LMFDB - Embedded newform 4006.2.a.g.1.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4006 = 2 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4006.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$31.9880710497$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.36
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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.60081 q^{3} +1.00000 q^{4} +1.01673 q^{5} -2.60081 q^{6} -1.30512 q^{7} -1.00000 q^{8} +3.76424 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.60081 q^{3} +1.00000 q^{4} +1.01673 q^{5} -2.60081 q^{6} -1.30512 q^{7} -1.00000 q^{8} +3.76424 q^{9} -1.01673 q^{10} -4.91572 q^{11} +2.60081 q^{12} +1.88493 q^{13} +1.30512 q^{14} +2.64432 q^{15} +1.00000 q^{16} -1.77495 q^{17} -3.76424 q^{18} -6.72737 q^{19} +1.01673 q^{20} -3.39437 q^{21} +4.91572 q^{22} +3.89860 q^{23} -2.60081 q^{24} -3.96626 q^{25} -1.88493 q^{26} +1.98764 q^{27} -1.30512 q^{28} -1.47458 q^{29} -2.64432 q^{30} -2.87638 q^{31} -1.00000 q^{32} -12.7849 q^{33} +1.77495 q^{34} -1.32695 q^{35} +3.76424 q^{36} -8.51268 q^{37} +6.72737 q^{38} +4.90235 q^{39} -1.01673 q^{40} +5.85833 q^{41} +3.39437 q^{42} -1.52639 q^{43} -4.91572 q^{44} +3.82720 q^{45} -3.89860 q^{46} -1.16716 q^{47} +2.60081 q^{48} -5.29667 q^{49} +3.96626 q^{50} -4.61632 q^{51} +1.88493 q^{52} -3.42899 q^{53} -1.98764 q^{54} -4.99795 q^{55} +1.30512 q^{56} -17.4966 q^{57} +1.47458 q^{58} -3.61230 q^{59} +2.64432 q^{60} +5.74092 q^{61} +2.87638 q^{62} -4.91277 q^{63} +1.00000 q^{64} +1.91646 q^{65} +12.7849 q^{66} -4.91185 q^{67} -1.77495 q^{68} +10.1395 q^{69} +1.32695 q^{70} -2.27572 q^{71} -3.76424 q^{72} +4.06233 q^{73} +8.51268 q^{74} -10.3155 q^{75} -6.72737 q^{76} +6.41560 q^{77} -4.90235 q^{78} +8.00999 q^{79} +1.01673 q^{80} -6.12323 q^{81} -5.85833 q^{82} +2.78614 q^{83} -3.39437 q^{84} -1.80464 q^{85} +1.52639 q^{86} -3.83511 q^{87} +4.91572 q^{88} +5.76902 q^{89} -3.82720 q^{90} -2.46006 q^{91} +3.89860 q^{92} -7.48094 q^{93} +1.16716 q^{94} -6.83991 q^{95} -2.60081 q^{96} -0.273900 q^{97} +5.29667 q^{98} -18.5039 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) $ 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.60081	1.50158	0.750791	−	0.660540i	$-0.229673\pi$
$3$	2.60081	1.50158	0.750791	+	0.660540i	$0.229673\pi$
$4$	1.00000	0.500000
$5$	1.01673	0.454695	0.227347	−	0.973814i	$-0.426995\pi$
$5$	1.01673	0.454695	0.227347	+	0.973814i	$0.426995\pi$
$6$	−2.60081	−1.06178
$7$	−1.30512	−0.493288	−0.246644	−	0.969106i	$-0.579328\pi$
$7$	−1.30512	−0.493288	−0.246644	+	0.969106i	$0.579328\pi$
$8$	−1.00000	−0.353553
$9$	3.76424	1.25475
$10$	−1.01673	−0.321518
$11$	−4.91572	−1.48215	−0.741073	−	0.671425i	$-0.765683\pi$
$11$	−4.91572	−1.48215	−0.741073	+	0.671425i	$0.765683\pi$
$12$	2.60081	0.750791
$13$	1.88493	0.522786	0.261393	−	0.965233i	$-0.415818\pi$
$13$	1.88493	0.522786	0.261393	+	0.965233i	$0.415818\pi$
$14$	1.30512	0.348807
$15$	2.64432	0.682761
$16$	1.00000	0.250000
$17$	−1.77495	−0.430489	−0.215244	−	0.976560i	$-0.569055\pi$
$17$	−1.77495	−0.430489	−0.215244	+	0.976560i	$0.569055\pi$
$18$	−3.76424	−0.887239
$19$	−6.72737	−1.54336	−0.771682	−	0.636008i	$-0.780584\pi$
$19$	−6.72737	−1.54336	−0.771682	+	0.636008i	$0.780584\pi$
$20$	1.01673	0.227347
$21$	−3.39437	−0.740712
$22$	4.91572	1.04804
$23$	3.89860	0.812914	0.406457	−	0.913670i	$-0.366764\pi$
$23$	3.89860	0.812914	0.406457	+	0.913670i	$0.366764\pi$
$24$	−2.60081	−0.530889
$25$	−3.96626	−0.793253
$26$	−1.88493	−0.369665
$27$	1.98764	0.382521
$28$	−1.30512	−0.246644
$29$	−1.47458	−0.273823	−0.136911	−	0.990583i	$-0.543718\pi$
$29$	−1.47458	−0.273823	−0.136911	+	0.990583i	$0.543718\pi$
$30$	−2.64432	−0.482785
$31$	−2.87638	−0.516614	−0.258307	−	0.966063i	$-0.583165\pi$
$31$	−2.87638	−0.516614	−0.258307	+	0.966063i	$0.583165\pi$
$32$	−1.00000	−0.176777
$33$	−12.7849	−2.22556
$34$	1.77495	0.304402
$35$	−1.32695	−0.224295
$36$	3.76424	0.627373
$37$	−8.51268	−1.39948	−0.699738	−	0.714399i	$-0.746700\pi$
$37$	−8.51268	−1.39948	−0.699738	+	0.714399i	$0.746700\pi$
$38$	6.72737	1.09132
$39$	4.90235	0.785005
$40$	−1.01673	−0.160759
$41$	5.85833	0.914917	0.457459	−	0.889231i	$-0.348760\pi$
$41$	5.85833	0.914917	0.457459	+	0.889231i	$0.348760\pi$
$42$	3.39437	0.523763
$43$	−1.52639	−0.232773	−0.116386	−	0.993204i	$-0.537131\pi$
$43$	−1.52639	−0.232773	−0.116386	+	0.993204i	$0.537131\pi$
$44$	−4.91572	−0.741073
$45$	3.82720	0.570526
$46$	−3.89860	−0.574817
$47$	−1.16716	−0.170248	−0.0851238	−	0.996370i	$-0.527129\pi$
$47$	−1.16716	−0.170248	−0.0851238	+	0.996370i	$0.527129\pi$
$48$	2.60081	0.375395
$49$	−5.29667	−0.756667
$50$	3.96626	0.560914
$51$	−4.61632	−0.646414
$52$	1.88493	0.261393
$53$	−3.42899	−0.471007	−0.235504	−	0.971873i	$-0.575674\pi$
$53$	−3.42899	−0.471007	−0.235504	+	0.971873i	$0.575674\pi$
$54$	−1.98764	−0.270483
$55$	−4.99795	−0.673924
$56$	1.30512	0.174404
$57$	−17.4966	−2.31749
$58$	1.47458	0.193622
$59$	−3.61230	−0.470282	−0.235141	−	0.971961i	$-0.575555\pi$
$59$	−3.61230	−0.470282	−0.235141	+	0.971961i	$0.575555\pi$
$60$	2.64432	0.341380
$61$	5.74092	0.735049	0.367525	−	0.930014i	$-0.380205\pi$
$61$	5.74092	0.735049	0.367525	+	0.930014i	$0.380205\pi$
$62$	2.87638	0.365301
$63$	−4.91277	−0.618951
$64$	1.00000	0.125000
$65$	1.91646	0.237708
$66$	12.7849	1.57371
$67$	−4.91185	−0.600078	−0.300039	−	0.953927i	$-0.597000\pi$
$67$	−4.91185	−0.600078	−0.300039	+	0.953927i	$0.597000\pi$
$68$	−1.77495	−0.215244
$69$	10.1395	1.22066
$70$	1.32695	0.158601
$71$	−2.27572	−0.270078	−0.135039	−	0.990840i	$-0.543116\pi$
$71$	−2.27572	−0.270078	−0.135039	+	0.990840i	$0.543116\pi$
$72$	−3.76424	−0.443620
$73$	4.06233	0.475459	0.237730	−	0.971331i	$-0.423597\pi$
$73$	4.06233	0.475459	0.237730	+	0.971331i	$0.423597\pi$
$74$	8.51268	0.989580
$75$	−10.3155	−1.19113
$76$	−6.72737	−0.771682
$77$	6.41560	0.731125
$78$	−4.90235	−0.555082
$79$	8.00999	0.901194	0.450597	−	0.892727i	$-0.351211\pi$
$79$	8.00999	0.901194	0.450597	+	0.892727i	$0.351211\pi$
$80$	1.01673	0.113674
$81$	−6.12323	−0.680359
$82$	−5.85833	−0.646944
$83$	2.78614	0.305819	0.152910	−	0.988240i	$-0.451136\pi$
$83$	2.78614	0.305819	0.152910	+	0.988240i	$0.451136\pi$
$84$	−3.39437	−0.370356
$85$	−1.80464	−0.195741
$86$	1.52639	0.164595
$87$	−3.83511	−0.411167
$88$	4.91572	0.524018
$89$	5.76902	0.611515	0.305757	−	0.952109i	$-0.401090\pi$
$89$	5.76902	0.611515	0.305757	+	0.952109i	$0.401090\pi$
$90$	−3.82720	−0.403423
$91$	−2.46006	−0.257884
$92$	3.89860	0.406457
$93$	−7.48094	−0.775737
$94$	1.16716	0.120383
$95$	−6.83991	−0.701760
$96$	−2.60081	−0.265445
$97$	−0.273900	−0.0278103	−0.0139052	−	0.999903i	$-0.504426\pi$
$97$	−0.273900	−0.0278103	−0.0139052	+	0.999903i	$0.504426\pi$
$98$	5.29667	0.535044
$99$	−18.5039	−1.85972
$100$	−3.96626	−0.396626
$101$	−16.9269	−1.68429	−0.842145	−	0.539251i	$-0.818707\pi$
$101$	−16.9269	−1.68429	−0.842145	+	0.539251i	$0.818707\pi$
$102$	4.61632	0.457084
$103$	14.8948	1.46763	0.733813	−	0.679351i	$-0.237739\pi$
$103$	14.8948	1.46763	0.733813	+	0.679351i	$0.237739\pi$
$104$	−1.88493	−0.184833
$105$	−3.45115	−0.336798
$106$	3.42899	0.333053
$107$	−3.13225	−0.302806	−0.151403	−	0.988472i	$-0.548379\pi$
$107$	−3.13225	−0.302806	−0.151403	+	0.988472i	$0.548379\pi$
$108$	1.98764	0.191261
$109$	−0.122582	−0.0117412	−0.00587061	−	0.999983i	$-0.501869\pi$
$109$	−0.122582	−0.0117412	−0.00587061	+	0.999983i	$0.501869\pi$
$110$	4.99795	0.476536
$111$	−22.1399	−2.10143
$112$	−1.30512	−0.123322
$113$	−16.5277	−1.55480	−0.777400	−	0.629007i	$-0.783462\pi$
$113$	−16.5277	−1.55480	−0.777400	+	0.629007i	$0.783462\pi$
$114$	17.4966	1.63871
$115$	3.96381	0.369628
$116$	−1.47458	−0.136911
$117$	7.09532	0.655963
$118$	3.61230	0.332539
$119$	2.31652	0.212355
$120$	−2.64432	−0.241392
$121$	13.1643	1.19676
$122$	−5.74092	−0.519758
$123$	15.2364	1.37382
$124$	−2.87638	−0.258307
$125$	−9.11625	−0.815382
$126$	4.91277	0.437665
$127$	19.5424	1.73411	0.867053	−	0.498217i	$-0.166012\pi$
$127$	19.5424	1.73411	0.867053	+	0.498217i	$0.166012\pi$
$128$	−1.00000	−0.0883883
$129$	−3.96986	−0.349527
$130$	−1.91646	−0.168085
$131$	2.09688	0.183205	0.0916024	−	0.995796i	$-0.470801\pi$
$131$	2.09688	0.183205	0.0916024	+	0.995796i	$0.470801\pi$
$132$	−12.7849	−1.11278
$133$	8.78001	0.761324
$134$	4.91185	0.424319
$135$	2.02089	0.173930
$136$	1.77495	0.152201
$137$	−16.9422	−1.44747	−0.723733	−	0.690080i	$-0.757575\pi$
$137$	−16.9422	−1.44747	−0.723733	+	0.690080i	$0.757575\pi$
$138$	−10.1395	−0.863134
$139$	−6.48289	−0.549871	−0.274936	−	0.961463i	$-0.588657\pi$
$139$	−6.48289	−0.549871	−0.274936	+	0.961463i	$0.588657\pi$
$140$	−1.32695	−0.112148
$141$	−3.03556	−0.255641
$142$	2.27572	0.190974
$143$	−9.26579	−0.774844
$144$	3.76424	0.313686
$145$	−1.49925	−0.124506
$146$	−4.06233	−0.336201
$147$	−13.7756	−1.13620
$148$	−8.51268	−0.699738
$149$	−16.1184	−1.32047	−0.660234	−	0.751060i	$-0.729543\pi$
$149$	−16.1184	−1.32047	−0.660234	+	0.751060i	$0.729543\pi$
$150$	10.3155	0.842259
$151$	7.65139	0.622661	0.311330	−	0.950302i	$-0.399225\pi$
$151$	7.65139	0.622661	0.311330	+	0.950302i	$0.399225\pi$
$152$	6.72737	0.545662
$153$	−6.68133	−0.540154
$154$	−6.41560	−0.516983
$155$	−2.92450	−0.234901
$156$	4.90235	0.392502
$157$	−10.4076	−0.830615	−0.415308	−	0.909681i	$-0.636326\pi$
$157$	−10.4076	−0.830615	−0.415308	+	0.909681i	$0.636326\pi$
$158$	−8.00999	−0.637240
$159$	−8.91816	−0.707256
$160$	−1.01673	−0.0803794
$161$	−5.08813	−0.401001
$162$	6.12323	0.481087
$163$	4.03622	0.316141	0.158071	−	0.987428i	$-0.449473\pi$
$163$	4.03622	0.316141	0.158071	+	0.987428i	$0.449473\pi$
$164$	5.85833	0.457459
$165$	−12.9987	−1.01195
$166$	−2.78614	−0.216247
$167$	4.17551	0.323111	0.161555	−	0.986864i	$-0.448349\pi$
$167$	4.17551	0.323111	0.161555	+	0.986864i	$0.448349\pi$
$168$	3.39437	0.261881
$169$	−9.44704	−0.726695
$170$	1.80464	0.138410
$171$	−25.3234	−1.93653
$172$	−1.52639	−0.116386
$173$	8.47705	0.644498	0.322249	−	0.946655i	$-0.395561\pi$
$173$	8.47705	0.644498	0.322249	+	0.946655i	$0.395561\pi$
$174$	3.83511	0.290739
$175$	5.17644	0.391302
$176$	−4.91572	−0.370536
$177$	−9.39493	−0.706166
$178$	−5.76902	−0.432406
$179$	7.22672	0.540151	0.270075	−	0.962839i	$-0.412951\pi$
$179$	7.22672	0.540151	0.270075	+	0.962839i	$0.412951\pi$
$180$	3.82720	0.285263
$181$	22.6958	1.68697	0.843483	−	0.537155i	$-0.180501\pi$
$181$	22.6958	1.68697	0.843483	+	0.537155i	$0.180501\pi$
$182$	2.46006	0.182352
$183$	14.9311	1.10374
$184$	−3.89860	−0.287409
$185$	−8.65508	−0.636334
$186$	7.48094	0.548529
$187$	8.72516	0.638047
$188$	−1.16716	−0.0851238
$189$	−2.59410	−0.188693
$190$	6.83991	0.496219
$191$	2.20843	0.159796	0.0798982	−	0.996803i	$-0.474540\pi$
$191$	2.20843	0.159796	0.0798982	+	0.996803i	$0.474540\pi$
$192$	2.60081	0.187698
$193$	−11.8884	−0.855747	−0.427873	−	0.903839i	$-0.640737\pi$
$193$	−11.8884	−0.855747	−0.427873	+	0.903839i	$0.640737\pi$
$194$	0.273900	0.0196649
$195$	4.98436	0.356937
$196$	−5.29667	−0.378333
$197$	−19.4329	−1.38454	−0.692269	−	0.721640i	$-0.743389\pi$
$197$	−19.4329	−1.38454	−0.692269	+	0.721640i	$0.743389\pi$
$198$	18.5039	1.31502
$199$	0.899039	0.0637312	0.0318656	−	0.999492i	$-0.489855\pi$
$199$	0.899039	0.0637312	0.0318656	+	0.999492i	$0.489855\pi$
$200$	3.96626	0.280457
$201$	−12.7748	−0.901066
$202$	16.9269	1.19097
$203$	1.92450	0.135073
$204$	−4.61632	−0.323207
$205$	5.95633	0.416008
$206$	−14.8948	−1.03777
$207$	14.6752	1.02000
$208$	1.88493	0.130696
$209$	33.0699	2.28749
$210$	3.45115	0.238152
$211$	24.6698	1.69834	0.849168	−	0.528123i	$-0.177104\pi$
$211$	24.6698	1.69834	0.849168	+	0.528123i	$0.177104\pi$
$212$	−3.42899	−0.235504
$213$	−5.91873	−0.405545
$214$	3.13225	0.214116
$215$	−1.55193	−0.105840
$216$	−1.98764	−0.135242
$217$	3.75402	0.254839
$218$	0.122582	0.00830229
$219$	10.5654	0.713941
$220$	−4.99795	−0.336962
$221$	−3.34566	−0.225053
$222$	22.1399	1.48593
$223$	15.8909	1.06413	0.532065	−	0.846703i	$-0.321416\pi$
$223$	15.8909	1.06413	0.532065	+	0.846703i	$0.321416\pi$
$224$	1.30512	0.0872019
$225$	−14.9300	−0.995330
$226$	16.5277	1.09941
$227$	−13.0476	−0.866001	−0.433001	−	0.901394i	$-0.642545\pi$
$227$	−13.0476	−0.866001	−0.433001	+	0.901394i	$0.642545\pi$
$228$	−17.4966	−1.15874
$229$	−26.4533	−1.74808	−0.874040	−	0.485853i	$-0.838509\pi$
$229$	−26.4533	−1.74808	−0.874040	+	0.485853i	$0.838509\pi$
$230$	−3.96381	−0.261366
$231$	16.6858	1.09784
$232$	1.47458	0.0968109
$233$	11.1623	0.731267	0.365634	−	0.930759i	$-0.380852\pi$
$233$	11.1623	0.731267	0.365634	+	0.930759i	$0.380852\pi$
$234$	−7.09532	−0.463836
$235$	−1.18668	−0.0774107
$236$	−3.61230	−0.235141
$237$	20.8325	1.35322
$238$	−2.31652	−0.150158
$239$	−8.78489	−0.568248	−0.284124	−	0.958788i	$-0.591703\pi$
$239$	−8.78489	−0.568248	−0.284124	+	0.958788i	$0.591703\pi$
$240$	2.64432	0.170690
$241$	27.0438	1.74205	0.871023	−	0.491242i	$-0.163457\pi$
$241$	27.0438	1.74205	0.871023	+	0.491242i	$0.163457\pi$
$242$	−13.1643	−0.846234
$243$	−21.8883	−1.40414
$244$	5.74092	0.367525
$245$	−5.38527	−0.344052
$246$	−15.2364	−0.971439
$247$	−12.6806	−0.806849
$248$	2.87638	0.182650
$249$	7.24625	0.459212
$250$	9.11625	0.576562
$251$	24.9162	1.57270	0.786350	−	0.617782i	$-0.211968\pi$
$251$	24.9162	1.57270	0.786350	+	0.617782i	$0.211968\pi$
$252$	−4.91277	−0.309476
$253$	−19.1644	−1.20486
$254$	−19.5424	−1.22620
$255$	−4.69354	−0.293921
$256$	1.00000	0.0625000
$257$	−15.5805	−0.971884	−0.485942	−	0.873991i	$-0.661523\pi$
$257$	−15.5805	−0.971884	−0.485942	+	0.873991i	$0.661523\pi$
$258$	3.96986	0.247153
$259$	11.1101	0.690345
$260$	1.91646	0.118854
$261$	−5.55067	−0.343578
$262$	−2.09688	−0.129545
$263$	31.0060	1.91191	0.955955	−	0.293515i	$-0.0948250\pi$
$263$	31.0060	1.91191	0.955955	+	0.293515i	$0.0948250\pi$
$264$	12.7849	0.786855
$265$	−3.48635	−0.214164
$266$	−8.78001	−0.538337
$267$	15.0042	0.918239
$268$	−4.91185	−0.300039
$269$	7.46760	0.455308	0.227654	−	0.973742i	$-0.426895\pi$
$269$	7.46760	0.455308	0.227654	+	0.973742i	$0.426895\pi$
$270$	−2.02089	−0.122987
$271$	−0.209410	−0.0127208	−0.00636038	−	0.999980i	$-0.502025\pi$
$271$	−0.209410	−0.0127208	−0.00636038	+	0.999980i	$0.502025\pi$
$272$	−1.77495	−0.107622
$273$	−6.39815	−0.387234
$274$	16.9422	1.02351
$275$	19.4970	1.17572
$276$	10.1395	0.610328
$277$	−27.7330	−1.66631	−0.833156	−	0.553038i	$-0.813468\pi$
$277$	−27.7330	−1.66631	−0.833156	+	0.553038i	$0.813468\pi$
$278$	6.48289	0.388818
$279$	−10.8274	−0.648219
$280$	1.32695	0.0793004
$281$	−18.8377	−1.12376	−0.561881	−	0.827218i	$-0.689922\pi$
$281$	−18.8377	−1.12376	−0.561881	+	0.827218i	$0.689922\pi$
$282$	3.03556	0.180765
$283$	−13.8864	−0.825460	−0.412730	−	0.910853i	$-0.635425\pi$
$283$	−13.8864	−0.825460	−0.412730	+	0.910853i	$0.635425\pi$
$284$	−2.27572	−0.135039
$285$	−17.7893	−1.05375
$286$	9.26579	0.547898
$287$	−7.64581	−0.451318
$288$	−3.76424	−0.221810
$289$	−13.8495	−0.814679
$290$	1.49925	0.0880388
$291$	−0.712363	−0.0417595
$292$	4.06233	0.237730
$293$	25.2296	1.47393	0.736963	−	0.675933i	$-0.236259\pi$
$293$	25.2296	1.47393	0.736963	+	0.675933i	$0.236259\pi$
$294$	13.7756	0.803412
$295$	−3.67273	−0.213835
$296$	8.51268	0.494790
$297$	−9.77067	−0.566952
$298$	16.1184	0.933711
$299$	7.34859	0.424980
$300$	−10.3155	−0.595567
$301$	1.99212	0.114824
$302$	−7.65139	−0.440288
$303$	−44.0237	−2.52910
$304$	−6.72737	−0.385841
$305$	5.83695	0.334223
$306$	6.68133	0.381946
$307$	23.1670	1.32221	0.661104	−	0.750294i	$-0.270088\pi$
$307$	23.1670	1.32221	0.661104	+	0.750294i	$0.270088\pi$
$308$	6.41560	0.365563
$309$	38.7386	2.20376
$310$	2.92450	0.166100
$311$	−2.86543	−0.162483	−0.0812417	−	0.996694i	$-0.525889\pi$
$311$	−2.86543	−0.162483	−0.0812417	+	0.996694i	$0.525889\pi$
$312$	−4.90235	−0.277541
$313$	11.1500	0.630233	0.315117	−	0.949053i	$-0.397956\pi$
$313$	11.1500	0.630233	0.315117	+	0.949053i	$0.397956\pi$
$314$	10.4076	0.587334
$315$	−4.99495	−0.281434
$316$	8.00999	0.450597
$317$	−16.2697	−0.913798	−0.456899	−	0.889519i	$-0.651040\pi$
$317$	−16.2697	−0.913798	−0.456899	+	0.889519i	$0.651040\pi$
$318$	8.91816	0.500105
$319$	7.24862	0.405845
$320$	1.01673	0.0568368
$321$	−8.14641	−0.454688
$322$	5.08813	0.283551
$323$	11.9408	0.664401
$324$	−6.12323	−0.340180
$325$	−7.47613	−0.414701
$326$	−4.03622	−0.223545
$327$	−0.318813	−0.0176304
$328$	−5.85833	−0.323472
$329$	1.52328	0.0839812
$330$	12.9987	0.715557
$331$	−3.36191	−0.184787	−0.0923936	−	0.995723i	$-0.529452\pi$
$331$	−3.36191	−0.184787	−0.0923936	+	0.995723i	$0.529452\pi$
$332$	2.78614	0.152910
$333$	−32.0438	−1.75599
$334$	−4.17551	−0.228474
$335$	−4.99402	−0.272852
$336$	−3.39437	−0.185178
$337$	−15.0365	−0.819091	−0.409545	−	0.912290i	$-0.634313\pi$
$337$	−15.0365	−0.819091	−0.409545	+	0.912290i	$0.634313\pi$
$338$	9.44704	0.513851
$339$	−42.9856	−2.33466
$340$	−1.80464	−0.0978705
$341$	14.1395	0.765696
$342$	25.3234	1.36933
$343$	16.0486	0.866543
$344$	1.52639	0.0822976
$345$	10.3091	0.555026
$346$	−8.47705	−0.455729
$347$	−33.3820	−1.79204	−0.896019	−	0.444017i	$-0.853553\pi$
$347$	−33.3820	−1.79204	−0.896019	+	0.444017i	$0.853553\pi$
$348$	−3.83511	−0.205583
$349$	37.1101	1.98646	0.993230	−	0.116163i	$-0.0370593\pi$
$349$	37.1101	1.98646	0.993230	+	0.116163i	$0.0370593\pi$
$350$	−5.17644	−0.276693
$351$	3.74656	0.199976
$352$	4.91572	0.262009
$353$	9.92411	0.528207	0.264103	−	0.964494i	$-0.414924\pi$
$353$	9.92411	0.528207	0.264103	+	0.964494i	$0.414924\pi$
$354$	9.39493	0.499335
$355$	−2.31379	−0.122803
$356$	5.76902	0.305757
$357$	6.02484	0.318868
$358$	−7.22672	−0.381944
$359$	25.7788	1.36056	0.680278	−	0.732955i	$-0.261859\pi$
$359$	25.7788	1.36056	0.680278	+	0.732955i	$0.261859\pi$
$360$	−3.82720	−0.201711
$361$	26.2575	1.38197
$362$	−22.6958	−1.19287
$363$	34.2379	1.79703
$364$	−2.46006	−0.128942
$365$	4.13028	0.216189
$366$	−14.9311	−0.780459
$367$	18.8048	0.981604	0.490802	−	0.871271i	$-0.336704\pi$
$367$	18.8048	0.981604	0.490802	+	0.871271i	$0.336704\pi$
$368$	3.89860	0.203229
$369$	22.0521	1.14799
$370$	8.65508	0.449956
$371$	4.47523	0.232342
$372$	−7.48094	−0.387869
$373$	−14.6950	−0.760880	−0.380440	−	0.924806i	$-0.624227\pi$
$373$	−14.6950	−0.760880	−0.380440	+	0.924806i	$0.624227\pi$
$374$	−8.72516	−0.451167
$375$	−23.7097	−1.22436
$376$	1.16716	0.0601916
$377$	−2.77948	−0.143150
$378$	2.59410	0.133426
$379$	−0.989555	−0.0508300	−0.0254150	−	0.999677i	$-0.508091\pi$
$379$	−0.989555	−0.0508300	−0.0254150	+	0.999677i	$0.508091\pi$
$380$	−6.83991	−0.350880
$381$	50.8261	2.60390
$382$	−2.20843	−0.112993
$383$	1.08838	0.0556138	0.0278069	−	0.999613i	$-0.491148\pi$
$383$	1.08838	0.0556138	0.0278069	+	0.999613i	$0.491148\pi$
$384$	−2.60081	−0.132722
$385$	6.52292	0.332439
$386$	11.8884	0.605104
$387$	−5.74570	−0.292070
$388$	−0.273900	−0.0139052
$389$	3.97484	0.201533	0.100766	−	0.994910i	$-0.467871\pi$
$389$	3.97484	0.201533	0.100766	+	0.994910i	$0.467871\pi$
$390$	−4.98436	−0.252393
$391$	−6.91982	−0.349950
$392$	5.29667	0.267522
$393$	5.45358	0.275097
$394$	19.4329	0.979016
$395$	8.14398	0.409768
$396$	−18.5039	−0.929858
$397$	−19.8504	−0.996261	−0.498131	−	0.867102i	$-0.665980\pi$
$397$	−19.8504	−0.996261	−0.498131	+	0.867102i	$0.665980\pi$
$398$	−0.899039	−0.0450648
$399$	22.8352	1.14319
$400$	−3.96626	−0.198313
$401$	6.88337	0.343739	0.171869	−	0.985120i	$-0.445019\pi$
$401$	6.88337	0.343739	0.171869	+	0.985120i	$0.445019\pi$
$402$	12.7748	0.637150
$403$	−5.42178	−0.270078
$404$	−16.9269	−0.842145
$405$	−6.22566	−0.309356
$406$	−1.92450	−0.0955113
$407$	41.8460	2.07423
$408$	4.61632	0.228542
$409$	30.4728	1.50678	0.753392	−	0.657572i	$-0.228416\pi$
$409$	30.4728	1.50678	0.753392	+	0.657572i	$0.228416\pi$
$410$	−5.95633	−0.294162
$411$	−44.0634	−2.17349
$412$	14.8948	0.733813
$413$	4.71448	0.231985
$414$	−14.6752	−0.721249
$415$	2.83275	0.139054
$416$	−1.88493	−0.0924163
$417$	−16.8608	−0.825676
$418$	−33.0699	−1.61750
$419$	−14.4782	−0.707304	−0.353652	−	0.935377i	$-0.615060\pi$
$419$	−14.4782	−0.707304	−0.353652	+	0.935377i	$0.615060\pi$
$420$	−3.45115	−0.168399
$421$	−22.1946	−1.08170	−0.540850	−	0.841119i	$-0.681897\pi$
$421$	−22.1946	−1.08170	−0.540850	+	0.841119i	$0.681897\pi$
$422$	−24.6698	−1.20090
$423$	−4.39346	−0.213617
$424$	3.42899	0.166526
$425$	7.03992	0.341486
$426$	5.91873	0.286763
$427$	−7.49258	−0.362591
$428$	−3.13225	−0.151403
$429$	−24.0986	−1.16349
$430$	1.55193	0.0748405
$431$	1.73382	0.0835150	0.0417575	−	0.999128i	$-0.486704\pi$
$431$	1.73382	0.0835150	0.0417575	+	0.999128i	$0.486704\pi$
$432$	1.98764	0.0956303
$433$	17.2554	0.829243	0.414621	−	0.909994i	$-0.363914\pi$
$433$	17.2554	0.829243	0.414621	+	0.909994i	$0.363914\pi$
$434$	−3.75402	−0.180199
$435$	−3.89926	−0.186955
$436$	−0.122582	−0.00587061
$437$	−26.2273	−1.25462
$438$	−10.5654	−0.504832
$439$	14.5508	0.694472	0.347236	−	0.937778i	$-0.387120\pi$
$439$	14.5508	0.694472	0.347236	+	0.937778i	$0.387120\pi$
$440$	4.99795	0.238268
$441$	−19.9379	−0.949424
$442$	3.34566	0.159137
$443$	−24.2057	−1.15005	−0.575023	−	0.818137i	$-0.695007\pi$
$443$	−24.2057	−1.15005	−0.575023	+	0.818137i	$0.695007\pi$
$444$	−22.1399	−1.05071
$445$	5.86552	0.278053
$446$	−15.8909	−0.752454
$447$	−41.9209	−1.98279
$448$	−1.30512	−0.0616610
$449$	28.4576	1.34300	0.671499	−	0.741006i	$-0.265651\pi$
$449$	28.4576	1.34300	0.671499	+	0.741006i	$0.265651\pi$
$450$	14.9300	0.703805
$451$	−28.7979	−1.35604
$452$	−16.5277	−0.777400
$453$	19.8998	0.934976
$454$	13.0476	0.612355
$455$	−2.50121	−0.117258
$456$	17.4966	0.819355
$457$	12.9516	0.605848	0.302924	−	0.953015i	$-0.402037\pi$
$457$	12.9516	0.605848	0.302924	+	0.953015i	$0.402037\pi$
$458$	26.4533	1.23608
$459$	−3.52796	−0.164671
$460$	3.96381	0.184814
$461$	−34.7331	−1.61768	−0.808842	−	0.588026i	$-0.799905\pi$
$461$	−34.7331	−1.61768	−0.808842	+	0.588026i	$0.799905\pi$
$462$	−16.6858	−0.776293
$463$	−17.6174	−0.818752	−0.409376	−	0.912366i	$-0.634253\pi$
$463$	−17.6174	−0.818752	−0.409376	+	0.912366i	$0.634253\pi$
$464$	−1.47458	−0.0684556
$465$	−7.60608	−0.352723
$466$	−11.1623	−0.517084
$467$	−15.9760	−0.739282	−0.369641	−	0.929175i	$-0.620519\pi$
$467$	−15.9760	−0.739282	−0.369641	+	0.929175i	$0.620519\pi$
$468$	7.09532	0.327981
$469$	6.41055	0.296012
$470$	1.18668	0.0547376
$471$	−27.0682	−1.24724
$472$	3.61230	0.166270
$473$	7.50332	0.345003
$474$	−20.8325	−0.956868
$475$	26.6825	1.22428
$476$	2.31652	0.106178
$477$	−12.9075	−0.590994
$478$	8.78489	0.401812
$479$	−31.0073	−1.41676	−0.708381	−	0.705831i	$-0.750574\pi$
$479$	−31.0073	−1.41676	−0.708381	+	0.705831i	$0.750574\pi$
$480$	−2.64432	−0.120696
$481$	−16.0458	−0.731626
$482$	−27.0438	−1.23181
$483$	−13.2333	−0.602135
$484$	13.1643	0.598378
$485$	−0.278482	−0.0126452
$486$	21.8883	0.992874
$487$	−25.3581	−1.14909	−0.574543	−	0.818475i	$-0.694820\pi$
$487$	−25.3581	−1.14909	−0.574543	+	0.818475i	$0.694820\pi$
$488$	−5.74092	−0.259879
$489$	10.4975	0.474711
$490$	5.38527	0.243282
$491$	−11.9560	−0.539565	−0.269782	−	0.962921i	$-0.586952\pi$
$491$	−11.9560	−0.539565	−0.269782	+	0.962921i	$0.586952\pi$
$492$	15.2364	0.686911
$493$	2.61731	0.117878
$494$	12.6806	0.570528
$495$	−18.8135	−0.845602
$496$	−2.87638	−0.129153
$497$	2.97009	0.133227
$498$	−7.24625	−0.324712
$499$	−2.99745	−0.134184	−0.0670921	−	0.997747i	$-0.521372\pi$
$499$	−2.99745	−0.134184	−0.0670921	+	0.997747i	$0.521372\pi$
$500$	−9.11625	−0.407691
$501$	10.8597	0.485177
$502$	−24.9162	−1.11207
$503$	−37.8596	−1.68808	−0.844038	−	0.536284i	$-0.819828\pi$
$503$	−37.8596	−1.68808	−0.844038	+	0.536284i	$0.819828\pi$
$504$	4.91277	0.218832
$505$	−17.2101	−0.765837
$506$	19.1644	0.851963
$507$	−24.5700	−1.09119
$508$	19.5424	0.867053
$509$	−33.2705	−1.47469	−0.737344	−	0.675517i	$-0.763920\pi$
$509$	−33.2705	−1.47469	−0.737344	+	0.675517i	$0.763920\pi$
$510$	4.69354	0.207833
$511$	−5.30182	−0.234539
$512$	−1.00000	−0.0441942
$513$	−13.3716	−0.590369
$514$	15.5805	0.687226
$515$	15.1439	0.667322
$516$	−3.96986	−0.174763
$517$	5.73743	0.252332
$518$	−11.1101	−0.488148
$519$	22.0472	0.967766
$520$	−1.91646	−0.0840424
$521$	−13.1761	−0.577256	−0.288628	−	0.957441i	$-0.593199\pi$
$521$	−13.1761	−0.577256	−0.288628	+	0.957441i	$0.593199\pi$
$522$	5.55067	0.242946
$523$	21.1123	0.923174	0.461587	−	0.887095i	$-0.347280\pi$
$523$	21.1123	0.923174	0.461587	+	0.887095i	$0.347280\pi$
$524$	2.09688	0.0916024
$525$	13.4630	0.587572
$526$	−31.0060	−1.35192
$527$	5.10544	0.222396
$528$	−12.7849	−0.556390
$529$	−7.80093	−0.339171
$530$	3.48635	0.151437
$531$	−13.5976	−0.590084
$532$	8.78001	0.380662
$533$	11.0425	0.478306
$534$	−15.0042	−0.649293
$535$	−3.18465	−0.137684
$536$	4.91185	0.212160
$537$	18.7954	0.811080
$538$	−7.46760	−0.321951
$539$	26.0369	1.12149
$540$	2.02089	0.0869651
$541$	29.2957	1.25952	0.629759	−	0.776790i	$-0.283154\pi$
$541$	29.2957	1.25952	0.629759	+	0.776790i	$0.283154\pi$
$542$	0.209410	0.00899493
$543$	59.0276	2.53312
$544$	1.77495	0.0761004
$545$	−0.124632	−0.00533866
$546$	6.39815	0.273816
$547$	9.14394	0.390966	0.195483	−	0.980707i	$-0.437372\pi$
$547$	9.14394	0.390966	0.195483	+	0.980707i	$0.437372\pi$
$548$	−16.9422	−0.723733
$549$	21.6102	0.922300
$550$	−19.4970	−0.831357
$551$	9.92004	0.422608
$552$	−10.1395	−0.431567
$553$	−10.4540	−0.444548
$554$	27.7330	1.17826
$555$	−22.5103	−0.955508
$556$	−6.48289	−0.274936
$557$	−17.4756	−0.740466	−0.370233	−	0.928939i	$-0.620722\pi$
$557$	−17.4756	−0.740466	−0.370233	+	0.928939i	$0.620722\pi$
$558$	10.8274	0.458360
$559$	−2.87714	−0.121690
$560$	−1.32695	−0.0560739
$561$	22.6925	0.958079
$562$	18.8377	0.794620
$563$	8.23651	0.347128	0.173564	−	0.984823i	$-0.444472\pi$
$563$	8.23651	0.347128	0.173564	+	0.984823i	$0.444472\pi$
$564$	−3.03556	−0.127820
$565$	−16.8042	−0.706959
$566$	13.8864	0.583689
$567$	7.99154	0.335613
$568$	2.27572	0.0954872
$569$	−27.2839	−1.14380	−0.571900	−	0.820323i	$-0.693793\pi$
$569$	−27.2839	−1.14380	−0.571900	+	0.820323i	$0.693793\pi$
$570$	17.7893	0.745113
$571$	−24.5821	−1.02873	−0.514365	−	0.857572i	$-0.671972\pi$
$571$	−24.5821	−1.02873	−0.514365	+	0.857572i	$0.671972\pi$
$572$	−9.26579	−0.387422
$573$	5.74372	0.239947
$574$	7.64581	0.319130
$575$	−15.4629	−0.644846
$576$	3.76424	0.156843
$577$	−6.81660	−0.283779	−0.141889	−	0.989883i	$-0.545318\pi$
$577$	−6.81660	−0.283779	−0.141889	+	0.989883i	$0.545318\pi$
$578$	13.8495	0.576065
$579$	−30.9196	−1.28497
$580$	−1.49925	−0.0622528
$581$	−3.63625	−0.150857
$582$	0.712363	0.0295284
$583$	16.8559	0.698101
$584$	−4.06233	−0.168100
$585$	7.21401	0.298263
$586$	−25.2296	−1.04222
$587$	−19.9023	−0.821456	−0.410728	−	0.911758i	$-0.634725\pi$
$587$	−19.9023	−0.821456	−0.410728	+	0.911758i	$0.634725\pi$
$588$	−13.7756	−0.568098
$589$	19.3505	0.797323
$590$	3.67273	0.151204
$591$	−50.5414	−2.07900
$592$	−8.51268	−0.349869
$593$	16.7359	0.687259	0.343630	−	0.939105i	$-0.388344\pi$
$593$	16.7359	0.687259	0.343630	+	0.939105i	$0.388344\pi$
$594$	9.77067	0.400895
$595$	2.35527	0.0965567
$596$	−16.1184	−0.660234
$597$	2.33823	0.0956976
$598$	−7.34859	−0.300506
$599$	17.0621	0.697138	0.348569	−	0.937283i	$-0.386668\pi$
$599$	17.0621	0.697138	0.348569	+	0.937283i	$0.386668\pi$
$600$	10.3155	0.421129
$601$	7.52291	0.306866	0.153433	−	0.988159i	$-0.450967\pi$
$601$	7.52291	0.306866	0.153433	+	0.988159i	$0.450967\pi$
$602$	−1.99212	−0.0811928
$603$	−18.4894	−0.752945
$604$	7.65139	0.311330
$605$	13.3845	0.544158
$606$	44.0237	1.78834
$607$	−3.66048	−0.148574	−0.0742872	−	0.997237i	$-0.523668\pi$
$607$	−3.66048	−0.148574	−0.0742872	+	0.997237i	$0.523668\pi$
$608$	6.72737	0.272831
$609$	5.00527	0.202824
$610$	−5.83695	−0.236331
$611$	−2.20001	−0.0890030
$612$	−6.68133	−0.270077
$613$	−9.63824	−0.389285	−0.194642	−	0.980874i	$-0.562355\pi$
$613$	−9.63824	−0.389285	−0.194642	+	0.980874i	$0.562355\pi$
$614$	−23.1670	−0.934942
$615$	15.4913	0.624670
$616$	−6.41560	−0.258492
$617$	17.2471	0.694342	0.347171	−	0.937802i	$-0.387142\pi$
$617$	17.2471	0.694342	0.347171	+	0.937802i	$0.387142\pi$
$618$	−38.7386	−1.55829
$619$	−26.8805	−1.08042	−0.540208	−	0.841531i	$-0.681655\pi$
$619$	−26.8805	−1.08042	−0.540208	+	0.841531i	$0.681655\pi$
$620$	−2.92450	−0.117451
$621$	7.74900	0.310957
$622$	2.86543	0.114893
$623$	−7.52925	−0.301653
$624$	4.90235	0.196251
$625$	10.5626	0.422503
$626$	−11.1500	−0.445642
$627$	86.0086	3.43485
$628$	−10.4076	−0.415308
$629$	15.1096	0.602459
$630$	4.99495	0.199004
$631$	−24.6060	−0.979551	−0.489776	−	0.871849i	$-0.662921\pi$
$631$	−24.6060	−0.979551	−0.489776	+	0.871849i	$0.662921\pi$
$632$	−8.00999	−0.318620
$633$	64.1615	2.55019
$634$	16.2697	0.646153
$635$	19.8693	0.788488
$636$	−8.91816	−0.353628
$637$	−9.98385	−0.395574
$638$	−7.24862	−0.286976
$639$	−8.56636	−0.338880
$640$	−1.01673	−0.0401897
$641$	30.8146	1.21710	0.608551	−	0.793515i	$-0.291751\pi$
$641$	30.8146	1.21710	0.608551	+	0.793515i	$0.291751\pi$
$642$	8.14641	0.321513
$643$	−37.5813	−1.48206	−0.741030	−	0.671472i	$-0.765662\pi$
$643$	−37.5813	−1.48206	−0.741030	+	0.671472i	$0.765662\pi$
$644$	−5.08813	−0.200501
$645$	−4.03627	−0.158928
$646$	−11.9408	−0.469803
$647$	−2.07724	−0.0816645	−0.0408323	−	0.999166i	$-0.513001\pi$
$647$	−2.07724	−0.0816645	−0.0408323	+	0.999166i	$0.513001\pi$
$648$	6.12323	0.240543
$649$	17.7571	0.697026
$650$	7.47613	0.293238
$651$	9.76351	0.382662
$652$	4.03622	0.158071
$653$	−5.48741	−0.214739	−0.107369	−	0.994219i	$-0.534243\pi$
$653$	−5.48741	−0.214739	−0.107369	+	0.994219i	$0.534243\pi$
$654$	0.318813	0.0124666
$655$	2.13195	0.0833022
$656$	5.85833	0.228729
$657$	15.2916	0.596581
$658$	−1.52328	−0.0593836
$659$	37.4723	1.45971	0.729856	−	0.683601i	$-0.239587\pi$
$659$	37.4723	1.45971	0.729856	+	0.683601i	$0.239587\pi$
$660$	−12.9987	−0.505975
$661$	−44.9373	−1.74786	−0.873928	−	0.486055i	$-0.838435\pi$
$661$	−44.9373	−1.74786	−0.873928	+	0.486055i	$0.838435\pi$
$662$	3.36191	0.130664
$663$	−8.70144	−0.337936
$664$	−2.78614	−0.108123
$665$	8.92688	0.346170
$666$	32.0438	1.24167
$667$	−5.74879	−0.222594
$668$	4.17551	0.161555
$669$	41.3292	1.59788
$670$	4.99402	0.192936
$671$	−28.2207	−1.08945
$672$	3.39437	0.130941
$673$	−17.2640	−0.665480	−0.332740	−	0.943019i	$-0.607973\pi$
$673$	−17.2640	−0.665480	−0.332740	+	0.943019i	$0.607973\pi$
$674$	15.0365	0.579185
$675$	−7.88350	−0.303436
$676$	−9.44704	−0.363348
$677$	−27.9729	−1.07508	−0.537542	−	0.843237i	$-0.680647\pi$
$677$	−27.9729	−1.07508	−0.537542	+	0.843237i	$0.680647\pi$
$678$	42.9856	1.65085
$679$	0.357472	0.0137185
$680$	1.80464	0.0692049
$681$	−33.9345	−1.30037
$682$	−14.1395	−0.541429
$683$	33.4202	1.27879	0.639395	−	0.768879i	$-0.279185\pi$
$683$	33.4202	1.27879	0.639395	+	0.768879i	$0.279185\pi$
$684$	−25.3234	−0.968265
$685$	−17.2256	−0.658155
$686$	−16.0486	−0.612738
$687$	−68.8000	−2.62488
$688$	−1.52639	−0.0581932
$689$	−6.46340	−0.246236
$690$	−10.3091	−0.392463
$691$	6.80772	0.258978	0.129489	−	0.991581i	$-0.458666\pi$
$691$	6.80772	0.258978	0.129489	+	0.991581i	$0.458666\pi$
$692$	8.47705	0.322249
$693$	24.1498	0.917376
$694$	33.3820	1.26716
$695$	−6.59133	−0.250024
$696$	3.83511	0.145369
$697$	−10.3982	−0.393862
$698$	−37.1101	−1.40464
$699$	29.0311	1.09806
$700$	5.17644	0.195651
$701$	7.45666	0.281634	0.140817	−	0.990036i	$-0.455027\pi$
$701$	7.45666	0.281634	0.140817	+	0.990036i	$0.455027\pi$
$702$	−3.74656	−0.141405
$703$	57.2680	2.15990
$704$	−4.91572	−0.185268
$705$	−3.08634	−0.116238
$706$	−9.92411	−0.373499
$707$	22.0916	0.830840
$708$	−9.39493	−0.353083
$709$	4.29196	0.161188	0.0805940	−	0.996747i	$-0.474318\pi$
$709$	4.29196	0.161188	0.0805940	+	0.996747i	$0.474318\pi$
$710$	2.31379	0.0868350
$711$	30.1515	1.13077
$712$	−5.76902	−0.216203
$713$	−11.2139	−0.419962
$714$	−6.02484	−0.225474
$715$	−9.42079	−0.352317
$716$	7.22672	0.270075
$717$	−22.8479	−0.853270
$718$	−25.7788	−0.962058
$719$	26.8748	1.00226	0.501131	−	0.865372i	$-0.332918\pi$
$719$	26.8748	1.00226	0.501131	+	0.865372i	$0.332918\pi$
$720$	3.82720	0.142631
$721$	−19.4395	−0.723963
$722$	−26.2575	−0.977204
$723$	70.3360	2.61582
$724$	22.6958	0.843483
$725$	5.84857	0.217210
$726$	−34.2379	−1.27069
$727$	40.7094	1.50983	0.754914	−	0.655823i	$-0.227678\pi$
$727$	40.7094	1.50983	0.754914	+	0.655823i	$0.227678\pi$
$728$	2.46006	0.0911758
$729$	−38.5577	−1.42806
$730$	−4.13028	−0.152869
$731$	2.70927	0.100206
$732$	14.9311	0.551868
$733$	21.7138	0.802019	0.401009	−	0.916074i	$-0.368660\pi$
$733$	21.7138	0.802019	0.401009	+	0.916074i	$0.368660\pi$
$734$	−18.8048	−0.694099
$735$	−14.0061	−0.516622
$736$	−3.89860	−0.143704
$737$	24.1453	0.889403
$738$	−22.0521	−0.811750
$739$	0.201172	0.00740022	0.00370011	−	0.999993i	$-0.498822\pi$
$739$	0.201172	0.00740022	0.00370011	+	0.999993i	$0.498822\pi$
$740$	−8.65508	−0.318167
$741$	−32.9799	−1.21155
$742$	−4.47523	−0.164291
$743$	−34.3205	−1.25910	−0.629548	−	0.776962i	$-0.716760\pi$
$743$	−34.3205	−1.25910	−0.629548	+	0.776962i	$0.716760\pi$
$744$	7.48094	0.274264
$745$	−16.3880	−0.600409
$746$	14.6950	0.538023
$747$	10.4877	0.383725
$748$	8.72516	0.319024
$749$	4.08796	0.149371
$750$	23.7097	0.865755
$751$	−27.0565	−0.987304	−0.493652	−	0.869659i	$-0.664338\pi$
$751$	−27.0565	−0.987304	−0.493652	+	0.869659i	$0.664338\pi$
$752$	−1.16716	−0.0425619
$753$	64.8025	2.36154
$754$	2.77948	0.101223
$755$	7.77938	0.283121
$756$	−2.59410	−0.0943466
$757$	17.1286	0.622551	0.311275	−	0.950320i	$-0.399244\pi$
$757$	17.1286	0.622551	0.311275	+	0.950320i	$0.399244\pi$
$758$	0.989555	0.0359423
$759$	−49.8431	−1.80919
$760$	6.83991	0.248109
$761$	−10.7557	−0.389893	−0.194947	−	0.980814i	$-0.562453\pi$
$761$	−10.7557	−0.389893	−0.194947	+	0.980814i	$0.562453\pi$
$762$	−50.8261	−1.84124
$763$	0.159984	0.00579180
$764$	2.20843	0.0798982
$765$	−6.79310	−0.245605
$766$	−1.08838	−0.0393249
$767$	−6.80894	−0.245857
$768$	2.60081	0.0938488
$769$	27.2802	0.983750	0.491875	−	0.870666i	$-0.336312\pi$
$769$	27.2802	0.983750	0.491875	+	0.870666i	$0.336312\pi$
$770$	−6.52292	−0.235070
$771$	−40.5220	−1.45936
$772$	−11.8884	−0.427873
$773$	−30.3705	−1.09235	−0.546176	−	0.837671i	$-0.683917\pi$
$773$	−30.3705	−1.09235	−0.546176	+	0.837671i	$0.683917\pi$
$774$	5.74570	0.206525
$775$	11.4085	0.409805
$776$	0.273900	0.00983244
$777$	28.8952	1.03661
$778$	−3.97484	−0.142505
$779$	−39.4112	−1.41205
$780$	4.98436	0.178469
$781$	11.1868	0.400296
$782$	6.91982	0.247452
$783$	−2.93093	−0.104743
$784$	−5.29667	−0.189167
$785$	−10.5817	−0.377676
$786$	−5.45358	−0.194523
$787$	2.59250	0.0924127	0.0462064	−	0.998932i	$-0.485287\pi$
$787$	2.59250	0.0924127	0.0462064	+	0.998932i	$0.485287\pi$
$788$	−19.4329	−0.692269
$789$	80.6407	2.87089
$790$	−8.14398	−0.289750
$791$	21.5707	0.766964
$792$	18.5039	0.657509
$793$	10.8212	0.384273
$794$	19.8504	0.704463
$795$	−9.06734	−0.321585
$796$	0.899039	0.0318656
$797$	−30.9639	−1.09680	−0.548400	−	0.836216i	$-0.684763\pi$
$797$	−30.9639	−1.09680	−0.548400	+	0.836216i	$0.684763\pi$
$798$	−22.8352	−0.808357
$799$	2.07165	0.0732897
$800$	3.96626	0.140229
$801$	21.7160	0.767296
$802$	−6.88337	−0.243060
$803$	−19.9693	−0.704700
$804$	−12.7748	−0.450533
$805$	−5.17325	−0.182333
$806$	5.42178	0.190974
$807$	19.4219	0.683682
$808$	16.9269	0.595486
$809$	−22.6974	−0.797996	−0.398998	−	0.916952i	$-0.630642\pi$
$809$	−22.6974	−0.797996	−0.398998	+	0.916952i	$0.630642\pi$
$810$	6.22566	0.218747
$811$	45.9250	1.61265	0.806323	−	0.591475i	$-0.201454\pi$
$811$	45.9250	1.61265	0.806323	+	0.591475i	$0.201454\pi$
$812$	1.92450	0.0675367
$813$	−0.544637	−0.0191012
$814$	−41.8460	−1.46670
$815$	4.10374	0.143748
$816$	−4.61632	−0.161603
$817$	10.2686	0.359253
$818$	−30.4728	−1.06546
$819$	−9.26023	−0.323579
$820$	5.95633	0.208004
$821$	21.5478	0.752022	0.376011	−	0.926615i	$-0.377295\pi$
$821$	21.5478	0.752022	0.376011	+	0.926615i	$0.377295\pi$
$822$	44.0634	1.53689
$823$	34.1696	1.19108	0.595539	−	0.803326i	$-0.296938\pi$
$823$	34.1696	1.19108	0.595539	+	0.803326i	$0.296938\pi$
$824$	−14.8948	−0.518884
$825$	50.7082	1.76543
$826$	−4.71448	−0.164038
$827$	−39.9219	−1.38822	−0.694110	−	0.719869i	$-0.744202\pi$
$827$	−39.9219	−1.38822	−0.694110	+	0.719869i	$0.744202\pi$
$828$	14.6752	0.510000
$829$	6.68846	0.232300	0.116150	−	0.993232i	$-0.462945\pi$
$829$	6.68846	0.232300	0.116150	+	0.993232i	$0.462945\pi$
$830$	−2.83275	−0.0983262
$831$	−72.1283	−2.50210
$832$	1.88493	0.0653482
$833$	9.40132	0.325737
$834$	16.8608	0.583841
$835$	4.24536	0.146917
$836$	33.0699	1.14375
$837$	−5.71721	−0.197616
$838$	14.4782	0.500140
$839$	−42.7770	−1.47683	−0.738413	−	0.674348i	$-0.764425\pi$
$839$	−42.7770	−1.47683	−0.738413	+	0.674348i	$0.764425\pi$
$840$	3.45115	0.119076
$841$	−26.8256	−0.925021
$842$	22.1946	0.764877
$843$	−48.9933	−1.68742
$844$	24.6698	0.849168
$845$	−9.60507	−0.330424
$846$	4.39346	0.151050
$847$	−17.1810	−0.590345
$848$	−3.42899	−0.117752
$849$	−36.1159	−1.23950
$850$	−7.03992	−0.241467
$851$	−33.1875	−1.13765
$852$	−5.91873	−0.202772
$853$	0.908650	0.0311116	0.0155558	−	0.999879i	$-0.495048\pi$
$853$	0.908650	0.0311116	0.0155558	+	0.999879i	$0.495048\pi$
$854$	7.49258	0.256391
$855$	−25.7470	−0.880530
$856$	3.13225	0.107058
$857$	17.9197	0.612125	0.306063	−	0.952011i	$-0.400988\pi$
$857$	17.9197	0.612125	0.306063	+	0.952011i	$0.400988\pi$
$858$	24.0986	0.822713
$859$	−2.09477	−0.0714727	−0.0357363	−	0.999361i	$-0.511378\pi$
$859$	−2.09477	−0.0714727	−0.0357363	+	0.999361i	$0.511378\pi$
$860$	−1.55193	−0.0529202
$861$	−19.8853	−0.677691
$862$	−1.73382	−0.0590540
$863$	−29.3800	−1.00011	−0.500053	−	0.865995i	$-0.666686\pi$
$863$	−29.3800	−1.00011	−0.500053	+	0.865995i	$0.666686\pi$
$864$	−1.98764	−0.0676208
$865$	8.61885	0.293050
$866$	−17.2554	−0.586363
$867$	−36.0201	−1.22331
$868$	3.75402	0.127420
$869$	−39.3749	−1.33570
$870$	3.89926	0.132197
$871$	−9.25850	−0.313712
$872$	0.122582	0.00415114
$873$	−1.03102	−0.0348949
$874$	26.2273	0.887152
$875$	11.8978	0.402219
$876$	10.5654	0.356970
$877$	−6.23708	−0.210611	−0.105306	−	0.994440i	$-0.533582\pi$
$877$	−6.23708	−0.210611	−0.105306	+	0.994440i	$0.533582\pi$
$878$	−14.5508	−0.491066
$879$	65.6174	2.21322
$880$	−4.99795	−0.168481
$881$	−20.7392	−0.698723	−0.349361	−	0.936988i	$-0.613601\pi$
$881$	−20.7392	−0.698723	−0.349361	+	0.936988i	$0.613601\pi$
$882$	19.9379	0.671344
$883$	40.9928	1.37952	0.689759	−	0.724039i	$-0.257716\pi$
$883$	40.9928	1.37952	0.689759	+	0.724039i	$0.257716\pi$
$884$	−3.34566	−0.112527
$885$	−9.55209	−0.321090
$886$	24.2057	0.813205
$887$	45.8821	1.54057	0.770285	−	0.637700i	$-0.220114\pi$
$887$	45.8821	1.54057	0.770285	+	0.637700i	$0.220114\pi$
$888$	22.1399	0.742967
$889$	−25.5051	−0.855414
$890$	−5.86552	−0.196613
$891$	30.1001	1.00839
$892$	15.8909	0.532065
$893$	7.85191	0.262754
$894$	41.9209	1.40204
$895$	7.34761	0.245604
$896$	1.30512	0.0436009
$897$	19.1123	0.638142
$898$	−28.4576	−0.949642
$899$	4.24145	0.141460
$900$	−14.9300	−0.497665
$901$	6.08628	0.202763
$902$	28.7979	0.958866
$903$	5.18114	0.172418
$904$	16.5277	0.549705
$905$	23.0755	0.767055
$906$	−19.8998	−0.661128
$907$	41.4015	1.37471	0.687356	−	0.726320i	$-0.258771\pi$
$907$	41.4015	1.37471	0.687356	+	0.726320i	$0.258771\pi$
$908$	−13.0476	−0.433001
$909$	−63.7169	−2.11336
$910$	2.50121	0.0829142
$911$	−24.4169	−0.808968	−0.404484	−	0.914545i	$-0.632549\pi$
$911$	−24.4169	−0.808968	−0.404484	+	0.914545i	$0.632549\pi$
$912$	−17.4966	−0.579372
$913$	−13.6959	−0.453268
$914$	−12.9516	−0.428399
$915$	15.1808	0.501863
$916$	−26.4533	−0.874040
$917$	−2.73667	−0.0903728
$918$	3.52796	0.116440
$919$	−6.79022	−0.223989	−0.111994	−	0.993709i	$-0.535724\pi$
$919$	−6.79022	−0.223989	−0.111994	+	0.993709i	$0.535724\pi$
$920$	−3.96381	−0.130683
$921$	60.2530	1.98540
$922$	34.7331	1.14387
$923$	−4.28958	−0.141193
$924$	16.6858	0.548922
$925$	33.7636	1.11014
$926$	17.6174	0.578945
$927$	56.0675	1.84150
$928$	1.47458	0.0484054
$929$	25.0513	0.821905	0.410953	−	0.911657i	$-0.365196\pi$
$929$	25.0513	0.821905	0.410953	+	0.911657i	$0.365196\pi$
$930$	7.60608	0.249413
$931$	35.6326	1.16781
$932$	11.1623	0.365634
$933$	−7.45244	−0.243982
$934$	15.9760	0.522751
$935$	8.87112	0.290117
$936$	−7.09532	−0.231918
$937$	2.87539	0.0939348	0.0469674	−	0.998896i	$-0.485044\pi$
$937$	2.87539	0.0939348	0.0469674	+	0.998896i	$0.485044\pi$
$938$	−6.41055	−0.209312
$939$	28.9990	0.946346
$940$	−1.18668	−0.0387053
$941$	−26.0676	−0.849781	−0.424890	−	0.905245i	$-0.639687\pi$
$941$	−26.0676	−0.849781	−0.424890	+	0.905245i	$0.639687\pi$
$942$	27.0682	0.881929
$943$	22.8393	0.743749
$944$	−3.61230	−0.117570
$945$	−2.63750	−0.0857977
$946$	−7.50332	−0.243954
$947$	45.4690	1.47754	0.738772	−	0.673956i	$-0.235406\pi$
$947$	45.4690	1.47754	0.738772	+	0.673956i	$0.235406\pi$
$948$	20.8325	0.676608
$949$	7.65720	0.248563
$950$	−26.6825	−0.865696
$951$	−42.3145	−1.37214
$952$	−2.31652	−0.0750789
$953$	23.4016	0.758052	0.379026	−	0.925386i	$-0.376259\pi$
$953$	23.4016	0.758052	0.379026	+	0.925386i	$0.376259\pi$
$954$	12.9075	0.417896
$955$	2.24537	0.0726586
$956$	−8.78489	−0.284124
$957$	18.8523	0.609409
$958$	31.0073	1.00180
$959$	22.1115	0.714018
$960$	2.64432	0.0853451
$961$	−22.7264	−0.733110
$962$	16.0458	0.517338
$963$	−11.7905	−0.379945
$964$	27.0438	0.871023
$965$	−12.0873	−0.389103
$966$	13.2333	0.425774
$967$	7.63521	0.245532	0.122766	−	0.992436i	$-0.460824\pi$
$967$	7.63521	0.245532	0.122766	+	0.992436i	$0.460824\pi$
$968$	−13.1643	−0.423117
$969$	31.0557	0.997652
$970$	0.278482	0.00894151
$971$	34.0414	1.09244	0.546220	−	0.837641i	$-0.316066\pi$
$971$	34.0414	1.09244	0.546220	+	0.837641i	$0.316066\pi$
$972$	−21.8883	−0.702068
$973$	8.46094	0.271245
$974$	25.3581	0.812526
$975$	−19.4440	−0.622707
$976$	5.74092	0.183762
$977$	38.2201	1.22277	0.611385	−	0.791333i	$-0.290613\pi$
$977$	38.2201	1.22277	0.611385	+	0.791333i	$0.290613\pi$
$978$	−10.4975	−0.335672
$979$	−28.3589	−0.906354
$980$	−5.38527	−0.172026
$981$	−0.461427	−0.0147322
$982$	11.9560	0.381530
$983$	18.8594	0.601522	0.300761	−	0.953700i	$-0.402759\pi$
$983$	18.8594	0.601522	0.300761	+	0.953700i	$0.402759\pi$
$984$	−15.2364	−0.485720
$985$	−19.7580	−0.629542
$986$	−2.61731	−0.0833520
$987$	3.96177	0.126105
$988$	−12.6806	−0.403424
$989$	−5.95079	−0.189224
$990$	18.8135	0.597931
$991$	−9.20345	−0.292357	−0.146179	−	0.989258i	$-0.546697\pi$
$991$	−9.20345	−0.292357	−0.146179	+	0.989258i	$0.546697\pi$
$992$	2.87638	0.0913252
$993$	−8.74370	−0.277473
$994$	−2.97009	−0.0942054
$995$	0.914078	0.0289782
$996$	7.24625	0.229606
$997$	−6.68560	−0.211735	−0.105868	−	0.994380i	$-0.533762\pi$
$997$	−6.68560	−0.211735	−0.105868	+	0.994380i	$0.533762\pi$
$998$	2.99745	0.0948826
$999$	−16.9201	−0.535329

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.g.1.36	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.g.1.36	✓	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4006 = 2 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.60081 q^{3} +1.00000 q^{4} +1.01673 q^{5} -2.60081 q^{6} -1.30512 q^{7} -1.00000 q^{8} +3.76424 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.60081 q^{3} +1.00000 q^{4} +1.01673 q^{5} -2.60081 q^{6} -1.30512 q^{7} -1.00000 q^{8} +3.76424 q^{9} -1.01673 q^{10} -4.91572 q^{11} +2.60081 q^{12} +1.88493 q^{13} +1.30512 q^{14} +2.64432 q^{15} +1.00000 q^{16} -1.77495 q^{17} -3.76424 q^{18} -6.72737 q^{19} +1.01673 q^{20} -3.39437 q^{21} +4.91572 q^{22} +3.89860 q^{23} -2.60081 q^{24} -3.96626 q^{25} -1.88493 q^{26} +1.98764 q^{27} -1.30512 q^{28} -1.47458 q^{29} -2.64432 q^{30} -2.87638 q^{31} -1.00000 q^{32} -12.7849 q^{33} +1.77495 q^{34} -1.32695 q^{35} +3.76424 q^{36} -8.51268 q^{37} +6.72737 q^{38} +4.90235 q^{39} -1.01673 q^{40} +5.85833 q^{41} +3.39437 q^{42} -1.52639 q^{43} -4.91572 q^{44} +3.82720 q^{45} -3.89860 q^{46} -1.16716 q^{47} +2.60081 q^{48} -5.29667 q^{49} +3.96626 q^{50} -4.61632 q^{51} +1.88493 q^{52} -3.42899 q^{53} -1.98764 q^{54} -4.99795 q^{55} +1.30512 q^{56} -17.4966 q^{57} +1.47458 q^{58} -3.61230 q^{59} +2.64432 q^{60} +5.74092 q^{61} +2.87638 q^{62} -4.91277 q^{63} +1.00000 q^{64} +1.91646 q^{65} +12.7849 q^{66} -4.91185 q^{67} -1.77495 q^{68} +10.1395 q^{69} +1.32695 q^{70} -2.27572 q^{71} -3.76424 q^{72} +4.06233 q^{73} +8.51268 q^{74} -10.3155 q^{75} -6.72737 q^{76} +6.41560 q^{77} -4.90235 q^{78} +8.00999 q^{79} +1.01673 q^{80} -6.12323 q^{81} -5.85833 q^{82} +2.78614 q^{83} -3.39437 q^{84} -1.80464 q^{85} +1.52639 q^{86} -3.83511 q^{87} +4.91572 q^{88} +5.76902 q^{89} -3.82720 q^{90} -2.46006 q^{91} +3.89860 q^{92} -7.48094 q^{93} +1.16716 q^{94} -6.83991 q^{95} -2.60081 q^{96} -0.273900 q^{97} +5.29667 q^{98} -18.5039 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * q^99

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