LMFDB - Embedded newform 4006.2.a.g.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4006,2,Mod(1,4006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4006, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4006 = 2 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4006.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:	$31.9880710497$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.779235 q^{3} +1.00000 q^{4} -0.867411 q^{5} +0.779235 q^{6} -3.45139 q^{7} -1.00000 q^{8} -2.39279 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.779235 q^{3} +1.00000 q^{4} -0.867411 q^{5} +0.779235 q^{6} -3.45139 q^{7} -1.00000 q^{8} -2.39279 q^{9} +0.867411 q^{10} +3.23634 q^{11} -0.779235 q^{12} +0.0959992 q^{13} +3.45139 q^{14} +0.675917 q^{15} +1.00000 q^{16} +5.34635 q^{17} +2.39279 q^{18} +1.96760 q^{19} -0.867411 q^{20} +2.68944 q^{21} -3.23634 q^{22} -4.56800 q^{23} +0.779235 q^{24} -4.24760 q^{25} -0.0959992 q^{26} +4.20225 q^{27} -3.45139 q^{28} -4.12205 q^{29} -0.675917 q^{30} +0.192159 q^{31} -1.00000 q^{32} -2.52187 q^{33} -5.34635 q^{34} +2.99377 q^{35} -2.39279 q^{36} +3.45176 q^{37} -1.96760 q^{38} -0.0748059 q^{39} +0.867411 q^{40} +6.89417 q^{41} -2.68944 q^{42} -3.27590 q^{43} +3.23634 q^{44} +2.07553 q^{45} +4.56800 q^{46} +11.3951 q^{47} -0.779235 q^{48} +4.91210 q^{49} +4.24760 q^{50} -4.16606 q^{51} +0.0959992 q^{52} -1.21545 q^{53} -4.20225 q^{54} -2.80724 q^{55} +3.45139 q^{56} -1.53323 q^{57} +4.12205 q^{58} +0.581098 q^{59} +0.675917 q^{60} -3.01819 q^{61} -0.192159 q^{62} +8.25846 q^{63} +1.00000 q^{64} -0.0832707 q^{65} +2.52187 q^{66} +9.49351 q^{67} +5.34635 q^{68} +3.55955 q^{69} -2.99377 q^{70} -14.4713 q^{71} +2.39279 q^{72} +11.7161 q^{73} -3.45176 q^{74} +3.30988 q^{75} +1.96760 q^{76} -11.1699 q^{77} +0.0748059 q^{78} +2.62921 q^{79} -0.867411 q^{80} +3.90384 q^{81} -6.89417 q^{82} +7.45027 q^{83} +2.68944 q^{84} -4.63748 q^{85} +3.27590 q^{86} +3.21205 q^{87} -3.23634 q^{88} +7.41702 q^{89} -2.07553 q^{90} -0.331331 q^{91} -4.56800 q^{92} -0.149737 q^{93} -11.3951 q^{94} -1.70672 q^{95} +0.779235 q^{96} -2.66158 q^{97} -4.91210 q^{98} -7.74389 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) $ 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * 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
$3$	−0.779235	−0.449891	−0.224946	−	0.974371i	$-0.572220\pi$
$3$	−0.779235	−0.449891	−0.224946	+	0.974371i	$0.572220\pi$
$4$	1.00000	0.500000
$5$	−0.867411	−0.387918	−0.193959	−	0.981010i	$-0.562133\pi$
$5$	−0.867411	−0.387918	−0.193959	+	0.981010i	$0.562133\pi$
$6$	0.779235	0.318121
$7$	−3.45139	−1.30450	−0.652252	−	0.758003i	$-0.726175\pi$
$7$	−3.45139	−1.30450	−0.652252	+	0.758003i	$0.726175\pi$
$8$	−1.00000	−0.353553
$9$	−2.39279	−0.797598
$10$	0.867411	0.274299
$11$	3.23634	0.975793	0.487897	−	0.872901i	$-0.337764\pi$
$11$	3.23634	0.975793	0.487897	+	0.872901i	$0.337764\pi$
$12$	−0.779235	−0.224946
$13$	0.0959992	0.0266254	0.0133127	−	0.999911i	$-0.495762\pi$
$13$	0.0959992	0.0266254	0.0133127	+	0.999911i	$0.495762\pi$
$14$	3.45139	0.922423
$15$	0.675917	0.174521
$16$	1.00000	0.250000
$17$	5.34635	1.29668	0.648340	−	0.761351i	$-0.275463\pi$
$17$	5.34635	1.29668	0.648340	+	0.761351i	$0.275463\pi$
$18$	2.39279	0.563987
$19$	1.96760	0.451400	0.225700	−	0.974197i	$-0.427533\pi$
$19$	1.96760	0.451400	0.225700	+	0.974197i	$0.427533\pi$
$20$	−0.867411	−0.193959
$21$	2.68944	0.586885
$22$	−3.23634	−0.689990
$23$	−4.56800	−0.952495	−0.476247	−	0.879311i	$-0.658003\pi$
$23$	−4.56800	−0.952495	−0.476247	+	0.879311i	$0.658003\pi$
$24$	0.779235	0.159061
$25$	−4.24760	−0.849520
$26$	−0.0959992	−0.0188270
$27$	4.20225	0.808724
$28$	−3.45139	−0.652252
$29$	−4.12205	−0.765446	−0.382723	−	0.923863i	$-0.625014\pi$
$29$	−4.12205	−0.765446	−0.382723	+	0.923863i	$0.625014\pi$
$30$	−0.675917	−0.123405
$31$	0.192159	0.0345128	0.0172564	−	0.999851i	$-0.494507\pi$
$31$	0.192159	0.0345128	0.0172564	+	0.999851i	$0.494507\pi$
$32$	−1.00000	−0.176777
$33$	−2.52187	−0.439001
$34$	−5.34635	−0.916892
$35$	2.99377	0.506040
$36$	−2.39279	−0.398799
$37$	3.45176	0.567466	0.283733	−	0.958903i	$-0.408427\pi$
$37$	3.45176	0.567466	0.283733	+	0.958903i	$0.408427\pi$
$38$	−1.96760	−0.319188
$39$	−0.0748059	−0.0119785
$40$	0.867411	0.137150
$41$	6.89417	1.07669	0.538344	−	0.842725i	$-0.319050\pi$
$41$	6.89417	1.07669	0.538344	+	0.842725i	$0.319050\pi$
$42$	−2.68944	−0.414990
$43$	−3.27590	−0.499570	−0.249785	−	0.968301i	$-0.580360\pi$
$43$	−3.27590	−0.499570	−0.249785	+	0.968301i	$0.580360\pi$
$44$	3.23634	0.487897
$45$	2.07553	0.309402
$46$	4.56800	0.673515
$47$	11.3951	1.66215	0.831074	−	0.556161i	$-0.187726\pi$
$47$	11.3951	1.66215	0.831074	+	0.556161i	$0.187726\pi$
$48$	−0.779235	−0.112473
$49$	4.91210	0.701729
$50$	4.24760	0.600701
$51$	−4.16606	−0.583365
$52$	0.0959992	0.0133127
$53$	−1.21545	−0.166955	−0.0834775	−	0.996510i	$-0.526603\pi$
$53$	−1.21545	−0.166955	−0.0834775	+	0.996510i	$0.526603\pi$
$54$	−4.20225	−0.571854
$55$	−2.80724	−0.378528
$56$	3.45139	0.461212
$57$	−1.53323	−0.203081
$58$	4.12205	0.541252
$59$	0.581098	0.0756525	0.0378263	−	0.999284i	$-0.487957\pi$
$59$	0.581098	0.0756525	0.0378263	+	0.999284i	$0.487957\pi$
$60$	0.675917	0.0872605
$61$	−3.01819	−0.386440	−0.193220	−	0.981155i	$-0.561893\pi$
$61$	−3.01819	−0.386440	−0.193220	+	0.981155i	$0.561893\pi$
$62$	−0.192159	−0.0244042
$63$	8.25846	1.04047
$64$	1.00000	0.125000
$65$	−0.0832707	−0.0103285
$66$	2.52187	0.310421
$67$	9.49351	1.15982	0.579908	−	0.814682i	$-0.303088\pi$
$67$	9.49351	1.15982	0.579908	+	0.814682i	$0.303088\pi$
$68$	5.34635	0.648340
$69$	3.55955	0.428519
$70$	−2.99377	−0.357824
$71$	−14.4713	−1.71743	−0.858715	−	0.512453i	$-0.828737\pi$
$71$	−14.4713	−1.71743	−0.858715	+	0.512453i	$0.828737\pi$
$72$	2.39279	0.281993
$73$	11.7161	1.37127	0.685634	−	0.727946i	$-0.259525\pi$
$73$	11.7161	1.37127	0.685634	+	0.727946i	$0.259525\pi$
$74$	−3.45176	−0.401259
$75$	3.30988	0.382192
$76$	1.96760	0.225700
$77$	−11.1699	−1.27293
$78$	0.0748059	0.00847010
$79$	2.62921	0.295810	0.147905	−	0.989002i	$-0.452747\pi$
$79$	2.62921	0.295810	0.147905	+	0.989002i	$0.452747\pi$
$80$	−0.867411	−0.0969795
$81$	3.90384	0.433760
$82$	−6.89417	−0.761334
$83$	7.45027	0.817773	0.408887	−	0.912585i	$-0.365917\pi$
$83$	7.45027	0.817773	0.408887	+	0.912585i	$0.365917\pi$
$84$	2.68944	0.293442
$85$	−4.63748	−0.503006
$86$	3.27590	0.353250
$87$	3.21205	0.344368
$88$	−3.23634	−0.344995
$89$	7.41702	0.786202	0.393101	−	0.919495i	$-0.371402\pi$
$89$	7.41702	0.786202	0.393101	+	0.919495i	$0.371402\pi$
$90$	−2.07553	−0.218781
$91$	−0.331331	−0.0347329
$92$	−4.56800	−0.476247
$93$	−0.149737	−0.0155270
$94$	−11.3951	−1.17532
$95$	−1.70672	−0.175106
$96$	0.779235	0.0795303
$97$	−2.66158	−0.270243	−0.135121	−	0.990829i	$-0.543142\pi$
$97$	−2.66158	−0.270243	−0.135121	+	0.990829i	$0.543142\pi$
$98$	−4.91210	−0.496197
$99$	−7.74389	−0.778290
$100$	−4.24760	−0.424760
$101$	1.05027	0.104506	0.0522530	−	0.998634i	$-0.483360\pi$
$101$	1.05027	0.104506	0.0522530	+	0.998634i	$0.483360\pi$
$102$	4.16606	0.412502
$103$	−12.3758	−1.21943	−0.609714	−	0.792622i	$-0.708716\pi$
$103$	−12.3758	−1.21943	−0.609714	+	0.792622i	$0.708716\pi$
$104$	−0.0959992	−0.00941349
$105$	−2.33285	−0.227663
$106$	1.21545	0.118055
$107$	5.13993	0.496896	0.248448	−	0.968645i	$-0.420080\pi$
$107$	5.13993	0.496896	0.248448	+	0.968645i	$0.420080\pi$
$108$	4.20225	0.404362
$109$	−18.7459	−1.79553	−0.897766	−	0.440472i	$-0.854811\pi$
$109$	−18.7459	−1.79553	−0.897766	+	0.440472i	$0.854811\pi$
$110$	2.80724	0.267659
$111$	−2.68973	−0.255298
$112$	−3.45139	−0.326126
$113$	−4.47243	−0.420731	−0.210365	−	0.977623i	$-0.567465\pi$
$113$	−4.47243	−0.420731	−0.210365	+	0.977623i	$0.567465\pi$
$114$	1.53323	0.143600
$115$	3.96234	0.369490
$116$	−4.12205	−0.382723
$117$	−0.229706	−0.0212363
$118$	−0.581098	−0.0534944
$119$	−18.4523	−1.69152
$120$	−0.675917	−0.0617025
$121$	−0.526105	−0.0478277
$122$	3.01819	0.273254
$123$	−5.37218	−0.484393
$124$	0.192159	0.0172564
$125$	8.02147	0.717462
$126$	−8.25846	−0.735723
$127$	−0.301641	−0.0267663	−0.0133832	−	0.999910i	$-0.504260\pi$
$127$	−0.301641	−0.0267663	−0.0133832	+	0.999910i	$0.504260\pi$
$128$	−1.00000	−0.0883883
$129$	2.55270	0.224752
$130$	0.0832707	0.00730333
$131$	7.50878	0.656045	0.328023	−	0.944670i	$-0.393618\pi$
$131$	7.50878	0.656045	0.328023	+	0.944670i	$0.393618\pi$
$132$	−2.52187	−0.219500
$133$	−6.79097	−0.588852
$134$	−9.49351	−0.820114
$135$	−3.64508	−0.313718
$136$	−5.34635	−0.458446
$137$	−19.3698	−1.65487	−0.827437	−	0.561558i	$-0.810202\pi$
$137$	−19.3698	−1.65487	−0.827437	+	0.561558i	$0.810202\pi$
$138$	−3.55955	−0.303009
$139$	−13.4646	−1.14205	−0.571025	−	0.820933i	$-0.693454\pi$
$139$	−13.4646	−1.14205	−0.571025	+	0.820933i	$0.693454\pi$
$140$	2.99377	0.253020
$141$	−8.87947	−0.747786
$142$	14.4713	1.21441
$143$	0.310686	0.0259809
$144$	−2.39279	−0.199399
$145$	3.57551	0.296930
$146$	−11.7161	−0.969633
$147$	−3.82768	−0.315702
$148$	3.45176	0.283733
$149$	−11.0624	−0.906263	−0.453132	−	0.891444i	$-0.649693\pi$
$149$	−11.0624	−0.906263	−0.453132	+	0.891444i	$0.649693\pi$
$150$	−3.30988	−0.270250
$151$	−18.5776	−1.51182	−0.755911	−	0.654674i	$-0.772806\pi$
$151$	−18.5776	−1.51182	−0.755911	+	0.654674i	$0.772806\pi$
$152$	−1.96760	−0.159594
$153$	−12.7927	−1.03423
$154$	11.1699	0.900094
$155$	−0.166681	−0.0133881
$156$	−0.0748059	−0.00598927
$157$	6.59557	0.526384	0.263192	−	0.964744i	$-0.415225\pi$
$157$	6.59557	0.526384	0.263192	+	0.964744i	$0.415225\pi$
$158$	−2.62921	−0.209169
$159$	0.947122	0.0751117
$160$	0.867411	0.0685748
$161$	15.7660	1.24253
$162$	−3.90384	−0.306715
$163$	21.3886	1.67529	0.837643	−	0.546218i	$-0.183933\pi$
$163$	21.3886	1.67529	0.837643	+	0.546218i	$0.183933\pi$
$164$	6.89417	0.538344
$165$	2.18750	0.170296
$166$	−7.45027	−0.578253
$167$	−2.21303	−0.171249	−0.0856246	−	0.996327i	$-0.527289\pi$
$167$	−2.21303	−0.171249	−0.0856246	+	0.996327i	$0.527289\pi$
$168$	−2.68944	−0.207495
$169$	−12.9908	−0.999291
$170$	4.63748	0.355679
$171$	−4.70807	−0.360035
$172$	−3.27590	−0.249785
$173$	−18.0587	−1.37298	−0.686489	−	0.727140i	$-0.740849\pi$
$173$	−18.0587	−1.37298	−0.686489	+	0.727140i	$0.740849\pi$
$174$	−3.21205	−0.243505
$175$	14.6601	1.10820
$176$	3.23634	0.243948
$177$	−0.452812	−0.0340354
$178$	−7.41702	−0.555929
$179$	−9.99822	−0.747302	−0.373651	−	0.927569i	$-0.621894\pi$
$179$	−9.99822	−0.747302	−0.373651	+	0.927569i	$0.621894\pi$
$180$	2.07553	0.154701
$181$	10.7591	0.799719	0.399859	−	0.916577i	$-0.369059\pi$
$181$	10.7591	0.799719	0.399859	+	0.916577i	$0.369059\pi$
$182$	0.331331	0.0245599
$183$	2.35188	0.173856
$184$	4.56800	0.336758
$185$	−2.99410	−0.220130
$186$	0.149737	0.0109793
$187$	17.3026	1.26529
$188$	11.3951	0.831074
$189$	−14.5036	−1.05498
$190$	1.70672	0.123819
$191$	−18.8593	−1.36461	−0.682306	−	0.731067i	$-0.739023\pi$
$191$	−18.8593	−1.36461	−0.682306	+	0.731067i	$0.739023\pi$
$192$	−0.779235	−0.0562364
$193$	−13.3166	−0.958547	−0.479273	−	0.877666i	$-0.659100\pi$
$193$	−13.3166	−0.958547	−0.479273	+	0.877666i	$0.659100\pi$
$194$	2.66158	0.191090
$195$	0.0648874	0.00464669
$196$	4.91210	0.350864
$197$	13.6777	0.974493	0.487247	−	0.873264i	$-0.338001\pi$
$197$	13.6777	0.974493	0.487247	+	0.873264i	$0.338001\pi$
$198$	7.74389	0.550334
$199$	3.84768	0.272755	0.136377	−	0.990657i	$-0.456454\pi$
$199$	3.84768	0.272755	0.136377	+	0.990657i	$0.456454\pi$
$200$	4.24760	0.300351
$201$	−7.39767	−0.521792
$202$	−1.05027	−0.0738969
$203$	14.2268	0.998527
$204$	−4.16606	−0.291683
$205$	−5.98008	−0.417667
$206$	12.3758	0.862265
$207$	10.9303	0.759708
$208$	0.0959992	0.00665635
$209$	6.36784	0.440473
$210$	2.33285	0.160982
$211$	0.276423	0.0190297	0.00951486	−	0.999955i	$-0.496971\pi$
$211$	0.276423	0.0190297	0.00951486	+	0.999955i	$0.496971\pi$
$212$	−1.21545	−0.0834775
$213$	11.2766	0.772657
$214$	−5.13993	−0.351358
$215$	2.84155	0.193792
$216$	−4.20225	−0.285927
$217$	−0.663217	−0.0450221
$218$	18.7459	1.26963
$219$	−9.12961	−0.616922
$220$	−2.80724	−0.189264
$221$	0.513245	0.0345246
$222$	2.68973	0.180523
$223$	4.91884	0.329390	0.164695	−	0.986345i	$-0.447336\pi$
$223$	4.91884	0.329390	0.164695	+	0.986345i	$0.447336\pi$
$224$	3.45139	0.230606
$225$	10.1636	0.677575
$226$	4.47243	0.297502
$227$	12.1843	0.808698	0.404349	−	0.914605i	$-0.367498\pi$
$227$	12.1843	0.808698	0.404349	+	0.914605i	$0.367498\pi$
$228$	−1.53323	−0.101540
$229$	28.5001	1.88334	0.941669	−	0.336541i	$-0.109257\pi$
$229$	28.5001	1.88334	0.941669	+	0.336541i	$0.109257\pi$
$230$	−3.96234	−0.261269
$231$	8.70395	0.572678
$232$	4.12205	0.270626
$233$	−16.2015	−1.06140	−0.530698	−	0.847561i	$-0.678070\pi$
$233$	−16.2015	−1.06140	−0.530698	+	0.847561i	$0.678070\pi$
$234$	0.229706	0.0150164
$235$	−9.88425	−0.644777
$236$	0.581098	0.0378263
$237$	−2.04878	−0.133082
$238$	18.4523	1.19609
$239$	−12.3676	−0.799997	−0.399998	−	0.916516i	$-0.630989\pi$
$239$	−12.3676	−0.799997	−0.399998	+	0.916516i	$0.630989\pi$
$240$	0.675917	0.0436302
$241$	−14.1994	−0.914663	−0.457332	−	0.889296i	$-0.651195\pi$
$241$	−14.1994	−0.914663	−0.457332	+	0.889296i	$0.651195\pi$
$242$	0.526105	0.0338193
$243$	−15.6488	−1.00387
$244$	−3.01819	−0.193220
$245$	−4.26081	−0.272213
$246$	5.37218	0.342518
$247$	0.188888	0.0120187
$248$	−0.192159	−0.0122021
$249$	−5.80551	−0.367909
$250$	−8.02147	−0.507322
$251$	−25.9160	−1.63580	−0.817902	−	0.575358i	$-0.804863\pi$
$251$	−25.9160	−1.63580	−0.817902	+	0.575358i	$0.804863\pi$
$252$	8.25846	0.520234
$253$	−14.7836	−0.929438
$254$	0.301641	0.0189266
$255$	3.61369	0.226298
$256$	1.00000	0.0625000
$257$	5.04209	0.314517	0.157259	−	0.987557i	$-0.449734\pi$
$257$	5.04209	0.314517	0.157259	+	0.987557i	$0.449734\pi$
$258$	−2.55270	−0.158924
$259$	−11.9134	−0.740262
$260$	−0.0832707	−0.00516423
$261$	9.86322	0.610518
$262$	−7.50878	−0.463894
$263$	22.4472	1.38415	0.692076	−	0.721825i	$-0.256696\pi$
$263$	22.4472	1.38415	0.692076	+	0.721825i	$0.256696\pi$
$264$	2.52187	0.155210
$265$	1.05430	0.0647649
$266$	6.79097	0.416381
$267$	−5.77960	−0.353706
$268$	9.49351	0.579908
$269$	−28.9496	−1.76509	−0.882543	−	0.470231i	$-0.844171\pi$
$269$	−28.9496	−1.76509	−0.882543	+	0.470231i	$0.844171\pi$
$270$	3.64508	0.221832
$271$	13.2887	0.807233	0.403617	−	0.914928i	$-0.367753\pi$
$271$	13.2887	0.807233	0.403617	+	0.914928i	$0.367753\pi$
$272$	5.34635	0.324170
$273$	0.258184	0.0156260
$274$	19.3698	1.17017
$275$	−13.7467	−0.828956
$276$	3.55955	0.214260
$277$	−22.1313	−1.32974	−0.664870	−	0.746959i	$-0.731513\pi$
$277$	−22.1313	−1.32974	−0.664870	+	0.746959i	$0.731513\pi$
$278$	13.4646	0.807552
$279$	−0.459797	−0.0275273
$280$	−2.99377	−0.178912
$281$	−1.85417	−0.110611	−0.0553054	−	0.998469i	$-0.517613\pi$
$281$	−1.85417	−0.110611	−0.0553054	+	0.998469i	$0.517613\pi$
$282$	8.87947	0.528765
$283$	−7.27477	−0.432440	−0.216220	−	0.976345i	$-0.569373\pi$
$283$	−7.27477	−0.432440	−0.216220	+	0.976345i	$0.569373\pi$
$284$	−14.4713	−0.858715
$285$	1.32994	0.0787787
$286$	−0.310686	−0.0183712
$287$	−23.7945	−1.40454
$288$	2.39279	0.140997
$289$	11.5835	0.681381
$290$	−3.57551	−0.209961
$291$	2.07400	0.121580
$292$	11.7161	0.685634
$293$	−10.0667	−0.588104	−0.294052	−	0.955789i	$-0.595004\pi$
$293$	−10.0667	−0.588104	−0.294052	+	0.955789i	$0.595004\pi$
$294$	3.82768	0.223235
$295$	−0.504051	−0.0293470
$296$	−3.45176	−0.200630
$297$	13.5999	0.789147
$298$	11.0624	0.640825
$299$	−0.438525	−0.0253605
$300$	3.30988	0.191096
$301$	11.3064	0.651691
$302$	18.5776	1.06902
$303$	−0.818408	−0.0470163
$304$	1.96760	0.112850
$305$	2.61801	0.149907
$306$	12.7927	0.731311
$307$	−5.07778	−0.289804	−0.144902	−	0.989446i	$-0.546287\pi$
$307$	−5.07778	−0.289804	−0.144902	+	0.989446i	$0.546287\pi$
$308$	−11.1699	−0.636463
$309$	9.64368	0.548610
$310$	0.166681	0.00946684
$311$	−26.8661	−1.52344	−0.761718	−	0.647909i	$-0.775644\pi$
$311$	−26.8661	−1.52344	−0.761718	+	0.647909i	$0.775644\pi$
$312$	0.0748059	0.00423505
$313$	3.90340	0.220633	0.110317	−	0.993897i	$-0.464814\pi$
$313$	3.90340	0.220633	0.110317	+	0.993897i	$0.464814\pi$
$314$	−6.59557	−0.372209
$315$	−7.16348	−0.403616
$316$	2.62921	0.147905
$317$	−11.3372	−0.636762	−0.318381	−	0.947963i	$-0.603139\pi$
$317$	−11.3372	−0.636762	−0.318381	+	0.947963i	$0.603139\pi$
$318$	−0.947122	−0.0531120
$319$	−13.3404	−0.746917
$320$	−0.867411	−0.0484897
$321$	−4.00521	−0.223549
$322$	−15.7660	−0.878603
$323$	10.5195	0.585321
$324$	3.90384	0.216880
$325$	−0.407766	−0.0226188
$326$	−21.3886	−1.18461
$327$	14.6075	0.807795
$328$	−6.89417	−0.380667
$329$	−39.3290	−2.16828
$330$	−2.18750	−0.120418
$331$	22.9868	1.26347	0.631733	−	0.775186i	$-0.282344\pi$
$331$	22.9868	1.26347	0.631733	+	0.775186i	$0.282344\pi$
$332$	7.45027	0.408887
$333$	−8.25935	−0.452610
$334$	2.21303	0.121091
$335$	−8.23477	−0.449914
$336$	2.68944	0.146721
$337$	−23.7930	−1.29609	−0.648045	−	0.761602i	$-0.724413\pi$
$337$	−23.7930	−1.29609	−0.648045	+	0.761602i	$0.724413\pi$
$338$	12.9908	0.706606
$339$	3.48507	0.189283
$340$	−4.63748	−0.251503
$341$	0.621892	0.0336774
$342$	4.70807	0.254583
$343$	7.20616	0.389096
$344$	3.27590	0.176625
$345$	−3.08759	−0.166230
$346$	18.0587	0.970843
$347$	8.54376	0.458653	0.229327	−	0.973350i	$-0.426348\pi$
$347$	8.54376	0.458653	0.229327	+	0.973350i	$0.426348\pi$
$348$	3.21205	0.172184
$349$	−4.21459	−0.225602	−0.112801	−	0.993618i	$-0.535982\pi$
$349$	−4.21459	−0.225602	−0.112801	+	0.993618i	$0.535982\pi$
$350$	−14.6601	−0.783617
$351$	0.403413	0.0215326
$352$	−3.23634	−0.172497
$353$	−33.4718	−1.78152	−0.890761	−	0.454472i	$-0.849828\pi$
$353$	−33.4718	−1.78152	−0.890761	+	0.454472i	$0.849828\pi$
$354$	0.452812	0.0240667
$355$	12.5526	0.666222
$356$	7.41702	0.393101
$357$	14.3787	0.761002
$358$	9.99822	0.528422
$359$	−8.74319	−0.461448	−0.230724	−	0.973019i	$-0.574109\pi$
$359$	−8.74319	−0.461448	−0.230724	+	0.973019i	$0.574109\pi$
$360$	−2.07553	−0.109390
$361$	−15.1285	−0.796238
$362$	−10.7591	−0.565486
$363$	0.409959	0.0215173
$364$	−0.331331	−0.0173664
$365$	−10.1627	−0.531939
$366$	−2.35188	−0.122935
$367$	26.4685	1.38164	0.690821	−	0.723025i	$-0.257249\pi$
$367$	26.4685	1.38164	0.690821	+	0.723025i	$0.257249\pi$
$368$	−4.56800	−0.238124
$369$	−16.4963	−0.858765
$370$	2.99410	0.155656
$371$	4.19500	0.217793
$372$	−0.149737	−0.00776351
$373$	−2.69198	−0.139386	−0.0696928	−	0.997568i	$-0.522202\pi$
$373$	−2.69198	−0.139386	−0.0696928	+	0.997568i	$0.522202\pi$
$374$	−17.3026	−0.894697
$375$	−6.25061	−0.322780
$376$	−11.3951	−0.587658
$377$	−0.395714	−0.0203803
$378$	14.5036	0.745985
$379$	1.93851	0.0995743	0.0497872	−	0.998760i	$-0.484146\pi$
$379$	1.93851	0.0995743	0.0497872	+	0.998760i	$0.484146\pi$
$380$	−1.70672	−0.0875530
$381$	0.235049	0.0120419
$382$	18.8593	0.964926
$383$	−12.7553	−0.651767	−0.325883	−	0.945410i	$-0.605662\pi$
$383$	−12.7553	−0.651767	−0.325883	+	0.945410i	$0.605662\pi$
$384$	0.779235	0.0397652
$385$	9.68887	0.493790
$386$	13.3166	0.677795
$387$	7.83856	0.398456
$388$	−2.66158	−0.135121
$389$	24.8983	1.26239	0.631196	−	0.775624i	$-0.282564\pi$
$389$	24.8983	1.26239	0.631196	+	0.775624i	$0.282564\pi$
$390$	−0.0648874	−0.00328570
$391$	−24.4222	−1.23508
$392$	−4.91210	−0.248099
$393$	−5.85111	−0.295149
$394$	−13.6777	−0.689071
$395$	−2.28061	−0.114750
$396$	−7.74389	−0.389145
$397$	4.20895	0.211241	0.105620	−	0.994407i	$-0.466317\pi$
$397$	4.20895	0.211241	0.105620	+	0.994407i	$0.466317\pi$
$398$	−3.84768	−0.192867
$399$	5.29176	0.264920
$400$	−4.24760	−0.212380
$401$	−2.63918	−0.131794	−0.0658972	−	0.997826i	$-0.520991\pi$
$401$	−2.63918	−0.131794	−0.0658972	+	0.997826i	$0.520991\pi$
$402$	7.39767	0.368962
$403$	0.0184471	0.000918917 0
$404$	1.05027	0.0522530
$405$	−3.38623	−0.168263
$406$	−14.2268	−0.706065
$407$	11.1711	0.553730
$408$	4.16606	0.206251
$409$	5.20799	0.257518	0.128759	−	0.991676i	$-0.458901\pi$
$409$	5.20799	0.257518	0.128759	+	0.991676i	$0.458901\pi$
$410$	5.98008	0.295335
$411$	15.0936	0.744514
$412$	−12.3758	−0.609714
$413$	−2.00560	−0.0986890
$414$	−10.9303	−0.537194
$415$	−6.46244	−0.317229
$416$	−0.0959992	−0.00470675
$417$	10.4921	0.513799
$418$	−6.36784	−0.311461
$419$	0.0975118	0.00476377	0.00238188	−	0.999997i	$-0.499242\pi$
$419$	0.0975118	0.00476377	0.00238188	+	0.999997i	$0.499242\pi$
$420$	−2.33285	−0.113832
$421$	−17.1483	−0.835756	−0.417878	−	0.908503i	$-0.637226\pi$
$421$	−17.1483	−0.835756	−0.417878	+	0.908503i	$0.637226\pi$
$422$	−0.276423	−0.0134560
$423$	−27.2662	−1.32573
$424$	1.21545	0.0590275
$425$	−22.7092	−1.10156
$426$	−11.2766	−0.546351
$427$	10.4170	0.504112
$428$	5.13993	0.248448
$429$	−0.242097	−0.0116886
$430$	−2.84155	−0.137032
$431$	−34.9830	−1.68507	−0.842535	−	0.538642i	$-0.818938\pi$
$431$	−34.9830	−1.68507	−0.842535	+	0.538642i	$0.818938\pi$
$432$	4.20225	0.202181
$433$	30.9613	1.48790	0.743952	−	0.668233i	$-0.232949\pi$
$433$	30.9613	1.48790	0.743952	+	0.668233i	$0.232949\pi$
$434$	0.663217	0.0318354
$435$	−2.78616	−0.133586
$436$	−18.7459	−0.897766
$437$	−8.98803	−0.429956
$438$	9.12961	0.436230
$439$	−3.18963	−0.152233	−0.0761164	−	0.997099i	$-0.524252\pi$
$439$	−3.18963	−0.152233	−0.0761164	+	0.997099i	$0.524252\pi$
$440$	2.80724	0.133830
$441$	−11.7536	−0.559697
$442$	−0.513245	−0.0244126
$443$	−1.23026	−0.0584512	−0.0292256	−	0.999573i	$-0.509304\pi$
$443$	−1.23026	−0.0584512	−0.0292256	+	0.999573i	$0.509304\pi$
$444$	−2.68973	−0.127649
$445$	−6.43360	−0.304982
$446$	−4.91884	−0.232914
$447$	8.62017	0.407720
$448$	−3.45139	−0.163063
$449$	12.7510	0.601759	0.300879	−	0.953662i	$-0.402720\pi$
$449$	12.7510	0.601759	0.300879	+	0.953662i	$0.402720\pi$
$450$	−10.1636	−0.479118
$451$	22.3119	1.05063
$452$	−4.47243	−0.210365
$453$	14.4763	0.680156
$454$	−12.1843	−0.571836
$455$	0.287400	0.0134735
$456$	1.53323	0.0717999
$457$	−40.6338	−1.90077	−0.950384	−	0.311080i	$-0.899309\pi$
$457$	−40.6338	−1.90077	−0.950384	+	0.311080i	$0.899309\pi$
$458$	−28.5001	−1.33172
$459$	22.4667	1.04866
$460$	3.96234	0.184745
$461$	11.5464	0.537768	0.268884	−	0.963173i	$-0.413345\pi$
$461$	11.5464	0.537768	0.268884	+	0.963173i	$0.413345\pi$
$462$	−8.70395	−0.404945
$463$	−9.95124	−0.462473	−0.231237	−	0.972898i	$-0.574277\pi$
$463$	−9.95124	−0.462473	−0.231237	+	0.972898i	$0.574277\pi$
$464$	−4.12205	−0.191361
$465$	0.129884	0.00602321
$466$	16.2015	0.750520
$467$	−3.65923	−0.169329	−0.0846645	−	0.996410i	$-0.526982\pi$
$467$	−3.65923	−0.169329	−0.0846645	+	0.996410i	$0.526982\pi$
$468$	−0.229706	−0.0106182
$469$	−32.7658	−1.51298
$470$	9.88425	0.455926
$471$	−5.13949	−0.236815
$472$	−0.581098	−0.0267472
$473$	−10.6019	−0.487477
$474$	2.04878	0.0941034
$475$	−8.35760	−0.383473
$476$	−18.4523	−0.845762
$477$	2.90832	0.133163
$478$	12.3676	0.565683
$479$	−2.48553	−0.113567	−0.0567835	−	0.998387i	$-0.518084\pi$
$479$	−2.48553	−0.113567	−0.0567835	+	0.998387i	$0.518084\pi$
$480$	−0.675917	−0.0308512
$481$	0.331366	0.0151090
$482$	14.1994	0.646765
$483$	−12.2854	−0.559005
$484$	−0.526105	−0.0239138
$485$	2.30869	0.104832
$486$	15.6488	0.709842
$487$	4.61836	0.209278	0.104639	−	0.994510i	$-0.466631\pi$
$487$	4.61836	0.209278	0.104639	+	0.994510i	$0.466631\pi$
$488$	3.01819	0.136627
$489$	−16.6668	−0.753697
$490$	4.26081	0.192484
$491$	4.91052	0.221609	0.110804	−	0.993842i	$-0.464657\pi$
$491$	4.91052	0.221609	0.110804	+	0.993842i	$0.464657\pi$
$492$	−5.37218	−0.242197
$493$	−22.0379	−0.992539
$494$	−0.188888	−0.00849849
$495$	6.71713	0.301913
$496$	0.192159	0.00862820
$497$	49.9462	2.24039
$498$	5.80551	0.260151
$499$	−4.25660	−0.190552	−0.0952758	−	0.995451i	$-0.530373\pi$
$499$	−4.25660	−0.190552	−0.0952758	+	0.995451i	$0.530373\pi$
$500$	8.02147	0.358731
$501$	1.72447	0.0770435
$502$	25.9160	1.15669
$503$	−11.9884	−0.534537	−0.267269	−	0.963622i	$-0.586121\pi$
$503$	−11.9884	−0.534537	−0.267269	+	0.963622i	$0.586121\pi$
$504$	−8.25846	−0.367861
$505$	−0.911017	−0.0405397
$506$	14.7836	0.657212
$507$	10.1229	0.449572
$508$	−0.301641	−0.0133832
$509$	−19.9944	−0.886235	−0.443117	−	0.896464i	$-0.646128\pi$
$509$	−19.9944	−0.886235	−0.443117	+	0.896464i	$0.646128\pi$
$510$	−3.61369	−0.160017
$511$	−40.4369	−1.78882
$512$	−1.00000	−0.0441942
$513$	8.26837	0.365058
$514$	−5.04209	−0.222397
$515$	10.7349	0.473038
$516$	2.55270	0.112376
$517$	36.8785	1.62191
$518$	11.9134	0.523444
$519$	14.0720	0.617691
$520$	0.0832707	0.00365166
$521$	−15.2285	−0.667173	−0.333587	−	0.942719i	$-0.608259\pi$
$521$	−15.2285	−0.667173	−0.333587	+	0.942719i	$0.608259\pi$
$522$	−9.86322	−0.431701
$523$	31.9781	1.39831	0.699153	−	0.714972i	$-0.253561\pi$
$523$	31.9781	1.39831	0.699153	+	0.714972i	$0.253561\pi$
$524$	7.50878	0.328023
$525$	−11.4237	−0.498570
$526$	−22.4472	−0.978743
$527$	1.02735	0.0447521
$528$	−2.52187	−0.109750
$529$	−2.13334	−0.0927537
$530$	−1.05430	−0.0457957
$531$	−1.39045	−0.0603403
$532$	−6.79097	−0.294426
$533$	0.661835	0.0286673
$534$	5.77960	0.250108
$535$	−4.45843	−0.192755
$536$	−9.49351	−0.410057
$537$	7.79096	0.336205
$538$	28.9496	1.24810
$539$	15.8972	0.684742
$540$	−3.64508	−0.156859
$541$	23.3171	1.00248	0.501240	−	0.865308i	$-0.332877\pi$
$541$	23.3171	1.00248	0.501240	+	0.865308i	$0.332877\pi$
$542$	−13.2887	−0.570800
$543$	−8.38388	−0.359787
$544$	−5.34635	−0.229223
$545$	16.2604	0.696519
$546$	−0.258184	−0.0110493
$547$	21.9020	0.936462	0.468231	−	0.883606i	$-0.344891\pi$
$547$	21.9020	0.936462	0.468231	+	0.883606i	$0.344891\pi$
$548$	−19.3698	−0.827437
$549$	7.22191	0.308224
$550$	13.7467	0.586160
$551$	−8.11057	−0.345522
$552$	−3.55955	−0.151504
$553$	−9.07445	−0.385885
$554$	22.1313	0.940268
$555$	2.33310	0.0990347
$556$	−13.4646	−0.571025
$557$	4.88359	0.206924	0.103462	−	0.994633i	$-0.467008\pi$
$557$	4.88359	0.206924	0.103462	+	0.994633i	$0.467008\pi$
$558$	0.459797	0.0194648
$559$	−0.314484	−0.0133013
$560$	2.99377	0.126510
$561$	−13.4828	−0.569244
$562$	1.85417	0.0782136
$563$	20.2065	0.851603	0.425802	−	0.904817i	$-0.359992\pi$
$563$	20.2065	0.851603	0.425802	+	0.904817i	$0.359992\pi$
$564$	−8.87947	−0.373893
$565$	3.87943	0.163209
$566$	7.27477	0.305781
$567$	−13.4737	−0.565841
$568$	14.4713	0.607203
$569$	6.24900	0.261972	0.130986	−	0.991384i	$-0.458186\pi$
$569$	6.24900	0.261972	0.130986	+	0.991384i	$0.458186\pi$
$570$	−1.32994	−0.0557049
$571$	−23.9895	−1.00393	−0.501964	−	0.864888i	$-0.667389\pi$
$571$	−23.9895	−1.00393	−0.501964	+	0.864888i	$0.667389\pi$
$572$	0.310686	0.0129904
$573$	14.6958	0.613927
$574$	23.7945	0.993163
$575$	19.4030	0.809163
$576$	−2.39279	−0.0996997
$577$	19.8350	0.825742	0.412871	−	0.910790i	$-0.364526\pi$
$577$	19.8350	0.825742	0.412871	+	0.910790i	$0.364526\pi$
$578$	−11.5835	−0.481809
$579$	10.3767	0.431242
$580$	3.57551	0.148465
$581$	−25.7138	−1.06679
$582$	−2.07400	−0.0859700
$583$	−3.93361	−0.162914
$584$	−11.7161	−0.484816
$585$	0.199250	0.00823796
$586$	10.0667	0.415853
$587$	3.89913	0.160934	0.0804671	−	0.996757i	$-0.474359\pi$
$587$	3.89913	0.160934	0.0804671	+	0.996757i	$0.474359\pi$
$588$	−3.82768	−0.157851
$589$	0.378093	0.0155791
$590$	0.504051	0.0207514
$591$	−10.6581	−0.438416
$592$	3.45176	0.141867
$593$	−13.3065	−0.546431	−0.273215	−	0.961953i	$-0.588087\pi$
$593$	−13.3065	−0.546431	−0.273215	+	0.961953i	$0.588087\pi$
$594$	−13.5999	−0.558011
$595$	16.0058	0.656172
$596$	−11.0624	−0.453132
$597$	−2.99824	−0.122710
$598$	0.438525	0.0179326
$599$	−1.00310	−0.0409855	−0.0204927	−	0.999790i	$-0.506523\pi$
$599$	−1.00310	−0.0409855	−0.0204927	+	0.999790i	$0.506523\pi$
$600$	−3.30988	−0.135125
$601$	−4.14151	−0.168936	−0.0844679	−	0.996426i	$-0.526919\pi$
$601$	−4.14151	−0.168936	−0.0844679	+	0.996426i	$0.526919\pi$
$602$	−11.3064	−0.460815
$603$	−22.7160	−0.925067
$604$	−18.5776	−0.755911
$605$	0.456349	0.0185532
$606$	0.818408	0.0332456
$607$	39.2901	1.59474	0.797368	−	0.603493i	$-0.206225\pi$
$607$	39.2901	1.59474	0.797368	+	0.603493i	$0.206225\pi$
$608$	−1.96760	−0.0797969
$609$	−11.0860	−0.449229
$610$	−2.61801	−0.106000
$611$	1.09392	0.0442553
$612$	−12.7927	−0.517115
$613$	−48.6851	−1.96637	−0.983187	−	0.182601i	$-0.941548\pi$
$613$	−48.6851	−1.96637	−0.983187	+	0.182601i	$0.941548\pi$
$614$	5.07778	0.204923
$615$	4.65989	0.187905
$616$	11.1699	0.450047
$617$	24.2435	0.976008	0.488004	−	0.872841i	$-0.337725\pi$
$617$	24.2435	0.976008	0.488004	+	0.872841i	$0.337725\pi$
$618$	−9.64368	−0.387926
$619$	28.7387	1.15511	0.577553	−	0.816353i	$-0.304008\pi$
$619$	28.7387	1.15511	0.577553	+	0.816353i	$0.304008\pi$
$620$	−0.166681	−0.00669407
$621$	−19.1959	−0.770305
$622$	26.8661	1.07723
$623$	−25.5990	−1.02560
$624$	−0.0748059	−0.00299463
$625$	14.2801	0.571204
$626$	−3.90340	−0.156011
$627$	−4.96204	−0.198165
$628$	6.59557	0.263192
$629$	18.4543	0.735822
$630$	7.16348	0.285400
$631$	17.5171	0.697346	0.348673	−	0.937244i	$-0.386632\pi$
$631$	17.5171	0.697346	0.348673	+	0.937244i	$0.386632\pi$
$632$	−2.62921	−0.104585
$633$	−0.215398	−0.00856131
$634$	11.3372	0.450259
$635$	0.261647	0.0103831
$636$	0.947122	0.0375558
$637$	0.471558	0.0186838
$638$	13.3404	0.528150
$639$	34.6269	1.36982
$640$	0.867411	0.0342874
$641$	−8.63427	−0.341033	−0.170517	−	0.985355i	$-0.554544\pi$
$641$	−8.63427	−0.341033	−0.170517	+	0.985355i	$0.554544\pi$
$642$	4.00521	0.158073
$643$	−6.19646	−0.244365	−0.122182	−	0.992508i	$-0.538989\pi$
$643$	−6.19646	−0.244365	−0.122182	+	0.992508i	$0.538989\pi$
$644$	15.7660	0.621266
$645$	−2.21424	−0.0871855
$646$	−10.5195	−0.413884
$647$	−35.5876	−1.39909	−0.699547	−	0.714587i	$-0.746615\pi$
$647$	−35.5876	−1.39909	−0.699547	+	0.714587i	$0.746615\pi$
$648$	−3.90384	−0.153357
$649$	1.88063	0.0738212
$650$	0.407766	0.0159939
$651$	0.516801	0.0202550
$652$	21.3886	0.837643
$653$	−17.7723	−0.695483	−0.347742	−	0.937590i	$-0.613051\pi$
$653$	−17.7723	−0.695483	−0.347742	+	0.937590i	$0.613051\pi$
$654$	−14.6075	−0.571197
$655$	−6.51320	−0.254492
$656$	6.89417	0.269172
$657$	−28.0343	−1.09372
$658$	39.3290	1.53320
$659$	−14.5964	−0.568595	−0.284297	−	0.958736i	$-0.591760\pi$
$659$	−14.5964	−0.568595	−0.284297	+	0.958736i	$0.591760\pi$
$660$	2.18750	0.0851482
$661$	7.25358	0.282132	0.141066	−	0.990000i	$-0.454947\pi$
$661$	7.25358	0.282132	0.141066	+	0.990000i	$0.454947\pi$
$662$	−22.9868	−0.893406
$663$	−0.399939	−0.0155323
$664$	−7.45027	−0.289127
$665$	5.89056	0.228426
$666$	8.25935	0.320043
$667$	18.8296	0.729083
$668$	−2.21303	−0.0856246
$669$	−3.83293	−0.148190
$670$	8.23477	0.318137
$671$	−9.76790	−0.377086
$672$	−2.68944	−0.103748
$673$	−34.9431	−1.34696	−0.673480	−	0.739206i	$-0.735201\pi$
$673$	−34.9431	−1.34696	−0.673480	+	0.739206i	$0.735201\pi$
$674$	23.7930	0.916473
$675$	−17.8495	−0.687027
$676$	−12.9908	−0.499646
$677$	−30.6635	−1.17849	−0.589246	−	0.807953i	$-0.700575\pi$
$677$	−30.6635	−1.17849	−0.589246	+	0.807953i	$0.700575\pi$
$678$	−3.48507	−0.133843
$679$	9.18616	0.352533
$680$	4.63748	0.177839
$681$	−9.49441	−0.363826
$682$	−0.621892	−0.0238135
$683$	−2.35310	−0.0900390	−0.0450195	−	0.998986i	$-0.514335\pi$
$683$	−2.35310	−0.0900390	−0.0450195	+	0.998986i	$0.514335\pi$
$684$	−4.70807	−0.180018
$685$	16.8016	0.641956
$686$	−7.20616	−0.275132
$687$	−22.2082	−0.847297
$688$	−3.27590	−0.124893
$689$	−0.116682	−0.00444524
$690$	3.08759	0.117543
$691$	−50.4834	−1.92048	−0.960240	−	0.279176i	$-0.909939\pi$
$691$	−50.4834	−1.92048	−0.960240	+	0.279176i	$0.909939\pi$
$692$	−18.0587	−0.686489
$693$	26.7272	1.01528
$694$	−8.54376	−0.324317
$695$	11.6793	0.443022
$696$	−3.21205	−0.121752
$697$	36.8587	1.39612
$698$	4.21459	0.159525
$699$	12.6248	0.477513
$700$	14.6601	0.554101
$701$	−44.6603	−1.68680	−0.843399	−	0.537288i	$-0.819449\pi$
$701$	−44.6603	−1.68680	−0.843399	+	0.537288i	$0.819449\pi$
$702$	−0.403413	−0.0152258
$703$	6.79170	0.256154
$704$	3.23634	0.121974
$705$	7.70215	0.290080
$706$	33.4718	1.25973
$707$	−3.62490	−0.136328
$708$	−0.452812	−0.0170177
$709$	13.0371	0.489617	0.244809	−	0.969571i	$-0.421275\pi$
$709$	13.0371	0.489617	0.244809	+	0.969571i	$0.421275\pi$
$710$	−12.5526	−0.471090
$711$	−6.29117	−0.235937
$712$	−7.41702	−0.277964
$713$	−0.877784	−0.0328733
$714$	−14.3787	−0.538110
$715$	−0.269492	−0.0100784
$716$	−9.99822	−0.373651
$717$	9.63730	0.359912
$718$	8.74319	0.326293
$719$	33.9522	1.26620	0.633102	−	0.774069i	$-0.281781\pi$
$719$	33.9522	1.26620	0.633102	+	0.774069i	$0.281781\pi$
$720$	2.07553	0.0773506
$721$	42.7139	1.59075
$722$	15.1285	0.563026
$723$	11.0647	0.411499
$724$	10.7591	0.399859
$725$	17.5088	0.650261
$726$	−0.409959	−0.0152150
$727$	7.56181	0.280452	0.140226	−	0.990120i	$-0.455217\pi$
$727$	7.56181	0.280452	0.140226	+	0.990120i	$0.455217\pi$
$728$	0.331331	0.0122799
$729$	0.482546	0.0178721
$730$	10.1627	0.376138
$731$	−17.5141	−0.647783
$732$	2.35188	0.0869281
$733$	38.3444	1.41628	0.708141	−	0.706071i	$-0.249534\pi$
$733$	38.3444	1.41628	0.708141	+	0.706071i	$0.249534\pi$
$734$	−26.4685	−0.976969
$735$	3.32017	0.122466
$736$	4.56800	0.168379
$737$	30.7242	1.13174
$738$	16.4963	0.607238
$739$	46.2671	1.70196	0.850981	−	0.525196i	$-0.176008\pi$
$739$	46.2671	1.70196	0.850981	+	0.525196i	$0.176008\pi$
$740$	−2.99410	−0.110065
$741$	−0.147188	−0.00540710
$742$	−4.19500	−0.154003
$743$	18.5448	0.680342	0.340171	−	0.940364i	$-0.389515\pi$
$743$	18.5448	0.680342	0.340171	+	0.940364i	$0.389515\pi$
$744$	0.149737	0.00548963
$745$	9.59560	0.351556
$746$	2.69198	0.0985606
$747$	−17.8270	−0.652254
$748$	17.3026	0.632646
$749$	−17.7399	−0.648202
$750$	6.25061	0.228240
$751$	10.4620	0.381762	0.190881	−	0.981613i	$-0.438866\pi$
$751$	10.4620	0.381762	0.190881	+	0.981613i	$0.438866\pi$
$752$	11.3951	0.415537
$753$	20.1946	0.735934
$754$	0.395714	0.0144110
$755$	16.1144	0.586463
$756$	−14.5036	−0.527491
$757$	46.4642	1.68877	0.844385	−	0.535736i	$-0.179966\pi$
$757$	46.4642	1.68877	0.844385	+	0.535736i	$0.179966\pi$
$758$	−1.93851	−0.0704097
$759$	11.5199	0.418146
$760$	1.70672	0.0619093
$761$	29.9129	1.08434	0.542171	−	0.840268i	$-0.317602\pi$
$761$	29.9129	1.08434	0.542171	+	0.840268i	$0.317602\pi$
$762$	−0.235049	−0.00851493
$763$	64.6995	2.34228
$764$	−18.8593	−0.682306
$765$	11.0965	0.401196
$766$	12.7553	0.460869
$767$	0.0557849	0.00201428
$768$	−0.779235	−0.0281182
$769$	15.2809	0.551043	0.275522	−	0.961295i	$-0.411149\pi$
$769$	15.2809	0.551043	0.275522	+	0.961295i	$0.411149\pi$
$770$	−9.68887	−0.349163
$771$	−3.92898	−0.141499
$772$	−13.3166	−0.479273
$773$	−46.5211	−1.67325	−0.836624	−	0.547778i	$-0.815474\pi$
$773$	−46.5211	−1.67325	−0.836624	+	0.547778i	$0.815474\pi$
$774$	−7.83856	−0.281751
$775$	−0.816215	−0.0293193
$776$	2.66158	0.0955452
$777$	9.28332	0.333037
$778$	−24.8983	−0.892646
$779$	13.5650	0.486017
$780$	0.0648874	0.00232334
$781$	−46.8341	−1.67586
$782$	24.4222	0.873334
$783$	−17.3219	−0.619034
$784$	4.91210	0.175432
$785$	−5.72106	−0.204194
$786$	5.85111	0.208702
$787$	29.4127	1.04845	0.524225	−	0.851580i	$-0.324355\pi$
$787$	29.4127	1.04845	0.524225	+	0.851580i	$0.324355\pi$
$788$	13.6777	0.487247
$789$	−17.4916	−0.622718
$790$	2.28061	0.0811404
$791$	15.4361	0.548845
$792$	7.74389	0.275167
$793$	−0.289744	−0.0102891
$794$	−4.20895	−0.149370
$795$	−0.821544	−0.0291372
$796$	3.84768	0.136377
$797$	−49.4209	−1.75058	−0.875289	−	0.483600i	$-0.839329\pi$
$797$	−49.4209	−1.75058	−0.875289	+	0.483600i	$0.839329\pi$
$798$	−5.29176	−0.187326
$799$	60.9223	2.15528
$800$	4.24760	0.150175
$801$	−17.7474	−0.627073
$802$	2.63918	0.0931927
$803$	37.9173	1.33807
$804$	−7.39767	−0.260896
$805$	−13.6756	−0.482001
$806$	−0.0184471	−0.000649772 0
$807$	22.5585	0.794097
$808$	−1.05027	−0.0369484
$809$	1.58840	0.0558450	0.0279225	−	0.999610i	$-0.491111\pi$
$809$	1.58840	0.0558450	0.0279225	+	0.999610i	$0.491111\pi$
$810$	3.38623	0.118980
$811$	21.0118	0.737824	0.368912	−	0.929464i	$-0.379730\pi$
$811$	21.0118	0.737824	0.368912	+	0.929464i	$0.379730\pi$
$812$	14.2268	0.499263
$813$	−10.3550	−0.363167
$814$	−11.1711	−0.391546
$815$	−18.5527	−0.649873
$816$	−4.16606	−0.145841
$817$	−6.44568	−0.225506
$818$	−5.20799	−0.182093
$819$	0.792806	0.0277029
$820$	−5.98008	−0.208833
$821$	−35.1367	−1.22628	−0.613140	−	0.789974i	$-0.710094\pi$
$821$	−35.1367	−1.22628	−0.613140	+	0.789974i	$0.710094\pi$
$822$	−15.0936	−0.526451
$823$	−2.54877	−0.0888445	−0.0444222	−	0.999013i	$-0.514145\pi$
$823$	−2.54877	−0.0888445	−0.0444222	+	0.999013i	$0.514145\pi$
$824$	12.3758	0.431133
$825$	10.7119	0.372940
$826$	2.00560	0.0697836
$827$	11.7412	0.408282	0.204141	−	0.978941i	$-0.434560\pi$
$827$	11.7412	0.408282	0.204141	+	0.978941i	$0.434560\pi$
$828$	10.9303	0.379854
$829$	17.3405	0.602261	0.301130	−	0.953583i	$-0.402636\pi$
$829$	17.3405	0.602261	0.301130	+	0.953583i	$0.402636\pi$
$830$	6.46244	0.224315
$831$	17.2455	0.598238
$832$	0.0959992	0.00332817
$833$	26.2618	0.909918
$834$	−10.4921	−0.363311
$835$	1.91960	0.0664306
$836$	6.36784	0.220236
$837$	0.807501	0.0279113
$838$	−0.0975118	−0.00336849
$839$	4.44264	0.153377	0.0766886	−	0.997055i	$-0.475565\pi$
$839$	4.44264	0.153377	0.0766886	+	0.997055i	$0.475565\pi$
$840$	2.33285	0.0804911
$841$	−12.0087	−0.414093
$842$	17.1483	0.590969
$843$	1.44484	0.0497628
$844$	0.276423	0.00951486
$845$	11.2683	0.387643
$846$	27.2662	0.937430
$847$	1.81579	0.0623914
$848$	−1.21545	−0.0417388
$849$	5.66875	0.194551
$850$	22.7092	0.778918
$851$	−15.7677	−0.540509
$852$	11.2766	0.386329
$853$	−4.20687	−0.144041	−0.0720203	−	0.997403i	$-0.522945\pi$
$853$	−4.20687	−0.144041	−0.0720203	+	0.997403i	$0.522945\pi$
$854$	−10.4170	−0.356461
$855$	4.08383	0.139664
$856$	−5.13993	−0.175679
$857$	−9.04752	−0.309058	−0.154529	−	0.987988i	$-0.549386\pi$
$857$	−9.04752	−0.309058	−0.154529	+	0.987988i	$0.549386\pi$
$858$	0.242097	0.00826507
$859$	4.53254	0.154648	0.0773241	−	0.997006i	$-0.475362\pi$
$859$	4.53254	0.154648	0.0773241	+	0.997006i	$0.475362\pi$
$860$	2.84155	0.0968961
$861$	18.5415	0.631892
$862$	34.9830	1.19152
$863$	−15.9516	−0.542998	−0.271499	−	0.962439i	$-0.587519\pi$
$863$	−15.9516	−0.542998	−0.271499	+	0.962439i	$0.587519\pi$
$864$	−4.20225	−0.142964
$865$	15.6643	0.532603
$866$	−30.9613	−1.05211
$867$	−9.02624	−0.306547
$868$	−0.663217	−0.0225110
$869$	8.50903	0.288649
$870$	2.78616	0.0944598
$871$	0.911369	0.0308806
$872$	18.7459	0.634817
$873$	6.36862	0.215545
$874$	8.98803	0.304025
$875$	−27.6852	−0.935931
$876$	−9.12961	−0.308461
$877$	19.3910	0.654786	0.327393	−	0.944888i	$-0.393830\pi$
$877$	19.3910	0.654786	0.327393	+	0.944888i	$0.393830\pi$
$878$	3.18963	0.107645
$879$	7.84434	0.264583
$880$	−2.80724	−0.0946319
$881$	−9.25692	−0.311873	−0.155937	−	0.987767i	$-0.549840\pi$
$881$	−9.25692	−0.311873	−0.155937	+	0.987767i	$0.549840\pi$
$882$	11.7536	0.395766
$883$	−1.20086	−0.0404122	−0.0202061	−	0.999796i	$-0.506432\pi$
$883$	−1.20086	−0.0404122	−0.0202061	+	0.999796i	$0.506432\pi$
$884$	0.513245	0.0172623
$885$	0.392774	0.0132029
$886$	1.23026	0.0413313
$887$	−33.8199	−1.13556	−0.567781	−	0.823180i	$-0.692198\pi$
$887$	−33.8199	−1.13556	−0.567781	+	0.823180i	$0.692198\pi$
$888$	2.68973	0.0902615
$889$	1.04108	0.0349167
$890$	6.43360	0.215655
$891$	12.6341	0.423260
$892$	4.91884	0.164695
$893$	22.4211	0.750293
$894$	−8.62017	−0.288302
$895$	8.67256	0.289892
$896$	3.45139	0.115303
$897$	0.341714	0.0114095
$898$	−12.7510	−0.425508
$899$	−0.792090	−0.0264177
$900$	10.1636	0.338787
$901$	−6.49823	−0.216487
$902$	−22.3119	−0.742905
$903$	−8.81036	−0.293190
$904$	4.47243	0.148751
$905$	−9.33257	−0.310225
$906$	−14.4763	−0.480943
$907$	24.3191	0.807503	0.403752	−	0.914869i	$-0.367706\pi$
$907$	24.3191	0.807503	0.403752	+	0.914869i	$0.367706\pi$
$908$	12.1843	0.404349
$909$	−2.51308	−0.0833537
$910$	−0.287400	−0.00952721
$911$	31.3793	1.03964	0.519821	−	0.854275i	$-0.325999\pi$
$911$	31.3793	1.03964	0.519821	+	0.854275i	$0.325999\pi$
$912$	−1.53323	−0.0507702
$913$	24.1116	0.797978
$914$	40.6338	1.34405
$915$	−2.04005	−0.0674419
$916$	28.5001	0.941669
$917$	−25.9157	−0.855813
$918$	−22.4667	−0.741512
$919$	10.1822	0.335879	0.167940	−	0.985797i	$-0.446289\pi$
$919$	10.1822	0.335879	0.167940	+	0.985797i	$0.446289\pi$
$920$	−3.96234	−0.130634
$921$	3.95679	0.130381
$922$	−11.5464	−0.380259
$923$	−1.38924	−0.0457273
$924$	8.70395	0.286339
$925$	−14.6617	−0.482074
$926$	9.95124	0.327018
$927$	29.6128	0.972613
$928$	4.12205	0.135313
$929$	18.3399	0.601714	0.300857	−	0.953669i	$-0.402727\pi$
$929$	18.3399	0.601714	0.300857	+	0.953669i	$0.402727\pi$
$930$	−0.129884	−0.00425905
$931$	9.66507	0.316760
$932$	−16.2015	−0.530698
$933$	20.9350	0.685380
$934$	3.65923	0.119734
$935$	−15.0085	−0.490829
$936$	0.229706	0.00750818
$937$	31.0179	1.01331	0.506656	−	0.862148i	$-0.330881\pi$
$937$	31.0179	1.01331	0.506656	+	0.862148i	$0.330881\pi$
$938$	32.7658	1.06984
$939$	−3.04166	−0.0992609
$940$	−9.88425	−0.322389
$941$	13.9596	0.455069	0.227534	−	0.973770i	$-0.426934\pi$
$941$	13.9596	0.455069	0.227534	+	0.973770i	$0.426934\pi$
$942$	5.13949	0.167454
$943$	−31.4926	−1.02554
$944$	0.581098	0.0189131
$945$	12.5806	0.409247
$946$	10.6019	0.344699
$947$	−29.8175	−0.968940	−0.484470	−	0.874808i	$-0.660988\pi$
$947$	−29.8175	−0.968940	−0.484470	+	0.874808i	$0.660988\pi$
$948$	−2.04878	−0.0665411
$949$	1.12474	0.0365105
$950$	8.35760	0.271156
$951$	8.83436	0.286474
$952$	18.4523	0.598044
$953$	−25.2102	−0.816637	−0.408318	−	0.912840i	$-0.633885\pi$
$953$	−25.2102	−0.816637	−0.408318	+	0.912840i	$0.633885\pi$
$954$	−2.90832	−0.0941605
$955$	16.3588	0.529357
$956$	−12.3676	−0.399998
$957$	10.3953	0.336031
$958$	2.48553	0.0803040
$959$	66.8528	2.15879
$960$	0.675917	0.0218151
$961$	−30.9631	−0.998809
$962$	−0.331366	−0.0106837
$963$	−12.2988	−0.396323
$964$	−14.1994	−0.457332
$965$	11.5509	0.371837
$966$	12.2854	0.395276
$967$	15.8056	0.508272	0.254136	−	0.967168i	$-0.418209\pi$
$967$	15.8056	0.508272	0.254136	+	0.967168i	$0.418209\pi$
$968$	0.526105	0.0169096
$969$	−8.19717	−0.263331
$970$	−2.30869	−0.0741274
$971$	−2.83347	−0.0909303	−0.0454652	−	0.998966i	$-0.514477\pi$
$971$	−2.83347	−0.0909303	−0.0454652	+	0.998966i	$0.514477\pi$
$972$	−15.6488	−0.501934
$973$	46.4715	1.48981
$974$	−4.61836	−0.147982
$975$	0.317745	0.0101760
$976$	−3.01819	−0.0966100
$977$	26.5337	0.848889	0.424445	−	0.905454i	$-0.360469\pi$
$977$	26.5337	0.848889	0.424445	+	0.905454i	$0.360469\pi$
$978$	16.6668	0.532944
$979$	24.0040	0.767171
$980$	−4.26081	−0.136107
$981$	44.8551	1.43211
$982$	−4.91052	−0.156701
$983$	53.5794	1.70892	0.854459	−	0.519519i	$-0.173889\pi$
$983$	53.5794	1.70892	0.854459	+	0.519519i	$0.173889\pi$
$984$	5.37218	0.171259
$985$	−11.8642	−0.378023
$986$	22.0379	0.701831
$987$	30.6465	0.975490
$988$	0.188888	0.00600934
$989$	14.9643	0.475838
$990$	−6.71713	−0.213485
$991$	−55.4201	−1.76048	−0.880239	−	0.474531i	$-0.842618\pi$
$991$	−55.4201	−1.76048	−0.880239	+	0.474531i	$0.842618\pi$
$992$	−0.192159	−0.00610106
$993$	−17.9121	−0.568423
$994$	−49.9462	−1.58420
$995$	−3.33752	−0.105806
$996$	−5.80551	−0.183955
$997$	−60.1035	−1.90350	−0.951748	−	0.306879i	$-0.900715\pi$
$997$	−60.1035	−1.90350	−0.951748	+	0.306879i	$0.900715\pi$
$998$	4.25660	0.134740
$999$	14.5052	0.458923

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.g.1.17	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.g.1.17	✓	40	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:	\( N \)	\(=\)	\( 4006 = 2 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.779235 q^{3} +1.00000 q^{4} -0.867411 q^{5} +0.779235 q^{6} -3.45139 q^{7} -1.00000 q^{8} -2.39279 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.779235 q^{3} +1.00000 q^{4} -0.867411 q^{5} +0.779235 q^{6} -3.45139 q^{7} -1.00000 q^{8} -2.39279 q^{9} +0.867411 q^{10} +3.23634 q^{11} -0.779235 q^{12} +0.0959992 q^{13} +3.45139 q^{14} +0.675917 q^{15} +1.00000 q^{16} +5.34635 q^{17} +2.39279 q^{18} +1.96760 q^{19} -0.867411 q^{20} +2.68944 q^{21} -3.23634 q^{22} -4.56800 q^{23} +0.779235 q^{24} -4.24760 q^{25} -0.0959992 q^{26} +4.20225 q^{27} -3.45139 q^{28} -4.12205 q^{29} -0.675917 q^{30} +0.192159 q^{31} -1.00000 q^{32} -2.52187 q^{33} -5.34635 q^{34} +2.99377 q^{35} -2.39279 q^{36} +3.45176 q^{37} -1.96760 q^{38} -0.0748059 q^{39} +0.867411 q^{40} +6.89417 q^{41} -2.68944 q^{42} -3.27590 q^{43} +3.23634 q^{44} +2.07553 q^{45} +4.56800 q^{46} +11.3951 q^{47} -0.779235 q^{48} +4.91210 q^{49} +4.24760 q^{50} -4.16606 q^{51} +0.0959992 q^{52} -1.21545 q^{53} -4.20225 q^{54} -2.80724 q^{55} +3.45139 q^{56} -1.53323 q^{57} +4.12205 q^{58} +0.581098 q^{59} +0.675917 q^{60} -3.01819 q^{61} -0.192159 q^{62} +8.25846 q^{63} +1.00000 q^{64} -0.0832707 q^{65} +2.52187 q^{66} +9.49351 q^{67} +5.34635 q^{68} +3.55955 q^{69} -2.99377 q^{70} -14.4713 q^{71} +2.39279 q^{72} +11.7161 q^{73} -3.45176 q^{74} +3.30988 q^{75} +1.96760 q^{76} -11.1699 q^{77} +0.0748059 q^{78} +2.62921 q^{79} -0.867411 q^{80} +3.90384 q^{81} -6.89417 q^{82} +7.45027 q^{83} +2.68944 q^{84} -4.63748 q^{85} +3.27590 q^{86} +3.21205 q^{87} -3.23634 q^{88} +7.41702 q^{89} -2.07553 q^{90} -0.331331 q^{91} -4.56800 q^{92} -0.149737 q^{93} -11.3951 q^{94} -1.70672 q^{95} +0.779235 q^{96} -2.66158 q^{97} -4.91210 q^{98} -7.74389 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * q^99

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