LMFDB - Embedded newform 4006.2.a.g.1.29

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			1.29
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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.65650 q^{3} +1.00000 q^{4} +0.507759 q^{5} -1.65650 q^{6} +5.04215 q^{7} -1.00000 q^{8} -0.255993 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.65650 q^{3} +1.00000 q^{4} +0.507759 q^{5} -1.65650 q^{6} +5.04215 q^{7} -1.00000 q^{8} -0.255993 q^{9} -0.507759 q^{10} -4.85605 q^{11} +1.65650 q^{12} -5.83719 q^{13} -5.04215 q^{14} +0.841106 q^{15} +1.00000 q^{16} -6.23157 q^{17} +0.255993 q^{18} +5.21613 q^{19} +0.507759 q^{20} +8.35234 q^{21} +4.85605 q^{22} +3.18261 q^{23} -1.65650 q^{24} -4.74218 q^{25} +5.83719 q^{26} -5.39357 q^{27} +5.04215 q^{28} -3.02906 q^{29} -0.841106 q^{30} -4.77706 q^{31} -1.00000 q^{32} -8.04407 q^{33} +6.23157 q^{34} +2.56020 q^{35} -0.255993 q^{36} -6.89186 q^{37} -5.21613 q^{38} -9.66933 q^{39} -0.507759 q^{40} +2.07575 q^{41} -8.35234 q^{42} -0.260359 q^{43} -4.85605 q^{44} -0.129983 q^{45} -3.18261 q^{46} +2.71856 q^{47} +1.65650 q^{48} +18.4233 q^{49} +4.74218 q^{50} -10.3226 q^{51} -5.83719 q^{52} +7.62023 q^{53} +5.39357 q^{54} -2.46570 q^{55} -5.04215 q^{56} +8.64054 q^{57} +3.02906 q^{58} -12.1775 q^{59} +0.841106 q^{60} -2.95105 q^{61} +4.77706 q^{62} -1.29075 q^{63} +1.00000 q^{64} -2.96389 q^{65} +8.04407 q^{66} -5.34473 q^{67} -6.23157 q^{68} +5.27200 q^{69} -2.56020 q^{70} -5.34818 q^{71} +0.255993 q^{72} -5.71959 q^{73} +6.89186 q^{74} -7.85544 q^{75} +5.21613 q^{76} -24.4849 q^{77} +9.66933 q^{78} +4.02298 q^{79} +0.507759 q^{80} -8.16649 q^{81} -2.07575 q^{82} -6.95919 q^{83} +8.35234 q^{84} -3.16414 q^{85} +0.260359 q^{86} -5.01765 q^{87} +4.85605 q^{88} -10.6665 q^{89} +0.129983 q^{90} -29.4320 q^{91} +3.18261 q^{92} -7.91321 q^{93} -2.71856 q^{94} +2.64854 q^{95} -1.65650 q^{96} +10.0623 q^{97} -18.4233 q^{98} +1.24311 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.65650	0.956383	0.478192	−	0.878256i	$-0.341292\pi$
$3$	1.65650	0.956383	0.478192	+	0.878256i	$0.341292\pi$
$4$	1.00000	0.500000
$5$	0.507759	0.227077	0.113538	−	0.993534i	$-0.463781\pi$
$5$	0.507759	0.227077	0.113538	+	0.993534i	$0.463781\pi$
$6$	−1.65650	−0.676265
$7$	5.04215	1.90575	0.952877	−	0.303358i	$-0.0981078\pi$
$7$	5.04215	1.90575	0.952877	+	0.303358i	$0.0981078\pi$
$8$	−1.00000	−0.353553
$9$	−0.255993	−0.0853309
$10$	−0.507759	−0.160568
$11$	−4.85605	−1.46415	−0.732077	−	0.681222i	$-0.761449\pi$
$11$	−4.85605	−1.46415	−0.732077	+	0.681222i	$0.761449\pi$
$12$	1.65650	0.478192
$13$	−5.83719	−1.61894	−0.809472	−	0.587158i	$-0.800247\pi$
$13$	−5.83719	−1.61894	−0.809472	+	0.587158i	$0.800247\pi$
$14$	−5.04215	−1.34757
$15$	0.841106	0.217173
$16$	1.00000	0.250000
$17$	−6.23157	−1.51138	−0.755689	−	0.654930i	$-0.772698\pi$
$17$	−6.23157	−1.51138	−0.755689	+	0.654930i	$0.772698\pi$
$18$	0.255993	0.0603381
$19$	5.21613	1.19666	0.598331	−	0.801249i	$-0.295831\pi$
$19$	5.21613	1.19666	0.598331	+	0.801249i	$0.295831\pi$
$20$	0.507759	0.113538
$21$	8.35234	1.82263
$22$	4.85605	1.03531
$23$	3.18261	0.663619	0.331810	−	0.943346i	$-0.392341\pi$
$23$	3.18261	0.663619	0.331810	+	0.943346i	$0.392341\pi$
$24$	−1.65650	−0.338133
$25$	−4.74218	−0.948436
$26$	5.83719	1.14477
$27$	−5.39357	−1.03799
$28$	5.04215	0.952877
$29$	−3.02906	−0.562482	−0.281241	−	0.959637i	$-0.590746\pi$
$29$	−3.02906	−0.562482	−0.281241	+	0.959637i	$0.590746\pi$
$30$	−0.841106	−0.153564
$31$	−4.77706	−0.857984	−0.428992	−	0.903308i	$-0.641131\pi$
$31$	−4.77706	−0.857984	−0.428992	+	0.903308i	$0.641131\pi$
$32$	−1.00000	−0.176777
$33$	−8.04407	−1.40029
$34$	6.23157	1.06871
$35$	2.56020	0.432753
$36$	−0.255993	−0.0426654
$37$	−6.89186	−1.13301	−0.566507	−	0.824057i	$-0.691706\pi$
$37$	−6.89186	−1.13301	−0.566507	+	0.824057i	$0.691706\pi$
$38$	−5.21613	−0.846167
$39$	−9.66933	−1.54833
$40$	−0.507759	−0.0802838
$41$	2.07575	0.324178	0.162089	−	0.986776i	$-0.448177\pi$
$41$	2.07575	0.324178	0.162089	+	0.986776i	$0.448177\pi$
$42$	−8.35234	−1.28879
$43$	−0.260359	−0.0397044	−0.0198522	−	0.999803i	$-0.506320\pi$
$43$	−0.260359	−0.0397044	−0.0198522	+	0.999803i	$0.506320\pi$
$44$	−4.85605	−0.732077
$45$	−0.129983	−0.0193767
$46$	−3.18261	−0.469250
$47$	2.71856	0.396543	0.198272	−	0.980147i	$-0.436467\pi$
$47$	2.71856	0.396543	0.198272	+	0.980147i	$0.436467\pi$
$48$	1.65650	0.239096
$49$	18.4233	2.63190
$50$	4.74218	0.670646
$51$	−10.3226	−1.44546
$52$	−5.83719	−0.809472
$53$	7.62023	1.04672	0.523360	−	0.852112i	$-0.324678\pi$
$53$	7.62023	1.04672	0.523360	+	0.852112i	$0.324678\pi$
$54$	5.39357	0.733971
$55$	−2.46570	−0.332476
$56$	−5.04215	−0.673786
$57$	8.64054	1.14447
$58$	3.02906	0.397735
$59$	−12.1775	−1.58537	−0.792686	−	0.609630i	$-0.791318\pi$
$59$	−12.1775	−1.58537	−0.792686	+	0.609630i	$0.791318\pi$
$60$	0.841106	0.108586
$61$	−2.95105	−0.377843	−0.188921	−	0.981992i	$-0.560499\pi$
$61$	−2.95105	−0.377843	−0.188921	+	0.981992i	$0.560499\pi$
$62$	4.77706	0.606687
$63$	−1.29075	−0.162620
$64$	1.00000	0.125000
$65$	−2.96389	−0.367625
$66$	8.04407	0.990156
$67$	−5.34473	−0.652963	−0.326482	−	0.945204i	$-0.605863\pi$
$67$	−5.34473	−0.652963	−0.326482	+	0.945204i	$0.605863\pi$
$68$	−6.23157	−0.755689
$69$	5.27200	0.634675
$70$	−2.56020	−0.306002
$71$	−5.34818	−0.634712	−0.317356	−	0.948307i	$-0.602795\pi$
$71$	−5.34818	−0.634712	−0.317356	+	0.948307i	$0.602795\pi$
$72$	0.255993	0.0301690
$73$	−5.71959	−0.669427	−0.334713	−	0.942320i	$-0.608640\pi$
$73$	−5.71959	−0.669427	−0.334713	+	0.942320i	$0.608640\pi$
$74$	6.89186	0.801162
$75$	−7.85544	−0.907068
$76$	5.21613	0.598331
$77$	−24.4849	−2.79032
$78$	9.66933	1.09484
$79$	4.02298	0.452621	0.226310	−	0.974055i	$-0.427334\pi$
$79$	4.02298	0.452621	0.226310	+	0.974055i	$0.427334\pi$
$80$	0.507759	0.0567692
$81$	−8.16649	−0.907388
$82$	−2.07575	−0.229228
$83$	−6.95919	−0.763870	−0.381935	−	0.924189i	$-0.624742\pi$
$83$	−6.95919	−0.763870	−0.381935	+	0.924189i	$0.624742\pi$
$84$	8.35234	0.911315
$85$	−3.16414	−0.343199
$86$	0.260359	0.0280753
$87$	−5.01765	−0.537948
$88$	4.85605	0.517657
$89$	−10.6665	−1.13064	−0.565322	−	0.824871i	$-0.691248\pi$
$89$	−10.6665	−1.13064	−0.565322	+	0.824871i	$0.691248\pi$
$90$	0.129983	0.0137014
$91$	−29.4320	−3.08531
$92$	3.18261	0.331810
$93$	−7.91321	−0.820562
$94$	−2.71856	−0.280398
$95$	2.64854	0.271734
$96$	−1.65650	−0.169066
$97$	10.0623	1.02167	0.510836	−	0.859678i	$-0.329336\pi$
$97$	10.0623	1.02167	0.510836	+	0.859678i	$0.329336\pi$
$98$	−18.4233	−1.86103
$99$	1.24311	0.124938
$100$	−4.74218	−0.474218
$101$	2.53994	0.252733	0.126367	−	0.991984i	$-0.459668\pi$
$101$	2.53994	0.252733	0.126367	+	0.991984i	$0.459668\pi$
$102$	10.3226	1.02209
$103$	−0.944556	−0.0930698	−0.0465349	−	0.998917i	$-0.514818\pi$
$103$	−0.944556	−0.0930698	−0.0465349	+	0.998917i	$0.514818\pi$
$104$	5.83719	0.572383
$105$	4.24098	0.413877
$106$	−7.62023	−0.740143
$107$	−16.1210	−1.55847	−0.779236	−	0.626730i	$-0.784393\pi$
$107$	−16.1210	−1.55847	−0.779236	+	0.626730i	$0.784393\pi$
$108$	−5.39357	−0.518996
$109$	1.81573	0.173915	0.0869575	−	0.996212i	$-0.472286\pi$
$109$	1.81573	0.173915	0.0869575	+	0.996212i	$0.472286\pi$
$110$	2.46570	0.235096
$111$	−11.4164	−1.08360
$112$	5.04215	0.476438
$113$	19.7963	1.86228	0.931142	−	0.364658i	$-0.118814\pi$
$113$	19.7963	1.86228	0.931142	+	0.364658i	$0.118814\pi$
$114$	−8.64054	−0.809260
$115$	1.61600	0.150693
$116$	−3.02906	−0.281241
$117$	1.49428	0.138146
$118$	12.1775	1.12103
$119$	−31.4205	−2.88031
$120$	−0.841106	−0.0767821
$121$	12.5812	1.14375
$122$	2.95105	0.267175
$123$	3.43849	0.310038
$124$	−4.77706	−0.428992
$125$	−4.94668	−0.442445
$126$	1.29075	0.114989
$127$	15.1940	1.34825	0.674127	−	0.738616i	$-0.264520\pi$
$127$	15.1940	1.34825	0.674127	+	0.738616i	$0.264520\pi$
$128$	−1.00000	−0.0883883
$129$	−0.431286	−0.0379726
$130$	2.96389	0.259950
$131$	−21.4484	−1.87396	−0.936978	−	0.349389i	$-0.886389\pi$
$131$	−21.4484	−1.87396	−0.936978	+	0.349389i	$0.886389\pi$
$132$	−8.04407	−0.700146
$133$	26.3005	2.28054
$134$	5.34473	0.461715
$135$	−2.73863	−0.235704
$136$	6.23157	0.534353
$137$	−2.31582	−0.197854	−0.0989271	−	0.995095i	$-0.531541\pi$
$137$	−2.31582	−0.197854	−0.0989271	+	0.995095i	$0.531541\pi$
$138$	−5.27200	−0.448783
$139$	−7.72294	−0.655051	−0.327526	−	0.944842i	$-0.606215\pi$
$139$	−7.72294	−0.655051	−0.327526	+	0.944842i	$0.606215\pi$
$140$	2.56020	0.216376
$141$	4.50331	0.379247
$142$	5.34818	0.448809
$143$	28.3457	2.37038
$144$	−0.255993	−0.0213327
$145$	−1.53803	−0.127727
$146$	5.71959	0.473356
$147$	30.5182	2.51710
$148$	−6.89186	−0.566507
$149$	1.06760	0.0874614	0.0437307	−	0.999043i	$-0.486076\pi$
$149$	1.06760	0.0874614	0.0437307	+	0.999043i	$0.486076\pi$
$150$	7.85544	0.641394
$151$	10.9029	0.887262	0.443631	−	0.896210i	$-0.353690\pi$
$151$	10.9029	0.887262	0.443631	+	0.896210i	$0.353690\pi$
$152$	−5.21613	−0.423084
$153$	1.59524	0.128967
$154$	24.4849	1.97305
$155$	−2.42559	−0.194828
$156$	−9.66933	−0.774166
$157$	−15.1578	−1.20973	−0.604863	−	0.796330i	$-0.706772\pi$
$157$	−15.1578	−1.20973	−0.604863	+	0.796330i	$0.706772\pi$
$158$	−4.02298	−0.320051
$159$	12.6230	1.00107
$160$	−0.507759	−0.0401419
$161$	16.0472	1.26470
$162$	8.16649	0.641620
$163$	16.2997	1.27669	0.638345	−	0.769750i	$-0.279619\pi$
$163$	16.2997	1.27669	0.638345	+	0.769750i	$0.279619\pi$
$164$	2.07575	0.162089
$165$	−4.08445	−0.317974
$166$	6.95919	0.540138
$167$	16.5983	1.28441	0.642206	−	0.766532i	$-0.278019\pi$
$167$	16.5983	1.28441	0.642206	+	0.766532i	$0.278019\pi$
$168$	−8.35234	−0.644397
$169$	21.0728	1.62098
$170$	3.16414	0.242678
$171$	−1.33529	−0.102112
$172$	−0.260359	−0.0198522
$173$	2.89584	0.220167	0.110083	−	0.993922i	$-0.464888\pi$
$173$	2.89584	0.220167	0.110083	+	0.993922i	$0.464888\pi$
$174$	5.01765	0.380387
$175$	−23.9108	−1.80749
$176$	−4.85605	−0.366039
$177$	−20.1720	−1.51622
$178$	10.6665	0.799486
$179$	−18.0606	−1.34991	−0.674955	−	0.737859i	$-0.735837\pi$
$179$	−18.0606	−1.34991	−0.674955	+	0.737859i	$0.735837\pi$
$180$	−0.129983	−0.00968834
$181$	25.2267	1.87508	0.937542	−	0.347873i	$-0.113096\pi$
$181$	25.2267	1.87508	0.937542	+	0.347873i	$0.113096\pi$
$182$	29.4320	2.18164
$183$	−4.88842	−0.361363
$184$	−3.18261	−0.234625
$185$	−3.49940	−0.257281
$186$	7.91321	0.580225
$187$	30.2608	2.21289
$188$	2.71856	0.198272
$189$	−27.1952	−1.97816
$190$	−2.64854	−0.192145
$191$	−0.174632	−0.0126360	−0.00631798	−	0.999980i	$-0.502011\pi$
$191$	−0.174632	−0.0126360	−0.00631798	+	0.999980i	$0.502011\pi$
$192$	1.65650	0.119548
$193$	12.8474	0.924773	0.462386	−	0.886679i	$-0.346993\pi$
$193$	12.8474	0.924773	0.462386	+	0.886679i	$0.346993\pi$
$194$	−10.0623	−0.722432
$195$	−4.90969	−0.351590
$196$	18.4233	1.31595
$197$	3.00218	0.213896	0.106948	−	0.994265i	$-0.465892\pi$
$197$	3.00218	0.213896	0.106948	+	0.994265i	$0.465892\pi$
$198$	−1.24311	−0.0883442
$199$	0.395367	0.0280268	0.0140134	−	0.999902i	$-0.495539\pi$
$199$	0.395367	0.0280268	0.0140134	+	0.999902i	$0.495539\pi$
$200$	4.74218	0.335323
$201$	−8.85358	−0.624483
$202$	−2.53994	−0.178709
$203$	−15.2730	−1.07195
$204$	−10.3226	−0.722729
$205$	1.05398	0.0736133
$206$	0.944556	0.0658103
$207$	−0.814724	−0.0566272
$208$	−5.83719	−0.404736
$209$	−25.3298	−1.75210
$210$	−4.24098	−0.292656
$211$	14.3154	0.985516	0.492758	−	0.870166i	$-0.335989\pi$
$211$	14.3154	0.985516	0.492758	+	0.870166i	$0.335989\pi$
$212$	7.62023	0.523360
$213$	−8.85928	−0.607028
$214$	16.1210	1.10201
$215$	−0.132200	−0.00901596
$216$	5.39357	0.366986
$217$	−24.0866	−1.63511
$218$	−1.81573	−0.122976
$219$	−9.47452	−0.640229
$220$	−2.46570	−0.166238
$221$	36.3749	2.44684
$222$	11.4164	0.766218
$223$	−6.78489	−0.454350	−0.227175	−	0.973854i	$-0.572949\pi$
$223$	−6.78489	−0.454350	−0.227175	+	0.973854i	$0.572949\pi$
$224$	−5.04215	−0.336893
$225$	1.21396	0.0809309
$226$	−19.7963	−1.31683
$227$	−9.89712	−0.656895	−0.328447	−	0.944522i	$-0.606525\pi$
$227$	−9.89712	−0.656895	−0.328447	+	0.944522i	$0.606525\pi$
$228$	8.64054	0.572233
$229$	13.5899	0.898046	0.449023	−	0.893520i	$-0.351772\pi$
$229$	13.5899	0.898046	0.449023	+	0.893520i	$0.351772\pi$
$230$	−1.61600	−0.106556
$231$	−40.5594	−2.66861
$232$	3.02906	0.198867
$233$	−22.7395	−1.48971	−0.744857	−	0.667224i	$-0.767482\pi$
$233$	−22.7395	−1.48971	−0.744857	+	0.667224i	$0.767482\pi$
$234$	−1.49428	−0.0976840
$235$	1.38038	0.0900458
$236$	−12.1775	−0.792686
$237$	6.66409	0.432879
$238$	31.4205	2.03669
$239$	19.4387	1.25738	0.628691	−	0.777655i	$-0.283591\pi$
$239$	19.4387	1.25738	0.628691	+	0.777655i	$0.283591\pi$
$240$	0.841106	0.0542931
$241$	−9.30394	−0.599319	−0.299660	−	0.954046i	$-0.596873\pi$
$241$	−9.30394	−0.599319	−0.299660	+	0.954046i	$0.596873\pi$
$242$	−12.5812	−0.808751
$243$	2.65287	0.170182
$244$	−2.95105	−0.188921
$245$	9.35459	0.597643
$246$	−3.43849	−0.219230
$247$	−30.4475	−1.93733
$248$	4.77706	0.303343
$249$	−11.5279	−0.730553
$250$	4.94668	0.312856
$251$	11.8796	0.749836	0.374918	−	0.927058i	$-0.377671\pi$
$251$	11.8796	0.749836	0.374918	+	0.927058i	$0.377671\pi$
$252$	−1.29075	−0.0813098
$253$	−15.4549	−0.971641
$254$	−15.1940	−0.953359
$255$	−5.24141	−0.328230
$256$	1.00000	0.0625000
$257$	−15.3695	−0.958721	−0.479360	−	0.877618i	$-0.659131\pi$
$257$	−15.3695	−0.958721	−0.479360	+	0.877618i	$0.659131\pi$
$258$	0.431286	0.0268507
$259$	−34.7498	−2.15925
$260$	−2.96389	−0.183812
$261$	0.775417	0.0479971
$262$	21.4484	1.32509
$263$	−22.2816	−1.37394	−0.686972	−	0.726684i	$-0.741060\pi$
$263$	−22.2816	−1.37394	−0.686972	+	0.726684i	$0.741060\pi$
$264$	8.04407	0.495078
$265$	3.86925	0.237686
$266$	−26.3005	−1.61259
$267$	−17.6691	−1.08133
$268$	−5.34473	−0.326482
$269$	1.13643	0.0692895	0.0346447	−	0.999400i	$-0.488970\pi$
$269$	1.13643	0.0692895	0.0346447	+	0.999400i	$0.488970\pi$
$270$	2.73863	0.166668
$271$	1.65344	0.100440	0.0502198	−	0.998738i	$-0.484008\pi$
$271$	1.65344	0.100440	0.0502198	+	0.998738i	$0.484008\pi$
$272$	−6.23157	−0.377845
$273$	−48.7542	−2.95074
$274$	2.31582	0.139904
$275$	23.0283	1.38866
$276$	5.27200	0.317337
$277$	15.0912	0.906744	0.453372	−	0.891322i	$-0.350221\pi$
$277$	15.0912	0.906744	0.453372	+	0.891322i	$0.350221\pi$
$278$	7.72294	0.463191
$279$	1.22289	0.0732126
$280$	−2.56020	−0.153001
$281$	15.3853	0.917807	0.458904	−	0.888486i	$-0.348242\pi$
$281$	15.3853	0.917807	0.458904	+	0.888486i	$0.348242\pi$
$282$	−4.50331	−0.268168
$283$	2.17251	0.129142	0.0645712	−	0.997913i	$-0.479432\pi$
$283$	2.17251	0.129142	0.0645712	+	0.997913i	$0.479432\pi$
$284$	−5.34818	−0.317356
$285$	4.38731	0.259882
$286$	−28.3457	−1.67611
$287$	10.4663	0.617803
$288$	0.255993	0.0150845
$289$	21.8325	1.28426
$290$	1.53803	0.0903164
$291$	16.6683	0.977111
$292$	−5.71959	−0.334713
$293$	−22.0532	−1.28836	−0.644181	−	0.764873i	$-0.722802\pi$
$293$	−22.0532	−1.28836	−0.644181	+	0.764873i	$0.722802\pi$
$294$	−30.5182	−1.77986
$295$	−6.18323	−0.360001
$296$	6.89186	0.400581
$297$	26.1914	1.51978
$298$	−1.06760	−0.0618446
$299$	−18.5775	−1.07436
$300$	−7.85544	−0.453534
$301$	−1.31277	−0.0756668
$302$	−10.9029	−0.627389
$303$	4.20742	0.241710
$304$	5.21613	0.299165
$305$	−1.49842	−0.0857994
$306$	−1.59524	−0.0911936
$307$	4.82059	0.275125	0.137563	−	0.990493i	$-0.456073\pi$
$307$	4.82059	0.275125	0.137563	+	0.990493i	$0.456073\pi$
$308$	−24.4849	−1.39516
$309$	−1.56466	−0.0890104
$310$	2.42559	0.137765
$311$	3.80288	0.215641	0.107821	−	0.994170i	$-0.465613\pi$
$311$	3.80288	0.215641	0.107821	+	0.994170i	$0.465613\pi$
$312$	9.66933	0.547418
$313$	−15.1708	−0.857506	−0.428753	−	0.903422i	$-0.641047\pi$
$313$	−15.1708	−0.857506	−0.428753	+	0.903422i	$0.641047\pi$
$314$	15.1578	0.855405
$315$	−0.655392	−0.0369272
$316$	4.02298	0.226310
$317$	8.05182	0.452235	0.226118	−	0.974100i	$-0.427397\pi$
$317$	8.05182	0.452235	0.226118	+	0.974100i	$0.427397\pi$
$318$	−12.6230	−0.707860
$319$	14.7093	0.823560
$320$	0.507759	0.0283846
$321$	−26.7044	−1.49050
$322$	−16.0472	−0.894274
$323$	−32.5047	−1.80861
$324$	−8.16649	−0.453694
$325$	27.6810	1.53547
$326$	−16.2997	−0.902756
$327$	3.00776	0.166329
$328$	−2.07575	−0.114614
$329$	13.7074	0.755714
$330$	4.08445	0.224842
$331$	14.3760	0.790177	0.395089	−	0.918643i	$-0.370714\pi$
$331$	14.3760	0.790177	0.395089	+	0.918643i	$0.370714\pi$
$332$	−6.95919	−0.381935
$333$	1.76426	0.0966811
$334$	−16.5983	−0.908216
$335$	−2.71384	−0.148273
$336$	8.35234	0.455658
$337$	−0.194672	−0.0106045	−0.00530224	−	0.999986i	$-0.501688\pi$
$337$	−0.194672	−0.0106045	−0.00530224	+	0.999986i	$0.501688\pi$
$338$	−21.0728	−1.14621
$339$	32.7927	1.78106
$340$	−3.16414	−0.171600
$341$	23.1976	1.25622
$342$	1.33529	0.0722042
$343$	57.5978	3.10999
$344$	0.260359	0.0140376
$345$	2.67691	0.144120
$346$	−2.89584	−0.155681
$347$	21.4859	1.15342	0.576712	−	0.816948i	$-0.304335\pi$
$347$	21.4859	1.15342	0.576712	+	0.816948i	$0.304335\pi$
$348$	−5.01765	−0.268974
$349$	−24.1285	−1.29157	−0.645785	−	0.763520i	$-0.723470\pi$
$349$	−24.1285	−1.29157	−0.645785	+	0.763520i	$0.723470\pi$
$350$	23.9108	1.27809
$351$	31.4833	1.68045
$352$	4.85605	0.258828
$353$	−15.9093	−0.846766	−0.423383	−	0.905951i	$-0.639158\pi$
$353$	−15.9093	−0.846766	−0.423383	+	0.905951i	$0.639158\pi$
$354$	20.1720	1.07213
$355$	−2.71559	−0.144128
$356$	−10.6665	−0.565322
$357$	−52.0482	−2.75468
$358$	18.0606	0.954530
$359$	−36.4640	−1.92449	−0.962247	−	0.272177i	$-0.912256\pi$
$359$	−36.4640	−1.92449	−0.962247	+	0.272177i	$0.912256\pi$
$360$	0.129983	0.00685069
$361$	8.20796	0.431998
$362$	−25.2267	−1.32588
$363$	20.8408	1.09386
$364$	−29.4320	−1.54265
$365$	−2.90417	−0.152011
$366$	4.88842	0.255522
$367$	−29.7254	−1.55165	−0.775826	−	0.630947i	$-0.782666\pi$
$367$	−29.7254	−1.55165	−0.775826	+	0.630947i	$0.782666\pi$
$368$	3.18261	0.165905
$369$	−0.531377	−0.0276624
$370$	3.49940	0.181925
$371$	38.4224	1.99479
$372$	−7.91321	−0.410281
$373$	−27.1730	−1.40696	−0.703481	−	0.710714i	$-0.748372\pi$
$373$	−27.1730	−1.40696	−0.703481	+	0.710714i	$0.748372\pi$
$374$	−30.2608	−1.56475
$375$	−8.19420	−0.423147
$376$	−2.71856	−0.140199
$377$	17.6812	0.910627
$378$	27.1952	1.39877
$379$	−28.0975	−1.44327	−0.721635	−	0.692274i	$-0.756609\pi$
$379$	−28.0975	−1.44327	−0.721635	+	0.692274i	$0.756609\pi$
$380$	2.64854	0.135867
$381$	25.1690	1.28945
$382$	0.174632	0.00893497
$383$	8.36633	0.427499	0.213750	−	0.976888i	$-0.431432\pi$
$383$	8.36633	0.427499	0.213750	+	0.976888i	$0.431432\pi$
$384$	−1.65650	−0.0845331
$385$	−12.4325	−0.633616
$386$	−12.8474	−0.653913
$387$	0.0666501	0.00338801
$388$	10.0623	0.510836
$389$	−4.83674	−0.245232	−0.122616	−	0.992454i	$-0.539128\pi$
$389$	−4.83674	−0.245232	−0.122616	+	0.992454i	$0.539128\pi$
$390$	4.90969	0.248612
$391$	−19.8326	−1.00298
$392$	−18.4233	−0.930516
$393$	−35.5294	−1.79222
$394$	−3.00218	−0.151248
$395$	2.04271	0.102780
$396$	1.24311	0.0624688
$397$	15.1427	0.759992	0.379996	−	0.924988i	$-0.375925\pi$
$397$	15.1427	0.759992	0.379996	+	0.924988i	$0.375925\pi$
$398$	−0.395367	−0.0198180
$399$	43.5669	2.18107
$400$	−4.74218	−0.237109
$401$	−20.9855	−1.04797	−0.523984	−	0.851728i	$-0.675555\pi$
$401$	−20.9855	−1.04797	−0.523984	+	0.851728i	$0.675555\pi$
$402$	8.85358	0.441576
$403$	27.8846	1.38903
$404$	2.53994	0.126367
$405$	−4.14661	−0.206047
$406$	15.2730	0.757984
$407$	33.4672	1.65891
$408$	10.3226	0.511046
$409$	−6.75915	−0.334219	−0.167109	−	0.985938i	$-0.553443\pi$
$409$	−6.75915	−0.334219	−0.167109	+	0.985938i	$0.553443\pi$
$410$	−1.05398	−0.0520525
$411$	−3.83617	−0.189224
$412$	−0.944556	−0.0465349
$413$	−61.4007	−3.02133
$414$	0.814724	0.0400415
$415$	−3.53359	−0.173457
$416$	5.83719	0.286192
$417$	−12.7931	−0.626480
$418$	25.3298	1.23892
$419$	27.1654	1.32712	0.663559	−	0.748124i	$-0.269045\pi$
$419$	27.1654	1.32712	0.663559	+	0.748124i	$0.269045\pi$
$420$	4.24098	0.206939
$421$	33.5018	1.63278	0.816390	−	0.577501i	$-0.195972\pi$
$421$	33.5018	1.63278	0.816390	+	0.577501i	$0.195972\pi$
$422$	−14.3154	−0.696865
$423$	−0.695932	−0.0338374
$424$	−7.62023	−0.370071
$425$	29.5512	1.43345
$426$	8.85928	0.429233
$427$	−14.8796	−0.720075
$428$	−16.1210	−0.779236
$429$	46.9547	2.26700
$430$	0.132200	0.00637524
$431$	6.12822	0.295186	0.147593	−	0.989048i	$-0.452847\pi$
$431$	6.12822	0.295186	0.147593	+	0.989048i	$0.452847\pi$
$432$	−5.39357	−0.259498
$433$	−3.96693	−0.190638	−0.0953191	−	0.995447i	$-0.530387\pi$
$433$	−3.96693	−0.190638	−0.0953191	+	0.995447i	$0.530387\pi$
$434$	24.0866	1.15620
$435$	−2.54776	−0.122156
$436$	1.81573	0.0869575
$437$	16.6009	0.794128
$438$	9.47452	0.452710
$439$	22.2627	1.06254	0.531270	−	0.847202i	$-0.321715\pi$
$439$	22.2627	1.06254	0.531270	+	0.847202i	$0.321715\pi$
$440$	2.46570	0.117548
$441$	−4.71622	−0.224582
$442$	−36.3749	−1.73018
$443$	−16.3653	−0.777541	−0.388770	−	0.921335i	$-0.627100\pi$
$443$	−16.3653	−0.777541	−0.388770	+	0.921335i	$0.627100\pi$
$444$	−11.4164	−0.541798
$445$	−5.41600	−0.256743
$446$	6.78489	0.321274
$447$	1.76849	0.0836466
$448$	5.04215	0.238219
$449$	15.3990	0.726726	0.363363	−	0.931648i	$-0.381629\pi$
$449$	15.3990	0.726726	0.363363	+	0.931648i	$0.381629\pi$
$450$	−1.21396	−0.0572268
$451$	−10.0800	−0.474646
$452$	19.7963	0.931142
$453$	18.0606	0.848563
$454$	9.89712	0.464495
$455$	−14.9444	−0.700602
$456$	−8.64054	−0.404630
$457$	−19.3812	−0.906613	−0.453307	−	0.891355i	$-0.649756\pi$
$457$	−19.3812	−0.906613	−0.453307	+	0.891355i	$0.649756\pi$
$458$	−13.5899	−0.635015
$459$	33.6104	1.56880
$460$	1.61600	0.0753463
$461$	−3.43011	−0.159756	−0.0798782	−	0.996805i	$-0.525453\pi$
$461$	−3.43011	−0.159756	−0.0798782	+	0.996805i	$0.525453\pi$
$462$	40.5594	1.88699
$463$	−1.28867	−0.0598894	−0.0299447	−	0.999552i	$-0.509533\pi$
$463$	−1.28867	−0.0598894	−0.0299447	+	0.999552i	$0.509533\pi$
$464$	−3.02906	−0.140620
$465$	−4.01801	−0.186331
$466$	22.7395	1.05339
$467$	−23.7459	−1.09883	−0.549415	−	0.835550i	$-0.685149\pi$
$467$	−23.7459	−1.09883	−0.549415	+	0.835550i	$0.685149\pi$
$468$	1.49428	0.0690730
$469$	−26.9489	−1.24439
$470$	−1.38038	−0.0636720
$471$	−25.1090	−1.15696
$472$	12.1775	0.560514
$473$	1.26432	0.0581334
$474$	−6.66409	−0.306092
$475$	−24.7358	−1.13496
$476$	−31.4205	−1.44016
$477$	−1.95072	−0.0893175
$478$	−19.4387	−0.889103
$479$	24.5218	1.12043	0.560215	−	0.828348i	$-0.310719\pi$
$479$	24.5218	1.12043	0.560215	+	0.828348i	$0.310719\pi$
$480$	−0.841106	−0.0383911
$481$	40.2291	1.83429
$482$	9.30394	0.423783
$483$	26.5822	1.20953
$484$	12.5812	0.571874
$485$	5.10923	0.231998
$486$	−2.65287	−0.120337
$487$	15.9913	0.724637	0.362319	−	0.932054i	$-0.381985\pi$
$487$	15.9913	0.724637	0.362319	+	0.932054i	$0.381985\pi$
$488$	2.95105	0.133588
$489$	27.0005	1.22101
$490$	−9.35459	−0.422597
$491$	−17.6834	−0.798043	−0.399021	−	0.916942i	$-0.630650\pi$
$491$	−17.6834	−0.798043	−0.399021	+	0.916942i	$0.630650\pi$
$492$	3.43849	0.155019
$493$	18.8758	0.850123
$494$	30.4475	1.36990
$495$	0.631202	0.0283704
$496$	−4.77706	−0.214496
$497$	−26.9663	−1.20960
$498$	11.5279	0.516579
$499$	−32.4087	−1.45081	−0.725406	−	0.688322i	$-0.758348\pi$
$499$	−32.4087	−1.45081	−0.725406	+	0.688322i	$0.758348\pi$
$500$	−4.94668	−0.221222
$501$	27.4951	1.22839
$502$	−11.8796	−0.530214
$503$	9.88657	0.440820	0.220410	−	0.975407i	$-0.429260\pi$
$503$	9.88657	0.440820	0.220410	+	0.975407i	$0.429260\pi$
$504$	1.29075	0.0574947
$505$	1.28968	0.0573899
$506$	15.4549	0.687054
$507$	34.9071	1.55028
$508$	15.1940	0.674127
$509$	−28.2894	−1.25391	−0.626953	−	0.779057i	$-0.715698\pi$
$509$	−28.2894	−1.25391	−0.626953	+	0.779057i	$0.715698\pi$
$510$	5.24141	0.232094
$511$	−28.8390	−1.27576
$512$	−1.00000	−0.0441942
$513$	−28.1335	−1.24213
$514$	15.3695	0.677918
$515$	−0.479607	−0.0211340
$516$	−0.431286	−0.0189863
$517$	−13.2015	−0.580600
$518$	34.7498	1.52682
$519$	4.79697	0.210564
$520$	2.96389	0.129975
$521$	−8.65732	−0.379284	−0.189642	−	0.981853i	$-0.560733\pi$
$521$	−8.65732	−0.379284	−0.189642	+	0.981853i	$0.560733\pi$
$522$	−0.775417	−0.0339391
$523$	−11.7897	−0.515526	−0.257763	−	0.966208i	$-0.582985\pi$
$523$	−11.7897	−0.515526	−0.257763	+	0.966208i	$0.582985\pi$
$524$	−21.4484	−0.936978
$525$	−39.6083	−1.72865
$526$	22.2816	0.971525
$527$	29.7686	1.29674
$528$	−8.04407	−0.350073
$529$	−12.8710	−0.559609
$530$	−3.86925	−0.168069
$531$	3.11734	0.135281
$532$	26.3005	1.14027
$533$	−12.1166	−0.524826
$534$	17.6691	0.764615
$535$	−8.18557	−0.353893
$536$	5.34473	0.230857
$537$	−29.9174	−1.29103
$538$	−1.13643	−0.0489951
$539$	−89.4643	−3.85350
$540$	−2.73863	−0.117852
$541$	−4.17866	−0.179655	−0.0898274	−	0.995957i	$-0.528632\pi$
$541$	−4.17866	−0.179655	−0.0898274	+	0.995957i	$0.528632\pi$
$542$	−1.65344	−0.0710215
$543$	41.7881	1.79330
$544$	6.23157	0.267176
$545$	0.921952	0.0394921
$546$	48.7542	2.08649
$547$	−40.8658	−1.74729	−0.873647	−	0.486561i	$-0.838251\pi$
$547$	−40.8658	−1.74729	−0.873647	+	0.486561i	$0.838251\pi$
$548$	−2.31582	−0.0989271
$549$	0.755447	0.0322417
$550$	−23.0283	−0.981928
$551$	−15.7999	−0.673100
$552$	−5.27200	−0.224391
$553$	20.2845	0.862584
$554$	−15.0912	−0.641165
$555$	−5.79678	−0.246060
$556$	−7.72294	−0.327526
$557$	26.6698	1.13003	0.565017	−	0.825079i	$-0.308869\pi$
$557$	26.6698	1.13003	0.565017	+	0.825079i	$0.308869\pi$
$558$	−1.22289	−0.0517691
$559$	1.51977	0.0642792
$560$	2.56020	0.108188
$561$	50.1272	2.11637
$562$	−15.3853	−0.648988
$563$	−15.2489	−0.642663	−0.321331	−	0.946967i	$-0.604130\pi$
$563$	−15.2489	−0.642663	−0.321331	+	0.946967i	$0.604130\pi$
$564$	4.50331	0.189624
$565$	10.0518	0.422882
$566$	−2.17251	−0.0913175
$567$	−41.1767	−1.72926
$568$	5.34818	0.224404
$569$	−14.0269	−0.588037	−0.294018	−	0.955800i	$-0.594993\pi$
$569$	−14.0269	−0.588037	−0.294018	+	0.955800i	$0.594993\pi$
$570$	−4.38731	−0.183764
$571$	11.0199	0.461168	0.230584	−	0.973052i	$-0.425936\pi$
$571$	11.0199	0.461168	0.230584	+	0.973052i	$0.425936\pi$
$572$	28.3457	1.18519
$573$	−0.289279	−0.0120848
$574$	−10.4663	−0.436853
$575$	−15.0925	−0.629401
$576$	−0.255993	−0.0106664
$577$	−31.3113	−1.30351	−0.651753	−	0.758431i	$-0.725966\pi$
$577$	−31.3113	−1.30351	−0.651753	+	0.758431i	$0.725966\pi$
$578$	−21.8325	−0.908112
$579$	21.2817	0.884437
$580$	−1.53803	−0.0638633
$581$	−35.0893	−1.45575
$582$	−16.6683	−0.690922
$583$	−37.0042	−1.53256
$584$	5.71959	0.236678
$585$	0.758733	0.0313698
$586$	22.0532	0.911010
$587$	−22.7299	−0.938163	−0.469082	−	0.883155i	$-0.655415\pi$
$587$	−22.7299	−0.938163	−0.469082	+	0.883155i	$0.655415\pi$
$588$	30.5182	1.25855
$589$	−24.9177	−1.02672
$590$	6.18323	0.254559
$591$	4.97312	0.204567
$592$	−6.89186	−0.283254
$593$	43.8551	1.80091	0.900456	−	0.434947i	$-0.143233\pi$
$593$	43.8551	1.80091	0.900456	+	0.434947i	$0.143233\pi$
$594$	−26.1914	−1.07465
$595$	−15.9541	−0.654053
$596$	1.06760	0.0437307
$597$	0.654927	0.0268044
$598$	18.5775	0.759689
$599$	5.73010	0.234126	0.117063	−	0.993125i	$-0.462652\pi$
$599$	5.73010	0.234126	0.117063	+	0.993125i	$0.462652\pi$
$600$	7.85544	0.320697
$601$	46.4522	1.89483	0.947413	−	0.320012i	$-0.103687\pi$
$601$	46.4522	1.89483	0.947413	+	0.320012i	$0.103687\pi$
$602$	1.31277	0.0535045
$603$	1.36821	0.0557179
$604$	10.9029	0.443631
$605$	6.38823	0.259719
$606$	−4.20742	−0.170915
$607$	−37.6137	−1.52669	−0.763347	−	0.645989i	$-0.776445\pi$
$607$	−37.6137	−1.52669	−0.763347	+	0.645989i	$0.776445\pi$
$608$	−5.21613	−0.211542
$609$	−25.2997	−1.02520
$610$	1.49842	0.0606693
$611$	−15.8688	−0.641982
$612$	1.59524	0.0644836
$613$	−25.1257	−1.01482	−0.507409	−	0.861705i	$-0.669397\pi$
$613$	−25.1257	−1.01482	−0.507409	+	0.861705i	$0.669397\pi$
$614$	−4.82059	−0.194543
$615$	1.74593	0.0704026
$616$	24.4849	0.986526
$617$	38.8757	1.56508	0.782539	−	0.622602i	$-0.213924\pi$
$617$	38.8757	1.56508	0.782539	+	0.622602i	$0.213924\pi$
$618$	1.56466	0.0629399
$619$	0.596485	0.0239748	0.0119874	−	0.999928i	$-0.496184\pi$
$619$	0.596485	0.0239748	0.0119874	+	0.999928i	$0.496184\pi$
$620$	−2.42559	−0.0974142
$621$	−17.1656	−0.688832
$622$	−3.80288	−0.152481
$623$	−53.7819	−2.15473
$624$	−9.66933	−0.387083
$625$	21.1992	0.847967
$626$	15.1708	0.606348
$627$	−41.9589	−1.67568
$628$	−15.1578	−0.604863
$629$	42.9471	1.71241
$630$	0.655392	0.0261115
$631$	−47.9680	−1.90957	−0.954787	−	0.297290i	$-0.903917\pi$
$631$	−47.9680	−1.90957	−0.954787	+	0.297290i	$0.903917\pi$
$632$	−4.02298	−0.160026
$633$	23.7136	0.942531
$634$	−8.05182	−0.319778
$635$	7.71492	0.306157
$636$	12.6230	0.500533
$637$	−107.540	−4.26089
$638$	−14.7093	−0.582345
$639$	1.36909	0.0541605
$640$	−0.507759	−0.0200710
$641$	−35.7115	−1.41052	−0.705260	−	0.708949i	$-0.749170\pi$
$641$	−35.7115	−1.41052	−0.705260	+	0.708949i	$0.749170\pi$
$642$	26.7044	1.05394
$643$	0.230402	0.00908616	0.00454308	−	0.999990i	$-0.498554\pi$
$643$	0.230402	0.00908616	0.00454308	+	0.999990i	$0.498554\pi$
$644$	16.0472	0.632348
$645$	−0.218990	−0.00862271
$646$	32.5047	1.27888
$647$	11.3507	0.446244	0.223122	−	0.974791i	$-0.428375\pi$
$647$	11.3507	0.446244	0.223122	+	0.974791i	$0.428375\pi$
$648$	8.16649	0.320810
$649$	59.1344	2.32123
$650$	−27.6810	−1.08574
$651$	−39.8996	−1.56379
$652$	16.2997	0.638345
$653$	48.2545	1.88834	0.944172	−	0.329454i	$-0.106865\pi$
$653$	48.2545	1.88834	0.944172	+	0.329454i	$0.106865\pi$
$654$	−3.00776	−0.117613
$655$	−10.8906	−0.425532
$656$	2.07575	0.0810445
$657$	1.46417	0.0571228
$658$	−13.7074	−0.534370
$659$	16.5376	0.644212	0.322106	−	0.946704i	$-0.395609\pi$
$659$	16.5376	0.644212	0.322106	+	0.946704i	$0.395609\pi$
$660$	−4.08445	−0.158987
$661$	28.0797	1.09217	0.546087	−	0.837728i	$-0.316117\pi$
$661$	28.0797	1.09217	0.546087	+	0.837728i	$0.316117\pi$
$662$	−14.3760	−0.558740
$663$	60.2551	2.34011
$664$	6.95919	0.270069
$665$	13.3543	0.517858
$666$	−1.76426	−0.0683639
$667$	−9.64030	−0.373274
$668$	16.5983	0.642206
$669$	−11.2392	−0.434533
$670$	2.71384	0.104845
$671$	14.3304	0.553220
$672$	−8.35234	−0.322199
$673$	−9.75083	−0.375867	−0.187933	−	0.982182i	$-0.560179\pi$
$673$	−9.75083	−0.375867	−0.187933	+	0.982182i	$0.560179\pi$
$674$	0.194672	0.00749850
$675$	25.5773	0.984469
$676$	21.0728	0.810490
$677$	−16.3160	−0.627077	−0.313538	−	0.949576i	$-0.601514\pi$
$677$	−16.3160	−0.627077	−0.313538	+	0.949576i	$0.601514\pi$
$678$	−32.7927	−1.25940
$679$	50.7357	1.94706
$680$	3.16414	0.121339
$681$	−16.3946	−0.628243
$682$	−23.1976	−0.888283
$683$	43.3942	1.66043	0.830216	−	0.557442i	$-0.188217\pi$
$683$	43.3942	1.66043	0.830216	+	0.557442i	$0.188217\pi$
$684$	−1.33529	−0.0510561
$685$	−1.17588	−0.0449281
$686$	−57.5978	−2.19910
$687$	22.5117	0.858876
$688$	−0.260359	−0.00992610
$689$	−44.4807	−1.69458
$690$	−2.67691	−0.101908
$691$	−31.4151	−1.19509	−0.597544	−	0.801836i	$-0.703857\pi$
$691$	−31.4151	−1.19509	−0.597544	+	0.801836i	$0.703857\pi$
$692$	2.89584	0.110083
$693$	6.26796	0.238100
$694$	−21.4859	−0.815594
$695$	−3.92140	−0.148747
$696$	5.01765	0.190193
$697$	−12.9352	−0.489956
$698$	24.1285	0.913277
$699$	−37.6681	−1.42474
$700$	−23.9108	−0.903743
$701$	48.3879	1.82758	0.913792	−	0.406182i	$-0.133140\pi$
$701$	48.3879	1.82758	0.913792	+	0.406182i	$0.133140\pi$
$702$	−31.4833	−1.18826
$703$	−35.9488	−1.35583
$704$	−4.85605	−0.183019
$705$	2.28660	0.0861183
$706$	15.9093	0.598754
$707$	12.8067	0.481647
$708$	−20.1720	−0.758112
$709$	40.0320	1.50343	0.751717	−	0.659485i	$-0.229226\pi$
$709$	40.0320	1.50343	0.751717	+	0.659485i	$0.229226\pi$
$710$	2.71559	0.101914
$711$	−1.02985	−0.0386226
$712$	10.6665	0.399743
$713$	−15.2035	−0.569375
$714$	52.0482	1.94786
$715$	14.3928	0.538259
$716$	−18.0606	−0.674955
$717$	32.2002	1.20254
$718$	36.4640	1.36082
$719$	9.97289	0.371926	0.185963	−	0.982557i	$-0.440460\pi$
$719$	9.97289	0.371926	0.185963	+	0.982557i	$0.440460\pi$
$720$	−0.129983	−0.00484417
$721$	−4.76259	−0.177368
$722$	−8.20796	−0.305469
$723$	−15.4120	−0.573179
$724$	25.2267	0.937542
$725$	14.3643	0.533478
$726$	−20.8408	−0.773476
$727$	24.0165	0.890724	0.445362	−	0.895351i	$-0.353075\pi$
$727$	24.0165	0.890724	0.445362	+	0.895351i	$0.353075\pi$
$728$	29.4320	1.09082
$729$	28.8940	1.07015
$730$	2.90417	0.107488
$731$	1.62245	0.0600084
$732$	−4.88842	−0.180681
$733$	4.37726	0.161678	0.0808389	−	0.996727i	$-0.474240\pi$
$733$	4.37726	0.161678	0.0808389	+	0.996727i	$0.474240\pi$
$734$	29.7254	1.09718
$735$	15.4959	0.571576
$736$	−3.18261	−0.117312
$737$	25.9543	0.956039
$738$	0.531377	0.0195603
$739$	49.9600	1.83781	0.918903	−	0.394482i	$-0.129076\pi$
$739$	49.9600	1.83781	0.918903	+	0.394482i	$0.129076\pi$
$740$	−3.49940	−0.128641
$741$	−50.4364	−1.85283
$742$	−38.4224	−1.41053
$743$	9.83063	0.360651	0.180325	−	0.983607i	$-0.442285\pi$
$743$	9.83063	0.360651	0.180325	+	0.983607i	$0.442285\pi$
$744$	7.91321	0.290113
$745$	0.542085	0.0198605
$746$	27.1730	0.994873
$747$	1.78150	0.0651817
$748$	30.2608	1.10645
$749$	−81.2843	−2.97006
$750$	8.19420	0.299210
$751$	7.63011	0.278427	0.139213	−	0.990262i	$-0.455543\pi$
$751$	7.63011	0.278427	0.139213	+	0.990262i	$0.455543\pi$
$752$	2.71856	0.0991358
$753$	19.6787	0.717131
$754$	−17.6812	−0.643910
$755$	5.53603	0.201477
$756$	−27.1952	−0.989079
$757$	30.9160	1.12366	0.561831	−	0.827252i	$-0.310097\pi$
$757$	30.9160	1.12366	0.561831	+	0.827252i	$0.310097\pi$
$758$	28.0975	1.02055
$759$	−25.6011	−0.929261
$760$	−2.64854	−0.0960725
$761$	−50.7610	−1.84008	−0.920042	−	0.391819i	$-0.871846\pi$
$761$	−50.7610	−1.84008	−0.920042	+	0.391819i	$0.871846\pi$
$762$	−25.1690	−0.911777
$763$	9.15516	0.331439
$764$	−0.174632	−0.00631798
$765$	0.809997	0.0292855
$766$	−8.36633	−0.302288
$767$	71.0822	2.56663
$768$	1.65650	0.0597740
$769$	−0.465444	−0.0167844	−0.00839218	−	0.999965i	$-0.502671\pi$
$769$	−0.465444	−0.0167844	−0.00839218	+	0.999965i	$0.502671\pi$
$770$	12.4325	0.448035
$771$	−25.4596	−0.916905
$772$	12.8474	0.462386
$773$	−16.9191	−0.608536	−0.304268	−	0.952586i	$-0.598412\pi$
$773$	−16.9191	−0.608536	−0.304268	+	0.952586i	$0.598412\pi$
$774$	−0.0666501	−0.00239569
$775$	22.6537	0.813743
$776$	−10.0623	−0.361216
$777$	−57.5632	−2.06507
$778$	4.83674	0.173405
$779$	10.8274	0.387931
$780$	−4.90969	−0.175795
$781$	25.9710	0.929316
$782$	19.8326	0.709214
$783$	16.3374	0.583852
$784$	18.4233	0.657974
$785$	−7.69652	−0.274701
$786$	35.5294	1.26729
$787$	−7.69952	−0.274458	−0.137229	−	0.990539i	$-0.543820\pi$
$787$	−7.69952	−0.274458	−0.137229	+	0.990539i	$0.543820\pi$
$788$	3.00218	0.106948
$789$	−36.9096	−1.31402
$790$	−2.04271	−0.0726763
$791$	99.8161	3.54905
$792$	−1.24311	−0.0441721
$793$	17.2258	0.611707
$794$	−15.1427	−0.537395
$795$	6.40942	0.227319
$796$	0.395367	0.0140134
$797$	40.0105	1.41725	0.708623	−	0.705587i	$-0.249317\pi$
$797$	40.0105	1.41725	0.708623	+	0.705587i	$0.249317\pi$
$798$	−43.5669	−1.54225
$799$	−16.9409	−0.599327
$800$	4.74218	0.167661
$801$	2.73054	0.0964788
$802$	20.9855	0.741025
$803$	27.7746	0.980144
$804$	−8.85358	−0.312242
$805$	8.14811	0.287183
$806$	−27.8846	−0.982192
$807$	1.88250	0.0662673
$808$	−2.53994	−0.0893546
$809$	−13.2730	−0.466654	−0.233327	−	0.972398i	$-0.574961\pi$
$809$	−13.2730	−0.466654	−0.233327	+	0.972398i	$0.574961\pi$
$810$	4.14661	0.145697
$811$	−44.4058	−1.55930	−0.779649	−	0.626217i	$-0.784602\pi$
$811$	−44.4058	−1.55930	−0.779649	+	0.626217i	$0.784602\pi$
$812$	−15.2730	−0.535976
$813$	2.73894	0.0960588
$814$	−33.4672	−1.17302
$815$	8.27632	0.289907
$816$	−10.3226	−0.361364
$817$	−1.35807	−0.0475127
$818$	6.75915	0.236328
$819$	7.53437	0.263272
$820$	1.05398	0.0368067
$821$	−16.5353	−0.577087	−0.288544	−	0.957467i	$-0.593171\pi$
$821$	−16.5353	−0.577087	−0.288544	+	0.957467i	$0.593171\pi$
$822$	3.83617	0.133802
$823$	30.4764	1.06234	0.531171	−	0.847265i	$-0.321752\pi$
$823$	30.4764	1.06234	0.531171	+	0.847265i	$0.321752\pi$
$824$	0.944556	0.0329052
$825$	38.1464	1.32809
$826$	61.4007	2.13640
$827$	−15.1971	−0.528454	−0.264227	−	0.964461i	$-0.585117\pi$
$827$	−15.1971	−0.528454	−0.264227	+	0.964461i	$0.585117\pi$
$828$	−0.814724	−0.0283136
$829$	−49.2221	−1.70955	−0.854777	−	0.518996i	$-0.826306\pi$
$829$	−49.2221	−1.70955	−0.854777	+	0.518996i	$0.826306\pi$
$830$	3.53359	0.122653
$831$	24.9987	0.867194
$832$	−5.83719	−0.202368
$833$	−114.806	−3.97779
$834$	12.7931	0.442988
$835$	8.42792	0.291660
$836$	−25.3298	−0.876048
$837$	25.7654	0.890581
$838$	−27.1654	−0.938414
$839$	−16.1698	−0.558242	−0.279121	−	0.960256i	$-0.590043\pi$
$839$	−16.1698	−0.558242	−0.279121	+	0.960256i	$0.590043\pi$
$840$	−4.24098	−0.146328
$841$	−19.8248	−0.683614
$842$	−33.5018	−1.15455
$843$	25.4857	0.877776
$844$	14.3154	0.492758
$845$	10.6999	0.368087
$846$	0.695932	0.0239267
$847$	63.4364	2.17970
$848$	7.62023	0.261680
$849$	3.59878	0.123510
$850$	−29.5512	−1.01360
$851$	−21.9341	−0.751890
$852$	−8.85928	−0.303514
$853$	43.1474	1.47734	0.738670	−	0.674067i	$-0.235454\pi$
$853$	43.1474	1.47734	0.738670	+	0.674067i	$0.235454\pi$
$854$	14.8796	0.509170
$855$	−0.678006	−0.0231873
$856$	16.1210	0.551003
$857$	−24.4089	−0.833792	−0.416896	−	0.908954i	$-0.636882\pi$
$857$	−24.4089	−0.833792	−0.416896	+	0.908954i	$0.636882\pi$
$858$	−46.9547	−1.60301
$859$	13.3581	0.455771	0.227886	−	0.973688i	$-0.426819\pi$
$859$	13.3581	0.455771	0.227886	+	0.973688i	$0.426819\pi$
$860$	−0.132200	−0.00450798
$861$	17.3374	0.590857
$862$	−6.12822	−0.208728
$863$	−38.4612	−1.30924	−0.654618	−	0.755960i	$-0.727171\pi$
$863$	−38.4612	−1.30924	−0.654618	+	0.755960i	$0.727171\pi$
$864$	5.39357	0.183493
$865$	1.47039	0.0499948
$866$	3.96693	0.134802
$867$	36.1656	1.22825
$868$	−24.0866	−0.817553
$869$	−19.5358	−0.662707
$870$	2.54776	0.0863771
$871$	31.1982	1.05711
$872$	−1.81573	−0.0614882
$873$	−2.57588	−0.0871803
$874$	−16.6009	−0.561533
$875$	−24.9419	−0.843191
$876$	−9.47452	−0.320114
$877$	−6.40754	−0.216367	−0.108184	−	0.994131i	$-0.534503\pi$
$877$	−6.40754	−0.216367	−0.108184	+	0.994131i	$0.534503\pi$
$878$	−22.2627	−0.751329
$879$	−36.5312	−1.23217
$880$	−2.46570	−0.0831189
$881$	−16.4212	−0.553246	−0.276623	−	0.960979i	$-0.589215\pi$
$881$	−16.4212	−0.553246	−0.276623	+	0.960979i	$0.589215\pi$
$882$	4.71622	0.158803
$883$	−47.3542	−1.59359	−0.796797	−	0.604247i	$-0.793474\pi$
$883$	−47.3542	−1.59359	−0.796797	+	0.604247i	$0.793474\pi$
$884$	36.3749	1.22342
$885$	−10.2425	−0.344299
$886$	16.3653	0.549804
$887$	42.7271	1.43464	0.717318	−	0.696746i	$-0.245369\pi$
$887$	42.7271	1.43464	0.717318	+	0.696746i	$0.245369\pi$
$888$	11.4164	0.383109
$889$	76.6106	2.56944
$890$	5.41600	0.181545
$891$	39.6569	1.32856
$892$	−6.78489	−0.227175
$893$	14.1804	0.474528
$894$	−1.76849	−0.0591471
$895$	−9.17042	−0.306533
$896$	−5.04215	−0.168446
$897$	−30.7737	−1.02750
$898$	−15.3990	−0.513873
$899$	14.4700	0.482601
$900$	1.21396	0.0404655
$901$	−47.4860	−1.58199
$902$	10.0800	0.335626
$903$	−2.17461	−0.0723665
$904$	−19.7963	−0.658417
$905$	12.8091	0.425788
$906$	−18.0606	−0.600024
$907$	−6.57273	−0.218244	−0.109122	−	0.994028i	$-0.534804\pi$
$907$	−6.57273	−0.218244	−0.109122	+	0.994028i	$0.534804\pi$
$908$	−9.89712	−0.328447
$909$	−0.650205	−0.0215659
$910$	14.9444	0.495401
$911$	−46.3088	−1.53428	−0.767139	−	0.641481i	$-0.778320\pi$
$911$	−46.3088	−1.53428	−0.767139	+	0.641481i	$0.778320\pi$
$912$	8.64054	0.286117
$913$	33.7942	1.11842
$914$	19.3812	0.641073
$915$	−2.48214	−0.0820571
$916$	13.5899	0.449023
$917$	−108.146	−3.57130
$918$	−33.6104	−1.10931
$919$	4.80491	0.158499	0.0792497	−	0.996855i	$-0.474748\pi$
$919$	4.80491	0.158499	0.0792497	+	0.996855i	$0.474748\pi$
$920$	−1.61600	−0.0532779
$921$	7.98532	0.263125
$922$	3.43011	0.112965
$923$	31.2183	1.02756
$924$	−40.5594	−1.33431
$925$	32.6824	1.07459
$926$	1.28867	0.0423482
$927$	0.241799	0.00794173
$928$	3.02906	0.0994337
$929$	12.7018	0.416732	0.208366	−	0.978051i	$-0.433186\pi$
$929$	12.7018	0.416732	0.208366	+	0.978051i	$0.433186\pi$
$930$	4.01801	0.131756
$931$	96.0981	3.14949
$932$	−22.7395	−0.744857
$933$	6.29948	0.206236
$934$	23.7459	0.776990
$935$	15.3652	0.502496
$936$	−1.49428	−0.0488420
$937$	−33.9947	−1.11056	−0.555279	−	0.831664i	$-0.687389\pi$
$937$	−33.9947	−1.11056	−0.555279	+	0.831664i	$0.687389\pi$
$938$	26.9489	0.879914
$939$	−25.1305	−0.820104
$940$	1.38038	0.0450229
$941$	32.3084	1.05322	0.526612	−	0.850106i	$-0.323462\pi$
$941$	32.3084	1.05322	0.526612	+	0.850106i	$0.323462\pi$
$942$	25.1090	0.818095
$943$	6.60630	0.215131
$944$	−12.1775	−0.396343
$945$	−13.8086	−0.449194
$946$	−1.26432	−0.0411065
$947$	30.2475	0.982913	0.491456	−	0.870902i	$-0.336465\pi$
$947$	30.2475	0.982913	0.491456	+	0.870902i	$0.336465\pi$
$948$	6.66409	0.216440
$949$	33.3863	1.08376
$950$	24.7358	0.802536
$951$	13.3379	0.432510
$952$	31.4205	1.01835
$953$	33.5916	1.08814	0.544070	−	0.839040i	$-0.316883\pi$
$953$	33.5916	1.08814	0.544070	+	0.839040i	$0.316883\pi$
$954$	1.95072	0.0631570
$955$	−0.0886712	−0.00286933
$956$	19.4387	0.628691
$957$	24.3659	0.787639
$958$	−24.5218	−0.792263
$959$	−11.6767	−0.377061
$960$	0.841106	0.0271466
$961$	−8.17974	−0.263863
$962$	−40.2291	−1.29704
$963$	4.12685	0.132986
$964$	−9.30394	−0.299660
$965$	6.52337	0.209995
$966$	−26.5822	−0.855269
$967$	41.4453	1.33279	0.666395	−	0.745599i	$-0.267836\pi$
$967$	41.4453	1.33279	0.666395	+	0.745599i	$0.267836\pi$
$968$	−12.5812	−0.404376
$969$	−53.8441	−1.72972
$970$	−5.10923	−0.164048
$971$	−10.4986	−0.336917	−0.168459	−	0.985709i	$-0.553879\pi$
$971$	−10.4986	−0.336917	−0.168459	+	0.985709i	$0.553879\pi$
$972$	2.65287	0.0850909
$973$	−38.9402	−1.24837
$974$	−15.9913	−0.512396
$975$	45.8537	1.46849
$976$	−2.95105	−0.0944607
$977$	−52.5589	−1.68151	−0.840755	−	0.541416i	$-0.817888\pi$
$977$	−52.5589	−1.68151	−0.840755	+	0.541416i	$0.817888\pi$
$978$	−27.0005	−0.863381
$979$	51.7969	1.65544
$980$	9.35459	0.298821
$981$	−0.464812	−0.0148403
$982$	17.6834	0.564301
$983$	−19.7912	−0.631241	−0.315620	−	0.948886i	$-0.602213\pi$
$983$	−19.7912	−0.631241	−0.315620	+	0.948886i	$0.602213\pi$
$984$	−3.43849	−0.109615
$985$	1.52438	0.0485709
$986$	−18.8758	−0.601128
$987$	22.7064	0.722752
$988$	−30.4475	−0.968664
$989$	−0.828621	−0.0263486
$990$	−0.631202	−0.0200609
$991$	−24.7120	−0.785003	−0.392501	−	0.919751i	$-0.628390\pi$
$991$	−24.7120	−0.785003	−0.392501	+	0.919751i	$0.628390\pi$
$992$	4.77706	0.151672
$993$	23.8139	0.755712
$994$	26.9663	0.855319
$995$	0.200751	0.00636424
$996$	−11.5279	−0.365276
$997$	−56.2337	−1.78094	−0.890470	−	0.455043i	$-0.849624\pi$
$997$	−56.2337	−1.78094	−0.890470	+	0.455043i	$0.849624\pi$
$998$	32.4087	1.02588
$999$	37.1717	1.17606

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.g.1.29	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.g.1.29	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.65650 q^{3} +1.00000 q^{4} +0.507759 q^{5} -1.65650 q^{6} +5.04215 q^{7} -1.00000 q^{8} -0.255993 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.65650 q^{3} +1.00000 q^{4} +0.507759 q^{5} -1.65650 q^{6} +5.04215 q^{7} -1.00000 q^{8} -0.255993 q^{9} -0.507759 q^{10} -4.85605 q^{11} +1.65650 q^{12} -5.83719 q^{13} -5.04215 q^{14} +0.841106 q^{15} +1.00000 q^{16} -6.23157 q^{17} +0.255993 q^{18} +5.21613 q^{19} +0.507759 q^{20} +8.35234 q^{21} +4.85605 q^{22} +3.18261 q^{23} -1.65650 q^{24} -4.74218 q^{25} +5.83719 q^{26} -5.39357 q^{27} +5.04215 q^{28} -3.02906 q^{29} -0.841106 q^{30} -4.77706 q^{31} -1.00000 q^{32} -8.04407 q^{33} +6.23157 q^{34} +2.56020 q^{35} -0.255993 q^{36} -6.89186 q^{37} -5.21613 q^{38} -9.66933 q^{39} -0.507759 q^{40} +2.07575 q^{41} -8.35234 q^{42} -0.260359 q^{43} -4.85605 q^{44} -0.129983 q^{45} -3.18261 q^{46} +2.71856 q^{47} +1.65650 q^{48} +18.4233 q^{49} +4.74218 q^{50} -10.3226 q^{51} -5.83719 q^{52} +7.62023 q^{53} +5.39357 q^{54} -2.46570 q^{55} -5.04215 q^{56} +8.64054 q^{57} +3.02906 q^{58} -12.1775 q^{59} +0.841106 q^{60} -2.95105 q^{61} +4.77706 q^{62} -1.29075 q^{63} +1.00000 q^{64} -2.96389 q^{65} +8.04407 q^{66} -5.34473 q^{67} -6.23157 q^{68} +5.27200 q^{69} -2.56020 q^{70} -5.34818 q^{71} +0.255993 q^{72} -5.71959 q^{73} +6.89186 q^{74} -7.85544 q^{75} +5.21613 q^{76} -24.4849 q^{77} +9.66933 q^{78} +4.02298 q^{79} +0.507759 q^{80} -8.16649 q^{81} -2.07575 q^{82} -6.95919 q^{83} +8.35234 q^{84} -3.16414 q^{85} +0.260359 q^{86} -5.01765 q^{87} +4.85605 q^{88} -10.6665 q^{89} +0.129983 q^{90} -29.4320 q^{91} +3.18261 q^{92} -7.91321 q^{93} -2.71856 q^{94} +2.64854 q^{95} -1.65650 q^{96} +10.0623 q^{97} -18.4233 q^{98} +1.24311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) \) 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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