.0891640	0.0445820	+	0.999006i	$0.485804\pi$
$998$	−13.4836	−0.426816
$999$	−17.6558	−0.558606

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.u.1.7	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.u.1.7	✓	9	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.94466 q^{3} +1.00000 q^{4} +4.05667 q^{5} -1.94466 q^{6} -2.97242 q^{7} -1.00000 q^{8} +0.781710 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.94466 q^{3} +1.00000 q^{4} +4.05667 q^{5} -1.94466 q^{6} -2.97242 q^{7} -1.00000 q^{8} +0.781710 q^{9} -4.05667 q^{10} -0.141416 q^{11} +1.94466 q^{12} +1.83078 q^{13} +2.97242 q^{14} +7.88885 q^{15} +1.00000 q^{16} +1.00000 q^{17} -0.781710 q^{18} +5.45325 q^{19} +4.05667 q^{20} -5.78036 q^{21} +0.141416 q^{22} -5.75850 q^{23} -1.94466 q^{24} +11.4566 q^{25} -1.83078 q^{26} -4.31382 q^{27} -2.97242 q^{28} +8.77949 q^{29} -7.88885 q^{30} -8.78000 q^{31} -1.00000 q^{32} -0.275007 q^{33} -1.00000 q^{34} -12.0581 q^{35} +0.781710 q^{36} +4.09285 q^{37} -5.45325 q^{38} +3.56026 q^{39} -4.05667 q^{40} +8.36372 q^{41} +5.78036 q^{42} +9.04794 q^{43} -0.141416 q^{44} +3.17114 q^{45} +5.75850 q^{46} +6.19574 q^{47} +1.94466 q^{48} +1.83530 q^{49} -11.4566 q^{50} +1.94466 q^{51} +1.83078 q^{52} +10.9972 q^{53} +4.31382 q^{54} -0.573678 q^{55} +2.97242 q^{56} +10.6047 q^{57} -8.77949 q^{58} -1.00000 q^{59} +7.88885 q^{60} +4.66652 q^{61} +8.78000 q^{62} -2.32357 q^{63} +1.00000 q^{64} +7.42689 q^{65} +0.275007 q^{66} +2.61009 q^{67} +1.00000 q^{68} -11.1983 q^{69} +12.0581 q^{70} +13.7301 q^{71} -0.781710 q^{72} -12.5132 q^{73} -4.09285 q^{74} +22.2792 q^{75} +5.45325 q^{76} +0.420348 q^{77} -3.56026 q^{78} -11.1344 q^{79} +4.05667 q^{80} -10.7341 q^{81} -8.36372 q^{82} -11.5836 q^{83} -5.78036 q^{84} +4.05667 q^{85} -9.04794 q^{86} +17.0731 q^{87} +0.141416 q^{88} -7.08263 q^{89} -3.17114 q^{90} -5.44186 q^{91} -5.75850 q^{92} -17.0741 q^{93} -6.19574 q^{94} +22.1220 q^{95} -1.94466 q^{96} +5.13089 q^{97} -1.83530 q^{98} -0.110546 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - q^{3} + 9 q^{4} + 7 q^{5} + q^{6} - 9 q^{8} + 20 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - q^3 + 9 * q^4 + 7 * q^5 + q^6 - 9 * q^8 + 20 * q^9	\( 9 q - 9 q^{2} - q^{3} + 9 q^{4} + 7 q^{5} + q^{6} - 9 q^{8} + 20 q^{9} - 7 q^{10} + 5 q^{11} - q^{12} + 25 q^{13} - 5 q^{15} + 9 q^{16} + 9 q^{17} - 20 q^{18} + 14 q^{19} + 7 q^{20} - 7 q^{21} - 5 q^{22} + 2 q^{23} + q^{24} + 20 q^{25} - 25 q^{26} - 10 q^{27} + 18 q^{29} + 5 q^{30} + 6 q^{31} - 9 q^{32} - 9 q^{33} - 9 q^{34} - 17 q^{35} + 20 q^{36} + 11 q^{37} - 14 q^{38} - 8 q^{39} - 7 q^{40} + 18 q^{41} + 7 q^{42} - 10 q^{43} + 5 q^{44} + 27 q^{45} - 2 q^{46} - 20 q^{47} - q^{48} + 13 q^{49} - 20 q^{50} - q^{51} + 25 q^{52} - 7 q^{53} + 10 q^{54} + 29 q^{55} + 17 q^{57} - 18 q^{58} - 9 q^{59} - 5 q^{60} + 30 q^{61} - 6 q^{62} - 47 q^{63} + 9 q^{64} + 8 q^{65} + 9 q^{66} + 6 q^{67} + 9 q^{68} + 20 q^{69} + 17 q^{70} + 30 q^{71} - 20 q^{72} - 11 q^{74} - 7 q^{75} + 14 q^{76} - 3 q^{77} + 8 q^{78} + 29 q^{79} + 7 q^{80} - 3 q^{81} - 18 q^{82} + 9 q^{83} - 7 q^{84} + 7 q^{85} + 10 q^{86} + 44 q^{87} - 5 q^{88} + 8 q^{89} - 27 q^{90} + 13 q^{91} + 2 q^{92} + 7 q^{93} + 20 q^{94} + 27 q^{95} + q^{96} - 13 q^{97} - 13 q^{98} - 19 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - q^3 + 9 * q^4 + 7 * q^5 + q^6 - 9 * q^8 + 20 * q^9 - 7 * q^10 + 5 * q^11 - q^12 + 25 * q^13 - 5 * q^15 + 9 * q^16 + 9 * q^17 - 20 * q^18 + 14 * q^19 + 7 * q^20 - 7 * q^21 - 5 * q^22 + 2 * q^23 + q^24 + 20 * q^25 - 25 * q^26 - 10 * q^27 + 18 * q^29 + 5 * q^30 + 6 * q^31 - 9 * q^32 - 9 * q^33 - 9 * q^34 - 17 * q^35 + 20 * q^36 + 11 * q^37 - 14 * q^38 - 8 * q^39 - 7 * q^40 + 18 * q^41 + 7 * q^42 - 10 * q^43 + 5 * q^44 + 27 * q^45 - 2 * q^46 - 20 * q^47 - q^48 + 13 * q^49 - 20 * q^50 - q^51 + 25 * q^52 - 7 * q^53 + 10 * q^54 + 29 * q^55 + 17 * q^57 - 18 * q^58 - 9 * q^59 - 5 * q^60 + 30 * q^61 - 6 * q^62 - 47 * q^63 + 9 * q^64 + 8 * q^65 + 9 * q^66 + 6 * q^67 + 9 * q^68 + 20 * q^69 + 17 * q^70 + 30 * q^71 - 20 * q^72 - 11 * q^74 - 7 * q^75 + 14 * q^76 - 3 * q^77 + 8 * q^78 + 29 * q^79 + 7 * q^80 - 3 * q^81 - 18 * q^82 + 9 * q^83 - 7 * q^84 + 7 * q^85 + 10 * q^86 + 44 * q^87 - 5 * q^88 + 8 * q^89 - 27 * q^90 + 13 * q^91 + 2 * q^92 + 7 * q^93 + 20 * q^94 + 27 * q^95 + q^96 - 13 * q^97 - 13 * q^98 - 19 * q^99

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