LMFDB - Embedded newform 4006.2.a.i.1.2

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:	$46$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.83861 q^{3} +1.00000 q^{4} -0.543432 q^{5} -2.83861 q^{6} -3.69136 q^{7} +1.00000 q^{8} +5.05769 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.83861 q^{3} +1.00000 q^{4} -0.543432 q^{5} -2.83861 q^{6} -3.69136 q^{7} +1.00000 q^{8} +5.05769 q^{9} -0.543432 q^{10} +5.47151 q^{11} -2.83861 q^{12} -1.45011 q^{13} -3.69136 q^{14} +1.54259 q^{15} +1.00000 q^{16} -0.276652 q^{17} +5.05769 q^{18} -0.0117392 q^{19} -0.543432 q^{20} +10.4783 q^{21} +5.47151 q^{22} -4.39931 q^{23} -2.83861 q^{24} -4.70468 q^{25} -1.45011 q^{26} -5.84098 q^{27} -3.69136 q^{28} +0.457896 q^{29} +1.54259 q^{30} +6.56989 q^{31} +1.00000 q^{32} -15.5315 q^{33} -0.276652 q^{34} +2.00600 q^{35} +5.05769 q^{36} -10.2186 q^{37} -0.0117392 q^{38} +4.11629 q^{39} -0.543432 q^{40} -0.712352 q^{41} +10.4783 q^{42} -7.70096 q^{43} +5.47151 q^{44} -2.74851 q^{45} -4.39931 q^{46} +6.17477 q^{47} -2.83861 q^{48} +6.62611 q^{49} -4.70468 q^{50} +0.785307 q^{51} -1.45011 q^{52} -3.79005 q^{53} -5.84098 q^{54} -2.97340 q^{55} -3.69136 q^{56} +0.0333230 q^{57} +0.457896 q^{58} +4.35905 q^{59} +1.54259 q^{60} +8.34485 q^{61} +6.56989 q^{62} -18.6697 q^{63} +1.00000 q^{64} +0.788035 q^{65} -15.5315 q^{66} +6.44915 q^{67} -0.276652 q^{68} +12.4879 q^{69} +2.00600 q^{70} -12.6388 q^{71} +5.05769 q^{72} +3.00643 q^{73} -10.2186 q^{74} +13.3547 q^{75} -0.0117392 q^{76} -20.1973 q^{77} +4.11629 q^{78} +2.89652 q^{79} -0.543432 q^{80} +1.40718 q^{81} -0.712352 q^{82} +3.16248 q^{83} +10.4783 q^{84} +0.150342 q^{85} -7.70096 q^{86} -1.29979 q^{87} +5.47151 q^{88} -0.204759 q^{89} -2.74851 q^{90} +5.35287 q^{91} -4.39931 q^{92} -18.6493 q^{93} +6.17477 q^{94} +0.00637946 q^{95} -2.83861 q^{96} +13.1026 q^{97} +6.62611 q^{98} +27.6732 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9}+O(q^{10}) $ 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9} + 23 q^{10} + 39 q^{11} + 21 q^{12} + 8 q^{13} + 26 q^{14} + 14 q^{15} + 46 q^{16} + 36 q^{17} + 59 q^{18} + 37 q^{19} + 23 q^{20} + 20 q^{21} + 39 q^{22} + 38 q^{23} + 21 q^{24} + 57 q^{25} + 8 q^{26} + 63 q^{27} + 26 q^{28} + 23 q^{29} + 14 q^{30} + 44 q^{31} + 46 q^{32} + 25 q^{33} + 36 q^{34} + 26 q^{35} + 59 q^{36} + 9 q^{37} + 37 q^{38} - 2 q^{39} + 23 q^{40} + 50 q^{41} + 20 q^{42} + 46 q^{43} + 39 q^{44} + 30 q^{45} + 38 q^{46} + 57 q^{47} + 21 q^{48} + 62 q^{49} + 57 q^{50} + 5 q^{51} + 8 q^{52} + 21 q^{53} + 63 q^{54} + 40 q^{55} + 26 q^{56} + 3 q^{57} + 23 q^{58} + 68 q^{59} + 14 q^{60} - q^{61} + 44 q^{62} + 40 q^{63} + 46 q^{64} + 18 q^{65} + 25 q^{66} + 42 q^{67} + 36 q^{68} - 7 q^{69} + 26 q^{70} + 67 q^{71} + 59 q^{72} + 48 q^{73} + 9 q^{74} + 71 q^{75} + 37 q^{76} - 5 q^{77} - 2 q^{78} + 40 q^{79} + 23 q^{80} + 82 q^{81} + 50 q^{82} + 48 q^{83} + 20 q^{84} - 68 q^{85} + 46 q^{86} + 18 q^{87} + 39 q^{88} + 90 q^{89} + 30 q^{90} + 9 q^{91} + 38 q^{92} - 42 q^{93} + 57 q^{94} + 6 q^{95} + 21 q^{96} + 46 q^{97} + 62 q^{98} + 61 q^{99}+O(q^{100}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9 + 23 * q^10 + 39 * q^11 + 21 * q^12 + 8 * q^13 + 26 * q^14 + 14 * q^15 + 46 * q^16 + 36 * q^17 + 59 * q^18 + 37 * q^19 + 23 * q^20 + 20 * q^21 + 39 * q^22 + 38 * q^23 + 21 * q^24 + 57 * q^25 + 8 * q^26 + 63 * q^27 + 26 * q^28 + 23 * q^29 + 14 * q^30 + 44 * q^31 + 46 * q^32 + 25 * q^33 + 36 * q^34 + 26 * q^35 + 59 * q^36 + 9 * q^37 + 37 * q^38 - 2 * q^39 + 23 * q^40 + 50 * q^41 + 20 * q^42 + 46 * q^43 + 39 * q^44 + 30 * q^45 + 38 * q^46 + 57 * q^47 + 21 * q^48 + 62 * q^49 + 57 * q^50 + 5 * q^51 + 8 * q^52 + 21 * q^53 + 63 * q^54 + 40 * q^55 + 26 * q^56 + 3 * q^57 + 23 * q^58 + 68 * q^59 + 14 * q^60 - q^61 + 44 * q^62 + 40 * q^63 + 46 * q^64 + 18 * q^65 + 25 * q^66 + 42 * q^67 + 36 * q^68 - 7 * q^69 + 26 * q^70 + 67 * q^71 + 59 * q^72 + 48 * q^73 + 9 * q^74 + 71 * q^75 + 37 * q^76 - 5 * q^77 - 2 * q^78 + 40 * q^79 + 23 * q^80 + 82 * q^81 + 50 * q^82 + 48 * q^83 + 20 * q^84 - 68 * q^85 + 46 * q^86 + 18 * q^87 + 39 * q^88 + 90 * q^89 + 30 * q^90 + 9 * q^91 + 38 * q^92 - 42 * q^93 + 57 * q^94 + 6 * q^95 + 21 * q^96 + 46 * q^97 + 62 * q^98 + 61 * 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
$3$	−2.83861	−1.63887	−0.819435	−	0.573172i	$-0.805713\pi$
$3$	−2.83861	−1.63887	−0.819435	+	0.573172i	$0.805713\pi$
$4$	1.00000	0.500000
$5$	−0.543432	−0.243030	−0.121515	−	0.992590i	$-0.538775\pi$
$5$	−0.543432	−0.243030	−0.121515	+	0.992590i	$0.538775\pi$
$6$	−2.83861	−1.15886
$7$	−3.69136	−1.39520	−0.697601	−	0.716487i	$-0.745749\pi$
$7$	−3.69136	−1.39520	−0.697601	+	0.716487i	$0.745749\pi$
$8$	1.00000	0.353553
$9$	5.05769	1.68590
$10$	−0.543432	−0.171848
$11$	5.47151	1.64972	0.824862	−	0.565334i	$-0.191253\pi$
$11$	5.47151	1.64972	0.824862	+	0.565334i	$0.191253\pi$
$12$	−2.83861	−0.819435
$13$	−1.45011	−0.402188	−0.201094	−	0.979572i	$-0.564450\pi$
$13$	−1.45011	−0.402188	−0.201094	+	0.979572i	$0.564450\pi$
$14$	−3.69136	−0.986556
$15$	1.54259	0.398295
$16$	1.00000	0.250000
$17$	−0.276652	−0.0670980	−0.0335490	−	0.999437i	$-0.510681\pi$
$17$	−0.276652	−0.0670980	−0.0335490	+	0.999437i	$0.510681\pi$
$18$	5.05769	1.19211
$19$	−0.0117392	−0.00269316	−0.00134658	−	0.999999i	$-0.500429\pi$
$19$	−0.0117392	−0.00269316	−0.00134658	+	0.999999i	$0.500429\pi$
$20$	−0.543432	−0.121515
$21$	10.4783	2.28655
$22$	5.47151	1.16653
$23$	−4.39931	−0.917319	−0.458660	−	0.888612i	$-0.651670\pi$
$23$	−4.39931	−0.917319	−0.458660	+	0.888612i	$0.651670\pi$
$24$	−2.83861	−0.579428
$25$	−4.70468	−0.940936
$26$	−1.45011	−0.284390
$27$	−5.84098	−1.12410
$28$	−3.69136	−0.697601
$29$	0.457896	0.0850292	0.0425146	−	0.999096i	$-0.486463\pi$
$29$	0.457896	0.0850292	0.0425146	+	0.999096i	$0.486463\pi$
$30$	1.54259	0.281637
$31$	6.56989	1.17999	0.589993	−	0.807408i	$-0.299130\pi$
$31$	6.56989	1.17999	0.589993	+	0.807408i	$0.299130\pi$
$32$	1.00000	0.176777
$33$	−15.5315	−2.70368
$34$	−0.276652	−0.0474454
$35$	2.00600	0.339076
$36$	5.05769	0.842949
$37$	−10.2186	−1.67992	−0.839962	−	0.542646i	$-0.817423\pi$
$37$	−10.2186	−1.67992	−0.839962	+	0.542646i	$0.817423\pi$
$38$	−0.0117392	−0.00190435
$39$	4.11629	0.659134
$40$	−0.543432	−0.0859241
$41$	−0.712352	−0.111251	−0.0556253	−	0.998452i	$-0.517715\pi$
$41$	−0.712352	−0.111251	−0.0556253	+	0.998452i	$0.517715\pi$
$42$	10.4783	1.61684
$43$	−7.70096	−1.17438	−0.587192	−	0.809447i	$-0.699767\pi$
$43$	−7.70096	−1.17438	−0.587192	+	0.809447i	$0.699767\pi$
$44$	5.47151	0.824862
$45$	−2.74851	−0.409724
$46$	−4.39931	−0.648643
$47$	6.17477	0.900682	0.450341	−	0.892857i	$-0.351302\pi$
$47$	6.17477	0.900682	0.450341	+	0.892857i	$0.351302\pi$
$48$	−2.83861	−0.409718
$49$	6.62611	0.946586
$50$	−4.70468	−0.665342
$51$	0.785307	0.109965
$52$	−1.45011	−0.201094
$53$	−3.79005	−0.520603	−0.260302	−	0.965527i	$-0.583822\pi$
$53$	−3.79005	−0.520603	−0.260302	+	0.965527i	$0.583822\pi$
$54$	−5.84098	−0.794857
$55$	−2.97340	−0.400933
$56$	−3.69136	−0.493278
$57$	0.0333230	0.00441374
$58$	0.457896	0.0601247
$59$	4.35905	0.567501	0.283750	−	0.958898i	$-0.408421\pi$
$59$	4.35905	0.567501	0.283750	+	0.958898i	$0.408421\pi$
$60$	1.54259	0.199147
$61$	8.34485	1.06845	0.534224	−	0.845343i	$-0.320604\pi$
$61$	8.34485	1.06845	0.534224	+	0.845343i	$0.320604\pi$
$62$	6.56989	0.834376
$63$	−18.6697	−2.35217
$64$	1.00000	0.125000
$65$	0.788035	0.0977437
$66$	−15.5315	−1.91179
$67$	6.44915	0.787889	0.393945	−	0.919134i	$-0.371110\pi$
$67$	6.44915	0.787889	0.393945	+	0.919134i	$0.371110\pi$
$68$	−0.276652	−0.0335490
$69$	12.4879	1.50337
$70$	2.00600	0.239763
$71$	−12.6388	−1.49995	−0.749974	−	0.661467i	$-0.769934\pi$
$71$	−12.6388	−1.49995	−0.749974	+	0.661467i	$0.769934\pi$
$72$	5.05769	0.596055
$73$	3.00643	0.351876	0.175938	−	0.984401i	$-0.443704\pi$
$73$	3.00643	0.351876	0.175938	+	0.984401i	$0.443704\pi$
$74$	−10.2186	−1.18789
$75$	13.3547	1.54207
$76$	−0.0117392	−0.00134658
$77$	−20.1973	−2.30170
$78$	4.11629	0.466078
$79$	2.89652	0.325884	0.162942	−	0.986636i	$-0.447902\pi$
$79$	2.89652	0.325884	0.162942	+	0.986636i	$0.447902\pi$
$80$	−0.543432	−0.0607575
$81$	1.40718	0.156353
$82$	−0.712352	−0.0786661
$83$	3.16248	0.347127	0.173564	−	0.984823i	$-0.444472\pi$
$83$	3.16248	0.347127	0.173564	+	0.984823i	$0.444472\pi$
$84$	10.4783	1.14328
$85$	0.150342	0.0163068
$86$	−7.70096	−0.830416
$87$	−1.29979	−0.139352
$88$	5.47151	0.583265
$89$	−0.204759	−0.0217044	−0.0108522	−	0.999941i	$-0.503454\pi$
$89$	−0.204759	−0.0217044	−0.0108522	+	0.999941i	$0.503454\pi$
$90$	−2.74851	−0.289719
$91$	5.35287	0.561133
$92$	−4.39931	−0.458660
$93$	−18.6493	−1.93385
$94$	6.17477	0.636878
$95$	0.00637946	0.000654519 0
$96$	−2.83861	−0.289714
$97$	13.1026	1.33037	0.665184	−	0.746680i	$-0.268353\pi$
$97$	13.1026	1.33037	0.665184	+	0.746680i	$0.268353\pi$
$98$	6.62611	0.669338
$99$	27.6732	2.78127
$100$	−4.70468	−0.470468
$101$	−3.89035	−0.387104	−0.193552	−	0.981090i	$-0.562001\pi$
$101$	−3.89035	−0.387104	−0.193552	+	0.981090i	$0.562001\pi$
$102$	0.785307	0.0777570
$103$	7.69456	0.758168	0.379084	−	0.925362i	$-0.376239\pi$
$103$	7.69456	0.758168	0.379084	+	0.925362i	$0.376239\pi$
$104$	−1.45011	−0.142195
$105$	−5.69425	−0.555702
$106$	−3.79005	−0.368122
$107$	0.797044	0.0770532	0.0385266	−	0.999258i	$-0.487734\pi$
$107$	0.797044	0.0770532	0.0385266	+	0.999258i	$0.487734\pi$
$108$	−5.84098	−0.562049
$109$	11.6625	1.11707	0.558535	−	0.829481i	$-0.311364\pi$
$109$	11.6625	1.11707	0.558535	+	0.829481i	$0.311364\pi$
$110$	−2.97340	−0.283502
$111$	29.0065	2.75318
$112$	−3.69136	−0.348800
$113$	−12.0707	−1.13552	−0.567758	−	0.823196i	$-0.692189\pi$
$113$	−12.0707	−1.13552	−0.567758	+	0.823196i	$0.692189\pi$
$114$	0.0333230	0.00312098
$115$	2.39072	0.222936
$116$	0.457896	0.0425146
$117$	−7.33420	−0.678047
$118$	4.35905	0.401283
$119$	1.02122	0.0936152
$120$	1.54259	0.140819
$121$	18.9375	1.72159
$122$	8.34485	0.755507
$123$	2.02209	0.182325
$124$	6.56989	0.589993
$125$	5.27383	0.471706
$126$	−18.6697	−1.66323
$127$	12.8438	1.13970	0.569850	−	0.821748i	$-0.307001\pi$
$127$	12.8438	1.13970	0.569850	+	0.821748i	$0.307001\pi$
$128$	1.00000	0.0883883
$129$	21.8600	1.92467
$130$	0.788035	0.0691153
$131$	13.0087	1.13657	0.568286	−	0.822831i	$-0.307607\pi$
$131$	13.0087	1.13657	0.568286	+	0.822831i	$0.307607\pi$
$132$	−15.5315	−1.35184
$133$	0.0433336	0.00375750
$134$	6.44915	0.557122
$135$	3.17418	0.273190
$136$	−0.276652	−0.0237227
$137$	4.21337	0.359973	0.179986	−	0.983669i	$-0.442395\pi$
$137$	4.21337	0.359973	0.179986	+	0.983669i	$0.442395\pi$
$138$	12.4879	1.06304
$139$	10.8490	0.920197	0.460098	−	0.887868i	$-0.347814\pi$
$139$	10.8490	0.920197	0.460098	+	0.887868i	$0.347814\pi$
$140$	2.00600	0.169538
$141$	−17.5277	−1.47610
$142$	−12.6388	−1.06062
$143$	−7.93429	−0.663499
$144$	5.05769	0.421474
$145$	−0.248835	−0.0206647
$146$	3.00643	0.248814
$147$	−18.8089	−1.55133
$148$	−10.2186	−0.839962
$149$	18.4113	1.50831	0.754156	−	0.656696i	$-0.228046\pi$
$149$	18.4113	1.50831	0.754156	+	0.656696i	$0.228046\pi$
$150$	13.3547	1.09041
$151$	8.33802	0.678538	0.339269	−	0.940689i	$-0.389820\pi$
$151$	8.33802	0.678538	0.339269	+	0.940689i	$0.389820\pi$
$152$	−0.0117392	−0.000952175 0
$153$	−1.39922	−0.113120
$154$	−20.1973	−1.62755
$155$	−3.57029	−0.286772
$156$	4.11629	0.329567
$157$	7.44658	0.594301	0.297151	−	0.954831i	$-0.403964\pi$
$157$	7.44658	0.594301	0.297151	+	0.954831i	$0.403964\pi$
$158$	2.89652	0.230435
$159$	10.7585	0.853201
$160$	−0.543432	−0.0429621
$161$	16.2394	1.27984
$162$	1.40718	0.110558
$163$	12.5206	0.980691	0.490346	−	0.871528i	$-0.336871\pi$
$163$	12.5206	0.980691	0.490346	+	0.871528i	$0.336871\pi$
$164$	−0.712352	−0.0556253
$165$	8.44030	0.657077
$166$	3.16248	0.245456
$167$	11.7998	0.913094	0.456547	−	0.889699i	$-0.349086\pi$
$167$	11.7998	0.913094	0.456547	+	0.889699i	$0.349086\pi$
$168$	10.4783	0.808419
$169$	−10.8972	−0.838245
$170$	0.150342	0.0115307
$171$	−0.0593733	−0.00454039
$172$	−7.70096	−0.587192
$173$	11.3780	0.865051	0.432525	−	0.901622i	$-0.357623\pi$
$173$	11.3780	0.865051	0.432525	+	0.901622i	$0.357623\pi$
$174$	−1.29979	−0.0985367
$175$	17.3667	1.31280
$176$	5.47151	0.412431
$177$	−12.3736	−0.930060
$178$	−0.204759	−0.0153474
$179$	7.02260	0.524894	0.262447	−	0.964946i	$-0.415470\pi$
$179$	7.02260	0.524894	0.262447	+	0.964946i	$0.415470\pi$
$180$	−2.74851	−0.204862
$181$	−23.5030	−1.74697	−0.873483	−	0.486855i	$-0.838144\pi$
$181$	−23.5030	−1.74697	−0.873483	+	0.486855i	$0.838144\pi$
$182$	5.35287	0.396781
$183$	−23.6878	−1.75105
$184$	−4.39931	−0.324321
$185$	5.55310	0.408272
$186$	−18.6493	−1.36744
$187$	−1.51371	−0.110693
$188$	6.17477	0.450341
$189$	21.5611	1.56834
$190$	0.00637946	0.000462814 0
$191$	−14.3544	−1.03865	−0.519324	−	0.854578i	$-0.673816\pi$
$191$	−14.3544	−1.03865	−0.519324	+	0.854578i	$0.673816\pi$
$192$	−2.83861	−0.204859
$193$	2.81565	0.202675	0.101337	−	0.994852i	$-0.467688\pi$
$193$	2.81565	0.202675	0.101337	+	0.994852i	$0.467688\pi$
$194$	13.1026	0.940712
$195$	−2.23692	−0.160189
$196$	6.62611	0.473293
$197$	−3.73393	−0.266031	−0.133016	−	0.991114i	$-0.542466\pi$
$197$	−3.73393	−0.266031	−0.133016	+	0.991114i	$0.542466\pi$
$198$	27.6732	1.96665
$199$	9.16341	0.649577	0.324789	−	0.945787i	$-0.394707\pi$
$199$	9.16341	0.649577	0.324789	+	0.945787i	$0.394707\pi$
$200$	−4.70468	−0.332671
$201$	−18.3066	−1.29125
$202$	−3.89035	−0.273724
$203$	−1.69026	−0.118633
$204$	0.785307	0.0549825
$205$	0.387115	0.0270373
$206$	7.69456	0.536105
$207$	−22.2504	−1.54651
$208$	−1.45011	−0.100547
$209$	−0.0642312	−0.00444297
$210$	−5.69425	−0.392940
$211$	4.32337	0.297633	0.148817	−	0.988865i	$-0.452454\pi$
$211$	4.32337	0.297633	0.148817	+	0.988865i	$0.452454\pi$
$212$	−3.79005	−0.260302
$213$	35.8766	2.45822
$214$	0.797044	0.0544848
$215$	4.18495	0.285411
$216$	−5.84098	−0.397428
$217$	−24.2518	−1.64632
$218$	11.6625	0.789888
$219$	−8.53406	−0.576679
$220$	−2.97340	−0.200466
$221$	0.401176	0.0269860
$222$	29.0065	1.94679
$223$	−5.20251	−0.348386	−0.174193	−	0.984712i	$-0.555732\pi$
$223$	−5.20251	−0.348386	−0.174193	+	0.984712i	$0.555732\pi$
$224$	−3.69136	−0.246639
$225$	−23.7948	−1.58632
$226$	−12.0707	−0.802931
$227$	2.06411	0.136999	0.0684997	−	0.997651i	$-0.478179\pi$
$227$	2.06411	0.136999	0.0684997	+	0.997651i	$0.478179\pi$
$228$	0.0333230	0.00220687
$229$	−20.8036	−1.37474	−0.687370	−	0.726307i	$-0.741235\pi$
$229$	−20.8036	−1.37474	−0.687370	+	0.726307i	$0.741235\pi$
$230$	2.39072	0.157640
$231$	57.3322	3.77218
$232$	0.457896	0.0300624
$233$	−0.164146	−0.0107536	−0.00537678	−	0.999986i	$-0.501711\pi$
$233$	−0.164146	−0.0107536	−0.00537678	+	0.999986i	$0.501711\pi$
$234$	−7.33420	−0.479452
$235$	−3.35556	−0.218893
$236$	4.35905	0.283750
$237$	−8.22208	−0.534082
$238$	1.02122	0.0661959
$239$	5.90585	0.382018	0.191009	−	0.981588i	$-0.438824\pi$
$239$	5.90585	0.382018	0.191009	+	0.981588i	$0.438824\pi$
$240$	1.54259	0.0995737
$241$	−4.57018	−0.294391	−0.147196	−	0.989107i	$-0.547025\pi$
$241$	−4.57018	−0.294391	−0.147196	+	0.989107i	$0.547025\pi$
$242$	18.9375	1.21735
$243$	13.5285	0.867855
$244$	8.34485	0.534224
$245$	−3.60084	−0.230049
$246$	2.02209	0.128924
$247$	0.0170231	0.00108316
$248$	6.56989	0.417188
$249$	−8.97704	−0.568897
$250$	5.27383	0.333547
$251$	16.1804	1.02130	0.510649	−	0.859789i	$-0.329405\pi$
$251$	16.1804	1.02130	0.510649	+	0.859789i	$0.329405\pi$
$252$	−18.6697	−1.17608
$253$	−24.0709	−1.51332
$254$	12.8438	0.805890
$255$	−0.426761	−0.0267248
$256$	1.00000	0.0625000
$257$	−30.5073	−1.90299	−0.951496	−	0.307662i	$-0.900453\pi$
$257$	−30.5073	−1.90299	−0.951496	+	0.307662i	$0.900453\pi$
$258$	21.8600	1.36094
$259$	37.7204	2.34383
$260$	0.788035	0.0488719
$261$	2.31590	0.143351
$262$	13.0087	0.803677
$263$	1.85028	0.114093	0.0570467	−	0.998372i	$-0.481832\pi$
$263$	1.85028	0.114093	0.0570467	+	0.998372i	$0.481832\pi$
$264$	−15.5315	−0.955897
$265$	2.05963	0.126522
$266$	0.0433336	0.00265695
$267$	0.581231	0.0355708
$268$	6.44915	0.393945
$269$	−1.73257	−0.105637	−0.0528183	−	0.998604i	$-0.516820\pi$
$269$	−1.73257	−0.105637	−0.0528183	+	0.998604i	$0.516820\pi$
$270$	3.17418	0.193174
$271$	23.9090	1.45237	0.726183	−	0.687502i	$-0.241293\pi$
$271$	23.9090	1.45237	0.726183	+	0.687502i	$0.241293\pi$
$272$	−0.276652	−0.0167745
$273$	−15.1947	−0.919624
$274$	4.21337	0.254539
$275$	−25.7417	−1.55228
$276$	12.4879	0.751684
$277$	23.4339	1.40801	0.704004	−	0.710196i	$-0.251393\pi$
$277$	23.4339	1.40801	0.704004	+	0.710196i	$0.251393\pi$
$278$	10.8490	0.650677
$279$	33.2285	1.98934
$280$	2.00600	0.119881
$281$	12.5192	0.746835	0.373417	−	0.927663i	$-0.378186\pi$
$281$	12.5192	0.746835	0.373417	+	0.927663i	$0.378186\pi$
$282$	−17.5277	−1.04376
$283$	32.9576	1.95913	0.979563	−	0.201136i	$-0.0644633\pi$
$283$	32.9576	1.95913	0.979563	+	0.201136i	$0.0644633\pi$
$284$	−12.6388	−0.749974
$285$	−0.0181088	−0.00107267
$286$	−7.93429	−0.469164
$287$	2.62954	0.155217
$288$	5.05769	0.298027
$289$	−16.9235	−0.995498
$290$	−0.248835	−0.0146121
$291$	−37.1931	−2.18030
$292$	3.00643	0.175938
$293$	0.462569	0.0270236	0.0135118	−	0.999909i	$-0.495699\pi$
$293$	0.462569	0.0270236	0.0135118	+	0.999909i	$0.495699\pi$
$294$	−18.8089	−1.09696
$295$	−2.36885	−0.137920
$296$	−10.2186	−0.593943
$297$	−31.9590	−1.85445
$298$	18.4113	1.06654
$299$	6.37948	0.368935
$300$	13.3547	0.771037
$301$	28.4270	1.63850
$302$	8.33802	0.479799
$303$	11.0432	0.634414
$304$	−0.0117392	−0.000673289 0
$305$	−4.53486	−0.259665
$306$	−1.39922	−0.0799882
$307$	−1.81027	−0.103318	−0.0516588	−	0.998665i	$-0.516451\pi$
$307$	−1.81027	−0.103318	−0.0516588	+	0.998665i	$0.516451\pi$
$308$	−20.1973	−1.15085
$309$	−21.8418	−1.24254
$310$	−3.57029	−0.202779
$311$	6.21157	0.352226	0.176113	−	0.984370i	$-0.443648\pi$
$311$	6.21157	0.352226	0.176113	+	0.984370i	$0.443648\pi$
$312$	4.11629	0.233039
$313$	12.1494	0.686727	0.343363	−	0.939203i	$-0.388434\pi$
$313$	12.1494	0.686727	0.343363	+	0.939203i	$0.388434\pi$
$314$	7.44658	0.420235
$315$	10.1457	0.571647
$316$	2.89652	0.162942
$317$	23.9837	1.34706	0.673531	−	0.739159i	$-0.264777\pi$
$317$	23.9837	1.34706	0.673531	+	0.739159i	$0.264777\pi$
$318$	10.7585	0.603304
$319$	2.50539	0.140275
$320$	−0.543432	−0.0303788
$321$	−2.26250	−0.126280
$322$	16.2394	0.904987
$323$	0.00324768	0.000180705 0
$324$	1.40718	0.0781765
$325$	6.82230	0.378433
$326$	12.5206	0.693453
$327$	−33.1054	−1.83073
$328$	−0.712352	−0.0393330
$329$	−22.7933	−1.25663
$330$	8.44030	0.464623
$331$	−13.8264	−0.759966	−0.379983	−	0.924994i	$-0.624070\pi$
$331$	−13.8264	−0.759966	−0.379983	+	0.924994i	$0.624070\pi$
$332$	3.16248	0.173564
$333$	−51.6824	−2.83218
$334$	11.7998	0.645655
$335$	−3.50468	−0.191481
$336$	10.4783	0.571639
$337$	26.7541	1.45739	0.728695	−	0.684838i	$-0.240127\pi$
$337$	26.7541	1.45739	0.728695	+	0.684838i	$0.240127\pi$
$338$	−10.8972	−0.592729
$339$	34.2640	1.86096
$340$	0.150342	0.00815342
$341$	35.9472	1.94665
$342$	−0.0593733	−0.00321054
$343$	1.38018	0.0745226
$344$	−7.70096	−0.415208
$345$	−6.78633	−0.365364
$346$	11.3780	0.611683
$347$	−1.14303	−0.0613612	−0.0306806	−	0.999529i	$-0.509767\pi$
$347$	−1.14303	−0.0613612	−0.0306806	+	0.999529i	$0.509767\pi$
$348$	−1.29979	−0.0696759
$349$	−13.8134	−0.739414	−0.369707	−	0.929148i	$-0.620542\pi$
$349$	−13.8134	−0.739414	−0.369707	+	0.929148i	$0.620542\pi$
$350$	17.3667	0.928287
$351$	8.47006	0.452098
$352$	5.47151	0.291633
$353$	−27.5808	−1.46798	−0.733989	−	0.679161i	$-0.762344\pi$
$353$	−27.5808	−1.46798	−0.733989	+	0.679161i	$0.762344\pi$
$354$	−12.3736	−0.657652
$355$	6.86832	0.364533
$356$	−0.204759	−0.0108522
$357$	−2.89885	−0.153423
$358$	7.02260	0.371156
$359$	−2.32525	−0.122722	−0.0613611	−	0.998116i	$-0.519544\pi$
$359$	−2.32525	−0.122722	−0.0613611	+	0.998116i	$0.519544\pi$
$360$	−2.74851	−0.144859
$361$	−18.9999	−0.999993
$362$	−23.5030	−1.23529
$363$	−53.7560	−2.82146
$364$	5.35287	0.280566
$365$	−1.63379	−0.0855164
$366$	−23.6878	−1.23818
$367$	0.536831	0.0280223	0.0140112	−	0.999902i	$-0.495540\pi$
$367$	0.536831	0.0280223	0.0140112	+	0.999902i	$0.495540\pi$
$368$	−4.39931	−0.229330
$369$	−3.60286	−0.187557
$370$	5.55310	0.288692
$371$	13.9904	0.726346
$372$	−18.6493	−0.966923
$373$	−17.5301	−0.907673	−0.453837	−	0.891085i	$-0.649945\pi$
$373$	−17.5301	−0.907673	−0.453837	+	0.891085i	$0.649945\pi$
$374$	−1.51371	−0.0782719
$375$	−14.9703	−0.773065
$376$	6.17477	0.318439
$377$	−0.663999	−0.0341977
$378$	21.5611	1.10899
$379$	−11.4726	−0.589310	−0.294655	−	0.955604i	$-0.595205\pi$
$379$	−11.4726	−0.589310	−0.294655	+	0.955604i	$0.595205\pi$
$380$	0.00637946	0.000327259 0
$381$	−36.4584	−1.86782
$382$	−14.3544	−0.734435
$383$	10.6974	0.546613	0.273306	−	0.961927i	$-0.411883\pi$
$383$	10.6974	0.546613	0.273306	+	0.961927i	$0.411883\pi$
$384$	−2.83861	−0.144857
$385$	10.9759	0.559382
$386$	2.81565	0.143313
$387$	−38.9491	−1.97989
$388$	13.1026	0.665184
$389$	23.5682	1.19495	0.597477	−	0.801886i	$-0.296170\pi$
$389$	23.5682	1.19495	0.597477	+	0.801886i	$0.296170\pi$
$390$	−2.23692	−0.113271
$391$	1.21708	0.0615503
$392$	6.62611	0.334669
$393$	−36.9265	−1.86269
$394$	−3.73393	−0.188113
$395$	−1.57406	−0.0791996
$396$	27.6732	1.39063
$397$	−29.2922	−1.47014	−0.735068	−	0.677994i	$-0.762850\pi$
$397$	−29.2922	−1.47014	−0.735068	+	0.677994i	$0.762850\pi$
$398$	9.16341	0.459320
$399$	−0.123007	−0.00615805
$400$	−4.70468	−0.235234
$401$	15.5843	0.778244	0.389122	−	0.921186i	$-0.372778\pi$
$401$	15.5843	0.778244	0.389122	+	0.921186i	$0.372778\pi$
$402$	−18.3066	−0.913051
$403$	−9.52705	−0.474576
$404$	−3.89035	−0.193552
$405$	−0.764705	−0.0379985
$406$	−1.69026	−0.0838861
$407$	−55.9111	−2.77141
$408$	0.785307	0.0388785
$409$	37.8260	1.87038	0.935188	−	0.354152i	$-0.115231\pi$
$409$	37.8260	1.87038	0.935188	+	0.354152i	$0.115231\pi$
$410$	0.387115	0.0191182
$411$	−11.9601	−0.589949
$412$	7.69456	0.379084
$413$	−16.0908	−0.791777
$414$	−22.2504	−1.09355
$415$	−1.71859	−0.0843624
$416$	−1.45011	−0.0710974
$417$	−30.7959	−1.50808
$418$	−0.0642312	−0.00314165
$419$	4.29392	0.209772	0.104886	−	0.994484i	$-0.466552\pi$
$419$	4.29392	0.209772	0.104886	+	0.994484i	$0.466552\pi$
$420$	−5.69425	−0.277851
$421$	−4.35803	−0.212398	−0.106199	−	0.994345i	$-0.533868\pi$
$421$	−4.35803	−0.212398	−0.106199	+	0.994345i	$0.533868\pi$
$422$	4.32337	0.210459
$423$	31.2301	1.51846
$424$	−3.79005	−0.184061
$425$	1.30156	0.0631349
$426$	35.8766	1.73822
$427$	−30.8038	−1.49070
$428$	0.797044	0.0385266
$429$	22.5223	1.08739
$430$	4.18495	0.201816
$431$	−20.2859	−0.977140	−0.488570	−	0.872525i	$-0.662481\pi$
$431$	−20.2859	−0.977140	−0.488570	+	0.872525i	$0.662481\pi$
$432$	−5.84098	−0.281024
$433$	21.7205	1.04382	0.521911	−	0.853000i	$-0.325219\pi$
$433$	21.7205	1.04382	0.521911	+	0.853000i	$0.325219\pi$
$434$	−24.2518	−1.16412
$435$	0.706346	0.0338667
$436$	11.6625	0.558535
$437$	0.0516444	0.00247049
$438$	−8.53406	−0.407773
$439$	8.86532	0.423119	0.211559	−	0.977365i	$-0.432146\pi$
$439$	8.86532	0.423119	0.211559	+	0.977365i	$0.432146\pi$
$440$	−2.97340	−0.141751
$441$	33.5128	1.59585
$442$	0.401176	0.0190820
$443$	−32.0894	−1.52462	−0.762308	−	0.647215i	$-0.775934\pi$
$443$	−32.0894	−1.52462	−0.762308	+	0.647215i	$0.775934\pi$
$444$	29.0065	1.37659
$445$	0.111273	0.00527483
$446$	−5.20251	−0.246346
$447$	−52.2624	−2.47193
$448$	−3.69136	−0.174400
$449$	40.9055	1.93045	0.965226	−	0.261417i	$-0.0841896\pi$
$449$	40.9055	1.93045	0.965226	+	0.261417i	$0.0841896\pi$
$450$	−23.7948	−1.12170
$451$	−3.89764	−0.183533
$452$	−12.0707	−0.567758
$453$	−23.6684	−1.11204
$454$	2.06411	0.0968733
$455$	−2.90892	−0.136372
$456$	0.0333230	0.00156049
$457$	−3.79617	−0.177577	−0.0887887	−	0.996050i	$-0.528300\pi$
$457$	−3.79617	−0.177577	−0.0887887	+	0.996050i	$0.528300\pi$
$458$	−20.8036	−0.972088
$459$	1.61592	0.0754247
$460$	2.39072	0.111468
$461$	−3.80202	−0.177078	−0.0885389	−	0.996073i	$-0.528220\pi$
$461$	−3.80202	−0.177078	−0.0885389	+	0.996073i	$0.528220\pi$
$462$	57.3322	2.66734
$463$	25.9914	1.20792	0.603961	−	0.797014i	$-0.293588\pi$
$463$	25.9914	1.20792	0.603961	+	0.797014i	$0.293588\pi$
$464$	0.457896	0.0212573
$465$	10.1346	0.469983
$466$	−0.164146	−0.00760392
$467$	22.4452	1.03864	0.519320	−	0.854580i	$-0.326185\pi$
$467$	22.4452	1.03864	0.519320	+	0.854580i	$0.326185\pi$
$468$	−7.33420	−0.339024
$469$	−23.8061	−1.09926
$470$	−3.35556	−0.154781
$471$	−21.1379	−0.973983
$472$	4.35905	0.200642
$473$	−42.1359	−1.93741
$474$	−8.22208	−0.377653
$475$	0.0552292	0.00253409
$476$	1.02122	0.0468076
$477$	−19.1689	−0.877684
$478$	5.90585	0.270127
$479$	−21.9013	−1.00070	−0.500348	−	0.865824i	$-0.666795\pi$
$479$	−21.9013	−1.00070	−0.500348	+	0.865824i	$0.666795\pi$
$480$	1.54259	0.0704093
$481$	14.8180	0.675645
$482$	−4.57018	−0.208166
$483$	−46.0973	−2.09750
$484$	18.9375	0.860794
$485$	−7.12037	−0.323319
$486$	13.5285	0.613666
$487$	30.0191	1.36029	0.680147	−	0.733076i	$-0.261916\pi$
$487$	30.0191	1.36029	0.680147	+	0.733076i	$0.261916\pi$
$488$	8.34485	0.377754
$489$	−35.5411	−1.60723
$490$	−3.60084	−0.162669
$491$	−14.7663	−0.666395	−0.333198	−	0.942857i	$-0.608128\pi$
$491$	−14.7663	−0.666395	−0.333198	+	0.942857i	$0.608128\pi$
$492$	2.02209	0.0911627
$493$	−0.126678	−0.00570529
$494$	0.0170231	0.000765906 0
$495$	−15.0385	−0.675931
$496$	6.56989	0.294997
$497$	46.6543	2.09273
$498$	−8.97704	−0.402271
$499$	−36.2828	−1.62424	−0.812120	−	0.583491i	$-0.801686\pi$
$499$	−36.2828	−1.62424	−0.812120	+	0.583491i	$0.801686\pi$
$500$	5.27383	0.235853
$501$	−33.4949	−1.49644
$502$	16.1804	0.722167
$503$	14.0829	0.627927	0.313963	−	0.949435i	$-0.398343\pi$
$503$	14.0829	0.627927	0.313963	+	0.949435i	$0.398343\pi$
$504$	−18.6697	−0.831616
$505$	2.11414	0.0940780
$506$	−24.0709	−1.07008
$507$	30.9328	1.37378
$508$	12.8438	0.569850
$509$	−24.9761	−1.10705	−0.553523	−	0.832834i	$-0.686717\pi$
$509$	−24.9761	−1.10705	−0.553523	+	0.832834i	$0.686717\pi$
$510$	−0.426761	−0.0188973
$511$	−11.0978	−0.490937
$512$	1.00000	0.0441942
$513$	0.0685685	0.00302737
$514$	−30.5073	−1.34562
$515$	−4.18147	−0.184258
$516$	21.8600	0.962333
$517$	33.7853	1.48588
$518$	37.7204	1.65734
$519$	−32.2976	−1.41771
$520$	0.788035	0.0345576
$521$	−1.89465	−0.0830059	−0.0415030	−	0.999138i	$-0.513215\pi$
$521$	−1.89465	−0.0830059	−0.0415030	+	0.999138i	$0.513215\pi$
$522$	2.31590	0.101364
$523$	−3.26743	−0.142875	−0.0714374	−	0.997445i	$-0.522759\pi$
$523$	−3.26743	−0.142875	−0.0714374	+	0.997445i	$0.522759\pi$
$524$	13.0087	0.568286
$525$	−49.2971	−2.15150
$526$	1.85028	0.0806762
$527$	−1.81757	−0.0791747
$528$	−15.5315	−0.675921
$529$	−3.64608	−0.158525
$530$	2.05963	0.0894647
$531$	22.0468	0.956748
$532$	0.0433336	0.00187875
$533$	1.03299	0.0447436
$534$	0.581231	0.0251523
$535$	−0.433139	−0.0187262
$536$	6.44915	0.278561
$537$	−19.9344	−0.860234
$538$	−1.73257	−0.0746963
$539$	36.2548	1.56161
$540$	3.17418	0.136595
$541$	4.02862	0.173204	0.0866018	−	0.996243i	$-0.472399\pi$
$541$	4.02862	0.173204	0.0866018	+	0.996243i	$0.472399\pi$
$542$	23.9090	1.02698
$543$	66.7159	2.86305
$544$	−0.276652	−0.0118614
$545$	−6.33780	−0.271482
$546$	−15.1947	−0.650273
$547$	37.6437	1.60953	0.804764	−	0.593595i	$-0.202292\pi$
$547$	37.6437	1.60953	0.804764	+	0.593595i	$0.202292\pi$
$548$	4.21337	0.179986
$549$	42.2057	1.80130
$550$	−25.7417	−1.09763
$551$	−0.00537534	−0.000228997 0
$552$	12.4879	0.531521
$553$	−10.6921	−0.454674
$554$	23.4339	0.995613
$555$	−15.7631	−0.669105
$556$	10.8490	0.460098
$557$	−35.9656	−1.52391	−0.761956	−	0.647629i	$-0.775761\pi$
$557$	−35.9656	−1.52391	−0.761956	+	0.647629i	$0.775761\pi$
$558$	33.2285	1.40667
$559$	11.1672	0.472323
$560$	2.00600	0.0847690
$561$	4.29682	0.181412
$562$	12.5192	0.528092
$563$	17.8057	0.750420	0.375210	−	0.926940i	$-0.377571\pi$
$563$	17.8057	0.750420	0.375210	+	0.926940i	$0.377571\pi$
$564$	−17.5277	−0.738051
$565$	6.55960	0.275965
$566$	32.9576	1.38531
$567$	−5.19439	−0.218144
$568$	−12.6388	−0.530312
$569$	33.1225	1.38857	0.694284	−	0.719701i	$-0.255721\pi$
$569$	33.1225	1.38857	0.694284	+	0.719701i	$0.255721\pi$
$570$	−0.0181088	−0.000758493 0
$571$	−10.1045	−0.422862	−0.211431	−	0.977393i	$-0.567812\pi$
$571$	−10.1045	−0.422862	−0.211431	+	0.977393i	$0.567812\pi$
$572$	−7.93429	−0.331749
$573$	40.7465	1.70221
$574$	2.62954	0.109755
$575$	20.6973	0.863139
$576$	5.05769	0.210737
$577$	−29.8508	−1.24271	−0.621353	−	0.783531i	$-0.713417\pi$
$577$	−29.8508	−1.24271	−0.621353	+	0.783531i	$0.713417\pi$
$578$	−16.9235	−0.703923
$579$	−7.99252	−0.332158
$580$	−0.248835	−0.0103323
$581$	−11.6738	−0.484312
$582$	−37.1931	−1.54171
$583$	−20.7373	−0.858851
$584$	3.00643	0.124407
$585$	3.98564	0.164786
$586$	0.462569	0.0191085
$587$	3.46774	0.143129	0.0715646	−	0.997436i	$-0.477201\pi$
$587$	3.46774	0.143129	0.0715646	+	0.997436i	$0.477201\pi$
$588$	−18.8089	−0.775666
$589$	−0.0771252	−0.00317789
$590$	−2.36885	−0.0975240
$591$	10.5992	0.435991
$592$	−10.2186	−0.419981
$593$	40.8452	1.67731	0.838656	−	0.544661i	$-0.183342\pi$
$593$	40.8452	1.67731	0.838656	+	0.544661i	$0.183342\pi$
$594$	−31.9590	−1.31129
$595$	−0.554964	−0.0227513
$596$	18.4113	0.754156
$597$	−26.0113	−1.06457
$598$	6.37948	0.260876
$599$	−12.8593	−0.525416	−0.262708	−	0.964875i	$-0.584616\pi$
$599$	−12.8593	−0.525416	−0.262708	+	0.964875i	$0.584616\pi$
$600$	13.3547	0.545205
$601$	5.30159	0.216256	0.108128	−	0.994137i	$-0.465514\pi$
$601$	5.30159	0.216256	0.108128	+	0.994137i	$0.465514\pi$
$602$	28.4270	1.15860
$603$	32.6178	1.32830
$604$	8.33802	0.339269
$605$	−10.2912	−0.418398
$606$	11.0432	0.448599
$607$	−14.6781	−0.595767	−0.297883	−	0.954602i	$-0.596281\pi$
$607$	−14.6781	−0.595767	−0.297883	+	0.954602i	$0.596281\pi$
$608$	−0.0117392	−0.000476088 0
$609$	4.79798	0.194424
$610$	−4.53486	−0.183611
$611$	−8.95408	−0.362243
$612$	−1.39922	−0.0565602
$613$	−10.8153	−0.436827	−0.218414	−	0.975856i	$-0.570088\pi$
$613$	−10.8153	−0.436827	−0.218414	+	0.975856i	$0.570088\pi$
$614$	−1.81027	−0.0730566
$615$	−1.09887	−0.0443106
$616$	−20.1973	−0.813773
$617$	20.5720	0.828198	0.414099	−	0.910232i	$-0.364097\pi$
$617$	20.5720	0.828198	0.414099	+	0.910232i	$0.364097\pi$
$618$	−21.8418	−0.878608
$619$	−23.6267	−0.949639	−0.474820	−	0.880083i	$-0.657487\pi$
$619$	−23.6267	−0.949639	−0.474820	+	0.880083i	$0.657487\pi$
$620$	−3.57029	−0.143386
$621$	25.6963	1.03116
$622$	6.21157	0.249061
$623$	0.755839	0.0302821
$624$	4.11629	0.164783
$625$	20.6574	0.826298
$626$	12.1494	0.485589
$627$	0.182327	0.00728145
$628$	7.44658	0.297151
$629$	2.82699	0.112719
$630$	10.1457	0.404216
$631$	−19.5511	−0.778318	−0.389159	−	0.921171i	$-0.627234\pi$
$631$	−19.5511	−0.778318	−0.389159	+	0.921171i	$0.627234\pi$
$632$	2.89652	0.115217
$633$	−12.2724	−0.487783
$634$	23.9837	0.952516
$635$	−6.97972	−0.276982
$636$	10.7585	0.426601
$637$	−9.60857	−0.380705
$638$	2.50539	0.0991892
$639$	−63.9231	−2.52876
$640$	−0.543432	−0.0214810
$641$	−8.59162	−0.339349	−0.169674	−	0.985500i	$-0.554272\pi$
$641$	−8.59162	−0.339349	−0.169674	+	0.985500i	$0.554272\pi$
$642$	−2.26250	−0.0892936
$643$	31.3192	1.23511	0.617554	−	0.786528i	$-0.288124\pi$
$643$	31.3192	1.23511	0.617554	+	0.786528i	$0.288124\pi$
$644$	16.2394	0.639922
$645$	−11.8794	−0.467752
$646$	0.00324768	0.000127778 0
$647$	35.8406	1.40904	0.704520	−	0.709685i	$-0.251163\pi$
$647$	35.8406	1.40904	0.704520	+	0.709685i	$0.251163\pi$
$648$	1.40718	0.0552791
$649$	23.8506	0.936219
$650$	6.82230	0.267593
$651$	68.8413	2.69810
$652$	12.5206	0.490346
$653$	−33.3307	−1.30433	−0.652166	−	0.758076i	$-0.726140\pi$
$653$	−33.3307	−1.30433	−0.652166	+	0.758076i	$0.726140\pi$
$654$	−33.1054	−1.29452
$655$	−7.06932	−0.276221
$656$	−0.712352	−0.0278127
$657$	15.2056	0.593226
$658$	−22.7933	−0.888574
$659$	−3.00612	−0.117102	−0.0585508	−	0.998284i	$-0.518648\pi$
$659$	−3.00612	−0.117102	−0.0585508	+	0.998284i	$0.518648\pi$
$660$	8.44030	0.328538
$661$	13.6174	0.529656	0.264828	−	0.964296i	$-0.414685\pi$
$661$	13.6174	0.529656	0.264828	+	0.964296i	$0.414685\pi$
$662$	−13.8264	−0.537377
$663$	−1.13878	−0.0442266
$664$	3.16248	0.122728
$665$	−0.0235488	−0.000913185 0
$666$	−51.6824	−2.00265
$667$	−2.01443	−0.0779989
$668$	11.7998	0.456547
$669$	14.7679	0.570959
$670$	−3.50468	−0.135397
$671$	45.6590	1.76265
$672$	10.4783	0.404210
$673$	0.337958	0.0130273	0.00651366	−	0.999979i	$-0.497927\pi$
$673$	0.337958	0.0130273	0.00651366	+	0.999979i	$0.497927\pi$
$674$	26.7541	1.03053
$675$	27.4800	1.05770
$676$	−10.8972	−0.419122
$677$	13.8482	0.532229	0.266115	−	0.963941i	$-0.414260\pi$
$677$	13.8482	0.532229	0.266115	+	0.963941i	$0.414260\pi$
$678$	34.2640	1.31590
$679$	−48.3663	−1.85613
$680$	0.150342	0.00576534
$681$	−5.85918	−0.224524
$682$	35.9472	1.37649
$683$	37.3954	1.43089	0.715447	−	0.698667i	$-0.246223\pi$
$683$	37.3954	1.43089	0.715447	+	0.698667i	$0.246223\pi$
$684$	−0.0593733	−0.00227019
$685$	−2.28968	−0.0874842
$686$	1.38018	0.0526955
$687$	59.0532	2.25302
$688$	−7.70096	−0.293596
$689$	5.49598	0.209380
$690$	−6.78633	−0.258351
$691$	18.5616	0.706116	0.353058	−	0.935601i	$-0.385142\pi$
$691$	18.5616	0.706116	0.353058	+	0.935601i	$0.385142\pi$
$692$	11.3780	0.432525
$693$	−102.152	−3.88042
$694$	−1.14303	−0.0433889
$695$	−5.89567	−0.223636
$696$	−1.29979	−0.0492683
$697$	0.197074	0.00746469
$698$	−13.8134	−0.522845
$699$	0.465946	0.0176237
$700$	17.3667	0.656398
$701$	−0.359127	−0.0135641	−0.00678203	−	0.999977i	$-0.502159\pi$
$701$	−0.359127	−0.0135641	−0.00678203	+	0.999977i	$0.502159\pi$
$702$	8.47006	0.319682
$703$	0.119958	0.00452430
$704$	5.47151	0.206215
$705$	9.52513	0.358737
$706$	−27.5808	−1.03802
$707$	14.3607	0.540089
$708$	−12.3736	−0.465030
$709$	−7.14050	−0.268167	−0.134084	−	0.990970i	$-0.542809\pi$
$709$	−7.14050	−0.268167	−0.134084	+	0.990970i	$0.542809\pi$
$710$	6.86832	0.257763
$711$	14.6497	0.549407
$712$	−0.204759	−0.00767368
$713$	−28.9030	−1.08242
$714$	−2.89885	−0.108487
$715$	4.31175	0.161250
$716$	7.02260	0.262447
$717$	−16.7644	−0.626078
$718$	−2.32525	−0.0867777
$719$	−21.8802	−0.815992	−0.407996	−	0.912984i	$-0.633772\pi$
$719$	−21.8802	−0.815992	−0.407996	+	0.912984i	$0.633772\pi$
$720$	−2.74851	−0.102431
$721$	−28.4034	−1.05780
$722$	−18.9999	−0.707102
$723$	12.9729	0.482469
$724$	−23.5030	−0.873483
$725$	−2.15426	−0.0800071
$726$	−53.7560	−1.99507
$727$	4.11600	0.152654	0.0763269	−	0.997083i	$-0.475681\pi$
$727$	4.11600	0.152654	0.0763269	+	0.997083i	$0.475681\pi$
$728$	5.35287	0.198390
$729$	−42.6237	−1.57866
$730$	−1.63379	−0.0604692
$731$	2.13049	0.0787989
$732$	−23.6878	−0.875525
$733$	−29.3870	−1.08543	−0.542716	−	0.839916i	$-0.682604\pi$
$733$	−29.3870	−1.08543	−0.542716	+	0.839916i	$0.682604\pi$
$734$	0.536831	0.0198148
$735$	10.2214	0.377021
$736$	−4.39931	−0.162161
$737$	35.2866	1.29980
$738$	−3.60286	−0.132623
$739$	−3.19785	−0.117635	−0.0588174	−	0.998269i	$-0.518733\pi$
$739$	−3.19785	−0.117635	−0.0588174	+	0.998269i	$0.518733\pi$
$740$	5.55310	0.204136
$741$	−0.0483220	−0.00177515
$742$	13.9904	0.513604
$743$	−40.8086	−1.49712	−0.748561	−	0.663066i	$-0.769255\pi$
$743$	−40.8086	−1.49712	−0.748561	+	0.663066i	$0.769255\pi$
$744$	−18.6493	−0.683718
$745$	−10.0053	−0.366565
$746$	−17.5301	−0.641822
$747$	15.9949	0.585221
$748$	−1.51371	−0.0553466
$749$	−2.94217	−0.107505
$750$	−14.9703	−0.546640
$751$	10.6373	0.388159	0.194079	−	0.980986i	$-0.437828\pi$
$751$	10.6373	0.388159	0.194079	+	0.980986i	$0.437828\pi$
$752$	6.17477	0.225171
$753$	−45.9298	−1.67378
$754$	−0.663999	−0.0241814
$755$	−4.53114	−0.164905
$756$	21.5611	0.784171
$757$	4.51786	0.164204	0.0821021	−	0.996624i	$-0.473837\pi$
$757$	4.51786	0.164204	0.0821021	+	0.996624i	$0.473837\pi$
$758$	−11.4726	−0.416705
$759$	68.3278	2.48014
$760$	0.00637946	0.000231407 0
$761$	12.6734	0.459410	0.229705	−	0.973260i	$-0.426224\pi$
$761$	12.6734	0.459410	0.229705	+	0.973260i	$0.426224\pi$
$762$	−36.4584	−1.32075
$763$	−43.0506	−1.55854
$764$	−14.3544	−0.519324
$765$	0.760381	0.0274916
$766$	10.6974	0.386514
$767$	−6.32110	−0.228242
$768$	−2.83861	−0.102429
$769$	11.9213	0.429894	0.214947	−	0.976626i	$-0.431042\pi$
$769$	11.9213	0.429894	0.214947	+	0.976626i	$0.431042\pi$
$770$	10.9759	0.395543
$771$	86.5982	3.11876
$772$	2.81565	0.101337
$773$	−43.5663	−1.56697	−0.783485	−	0.621411i	$-0.786560\pi$
$773$	−43.5663	−1.56697	−0.783485	+	0.621411i	$0.786560\pi$
$774$	−38.9491	−1.40000
$775$	−30.9092	−1.11029
$776$	13.1026	0.470356
$777$	−107.073	−3.84124
$778$	23.5682	0.844960
$779$	0.00836244	0.000299615 0
$780$	−2.23692	−0.0800947
$781$	−69.1533	−2.47450
$782$	1.21708	0.0435226
$783$	−2.67456	−0.0955811
$784$	6.62611	0.236647
$785$	−4.04671	−0.144433
$786$	−36.9265	−1.31712
$787$	2.02625	0.0722281	0.0361140	−	0.999348i	$-0.488502\pi$
$787$	2.02625	0.0722281	0.0361140	+	0.999348i	$0.488502\pi$
$788$	−3.73393	−0.133016
$789$	−5.25223	−0.186984
$790$	−1.57406	−0.0560026
$791$	44.5572	1.58427
$792$	27.6732	0.983326
$793$	−12.1009	−0.429717
$794$	−29.2922	−1.03954
$795$	−5.84649	−0.207354
$796$	9.16341	0.324789
$797$	−31.1780	−1.10438	−0.552190	−	0.833718i	$-0.686208\pi$
$797$	−31.1780	−1.10438	−0.552190	+	0.833718i	$0.686208\pi$
$798$	−0.123007	−0.00435440
$799$	−1.70826	−0.0604340
$800$	−4.70468	−0.166336
$801$	−1.03561	−0.0365915
$802$	15.5843	0.550302
$803$	16.4497	0.580497
$804$	−18.3066	−0.645625
$805$	−8.82501	−0.311041
$806$	−9.52705	−0.335576
$807$	4.91808	0.173125
$808$	−3.89035	−0.136862
$809$	23.8719	0.839291	0.419646	−	0.907688i	$-0.362154\pi$
$809$	23.8719	0.839291	0.419646	+	0.907688i	$0.362154\pi$
$810$	−0.764705	−0.0268690
$811$	−50.0675	−1.75811	−0.879054	−	0.476722i	$-0.841825\pi$
$811$	−50.0675	−1.75811	−0.879054	+	0.476722i	$0.841825\pi$
$812$	−1.69026	−0.0593164
$813$	−67.8681	−2.38024
$814$	−55.9111	−1.95968
$815$	−6.80411	−0.238337
$816$	0.785307	0.0274912
$817$	0.0904031	0.00316280
$818$	37.8260	1.32256
$819$	27.0732	0.946013
$820$	0.387115	0.0135186
$821$	−23.5684	−0.822542	−0.411271	−	0.911513i	$-0.634915\pi$
$821$	−23.5684	−0.822542	−0.411271	+	0.911513i	$0.634915\pi$
$822$	−11.9601	−0.417157
$823$	−0.843988	−0.0294196	−0.0147098	−	0.999892i	$-0.504682\pi$
$823$	−0.843988	−0.0294196	−0.0147098	+	0.999892i	$0.504682\pi$
$824$	7.69456	0.268053
$825$	73.0707	2.54399
$826$	−16.0908	−0.559871
$827$	−14.9983	−0.521542	−0.260771	−	0.965401i	$-0.583977\pi$
$827$	−14.9983	−0.521542	−0.260771	+	0.965401i	$0.583977\pi$
$828$	−22.2504	−0.773253
$829$	0.430352	0.0149468	0.00747338	−	0.999972i	$-0.497621\pi$
$829$	0.430352	0.0149468	0.00747338	+	0.999972i	$0.497621\pi$
$830$	−1.71859	−0.0596532
$831$	−66.5198	−2.30754
$832$	−1.45011	−0.0502735
$833$	−1.83313	−0.0635140
$834$	−30.7959	−1.06638
$835$	−6.41238	−0.221909
$836$	−0.0642312	−0.00222148
$837$	−38.3746	−1.32642
$838$	4.29392	0.148331
$839$	−21.1261	−0.729354	−0.364677	−	0.931134i	$-0.618821\pi$
$839$	−21.1261	−0.729354	−0.364677	+	0.931134i	$0.618821\pi$
$840$	−5.69425	−0.196470
$841$	−28.7903	−0.992770
$842$	−4.35803	−0.150188
$843$	−35.5372	−1.22397
$844$	4.32337	0.148817
$845$	5.92188	0.203719
$846$	31.2301	1.07371
$847$	−69.9049	−2.40196
$848$	−3.79005	−0.130151
$849$	−93.5537	−3.21076
$850$	1.30156	0.0446431
$851$	44.9547	1.54103
$852$	35.8766	1.22911
$853$	−42.7117	−1.46242	−0.731211	−	0.682151i	$-0.761045\pi$
$853$	−42.7117	−1.46242	−0.731211	+	0.682151i	$0.761045\pi$
$854$	−30.8038	−1.05408
$855$	0.0322653	0.00110345
$856$	0.797044	0.0272424
$857$	26.9285	0.919861	0.459931	−	0.887955i	$-0.347874\pi$
$857$	26.9285	0.919861	0.459931	+	0.887955i	$0.347874\pi$
$858$	22.5223	0.768900
$859$	16.2871	0.555710	0.277855	−	0.960623i	$-0.410377\pi$
$859$	16.2871	0.555710	0.277855	+	0.960623i	$0.410377\pi$
$860$	4.18495	0.142705
$861$	−7.46424	−0.254381
$862$	−20.2859	−0.690942
$863$	25.3315	0.862295	0.431148	−	0.902281i	$-0.358109\pi$
$863$	25.3315	0.862295	0.431148	+	0.902281i	$0.358109\pi$
$864$	−5.84098	−0.198714
$865$	−6.18315	−0.210233
$866$	21.7205	0.738094
$867$	48.0391	1.63149
$868$	−24.2518	−0.823159
$869$	15.8483	0.537618
$870$	0.706346	0.0239474
$871$	−9.35197	−0.316880
$872$	11.6625	0.394944
$873$	66.2689	2.24286
$874$	0.0516444	0.00174690
$875$	−19.4676	−0.658125
$876$	−8.53406	−0.288339
$877$	38.0217	1.28390	0.641951	−	0.766745i	$-0.278125\pi$
$877$	38.0217	1.28390	0.641951	+	0.766745i	$0.278125\pi$
$878$	8.86532	0.299190
$879$	−1.31305	−0.0442881
$880$	−2.97340	−0.100233
$881$	20.8008	0.700798	0.350399	−	0.936600i	$-0.386046\pi$
$881$	20.8008	0.700798	0.350399	+	0.936600i	$0.386046\pi$
$882$	33.5128	1.12843
$883$	−32.6183	−1.09769	−0.548846	−	0.835923i	$-0.684933\pi$
$883$	−32.6183	−1.09769	−0.548846	+	0.835923i	$0.684933\pi$
$884$	0.401176	0.0134930
$885$	6.72423	0.226033
$886$	−32.0894	−1.07807
$887$	31.5987	1.06098	0.530490	−	0.847691i	$-0.322008\pi$
$887$	31.5987	1.06098	0.530490	+	0.847691i	$0.322008\pi$
$888$	29.0065	0.973395
$889$	−47.4109	−1.59011
$890$	0.111273	0.00372987
$891$	7.69939	0.257939
$892$	−5.20251	−0.174193
$893$	−0.0724868	−0.00242568
$894$	−52.2624	−1.74792
$895$	−3.81631	−0.127565
$896$	−3.69136	−0.123320
$897$	−18.1088	−0.604636
$898$	40.9055	1.36504
$899$	3.00833	0.100333
$900$	−23.7948	−0.793161
$901$	1.04852	0.0349314
$902$	−3.89764	−0.129777
$903$	−80.6930	−2.68530
$904$	−12.0707	−0.401465
$905$	12.7723	0.424565
$906$	−23.6684	−0.786328
$907$	−4.64022	−0.154076	−0.0770380	−	0.997028i	$-0.524546\pi$
$907$	−4.64022	−0.154076	−0.0770380	+	0.997028i	$0.524546\pi$
$908$	2.06411	0.0684997
$909$	−19.6762	−0.652618
$910$	−2.90892	−0.0964297
$911$	−56.4301	−1.86961	−0.934806	−	0.355159i	$-0.884427\pi$
$911$	−56.4301	−1.86961	−0.934806	+	0.355159i	$0.884427\pi$
$912$	0.0333230	0.00110343
$913$	17.3036	0.572664
$914$	−3.79617	−0.125566
$915$	12.8727	0.425558
$916$	−20.8036	−0.687370
$917$	−48.0196	−1.58575
$918$	1.61592	0.0533333
$919$	27.4905	0.906828	0.453414	−	0.891300i	$-0.350206\pi$
$919$	27.4905	0.906828	0.453414	+	0.891300i	$0.350206\pi$
$920$	2.39072	0.0788199
$921$	5.13865	0.169324
$922$	−3.80202	−0.125213
$923$	18.3276	0.603261
$924$	57.3322	1.88609
$925$	48.0751	1.58070
$926$	25.9914	0.854130
$927$	38.9167	1.27819
$928$	0.457896	0.0150312
$929$	20.1089	0.659751	0.329876	−	0.944024i	$-0.392993\pi$
$929$	20.1089	0.659751	0.329876	+	0.944024i	$0.392993\pi$
$930$	10.1346	0.332328
$931$	−0.0777852	−0.00254931
$932$	−0.164146	−0.00537678
$933$	−17.6322	−0.577253
$934$	22.4452	0.734429
$935$	0.822596	0.0269018
$936$	−7.33420	−0.239726
$937$	50.4138	1.64695	0.823474	−	0.567354i	$-0.192033\pi$
$937$	50.4138	1.64695	0.823474	+	0.567354i	$0.192033\pi$
$938$	−23.8061	−0.777297
$939$	−34.4875	−1.12546
$940$	−3.35556	−0.109446
$941$	−19.5074	−0.635924	−0.317962	−	0.948103i	$-0.602998\pi$
$941$	−19.5074	−0.635924	−0.317962	+	0.948103i	$0.602998\pi$
$942$	−21.1379	−0.688710
$943$	3.13385	0.102052
$944$	4.35905	0.141875
$945$	−11.7170	−0.381154
$946$	−42.1359	−1.36996
$947$	55.9419	1.81787	0.908933	−	0.416942i	$-0.136898\pi$
$947$	55.9419	1.81787	0.908933	+	0.416942i	$0.136898\pi$
$948$	−8.22208	−0.267041
$949$	−4.35964	−0.141520
$950$	0.0552292	0.00179187
$951$	−68.0804	−2.20766
$952$	1.02122	0.0330980
$953$	−9.46592	−0.306631	−0.153316	−	0.988177i	$-0.548995\pi$
$953$	−9.46592	−0.306631	−0.153316	+	0.988177i	$0.548995\pi$
$954$	−19.1689	−0.620616
$955$	7.80063	0.252423
$956$	5.90585	0.191009
$957$	−7.11181	−0.229892
$958$	−21.9013	−0.707599
$959$	−15.5531	−0.502234
$960$	1.54259	0.0497869
$961$	12.1634	0.392368
$962$	14.8180	0.477753
$963$	4.03120	0.129904
$964$	−4.57018	−0.147196
$965$	−1.53011	−0.0492561
$966$	−46.0973	−1.48316
$967$	−7.15794	−0.230184	−0.115092	−	0.993355i	$-0.536716\pi$
$967$	−7.15794	−0.230184	−0.115092	+	0.993355i	$0.536716\pi$
$968$	18.9375	0.608673
$969$	−0.00921887	−0.000296153 0
$970$	−7.12037	−0.228621
$971$	−6.05058	−0.194172	−0.0970862	−	0.995276i	$-0.530952\pi$
$971$	−6.05058	−0.194172	−0.0970862	+	0.995276i	$0.530952\pi$
$972$	13.5285	0.433928
$973$	−40.0474	−1.28386
$974$	30.0191	0.961873
$975$	−19.3658	−0.620203
$976$	8.34485	0.267112
$977$	55.3310	1.77020	0.885098	−	0.465404i	$-0.154091\pi$
$977$	55.3310	1.77020	0.885098	+	0.465404i	$0.154091\pi$
$978$	−35.5411	−1.13648
$979$	−1.12034	−0.0358063
$980$	−3.60084	−0.115025
$981$	58.9856	1.88327
$982$	−14.7663	−0.471213
$983$	55.2315	1.76161	0.880806	−	0.473477i	$-0.157001\pi$
$983$	55.2315	1.76161	0.880806	+	0.473477i	$0.157001\pi$
$984$	2.02209	0.0644618
$985$	2.02914	0.0646536
$986$	−0.126678	−0.00403425
$987$	64.7011	2.05946
$988$	0.0170231	0.000541578 0
$989$	33.8789	1.07729
$990$	−15.0385	−0.477956
$991$	−2.94659	−0.0936015	−0.0468008	−	0.998904i	$-0.514903\pi$
$991$	−2.94659	−0.0936015	−0.0468008	+	0.998904i	$0.514903\pi$
$992$	6.56989	0.208594
$993$	39.2476	1.24549
$994$	46.6543	1.47978
$995$	−4.97969	−0.157867
$996$	−8.97704	−0.284448
$997$	24.7356	0.783385	0.391693	−	0.920096i	$-0.371890\pi$
$997$	24.7356	0.783385	0.391693	+	0.920096i	$0.371890\pi$
$998$	−36.2828	−1.14851
$999$	59.6865	1.88840

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.i.1.2	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.i.1.2	✓	46	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.83861 q^{3} +1.00000 q^{4} -0.543432 q^{5} -2.83861 q^{6} -3.69136 q^{7} +1.00000 q^{8} +5.05769 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.83861 q^{3} +1.00000 q^{4} -0.543432 q^{5} -2.83861 q^{6} -3.69136 q^{7} +1.00000 q^{8} +5.05769 q^{9} -0.543432 q^{10} +5.47151 q^{11} -2.83861 q^{12} -1.45011 q^{13} -3.69136 q^{14} +1.54259 q^{15} +1.00000 q^{16} -0.276652 q^{17} +5.05769 q^{18} -0.0117392 q^{19} -0.543432 q^{20} +10.4783 q^{21} +5.47151 q^{22} -4.39931 q^{23} -2.83861 q^{24} -4.70468 q^{25} -1.45011 q^{26} -5.84098 q^{27} -3.69136 q^{28} +0.457896 q^{29} +1.54259 q^{30} +6.56989 q^{31} +1.00000 q^{32} -15.5315 q^{33} -0.276652 q^{34} +2.00600 q^{35} +5.05769 q^{36} -10.2186 q^{37} -0.0117392 q^{38} +4.11629 q^{39} -0.543432 q^{40} -0.712352 q^{41} +10.4783 q^{42} -7.70096 q^{43} +5.47151 q^{44} -2.74851 q^{45} -4.39931 q^{46} +6.17477 q^{47} -2.83861 q^{48} +6.62611 q^{49} -4.70468 q^{50} +0.785307 q^{51} -1.45011 q^{52} -3.79005 q^{53} -5.84098 q^{54} -2.97340 q^{55} -3.69136 q^{56} +0.0333230 q^{57} +0.457896 q^{58} +4.35905 q^{59} +1.54259 q^{60} +8.34485 q^{61} +6.56989 q^{62} -18.6697 q^{63} +1.00000 q^{64} +0.788035 q^{65} -15.5315 q^{66} +6.44915 q^{67} -0.276652 q^{68} +12.4879 q^{69} +2.00600 q^{70} -12.6388 q^{71} +5.05769 q^{72} +3.00643 q^{73} -10.2186 q^{74} +13.3547 q^{75} -0.0117392 q^{76} -20.1973 q^{77} +4.11629 q^{78} +2.89652 q^{79} -0.543432 q^{80} +1.40718 q^{81} -0.712352 q^{82} +3.16248 q^{83} +10.4783 q^{84} +0.150342 q^{85} -7.70096 q^{86} -1.29979 q^{87} +5.47151 q^{88} -0.204759 q^{89} -2.74851 q^{90} +5.35287 q^{91} -4.39931 q^{92} -18.6493 q^{93} +6.17477 q^{94} +0.00637946 q^{95} -2.83861 q^{96} +13.1026 q^{97} +6.62611 q^{98} +27.6732 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9}+O(q^{10}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9} + 23 q^{10} + 39 q^{11} + 21 q^{12} + 8 q^{13} + 26 q^{14} + 14 q^{15} + 46 q^{16} + 36 q^{17} + 59 q^{18} + 37 q^{19} + 23 q^{20} + 20 q^{21} + 39 q^{22} + 38 q^{23} + 21 q^{24} + 57 q^{25} + 8 q^{26} + 63 q^{27} + 26 q^{28} + 23 q^{29} + 14 q^{30} + 44 q^{31} + 46 q^{32} + 25 q^{33} + 36 q^{34} + 26 q^{35} + 59 q^{36} + 9 q^{37} + 37 q^{38} - 2 q^{39} + 23 q^{40} + 50 q^{41} + 20 q^{42} + 46 q^{43} + 39 q^{44} + 30 q^{45} + 38 q^{46} + 57 q^{47} + 21 q^{48} + 62 q^{49} + 57 q^{50} + 5 q^{51} + 8 q^{52} + 21 q^{53} + 63 q^{54} + 40 q^{55} + 26 q^{56} + 3 q^{57} + 23 q^{58} + 68 q^{59} + 14 q^{60} - q^{61} + 44 q^{62} + 40 q^{63} + 46 q^{64} + 18 q^{65} + 25 q^{66} + 42 q^{67} + 36 q^{68} - 7 q^{69} + 26 q^{70} + 67 q^{71} + 59 q^{72} + 48 q^{73} + 9 q^{74} + 71 q^{75} + 37 q^{76} - 5 q^{77} - 2 q^{78} + 40 q^{79} + 23 q^{80} + 82 q^{81} + 50 q^{82} + 48 q^{83} + 20 q^{84} - 68 q^{85} + 46 q^{86} + 18 q^{87} + 39 q^{88} + 90 q^{89} + 30 q^{90} + 9 q^{91} + 38 q^{92} - 42 q^{93} + 57 q^{94} + 6 q^{95} + 21 q^{96} + 46 q^{97} + 62 q^{98} + 61 q^{99}+O(q^{100}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9 + 23 * q^10 + 39 * q^11 + 21 * q^12 + 8 * q^13 + 26 * q^14 + 14 * q^15 + 46 * q^16 + 36 * q^17 + 59 * q^18 + 37 * q^19 + 23 * q^20 + 20 * q^21 + 39 * q^22 + 38 * q^23 + 21 * q^24 + 57 * q^25 + 8 * q^26 + 63 * q^27 + 26 * q^28 + 23 * q^29 + 14 * q^30 + 44 * q^31 + 46 * q^32 + 25 * q^33 + 36 * q^34 + 26 * q^35 + 59 * q^36 + 9 * q^37 + 37 * q^38 - 2 * q^39 + 23 * q^40 + 50 * q^41 + 20 * q^42 + 46 * q^43 + 39 * q^44 + 30 * q^45 + 38 * q^46 + 57 * q^47 + 21 * q^48 + 62 * q^49 + 57 * q^50 + 5 * q^51 + 8 * q^52 + 21 * q^53 + 63 * q^54 + 40 * q^55 + 26 * q^56 + 3 * q^57 + 23 * q^58 + 68 * q^59 + 14 * q^60 - q^61 + 44 * q^62 + 40 * q^63 + 46 * q^64 + 18 * q^65 + 25 * q^66 + 42 * q^67 + 36 * q^68 - 7 * q^69 + 26 * q^70 + 67 * q^71 + 59 * q^72 + 48 * q^73 + 9 * q^74 + 71 * q^75 + 37 * q^76 - 5 * q^77 - 2 * q^78 + 40 * q^79 + 23 * q^80 + 82 * q^81 + 50 * q^82 + 48 * q^83 + 20 * q^84 - 68 * q^85 + 46 * q^86 + 18 * q^87 + 39 * q^88 + 90 * q^89 + 30 * q^90 + 9 * q^91 + 38 * q^92 - 42 * q^93 + 57 * q^94 + 6 * q^95 + 21 * q^96 + 46 * q^97 + 62 * q^98 + 61 * q^99

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