LMFDB - Embedded newform 4006.2.a.g.1.32

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			1.32
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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.81349 q^{3} +1.00000 q^{4} +1.21192 q^{5} -1.81349 q^{6} -2.11157 q^{7} -1.00000 q^{8} +0.288748 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.81349 q^{3} +1.00000 q^{4} +1.21192 q^{5} -1.81349 q^{6} -2.11157 q^{7} -1.00000 q^{8} +0.288748 q^{9} -1.21192 q^{10} +1.44990 q^{11} +1.81349 q^{12} -1.15349 q^{13} +2.11157 q^{14} +2.19780 q^{15} +1.00000 q^{16} -2.16444 q^{17} -0.288748 q^{18} +4.58112 q^{19} +1.21192 q^{20} -3.82930 q^{21} -1.44990 q^{22} -3.56278 q^{23} -1.81349 q^{24} -3.53125 q^{25} +1.15349 q^{26} -4.91683 q^{27} -2.11157 q^{28} -2.53756 q^{29} -2.19780 q^{30} -5.95667 q^{31} -1.00000 q^{32} +2.62938 q^{33} +2.16444 q^{34} -2.55905 q^{35} +0.288748 q^{36} +1.48632 q^{37} -4.58112 q^{38} -2.09184 q^{39} -1.21192 q^{40} -2.71906 q^{41} +3.82930 q^{42} +0.511524 q^{43} +1.44990 q^{44} +0.349939 q^{45} +3.56278 q^{46} -1.79666 q^{47} +1.81349 q^{48} -2.54129 q^{49} +3.53125 q^{50} -3.92519 q^{51} -1.15349 q^{52} -6.91640 q^{53} +4.91683 q^{54} +1.75716 q^{55} +2.11157 q^{56} +8.30782 q^{57} +2.53756 q^{58} -6.75049 q^{59} +2.19780 q^{60} -0.358765 q^{61} +5.95667 q^{62} -0.609710 q^{63} +1.00000 q^{64} -1.39794 q^{65} -2.62938 q^{66} -1.39021 q^{67} -2.16444 q^{68} -6.46108 q^{69} +2.55905 q^{70} +14.6046 q^{71} -0.288748 q^{72} +11.8686 q^{73} -1.48632 q^{74} -6.40389 q^{75} +4.58112 q^{76} -3.06155 q^{77} +2.09184 q^{78} -16.9225 q^{79} +1.21192 q^{80} -9.78287 q^{81} +2.71906 q^{82} +2.26172 q^{83} -3.82930 q^{84} -2.62312 q^{85} -0.511524 q^{86} -4.60185 q^{87} -1.44990 q^{88} +16.8573 q^{89} -0.349939 q^{90} +2.43567 q^{91} -3.56278 q^{92} -10.8024 q^{93} +1.79666 q^{94} +5.55194 q^{95} -1.81349 q^{96} +9.24796 q^{97} +2.54129 q^{98} +0.418655 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.81349	1.04702	0.523510	−	0.852020i	$-0.324622\pi$
$3$	1.81349	1.04702	0.523510	+	0.852020i	$0.324622\pi$
$4$	1.00000	0.500000
$5$	1.21192	0.541986	0.270993	−	0.962581i	$-0.412648\pi$
$5$	1.21192	0.541986	0.270993	+	0.962581i	$0.412648\pi$
$6$	−1.81349	−0.740354
$7$	−2.11157	−0.798097	−0.399048	−	0.916930i	$-0.630659\pi$
$7$	−2.11157	−0.798097	−0.399048	+	0.916930i	$0.630659\pi$
$8$	−1.00000	−0.353553
$9$	0.288748	0.0962493
$10$	−1.21192	−0.383242
$11$	1.44990	0.437161	0.218580	−	0.975819i	$-0.429857\pi$
$11$	1.44990	0.437161	0.218580	+	0.975819i	$0.429857\pi$
$12$	1.81349	0.523510
$13$	−1.15349	−0.319920	−0.159960	−	0.987123i	$-0.551137\pi$
$13$	−1.15349	−0.319920	−0.159960	+	0.987123i	$0.551137\pi$
$14$	2.11157	0.564340
$15$	2.19780	0.567470
$16$	1.00000	0.250000
$17$	−2.16444	−0.524954	−0.262477	−	0.964938i	$-0.584539\pi$
$17$	−2.16444	−0.524954	−0.262477	+	0.964938i	$0.584539\pi$
$18$	−0.288748	−0.0680585
$19$	4.58112	1.05098	0.525491	−	0.850799i	$-0.323882\pi$
$19$	4.58112	1.05098	0.525491	+	0.850799i	$0.323882\pi$
$20$	1.21192	0.270993
$21$	−3.82930	−0.835623
$22$	−1.44990	−0.309119
$23$	−3.56278	−0.742892	−0.371446	−	0.928455i	$-0.621138\pi$
$23$	−3.56278	−0.742892	−0.371446	+	0.928455i	$0.621138\pi$
$24$	−1.81349	−0.370177
$25$	−3.53125	−0.706251
$26$	1.15349	0.226218
$27$	−4.91683	−0.946244
$28$	−2.11157	−0.399048
$29$	−2.53756	−0.471214	−0.235607	−	0.971848i	$-0.575708\pi$
$29$	−2.53756	−0.471214	−0.235607	+	0.971848i	$0.575708\pi$
$30$	−2.19780	−0.401262
$31$	−5.95667	−1.06985	−0.534925	−	0.844900i	$-0.679660\pi$
$31$	−5.95667	−1.06985	−0.534925	+	0.844900i	$0.679660\pi$
$32$	−1.00000	−0.176777
$33$	2.62938	0.457715
$34$	2.16444	0.371198
$35$	−2.55905	−0.432558
$36$	0.288748	0.0481246
$37$	1.48632	0.244350	0.122175	−	0.992509i	$-0.461013\pi$
$37$	1.48632	0.244350	0.122175	+	0.992509i	$0.461013\pi$
$38$	−4.58112	−0.743156
$39$	−2.09184	−0.334963
$40$	−1.21192	−0.191621
$41$	−2.71906	−0.424646	−0.212323	−	0.977200i	$-0.568103\pi$
$41$	−2.71906	−0.424646	−0.212323	+	0.977200i	$0.568103\pi$
$42$	3.82930	0.590875
$43$	0.511524	0.0780067	0.0390033	−	0.999239i	$-0.487582\pi$
$43$	0.511524	0.0780067	0.0390033	+	0.999239i	$0.487582\pi$
$44$	1.44990	0.218580
$45$	0.349939	0.0521658
$46$	3.56278	0.525304
$47$	−1.79666	−0.262069	−0.131035	−	0.991378i	$-0.541830\pi$
$47$	−1.79666	−0.262069	−0.131035	+	0.991378i	$0.541830\pi$
$48$	1.81349	0.261755
$49$	−2.54129	−0.363041
$50$	3.53125	0.499395
$51$	−3.92519	−0.549637
$52$	−1.15349	−0.159960
$53$	−6.91640	−0.950041	−0.475020	−	0.879975i	$-0.657559\pi$
$53$	−6.91640	−0.950041	−0.475020	+	0.879975i	$0.657559\pi$
$54$	4.91683	0.669096
$55$	1.75716	0.236935
$56$	2.11157	0.282170
$57$	8.30782	1.10040
$58$	2.53756	0.333198
$59$	−6.75049	−0.878840	−0.439420	−	0.898282i	$-0.644816\pi$
$59$	−6.75049	−0.878840	−0.439420	+	0.898282i	$0.644816\pi$
$60$	2.19780	0.283735
$61$	−0.358765	−0.0459352	−0.0229676	−	0.999736i	$-0.507311\pi$
$61$	−0.358765	−0.0459352	−0.0229676	+	0.999736i	$0.507311\pi$
$62$	5.95667	0.756498
$63$	−0.609710	−0.0768163
$64$	1.00000	0.125000
$65$	−1.39794	−0.173393
$66$	−2.62938	−0.323654
$67$	−1.39021	−0.169841	−0.0849205	−	0.996388i	$-0.527064\pi$
$67$	−1.39021	−0.169841	−0.0849205	+	0.996388i	$0.527064\pi$
$68$	−2.16444	−0.262477
$69$	−6.46108	−0.777822
$70$	2.55905	0.305864
$71$	14.6046	1.73324	0.866622	−	0.498965i	$-0.166286\pi$
$71$	14.6046	1.73324	0.866622	+	0.498965i	$0.166286\pi$
$72$	−0.288748	−0.0340293
$73$	11.8686	1.38911	0.694556	−	0.719438i	$-0.255601\pi$
$73$	11.8686	1.38911	0.694556	+	0.719438i	$0.255601\pi$
$74$	−1.48632	−0.172781
$75$	−6.40389	−0.739458
$76$	4.58112	0.525491
$77$	−3.06155	−0.348896
$78$	2.09184	0.236855
$79$	−16.9225	−1.90393	−0.951965	−	0.306207i	$-0.900940\pi$
$79$	−16.9225	−1.90393	−0.951965	+	0.306207i	$0.900940\pi$
$80$	1.21192	0.135497
$81$	−9.78287	−1.08699
$82$	2.71906	0.300270
$83$	2.26172	0.248256	0.124128	−	0.992266i	$-0.460387\pi$
$83$	2.26172	0.248256	0.124128	+	0.992266i	$0.460387\pi$
$84$	−3.82930	−0.417811
$85$	−2.62312	−0.284518
$86$	−0.511524	−0.0551591
$87$	−4.60185	−0.493370
$88$	−1.44990	−0.154560
$89$	16.8573	1.78686	0.893432	−	0.449198i	$-0.148290\pi$
$89$	16.8573	1.78686	0.893432	+	0.449198i	$0.148290\pi$
$90$	−0.349939	−0.0368868
$91$	2.43567	0.255328
$92$	−3.56278	−0.371446
$93$	−10.8024	−1.12015
$94$	1.79666	0.185311
$95$	5.55194	0.569617
$96$	−1.81349	−0.185089
$97$	9.24796	0.938988	0.469494	−	0.882936i	$-0.344436\pi$
$97$	9.24796	0.938988	0.469494	+	0.882936i	$0.344436\pi$
$98$	2.54129	0.256709
$99$	0.418655	0.0420764
$100$	−3.53125	−0.353125
$101$	−5.36539	−0.533876	−0.266938	−	0.963714i	$-0.586012\pi$
$101$	−5.36539	−0.533876	−0.266938	+	0.963714i	$0.586012\pi$
$102$	3.92519	0.388652
$103$	−0.535058	−0.0527208	−0.0263604	−	0.999653i	$-0.508392\pi$
$103$	−0.535058	−0.0527208	−0.0263604	+	0.999653i	$0.508392\pi$
$104$	1.15349	0.113109
$105$	−4.64081	−0.452896
$106$	6.91640	0.671780
$107$	−15.2682	−1.47603	−0.738017	−	0.674782i	$-0.764238\pi$
$107$	−15.2682	−1.47603	−0.738017	+	0.674782i	$0.764238\pi$
$108$	−4.91683	−0.473122
$109$	−12.9728	−1.24257	−0.621285	−	0.783585i	$-0.713389\pi$
$109$	−12.9728	−1.24257	−0.621285	+	0.783585i	$0.713389\pi$
$110$	−1.75716	−0.167538
$111$	2.69543	0.255839
$112$	−2.11157	−0.199524
$113$	−0.261879	−0.0246355	−0.0123177	−	0.999924i	$-0.503921\pi$
$113$	−0.261879	−0.0246355	−0.0123177	+	0.999924i	$0.503921\pi$
$114$	−8.30782	−0.778098
$115$	−4.31780	−0.402637
$116$	−2.53756	−0.235607
$117$	−0.333068	−0.0307921
$118$	6.75049	0.621433
$119$	4.57036	0.418964
$120$	−2.19780	−0.200631
$121$	−8.89780	−0.808891
$122$	0.358765	0.0324811
$123$	−4.93099	−0.444612
$124$	−5.95667	−0.534925
$125$	−10.3392	−0.924765
$126$	0.609710	0.0543173
$127$	−4.33868	−0.384995	−0.192498	−	0.981297i	$-0.561659\pi$
$127$	−4.33868	−0.384995	−0.192498	+	0.981297i	$0.561659\pi$
$128$	−1.00000	−0.0883883
$129$	0.927644	0.0816745
$130$	1.39794	0.122607
$131$	−13.3407	−1.16559	−0.582793	−	0.812621i	$-0.698040\pi$
$131$	−13.3407	−1.16559	−0.582793	+	0.812621i	$0.698040\pi$
$132$	2.62938	0.228858
$133$	−9.67334	−0.838785
$134$	1.39021	0.120096
$135$	−5.95880	−0.512852
$136$	2.16444	0.185599
$137$	0.781881	0.0668006	0.0334003	−	0.999442i	$-0.489366\pi$
$137$	0.781881	0.0668006	0.0334003	+	0.999442i	$0.489366\pi$
$138$	6.46108	0.550003
$139$	3.26383	0.276834	0.138417	−	0.990374i	$-0.455799\pi$
$139$	3.26383	0.276834	0.138417	+	0.990374i	$0.455799\pi$
$140$	−2.55905	−0.216279
$141$	−3.25822	−0.274391
$142$	−14.6046	−1.22559
$143$	−1.67244	−0.139857
$144$	0.288748	0.0240623
$145$	−3.07532	−0.255391
$146$	−11.8686	−0.982251
$147$	−4.60860	−0.380111
$148$	1.48632	0.122175
$149$	2.86353	0.234589	0.117295	−	0.993097i	$-0.462578\pi$
$149$	2.86353	0.234589	0.117295	+	0.993097i	$0.462578\pi$
$150$	6.40389	0.522876
$151$	−3.51006	−0.285644	−0.142822	−	0.989748i	$-0.545618\pi$
$151$	−3.51006	−0.285644	−0.142822	+	0.989748i	$0.545618\pi$
$152$	−4.58112	−0.371578
$153$	−0.624977	−0.0505264
$154$	3.06155	0.246707
$155$	−7.21900	−0.579844
$156$	−2.09184	−0.167481
$157$	13.9700	1.11493	0.557465	−	0.830200i	$-0.311774\pi$
$157$	13.9700	1.11493	0.557465	+	0.830200i	$0.311774\pi$
$158$	16.9225	1.34628
$159$	−12.5428	−0.994711
$160$	−1.21192	−0.0958106
$161$	7.52305	0.592900
$162$	9.78287	0.768615
$163$	7.64421	0.598741	0.299370	−	0.954137i	$-0.403223\pi$
$163$	7.64421	0.598741	0.299370	+	0.954137i	$0.403223\pi$
$164$	−2.71906	−0.212323
$165$	3.18659	0.248076
$166$	−2.26172	−0.175544
$167$	1.63713	0.126685	0.0633423	−	0.997992i	$-0.479824\pi$
$167$	1.63713	0.126685	0.0633423	+	0.997992i	$0.479824\pi$
$168$	3.82930	0.295437
$169$	−11.6695	−0.897651
$170$	2.62312	0.201184
$171$	1.32279	0.101156
$172$	0.511524	0.0390033
$173$	22.3646	1.70035	0.850175	−	0.526500i	$-0.176496\pi$
$173$	22.3646	1.70035	0.850175	+	0.526500i	$0.176496\pi$
$174$	4.60185	0.348865
$175$	7.45647	0.563657
$176$	1.44990	0.109290
$177$	−12.2420	−0.920162
$178$	−16.8573	−1.26350
$179$	−9.82543	−0.734387	−0.367194	−	0.930145i	$-0.619681\pi$
$179$	−9.82543	−0.734387	−0.367194	+	0.930145i	$0.619681\pi$
$180$	0.349939	0.0260829
$181$	−12.9191	−0.960269	−0.480135	−	0.877195i	$-0.659412\pi$
$181$	−12.9191	−0.960269	−0.480135	+	0.877195i	$0.659412\pi$
$182$	−2.43567	−0.180544
$183$	−0.650617	−0.0480950
$184$	3.56278	0.262652
$185$	1.80130	0.132434
$186$	10.8024	0.792068
$187$	−3.13822	−0.229489
$188$	−1.79666	−0.131035
$189$	10.3822	0.755195
$190$	−5.55194	−0.402780
$191$	−17.3693	−1.25679	−0.628397	−	0.777892i	$-0.716289\pi$
$191$	−17.3693	−1.25679	−0.628397	+	0.777892i	$0.716289\pi$
$192$	1.81349	0.130877
$193$	0.232198	0.0167139	0.00835697	−	0.999965i	$-0.497340\pi$
$193$	0.232198	0.0167139	0.00835697	+	0.999965i	$0.497340\pi$
$194$	−9.24796	−0.663965
$195$	−2.53514	−0.181545
$196$	−2.54129	−0.181521
$197$	−14.0568	−1.00150	−0.500752	−	0.865591i	$-0.666943\pi$
$197$	−14.0568	−1.00150	−0.500752	+	0.865591i	$0.666943\pi$
$198$	−0.418655	−0.0297525
$199$	−21.7735	−1.54348	−0.771742	−	0.635936i	$-0.780614\pi$
$199$	−21.7735	−1.54348	−0.771742	+	0.635936i	$0.780614\pi$
$200$	3.53125	0.249697
$201$	−2.52113	−0.177827
$202$	5.36539	0.377507
$203$	5.35823	0.376074
$204$	−3.92519	−0.274818
$205$	−3.29528	−0.230152
$206$	0.535058	0.0372792
$207$	−1.02875	−0.0715028
$208$	−1.15349	−0.0799801
$209$	6.64216	0.459447
$210$	4.64081	0.320246
$211$	28.1808	1.94005	0.970023	−	0.243011i	$-0.0781352\pi$
$211$	28.1808	1.94005	0.970023	+	0.243011i	$0.0781352\pi$
$212$	−6.91640	−0.475020
$213$	26.4853	1.81474
$214$	15.2682	1.04371
$215$	0.619926	0.0422786
$216$	4.91683	0.334548
$217$	12.5779	0.853844
$218$	12.9728	0.878630
$219$	21.5236	1.45443
$220$	1.75716	0.118468
$221$	2.49666	0.167943
$222$	−2.69543	−0.180905
$223$	4.50328	0.301562	0.150781	−	0.988567i	$-0.451821\pi$
$223$	4.50328	0.301562	0.150781	+	0.988567i	$0.451821\pi$
$224$	2.11157	0.141085
$225$	−1.01964	−0.0679761
$226$	0.261879	0.0174199
$227$	16.6069	1.10224	0.551118	−	0.834427i	$-0.314202\pi$
$227$	16.6069	1.10224	0.551118	+	0.834427i	$0.314202\pi$
$228$	8.30782	0.550199
$229$	13.4972	0.891922	0.445961	−	0.895052i	$-0.352862\pi$
$229$	13.4972	0.891922	0.445961	+	0.895052i	$0.352862\pi$
$230$	4.31780	0.284708
$231$	−5.55210	−0.365301
$232$	2.53756	0.166599
$233$	−9.14002	−0.598783	−0.299391	−	0.954130i	$-0.596784\pi$
$233$	−9.14002	−0.598783	−0.299391	+	0.954130i	$0.596784\pi$
$234$	0.333068	0.0217733
$235$	−2.17740	−0.142038
$236$	−6.75049	−0.439420
$237$	−30.6888	−1.99345
$238$	−4.57036	−0.296252
$239$	21.2908	1.37719	0.688593	−	0.725148i	$-0.258229\pi$
$239$	21.2908	1.37719	0.688593	+	0.725148i	$0.258229\pi$
$240$	2.19780	0.141868
$241$	−16.7940	−1.08180	−0.540900	−	0.841087i	$-0.681916\pi$
$241$	−16.7940	−1.08180	−0.540900	+	0.841087i	$0.681916\pi$
$242$	8.89780	0.571972
$243$	−2.99065	−0.191850
$244$	−0.358765	−0.0229676
$245$	−3.07984	−0.196763
$246$	4.93099	0.314388
$247$	−5.28427	−0.336230
$248$	5.95667	0.378249
$249$	4.10161	0.259929
$250$	10.3392	0.653907
$251$	−0.249407	−0.0157424	−0.00787122	−	0.999969i	$-0.502506\pi$
$251$	−0.249407	−0.0157424	−0.00787122	+	0.999969i	$0.502506\pi$
$252$	−0.609710	−0.0384081
$253$	−5.16567	−0.324763
$254$	4.33868	0.272233
$255$	−4.75701	−0.297896
$256$	1.00000	0.0625000
$257$	−4.00530	−0.249844	−0.124922	−	0.992167i	$-0.539868\pi$
$257$	−4.00530	−0.249844	−0.124922	+	0.992167i	$0.539868\pi$
$258$	−0.927644	−0.0577526
$259$	−3.13847	−0.195015
$260$	−1.39794	−0.0866963
$261$	−0.732716	−0.0453540
$262$	13.3407	0.824193
$263$	−11.9416	−0.736349	−0.368175	−	0.929757i	$-0.620017\pi$
$263$	−11.9416	−0.736349	−0.368175	+	0.929757i	$0.620017\pi$
$264$	−2.62938	−0.161827
$265$	−8.38211	−0.514909
$266$	9.67334	0.593110
$267$	30.5705	1.87088
$268$	−1.39021	−0.0849205
$269$	13.9945	0.853260	0.426630	−	0.904426i	$-0.359701\pi$
$269$	13.9945	0.853260	0.426630	+	0.904426i	$0.359701\pi$
$270$	5.95880	0.362641
$271$	−22.8737	−1.38948	−0.694740	−	0.719261i	$-0.744480\pi$
$271$	−22.8737	−1.38948	−0.694740	+	0.719261i	$0.744480\pi$
$272$	−2.16444	−0.131238
$273$	4.41706	0.267333
$274$	−0.781881	−0.0472352
$275$	−5.11996	−0.308745
$276$	−6.46108	−0.388911
$277$	17.7255	1.06502	0.532511	−	0.846423i	$-0.321249\pi$
$277$	17.7255	1.06502	0.532511	+	0.846423i	$0.321249\pi$
$278$	−3.26383	−0.195751
$279$	−1.71998	−0.102972
$280$	2.55905	0.152932
$281$	−28.3910	−1.69367	−0.846833	−	0.531858i	$-0.821494\pi$
$281$	−28.3910	−1.69367	−0.846833	+	0.531858i	$0.821494\pi$
$282$	3.25822	0.194024
$283$	30.0144	1.78417	0.892084	−	0.451869i	$-0.149242\pi$
$283$	30.0144	1.78417	0.892084	+	0.451869i	$0.149242\pi$
$284$	14.6046	0.866622
$285$	10.0684	0.596400
$286$	1.67244	0.0988935
$287$	5.74147	0.338908
$288$	−0.288748	−0.0170146
$289$	−12.3152	−0.724424
$290$	3.07532	0.180589
$291$	16.7711	0.983138
$292$	11.8686	0.694556
$293$	7.49617	0.437931	0.218966	−	0.975733i	$-0.429732\pi$
$293$	7.49617	0.437931	0.218966	+	0.975733i	$0.429732\pi$
$294$	4.60860	0.268779
$295$	−8.18105	−0.476319
$296$	−1.48632	−0.0863907
$297$	−7.12890	−0.413661
$298$	−2.86353	−0.165880
$299$	4.10964	0.237666
$300$	−6.40389	−0.369729
$301$	−1.08012	−0.0622569
$302$	3.51006	0.201981
$303$	−9.73008	−0.558978
$304$	4.58112	0.262745
$305$	−0.434794	−0.0248962
$306$	0.624977	0.0357276
$307$	5.81502	0.331881	0.165940	−	0.986136i	$-0.446934\pi$
$307$	5.81502	0.331881	0.165940	+	0.986136i	$0.446934\pi$
$308$	−3.06155	−0.174448
$309$	−0.970322	−0.0551997
$310$	7.21900	0.410012
$311$	−7.86767	−0.446135	−0.223067	−	0.974803i	$-0.571607\pi$
$311$	−7.86767	−0.446135	−0.223067	+	0.974803i	$0.571607\pi$
$312$	2.09184	0.118427
$313$	11.4852	0.649180	0.324590	−	0.945855i	$-0.394774\pi$
$313$	11.4852	0.649180	0.324590	+	0.945855i	$0.394774\pi$
$314$	−13.9700	−0.788375
$315$	−0.738919	−0.0416334
$316$	−16.9225	−0.951965
$317$	−21.4283	−1.20353	−0.601766	−	0.798672i	$-0.705536\pi$
$317$	−21.4283	−1.20353	−0.601766	+	0.798672i	$0.705536\pi$
$318$	12.5428	0.703367
$319$	−3.67921	−0.205996
$320$	1.21192	0.0677483
$321$	−27.6888	−1.54544
$322$	−7.52305	−0.419243
$323$	−9.91556	−0.551716
$324$	−9.78287	−0.543493
$325$	4.07326	0.225944
$326$	−7.64421	−0.423374
$327$	−23.5261	−1.30099
$328$	2.71906	0.150135
$329$	3.79376	0.209157
$330$	−3.18659	−0.175416
$331$	17.5954	0.967133	0.483566	−	0.875308i	$-0.339341\pi$
$331$	17.5954	0.967133	0.483566	+	0.875308i	$0.339341\pi$
$332$	2.26172	0.124128
$333$	0.429172	0.0235185
$334$	−1.63713	−0.0895795
$335$	−1.68482	−0.0920515
$336$	−3.82930	−0.208906
$337$	−6.44746	−0.351215	−0.175608	−	0.984460i	$-0.556189\pi$
$337$	−6.44746	−0.351215	−0.175608	+	0.984460i	$0.556189\pi$
$338$	11.6695	0.634735
$339$	−0.474915	−0.0257938
$340$	−2.62312	−0.142259
$341$	−8.63656	−0.467696
$342$	−1.32279	−0.0715282
$343$	20.1471	1.08784
$344$	−0.511524	−0.0275795
$345$	−7.83030	−0.421569
$346$	−22.3646	−1.20233
$347$	0.355481	0.0190832	0.00954161	−	0.999954i	$-0.496963\pi$
$347$	0.355481	0.0190832	0.00954161	+	0.999954i	$0.496963\pi$
$348$	−4.60185	−0.246685
$349$	−23.7147	−1.26942	−0.634710	−	0.772750i	$-0.718881\pi$
$349$	−23.7147	−1.26942	−0.634710	+	0.772750i	$0.718881\pi$
$350$	−7.45647	−0.398565
$351$	5.67151	0.302723
$352$	−1.44990	−0.0772798
$353$	1.79863	0.0957315	0.0478658	−	0.998854i	$-0.484758\pi$
$353$	1.79863	0.0957315	0.0478658	+	0.998854i	$0.484758\pi$
$354$	12.2420	0.650653
$355$	17.6996	0.939395
$356$	16.8573	0.893432
$357$	8.28830	0.438663
$358$	9.82543	0.519290
$359$	19.0360	1.00468	0.502341	−	0.864669i	$-0.332472\pi$
$359$	19.0360	1.00468	0.502341	+	0.864669i	$0.332472\pi$
$360$	−0.349939	−0.0184434
$361$	1.98666	0.104561
$362$	12.9191	0.679013
$363$	−16.1361	−0.846924
$364$	2.43567	0.127664
$365$	14.3838	0.752880
$366$	0.650617	0.0340083
$367$	−2.14706	−0.112075	−0.0560377	−	0.998429i	$-0.517847\pi$
$367$	−2.14706	−0.112075	−0.0560377	+	0.998429i	$0.517847\pi$
$368$	−3.56278	−0.185723
$369$	−0.785122	−0.0408718
$370$	−1.80130	−0.0936451
$371$	14.6044	0.758224
$372$	−10.8024	−0.560077
$373$	12.8524	0.665473	0.332737	−	0.943020i	$-0.392028\pi$
$373$	12.8524	0.665473	0.332737	+	0.943020i	$0.392028\pi$
$374$	3.13822	0.162273
$375$	−18.7500	−0.968246
$376$	1.79666	0.0926554
$377$	2.92705	0.150751
$378$	−10.3822	−0.534003
$379$	9.31240	0.478346	0.239173	−	0.970977i	$-0.423124\pi$
$379$	9.31240	0.478346	0.239173	+	0.970977i	$0.423124\pi$
$380$	5.55194	0.284809
$381$	−7.86815	−0.403097
$382$	17.3693	0.888688
$383$	−30.5403	−1.56053	−0.780267	−	0.625446i	$-0.784917\pi$
$383$	−30.5403	−1.56053	−0.780267	+	0.625446i	$0.784917\pi$
$384$	−1.81349	−0.0925443
$385$	−3.71035	−0.189097
$386$	−0.232198	−0.0118185
$387$	0.147701	0.00750809
$388$	9.24796	0.469494
$389$	−8.22065	−0.416803	−0.208402	−	0.978043i	$-0.566826\pi$
$389$	−8.22065	−0.416803	−0.208402	+	0.978043i	$0.566826\pi$
$390$	2.53514	0.128372
$391$	7.71143	0.389984
$392$	2.54129	0.128354
$393$	−24.1933	−1.22039
$394$	14.0568	0.708170
$395$	−20.5087	−1.03190
$396$	0.418655	0.0210382
$397$	14.1810	0.711726	0.355863	−	0.934538i	$-0.384187\pi$
$397$	14.1810	0.711726	0.355863	+	0.934538i	$0.384187\pi$
$398$	21.7735	1.09141
$399$	−17.5425	−0.878224
$400$	−3.53125	−0.176563
$401$	−6.37669	−0.318437	−0.159218	−	0.987243i	$-0.550897\pi$
$401$	−6.37669	−0.318437	−0.159218	+	0.987243i	$0.550897\pi$
$402$	2.52113	0.125743
$403$	6.87096	0.342267
$404$	−5.36539	−0.266938
$405$	−11.8560	−0.589131
$406$	−5.35823	−0.265925
$407$	2.15501	0.106820
$408$	3.92519	0.194326
$409$	−1.30707	−0.0646305	−0.0323152	−	0.999478i	$-0.510288\pi$
$409$	−1.30707	−0.0646305	−0.0323152	+	0.999478i	$0.510288\pi$
$410$	3.29528	0.162742
$411$	1.41793	0.0699415
$412$	−0.535058	−0.0263604
$413$	14.2541	0.701399
$414$	1.02875	0.0505601
$415$	2.74102	0.134551
$416$	1.15349	0.0565545
$417$	5.91892	0.289851
$418$	−6.64216	−0.324878
$419$	−22.2844	−1.08867	−0.544333	−	0.838869i	$-0.683217\pi$
$419$	−22.2844	−1.08867	−0.544333	+	0.838869i	$0.683217\pi$
$420$	−4.64081	−0.226448
$421$	−19.4465	−0.947764	−0.473882	−	0.880588i	$-0.657148\pi$
$421$	−19.4465	−0.947764	−0.473882	+	0.880588i	$0.657148\pi$
$422$	−28.1808	−1.37182
$423$	−0.518780	−0.0252240
$424$	6.91640	0.335890
$425$	7.64319	0.370749
$426$	−26.4853	−1.28322
$427$	0.757556	0.0366607
$428$	−15.2682	−0.738017
$429$	−3.03296	−0.146433
$430$	−0.619926	−0.0298955
$431$	11.6538	0.561344	0.280672	−	0.959804i	$-0.409443\pi$
$431$	11.6538	0.561344	0.280672	+	0.959804i	$0.409443\pi$
$432$	−4.91683	−0.236561
$433$	−6.45296	−0.310109	−0.155055	−	0.987906i	$-0.549555\pi$
$433$	−6.45296	−0.310109	−0.155055	+	0.987906i	$0.549555\pi$
$434$	−12.5779	−0.603759
$435$	−5.57706	−0.267400
$436$	−12.9728	−0.621285
$437$	−16.3215	−0.780765
$438$	−21.5236	−1.02844
$439$	32.7434	1.56276	0.781379	−	0.624057i	$-0.214517\pi$
$439$	32.7434	1.56276	0.781379	+	0.624057i	$0.214517\pi$
$440$	−1.75716	−0.0837692
$441$	−0.733792	−0.0349425
$442$	−2.49666	−0.118754
$443$	−6.76443	−0.321388	−0.160694	−	0.987004i	$-0.551373\pi$
$443$	−6.76443	−0.321388	−0.160694	+	0.987004i	$0.551373\pi$
$444$	2.69543	0.127919
$445$	20.4296	0.968457
$446$	−4.50328	−0.213236
$447$	5.19298	0.245619
$448$	−2.11157	−0.0997621
$449$	−10.2013	−0.481427	−0.240714	−	0.970596i	$-0.577381\pi$
$449$	−10.2013	−0.481427	−0.240714	+	0.970596i	$0.577381\pi$
$450$	1.01964	0.0480664
$451$	−3.94236	−0.185638
$452$	−0.261879	−0.0123177
$453$	−6.36545	−0.299075
$454$	−16.6069	−0.779398
$455$	2.95183	0.138384
$456$	−8.30782	−0.389049
$457$	28.6477	1.34008	0.670041	−	0.742324i	$-0.266277\pi$
$457$	28.6477	1.34008	0.670041	+	0.742324i	$0.266277\pi$
$458$	−13.4972	−0.630684
$459$	10.6422	0.496735
$460$	−4.31780	−0.201319
$461$	−17.4614	−0.813259	−0.406629	−	0.913593i	$-0.633296\pi$
$461$	−17.4614	−0.813259	−0.406629	+	0.913593i	$0.633296\pi$
$462$	5.55210	0.258307
$463$	35.8836	1.66765	0.833827	−	0.552026i	$-0.186145\pi$
$463$	35.8836	1.66765	0.833827	+	0.552026i	$0.186145\pi$
$464$	−2.53756	−0.117803
$465$	−13.0916	−0.607108
$466$	9.14002	0.423403
$467$	6.32373	0.292627	0.146314	−	0.989238i	$-0.453259\pi$
$467$	6.32373	0.292627	0.146314	+	0.989238i	$0.453259\pi$
$468$	−0.333068	−0.0153961
$469$	2.93552	0.135550
$470$	2.17740	0.100436
$471$	25.3345	1.16735
$472$	6.75049	0.310717
$473$	0.741658	0.0341014
$474$	30.6888	1.40958
$475$	−16.1771	−0.742256
$476$	4.57036	0.209482
$477$	−1.99710	−0.0914407
$478$	−21.2908	−0.973818
$479$	−19.2416	−0.879169	−0.439585	−	0.898201i	$-0.644874\pi$
$479$	−19.2416	−0.879169	−0.439585	+	0.898201i	$0.644874\pi$
$480$	−2.19780	−0.100316
$481$	−1.71446	−0.0781725
$482$	16.7940	0.764948
$483$	13.6430	0.620777
$484$	−8.89780	−0.404445
$485$	11.2078	0.508919
$486$	2.99065	0.135659
$487$	−22.9561	−1.04024	−0.520120	−	0.854093i	$-0.674113\pi$
$487$	−22.9561	−1.04024	−0.520120	+	0.854093i	$0.674113\pi$
$488$	0.358765	0.0162405
$489$	13.8627	0.626893
$490$	3.07984	0.139133
$491$	−34.5279	−1.55822	−0.779110	−	0.626887i	$-0.784329\pi$
$491$	−34.5279	−1.55822	−0.779110	+	0.626887i	$0.784329\pi$
$492$	−4.93099	−0.222306
$493$	5.49240	0.247365
$494$	5.28427	0.237751
$495$	0.507375	0.0228048
$496$	−5.95667	−0.267462
$497$	−30.8385	−1.38330
$498$	−4.10161	−0.183797
$499$	9.21400	0.412475	0.206238	−	0.978502i	$-0.433878\pi$
$499$	9.21400	0.412475	0.206238	+	0.978502i	$0.433878\pi$
$500$	−10.3392	−0.462382
$501$	2.96891	0.132641
$502$	0.249407	0.0111316
$503$	34.7193	1.54806	0.774029	−	0.633150i	$-0.218239\pi$
$503$	34.7193	1.54806	0.774029	+	0.633150i	$0.218239\pi$
$504$	0.609710	0.0271586
$505$	−6.50241	−0.289353
$506$	5.16567	0.229642
$507$	−21.1625	−0.939858
$508$	−4.33868	−0.192498
$509$	−7.18148	−0.318314	−0.159157	−	0.987253i	$-0.550878\pi$
$509$	−7.18148	−0.318314	−0.159157	+	0.987253i	$0.550878\pi$
$510$	4.75701	0.210644
$511$	−25.0613	−1.10865
$512$	−1.00000	−0.0441942
$513$	−22.5246	−0.994485
$514$	4.00530	0.176666
$515$	−0.648446	−0.0285740
$516$	0.927644	0.0408373
$517$	−2.60497	−0.114566
$518$	3.13847	0.137896
$519$	40.5580	1.78030
$520$	1.39794	0.0613035
$521$	4.15762	0.182149	0.0910743	−	0.995844i	$-0.470970\pi$
$521$	4.15762	0.182149	0.0910743	+	0.995844i	$0.470970\pi$
$522$	0.732716	0.0320701
$523$	−1.04113	−0.0455256	−0.0227628	−	0.999741i	$-0.507246\pi$
$523$	−1.04113	−0.0455256	−0.0227628	+	0.999741i	$0.507246\pi$
$524$	−13.3407	−0.582793
$525$	13.5222	0.590159
$526$	11.9416	0.520678
$527$	12.8929	0.561622
$528$	2.62938	0.114429
$529$	−10.3066	−0.448111
$530$	8.38211	0.364096
$531$	−1.94919	−0.0845877
$532$	−9.67334	−0.419392
$533$	3.13641	0.135853
$534$	−30.5705	−1.32291
$535$	−18.5038	−0.799991
$536$	1.39021	0.0600479
$537$	−17.8183	−0.768917
$538$	−13.9945	−0.603346
$539$	−3.68461	−0.158707
$540$	−5.95880	−0.256426
$541$	−18.0754	−0.777120	−0.388560	−	0.921423i	$-0.627027\pi$
$541$	−18.0754	−0.777120	−0.388560	+	0.921423i	$0.627027\pi$
$542$	22.8737	0.982510
$543$	−23.4287	−1.00542
$544$	2.16444	0.0927996
$545$	−15.7220	−0.673456
$546$	−4.41706	−0.189033
$547$	37.5738	1.60654	0.803270	−	0.595616i	$-0.203092\pi$
$547$	37.5738	1.60654	0.803270	+	0.595616i	$0.203092\pi$
$548$	0.781881	0.0334003
$549$	−0.103593	−0.00442123
$550$	5.11996	0.218316
$551$	−11.6249	−0.495237
$552$	6.46108	0.275002
$553$	35.7330	1.51952
$554$	−17.7255	−0.753084
$555$	3.26664	0.138661
$556$	3.26383	0.138417
$557$	−23.0462	−0.976499	−0.488249	−	0.872704i	$-0.662364\pi$
$557$	−23.0462	−0.976499	−0.488249	+	0.872704i	$0.662364\pi$
$558$	1.71998	0.0728124
$559$	−0.590038	−0.0249559
$560$	−2.55905	−0.108139
$561$	−5.69112	−0.240279
$562$	28.3910	1.19760
$563$	36.3156	1.53052	0.765261	−	0.643721i	$-0.222610\pi$
$563$	36.3156	1.53052	0.765261	+	0.643721i	$0.222610\pi$
$564$	−3.25822	−0.137196
$565$	−0.317376	−0.0133521
$566$	−30.0144	−1.26160
$567$	20.6572	0.867520
$568$	−14.6046	−0.612794
$569$	24.5770	1.03032	0.515161	−	0.857094i	$-0.327732\pi$
$569$	24.5770	1.03032	0.515161	+	0.857094i	$0.327732\pi$
$570$	−10.0684	−0.421719
$571$	35.3759	1.48044	0.740218	−	0.672367i	$-0.234722\pi$
$571$	35.3759	1.48044	0.740218	+	0.672367i	$0.234722\pi$
$572$	−1.67244	−0.0699283
$573$	−31.4990	−1.31589
$574$	−5.74147	−0.239644
$575$	12.5811	0.524668
$576$	0.288748	0.0120312
$577$	−2.18110	−0.0908004	−0.0454002	−	0.998969i	$-0.514456\pi$
$577$	−2.18110	−0.0908004	−0.0454002	+	0.998969i	$0.514456\pi$
$578$	12.3152	0.512245
$579$	0.421088	0.0174998
$580$	−3.07532	−0.127696
$581$	−4.77577	−0.198132
$582$	−16.7711	−0.695184
$583$	−10.0281	−0.415320
$584$	−11.8686	−0.491125
$585$	−0.403651	−0.0166889
$586$	−7.49617	−0.309664
$587$	−8.45802	−0.349100	−0.174550	−	0.984648i	$-0.555847\pi$
$587$	−8.45802	−0.349100	−0.174550	+	0.984648i	$0.555847\pi$
$588$	−4.60860	−0.190056
$589$	−27.2882	−1.12439
$590$	8.18105	0.336808
$591$	−25.4918	−1.04859
$592$	1.48632	0.0610874
$593$	−6.74033	−0.276792	−0.138396	−	0.990377i	$-0.544195\pi$
$593$	−6.74033	−0.276792	−0.138396	+	0.990377i	$0.544195\pi$
$594$	7.12890	0.292502
$595$	5.53890	0.227073
$596$	2.86353	0.117295
$597$	−39.4861	−1.61606
$598$	−4.10964	−0.168055
$599$	−45.7406	−1.86891	−0.934454	−	0.356083i	$-0.884112\pi$
$599$	−45.7406	−1.86891	−0.934454	+	0.356083i	$0.884112\pi$
$600$	6.40389	0.261438
$601$	−15.6693	−0.639164	−0.319582	−	0.947559i	$-0.603542\pi$
$601$	−15.6693	−0.639164	−0.319582	+	0.947559i	$0.603542\pi$
$602$	1.08012	0.0440223
$603$	−0.401420	−0.0163471
$604$	−3.51006	−0.142822
$605$	−10.7834	−0.438408
$606$	9.73008	0.395257
$607$	−32.6706	−1.32606	−0.663029	−	0.748593i	$-0.730730\pi$
$607$	−32.6706	−1.32606	−0.663029	+	0.748593i	$0.730730\pi$
$608$	−4.58112	−0.185789
$609$	9.71710	0.393757
$610$	0.434794	0.0176043
$611$	2.07242	0.0838413
$612$	−0.624977	−0.0252632
$613$	27.6417	1.11644	0.558220	−	0.829693i	$-0.311485\pi$
$613$	27.6417	1.11644	0.558220	+	0.829693i	$0.311485\pi$
$614$	−5.81502	−0.234675
$615$	−5.97595	−0.240974
$616$	3.06155	0.123354
$617$	−13.0038	−0.523514	−0.261757	−	0.965134i	$-0.584302\pi$
$617$	−13.0038	−0.523514	−0.261757	+	0.965134i	$0.584302\pi$
$618$	0.970322	0.0390321
$619$	27.8240	1.11834	0.559171	−	0.829052i	$-0.311119\pi$
$619$	27.8240	1.11834	0.559171	+	0.829052i	$0.311119\pi$
$620$	−7.21900	−0.289922
$621$	17.5176	0.702957
$622$	7.86767	0.315465
$623$	−35.5952	−1.42609
$624$	−2.09184	−0.0837407
$625$	5.12602	0.205041
$626$	−11.4852	−0.459040
$627$	12.0455	0.481050
$628$	13.9700	0.557465
$629$	−3.21705	−0.128272
$630$	0.738919	0.0294392
$631$	19.3308	0.769547	0.384774	−	0.923011i	$-0.374280\pi$
$631$	19.3308	0.769547	0.384774	+	0.923011i	$0.374280\pi$
$632$	16.9225	0.673141
$633$	51.1056	2.03127
$634$	21.4283	0.851026
$635$	−5.25812	−0.208662
$636$	−12.5428	−0.497355
$637$	2.93135	0.116144
$638$	3.67921	0.145661
$639$	4.21704	0.166824
$640$	−1.21192	−0.0479053
$641$	−5.71228	−0.225622	−0.112811	−	0.993616i	$-0.535985\pi$
$641$	−5.71228	−0.225622	−0.112811	+	0.993616i	$0.535985\pi$
$642$	27.6888	1.09279
$643$	−28.9835	−1.14300	−0.571499	−	0.820603i	$-0.693638\pi$
$643$	−28.9835	−1.14300	−0.571499	+	0.820603i	$0.693638\pi$
$644$	7.52305	0.296450
$645$	1.12423	0.0442665
$646$	9.91556	0.390122
$647$	7.37610	0.289984	0.144992	−	0.989433i	$-0.453684\pi$
$647$	7.37610	0.289984	0.144992	+	0.989433i	$0.453684\pi$
$648$	9.78287	0.384307
$649$	−9.78753	−0.384194
$650$	−4.07326	−0.159767
$651$	22.8099	0.893991
$652$	7.64421	0.299370
$653$	−40.4953	−1.58470	−0.792351	−	0.610065i	$-0.791143\pi$
$653$	−40.4953	−1.58470	−0.792351	+	0.610065i	$0.791143\pi$
$654$	23.5261	0.919942
$655$	−16.1679	−0.631732
$656$	−2.71906	−0.106161
$657$	3.42703	0.133701
$658$	−3.79376	−0.147896
$659$	−7.72841	−0.301056	−0.150528	−	0.988606i	$-0.548097\pi$
$659$	−7.72841	−0.301056	−0.150528	+	0.988606i	$0.548097\pi$
$660$	3.18659	0.124038
$661$	−18.3875	−0.715192	−0.357596	−	0.933876i	$-0.616404\pi$
$661$	−18.3875	−0.715192	−0.357596	+	0.933876i	$0.616404\pi$
$662$	−17.5954	−0.683866
$663$	4.52767	0.175840
$664$	−2.26172	−0.0877718
$665$	−11.7233	−0.454610
$666$	−0.429172	−0.0166301
$667$	9.04079	0.350061
$668$	1.63713	0.0633423
$669$	8.16665	0.315741
$670$	1.68482	0.0650903
$671$	−0.520173	−0.0200810
$672$	3.82930	0.147719
$673$	−8.75257	−0.337387	−0.168693	−	0.985669i	$-0.553955\pi$
$673$	−8.75257	−0.337387	−0.168693	+	0.985669i	$0.553955\pi$
$674$	6.44746	0.248347
$675$	17.3626	0.668286
$676$	−11.6695	−0.448825
$677$	15.8714	0.609987	0.304994	−	0.952354i	$-0.401346\pi$
$677$	15.8714	0.609987	0.304994	+	0.952354i	$0.401346\pi$
$678$	0.474915	0.0182390
$679$	−19.5277	−0.749403
$680$	2.62312	0.100592
$681$	30.1164	1.15406
$682$	8.63656	0.330711
$683$	24.8834	0.952135	0.476068	−	0.879409i	$-0.342062\pi$
$683$	24.8834	0.952135	0.476068	+	0.879409i	$0.342062\pi$
$684$	1.32279	0.0505781
$685$	0.947577	0.0362050
$686$	−20.1471	−0.769218
$687$	24.4771	0.933859
$688$	0.511524	0.0195017
$689$	7.97800	0.303937
$690$	7.83030	0.298094
$691$	−11.1549	−0.424354	−0.212177	−	0.977231i	$-0.568055\pi$
$691$	−11.1549	−0.424354	−0.212177	+	0.977231i	$0.568055\pi$
$692$	22.3646	0.850175
$693$	−0.884017	−0.0335810
$694$	−0.355481	−0.0134939
$695$	3.95549	0.150040
$696$	4.60185	0.174433
$697$	5.88524	0.222919
$698$	23.7147	0.897616
$699$	−16.5753	−0.626937
$700$	7.45647	0.281828
$701$	4.03035	0.152224	0.0761120	−	0.997099i	$-0.475749\pi$
$701$	4.03035	0.152224	0.0761120	+	0.997099i	$0.475749\pi$
$702$	−5.67151	−0.214057
$703$	6.80902	0.256807
$704$	1.44990	0.0546451
$705$	−3.94869	−0.148716
$706$	−1.79863	−0.0676924
$707$	11.3294	0.426085
$708$	−12.2420	−0.460081
$709$	−25.5956	−0.961262	−0.480631	−	0.876923i	$-0.659592\pi$
$709$	−25.5956	−0.961262	−0.480631	+	0.876923i	$0.659592\pi$
$710$	−17.6996	−0.664253
$711$	−4.88633	−0.183252
$712$	−16.8573	−0.631752
$713$	21.2223	0.794783
$714$	−8.28830	−0.310182
$715$	−2.02686	−0.0758004
$716$	−9.82543	−0.367194
$717$	38.6106	1.44194
$718$	−19.0360	−0.710418
$719$	37.0293	1.38096	0.690479	−	0.723352i	$-0.257400\pi$
$719$	37.0293	1.38096	0.690479	+	0.723352i	$0.257400\pi$
$720$	0.349939	0.0130415
$721$	1.12981	0.0420763
$722$	−1.98666	−0.0739360
$723$	−30.4558	−1.13267
$724$	−12.9191	−0.480135
$725$	8.96078	0.332795
$726$	16.1361	0.598866
$727$	−15.8349	−0.587285	−0.293643	−	0.955915i	$-0.594868\pi$
$727$	−15.8349	−0.587285	−0.293643	+	0.955915i	$0.594868\pi$
$728$	−2.43567	−0.0902719
$729$	23.9251	0.886115
$730$	−14.3838	−0.532367
$731$	−1.10716	−0.0409499
$732$	−0.650617	−0.0240475
$733$	−5.68168	−0.209858	−0.104929	−	0.994480i	$-0.533461\pi$
$733$	−5.68168	−0.209858	−0.104929	+	0.994480i	$0.533461\pi$
$734$	2.14706	0.0792492
$735$	−5.58525	−0.206015
$736$	3.56278	0.131326
$737$	−2.01566	−0.0742478
$738$	0.785122	0.0289008
$739$	−8.81325	−0.324201	−0.162100	−	0.986774i	$-0.551827\pi$
$739$	−8.81325	−0.324201	−0.162100	+	0.986774i	$0.551827\pi$
$740$	1.80130	0.0662171
$741$	−9.58298	−0.352040
$742$	−14.6044	−0.536146
$743$	−41.2531	−1.51343	−0.756714	−	0.653746i	$-0.773197\pi$
$743$	−41.2531	−1.51343	−0.756714	+	0.653746i	$0.773197\pi$
$744$	10.8024	0.396034
$745$	3.47036	0.127144
$746$	−12.8524	−0.470561
$747$	0.653067	0.0238945
$748$	−3.13822	−0.114745
$749$	32.2399	1.17802
$750$	18.7500	0.684654
$751$	13.1305	0.479138	0.239569	−	0.970879i	$-0.422994\pi$
$751$	13.1305	0.479138	0.239569	+	0.970879i	$0.422994\pi$
$752$	−1.79666	−0.0655173
$753$	−0.452298	−0.0164826
$754$	−2.92705	−0.106597
$755$	−4.25390	−0.154815
$756$	10.3822	0.377597
$757$	33.3589	1.21245	0.606226	−	0.795293i	$-0.292683\pi$
$757$	33.3589	1.21245	0.606226	+	0.795293i	$0.292683\pi$
$758$	−9.31240	−0.338242
$759$	−9.36790	−0.340033
$760$	−5.55194	−0.201390
$761$	6.01833	0.218164	0.109082	−	0.994033i	$-0.465209\pi$
$761$	6.01833	0.218164	0.109082	+	0.994033i	$0.465209\pi$
$762$	7.86815	0.285033
$763$	27.3930	0.991691
$764$	−17.3693	−0.628397
$765$	−0.757422	−0.0273846
$766$	30.5403	1.10346
$767$	7.78663	0.281159
$768$	1.81349	0.0654387
$769$	51.7444	1.86595	0.932975	−	0.359941i	$-0.117203\pi$
$769$	51.7444	1.86595	0.932975	+	0.359941i	$0.117203\pi$
$770$	3.71035	0.133712
$771$	−7.26358	−0.261591
$772$	0.232198	0.00835697
$773$	3.77096	0.135632	0.0678159	−	0.997698i	$-0.478397\pi$
$773$	3.77096	0.135632	0.0678159	+	0.997698i	$0.478397\pi$
$774$	−0.147701	−0.00530902
$775$	21.0345	0.755582
$776$	−9.24796	−0.331982
$777$	−5.69158	−0.204184
$778$	8.22065	0.294725
$779$	−12.4563	−0.446295
$780$	−2.53514	−0.0907727
$781$	21.1751	0.757706
$782$	−7.71143	−0.275760
$783$	12.4768	0.445883
$784$	−2.54129	−0.0907603
$785$	16.9305	0.604277
$786$	24.1933	0.862946
$787$	51.4033	1.83233	0.916164	−	0.400803i	$-0.131269\pi$
$787$	51.4033	1.83233	0.916164	+	0.400803i	$0.131269\pi$
$788$	−14.0568	−0.500752
$789$	−21.6559	−0.770972
$790$	20.5087	0.729666
$791$	0.552974	0.0196615
$792$	−0.418655	−0.0148762
$793$	0.413832	0.0146956
$794$	−14.1810	−0.503266
$795$	−15.2009	−0.539120
$796$	−21.7735	−0.771742
$797$	−25.5348	−0.904491	−0.452245	−	0.891894i	$-0.649377\pi$
$797$	−25.5348	−0.904491	−0.452245	+	0.891894i	$0.649377\pi$
$798$	17.5425	0.620998
$799$	3.88875	0.137574
$800$	3.53125	0.124849
$801$	4.86749	0.171984
$802$	6.37669	0.225169
$803$	17.2082	0.607265
$804$	−2.52113	−0.0889134
$805$	9.11733	0.321344
$806$	−6.87096	−0.242019
$807$	25.3789	0.893380
$808$	5.36539	0.188754
$809$	−9.86967	−0.346999	−0.173500	−	0.984834i	$-0.555508\pi$
$809$	−9.86967	−0.346999	−0.173500	+	0.984834i	$0.555508\pi$
$810$	11.8560	0.416579
$811$	−14.0369	−0.492902	−0.246451	−	0.969155i	$-0.579264\pi$
$811$	−14.0369	−0.492902	−0.246451	+	0.969155i	$0.579264\pi$
$812$	5.35823	0.188037
$813$	−41.4813	−1.45481
$814$	−2.15501	−0.0755332
$815$	9.26416	0.324509
$816$	−3.92519	−0.137409
$817$	2.34335	0.0819836
$818$	1.30707	0.0457007
$819$	0.703294	0.0245751
$820$	−3.29528	−0.115076
$821$	12.2309	0.426861	0.213431	−	0.976958i	$-0.431536\pi$
$821$	12.2309	0.426861	0.213431	+	0.976958i	$0.431536\pi$
$822$	−1.41793	−0.0494561
$823$	−46.2216	−1.61118	−0.805592	−	0.592470i	$-0.798153\pi$
$823$	−46.2216	−1.61118	−0.805592	+	0.592470i	$0.798153\pi$
$824$	0.535058	0.0186396
$825$	−9.28499	−0.323262
$826$	−14.2541	−0.495964
$827$	9.59824	0.333763	0.166882	−	0.985977i	$-0.446630\pi$
$827$	9.59824	0.333763	0.166882	+	0.985977i	$0.446630\pi$
$828$	−1.02875	−0.0357514
$829$	47.8741	1.66274	0.831368	−	0.555723i	$-0.187558\pi$
$829$	47.8741	1.66274	0.831368	+	0.555723i	$0.187558\pi$
$830$	−2.74102	−0.0951422
$831$	32.1450	1.11510
$832$	−1.15349	−0.0399901
$833$	5.50047	0.190580
$834$	−5.91892	−0.204955
$835$	1.98406	0.0686613
$836$	6.64216	0.229724
$837$	29.2879	1.01234
$838$	22.2844	0.769804
$839$	−20.8677	−0.720434	−0.360217	−	0.932869i	$-0.617297\pi$
$839$	−20.8677	−0.720434	−0.360217	+	0.932869i	$0.617297\pi$
$840$	4.64081	0.160123
$841$	−22.5608	−0.777958
$842$	19.4465	0.670171
$843$	−51.4869	−1.77330
$844$	28.1808	0.970023
$845$	−14.1424	−0.486515
$846$	0.518780	0.0178360
$847$	18.7883	0.645573
$848$	−6.91640	−0.237510
$849$	54.4308	1.86806
$850$	−7.64319	−0.262159
$851$	−5.29544	−0.181525
$852$	26.4853	0.907370
$853$	49.3510	1.68975	0.844873	−	0.534966i	$-0.179676\pi$
$853$	49.3510	1.68975	0.844873	+	0.534966i	$0.179676\pi$
$854$	−0.757556	−0.0259230
$855$	1.60311	0.0548253
$856$	15.2682	0.521857
$857$	−35.0244	−1.19641	−0.598206	−	0.801342i	$-0.704119\pi$
$857$	−35.0244	−1.19641	−0.598206	+	0.801342i	$0.704119\pi$
$858$	3.03296	0.103543
$859$	48.3616	1.65008	0.825038	−	0.565077i	$-0.191154\pi$
$859$	48.3616	1.65008	0.825038	+	0.565077i	$0.191154\pi$
$860$	0.619926	0.0211393
$861$	10.4121	0.354844
$862$	−11.6538	−0.396930
$863$	−29.7644	−1.01319	−0.506596	−	0.862184i	$-0.669096\pi$
$863$	−29.7644	−1.01319	−0.506596	+	0.862184i	$0.669096\pi$
$864$	4.91683	0.167274
$865$	27.1041	0.921567
$866$	6.45296	0.219280
$867$	−22.3335	−0.758485
$868$	12.5779	0.426922
$869$	−24.5359	−0.832323
$870$	5.57706	0.189080
$871$	1.60359	0.0543356
$872$	12.9728	0.439315
$873$	2.67033	0.0903769
$874$	16.3215	0.552085
$875$	21.8319	0.738052
$876$	21.5236	0.727214
$877$	4.40983	0.148909	0.0744546	−	0.997224i	$-0.476278\pi$
$877$	4.40983	0.148909	0.0744546	+	0.997224i	$0.476278\pi$
$878$	−32.7434	−1.10504
$879$	13.5942	0.458522
$880$	1.75716	0.0592338
$881$	42.8805	1.44468	0.722341	−	0.691538i	$-0.243066\pi$
$881$	42.8805	1.44468	0.722341	+	0.691538i	$0.243066\pi$
$882$	0.733792	0.0247081
$883$	5.75320	0.193610	0.0968052	−	0.995303i	$-0.469138\pi$
$883$	5.75320	0.193610	0.0968052	+	0.995303i	$0.469138\pi$
$884$	2.49666	0.0839717
$885$	−14.8363	−0.498715
$886$	6.76443	0.227256
$887$	42.4673	1.42591	0.712957	−	0.701208i	$-0.247356\pi$
$887$	42.4673	1.42591	0.712957	+	0.701208i	$0.247356\pi$
$888$	−2.69543	−0.0904527
$889$	9.16140	0.307264
$890$	−20.4296	−0.684802
$891$	−14.1842	−0.475187
$892$	4.50328	0.150781
$893$	−8.23069	−0.275430
$894$	−5.19298	−0.173679
$895$	−11.9076	−0.398028
$896$	2.11157	0.0705425
$897$	7.45278	0.248841
$898$	10.2013	0.340420
$899$	15.1154	0.504128
$900$	−1.01964	−0.0339881
$901$	14.9701	0.498727
$902$	3.94236	0.131266
$903$	−1.95878	−0.0651842
$904$	0.261879	0.00870996
$905$	−15.6569	−0.520453
$906$	6.36545	0.211478
$907$	−1.00612	−0.0334076	−0.0167038	−	0.999860i	$-0.505317\pi$
$907$	−1.00612	−0.0334076	−0.0167038	+	0.999860i	$0.505317\pi$
$908$	16.6069	0.551118
$909$	−1.54924	−0.0513852
$910$	−2.95183	−0.0978523
$911$	28.2717	0.936683	0.468341	−	0.883548i	$-0.344852\pi$
$911$	28.2717	0.936683	0.468341	+	0.883548i	$0.344852\pi$
$912$	8.30782	0.275099
$913$	3.27926	0.108528
$914$	−28.6477	−0.947581
$915$	−0.788495	−0.0260668
$916$	13.4972	0.445961
$917$	28.1698	0.930250
$918$	−10.6422	−0.351244
$919$	40.5397	1.33728	0.668640	−	0.743586i	$-0.266877\pi$
$919$	40.5397	1.33728	0.668640	+	0.743586i	$0.266877\pi$
$920$	4.31780	0.142354
$921$	10.5455	0.347485
$922$	17.4614	0.575061
$923$	−16.8462	−0.554500
$924$	−5.55210	−0.182651
$925$	−5.24858	−0.172572
$926$	−35.8836	−1.17921
$927$	−0.154497	−0.00507434
$928$	2.53756	0.0832996
$929$	20.9063	0.685914	0.342957	−	0.939351i	$-0.388571\pi$
$929$	20.9063	0.685914	0.342957	+	0.939351i	$0.388571\pi$
$930$	13.0916	0.429290
$931$	−11.6420	−0.381550
$932$	−9.14002	−0.299391
$933$	−14.2679	−0.467112
$934$	−6.32373	−0.206919
$935$	−3.80326	−0.124380
$936$	0.333068	0.0108867
$937$	23.1423	0.756025	0.378012	−	0.925801i	$-0.376608\pi$
$937$	23.1423	0.756025	0.378012	+	0.925801i	$0.376608\pi$
$938$	−2.93552	−0.0958480
$939$	20.8282	0.679704
$940$	−2.17740	−0.0710189
$941$	−42.2809	−1.37832	−0.689158	−	0.724611i	$-0.742020\pi$
$941$	−42.2809	−1.37832	−0.689158	+	0.724611i	$0.742020\pi$
$942$	−25.3345	−0.825444
$943$	9.68742	0.315466
$944$	−6.75049	−0.219710
$945$	12.5824	0.409305
$946$	−0.741658	−0.0241134
$947$	−41.5819	−1.35123	−0.675614	−	0.737255i	$-0.736122\pi$
$947$	−41.5819	−1.35123	−0.675614	+	0.737255i	$0.736122\pi$
$948$	−30.6888	−0.996725
$949$	−13.6903	−0.444405
$950$	16.1771	0.524854
$951$	−38.8600	−1.26012
$952$	−4.57036	−0.148126
$953$	16.6763	0.540200	0.270100	−	0.962832i	$-0.412943\pi$
$953$	16.6763	0.540200	0.270100	+	0.962832i	$0.412943\pi$
$954$	1.99710	0.0646584
$955$	−21.0501	−0.681166
$956$	21.2908	0.688593
$957$	−6.67220	−0.215682
$958$	19.2416	0.621666
$959$	−1.65099	−0.0533134
$960$	2.19780	0.0709338
$961$	4.48192	0.144578
$962$	1.71446	0.0552763
$963$	−4.40867	−0.142067
$964$	−16.7940	−0.540900
$965$	0.281405	0.00905873
$966$	−13.6430	−0.438956
$967$	−50.9743	−1.63922	−0.819611	−	0.572921i	$-0.805810\pi$
$967$	−50.9743	−1.63922	−0.819611	+	0.572921i	$0.805810\pi$
$968$	8.89780	0.285986
$969$	−17.9818	−0.577658
$970$	−11.2078	−0.359860
$971$	60.1123	1.92910	0.964548	−	0.263907i	$-0.0850114\pi$
$971$	60.1123	1.92910	0.964548	+	0.263907i	$0.0850114\pi$
$972$	−2.99065	−0.0959251
$973$	−6.89179	−0.220941
$974$	22.9561	0.735561
$975$	7.38683	0.236568
$976$	−0.358765	−0.0114838
$977$	2.24937	0.0719638	0.0359819	−	0.999352i	$-0.488544\pi$
$977$	2.24937	0.0719638	0.0359819	+	0.999352i	$0.488544\pi$
$978$	−13.8627	−0.443280
$979$	24.4413	0.781147
$980$	−3.07984	−0.0983817
$981$	−3.74587	−0.119596
$982$	34.5279	1.10183
$983$	−45.7344	−1.45870	−0.729350	−	0.684140i	$-0.760178\pi$
$983$	−45.7344	−1.45870	−0.729350	+	0.684140i	$0.760178\pi$
$984$	4.93099	0.157194
$985$	−17.0357	−0.542801
$986$	−5.49240	−0.174914
$987$	6.87994	0.218991
$988$	−5.28427	−0.168115
$989$	−1.82245	−0.0579505
$990$	−0.507375	−0.0161255
$991$	0.367928	0.0116876	0.00584381	−	0.999983i	$-0.498140\pi$
$991$	0.367928	0.0116876	0.00584381	+	0.999983i	$0.498140\pi$
$992$	5.95667	0.189124
$993$	31.9092	1.01261
$994$	30.8385	0.978139
$995$	−26.3877	−0.836548
$996$	4.10161	0.129964
$997$	22.5016	0.712633	0.356317	−	0.934365i	$-0.384032\pi$
$997$	22.5016	0.712633	0.356317	+	0.934365i	$0.384032\pi$
$998$	−9.21400	−0.291664
$999$	−7.30799	−0.231215

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.g.1.32	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.g.1.32	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.81349 q^{3} +1.00000 q^{4} +1.21192 q^{5} -1.81349 q^{6} -2.11157 q^{7} -1.00000 q^{8} +0.288748 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.81349 q^{3} +1.00000 q^{4} +1.21192 q^{5} -1.81349 q^{6} -2.11157 q^{7} -1.00000 q^{8} +0.288748 q^{9} -1.21192 q^{10} +1.44990 q^{11} +1.81349 q^{12} -1.15349 q^{13} +2.11157 q^{14} +2.19780 q^{15} +1.00000 q^{16} -2.16444 q^{17} -0.288748 q^{18} +4.58112 q^{19} +1.21192 q^{20} -3.82930 q^{21} -1.44990 q^{22} -3.56278 q^{23} -1.81349 q^{24} -3.53125 q^{25} +1.15349 q^{26} -4.91683 q^{27} -2.11157 q^{28} -2.53756 q^{29} -2.19780 q^{30} -5.95667 q^{31} -1.00000 q^{32} +2.62938 q^{33} +2.16444 q^{34} -2.55905 q^{35} +0.288748 q^{36} +1.48632 q^{37} -4.58112 q^{38} -2.09184 q^{39} -1.21192 q^{40} -2.71906 q^{41} +3.82930 q^{42} +0.511524 q^{43} +1.44990 q^{44} +0.349939 q^{45} +3.56278 q^{46} -1.79666 q^{47} +1.81349 q^{48} -2.54129 q^{49} +3.53125 q^{50} -3.92519 q^{51} -1.15349 q^{52} -6.91640 q^{53} +4.91683 q^{54} +1.75716 q^{55} +2.11157 q^{56} +8.30782 q^{57} +2.53756 q^{58} -6.75049 q^{59} +2.19780 q^{60} -0.358765 q^{61} +5.95667 q^{62} -0.609710 q^{63} +1.00000 q^{64} -1.39794 q^{65} -2.62938 q^{66} -1.39021 q^{67} -2.16444 q^{68} -6.46108 q^{69} +2.55905 q^{70} +14.6046 q^{71} -0.288748 q^{72} +11.8686 q^{73} -1.48632 q^{74} -6.40389 q^{75} +4.58112 q^{76} -3.06155 q^{77} +2.09184 q^{78} -16.9225 q^{79} +1.21192 q^{80} -9.78287 q^{81} +2.71906 q^{82} +2.26172 q^{83} -3.82930 q^{84} -2.62312 q^{85} -0.511524 q^{86} -4.60185 q^{87} -1.44990 q^{88} +16.8573 q^{89} -0.349939 q^{90} +2.43567 q^{91} -3.56278 q^{92} -10.8024 q^{93} +1.79666 q^{94} +5.55194 q^{95} -1.81349 q^{96} +9.24796 q^{97} +2.54129 q^{98} +0.418655 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) \) 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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