LMFDB - Embedded newform 4006.2.a.h.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:	$0$
Dimension:	$42$
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.545281 q^{3} +1.00000 q^{4} +0.119242 q^{5} +0.545281 q^{6} +0.291946 q^{7} -1.00000 q^{8} -2.70267 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.545281 q^{3} +1.00000 q^{4} +0.119242 q^{5} +0.545281 q^{6} +0.291946 q^{7} -1.00000 q^{8} -2.70267 q^{9} -0.119242 q^{10} -4.66250 q^{11} -0.545281 q^{12} +1.05800 q^{13} -0.291946 q^{14} -0.0650206 q^{15} +1.00000 q^{16} -5.96997 q^{17} +2.70267 q^{18} -8.57349 q^{19} +0.119242 q^{20} -0.159192 q^{21} +4.66250 q^{22} +6.00058 q^{23} +0.545281 q^{24} -4.98578 q^{25} -1.05800 q^{26} +3.10956 q^{27} +0.291946 q^{28} -4.24070 q^{29} +0.0650206 q^{30} -3.60482 q^{31} -1.00000 q^{32} +2.54237 q^{33} +5.96997 q^{34} +0.0348123 q^{35} -2.70267 q^{36} +5.16178 q^{37} +8.57349 q^{38} -0.576908 q^{39} -0.119242 q^{40} -2.33034 q^{41} +0.159192 q^{42} +1.40411 q^{43} -4.66250 q^{44} -0.322273 q^{45} -6.00058 q^{46} +8.36511 q^{47} -0.545281 q^{48} -6.91477 q^{49} +4.98578 q^{50} +3.25531 q^{51} +1.05800 q^{52} +10.9808 q^{53} -3.10956 q^{54} -0.555968 q^{55} -0.291946 q^{56} +4.67496 q^{57} +4.24070 q^{58} +6.39186 q^{59} -0.0650206 q^{60} -6.28081 q^{61} +3.60482 q^{62} -0.789033 q^{63} +1.00000 q^{64} +0.126159 q^{65} -2.54237 q^{66} +8.36676 q^{67} -5.96997 q^{68} -3.27200 q^{69} -0.0348123 q^{70} +4.66163 q^{71} +2.70267 q^{72} +13.5699 q^{73} -5.16178 q^{74} +2.71865 q^{75} -8.57349 q^{76} -1.36120 q^{77} +0.576908 q^{78} -6.37230 q^{79} +0.119242 q^{80} +6.41243 q^{81} +2.33034 q^{82} -6.94158 q^{83} -0.159192 q^{84} -0.711873 q^{85} -1.40411 q^{86} +2.31237 q^{87} +4.66250 q^{88} +1.15405 q^{89} +0.322273 q^{90} +0.308879 q^{91} +6.00058 q^{92} +1.96564 q^{93} -8.36511 q^{94} -1.02232 q^{95} +0.545281 q^{96} -2.50213 q^{97} +6.91477 q^{98} +12.6012 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9}+O(q^{10}) $ 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9} - 27 q^{10} + 23 q^{11} + 15 q^{13} + 10 q^{14} + 6 q^{15} + 42 q^{16} + 14 q^{17} - 56 q^{18} - 4 q^{19} + 27 q^{20} + 26 q^{21} - 23 q^{22} + 12 q^{23} + 45 q^{25} - 15 q^{26} - 3 q^{27} - 10 q^{28} + 41 q^{29} - 6 q^{30} + 18 q^{31} - 42 q^{32} + 25 q^{33} - 14 q^{34} + 8 q^{35} + 56 q^{36} + 33 q^{37} + 4 q^{38} + 10 q^{39} - 27 q^{40} + 84 q^{41} - 26 q^{42} - 36 q^{43} + 23 q^{44} + 66 q^{45} - 12 q^{46} + 28 q^{47} + 58 q^{49} - 45 q^{50} + 17 q^{51} + 15 q^{52} + 68 q^{53} + 3 q^{54} - 28 q^{55} + 10 q^{56} - 9 q^{57} - 41 q^{58} + 59 q^{59} + 6 q^{60} + 41 q^{61} - 18 q^{62} - 28 q^{63} + 42 q^{64} + 44 q^{65} - 25 q^{66} + 14 q^{68} + 67 q^{69} - 8 q^{70} + 69 q^{71} - 56 q^{72} - 27 q^{73} - 33 q^{74} + 14 q^{75} - 4 q^{76} + 43 q^{77} - 10 q^{78} - 19 q^{79} + 27 q^{80} + 74 q^{81} - 84 q^{82} + 20 q^{83} + 26 q^{84} + 16 q^{85} + 36 q^{86} - 28 q^{87} - 23 q^{88} + 123 q^{89} - 66 q^{90} - 9 q^{91} + 12 q^{92} + 48 q^{93} - 28 q^{94} + 28 q^{95} + 10 q^{97} - 58 q^{98} + 75 q^{99}+O(q^{100}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9 - 27 * q^10 + 23 * q^11 + 15 * q^13 + 10 * q^14 + 6 * q^15 + 42 * q^16 + 14 * q^17 - 56 * q^18 - 4 * q^19 + 27 * q^20 + 26 * q^21 - 23 * q^22 + 12 * q^23 + 45 * q^25 - 15 * q^26 - 3 * q^27 - 10 * q^28 + 41 * q^29 - 6 * q^30 + 18 * q^31 - 42 * q^32 + 25 * q^33 - 14 * q^34 + 8 * q^35 + 56 * q^36 + 33 * q^37 + 4 * q^38 + 10 * q^39 - 27 * q^40 + 84 * q^41 - 26 * q^42 - 36 * q^43 + 23 * q^44 + 66 * q^45 - 12 * q^46 + 28 * q^47 + 58 * q^49 - 45 * q^50 + 17 * q^51 + 15 * q^52 + 68 * q^53 + 3 * q^54 - 28 * q^55 + 10 * q^56 - 9 * q^57 - 41 * q^58 + 59 * q^59 + 6 * q^60 + 41 * q^61 - 18 * q^62 - 28 * q^63 + 42 * q^64 + 44 * q^65 - 25 * q^66 + 14 * q^68 + 67 * q^69 - 8 * q^70 + 69 * q^71 - 56 * q^72 - 27 * q^73 - 33 * q^74 + 14 * q^75 - 4 * q^76 + 43 * q^77 - 10 * q^78 - 19 * q^79 + 27 * q^80 + 74 * q^81 - 84 * q^82 + 20 * q^83 + 26 * q^84 + 16 * q^85 + 36 * q^86 - 28 * q^87 - 23 * q^88 + 123 * q^89 - 66 * q^90 - 9 * q^91 + 12 * q^92 + 48 * q^93 - 28 * q^94 + 28 * q^95 + 10 * q^97 - 58 * q^98 + 75 * 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
$3$	−0.545281	−0.314818	−0.157409	−	0.987533i	$-0.550314\pi$
$3$	−0.545281	−0.314818	−0.157409	+	0.987533i	$0.550314\pi$
$4$	1.00000	0.500000
$5$	0.119242	0.0533268	0.0266634	−	0.999644i	$-0.491512\pi$
$5$	0.119242	0.0533268	0.0266634	+	0.999644i	$0.491512\pi$
$6$	0.545281	0.222610
$7$	0.291946	0.110345	0.0551726	−	0.998477i	$-0.482429\pi$
$7$	0.291946	0.110345	0.0551726	+	0.998477i	$0.482429\pi$
$8$	−1.00000	−0.353553
$9$	−2.70267	−0.900890
$10$	−0.119242	−0.0377078
$11$	−4.66250	−1.40580	−0.702898	−	0.711291i	$-0.748111\pi$
$11$	−4.66250	−1.40580	−0.702898	+	0.711291i	$0.748111\pi$
$12$	−0.545281	−0.157409
$13$	1.05800	0.293437	0.146718	−	0.989178i	$-0.453129\pi$
$13$	1.05800	0.293437	0.146718	+	0.989178i	$0.453129\pi$
$14$	−0.291946	−0.0780258
$15$	−0.0650206	−0.0167882
$16$	1.00000	0.250000
$17$	−5.96997	−1.44793	−0.723965	−	0.689837i	$-0.757682\pi$
$17$	−5.96997	−1.44793	−0.723965	+	0.689837i	$0.757682\pi$
$18$	2.70267	0.637025
$19$	−8.57349	−1.96689	−0.983447	−	0.181198i	$-0.942003\pi$
$19$	−8.57349	−1.96689	−0.983447	+	0.181198i	$0.942003\pi$
$20$	0.119242	0.0266634
$21$	−0.159192	−0.0347386
$22$	4.66250	0.994048
$23$	6.00058	1.25121	0.625604	−	0.780141i	$-0.284853\pi$
$23$	6.00058	1.25121	0.625604	+	0.780141i	$0.284853\pi$
$24$	0.545281	0.111305
$25$	−4.98578	−0.997156
$26$	−1.05800	−0.207491
$27$	3.10956	0.598434
$28$	0.291946	0.0551726
$29$	−4.24070	−0.787478	−0.393739	−	0.919222i	$-0.628819\pi$
$29$	−4.24070	−0.787478	−0.393739	+	0.919222i	$0.628819\pi$
$30$	0.0650206	0.0118711
$31$	−3.60482	−0.647445	−0.323722	−	0.946152i	$-0.604934\pi$
$31$	−3.60482	−0.647445	−0.323722	+	0.946152i	$0.604934\pi$
$32$	−1.00000	−0.176777
$33$	2.54237	0.442570
$34$	5.96997	1.02384
$35$	0.0348123	0.00588436
$36$	−2.70267	−0.450445
$37$	5.16178	0.848591	0.424295	−	0.905524i	$-0.360522\pi$
$37$	5.16178	0.848591	0.424295	+	0.905524i	$0.360522\pi$
$38$	8.57349	1.39080
$39$	−0.576908	−0.0923792
$40$	−0.119242	−0.0188539
$41$	−2.33034	−0.363937	−0.181969	−	0.983304i	$-0.558247\pi$
$41$	−2.33034	−0.363937	−0.181969	+	0.983304i	$0.558247\pi$
$42$	0.159192	0.0245639
$43$	1.40411	0.214125	0.107063	−	0.994252i	$-0.465855\pi$
$43$	1.40411	0.214125	0.107063	+	0.994252i	$0.465855\pi$
$44$	−4.66250	−0.702898
$45$	−0.322273	−0.0480416
$46$	−6.00058	−0.884738
$47$	8.36511	1.22018	0.610089	−	0.792333i	$-0.291134\pi$
$47$	8.36511	1.22018	0.610089	+	0.792333i	$0.291134\pi$
$48$	−0.545281	−0.0787045
$49$	−6.91477	−0.987824
$50$	4.98578	0.705096
$51$	3.25531	0.455834
$52$	1.05800	0.146718
$53$	10.9808	1.50833	0.754163	−	0.656687i	$-0.228043\pi$
$53$	10.9808	1.50833	0.754163	+	0.656687i	$0.228043\pi$
$54$	−3.10956	−0.423157
$55$	−0.555968	−0.0749667
$56$	−0.291946	−0.0390129
$57$	4.67496	0.619213
$58$	4.24070	0.556831
$59$	6.39186	0.832150	0.416075	−	0.909330i	$-0.363405\pi$
$59$	6.39186	0.832150	0.416075	+	0.909330i	$0.363405\pi$
$60$	−0.0650206	−0.00839412
$61$	−6.28081	−0.804175	−0.402087	−	0.915601i	$-0.631715\pi$
$61$	−6.28081	−0.804175	−0.402087	+	0.915601i	$0.631715\pi$
$62$	3.60482	0.457813
$63$	−0.789033	−0.0994088
$64$	1.00000	0.125000
$65$	0.126159	0.0156481
$66$	−2.54237	−0.312944
$67$	8.36676	1.02216	0.511081	−	0.859533i	$-0.329245\pi$
$67$	8.36676	1.02216	0.511081	+	0.859533i	$0.329245\pi$
$68$	−5.96997	−0.723965
$69$	−3.27200	−0.393903
$70$	−0.0348123	−0.00416087
$71$	4.66163	0.553234	0.276617	−	0.960980i	$-0.410787\pi$
$71$	4.66163	0.553234	0.276617	+	0.960980i	$0.410787\pi$
$72$	2.70267	0.318513
$73$	13.5699	1.58824	0.794121	−	0.607759i	$-0.207931\pi$
$73$	13.5699	1.58824	0.794121	+	0.607759i	$0.207931\pi$
$74$	−5.16178	−0.600044
$75$	2.71865	0.313923
$76$	−8.57349	−0.983447
$77$	−1.36120	−0.155123
$78$	0.576908	0.0653220
$79$	−6.37230	−0.716939	−0.358470	−	0.933541i	$-0.616701\pi$
$79$	−6.37230	−0.716939	−0.358470	+	0.933541i	$0.616701\pi$
$80$	0.119242	0.0133317
$81$	6.41243	0.712492
$82$	2.33034	0.257343
$83$	−6.94158	−0.761937	−0.380969	−	0.924588i	$-0.624409\pi$
$83$	−6.94158	−0.761937	−0.380969	+	0.924588i	$0.624409\pi$
$84$	−0.159192	−0.0173693
$85$	−0.711873	−0.0772135
$86$	−1.40411	−0.151409
$87$	2.31237	0.247912
$88$	4.66250	0.497024
$89$	1.15405	0.122329	0.0611645	−	0.998128i	$-0.480519\pi$
$89$	1.15405	0.122329	0.0611645	+	0.998128i	$0.480519\pi$
$90$	0.322273	0.0339705
$91$	0.308879	0.0323793
$92$	6.00058	0.625604
$93$	1.96564	0.203827
$94$	−8.36511	−0.862796
$95$	−1.02232	−0.104888
$96$	0.545281	0.0556525
$97$	−2.50213	−0.254053	−0.127026	−	0.991899i	$-0.540543\pi$
$97$	−2.50213	−0.254053	−0.127026	+	0.991899i	$0.540543\pi$
$98$	6.91477	0.698497
$99$	12.6012	1.26647
$100$	−4.98578	−0.498578
$101$	6.92129	0.688694	0.344347	−	0.938842i	$-0.388100\pi$
$101$	6.92129	0.688694	0.344347	+	0.938842i	$0.388100\pi$
$102$	−3.25531	−0.322324
$103$	3.13286	0.308690	0.154345	−	0.988017i	$-0.450673\pi$
$103$	3.13286	0.308690	0.154345	+	0.988017i	$0.450673\pi$
$104$	−1.05800	−0.103746
$105$	−0.0189825	−0.00185250
$106$	−10.9808	−1.06655
$107$	0.933746	0.0902686	0.0451343	−	0.998981i	$-0.485628\pi$
$107$	0.933746	0.0902686	0.0451343	+	0.998981i	$0.485628\pi$
$108$	3.10956	0.299217
$109$	1.94679	0.186468	0.0932341	−	0.995644i	$-0.470279\pi$
$109$	1.94679	0.186468	0.0932341	+	0.995644i	$0.470279\pi$
$110$	0.555968	0.0530094
$111$	−2.81462	−0.267152
$112$	0.291946	0.0275863
$113$	19.5527	1.83936	0.919680	−	0.392669i	$-0.128448\pi$
$113$	19.5527	1.83936	0.919680	+	0.392669i	$0.128448\pi$
$114$	−4.67496	−0.437850
$115$	0.715524	0.0667230
$116$	−4.24070	−0.393739
$117$	−2.85943	−0.264354
$118$	−6.39186	−0.588419
$119$	−1.74291	−0.159772
$120$	0.0650206	0.00593554
$121$	10.7389	0.976262
$122$	6.28081	0.568637
$123$	1.27069	0.114574
$124$	−3.60482	−0.323722
$125$	−1.19073	−0.106502
$126$	0.789033	0.0702926
$127$	−17.3948	−1.54354	−0.771768	−	0.635904i	$-0.780628\pi$
$127$	−17.3948	−1.54354	−0.771768	+	0.635904i	$0.780628\pi$
$128$	−1.00000	−0.0883883
$129$	−0.765635	−0.0674104
$130$	−0.126159	−0.0110649
$131$	6.95794	0.607918	0.303959	−	0.952685i	$-0.401691\pi$
$131$	6.95794	0.607918	0.303959	+	0.952685i	$0.401691\pi$
$132$	2.54237	0.221285
$133$	−2.50299	−0.217037
$134$	−8.36676	−0.722778
$135$	0.370791	0.0319126
$136$	5.96997	0.511920
$137$	10.4295	0.891048	0.445524	−	0.895270i	$-0.353017\pi$
$137$	10.4295	0.891048	0.445524	+	0.895270i	$0.353017\pi$
$138$	3.27200	0.278531
$139$	−8.17195	−0.693135	−0.346568	−	0.938025i	$-0.612653\pi$
$139$	−8.17195	−0.693135	−0.346568	+	0.938025i	$0.612653\pi$
$140$	0.0348123	0.00294218
$141$	−4.56134	−0.384134
$142$	−4.66163	−0.391195
$143$	−4.93293	−0.412513
$144$	−2.70267	−0.225222
$145$	−0.505671	−0.0419937
$146$	−13.5699	−1.12306
$147$	3.77049	0.310985
$148$	5.16178	0.424295
$149$	−6.60490	−0.541094	−0.270547	−	0.962707i	$-0.587205\pi$
$149$	−6.60490	−0.541094	−0.270547	+	0.962707i	$0.587205\pi$
$150$	−2.71865	−0.221977
$151$	−2.77808	−0.226077	−0.113039	−	0.993591i	$-0.536058\pi$
$151$	−2.77808	−0.226077	−0.113039	+	0.993591i	$0.536058\pi$
$152$	8.57349	0.695402
$153$	16.1348	1.30442
$154$	1.36120	0.109688
$155$	−0.429848	−0.0345262
$156$	−0.576908	−0.0461896
$157$	−5.21579	−0.416265	−0.208133	−	0.978101i	$-0.566739\pi$
$157$	−5.21579	−0.416265	−0.208133	+	0.978101i	$0.566739\pi$
$158$	6.37230	0.506953
$159$	−5.98761	−0.474848
$160$	−0.119242	−0.00942694
$161$	1.75184	0.138065
$162$	−6.41243	−0.503808
$163$	−14.6254	−1.14555	−0.572776	−	0.819712i	$-0.694134\pi$
$163$	−14.6254	−1.14555	−0.572776	+	0.819712i	$0.694134\pi$
$164$	−2.33034	−0.181969
$165$	0.303158	0.0236009
$166$	6.94158	0.538771
$167$	−3.35652	−0.259735	−0.129868	−	0.991531i	$-0.541455\pi$
$167$	−3.35652	−0.259735	−0.129868	+	0.991531i	$0.541455\pi$
$168$	0.159192	0.0122820
$169$	−11.8806	−0.913895
$170$	0.711873	0.0545982
$171$	23.1713	1.77195
$172$	1.40411	0.107063
$173$	6.40345	0.486845	0.243423	−	0.969920i	$-0.421730\pi$
$173$	6.40345	0.486845	0.243423	+	0.969920i	$0.421730\pi$
$174$	−2.31237	−0.175300
$175$	−1.45558	−0.110031
$176$	−4.66250	−0.351449
$177$	−3.48536	−0.261976
$178$	−1.15405	−0.0864996
$179$	−12.0414	−0.900020	−0.450010	−	0.893024i	$-0.648580\pi$
$179$	−12.0414	−0.900020	−0.450010	+	0.893024i	$0.648580\pi$
$180$	−0.322273	−0.0240208
$181$	1.36572	0.101513	0.0507567	−	0.998711i	$-0.483837\pi$
$181$	1.36572	0.101513	0.0507567	+	0.998711i	$0.483837\pi$
$182$	−0.308879	−0.0228957
$183$	3.42480	0.253169
$184$	−6.00058	−0.442369
$185$	0.615503	0.0452527
$186$	−1.96564	−0.144128
$187$	27.8350	2.03549
$188$	8.36511	0.610089
$189$	0.907822	0.0660343
$190$	1.02232	0.0741672
$191$	9.30593	0.673354	0.336677	−	0.941620i	$-0.390697\pi$
$191$	9.30593	0.673354	0.336677	+	0.941620i	$0.390697\pi$
$192$	−0.545281	−0.0393522
$193$	−8.21659	−0.591443	−0.295722	−	0.955274i	$-0.595560\pi$
$193$	−8.21659	−0.591443	−0.295722	+	0.955274i	$0.595560\pi$
$194$	2.50213	0.179643
$195$	−0.0687919	−0.00492629
$196$	−6.91477	−0.493912
$197$	6.61885	0.471574	0.235787	−	0.971805i	$-0.424233\pi$
$197$	6.61885	0.471574	0.235787	+	0.971805i	$0.424233\pi$
$198$	−12.6012	−0.895527
$199$	1.79785	0.127446	0.0637230	−	0.997968i	$-0.479703\pi$
$199$	1.79785	0.127446	0.0637230	+	0.997968i	$0.479703\pi$
$200$	4.98578	0.352548
$201$	−4.56223	−0.321795
$202$	−6.92129	−0.486980
$203$	−1.23805	−0.0868944
$204$	3.25531	0.227917
$205$	−0.277875	−0.0194076
$206$	−3.13286	−0.218277
$207$	−16.2176	−1.12720
$208$	1.05800	0.0733592
$209$	39.9739	2.76505
$210$	0.0189825	0.00130992
$211$	−9.38983	−0.646422	−0.323211	−	0.946327i	$-0.604762\pi$
$211$	−9.38983	−0.646422	−0.323211	+	0.946327i	$0.604762\pi$
$212$	10.9808	0.754163
$213$	−2.54190	−0.174168
$214$	−0.933746	−0.0638296
$215$	0.167430	0.0114186
$216$	−3.10956	−0.211578
$217$	−1.05241	−0.0714424
$218$	−1.94679	−0.131853
$219$	−7.39943	−0.500007
$220$	−0.555968	−0.0374833
$221$	−6.31624	−0.424876
$222$	2.81462	0.188905
$223$	−7.23903	−0.484761	−0.242381	−	0.970181i	$-0.577928\pi$
$223$	−7.23903	−0.484761	−0.242381	+	0.970181i	$0.577928\pi$
$224$	−0.291946	−0.0195064
$225$	13.4749	0.898328
$226$	−19.5527	−1.30062
$227$	13.9235	0.924135	0.462067	−	0.886845i	$-0.347108\pi$
$227$	13.9235	0.924135	0.462067	+	0.886845i	$0.347108\pi$
$228$	4.67496	0.309607
$229$	12.1967	0.805979	0.402989	−	0.915205i	$-0.367971\pi$
$229$	12.1967	0.805979	0.402989	+	0.915205i	$0.367971\pi$
$230$	−0.715524	−0.0471803
$231$	0.742234	0.0488354
$232$	4.24070	0.278416
$233$	−6.03368	−0.395279	−0.197640	−	0.980275i	$-0.563328\pi$
$233$	−6.03368	−0.395279	−0.197640	+	0.980275i	$0.563328\pi$
$234$	2.85943	0.186927
$235$	0.997477	0.0650682
$236$	6.39186	0.416075
$237$	3.47469	0.225705
$238$	1.74291	0.112976
$239$	−10.6542	−0.689162	−0.344581	−	0.938757i	$-0.611979\pi$
$239$	−10.6542	−0.689162	−0.344581	+	0.938757i	$0.611979\pi$
$240$	−0.0650206	−0.00419706
$241$	19.1409	1.23297	0.616485	−	0.787366i	$-0.288556\pi$
$241$	19.1409	1.23297	0.616485	+	0.787366i	$0.288556\pi$
$242$	−10.7389	−0.690322
$243$	−12.8252	−0.822739
$244$	−6.28081	−0.402087
$245$	−0.824534	−0.0526775
$246$	−1.27069	−0.0810161
$247$	−9.07077	−0.577159
$248$	3.60482	0.228906
$249$	3.78511	0.239871
$250$	1.19073	0.0753083
$251$	12.2154	0.771032	0.385516	−	0.922701i	$-0.374023\pi$
$251$	12.2154	0.771032	0.385516	+	0.922701i	$0.374023\pi$
$252$	−0.789033	−0.0497044
$253$	−27.9777	−1.75894
$254$	17.3948	1.09145
$255$	0.388171	0.0243082
$256$	1.00000	0.0625000
$257$	16.2686	1.01480	0.507402	−	0.861709i	$-0.330606\pi$
$257$	16.2686	1.01480	0.507402	+	0.861709i	$0.330606\pi$
$258$	0.765635	0.0476664
$259$	1.50696	0.0936379
$260$	0.126159	0.00782403
$261$	11.4612	0.709431
$262$	−6.95794	−0.429863
$263$	−29.7244	−1.83289	−0.916444	−	0.400163i	$-0.868953\pi$
$263$	−29.7244	−1.83289	−0.916444	+	0.400163i	$0.868953\pi$
$264$	−2.54237	−0.156472
$265$	1.30938	0.0804343
$266$	2.50299	0.153468
$267$	−0.629281	−0.0385113
$268$	8.36676	0.511081
$269$	0.305195	0.0186081	0.00930405	−	0.999957i	$-0.497038\pi$
$269$	0.305195	0.0186081	0.00930405	+	0.999957i	$0.497038\pi$
$270$	−0.370791	−0.0225656
$271$	−6.73339	−0.409025	−0.204512	−	0.978864i	$-0.565561\pi$
$271$	−6.73339	−0.409025	−0.204512	+	0.978864i	$0.565561\pi$
$272$	−5.96997	−0.361982
$273$	−0.168426	−0.0101936
$274$	−10.4295	−0.630066
$275$	23.2462	1.40180
$276$	−3.27200	−0.196951
$277$	0.422845	0.0254063	0.0127031	−	0.999919i	$-0.495956\pi$
$277$	0.422845	0.0254063	0.0127031	+	0.999919i	$0.495956\pi$
$278$	8.17195	0.490121
$279$	9.74264	0.583276
$280$	−0.0348123	−0.00208043
$281$	−23.3077	−1.39042	−0.695209	−	0.718808i	$-0.744688\pi$
$281$	−23.3077	−1.39042	−0.695209	+	0.718808i	$0.744688\pi$
$282$	4.56134	0.271624
$283$	19.4808	1.15801	0.579006	−	0.815323i	$-0.303441\pi$
$283$	19.4808	1.15801	0.579006	+	0.815323i	$0.303441\pi$
$284$	4.66163	0.276617
$285$	0.557454	0.0330207
$286$	4.93293	0.291690
$287$	−0.680332	−0.0401587
$288$	2.70267	0.159256
$289$	18.6405	1.09650
$290$	0.505671	0.0296941
$291$	1.36436	0.0799804
$292$	13.5699	0.794121
$293$	−3.85497	−0.225210	−0.112605	−	0.993640i	$-0.535919\pi$
$293$	−3.85497	−0.225210	−0.112605	+	0.993640i	$0.535919\pi$
$294$	−3.77049	−0.219899
$295$	0.762181	0.0443759
$296$	−5.16178	−0.300022
$297$	−14.4983	−0.841276
$298$	6.60490	0.382611
$299$	6.34863	0.367151
$300$	2.71865	0.156961
$301$	0.409925	0.0236277
$302$	2.77808	0.159861
$303$	−3.77405	−0.216813
$304$	−8.57349	−0.491723
$305$	−0.748939	−0.0428841
$306$	−16.1348	−0.922368
$307$	−10.4077	−0.593997	−0.296998	−	0.954878i	$-0.595986\pi$
$307$	−10.4077	−0.593997	−0.296998	+	0.954878i	$0.595986\pi$
$308$	−1.36120	−0.0775614
$309$	−1.70829	−0.0971811
$310$	0.429848	0.0244137
$311$	34.7115	1.96831	0.984154	−	0.177317i	$-0.0567417\pi$
$311$	34.7115	1.96831	0.984154	+	0.177317i	$0.0567417\pi$
$312$	0.576908	0.0326610
$313$	28.4710	1.60928	0.804638	−	0.593766i	$-0.202360\pi$
$313$	28.4710	1.60928	0.804638	+	0.593766i	$0.202360\pi$
$314$	5.21579	0.294344
$315$	−0.0940862	−0.00530116
$316$	−6.37230	−0.358470
$317$	−29.9951	−1.68469	−0.842347	−	0.538935i	$-0.818827\pi$
$317$	−29.9951	−1.68469	−0.842347	+	0.538935i	$0.818827\pi$
$318$	5.98761	0.335768
$319$	19.7723	1.10703
$320$	0.119242	0.00666586
$321$	−0.509154	−0.0284182
$322$	−1.75184	−0.0976265
$323$	51.1834	2.84792
$324$	6.41243	0.356246
$325$	−5.27497	−0.292603
$326$	14.6254	0.810028
$327$	−1.06154	−0.0587036
$328$	2.33034	0.128671
$329$	2.44216	0.134641
$330$	−0.303158	−0.0166883
$331$	−8.63526	−0.474637	−0.237318	−	0.971432i	$-0.576268\pi$
$331$	−8.63526	−0.474637	−0.237318	+	0.971432i	$0.576268\pi$
$332$	−6.94158	−0.380969
$333$	−13.9506	−0.764486
$334$	3.35652	0.183661
$335$	0.997672	0.0545087
$336$	−0.159192	−0.00868466
$337$	−7.01909	−0.382354	−0.191177	−	0.981556i	$-0.561231\pi$
$337$	−7.01909	−0.382354	−0.191177	+	0.981556i	$0.561231\pi$
$338$	11.8806	0.646221
$339$	−10.6617	−0.579064
$340$	−0.711873	−0.0386068
$341$	16.8075	0.910175
$342$	−23.1713	−1.25296
$343$	−4.06236	−0.219347
$344$	−1.40411	−0.0757046
$345$	−0.390162	−0.0210056
$346$	−6.40345	−0.344252
$347$	27.6881	1.48638	0.743188	−	0.669082i	$-0.233313\pi$
$347$	27.6881	1.48638	0.743188	+	0.669082i	$0.233313\pi$
$348$	2.31237	0.123956
$349$	−8.29379	−0.443956	−0.221978	−	0.975052i	$-0.571251\pi$
$349$	−8.29379	−0.443956	−0.221978	+	0.975052i	$0.571251\pi$
$350$	1.45558	0.0778039
$351$	3.28992	0.175603
$352$	4.66250	0.248512
$353$	−2.92907	−0.155899	−0.0779493	−	0.996957i	$-0.524837\pi$
$353$	−2.92907	−0.155899	−0.0779493	+	0.996957i	$0.524837\pi$
$354$	3.48536	0.185245
$355$	0.555864	0.0295022
$356$	1.15405	0.0611645
$357$	0.950373	0.0502991
$358$	12.0414	0.636410
$359$	−6.95621	−0.367135	−0.183567	−	0.983007i	$-0.558765\pi$
$359$	−6.95621	−0.367135	−0.183567	+	0.983007i	$0.558765\pi$
$360$	0.322273	0.0169853
$361$	54.5047	2.86867
$362$	−1.36572	−0.0717809
$363$	−5.85571	−0.307345
$364$	0.308879	0.0161897
$365$	1.61811	0.0846960
$366$	−3.42480	−0.179017
$367$	−28.8543	−1.50618	−0.753090	−	0.657917i	$-0.771438\pi$
$367$	−28.8543	−1.50618	−0.753090	+	0.657917i	$0.771438\pi$
$368$	6.00058	0.312802
$369$	6.29813	0.327867
$370$	−0.615503	−0.0319985
$371$	3.20579	0.166436
$372$	1.96564	0.101914
$373$	30.2726	1.56745	0.783727	−	0.621105i	$-0.213316\pi$
$373$	30.2726	1.56745	0.783727	+	0.621105i	$0.213316\pi$
$374$	−27.8350	−1.43931
$375$	0.649282	0.0335288
$376$	−8.36511	−0.431398
$377$	−4.48667	−0.231075
$378$	−0.907822	−0.0466933
$379$	−19.8796	−1.02115	−0.510573	−	0.859835i	$-0.670567\pi$
$379$	−19.8796	−1.02115	−0.510573	+	0.859835i	$0.670567\pi$
$380$	−1.02232	−0.0524441
$381$	9.48504	0.485933
$382$	−9.30593	−0.476133
$383$	32.9757	1.68498	0.842489	−	0.538713i	$-0.181089\pi$
$383$	32.9757	1.68498	0.842489	+	0.538713i	$0.181089\pi$
$384$	0.545281	0.0278262
$385$	−0.162312	−0.00827221
$386$	8.21659	0.418214
$387$	−3.79485	−0.192903
$388$	−2.50213	−0.127026
$389$	35.0917	1.77922	0.889610	−	0.456721i	$-0.150976\pi$
$389$	35.0917	1.77922	0.889610	+	0.456721i	$0.150976\pi$
$390$	0.0687919	0.00348342
$391$	−35.8233	−1.81166
$392$	6.91477	0.349249
$393$	−3.79403	−0.191384
$394$	−6.61885	−0.333453
$395$	−0.759848	−0.0382321
$396$	12.6012	0.633233
$397$	28.7572	1.44328	0.721641	−	0.692267i	$-0.243388\pi$
$397$	28.7572	1.44328	0.721641	+	0.692267i	$0.243388\pi$
$398$	−1.79785	−0.0901179
$399$	1.36483	0.0683272
$400$	−4.98578	−0.249289
$401$	−8.13394	−0.406190	−0.203095	−	0.979159i	$-0.565100\pi$
$401$	−8.13394	−0.406190	−0.203095	+	0.979159i	$0.565100\pi$
$402$	4.56223	0.227543
$403$	−3.81391	−0.189984
$404$	6.92129	0.344347
$405$	0.764633	0.0379949
$406$	1.23805	0.0614436
$407$	−24.0668	−1.19295
$408$	−3.25531	−0.161162
$409$	12.0825	0.597441	0.298721	−	0.954341i	$-0.403440\pi$
$409$	12.0825	0.597441	0.298721	+	0.954341i	$0.403440\pi$
$410$	0.277875	0.0137233
$411$	−5.68698	−0.280518
$412$	3.13286	0.154345
$413$	1.86608	0.0918237
$414$	16.2176	0.797051
$415$	−0.827731	−0.0406317
$416$	−1.05800	−0.0518728
$417$	4.45600	0.218211
$418$	−39.9739	−1.95519
$419$	−24.2155	−1.18300	−0.591502	−	0.806303i	$-0.701465\pi$
$419$	−24.2155	−1.18300	−0.591502	+	0.806303i	$0.701465\pi$
$420$	−0.0189825	−0.000926251 0
$421$	15.9462	0.777172	0.388586	−	0.921412i	$-0.372964\pi$
$421$	15.9462	0.777172	0.388586	+	0.921412i	$0.372964\pi$
$422$	9.38983	0.457090
$423$	−22.6081	−1.09925
$424$	−10.9808	−0.533274
$425$	29.7649	1.44381
$426$	2.54190	0.123155
$427$	−1.83366	−0.0887368
$428$	0.933746	0.0451343
$429$	2.68983	0.129866
$430$	−0.167430	−0.00807418
$431$	−15.3932	−0.741463	−0.370731	−	0.928740i	$-0.620893\pi$
$431$	−15.3932	−0.741463	−0.370731	+	0.928740i	$0.620893\pi$
$432$	3.10956	0.149609
$433$	28.9416	1.39085	0.695423	−	0.718600i	$-0.255217\pi$
$433$	28.9416	1.39085	0.695423	+	0.718600i	$0.255217\pi$
$434$	1.05241	0.0505174
$435$	0.275733	0.0132204
$436$	1.94679	0.0932341
$437$	−51.4459	−2.46099
$438$	7.39943	0.353559
$439$	13.9711	0.666804	0.333402	−	0.942785i	$-0.391803\pi$
$439$	13.9711	0.666804	0.333402	+	0.942785i	$0.391803\pi$
$440$	0.555968	0.0265047
$441$	18.6883	0.889920
$442$	6.31624	0.300433
$443$	26.9442	1.28016	0.640078	−	0.768310i	$-0.278902\pi$
$443$	26.9442	1.28016	0.640078	+	0.768310i	$0.278902\pi$
$444$	−2.81462	−0.133576
$445$	0.137612	0.00652342
$446$	7.23903	0.342778
$447$	3.60152	0.170346
$448$	0.291946	0.0137931
$449$	−10.8014	−0.509748	−0.254874	−	0.966974i	$-0.582034\pi$
$449$	−10.8014	−0.509748	−0.254874	+	0.966974i	$0.582034\pi$
$450$	−13.4749	−0.635214
$451$	10.8652	0.511622
$452$	19.5527	0.919680
$453$	1.51484	0.0711732
$454$	−13.9235	−0.653462
$455$	0.0368315	0.00172669
$456$	−4.67496	−0.218925
$457$	−31.8581	−1.49026	−0.745128	−	0.666921i	$-0.767612\pi$
$457$	−31.8581	−1.49026	−0.745128	+	0.666921i	$0.767612\pi$
$458$	−12.1967	−0.569913
$459$	−18.5639	−0.866491
$460$	0.715524	0.0333615
$461$	2.82144	0.131408	0.0657038	−	0.997839i	$-0.479071\pi$
$461$	2.82144	0.131408	0.0657038	+	0.997839i	$0.479071\pi$
$462$	−0.742234	−0.0345319
$463$	37.6080	1.74779	0.873896	−	0.486113i	$-0.161586\pi$
$463$	37.6080	1.74779	0.873896	+	0.486113i	$0.161586\pi$
$464$	−4.24070	−0.196870
$465$	0.234388	0.0108695
$466$	6.03368	0.279505
$467$	4.86900	0.225310	0.112655	−	0.993634i	$-0.464064\pi$
$467$	4.86900	0.225310	0.112655	+	0.993634i	$0.464064\pi$
$468$	−2.85943	−0.132177
$469$	2.44264	0.112791
$470$	−0.997477	−0.0460102
$471$	2.84407	0.131048
$472$	−6.39186	−0.294209
$473$	−6.54667	−0.301016
$474$	−3.47469	−0.159598
$475$	42.7455	1.96130
$476$	−1.74291	−0.0798860
$477$	−29.6774	−1.35884
$478$	10.6542	0.487311
$479$	−29.9514	−1.36851	−0.684257	−	0.729241i	$-0.739874\pi$
$479$	−29.9514	−1.36851	−0.684257	+	0.729241i	$0.739874\pi$
$480$	0.0650206	0.00296777
$481$	5.46117	0.249008
$482$	−19.1409	−0.871842
$483$	−0.955247	−0.0434653
$484$	10.7389	0.488131
$485$	−0.298360	−0.0135478
$486$	12.8252	0.581765
$487$	31.4885	1.42688	0.713441	−	0.700715i	$-0.247136\pi$
$487$	31.4885	1.42688	0.713441	+	0.700715i	$0.247136\pi$
$488$	6.28081	0.284319
$489$	7.97497	0.360641
$490$	0.824534	0.0372486
$491$	38.2320	1.72539	0.862693	−	0.505727i	$-0.168776\pi$
$491$	38.2320	1.72539	0.862693	+	0.505727i	$0.168776\pi$
$492$	1.27069	0.0572870
$493$	25.3168	1.14021
$494$	9.07077	0.408113
$495$	1.50260	0.0675367
$496$	−3.60482	−0.161861
$497$	1.36094	0.0610467
$498$	−3.78511	−0.169615
$499$	39.3979	1.76369	0.881846	−	0.471538i	$-0.156301\pi$
$499$	39.3979	1.76369	0.881846	+	0.471538i	$0.156301\pi$
$500$	−1.19073	−0.0532510
$501$	1.83025	0.0817694
$502$	−12.2154	−0.545202
$503$	−38.9984	−1.73885	−0.869426	−	0.494063i	$-0.835511\pi$
$503$	−38.9984	−1.73885	−0.869426	+	0.494063i	$0.835511\pi$
$504$	0.789033	0.0351463
$505$	0.825312	0.0367259
$506$	27.9777	1.24376
$507$	6.47828	0.287710
$508$	−17.3948	−0.771768
$509$	2.64029	0.117029	0.0585145	−	0.998287i	$-0.481364\pi$
$509$	2.64029	0.117029	0.0585145	+	0.998287i	$0.481364\pi$
$510$	−0.388171	−0.0171885
$511$	3.96169	0.175255
$512$	−1.00000	−0.0441942
$513$	−26.6597	−1.17706
$514$	−16.2686	−0.717575
$515$	0.373570	0.0164614
$516$	−0.765635	−0.0337052
$517$	−39.0023	−1.71532
$518$	−1.50696	−0.0662120
$519$	−3.49168	−0.153268
$520$	−0.126159	−0.00553243
$521$	−10.9113	−0.478031	−0.239015	−	0.971016i	$-0.576825\pi$
$521$	−10.9113	−0.478031	−0.239015	+	0.971016i	$0.576825\pi$
$522$	−11.4612	−0.501644
$523$	−31.1533	−1.36224	−0.681119	−	0.732172i	$-0.738507\pi$
$523$	−31.1533	−1.36224	−0.681119	+	0.732172i	$0.738507\pi$
$524$	6.95794	0.303959
$525$	0.793699	0.0346398
$526$	29.7244	1.29605
$527$	21.5207	0.937455
$528$	2.54237	0.110642
$529$	13.0070	0.565522
$530$	−1.30938	−0.0568756
$531$	−17.2751	−0.749675
$532$	−2.50299	−0.108519
$533$	−2.46550	−0.106793
$534$	0.629281	0.0272316
$535$	0.111342	0.00481374
$536$	−8.36676	−0.361389
$537$	6.56597	0.283342
$538$	−0.305195	−0.0131579
$539$	32.2401	1.38868
$540$	0.370791	0.0159563
$541$	21.0358	0.904398	0.452199	−	0.891917i	$-0.350640\pi$
$541$	21.0358	0.904398	0.452199	+	0.891917i	$0.350640\pi$
$542$	6.73339	0.289224
$543$	−0.744703	−0.0319583
$544$	5.96997	0.255960
$545$	0.232140	0.00994376
$546$	0.168426	0.00720796
$547$	−8.41912	−0.359976	−0.179988	−	0.983669i	$-0.557606\pi$
$547$	−8.41912	−0.359976	−0.179988	+	0.983669i	$0.557606\pi$
$548$	10.4295	0.445524
$549$	16.9749	0.724473
$550$	−23.2462	−0.991221
$551$	36.3576	1.54889
$552$	3.27200	0.139266
$553$	−1.86037	−0.0791108
$554$	−0.422845	−0.0179650
$555$	−0.335622	−0.0142464
$556$	−8.17195	−0.346568
$557$	18.4977	0.783772	0.391886	−	0.920014i	$-0.371823\pi$
$557$	18.4977	0.783772	0.391886	+	0.920014i	$0.371823\pi$
$558$	−9.74264	−0.412439
$559$	1.48555	0.0628322
$560$	0.0348123	0.00147109
$561$	−15.1779	−0.640810
$562$	23.3077	0.983174
$563$	35.5126	1.49668	0.748338	−	0.663318i	$-0.230852\pi$
$563$	35.5126	1.49668	0.748338	+	0.663318i	$0.230852\pi$
$564$	−4.56134	−0.192067
$565$	2.33151	0.0980873
$566$	−19.4808	−0.818838
$567$	1.87208	0.0786200
$568$	−4.66163	−0.195598
$569$	25.0502	1.05016	0.525079	−	0.851054i	$-0.324036\pi$
$569$	25.0502	1.05016	0.525079	+	0.851054i	$0.324036\pi$
$570$	−0.557454	−0.0233492
$571$	−8.41114	−0.351995	−0.175998	−	0.984391i	$-0.556315\pi$
$571$	−8.41114	−0.351995	−0.175998	+	0.984391i	$0.556315\pi$
$572$	−4.93293	−0.206256
$573$	−5.07435	−0.211984
$574$	0.680332	0.0283965
$575$	−29.9176	−1.24765
$576$	−2.70267	−0.112611
$577$	8.12695	0.338329	0.169165	−	0.985588i	$-0.445893\pi$
$577$	8.12695	0.338329	0.169165	+	0.985588i	$0.445893\pi$
$578$	−18.6405	−0.775343
$579$	4.48035	0.186197
$580$	−0.505671	−0.0209969
$581$	−2.02656	−0.0840761
$582$	−1.36436	−0.0565547
$583$	−51.1979	−2.12040
$584$	−13.5699	−0.561529
$585$	−0.340965	−0.0140972
$586$	3.85497	0.159247
$587$	13.0265	0.537660	0.268830	−	0.963188i	$-0.413363\pi$
$587$	13.0265	0.537660	0.268830	+	0.963188i	$0.413363\pi$
$588$	3.77049	0.155492
$589$	30.9059	1.27346
$590$	−0.762181	−0.0313785
$591$	−3.60913	−0.148460
$592$	5.16178	0.212148
$593$	−15.7983	−0.648759	−0.324379	−	0.945927i	$-0.605155\pi$
$593$	−15.7983	−0.648759	−0.324379	+	0.945927i	$0.605155\pi$
$594$	14.4983	0.594872
$595$	−0.207828	−0.00852014
$596$	−6.60490	−0.270547
$597$	−0.980331	−0.0401223
$598$	−6.34863	−0.259615
$599$	−24.6247	−1.00614	−0.503070	−	0.864246i	$-0.667796\pi$
$599$	−24.6247	−1.00614	−0.503070	+	0.864246i	$0.667796\pi$
$600$	−2.71865	−0.110988
$601$	−32.4692	−1.32444	−0.662222	−	0.749307i	$-0.730387\pi$
$601$	−32.4692	−1.32444	−0.662222	+	0.749307i	$0.730387\pi$
$602$	−0.409925	−0.0167073
$603$	−22.6126	−0.920855
$604$	−2.77808	−0.113039
$605$	1.28053	0.0520610
$606$	3.77405	0.153310
$607$	−22.3707	−0.907998	−0.453999	−	0.891002i	$-0.650003\pi$
$607$	−22.3707	−0.907998	−0.453999	+	0.891002i	$0.650003\pi$
$608$	8.57349	0.347701
$609$	0.675087	0.0273559
$610$	0.748939	0.0303236
$611$	8.85031	0.358045
$612$	16.1348	0.652212
$613$	−17.4179	−0.703501	−0.351751	−	0.936094i	$-0.614414\pi$
$613$	−17.4179	−0.703501	−0.351751	+	0.936094i	$0.614414\pi$
$614$	10.4077	0.420019
$615$	0.151520	0.00610987
$616$	1.36120	0.0548442
$617$	12.8195	0.516094	0.258047	−	0.966132i	$-0.416921\pi$
$617$	12.8195	0.516094	0.258047	+	0.966132i	$0.416921\pi$
$618$	1.70829	0.0687174
$619$	−5.87213	−0.236021	−0.118010	−	0.993012i	$-0.537652\pi$
$619$	−5.87213	−0.236021	−0.118010	+	0.993012i	$0.537652\pi$
$620$	−0.429848	−0.0172631
$621$	18.6591	0.748766
$622$	−34.7115	−1.39180
$623$	0.336920	0.0134984
$624$	−0.576908	−0.0230948
$625$	24.7869	0.991477
$626$	−28.4710	−1.13793
$627$	−21.7970	−0.870488
$628$	−5.21579	−0.208133
$629$	−30.8156	−1.22870
$630$	0.0940862	0.00374848
$631$	−11.0267	−0.438965	−0.219482	−	0.975616i	$-0.570437\pi$
$631$	−11.0267	−0.438965	−0.219482	+	0.975616i	$0.570437\pi$
$632$	6.37230	0.253476
$633$	5.12009	0.203505
$634$	29.9951	1.19126
$635$	−2.07420	−0.0823119
$636$	−5.98761	−0.237424
$637$	−7.31584	−0.289864
$638$	−19.7723	−0.782791
$639$	−12.5988	−0.498403
$640$	−0.119242	−0.00471347
$641$	15.7520	0.622168	0.311084	−	0.950382i	$-0.399308\pi$
$641$	15.7520	0.622168	0.311084	+	0.950382i	$0.399308\pi$
$642$	0.509154	0.0200947
$643$	−39.5237	−1.55866	−0.779331	−	0.626612i	$-0.784441\pi$
$643$	−39.5237	−1.55866	−0.779331	+	0.626612i	$0.784441\pi$
$644$	1.75184	0.0690324
$645$	−0.0912962	−0.00359478
$646$	−51.1834	−2.01379
$647$	−28.3905	−1.11615	−0.558073	−	0.829792i	$-0.688459\pi$
$647$	−28.3905	−1.11615	−0.558073	+	0.829792i	$0.688459\pi$
$648$	−6.41243	−0.251904
$649$	−29.8020	−1.16983
$650$	5.27497	0.206901
$651$	0.573860	0.0224914
$652$	−14.6254	−0.572776
$653$	5.85363	0.229070	0.114535	−	0.993419i	$-0.463462\pi$
$653$	5.85363	0.229070	0.114535	+	0.993419i	$0.463462\pi$
$654$	1.06154	0.0415097
$655$	0.829682	0.0324183
$656$	−2.33034	−0.0909843
$657$	−36.6751	−1.43083
$658$	−2.44216	−0.0952053
$659$	−23.0214	−0.896787	−0.448393	−	0.893836i	$-0.648004\pi$
$659$	−23.0214	−0.896787	−0.448393	+	0.893836i	$0.648004\pi$
$660$	0.303158	0.0118004
$661$	−22.8137	−0.887350	−0.443675	−	0.896188i	$-0.646326\pi$
$661$	−22.8137	−0.887350	−0.443675	+	0.896188i	$0.646326\pi$
$662$	8.63526	0.335619
$663$	3.44412	0.133759
$664$	6.94158	0.269385
$665$	−0.298463	−0.0115739
$666$	13.9506	0.540574
$667$	−25.4467	−0.985299
$668$	−3.35652	−0.129868
$669$	3.94730	0.152612
$670$	−0.997672	−0.0385434
$671$	29.2842	1.13051
$672$	0.159192	0.00614098
$673$	−44.6627	−1.72162	−0.860811	−	0.508925i	$-0.830043\pi$
$673$	−44.6627	−1.72162	−0.860811	+	0.508925i	$0.830043\pi$
$674$	7.01909	0.270365
$675$	−15.5036	−0.596732
$676$	−11.8806	−0.456947
$677$	−13.0440	−0.501320	−0.250660	−	0.968075i	$-0.580648\pi$
$677$	−13.0440	−0.501320	−0.250660	+	0.968075i	$0.580648\pi$
$678$	10.6617	0.409460
$679$	−0.730487	−0.0280335
$680$	0.711873	0.0272991
$681$	−7.59221	−0.290934
$682$	−16.8075	−0.643591
$683$	0.923548	0.0353386	0.0176693	−	0.999844i	$-0.494375\pi$
$683$	0.923548	0.0353386	0.0176693	+	0.999844i	$0.494375\pi$
$684$	23.1713	0.885977
$685$	1.24363	0.0475168
$686$	4.06236	0.155102
$687$	−6.65061	−0.253737
$688$	1.40411	0.0535313
$689$	11.6177	0.442599
$690$	0.390162	0.0148532
$691$	−36.3415	−1.38249	−0.691247	−	0.722618i	$-0.742938\pi$
$691$	−36.3415	−1.38249	−0.691247	+	0.722618i	$0.742938\pi$
$692$	6.40345	0.243423
$693$	3.67886	0.139748
$694$	−27.6881	−1.05103
$695$	−0.974443	−0.0369627
$696$	−2.31237	−0.0876502
$697$	13.9120	0.526956
$698$	8.29379	0.313924
$699$	3.29005	0.124441
$700$	−1.45558	−0.0550157
$701$	−26.6973	−1.00834	−0.504172	−	0.863604i	$-0.668202\pi$
$701$	−26.6973	−1.00834	−0.504172	+	0.863604i	$0.668202\pi$
$702$	−3.28992	−0.124170
$703$	−44.2544	−1.66909
$704$	−4.66250	−0.175724
$705$	−0.543905	−0.0204846
$706$	2.92907	0.110237
$707$	2.02064	0.0759941
$708$	−3.48536	−0.130988
$709$	7.60836	0.285738	0.142869	−	0.989742i	$-0.454367\pi$
$709$	7.60836	0.285738	0.142869	+	0.989742i	$0.454367\pi$
$710$	−0.555864	−0.0208612
$711$	17.2222	0.645883
$712$	−1.15405	−0.0432498
$713$	−21.6310	−0.810088
$714$	−0.950373	−0.0355668
$715$	−0.588215	−0.0219980
$716$	−12.0414	−0.450010
$717$	5.80952	0.216961
$718$	6.95621	0.259604
$719$	−10.5891	−0.394906	−0.197453	−	0.980312i	$-0.563267\pi$
$719$	−10.5891	−0.394906	−0.197453	+	0.980312i	$0.563267\pi$
$720$	−0.322273	−0.0120104
$721$	0.914625	0.0340624
$722$	−54.5047	−2.02846
$723$	−10.4371	−0.388161
$724$	1.36572	0.0507567
$725$	21.1432	0.785239
$726$	5.85571	0.217326
$727$	17.3880	0.644884	0.322442	−	0.946589i	$-0.395496\pi$
$727$	17.3880	0.644884	0.322442	+	0.946589i	$0.395496\pi$
$728$	−0.308879	−0.0114478
$729$	−12.2439	−0.453479
$730$	−1.61811	−0.0598891
$731$	−8.38250	−0.310038
$732$	3.42480	0.126584
$733$	−1.21242	−0.0447819	−0.0223909	−	0.999749i	$-0.507128\pi$
$733$	−1.21242	−0.0447819	−0.0223909	+	0.999749i	$0.507128\pi$
$734$	28.8543	1.06503
$735$	0.449602	0.0165838
$736$	−6.00058	−0.221184
$737$	−39.0100	−1.43695
$738$	−6.29813	−0.231837
$739$	−8.50339	−0.312802	−0.156401	−	0.987694i	$-0.549989\pi$
$739$	−8.50339	−0.312802	−0.156401	+	0.987694i	$0.549989\pi$
$740$	0.615503	0.0226263
$741$	4.94612	0.181700
$742$	−3.20579	−0.117688
$743$	7.63912	0.280252	0.140126	−	0.990134i	$-0.455249\pi$
$743$	7.63912	0.280252	0.140126	+	0.990134i	$0.455249\pi$
$744$	−1.96564	−0.0720638
$745$	−0.787584	−0.0288548
$746$	−30.2726	−1.10836
$747$	18.7608	0.686421
$748$	27.8350	1.01775
$749$	0.272603	0.00996071
$750$	−0.649282	−0.0237084
$751$	39.7295	1.44975	0.724876	−	0.688880i	$-0.241897\pi$
$751$	39.7295	1.44975	0.724876	+	0.688880i	$0.241897\pi$
$752$	8.36511	0.305044
$753$	−6.66085	−0.242735
$754$	4.48667	0.163395
$755$	−0.331265	−0.0120560
$756$	0.907822	0.0330172
$757$	12.3761	0.449816	0.224908	−	0.974380i	$-0.427792\pi$
$757$	12.3761	0.449816	0.224908	+	0.974380i	$0.427792\pi$
$758$	19.8796	0.722059
$759$	15.2557	0.553747
$760$	1.02232	0.0370836
$761$	−19.0773	−0.691552	−0.345776	−	0.938317i	$-0.612384\pi$
$761$	−19.0773	−0.691552	−0.345776	+	0.938317i	$0.612384\pi$
$762$	−9.48504	−0.343607
$763$	0.568356	0.0205759
$764$	9.30593	0.336677
$765$	1.92396	0.0695609
$766$	−32.9757	−1.19146
$767$	6.76261	0.244184
$768$	−0.545281	−0.0196761
$769$	42.0085	1.51486	0.757432	−	0.652914i	$-0.226454\pi$
$769$	42.0085	1.51486	0.757432	+	0.652914i	$0.226454\pi$
$770$	0.162312	0.00584933
$771$	−8.87093	−0.319479
$772$	−8.21659	−0.295722
$773$	31.5015	1.13303	0.566515	−	0.824052i	$-0.308292\pi$
$773$	31.5015	1.13303	0.566515	+	0.824052i	$0.308292\pi$
$774$	3.79485	0.136403
$775$	17.9728	0.645604
$776$	2.50213	0.0898213
$777$	−0.821716	−0.0294789
$778$	−35.0917	−1.25810
$779$	19.9791	0.715826
$780$	−0.0687919	−0.00246315
$781$	−21.7348	−0.777734
$782$	35.8233	1.28104
$783$	−13.1867	−0.471254
$784$	−6.91477	−0.246956
$785$	−0.621943	−0.0221981
$786$	3.79403	0.135329
$787$	34.8805	1.24336	0.621678	−	0.783273i	$-0.286451\pi$
$787$	34.8805	1.24336	0.621678	+	0.783273i	$0.286451\pi$
$788$	6.61885	0.235787
$789$	16.2082	0.577026
$790$	0.759848	0.0270342
$791$	5.70832	0.202964
$792$	−12.6012	−0.447764
$793$	−6.64511	−0.235975
$794$	−28.7572	−1.02055
$795$	−0.713977	−0.0253222
$796$	1.79785	0.0637230
$797$	23.6381	0.837303	0.418652	−	0.908147i	$-0.362503\pi$
$797$	23.6381	0.837303	0.418652	+	0.908147i	$0.362503\pi$
$798$	−1.36483	−0.0483146
$799$	−49.9395	−1.76673
$800$	4.98578	0.176274
$801$	−3.11901	−0.110205
$802$	8.13394	0.287219
$803$	−63.2699	−2.23274
$804$	−4.56223	−0.160897
$805$	0.208894	0.00736256
$806$	3.81391	0.134339
$807$	−0.166417	−0.00585816
$808$	−6.92129	−0.243490
$809$	−4.38068	−0.154016	−0.0770082	−	0.997030i	$-0.524537\pi$
$809$	−4.38068	−0.154016	−0.0770082	+	0.997030i	$0.524537\pi$
$810$	−0.764633	−0.0268665
$811$	51.4109	1.80528	0.902640	−	0.430396i	$-0.141626\pi$
$811$	51.4109	1.80528	0.902640	+	0.430396i	$0.141626\pi$
$812$	−1.23805	−0.0434472
$813$	3.67159	0.128768
$814$	24.0668	0.843540
$815$	−1.74397	−0.0610887
$816$	3.25531	0.113959
$817$	−12.0381	−0.421161
$818$	−12.0825	−0.422455
$819$	−0.834798	−0.0291702
$820$	−0.277875	−0.00970382
$821$	37.6152	1.31278	0.656390	−	0.754422i	$-0.272083\pi$
$821$	37.6152	1.31278	0.656390	+	0.754422i	$0.272083\pi$
$822$	5.68698	0.198356
$823$	19.0995	0.665766	0.332883	−	0.942968i	$-0.391979\pi$
$823$	19.0995	0.665766	0.332883	+	0.942968i	$0.391979\pi$
$824$	−3.13286	−0.109138
$825$	−12.6757	−0.441311
$826$	−1.86608	−0.0649292
$827$	22.5195	0.783081	0.391540	−	0.920161i	$-0.371942\pi$
$827$	22.5195	0.783081	0.391540	+	0.920161i	$0.371942\pi$
$828$	−16.2176	−0.563600
$829$	−11.6959	−0.406215	−0.203107	−	0.979156i	$-0.565104\pi$
$829$	−11.6959	−0.406215	−0.203107	+	0.979156i	$0.565104\pi$
$830$	0.827731	0.0287309
$831$	−0.230569	−0.00799835
$832$	1.05800	0.0366796
$833$	41.2809	1.43030
$834$	−4.45600	−0.154299
$835$	−0.400240	−0.0138509
$836$	39.9739	1.38253
$837$	−11.2094	−0.387453
$838$	24.2155	0.836510
$839$	2.67218	0.0922538	0.0461269	−	0.998936i	$-0.485312\pi$
$839$	2.67218	0.0922538	0.0461269	+	0.998936i	$0.485312\pi$
$840$	0.0189825	0.000654958 0
$841$	−11.0165	−0.379878
$842$	−15.9462	−0.549544
$843$	12.7092	0.437729
$844$	−9.38983	−0.323211
$845$	−1.41668	−0.0487351
$846$	22.6081	0.777284
$847$	3.13517	0.107726
$848$	10.9808	0.377082
$849$	−10.6225	−0.364563
$850$	−29.7649	−1.02093
$851$	30.9737	1.06176
$852$	−2.54190	−0.0870840
$853$	7.92025	0.271184	0.135592	−	0.990765i	$-0.456706\pi$
$853$	7.92025	0.271184	0.135592	+	0.990765i	$0.456706\pi$
$854$	1.83366	0.0627464
$855$	2.76300	0.0944927
$856$	−0.933746	−0.0319148
$857$	34.3826	1.17449	0.587243	−	0.809410i	$-0.300213\pi$
$857$	34.3826	1.17449	0.587243	+	0.809410i	$0.300213\pi$
$858$	−2.68983	−0.0918294
$859$	−21.0581	−0.718492	−0.359246	−	0.933243i	$-0.616966\pi$
$859$	−21.0581	−0.718492	−0.359246	+	0.933243i	$0.616966\pi$
$860$	0.167430	0.00570931
$861$	0.370972	0.0126427
$862$	15.3932	0.524293
$863$	−8.59268	−0.292498	−0.146249	−	0.989248i	$-0.546720\pi$
$863$	−8.59268	−0.292498	−0.146249	+	0.989248i	$0.546720\pi$
$864$	−3.10956	−0.105789
$865$	0.763563	0.0259619
$866$	−28.9416	−0.983477
$867$	−10.1643	−0.345198
$868$	−1.05241	−0.0357212
$869$	29.7108	1.00787
$870$	−0.275733	−0.00934822
$871$	8.85205	0.299940
$872$	−1.94679	−0.0659265
$873$	6.76243	0.228874
$874$	51.4459	1.74018
$875$	−0.347628	−0.0117520
$876$	−7.39943	−0.250004
$877$	38.3538	1.29512	0.647558	−	0.762016i	$-0.275790\pi$
$877$	38.3538	1.29512	0.647558	+	0.762016i	$0.275790\pi$
$878$	−13.9711	−0.471502
$879$	2.10204	0.0709000
$880$	−0.555968	−0.0187417
$881$	−8.43318	−0.284121	−0.142060	−	0.989858i	$-0.545373\pi$
$881$	−8.43318	−0.284121	−0.142060	+	0.989858i	$0.545373\pi$
$882$	−18.6883	−0.629269
$883$	6.28687	0.211570	0.105785	−	0.994389i	$-0.466264\pi$
$883$	6.28687	0.211570	0.105785	+	0.994389i	$0.466264\pi$
$884$	−6.31624	−0.212438
$885$	−0.415603	−0.0139703
$886$	−26.9442	−0.905207
$887$	−41.6086	−1.39708	−0.698540	−	0.715571i	$-0.746166\pi$
$887$	−41.6086	−1.39708	−0.698540	+	0.715571i	$0.746166\pi$
$888$	2.81462	0.0944524
$889$	−5.07833	−0.170322
$890$	−0.137612	−0.00461275
$891$	−29.8979	−1.00162
$892$	−7.23903	−0.242381
$893$	−71.7182	−2.39996
$894$	−3.60152	−0.120453
$895$	−1.43585	−0.0479952
$896$	−0.291946	−0.00975322
$897$	−3.46179	−0.115586
$898$	10.8014	0.360447
$899$	15.2870	0.509849
$900$	13.4749	0.449164
$901$	−65.5549	−2.18395
$902$	−10.8652	−0.361771
$903$	−0.223524	−0.00743841
$904$	−19.5527	−0.650312
$905$	0.162852	0.00541339
$906$	−1.51484	−0.0503270
$907$	−21.3145	−0.707735	−0.353867	−	0.935296i	$-0.615134\pi$
$907$	−21.3145	−0.707735	−0.353867	+	0.935296i	$0.615134\pi$
$908$	13.9235	0.462067
$909$	−18.7060	−0.620437
$910$	−0.0368315	−0.00122095
$911$	−55.7021	−1.84549	−0.922746	−	0.385408i	$-0.874061\pi$
$911$	−55.7021	−1.84549	−0.922746	+	0.385408i	$0.874061\pi$
$912$	4.67496	0.154803
$913$	32.3651	1.07113
$914$	31.8581	1.05377
$915$	0.408382	0.0135007
$916$	12.1967	0.402989
$917$	2.03134	0.0670808
$918$	18.5639	0.612701
$919$	27.7860	0.916576	0.458288	−	0.888804i	$-0.348463\pi$
$919$	27.7860	0.916576	0.458288	+	0.888804i	$0.348463\pi$
$920$	−0.715524	−0.0235901
$921$	5.67510	0.187001
$922$	−2.82144	−0.0929192
$923$	4.93202	0.162339
$924$	0.742234	0.0244177
$925$	−25.7355	−0.846177
$926$	−37.6080	−1.23588
$927$	−8.46708	−0.278095
$928$	4.24070	0.139208
$929$	9.47277	0.310792	0.155396	−	0.987852i	$-0.450335\pi$
$929$	9.47277	0.310792	0.155396	+	0.987852i	$0.450335\pi$
$930$	−0.234388	−0.00768587
$931$	59.2837	1.94294
$932$	−6.03368	−0.197640
$933$	−18.9275	−0.619659
$934$	−4.86900	−0.159318
$935$	3.31911	0.108546
$936$	2.85943	0.0934634
$937$	6.11072	0.199629	0.0998143	−	0.995006i	$-0.468175\pi$
$937$	6.11072	0.199629	0.0998143	+	0.995006i	$0.468175\pi$
$938$	−2.44264	−0.0797550
$939$	−15.5247	−0.506629
$940$	0.997477	0.0325341
$941$	−0.0940219	−0.00306502	−0.00153251	−	0.999999i	$-0.500488\pi$
$941$	−0.0940219	−0.00306502	−0.00153251	+	0.999999i	$0.500488\pi$
$942$	−2.84407	−0.0926648
$943$	−13.9834	−0.455361
$944$	6.39186	0.208037
$945$	0.108251	0.00352140
$946$	6.54667	0.212851
$947$	−25.5706	−0.830933	−0.415466	−	0.909608i	$-0.636382\pi$
$947$	−25.5706	−0.830933	−0.415466	+	0.909608i	$0.636382\pi$
$948$	3.47469	0.112853
$949$	14.3570	0.466049
$950$	−42.7455	−1.38685
$951$	16.3558	0.530372
$952$	1.74291	0.0564879
$953$	52.3372	1.69537	0.847683	−	0.530503i	$-0.177997\pi$
$953$	52.3372	1.69537	0.847683	+	0.530503i	$0.177997\pi$
$954$	29.6774	0.960842
$955$	1.10966	0.0359078
$956$	−10.6542	−0.344581
$957$	−10.7814	−0.348514
$958$	29.9514	0.967686
$959$	3.04484	0.0983229
$960$	−0.0650206	−0.00209853
$961$	−18.0053	−0.580815
$962$	−5.46117	−0.176075
$963$	−2.52361	−0.0813221
$964$	19.1409	0.616485
$965$	−0.979766	−0.0315398
$966$	0.955247	0.0307346
$967$	36.3898	1.17022	0.585108	−	0.810955i	$-0.301052\pi$
$967$	36.3898	1.17022	0.585108	+	0.810955i	$0.301052\pi$
$968$	−10.7389	−0.345161
$969$	−27.9093	−0.896577
$970$	0.298360	0.00957977
$971$	6.72660	0.215867	0.107933	−	0.994158i	$-0.465577\pi$
$971$	6.72660	0.215867	0.107933	+	0.994158i	$0.465577\pi$
$972$	−12.8252	−0.411370
$973$	−2.38577	−0.0764841
$974$	−31.4885	−1.00896
$975$	2.87634	0.0921165
$976$	−6.28081	−0.201044
$977$	−11.4608	−0.366665	−0.183332	−	0.983051i	$-0.558688\pi$
$977$	−11.4608	−0.366665	−0.183332	+	0.983051i	$0.558688\pi$
$978$	−7.97497	−0.255011
$979$	−5.38075	−0.171970
$980$	−0.824534	−0.0263388
$981$	−5.26152	−0.167987
$982$	−38.2320	−1.22003
$983$	23.0930	0.736551	0.368275	−	0.929717i	$-0.379948\pi$
$983$	23.0930	0.736551	0.368275	+	0.929717i	$0.379948\pi$
$984$	−1.27069	−0.0405080
$985$	0.789248	0.0251475
$986$	−25.3168	−0.806252
$987$	−1.33166	−0.0423873
$988$	−9.07077	−0.288580
$989$	8.42549	0.267915
$990$	−1.50260	−0.0477556
$991$	−19.7334	−0.626852	−0.313426	−	0.949613i	$-0.601477\pi$
$991$	−19.7334	−0.626852	−0.313426	+	0.949613i	$0.601477\pi$
$992$	3.60482	0.114453
$993$	4.70864	0.149424
$994$	−1.36094	−0.0431665
$995$	0.214380	0.00679629
$996$	3.78511	0.119936
$997$	49.1750	1.55739	0.778694	−	0.627404i	$-0.215882\pi$
$997$	49.1750	1.55739	0.778694	+	0.627404i	$0.215882\pi$
$998$	−39.3979	−1.24712
$999$	16.0508	0.507826

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.h.1.17	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.h.1.17	✓	42	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.545281 q^{3} +1.00000 q^{4} +0.119242 q^{5} +0.545281 q^{6} +0.291946 q^{7} -1.00000 q^{8} -2.70267 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.545281 q^{3} +1.00000 q^{4} +0.119242 q^{5} +0.545281 q^{6} +0.291946 q^{7} -1.00000 q^{8} -2.70267 q^{9} -0.119242 q^{10} -4.66250 q^{11} -0.545281 q^{12} +1.05800 q^{13} -0.291946 q^{14} -0.0650206 q^{15} +1.00000 q^{16} -5.96997 q^{17} +2.70267 q^{18} -8.57349 q^{19} +0.119242 q^{20} -0.159192 q^{21} +4.66250 q^{22} +6.00058 q^{23} +0.545281 q^{24} -4.98578 q^{25} -1.05800 q^{26} +3.10956 q^{27} +0.291946 q^{28} -4.24070 q^{29} +0.0650206 q^{30} -3.60482 q^{31} -1.00000 q^{32} +2.54237 q^{33} +5.96997 q^{34} +0.0348123 q^{35} -2.70267 q^{36} +5.16178 q^{37} +8.57349 q^{38} -0.576908 q^{39} -0.119242 q^{40} -2.33034 q^{41} +0.159192 q^{42} +1.40411 q^{43} -4.66250 q^{44} -0.322273 q^{45} -6.00058 q^{46} +8.36511 q^{47} -0.545281 q^{48} -6.91477 q^{49} +4.98578 q^{50} +3.25531 q^{51} +1.05800 q^{52} +10.9808 q^{53} -3.10956 q^{54} -0.555968 q^{55} -0.291946 q^{56} +4.67496 q^{57} +4.24070 q^{58} +6.39186 q^{59} -0.0650206 q^{60} -6.28081 q^{61} +3.60482 q^{62} -0.789033 q^{63} +1.00000 q^{64} +0.126159 q^{65} -2.54237 q^{66} +8.36676 q^{67} -5.96997 q^{68} -3.27200 q^{69} -0.0348123 q^{70} +4.66163 q^{71} +2.70267 q^{72} +13.5699 q^{73} -5.16178 q^{74} +2.71865 q^{75} -8.57349 q^{76} -1.36120 q^{77} +0.576908 q^{78} -6.37230 q^{79} +0.119242 q^{80} +6.41243 q^{81} +2.33034 q^{82} -6.94158 q^{83} -0.159192 q^{84} -0.711873 q^{85} -1.40411 q^{86} +2.31237 q^{87} +4.66250 q^{88} +1.15405 q^{89} +0.322273 q^{90} +0.308879 q^{91} +6.00058 q^{92} +1.96564 q^{93} -8.36511 q^{94} -1.02232 q^{95} +0.545281 q^{96} -2.50213 q^{97} +6.91477 q^{98} +12.6012 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9}+O(q^{10}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9} - 27 q^{10} + 23 q^{11} + 15 q^{13} + 10 q^{14} + 6 q^{15} + 42 q^{16} + 14 q^{17} - 56 q^{18} - 4 q^{19} + 27 q^{20} + 26 q^{21} - 23 q^{22} + 12 q^{23} + 45 q^{25} - 15 q^{26} - 3 q^{27} - 10 q^{28} + 41 q^{29} - 6 q^{30} + 18 q^{31} - 42 q^{32} + 25 q^{33} - 14 q^{34} + 8 q^{35} + 56 q^{36} + 33 q^{37} + 4 q^{38} + 10 q^{39} - 27 q^{40} + 84 q^{41} - 26 q^{42} - 36 q^{43} + 23 q^{44} + 66 q^{45} - 12 q^{46} + 28 q^{47} + 58 q^{49} - 45 q^{50} + 17 q^{51} + 15 q^{52} + 68 q^{53} + 3 q^{54} - 28 q^{55} + 10 q^{56} - 9 q^{57} - 41 q^{58} + 59 q^{59} + 6 q^{60} + 41 q^{61} - 18 q^{62} - 28 q^{63} + 42 q^{64} + 44 q^{65} - 25 q^{66} + 14 q^{68} + 67 q^{69} - 8 q^{70} + 69 q^{71} - 56 q^{72} - 27 q^{73} - 33 q^{74} + 14 q^{75} - 4 q^{76} + 43 q^{77} - 10 q^{78} - 19 q^{79} + 27 q^{80} + 74 q^{81} - 84 q^{82} + 20 q^{83} + 26 q^{84} + 16 q^{85} + 36 q^{86} - 28 q^{87} - 23 q^{88} + 123 q^{89} - 66 q^{90} - 9 q^{91} + 12 q^{92} + 48 q^{93} - 28 q^{94} + 28 q^{95} + 10 q^{97} - 58 q^{98} + 75 q^{99}+O(q^{100}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9 - 27 * q^10 + 23 * q^11 + 15 * q^13 + 10 * q^14 + 6 * q^15 + 42 * q^16 + 14 * q^17 - 56 * q^18 - 4 * q^19 + 27 * q^20 + 26 * q^21 - 23 * q^22 + 12 * q^23 + 45 * q^25 - 15 * q^26 - 3 * q^27 - 10 * q^28 + 41 * q^29 - 6 * q^30 + 18 * q^31 - 42 * q^32 + 25 * q^33 - 14 * q^34 + 8 * q^35 + 56 * q^36 + 33 * q^37 + 4 * q^38 + 10 * q^39 - 27 * q^40 + 84 * q^41 - 26 * q^42 - 36 * q^43 + 23 * q^44 + 66 * q^45 - 12 * q^46 + 28 * q^47 + 58 * q^49 - 45 * q^50 + 17 * q^51 + 15 * q^52 + 68 * q^53 + 3 * q^54 - 28 * q^55 + 10 * q^56 - 9 * q^57 - 41 * q^58 + 59 * q^59 + 6 * q^60 + 41 * q^61 - 18 * q^62 - 28 * q^63 + 42 * q^64 + 44 * q^65 - 25 * q^66 + 14 * q^68 + 67 * q^69 - 8 * q^70 + 69 * q^71 - 56 * q^72 - 27 * q^73 - 33 * q^74 + 14 * q^75 - 4 * q^76 + 43 * q^77 - 10 * q^78 - 19 * q^79 + 27 * q^80 + 74 * q^81 - 84 * q^82 + 20 * q^83 + 26 * q^84 + 16 * q^85 + 36 * q^86 - 28 * q^87 - 23 * q^88 + 123 * q^89 - 66 * q^90 - 9 * q^91 + 12 * q^92 + 48 * q^93 - 28 * q^94 + 28 * q^95 + 10 * q^97 - 58 * q^98 + 75 * q^99

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