LMFDB - Embedded newform 6002.2.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, 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("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$1$
Dimension:	$47$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.82438 q^{3} +1.00000 q^{4} -1.67949 q^{5} -2.82438 q^{6} +4.44281 q^{7} +1.00000 q^{8} +4.97711 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.82438 q^{3} +1.00000 q^{4} -1.67949 q^{5} -2.82438 q^{6} +4.44281 q^{7} +1.00000 q^{8} +4.97711 q^{9} -1.67949 q^{10} -0.291683 q^{11} -2.82438 q^{12} -1.11636 q^{13} +4.44281 q^{14} +4.74350 q^{15} +1.00000 q^{16} +6.41845 q^{17} +4.97711 q^{18} -6.21280 q^{19} -1.67949 q^{20} -12.5482 q^{21} -0.291683 q^{22} -0.0504378 q^{23} -2.82438 q^{24} -2.17933 q^{25} -1.11636 q^{26} -5.58410 q^{27} +4.44281 q^{28} -8.58044 q^{29} +4.74350 q^{30} -4.85515 q^{31} +1.00000 q^{32} +0.823822 q^{33} +6.41845 q^{34} -7.46163 q^{35} +4.97711 q^{36} -8.46466 q^{37} -6.21280 q^{38} +3.15301 q^{39} -1.67949 q^{40} -5.07887 q^{41} -12.5482 q^{42} +9.67466 q^{43} -0.291683 q^{44} -8.35898 q^{45} -0.0504378 q^{46} +3.87907 q^{47} -2.82438 q^{48} +12.7385 q^{49} -2.17933 q^{50} -18.1281 q^{51} -1.11636 q^{52} +1.70283 q^{53} -5.58410 q^{54} +0.489877 q^{55} +4.44281 q^{56} +17.5473 q^{57} -8.58044 q^{58} -11.5534 q^{59} +4.74350 q^{60} +11.6675 q^{61} -4.85515 q^{62} +22.1123 q^{63} +1.00000 q^{64} +1.87490 q^{65} +0.823822 q^{66} -7.46949 q^{67} +6.41845 q^{68} +0.142455 q^{69} -7.46163 q^{70} -4.96952 q^{71} +4.97711 q^{72} +11.8199 q^{73} -8.46466 q^{74} +6.15524 q^{75} -6.21280 q^{76} -1.29589 q^{77} +3.15301 q^{78} -6.15302 q^{79} -1.67949 q^{80} +0.840286 q^{81} -5.07887 q^{82} +14.0089 q^{83} -12.5482 q^{84} -10.7797 q^{85} +9.67466 q^{86} +24.2344 q^{87} -0.291683 q^{88} +14.6331 q^{89} -8.35898 q^{90} -4.95975 q^{91} -0.0504378 q^{92} +13.7128 q^{93} +3.87907 q^{94} +10.4343 q^{95} -2.82438 q^{96} -11.7240 q^{97} +12.7385 q^{98} -1.45174 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9} - 14 q^{10} - 30 q^{11} - 13 q^{12} - 39 q^{13} - 17 q^{14} - 18 q^{15} + 47 q^{16} - 26 q^{17} + 12 q^{18} - 23 q^{19} - 14 q^{20} - 39 q^{21} - 30 q^{22} - 25 q^{23} - 13 q^{24} - 19 q^{25} - 39 q^{26} - 46 q^{27} - 17 q^{28} - 53 q^{29} - 18 q^{30} - 23 q^{31} + 47 q^{32} - 26 q^{33} - 26 q^{34} - 31 q^{35} + 12 q^{36} - 83 q^{37} - 23 q^{38} - 9 q^{39} - 14 q^{40} - 48 q^{41} - 39 q^{42} - 78 q^{43} - 30 q^{44} - 27 q^{45} - 25 q^{46} - 15 q^{47} - 13 q^{48} - 12 q^{49} - 19 q^{50} - 47 q^{51} - 39 q^{52} - 76 q^{53} - 46 q^{54} - 39 q^{55} - 17 q^{56} - 44 q^{57} - 53 q^{58} - 33 q^{59} - 18 q^{60} - 33 q^{61} - 23 q^{62} - 7 q^{63} + 47 q^{64} - 67 q^{65} - 26 q^{66} - 85 q^{67} - 26 q^{68} - 33 q^{69} - 31 q^{70} - 17 q^{71} + 12 q^{72} - 59 q^{73} - 83 q^{74} - 21 q^{75} - 23 q^{76} - 59 q^{77} - 9 q^{78} - 49 q^{79} - 14 q^{80} - 41 q^{81} - 48 q^{82} - 30 q^{83} - 39 q^{84} - 84 q^{85} - 78 q^{86} + 9 q^{87} - 30 q^{88} - 50 q^{89} - 27 q^{90} - 42 q^{91} - 25 q^{92} - 43 q^{93} - 15 q^{94} + 8 q^{95} - 13 q^{96} - 49 q^{97} - 12 q^{98} - 49 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9 - 14 * q^10 - 30 * q^11 - 13 * q^12 - 39 * q^13 - 17 * q^14 - 18 * q^15 + 47 * q^16 - 26 * q^17 + 12 * q^18 - 23 * q^19 - 14 * q^20 - 39 * q^21 - 30 * q^22 - 25 * q^23 - 13 * q^24 - 19 * q^25 - 39 * q^26 - 46 * q^27 - 17 * q^28 - 53 * q^29 - 18 * q^30 - 23 * q^31 + 47 * q^32 - 26 * q^33 - 26 * q^34 - 31 * q^35 + 12 * q^36 - 83 * q^37 - 23 * q^38 - 9 * q^39 - 14 * q^40 - 48 * q^41 - 39 * q^42 - 78 * q^43 - 30 * q^44 - 27 * q^45 - 25 * q^46 - 15 * q^47 - 13 * q^48 - 12 * q^49 - 19 * q^50 - 47 * q^51 - 39 * q^52 - 76 * q^53 - 46 * q^54 - 39 * q^55 - 17 * q^56 - 44 * q^57 - 53 * q^58 - 33 * q^59 - 18 * q^60 - 33 * q^61 - 23 * q^62 - 7 * q^63 + 47 * q^64 - 67 * q^65 - 26 * q^66 - 85 * q^67 - 26 * q^68 - 33 * q^69 - 31 * q^70 - 17 * q^71 + 12 * q^72 - 59 * q^73 - 83 * q^74 - 21 * q^75 - 23 * q^76 - 59 * q^77 - 9 * q^78 - 49 * q^79 - 14 * q^80 - 41 * q^81 - 48 * q^82 - 30 * q^83 - 39 * q^84 - 84 * q^85 - 78 * q^86 + 9 * q^87 - 30 * q^88 - 50 * q^89 - 27 * q^90 - 42 * q^91 - 25 * q^92 - 43 * q^93 - 15 * q^94 + 8 * q^95 - 13 * q^96 - 49 * q^97 - 12 * q^98 - 49 * 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
$3$	−2.82438	−1.63066	−0.815328	−	0.579000i	$-0.803443\pi$
$3$	−2.82438	−1.63066	−0.815328	+	0.579000i	$0.803443\pi$
$4$	1.00000	0.500000
$5$	−1.67949	−0.751089	−0.375544	−	0.926804i	$-0.622544\pi$
$5$	−1.67949	−0.751089	−0.375544	+	0.926804i	$0.622544\pi$
$6$	−2.82438	−1.15305
$7$	4.44281	1.67922	0.839612	−	0.543187i	$-0.182783\pi$
$7$	4.44281	1.67922	0.839612	+	0.543187i	$0.182783\pi$
$8$	1.00000	0.353553
$9$	4.97711	1.65904
$10$	−1.67949	−0.531100
$11$	−0.291683	−0.0879456	−0.0439728	−	0.999033i	$-0.514001\pi$
$11$	−0.291683	−0.0879456	−0.0439728	+	0.999033i	$0.514001\pi$
$12$	−2.82438	−0.815328
$13$	−1.11636	−0.309621	−0.154811	−	0.987944i	$-0.549477\pi$
$13$	−1.11636	−0.309621	−0.154811	+	0.987944i	$0.549477\pi$
$14$	4.44281	1.18739
$15$	4.74350	1.22477
$16$	1.00000	0.250000
$17$	6.41845	1.55670	0.778351	−	0.627829i	$-0.216056\pi$
$17$	6.41845	1.55670	0.778351	+	0.627829i	$0.216056\pi$
$18$	4.97711	1.17312
$19$	−6.21280	−1.42531	−0.712657	−	0.701512i	$-0.752509\pi$
$19$	−6.21280	−1.42531	−0.712657	+	0.701512i	$0.752509\pi$
$20$	−1.67949	−0.375544
$21$	−12.5482	−2.73823
$22$	−0.291683	−0.0621869
$23$	−0.0504378	−0.0105170	−0.00525850	−	0.999986i	$-0.501674\pi$
$23$	−0.0504378	−0.0105170	−0.00525850	+	0.999986i	$0.501674\pi$
$24$	−2.82438	−0.576524
$25$	−2.17933	−0.435865
$26$	−1.11636	−0.218935
$27$	−5.58410	−1.07466
$28$	4.44281	0.839612
$29$	−8.58044	−1.59335	−0.796673	−	0.604410i	$-0.793409\pi$
$29$	−8.58044	−1.59335	−0.796673	+	0.604410i	$0.793409\pi$
$30$	4.74350	0.866041
$31$	−4.85515	−0.872010	−0.436005	−	0.899944i	$-0.643607\pi$
$31$	−4.85515	−0.872010	−0.436005	+	0.899944i	$0.643607\pi$
$32$	1.00000	0.176777
$33$	0.823822	0.143409
$34$	6.41845	1.10076
$35$	−7.46163	−1.26125
$36$	4.97711	0.829518
$37$	−8.46466	−1.39158	−0.695791	−	0.718244i	$-0.744946\pi$
$37$	−8.46466	−1.39158	−0.695791	+	0.718244i	$0.744946\pi$
$38$	−6.21280	−1.00785
$39$	3.15301	0.504886
$40$	−1.67949	−0.265550
$41$	−5.07887	−0.793187	−0.396593	−	0.917994i	$-0.629808\pi$
$41$	−5.07887	−0.793187	−0.396593	+	0.917994i	$0.629808\pi$
$42$	−12.5482	−1.93622
$43$	9.67466	1.47537	0.737686	−	0.675144i	$-0.235918\pi$
$43$	9.67466	1.47537	0.737686	+	0.675144i	$0.235918\pi$
$44$	−0.291683	−0.0439728
$45$	−8.35898	−1.24608
$46$	−0.0504378	−0.00743664
$47$	3.87907	0.565821	0.282911	−	0.959146i	$-0.408700\pi$
$47$	3.87907	0.565821	0.282911	+	0.959146i	$0.408700\pi$
$48$	−2.82438	−0.407664
$49$	12.7385	1.81979
$50$	−2.17933	−0.308203
$51$	−18.1281	−2.53845
$52$	−1.11636	−0.154811
$53$	1.70283	0.233902	0.116951	−	0.993138i	$-0.462688\pi$
$53$	1.70283	0.233902	0.116951	+	0.993138i	$0.462688\pi$
$54$	−5.58410	−0.759900
$55$	0.489877	0.0660550
$56$	4.44281	0.593695
$57$	17.5473	2.32420
$58$	−8.58044	−1.12667
$59$	−11.5534	−1.50412	−0.752061	−	0.659093i	$-0.770940\pi$
$59$	−11.5534	−1.50412	−0.752061	+	0.659093i	$0.770940\pi$
$60$	4.74350	0.612384
$61$	11.6675	1.49387	0.746936	−	0.664896i	$-0.231524\pi$
$61$	11.6675	1.49387	0.746936	+	0.664896i	$0.231524\pi$
$62$	−4.85515	−0.616604
$63$	22.1123	2.78589
$64$	1.00000	0.125000
$65$	1.87490	0.232553
$66$	0.823822	0.101405
$67$	−7.46949	−0.912544	−0.456272	−	0.889840i	$-0.650816\pi$
$67$	−7.46949	−0.912544	−0.456272	+	0.889840i	$0.650816\pi$
$68$	6.41845	0.778351
$69$	0.142455	0.0171496
$70$	−7.46163	−0.891836
$71$	−4.96952	−0.589774	−0.294887	−	0.955532i	$-0.595282\pi$
$71$	−4.96952	−0.589774	−0.294887	+	0.955532i	$0.595282\pi$
$72$	4.97711	0.586558
$73$	11.8199	1.38342	0.691709	−	0.722177i	$-0.256858\pi$
$73$	11.8199	1.38342	0.691709	+	0.722177i	$0.256858\pi$
$74$	−8.46466	−0.983997
$75$	6.15524	0.710746
$76$	−6.21280	−0.712657
$77$	−1.29589	−0.147680
$78$	3.15301	0.357008
$79$	−6.15302	−0.692268	−0.346134	−	0.938185i	$-0.612506\pi$
$79$	−6.15302	−0.692268	−0.346134	+	0.938185i	$0.612506\pi$
$80$	−1.67949	−0.187772
$81$	0.840286	0.0933651
$82$	−5.07887	−0.560868
$83$	14.0089	1.53768	0.768838	−	0.639444i	$-0.220835\pi$
$83$	14.0089	1.53768	0.768838	+	0.639444i	$0.220835\pi$
$84$	−12.5482	−1.36912
$85$	−10.7797	−1.16922
$86$	9.67466	1.04325
$87$	24.2344	2.59820
$88$	−0.291683	−0.0310935
$89$	14.6331	1.55110	0.775552	−	0.631283i	$-0.217471\pi$
$89$	14.6331	1.55110	0.775552	+	0.631283i	$0.217471\pi$
$90$	−8.35898	−0.881114
$91$	−4.95975	−0.519924
$92$	−0.0504378	−0.00525850
$93$	13.7128	1.42195
$94$	3.87907	0.400096
$95$	10.4343	1.07054
$96$	−2.82438	−0.288262
$97$	−11.7240	−1.19040	−0.595198	−	0.803579i	$-0.702926\pi$
$97$	−11.7240	−1.19040	−0.595198	+	0.803579i	$0.702926\pi$
$98$	12.7385	1.28679
$99$	−1.45174	−0.145905
$100$	−2.17933	−0.217933
$101$	−14.3832	−1.43119	−0.715593	−	0.698518i	$-0.753843\pi$
$101$	−14.3832	−1.43119	−0.715593	+	0.698518i	$0.753843\pi$
$102$	−18.1281	−1.79495
$103$	−5.50465	−0.542389	−0.271195	−	0.962525i	$-0.587419\pi$
$103$	−5.50465	−0.542389	−0.271195	+	0.962525i	$0.587419\pi$
$104$	−1.11636	−0.109468
$105$	21.0745	2.05666
$106$	1.70283	0.165394
$107$	2.84788	0.275315	0.137658	−	0.990480i	$-0.456043\pi$
$107$	2.84788	0.275315	0.137658	+	0.990480i	$0.456043\pi$
$108$	−5.58410	−0.537330
$109$	−8.01144	−0.767356	−0.383678	−	0.923467i	$-0.625343\pi$
$109$	−8.01144	−0.767356	−0.383678	+	0.923467i	$0.625343\pi$
$110$	0.489877	0.0467079
$111$	23.9074	2.26919
$112$	4.44281	0.419806
$113$	4.45135	0.418748	0.209374	−	0.977836i	$-0.432857\pi$
$113$	4.45135	0.418748	0.209374	+	0.977836i	$0.432857\pi$
$114$	17.5473	1.64346
$115$	0.0847095	0.00789920
$116$	−8.58044	−0.796673
$117$	−5.55623	−0.513673
$118$	−11.5534	−1.06358
$119$	28.5159	2.61405
$120$	4.74350	0.433021
$121$	−10.9149	−0.992266
$122$	11.6675	1.05633
$123$	14.3447	1.29341
$124$	−4.85515	−0.436005
$125$	12.0576	1.07846
$126$	22.1123	1.96992
$127$	−4.29815	−0.381399	−0.190699	−	0.981648i	$-0.561076\pi$
$127$	−4.29815	−0.381399	−0.190699	+	0.981648i	$0.561076\pi$
$128$	1.00000	0.0883883
$129$	−27.3249	−2.40582
$130$	1.87490	0.164440
$131$	−0.503462	−0.0439876	−0.0219938	−	0.999758i	$-0.507001\pi$
$131$	−0.503462	−0.0439876	−0.0219938	+	0.999758i	$0.507001\pi$
$132$	0.823822	0.0717045
$133$	−27.6023	−2.39342
$134$	−7.46949	−0.645266
$135$	9.37842	0.807166
$136$	6.41845	0.550378
$137$	−17.8278	−1.52314	−0.761568	−	0.648086i	$-0.775570\pi$
$137$	−17.8278	−1.52314	−0.761568	+	0.648086i	$0.775570\pi$
$138$	0.142455	0.0121266
$139$	−4.14045	−0.351188	−0.175594	−	0.984463i	$-0.556185\pi$
$139$	−4.14045	−0.351188	−0.175594	+	0.984463i	$0.556185\pi$
$140$	−7.46163	−0.630623
$141$	−10.9560	−0.922659
$142$	−4.96952	−0.417033
$143$	0.325622	0.0272298
$144$	4.97711	0.414759
$145$	14.4107	1.19675
$146$	11.8199	0.978224
$147$	−35.9784	−2.96745
$148$	−8.46466	−0.695791
$149$	−16.7494	−1.37216	−0.686082	−	0.727524i	$-0.740671\pi$
$149$	−16.7494	−1.37216	−0.686082	+	0.727524i	$0.740671\pi$
$150$	6.15524	0.502573
$151$	16.1993	1.31828	0.659139	−	0.752021i	$-0.270921\pi$
$151$	16.1993	1.31828	0.659139	+	0.752021i	$0.270921\pi$
$152$	−6.21280	−0.503925
$153$	31.9453	2.58263
$154$	−1.29589	−0.104426
$155$	8.15415	0.654957
$156$	3.15301	0.252443
$157$	3.58179	0.285858	0.142929	−	0.989733i	$-0.454348\pi$
$157$	3.58179	0.285858	0.142929	+	0.989733i	$0.454348\pi$
$158$	−6.15302	−0.489508
$159$	−4.80945	−0.381414
$160$	−1.67949	−0.132775
$161$	−0.224085	−0.0176604
$162$	0.840286	0.0660191
$163$	−18.1294	−1.42001	−0.710003	−	0.704199i	$-0.751306\pi$
$163$	−18.1294	−1.42001	−0.710003	+	0.704199i	$0.751306\pi$
$164$	−5.07887	−0.396593
$165$	−1.38360	−0.107713
$166$	14.0089	1.08730
$167$	−1.76173	−0.136327	−0.0681636	−	0.997674i	$-0.521714\pi$
$167$	−1.76173	−0.136327	−0.0681636	+	0.997674i	$0.521714\pi$
$168$	−12.5482	−0.968112
$169$	−11.7537	−0.904135
$170$	−10.7797	−0.826765
$171$	−30.9218	−2.36465
$172$	9.67466	0.737686
$173$	21.8206	1.65899	0.829494	−	0.558516i	$-0.188629\pi$
$173$	21.8206	1.65899	0.829494	+	0.558516i	$0.188629\pi$
$174$	24.2344	1.83720
$175$	−9.68233	−0.731915
$176$	−0.291683	−0.0219864
$177$	32.6311	2.45270
$178$	14.6331	1.09680
$179$	−5.46865	−0.408746	−0.204373	−	0.978893i	$-0.565516\pi$
$179$	−5.46865	−0.408746	−0.204373	+	0.978893i	$0.565516\pi$
$180$	−8.35898	−0.623042
$181$	−2.02565	−0.150566	−0.0752828	−	0.997162i	$-0.523986\pi$
$181$	−2.02565	−0.150566	−0.0752828	+	0.997162i	$0.523986\pi$
$182$	−4.95975	−0.367641
$183$	−32.9534	−2.43599
$184$	−0.0504378	−0.00371832
$185$	14.2163	1.04520
$186$	13.7128	1.00547
$187$	−1.87215	−0.136905
$188$	3.87907	0.282911
$189$	−24.8091	−1.80460
$190$	10.4343	0.756985
$191$	−26.9793	−1.95215	−0.976076	−	0.217429i	$-0.930233\pi$
$191$	−26.9793	−1.95215	−0.976076	+	0.217429i	$0.930233\pi$
$192$	−2.82438	−0.203832
$193$	−1.07690	−0.0775170	−0.0387585	−	0.999249i	$-0.512340\pi$
$193$	−1.07690	−0.0775170	−0.0387585	+	0.999249i	$0.512340\pi$
$194$	−11.7240	−0.841737
$195$	−5.29544	−0.379214
$196$	12.7385	0.909895
$197$	−2.74688	−0.195707	−0.0978537	−	0.995201i	$-0.531198\pi$
$197$	−2.74688	−0.195707	−0.0978537	+	0.995201i	$0.531198\pi$
$198$	−1.45174	−0.103170
$199$	3.61533	0.256284	0.128142	−	0.991756i	$-0.459099\pi$
$199$	3.61533	0.256284	0.128142	+	0.991756i	$0.459099\pi$
$200$	−2.17933	−0.154102
$201$	21.0967	1.48804
$202$	−14.3832	−1.01200
$203$	−38.1212	−2.67559
$204$	−18.1281	−1.26922
$205$	8.52990	0.595754
$206$	−5.50465	−0.383527
$207$	−0.251034	−0.0174481
$208$	−1.11636	−0.0774054
$209$	1.81217	0.125350
$210$	21.0745	1.45428
$211$	26.2868	1.80966	0.904829	−	0.425775i	$-0.139998\pi$
$211$	26.2868	1.80966	0.904829	+	0.425775i	$0.139998\pi$
$212$	1.70283	0.116951
$213$	14.0358	0.961718
$214$	2.84788	0.194677
$215$	−16.2485	−1.10814
$216$	−5.58410	−0.379950
$217$	−21.5705	−1.46430
$218$	−8.01144	−0.542603
$219$	−33.3839	−2.25588
$220$	0.489877	0.0330275
$221$	−7.16528	−0.481989
$222$	23.9074	1.60456
$223$	9.25243	0.619589	0.309794	−	0.950804i	$-0.399740\pi$
$223$	9.25243	0.619589	0.309794	+	0.950804i	$0.399740\pi$
$224$	4.44281	0.296848
$225$	−10.8467	−0.723117
$226$	4.45135	0.296100
$227$	5.30033	0.351795	0.175898	−	0.984408i	$-0.443717\pi$
$227$	5.30033	0.351795	0.175898	+	0.984408i	$0.443717\pi$
$228$	17.5473	1.16210
$229$	−8.62163	−0.569733	−0.284867	−	0.958567i	$-0.591949\pi$
$229$	−8.62163	−0.569733	−0.284867	+	0.958567i	$0.591949\pi$
$230$	0.0847095	0.00558558
$231$	3.66008	0.240816
$232$	−8.58044	−0.563333
$233$	−0.306596	−0.0200857	−0.0100429	−	0.999950i	$-0.503197\pi$
$233$	−0.306596	−0.0200857	−0.0100429	+	0.999950i	$0.503197\pi$
$234$	−5.55623	−0.363222
$235$	−6.51485	−0.424982
$236$	−11.5534	−0.752061
$237$	17.3784	1.12885
$238$	28.5159	1.84841
$239$	−5.92792	−0.383446	−0.191723	−	0.981449i	$-0.561407\pi$
$239$	−5.92792	−0.383446	−0.191723	+	0.981449i	$0.561407\pi$
$240$	4.74350	0.306192
$241$	−12.1143	−0.780352	−0.390176	−	0.920740i	$-0.627586\pi$
$241$	−12.1143	−0.780352	−0.390176	+	0.920740i	$0.627586\pi$
$242$	−10.9149	−0.701638
$243$	14.3790	0.922415
$244$	11.6675	0.746936
$245$	−21.3942	−1.36682
$246$	14.3447	0.914582
$247$	6.93570	0.441308
$248$	−4.85515	−0.308302
$249$	−39.5664	−2.50742
$250$	12.0576	0.762588
$251$	−26.7764	−1.69011	−0.845057	−	0.534676i	$-0.820434\pi$
$251$	−26.7764	−1.69011	−0.845057	+	0.534676i	$0.820434\pi$
$252$	22.1123	1.39295
$253$	0.0147118	0.000924924 0
$254$	−4.29815	−0.269690
$255$	30.4459	1.90660
$256$	1.00000	0.0625000
$257$	−10.9266	−0.681584	−0.340792	−	0.940139i	$-0.610695\pi$
$257$	−10.9266	−0.681584	−0.340792	+	0.940139i	$0.610695\pi$
$258$	−27.3249	−1.70117
$259$	−37.6069	−2.33678
$260$	1.87490	0.116277
$261$	−42.7058	−2.64342
$262$	−0.503462	−0.0311040
$263$	20.3817	1.25679	0.628396	−	0.777894i	$-0.283712\pi$
$263$	20.3817	1.25679	0.628396	+	0.777894i	$0.283712\pi$
$264$	0.823822	0.0507027
$265$	−2.85989	−0.175681
$266$	−27.6023	−1.69240
$267$	−41.3294	−2.52932
$268$	−7.46949	−0.456272
$269$	−25.0279	−1.52598	−0.762989	−	0.646411i	$-0.776269\pi$
$269$	−25.0279	−1.52598	−0.762989	+	0.646411i	$0.776269\pi$
$270$	9.37842	0.570753
$271$	−8.28593	−0.503334	−0.251667	−	0.967814i	$-0.580979\pi$
$271$	−8.28593	−0.503334	−0.251667	+	0.967814i	$0.580979\pi$
$272$	6.41845	0.389176
$273$	14.0082	0.847816
$274$	−17.8278	−1.07702
$275$	0.635672	0.0383325
$276$	0.142455	0.00857480
$277$	−19.0416	−1.14410	−0.572049	−	0.820220i	$-0.693851\pi$
$277$	−19.0416	−1.14410	−0.572049	+	0.820220i	$0.693851\pi$
$278$	−4.14045	−0.248327
$279$	−24.1646	−1.44670
$280$	−7.46163	−0.445918
$281$	−17.5571	−1.04737	−0.523684	−	0.851912i	$-0.675443\pi$
$281$	−17.5571	−1.04737	−0.523684	+	0.851912i	$0.675443\pi$
$282$	−10.9560	−0.652418
$283$	−7.26943	−0.432123	−0.216061	−	0.976380i	$-0.569321\pi$
$283$	−7.26943	−0.432123	−0.216061	+	0.976380i	$0.569321\pi$
$284$	−4.96952	−0.294887
$285$	−29.4704	−1.74568
$286$	0.325622	0.0192544
$287$	−22.5645	−1.33194
$288$	4.97711	0.293279
$289$	24.1965	1.42332
$290$	14.4107	0.846227
$291$	33.1131	1.94112
$292$	11.8199	0.691709
$293$	18.2479	1.06605	0.533026	−	0.846099i	$-0.321055\pi$
$293$	18.2479	1.06605	0.533026	+	0.846099i	$0.321055\pi$
$294$	−35.9784	−2.09830
$295$	19.4037	1.12973
$296$	−8.46466	−0.491999
$297$	1.62879	0.0945117
$298$	−16.7494	−0.970267
$299$	0.0563065	0.00325629
$300$	6.15524	0.355373
$301$	42.9827	2.47748
$302$	16.1993	0.932164
$303$	40.6237	2.33377
$304$	−6.21280	−0.356329
$305$	−19.5954	−1.12203
$306$	31.9453	1.82619
$307$	0.865853	0.0494168	0.0247084	−	0.999695i	$-0.492134\pi$
$307$	0.865853	0.0494168	0.0247084	+	0.999695i	$0.492134\pi$
$308$	−1.29589	−0.0738402
$309$	15.5472	0.884450
$310$	8.15415	0.463125
$311$	−12.7502	−0.722998	−0.361499	−	0.932373i	$-0.617735\pi$
$311$	−12.7502	−0.722998	−0.361499	+	0.932373i	$0.617735\pi$
$312$	3.15301	0.178504
$313$	18.9062	1.06864	0.534321	−	0.845282i	$-0.320567\pi$
$313$	18.9062	1.06864	0.534321	+	0.845282i	$0.320567\pi$
$314$	3.58179	0.202132
$315$	−37.1374	−2.09245
$316$	−6.15302	−0.346134
$317$	32.5127	1.82610	0.913048	−	0.407852i	$-0.133722\pi$
$317$	32.5127	1.82610	0.913048	+	0.407852i	$0.133722\pi$
$318$	−4.80945	−0.269700
$319$	2.50276	0.140128
$320$	−1.67949	−0.0938861
$321$	−8.04350	−0.448944
$322$	−0.224085	−0.0124878
$323$	−39.8766	−2.21879
$324$	0.840286	0.0466826
$325$	2.43290	0.134953
$326$	−18.1294	−1.00410
$327$	22.6273	1.25129
$328$	−5.07887	−0.280434
$329$	17.2340	0.950140
$330$	−1.38360	−0.0761645
$331$	−31.6061	−1.73723	−0.868614	−	0.495489i	$-0.834989\pi$
$331$	−31.6061	−1.73723	−0.868614	+	0.495489i	$0.834989\pi$
$332$	14.0089	0.768838
$333$	−42.1295	−2.30869
$334$	−1.76173	−0.0963978
$335$	12.5449	0.685401
$336$	−12.5482	−0.684559
$337$	−11.6232	−0.633157	−0.316579	−	0.948566i	$-0.602534\pi$
$337$	−11.6232	−0.633157	−0.316579	+	0.948566i	$0.602534\pi$
$338$	−11.7537	−0.639320
$339$	−12.5723	−0.682834
$340$	−10.7797	−0.584611
$341$	1.41616	0.0766895
$342$	−30.9218	−1.67206
$343$	25.4952	1.37661
$344$	9.67466	0.521623
$345$	−0.239252	−0.0128809
$346$	21.8206	1.17308
$347$	21.2086	1.13854	0.569268	−	0.822152i	$-0.307227\pi$
$347$	21.2086	1.13854	0.569268	+	0.822152i	$0.307227\pi$
$348$	24.2344	1.29910
$349$	1.05328	0.0563807	0.0281903	−	0.999603i	$-0.491026\pi$
$349$	1.05328	0.0563807	0.0281903	+	0.999603i	$0.491026\pi$
$350$	−9.68233	−0.517542
$351$	6.23385	0.332738
$352$	−0.291683	−0.0155467
$353$	−2.19635	−0.116900	−0.0584499	−	0.998290i	$-0.518616\pi$
$353$	−2.19635	−0.116900	−0.0584499	+	0.998290i	$0.518616\pi$
$354$	32.6311	1.73432
$355$	8.34624	0.442973
$356$	14.6331	0.775552
$357$	−80.5398	−4.26262
$358$	−5.46865	−0.289027
$359$	12.2752	0.647858	0.323929	−	0.946081i	$-0.394996\pi$
$359$	12.2752	0.647858	0.323929	+	0.946081i	$0.394996\pi$
$360$	−8.35898	−0.440557
$361$	19.5989	1.03152
$362$	−2.02565	−0.106466
$363$	30.8279	1.61804
$364$	−4.95975	−0.259962
$365$	−19.8514	−1.03907
$366$	−32.9534	−1.72250
$367$	−14.8625	−0.775819	−0.387909	−	0.921698i	$-0.626803\pi$
$367$	−14.8625	−0.775819	−0.387909	+	0.921698i	$0.626803\pi$
$368$	−0.0504378	−0.00262925
$369$	−25.2781	−1.31593
$370$	14.2163	0.739069
$371$	7.56537	0.392774
$372$	13.7128	0.710974
$373$	−20.7108	−1.07237	−0.536183	−	0.844102i	$-0.680134\pi$
$373$	−20.7108	−1.07237	−0.536183	+	0.844102i	$0.680134\pi$
$374$	−1.87215	−0.0968066
$375$	−34.0552	−1.75860
$376$	3.87907	0.200048
$377$	9.57882	0.493334
$378$	−24.8091	−1.27604
$379$	4.51037	0.231682	0.115841	−	0.993268i	$-0.463044\pi$
$379$	4.51037	0.231682	0.115841	+	0.993268i	$0.463044\pi$
$380$	10.4343	0.535269
$381$	12.1396	0.621930
$382$	−26.9793	−1.38038
$383$	38.2854	1.95629	0.978146	−	0.207917i	$-0.0666685\pi$
$383$	38.2854	1.95629	0.978146	+	0.207917i	$0.0666685\pi$
$384$	−2.82438	−0.144131
$385$	2.17643	0.110921
$386$	−1.07690	−0.0548128
$387$	48.1519	2.44770
$388$	−11.7240	−0.595198
$389$	−4.86464	−0.246647	−0.123324	−	0.992367i	$-0.539355\pi$
$389$	−4.86464	−0.246647	−0.123324	+	0.992367i	$0.539355\pi$
$390$	−5.29544	−0.268145
$391$	−0.323732	−0.0163718
$392$	12.7385	0.643393
$393$	1.42197	0.0717287
$394$	−2.74688	−0.138386
$395$	10.3339	0.519955
$396$	−1.45174	−0.0729525
$397$	11.7074	0.587579	0.293790	−	0.955870i	$-0.405084\pi$
$397$	11.7074	0.587579	0.293790	+	0.955870i	$0.405084\pi$
$398$	3.61533	0.181220
$399$	77.9593	3.90284
$400$	−2.17933	−0.108966
$401$	−27.7391	−1.38522	−0.692611	−	0.721311i	$-0.743540\pi$
$401$	−27.7391	−1.38522	−0.692611	+	0.721311i	$0.743540\pi$
$402$	21.0967	1.05221
$403$	5.42007	0.269993
$404$	−14.3832	−0.715593
$405$	−1.41125	−0.0701255
$406$	−38.1212	−1.89192
$407$	2.46899	0.122384
$408$	−18.1281	−0.897476
$409$	−8.06878	−0.398976	−0.199488	−	0.979900i	$-0.563928\pi$
$409$	−8.06878	−0.398976	−0.199488	+	0.979900i	$0.563928\pi$
$410$	8.52990	0.421262
$411$	50.3526	2.48371
$412$	−5.50465	−0.271195
$413$	−51.3295	−2.52576
$414$	−0.251034	−0.0123377
$415$	−23.5277	−1.15493
$416$	−1.11636	−0.0547339
$417$	11.6942	0.572667
$418$	1.81217	0.0886360
$419$	33.3712	1.63029	0.815144	−	0.579258i	$-0.196657\pi$
$419$	33.3712	1.63029	0.815144	+	0.579258i	$0.196657\pi$
$420$	21.0745	1.02833
$421$	2.82704	0.137781	0.0688907	−	0.997624i	$-0.478054\pi$
$421$	2.82704	0.137781	0.0688907	+	0.997624i	$0.478054\pi$
$422$	26.2868	1.27962
$423$	19.3066	0.938718
$424$	1.70283	0.0826970
$425$	−13.9879	−0.678513
$426$	14.0358	0.680037
$427$	51.8365	2.50854
$428$	2.84788	0.137658
$429$	−0.919678	−0.0444025
$430$	−16.2485	−0.783570
$431$	18.5293	0.892524	0.446262	−	0.894902i	$-0.352755\pi$
$431$	18.5293	0.892524	0.446262	+	0.894902i	$0.352755\pi$
$432$	−5.58410	−0.268665
$433$	−17.8320	−0.856953	−0.428476	−	0.903553i	$-0.640949\pi$
$433$	−17.8320	−0.856953	−0.428476	+	0.903553i	$0.640949\pi$
$434$	−21.5705	−1.03542
$435$	−40.7013	−1.95148
$436$	−8.01144	−0.383678
$437$	0.313360	0.0149900
$438$	−33.3839	−1.59515
$439$	−30.7441	−1.46733	−0.733667	−	0.679509i	$-0.762193\pi$
$439$	−30.7441	−1.46733	−0.733667	+	0.679509i	$0.762193\pi$
$440$	0.489877	0.0233540
$441$	63.4011	3.01910
$442$	−7.16528	−0.340817
$443$	39.6137	1.88210	0.941051	−	0.338264i	$-0.109840\pi$
$443$	39.6137	1.88210	0.941051	+	0.338264i	$0.109840\pi$
$444$	23.9074	1.13460
$445$	−24.5761	−1.16502
$446$	9.25243	0.438115
$447$	47.3067	2.23753
$448$	4.44281	0.209903
$449$	−23.4077	−1.10468	−0.552339	−	0.833619i	$-0.686265\pi$
$449$	−23.4077	−1.10468	−0.552339	+	0.833619i	$0.686265\pi$
$450$	−10.8467	−0.511321
$451$	1.48142	0.0697573
$452$	4.45135	0.209374
$453$	−45.7529	−2.14966
$454$	5.30033	0.248757
$455$	8.32984	0.390509
$456$	17.5473	0.821728
$457$	−17.4650	−0.816980	−0.408490	−	0.912763i	$-0.633945\pi$
$457$	−17.4650	−0.816980	−0.408490	+	0.912763i	$0.633945\pi$
$458$	−8.62163	−0.402862
$459$	−35.8413	−1.67293
$460$	0.0847095	0.00394960
$461$	−12.4154	−0.578242	−0.289121	−	0.957293i	$-0.593363\pi$
$461$	−12.4154	−0.578242	−0.289121	+	0.957293i	$0.593363\pi$
$462$	3.66008	0.170282
$463$	−40.8781	−1.89977	−0.949883	−	0.312605i	$-0.898798\pi$
$463$	−40.8781	−1.89977	−0.949883	+	0.312605i	$0.898798\pi$
$464$	−8.58044	−0.398337
$465$	−23.0304	−1.06801
$466$	−0.306596	−0.0142028
$467$	−27.4715	−1.27123	−0.635615	−	0.772006i	$-0.719253\pi$
$467$	−27.4715	−1.27123	−0.635615	+	0.772006i	$0.719253\pi$
$468$	−5.55623	−0.256837
$469$	−33.1855	−1.53236
$470$	−6.51485	−0.300508
$471$	−10.1163	−0.466135
$472$	−11.5534	−0.531788
$473$	−2.82193	−0.129753
$474$	17.3784	0.798218
$475$	13.5397	0.621245
$476$	28.5159	1.30703
$477$	8.47519	0.388052
$478$	−5.92792	−0.271137
$479$	18.4370	0.842406	0.421203	−	0.906966i	$-0.361608\pi$
$479$	18.4370	0.842406	0.421203	+	0.906966i	$0.361608\pi$
$480$	4.74350	0.216510
$481$	9.44958	0.430864
$482$	−12.1143	−0.551792
$483$	0.632901	0.0287980
$484$	−10.9149	−0.496133
$485$	19.6904	0.894093
$486$	14.3790	0.652246
$487$	0.533341	0.0241680	0.0120840	−	0.999927i	$-0.496153\pi$
$487$	0.533341	0.0241680	0.0120840	+	0.999927i	$0.496153\pi$
$488$	11.6675	0.528163
$489$	51.2043	2.31554
$490$	−21.3942	−0.966491
$491$	7.77639	0.350943	0.175472	−	0.984484i	$-0.443855\pi$
$491$	7.77639	0.350943	0.175472	+	0.984484i	$0.443855\pi$
$492$	14.3447	0.646707
$493$	−55.0731	−2.48037
$494$	6.93570	0.312052
$495$	2.43817	0.109588
$496$	−4.85515	−0.218002
$497$	−22.0786	−0.990362
$498$	−39.5664	−1.77301
$499$	−33.3689	−1.49380	−0.746900	−	0.664937i	$-0.768458\pi$
$499$	−33.3689	−1.49380	−0.746900	+	0.664937i	$0.768458\pi$
$500$	12.0576	0.539231
$501$	4.97580	0.222303
$502$	−26.7764	−1.19509
$503$	−7.89276	−0.351921	−0.175960	−	0.984397i	$-0.556303\pi$
$503$	−7.89276	−0.351921	−0.175960	+	0.984397i	$0.556303\pi$
$504$	22.1123	0.984962
$505$	24.1564	1.07495
$506$	0.0147118	0.000654020 0
$507$	33.1970	1.47433
$508$	−4.29815	−0.190699
$509$	−22.1335	−0.981049	−0.490525	−	0.871427i	$-0.663195\pi$
$509$	−22.1335	−0.981049	−0.490525	+	0.871427i	$0.663195\pi$
$510$	30.4459	1.34817
$511$	52.5136	2.32307
$512$	1.00000	0.0441942
$513$	34.6929	1.53173
$514$	−10.9266	−0.481952
$515$	9.24498	0.407383
$516$	−27.3249	−1.20291
$517$	−1.13146	−0.0497615
$518$	−37.6069	−1.65235
$519$	−61.6296	−2.70524
$520$	1.87490	0.0822200
$521$	−8.94960	−0.392089	−0.196044	−	0.980595i	$-0.562810\pi$
$521$	−8.94960	−0.392089	−0.196044	+	0.980595i	$0.562810\pi$
$522$	−42.7058	−1.86918
$523$	4.79536	0.209686	0.104843	−	0.994489i	$-0.466566\pi$
$523$	4.79536	0.209686	0.104843	+	0.994489i	$0.466566\pi$
$524$	−0.503462	−0.0219938
$525$	27.3466	1.19350
$526$	20.3817	0.888686
$527$	−31.1625	−1.35746
$528$	0.823822	0.0358522
$529$	−22.9975	−0.999889
$530$	−2.85989	−0.124226
$531$	−57.5024	−2.49539
$532$	−27.6023	−1.19671
$533$	5.66983	0.245588
$534$	−41.3294	−1.78850
$535$	−4.78298	−0.206786
$536$	−7.46949	−0.322633
$537$	15.4455	0.666524
$538$	−25.0279	−1.07903
$539$	−3.71561	−0.160043
$540$	9.37842	0.403583
$541$	−36.7821	−1.58139	−0.790693	−	0.612212i	$-0.790280\pi$
$541$	−36.7821	−1.58139	−0.790693	+	0.612212i	$0.790280\pi$
$542$	−8.28593	−0.355911
$543$	5.72121	0.245521
$544$	6.41845	0.275189
$545$	13.4551	0.576353
$546$	14.0082	0.599496
$547$	−22.3117	−0.953978	−0.476989	−	0.878909i	$-0.658272\pi$
$547$	−22.3117	−0.953978	−0.476989	+	0.878909i	$0.658272\pi$
$548$	−17.8278	−0.761568
$549$	58.0705	2.47839
$550$	0.635672	0.0271051
$551$	53.3085	2.27102
$552$	0.142455	0.00606330
$553$	−27.3367	−1.16247
$554$	−19.0416	−0.808999
$555$	−40.1521	−1.70436
$556$	−4.14045	−0.175594
$557$	33.7419	1.42969	0.714845	−	0.699283i	$-0.246497\pi$
$557$	33.7419	1.42969	0.714845	+	0.699283i	$0.246497\pi$
$558$	−24.1646	−1.02297
$559$	−10.8004	−0.456807
$560$	−7.46163	−0.315312
$561$	5.28766	0.223245
$562$	−17.5571	−0.740601
$563$	−20.7005	−0.872421	−0.436211	−	0.899845i	$-0.643680\pi$
$563$	−20.7005	−0.872421	−0.436211	+	0.899845i	$0.643680\pi$
$564$	−10.9560	−0.461329
$565$	−7.47599	−0.314517
$566$	−7.26943	−0.305557
$567$	3.73323	0.156781
$568$	−4.96952	−0.208517
$569$	7.45302	0.312447	0.156224	−	0.987722i	$-0.450068\pi$
$569$	7.45302	0.312447	0.156224	+	0.987722i	$0.450068\pi$
$570$	−29.4704	−1.23438
$571$	−24.2054	−1.01297	−0.506483	−	0.862250i	$-0.669055\pi$
$571$	−24.2054	−1.01297	−0.506483	+	0.862250i	$0.669055\pi$
$572$	0.325622	0.0136149
$573$	76.1997	3.18329
$574$	−22.5645	−0.941822
$575$	0.109920	0.00458400
$576$	4.97711	0.207380
$577$	−14.6893	−0.611523	−0.305761	−	0.952108i	$-0.598911\pi$
$577$	−14.6893	−0.611523	−0.305761	+	0.952108i	$0.598911\pi$
$578$	24.1965	1.00644
$579$	3.04158	0.126404
$580$	14.4107	0.598373
$581$	62.2388	2.58210
$582$	33.1131	1.37258
$583$	−0.496687	−0.0205707
$584$	11.8199	0.489112
$585$	9.33160	0.385814
$586$	18.2479	0.753812
$587$	4.53758	0.187286	0.0936430	−	0.995606i	$-0.470149\pi$
$587$	4.53758	0.187286	0.0936430	+	0.995606i	$0.470149\pi$
$588$	−35.9784	−1.48373
$589$	30.1641	1.24289
$590$	19.4037	0.798839
$591$	7.75824	0.319131
$592$	−8.46466	−0.347896
$593$	−17.4658	−0.717235	−0.358617	−	0.933485i	$-0.616752\pi$
$593$	−17.4658	−0.717235	−0.358617	+	0.933485i	$0.616752\pi$
$594$	1.62879	0.0668299
$595$	−47.8921	−1.96339
$596$	−16.7494	−0.686082
$597$	−10.2111	−0.417911
$598$	0.0563065	0.00230254
$599$	−1.37468	−0.0561677	−0.0280839	−	0.999606i	$-0.508941\pi$
$599$	−1.37468	−0.0561677	−0.0280839	+	0.999606i	$0.508941\pi$
$600$	6.15524	0.251287
$601$	25.6954	1.04814	0.524068	−	0.851676i	$-0.324414\pi$
$601$	25.6954	1.04814	0.524068	+	0.851676i	$0.324414\pi$
$602$	42.9827	1.75184
$603$	−37.1765	−1.51394
$604$	16.1993	0.659139
$605$	18.3315	0.745280
$606$	40.6237	1.65022
$607$	6.49232	0.263515	0.131758	−	0.991282i	$-0.457938\pi$
$607$	6.49232	0.263515	0.131758	+	0.991282i	$0.457938\pi$
$608$	−6.21280	−0.251962
$609$	107.669	4.36296
$610$	−19.5954	−0.793395
$611$	−4.33043	−0.175190
$612$	31.9453	1.29131
$613$	33.9021	1.36929	0.684646	−	0.728876i	$-0.259957\pi$
$613$	33.9021	1.36929	0.684646	+	0.728876i	$0.259957\pi$
$614$	0.865853	0.0349430
$615$	−24.0916	−0.971469
$616$	−1.29589	−0.0522129
$617$	−22.8289	−0.919057	−0.459528	−	0.888163i	$-0.651982\pi$
$617$	−22.8289	−0.919057	−0.459528	+	0.888163i	$0.651982\pi$
$618$	15.5472	0.625401
$619$	20.9412	0.841697	0.420848	−	0.907131i	$-0.361732\pi$
$619$	20.9412	0.841697	0.420848	+	0.907131i	$0.361732\pi$
$620$	8.15415	0.327479
$621$	0.281650	0.0113022
$622$	−12.7502	−0.511237
$623$	65.0120	2.60465
$624$	3.15301	0.126221
$625$	−9.35390	−0.374156
$626$	18.9062	0.755644
$627$	−5.11824	−0.204403
$628$	3.58179	0.142929
$629$	−54.3300	−2.16628
$630$	−37.1374	−1.47959
$631$	28.4136	1.13113	0.565564	−	0.824705i	$-0.308659\pi$
$631$	28.4136	1.13113	0.565564	+	0.824705i	$0.308659\pi$
$632$	−6.15302	−0.244754
$633$	−74.2439	−2.95093
$634$	32.5127	1.29124
$635$	7.21868	0.286464
$636$	−4.80945	−0.190707
$637$	−14.2207	−0.563446
$638$	2.50276	0.0990854
$639$	−24.7339	−0.978456
$640$	−1.67949	−0.0663875
$641$	11.1639	0.440946	0.220473	−	0.975393i	$-0.429240\pi$
$641$	11.1639	0.440946	0.220473	+	0.975393i	$0.429240\pi$
$642$	−8.04350	−0.317451
$643$	−39.0942	−1.54172	−0.770862	−	0.637002i	$-0.780174\pi$
$643$	−39.0942	−1.54172	−0.770862	+	0.637002i	$0.780174\pi$
$644$	−0.224085	−0.00883019
$645$	45.8918	1.80699
$646$	−39.8766	−1.56892
$647$	−8.55184	−0.336208	−0.168104	−	0.985769i	$-0.553764\pi$
$647$	−8.55184	−0.336208	−0.168104	+	0.985769i	$0.553764\pi$
$648$	0.840286	0.0330095
$649$	3.36992	0.132281
$650$	2.43290	0.0954264
$651$	60.9232	2.38777
$652$	−18.1294	−0.710003
$653$	6.99422	0.273705	0.136853	−	0.990591i	$-0.456301\pi$
$653$	6.99422	0.273705	0.136853	+	0.990591i	$0.456301\pi$
$654$	22.6273	0.884798
$655$	0.845557	0.0330386
$656$	−5.07887	−0.198297
$657$	58.8290	2.29514
$658$	17.2340	0.671850
$659$	−25.8934	−1.00866	−0.504332	−	0.863510i	$-0.668261\pi$
$659$	−25.8934	−1.00866	−0.504332	+	0.863510i	$0.668261\pi$
$660$	−1.38360	−0.0538564
$661$	−14.7826	−0.574977	−0.287489	−	0.957784i	$-0.592820\pi$
$661$	−14.7826	−0.574977	−0.287489	+	0.957784i	$0.592820\pi$
$662$	−31.6061	−1.22841
$663$	20.2374	0.785957
$664$	14.0089	0.543650
$665$	46.3576	1.79767
$666$	−42.1295	−1.63249
$667$	0.432778	0.0167572
$668$	−1.76173	−0.0681636
$669$	−26.1324	−1.01034
$670$	12.5449	0.484652
$671$	−3.40321	−0.131379
$672$	−12.5482	−0.484056
$673$	−31.0064	−1.19521	−0.597605	−	0.801790i	$-0.703881\pi$
$673$	−31.0064	−1.19521	−0.597605	+	0.801790i	$0.703881\pi$
$674$	−11.6232	−0.447710
$675$	12.1696	0.468408
$676$	−11.7537	−0.452067
$677$	−3.77784	−0.145194	−0.0725971	−	0.997361i	$-0.523129\pi$
$677$	−3.77784	−0.145194	−0.0725971	+	0.997361i	$0.523129\pi$
$678$	−12.5723	−0.482836
$679$	−52.0876	−1.99894
$680$	−10.7797	−0.413383
$681$	−14.9701	−0.573657
$682$	1.41616	0.0542276
$683$	14.0232	0.536582	0.268291	−	0.963338i	$-0.413541\pi$
$683$	14.0232	0.536582	0.268291	+	0.963338i	$0.413541\pi$
$684$	−30.9218	−1.18232
$685$	29.9416	1.14401
$686$	25.4952	0.973412
$687$	24.3507	0.929039
$688$	9.67466	0.368843
$689$	−1.90097	−0.0724212
$690$	−0.239252	−0.00910815
$691$	−2.60304	−0.0990243	−0.0495121	−	0.998774i	$-0.515767\pi$
$691$	−2.60304	−0.0990243	−0.0495121	+	0.998774i	$0.515767\pi$
$692$	21.8206	0.829494
$693$	−6.44978	−0.245007
$694$	21.2086	0.805067
$695$	6.95382	0.263774
$696$	24.2344	0.918602
$697$	−32.5985	−1.23476
$698$	1.05328	0.0398672
$699$	0.865942	0.0327529
$700$	−9.68233	−0.365958
$701$	11.0003	0.415474	0.207737	−	0.978185i	$-0.433390\pi$
$701$	11.0003	0.415474	0.207737	+	0.978185i	$0.433390\pi$
$702$	6.23385	0.235281
$703$	52.5893	1.98344
$704$	−0.291683	−0.0109932
$705$	18.4004	0.692999
$706$	−2.19635	−0.0826606
$707$	−63.9019	−2.40328
$708$	32.6311	1.22635
$709$	34.0007	1.27692	0.638462	−	0.769653i	$-0.279571\pi$
$709$	34.0007	1.27692	0.638462	+	0.769653i	$0.279571\pi$
$710$	8.34624	0.313229
$711$	−30.6242	−1.14850
$712$	14.6331	0.548398
$713$	0.244883	0.00917093
$714$	−80.5398	−3.01413
$715$	−0.546877	−0.0204520
$716$	−5.46865	−0.204373
$717$	16.7427	0.625267
$718$	12.2752	0.458105
$719$	43.6775	1.62890	0.814448	−	0.580236i	$-0.197040\pi$
$719$	43.6775	1.62890	0.814448	+	0.580236i	$0.197040\pi$
$720$	−8.35898	−0.311521
$721$	−24.4561	−0.910793
$722$	19.5989	0.729396
$723$	34.2154	1.27248
$724$	−2.02565	−0.0752828
$725$	18.6996	0.694485
$726$	30.8279	1.14413
$727$	17.2262	0.638883	0.319442	−	0.947606i	$-0.396505\pi$
$727$	17.2262	0.638883	0.319442	+	0.947606i	$0.396505\pi$
$728$	−4.95975	−0.183821
$729$	−43.1326	−1.59751
$730$	−19.8514	−0.734733
$731$	62.0964	2.29672
$732$	−32.9534	−1.21799
$733$	−9.51060	−0.351282	−0.175641	−	0.984454i	$-0.556200\pi$
$733$	−9.51060	−0.351282	−0.175641	+	0.984454i	$0.556200\pi$
$734$	−14.8625	−0.548587
$735$	60.4253	2.22882
$736$	−0.0504378	−0.00185916
$737$	2.17872	0.0802542
$738$	−25.2781	−0.930500
$739$	−2.96657	−0.109127	−0.0545636	−	0.998510i	$-0.517377\pi$
$739$	−2.96657	−0.109127	−0.0545636	+	0.998510i	$0.517377\pi$
$740$	14.2163	0.522601
$741$	−19.5890	−0.719621
$742$	7.56537	0.277733
$743$	12.6937	0.465687	0.232843	−	0.972514i	$-0.425197\pi$
$743$	12.6937	0.465687	0.232843	+	0.972514i	$0.425197\pi$
$744$	13.7128	0.502734
$745$	28.1304	1.03062
$746$	−20.7108	−0.758277
$747$	69.7238	2.55106
$748$	−1.87215	−0.0684526
$749$	12.6526	0.462316
$750$	−34.0552	−1.24352
$751$	24.7665	0.903743	0.451871	−	0.892083i	$-0.350757\pi$
$751$	24.7665	0.903743	0.451871	+	0.892083i	$0.350757\pi$
$752$	3.87907	0.141455
$753$	75.6268	2.75599
$754$	9.57882	0.348840
$755$	−27.2065	−0.990144
$756$	−24.8091	−0.902298
$757$	−33.7908	−1.22815	−0.614074	−	0.789248i	$-0.710471\pi$
$757$	−33.7908	−1.22815	−0.614074	+	0.789248i	$0.710471\pi$
$758$	4.51037	0.163824
$759$	−0.0415517	−0.00150823
$760$	10.4343	0.378492
$761$	29.6334	1.07421	0.537104	−	0.843516i	$-0.319518\pi$
$761$	29.6334	1.07421	0.537104	+	0.843516i	$0.319518\pi$
$762$	12.1396	0.439771
$763$	−35.5933	−1.28856
$764$	−26.9793	−0.976076
$765$	−53.6517	−1.93978
$766$	38.2854	1.38331
$767$	12.8977	0.465709
$768$	−2.82438	−0.101916
$769$	−25.7625	−0.929019	−0.464509	−	0.885568i	$-0.653769\pi$
$769$	−25.7625	−0.929019	−0.464509	+	0.885568i	$0.653769\pi$
$770$	2.17643	0.0784330
$771$	30.8609	1.11143
$772$	−1.07690	−0.0387585
$773$	−1.01685	−0.0365735	−0.0182868	−	0.999833i	$-0.505821\pi$
$773$	−1.01685	−0.0365735	−0.0182868	+	0.999833i	$0.505821\pi$
$774$	48.1519	1.73078
$775$	10.5810	0.380079
$776$	−11.7240	−0.420868
$777$	106.216	3.81048
$778$	−4.86464	−0.174406
$779$	31.5540	1.13054
$780$	−5.29544	−0.189607
$781$	1.44952	0.0518680
$782$	−0.323732	−0.0115766
$783$	47.9140	1.71231
$784$	12.7385	0.454948
$785$	−6.01556	−0.214705
$786$	1.42197	0.0507198
$787$	33.8551	1.20681	0.603403	−	0.797437i	$-0.293811\pi$
$787$	33.8551	1.20681	0.603403	+	0.797437i	$0.293811\pi$
$788$	−2.74688	−0.0978537
$789$	−57.5657	−2.04939
$790$	10.3339	0.367664
$791$	19.7765	0.703172
$792$	−1.45174	−0.0515852
$793$	−13.0251	−0.462535
$794$	11.7074	0.415481
$795$	8.07740	0.286476
$796$	3.61533	0.128142
$797$	10.4826	0.371311	0.185655	−	0.982615i	$-0.440559\pi$
$797$	10.4826	0.371311	0.185655	+	0.982615i	$0.440559\pi$
$798$	77.9593	2.75973
$799$	24.8976	0.880815
$800$	−2.17933	−0.0770508
$801$	72.8305	2.57334
$802$	−27.7391	−0.979500
$803$	−3.44767	−0.121665
$804$	21.0967	0.744022
$805$	0.376348	0.0132645
$806$	5.42007	0.190914
$807$	70.6883	2.48834
$808$	−14.3832	−0.506000
$809$	−21.8314	−0.767551	−0.383775	−	0.923426i	$-0.625376\pi$
$809$	−21.8314	−0.767551	−0.383775	+	0.923426i	$0.625376\pi$
$810$	−1.41125	−0.0495862
$811$	−12.6765	−0.445133	−0.222567	−	0.974917i	$-0.571443\pi$
$811$	−12.6765	−0.445133	−0.222567	+	0.974917i	$0.571443\pi$
$812$	−38.1212	−1.33779
$813$	23.4026	0.820765
$814$	2.46899	0.0865382
$815$	30.4481	1.06655
$816$	−18.1281	−0.634611
$817$	−60.1068	−2.10287
$818$	−8.06878	−0.282118
$819$	−24.6852	−0.862572
$820$	8.52990	0.297877
$821$	22.4458	0.783365	0.391683	−	0.920100i	$-0.371893\pi$
$821$	22.4458	0.783365	0.391683	+	0.920100i	$0.371893\pi$
$822$	50.3526	1.75625
$823$	−25.4444	−0.886936	−0.443468	−	0.896290i	$-0.646252\pi$
$823$	−25.4444	−0.886936	−0.443468	+	0.896290i	$0.646252\pi$
$824$	−5.50465	−0.191764
$825$	−1.79538	−0.0625070
$826$	−51.3295	−1.78598
$827$	8.01914	0.278853	0.139426	−	0.990232i	$-0.455474\pi$
$827$	8.01914	0.278853	0.139426	+	0.990232i	$0.455474\pi$
$828$	−0.251034	−0.00872404
$829$	15.1161	0.525003	0.262501	−	0.964932i	$-0.415453\pi$
$829$	15.1161	0.525003	0.262501	+	0.964932i	$0.415453\pi$
$830$	−23.5277	−0.816659
$831$	53.7806	1.86563
$832$	−1.11636	−0.0387027
$833$	81.7617	2.83287
$834$	11.6942	0.404937
$835$	2.95881	0.102394
$836$	1.81217	0.0626751
$837$	27.1116	0.937115
$838$	33.3712	1.15279
$839$	55.1526	1.90408	0.952040	−	0.305972i	$-0.0989815\pi$
$839$	55.1526	1.90408	0.952040	+	0.305972i	$0.0989815\pi$
$840$	21.0745	0.727138
$841$	44.6239	1.53875
$842$	2.82704	0.0974262
$843$	49.5879	1.70790
$844$	26.2868	0.904829
$845$	19.7403	0.679085
$846$	19.3066	0.663774
$847$	−48.4929	−1.66624
$848$	1.70283	0.0584756
$849$	20.5316	0.704643
$850$	−13.9879	−0.479781
$851$	0.426939	0.0146353
$852$	14.0358	0.480859
$853$	3.83957	0.131464	0.0657321	−	0.997837i	$-0.479062\pi$
$853$	3.83957	0.131464	0.0657321	+	0.997837i	$0.479062\pi$
$854$	51.8365	1.77381
$855$	51.9327	1.77606
$856$	2.84788	0.0973386
$857$	−15.4621	−0.528176	−0.264088	−	0.964499i	$-0.585071\pi$
$857$	−15.4621	−0.528176	−0.264088	+	0.964499i	$0.585071\pi$
$858$	−0.919678	−0.0313973
$859$	5.90136	0.201352	0.100676	−	0.994919i	$-0.467899\pi$
$859$	5.90136	0.201352	0.100676	+	0.994919i	$0.467899\pi$
$860$	−16.2485	−0.554068
$861$	63.7305	2.17193
$862$	18.5293	0.631110
$863$	−17.0351	−0.579883	−0.289942	−	0.957044i	$-0.593636\pi$
$863$	−17.0351	−0.579883	−0.289942	+	0.957044i	$0.593636\pi$
$864$	−5.58410	−0.189975
$865$	−36.6474	−1.24605
$866$	−17.8320	−0.605957
$867$	−68.3401	−2.32095
$868$	−21.5705	−0.732150
$869$	1.79473	0.0608820
$870$	−40.7013	−1.37990
$871$	8.33861	0.282543
$872$	−8.01144	−0.271301
$873$	−58.3518	−1.97491
$874$	0.313360	0.0105996
$875$	53.5695	1.81098
$876$	−33.3839	−1.12794
$877$	−19.4616	−0.657171	−0.328586	−	0.944474i	$-0.606572\pi$
$877$	−19.4616	−0.657171	−0.328586	+	0.944474i	$0.606572\pi$
$878$	−30.7441	−1.03756
$879$	−51.5388	−1.73836
$880$	0.489877	0.0165137
$881$	5.74555	0.193572	0.0967862	−	0.995305i	$-0.469144\pi$
$881$	5.74555	0.193572	0.0967862	+	0.995305i	$0.469144\pi$
$882$	63.4011	2.13483
$883$	46.8180	1.57555	0.787776	−	0.615961i	$-0.211232\pi$
$883$	46.8180	1.57555	0.787776	+	0.615961i	$0.211232\pi$
$884$	−7.16528	−0.240994
$885$	−54.8035	−1.84220
$886$	39.6137	1.33085
$887$	25.6969	0.862817	0.431408	−	0.902157i	$-0.358017\pi$
$887$	25.6969	0.862817	0.431408	+	0.902157i	$0.358017\pi$
$888$	23.9074	0.802280
$889$	−19.0958	−0.640454
$890$	−24.5761	−0.823792
$891$	−0.245097	−0.00821105
$892$	9.25243	0.309794
$893$	−24.0999	−0.806473
$894$	47.3067	1.58217
$895$	9.18452	0.307005
$896$	4.44281	0.148424
$897$	−0.159031	−0.00530988
$898$	−23.4077	−0.781126
$899$	41.6593	1.38941
$900$	−10.8467	−0.361558
$901$	10.9296	0.364116
$902$	1.48142	0.0493259
$903$	−121.399	−4.03992
$904$	4.45135	0.148050
$905$	3.40206	0.113088
$906$	−45.7529	−1.52004
$907$	20.8681	0.692915	0.346458	−	0.938066i	$-0.387384\pi$
$907$	20.8681	0.692915	0.346458	+	0.938066i	$0.387384\pi$
$908$	5.30033	0.175898
$909$	−71.5869	−2.37439
$910$	8.32984	0.276131
$911$	−23.9543	−0.793640	−0.396820	−	0.917896i	$-0.629886\pi$
$911$	−23.9543	−0.793640	−0.396820	+	0.917896i	$0.629886\pi$
$912$	17.5473	0.581049
$913$	−4.08615	−0.135232
$914$	−17.4650	−0.577692
$915$	55.3449	1.82964
$916$	−8.62163	−0.284867
$917$	−2.23678	−0.0738651
$918$	−35.8413	−1.18294
$919$	40.6556	1.34110	0.670552	−	0.741862i	$-0.266057\pi$
$919$	40.6556	1.34110	0.670552	+	0.741862i	$0.266057\pi$
$920$	0.0847095	0.00279279
$921$	−2.44550	−0.0805818
$922$	−12.4154	−0.408879
$923$	5.54776	0.182607
$924$	3.66008	0.120408
$925$	18.4473	0.606542
$926$	−40.8781	−1.34334
$927$	−27.3972	−0.899844
$928$	−8.58044	−0.281667
$929$	−46.4089	−1.52263	−0.761314	−	0.648383i	$-0.775445\pi$
$929$	−46.4089	−1.52263	−0.761314	+	0.648383i	$0.775445\pi$
$930$	−23.0304	−0.755196
$931$	−79.1420	−2.59377
$932$	−0.306596	−0.0100429
$933$	36.0114	1.17896
$934$	−27.4715	−0.898895
$935$	3.14425	0.102828
$936$	−5.55623	−0.181611
$937$	49.8816	1.62956	0.814780	−	0.579770i	$-0.196857\pi$
$937$	49.8816	1.62956	0.814780	+	0.579770i	$0.196857\pi$
$938$	−33.1855	−1.08355
$939$	−53.3983	−1.74259
$940$	−6.51485	−0.212491
$941$	−18.2736	−0.595701	−0.297850	−	0.954613i	$-0.596270\pi$
$941$	−18.2736	−0.595701	−0.297850	+	0.954613i	$0.596270\pi$
$942$	−10.1163	−0.329607
$943$	0.256167	0.00834194
$944$	−11.5534	−0.376031
$945$	41.6665	1.35541
$946$	−2.82193	−0.0917489
$947$	20.5915	0.669134	0.334567	−	0.942372i	$-0.391410\pi$
$947$	20.5915	0.669134	0.334567	+	0.942372i	$0.391410\pi$
$948$	17.3784	0.564425
$949$	−13.1952	−0.428336
$950$	13.5397	0.439287
$951$	−91.8282	−2.97773
$952$	28.5159	0.924207
$953$	46.4123	1.50344	0.751722	−	0.659481i	$-0.229224\pi$
$953$	46.4123	1.50344	0.751722	+	0.659481i	$0.229224\pi$
$954$	8.47519	0.274394
$955$	45.3113	1.46624
$956$	−5.92792	−0.191723
$957$	−7.06875	−0.228500
$958$	18.4370	0.595671
$959$	−79.2057	−2.55768
$960$	4.74350	0.153096
$961$	−7.42756	−0.239599
$962$	9.44958	0.304667
$963$	14.1742	0.456758
$964$	−12.1143	−0.390176
$965$	1.80864	0.0582222
$966$	0.632901	0.0203633
$967$	33.1822	1.06707	0.533534	−	0.845778i	$-0.320863\pi$
$967$	33.1822	1.06707	0.533534	+	0.845778i	$0.320863\pi$
$968$	−10.9149	−0.350819
$969$	112.626	3.61808
$970$	19.6904	0.632219
$971$	48.9180	1.56985	0.784926	−	0.619589i	$-0.212701\pi$
$971$	48.9180	1.56985	0.784926	+	0.619589i	$0.212701\pi$
$972$	14.3790	0.461207
$973$	−18.3952	−0.589723
$974$	0.533341	0.0170893
$975$	−6.87144	−0.220062
$976$	11.6675	0.373468
$977$	45.3299	1.45023	0.725117	−	0.688626i	$-0.241786\pi$
$977$	45.3299	1.45023	0.725117	+	0.688626i	$0.241786\pi$
$978$	51.2043	1.63733
$979$	−4.26822	−0.136413
$980$	−21.3942	−0.683412
$981$	−39.8738	−1.27307
$982$	7.77639	0.248154
$983$	6.29700	0.200843	0.100421	−	0.994945i	$-0.467981\pi$
$983$	6.29700	0.200843	0.100421	+	0.994945i	$0.467981\pi$
$984$	14.3447	0.457291
$985$	4.61335	0.146994
$986$	−55.0731	−1.75388
$987$	−48.6753	−1.54935
$988$	6.93570	0.220654
$989$	−0.487968	−0.0155165
$990$	2.43817	0.0774901
$991$	−30.7148	−0.975689	−0.487844	−	0.872931i	$-0.662217\pi$
$991$	−30.7148	−0.975689	−0.487844	+	0.872931i	$0.662217\pi$
$992$	−4.85515	−0.154151
$993$	89.2676	2.83282
$994$	−22.0786	−0.700292
$995$	−6.07190	−0.192492
$996$	−39.5664	−1.25371
$997$	−41.3479	−1.30950	−0.654750	−	0.755845i	$-0.727226\pi$
$997$	−41.3479	−1.30950	−0.654750	+	0.755845i	$0.727226\pi$
$998$	−33.3689	−1.05628
$999$	47.2675	1.49548

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.a.1.4	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.a.1.4	✓	47	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.82438 q^{3} +1.00000 q^{4} -1.67949 q^{5} -2.82438 q^{6} +4.44281 q^{7} +1.00000 q^{8} +4.97711 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.82438 q^{3} +1.00000 q^{4} -1.67949 q^{5} -2.82438 q^{6} +4.44281 q^{7} +1.00000 q^{8} +4.97711 q^{9} -1.67949 q^{10} -0.291683 q^{11} -2.82438 q^{12} -1.11636 q^{13} +4.44281 q^{14} +4.74350 q^{15} +1.00000 q^{16} +6.41845 q^{17} +4.97711 q^{18} -6.21280 q^{19} -1.67949 q^{20} -12.5482 q^{21} -0.291683 q^{22} -0.0504378 q^{23} -2.82438 q^{24} -2.17933 q^{25} -1.11636 q^{26} -5.58410 q^{27} +4.44281 q^{28} -8.58044 q^{29} +4.74350 q^{30} -4.85515 q^{31} +1.00000 q^{32} +0.823822 q^{33} +6.41845 q^{34} -7.46163 q^{35} +4.97711 q^{36} -8.46466 q^{37} -6.21280 q^{38} +3.15301 q^{39} -1.67949 q^{40} -5.07887 q^{41} -12.5482 q^{42} +9.67466 q^{43} -0.291683 q^{44} -8.35898 q^{45} -0.0504378 q^{46} +3.87907 q^{47} -2.82438 q^{48} +12.7385 q^{49} -2.17933 q^{50} -18.1281 q^{51} -1.11636 q^{52} +1.70283 q^{53} -5.58410 q^{54} +0.489877 q^{55} +4.44281 q^{56} +17.5473 q^{57} -8.58044 q^{58} -11.5534 q^{59} +4.74350 q^{60} +11.6675 q^{61} -4.85515 q^{62} +22.1123 q^{63} +1.00000 q^{64} +1.87490 q^{65} +0.823822 q^{66} -7.46949 q^{67} +6.41845 q^{68} +0.142455 q^{69} -7.46163 q^{70} -4.96952 q^{71} +4.97711 q^{72} +11.8199 q^{73} -8.46466 q^{74} +6.15524 q^{75} -6.21280 q^{76} -1.29589 q^{77} +3.15301 q^{78} -6.15302 q^{79} -1.67949 q^{80} +0.840286 q^{81} -5.07887 q^{82} +14.0089 q^{83} -12.5482 q^{84} -10.7797 q^{85} +9.67466 q^{86} +24.2344 q^{87} -0.291683 q^{88} +14.6331 q^{89} -8.35898 q^{90} -4.95975 q^{91} -0.0504378 q^{92} +13.7128 q^{93} +3.87907 q^{94} +10.4343 q^{95} -2.82438 q^{96} -11.7240 q^{97} +12.7385 q^{98} -1.45174 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9} - 14 q^{10} - 30 q^{11} - 13 q^{12} - 39 q^{13} - 17 q^{14} - 18 q^{15} + 47 q^{16} - 26 q^{17} + 12 q^{18} - 23 q^{19} - 14 q^{20} - 39 q^{21} - 30 q^{22} - 25 q^{23} - 13 q^{24} - 19 q^{25} - 39 q^{26} - 46 q^{27} - 17 q^{28} - 53 q^{29} - 18 q^{30} - 23 q^{31} + 47 q^{32} - 26 q^{33} - 26 q^{34} - 31 q^{35} + 12 q^{36} - 83 q^{37} - 23 q^{38} - 9 q^{39} - 14 q^{40} - 48 q^{41} - 39 q^{42} - 78 q^{43} - 30 q^{44} - 27 q^{45} - 25 q^{46} - 15 q^{47} - 13 q^{48} - 12 q^{49} - 19 q^{50} - 47 q^{51} - 39 q^{52} - 76 q^{53} - 46 q^{54} - 39 q^{55} - 17 q^{56} - 44 q^{57} - 53 q^{58} - 33 q^{59} - 18 q^{60} - 33 q^{61} - 23 q^{62} - 7 q^{63} + 47 q^{64} - 67 q^{65} - 26 q^{66} - 85 q^{67} - 26 q^{68} - 33 q^{69} - 31 q^{70} - 17 q^{71} + 12 q^{72} - 59 q^{73} - 83 q^{74} - 21 q^{75} - 23 q^{76} - 59 q^{77} - 9 q^{78} - 49 q^{79} - 14 q^{80} - 41 q^{81} - 48 q^{82} - 30 q^{83} - 39 q^{84} - 84 q^{85} - 78 q^{86} + 9 q^{87} - 30 q^{88} - 50 q^{89} - 27 q^{90} - 42 q^{91} - 25 q^{92} - 43 q^{93} - 15 q^{94} + 8 q^{95} - 13 q^{96} - 49 q^{97} - 12 q^{98} - 49 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9 - 14 * q^10 - 30 * q^11 - 13 * q^12 - 39 * q^13 - 17 * q^14 - 18 * q^15 + 47 * q^16 - 26 * q^17 + 12 * q^18 - 23 * q^19 - 14 * q^20 - 39 * q^21 - 30 * q^22 - 25 * q^23 - 13 * q^24 - 19 * q^25 - 39 * q^26 - 46 * q^27 - 17 * q^28 - 53 * q^29 - 18 * q^30 - 23 * q^31 + 47 * q^32 - 26 * q^33 - 26 * q^34 - 31 * q^35 + 12 * q^36 - 83 * q^37 - 23 * q^38 - 9 * q^39 - 14 * q^40 - 48 * q^41 - 39 * q^42 - 78 * q^43 - 30 * q^44 - 27 * q^45 - 25 * q^46 - 15 * q^47 - 13 * q^48 - 12 * q^49 - 19 * q^50 - 47 * q^51 - 39 * q^52 - 76 * q^53 - 46 * q^54 - 39 * q^55 - 17 * q^56 - 44 * q^57 - 53 * q^58 - 33 * q^59 - 18 * q^60 - 33 * q^61 - 23 * q^62 - 7 * q^63 + 47 * q^64 - 67 * q^65 - 26 * q^66 - 85 * q^67 - 26 * q^68 - 33 * q^69 - 31 * q^70 - 17 * q^71 + 12 * q^72 - 59 * q^73 - 83 * q^74 - 21 * q^75 - 23 * q^76 - 59 * q^77 - 9 * q^78 - 49 * q^79 - 14 * q^80 - 41 * q^81 - 48 * q^82 - 30 * q^83 - 39 * q^84 - 84 * q^85 - 78 * q^86 + 9 * q^87 - 30 * q^88 - 50 * q^89 - 27 * q^90 - 42 * q^91 - 25 * q^92 - 43 * q^93 - 15 * q^94 + 8 * q^95 - 13 * q^96 - 49 * q^97 - 12 * q^98 - 49 * q^99

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