LMFDB - Embedded newform 4006.2.a.g.1.8

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			1.8
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.94007 q^{3} +1.00000 q^{4} -0.275091 q^{5} +1.94007 q^{6} -2.80268 q^{7} -1.00000 q^{8} +0.763873 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.94007 q^{3} +1.00000 q^{4} -0.275091 q^{5} +1.94007 q^{6} -2.80268 q^{7} -1.00000 q^{8} +0.763873 q^{9} +0.275091 q^{10} -2.43291 q^{11} -1.94007 q^{12} +1.63440 q^{13} +2.80268 q^{14} +0.533696 q^{15} +1.00000 q^{16} -1.12271 q^{17} -0.763873 q^{18} +6.24346 q^{19} -0.275091 q^{20} +5.43740 q^{21} +2.43291 q^{22} -5.13618 q^{23} +1.94007 q^{24} -4.92432 q^{25} -1.63440 q^{26} +4.33824 q^{27} -2.80268 q^{28} -3.36352 q^{29} -0.533696 q^{30} +7.35325 q^{31} -1.00000 q^{32} +4.72002 q^{33} +1.12271 q^{34} +0.770993 q^{35} +0.763873 q^{36} +10.5709 q^{37} -6.24346 q^{38} -3.17085 q^{39} +0.275091 q^{40} -8.26556 q^{41} -5.43740 q^{42} +11.1306 q^{43} -2.43291 q^{44} -0.210135 q^{45} +5.13618 q^{46} -1.86722 q^{47} -1.94007 q^{48} +0.855018 q^{49} +4.92432 q^{50} +2.17813 q^{51} +1.63440 q^{52} +6.50923 q^{53} -4.33824 q^{54} +0.669273 q^{55} +2.80268 q^{56} -12.1127 q^{57} +3.36352 q^{58} +6.17307 q^{59} +0.533696 q^{60} +2.40011 q^{61} -7.35325 q^{62} -2.14089 q^{63} +1.00000 q^{64} -0.449609 q^{65} -4.72002 q^{66} -3.85137 q^{67} -1.12271 q^{68} +9.96455 q^{69} -0.770993 q^{70} -4.38439 q^{71} -0.763873 q^{72} -0.249004 q^{73} -10.5709 q^{74} +9.55354 q^{75} +6.24346 q^{76} +6.81868 q^{77} +3.17085 q^{78} -12.4573 q^{79} -0.275091 q^{80} -10.7081 q^{81} +8.26556 q^{82} +16.6569 q^{83} +5.43740 q^{84} +0.308846 q^{85} -11.1306 q^{86} +6.52546 q^{87} +2.43291 q^{88} -8.22939 q^{89} +0.210135 q^{90} -4.58070 q^{91} -5.13618 q^{92} -14.2658 q^{93} +1.86722 q^{94} -1.71752 q^{95} +1.94007 q^{96} +1.29351 q^{97} -0.855018 q^{98} -1.85844 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.94007	−1.12010	−0.560050	−	0.828459i	$-0.689218\pi$
$3$	−1.94007	−1.12010	−0.560050	+	0.828459i	$0.689218\pi$
$4$	1.00000	0.500000
$5$	−0.275091	−0.123025	−0.0615123	−	0.998106i	$-0.519592\pi$
$5$	−0.275091	−0.123025	−0.0615123	+	0.998106i	$0.519592\pi$
$6$	1.94007	0.792030
$7$	−2.80268	−1.05931	−0.529657	−	0.848212i	$-0.677679\pi$
$7$	−2.80268	−1.05931	−0.529657	+	0.848212i	$0.677679\pi$
$8$	−1.00000	−0.353553
$9$	0.763873	0.254624
$10$	0.275091	0.0869915
$11$	−2.43291	−0.733551	−0.366776	−	0.930309i	$-0.619538\pi$
$11$	−2.43291	−0.733551	−0.366776	+	0.930309i	$0.619538\pi$
$12$	−1.94007	−0.560050
$13$	1.63440	0.453301	0.226650	−	0.973976i	$-0.427223\pi$
$13$	1.63440	0.453301	0.226650	+	0.973976i	$0.427223\pi$
$14$	2.80268	0.749048
$15$	0.533696	0.137800
$16$	1.00000	0.250000
$17$	−1.12271	−0.272296	−0.136148	−	0.990689i	$-0.543472\pi$
$17$	−1.12271	−0.272296	−0.136148	+	0.990689i	$0.543472\pi$
$18$	−0.763873	−0.180047
$19$	6.24346	1.43235	0.716174	−	0.697922i	$-0.245892\pi$
$19$	6.24346	1.43235	0.716174	+	0.697922i	$0.245892\pi$
$20$	−0.275091	−0.0615123
$21$	5.43740	1.18654
$22$	2.43291	0.518699
$23$	−5.13618	−1.07097	−0.535484	−	0.844545i	$-0.679871\pi$
$23$	−5.13618	−1.07097	−0.535484	+	0.844545i	$0.679871\pi$
$24$	1.94007	0.396015
$25$	−4.92432	−0.984865
$26$	−1.63440	−0.320532
$27$	4.33824	0.834895
$28$	−2.80268	−0.529657
$29$	−3.36352	−0.624589	−0.312295	−	0.949985i	$-0.601098\pi$
$29$	−3.36352	−0.624589	−0.312295	+	0.949985i	$0.601098\pi$
$30$	−0.533696	−0.0974391
$31$	7.35325	1.32068	0.660341	−	0.750966i	$-0.270412\pi$
$31$	7.35325	1.32068	0.660341	+	0.750966i	$0.270412\pi$
$32$	−1.00000	−0.176777
$33$	4.72002	0.821651
$34$	1.12271	0.192542
$35$	0.770993	0.130322
$36$	0.763873	0.127312
$37$	10.5709	1.73785	0.868926	−	0.494942i	$-0.164811\pi$
$37$	10.5709	1.73785	0.868926	+	0.494942i	$0.164811\pi$
$38$	−6.24346	−1.01282
$39$	−3.17085	−0.507742
$40$	0.275091	0.0434957
$41$	−8.26556	−1.29086	−0.645432	−	0.763818i	$-0.723323\pi$
$41$	−8.26556	−1.29086	−0.645432	+	0.763818i	$0.723323\pi$
$42$	−5.43740	−0.839009
$43$	11.1306	1.69741	0.848703	−	0.528869i	$-0.177384\pi$
$43$	11.1306	1.69741	0.848703	+	0.528869i	$0.177384\pi$
$44$	−2.43291	−0.366776
$45$	−0.210135	−0.0313250
$46$	5.13618	0.757288
$47$	−1.86722	−0.272363	−0.136181	−	0.990684i	$-0.543483\pi$
$47$	−1.86722	−0.272363	−0.136181	+	0.990684i	$0.543483\pi$
$48$	−1.94007	−0.280025
$49$	0.855018	0.122145
$50$	4.92432	0.696405
$51$	2.17813	0.304999
$52$	1.63440	0.226650
$53$	6.50923	0.894111	0.447056	−	0.894506i	$-0.352473\pi$
$53$	6.50923	0.894111	0.447056	+	0.894506i	$0.352473\pi$
$54$	−4.33824	−0.590360
$55$	0.669273	0.0902448
$56$	2.80268	0.374524
$57$	−12.1127	−1.60437
$58$	3.36352	0.441651
$59$	6.17307	0.803666	0.401833	−	0.915713i	$-0.368373\pi$
$59$	6.17307	0.803666	0.401833	+	0.915713i	$0.368373\pi$
$60$	0.533696	0.0688999
$61$	2.40011	0.307303	0.153651	−	0.988125i	$-0.450897\pi$
$61$	2.40011	0.307303	0.153651	+	0.988125i	$0.450897\pi$
$62$	−7.35325	−0.933863
$63$	−2.14089	−0.269727
$64$	1.00000	0.125000
$65$	−0.449609	−0.0557671
$66$	−4.72002	−0.580995
$67$	−3.85137	−0.470520	−0.235260	−	0.971933i	$-0.575594\pi$
$67$	−3.85137	−0.470520	−0.235260	+	0.971933i	$0.575594\pi$
$68$	−1.12271	−0.136148
$69$	9.96455	1.19959
$70$	−0.770993	−0.0921512
$71$	−4.38439	−0.520332	−0.260166	−	0.965564i	$-0.583777\pi$
$71$	−4.38439	−0.520332	−0.260166	+	0.965564i	$0.583777\pi$
$72$	−0.763873	−0.0900233
$73$	−0.249004	−0.0291437	−0.0145719	−	0.999894i	$-0.504639\pi$
$73$	−0.249004	−0.0291437	−0.0145719	+	0.999894i	$0.504639\pi$
$74$	−10.5709	−1.22885
$75$	9.55354	1.10315
$76$	6.24346	0.716174
$77$	6.81868	0.777061
$78$	3.17085	0.359028
$79$	−12.4573	−1.40156	−0.700781	−	0.713377i	$-0.747165\pi$
$79$	−12.4573	−1.40156	−0.700781	+	0.713377i	$0.747165\pi$
$80$	−0.275091	−0.0307561
$81$	−10.7081	−1.18979
$82$	8.26556	0.912779
$83$	16.6569	1.82834	0.914168	−	0.405334i	$-0.132845\pi$
$83$	16.6569	1.82834	0.914168	+	0.405334i	$0.132845\pi$
$84$	5.43740	0.593269
$85$	0.308846	0.0334991
$86$	−11.1306	−1.20025
$87$	6.52546	0.699602
$88$	2.43291	0.259350
$89$	−8.22939	−0.872313	−0.436157	−	0.899871i	$-0.643661\pi$
$89$	−8.22939	−0.872313	−0.436157	+	0.899871i	$0.643661\pi$
$90$	0.210135	0.0221501
$91$	−4.58070	−0.480187
$92$	−5.13618	−0.535484
$93$	−14.2658	−1.47930
$94$	1.86722	0.192589
$95$	−1.71752	−0.176214
$96$	1.94007	0.198008
$97$	1.29351	0.131336	0.0656681	−	0.997842i	$-0.479082\pi$
$97$	1.29351	0.131336	0.0656681	+	0.997842i	$0.479082\pi$
$98$	−0.855018	−0.0863699
$99$	−1.85844	−0.186780
$100$	−4.92432	−0.492432
$101$	−0.460574	−0.0458288	−0.0229144	−	0.999737i	$-0.507295\pi$
$101$	−0.460574	−0.0458288	−0.0229144	+	0.999737i	$0.507295\pi$
$102$	−2.17813	−0.215667
$103$	5.21367	0.513718	0.256859	−	0.966449i	$-0.417312\pi$
$103$	5.21367	0.513718	0.256859	+	0.966449i	$0.417312\pi$
$104$	−1.63440	−0.160266
$105$	−1.49578	−0.145973
$106$	−6.50923	−0.632232
$107$	3.51857	0.340153	0.170077	−	0.985431i	$-0.445598\pi$
$107$	3.51857	0.340153	0.170077	+	0.985431i	$0.445598\pi$
$108$	4.33824	0.417448
$109$	4.16929	0.399345	0.199673	−	0.979863i	$-0.436012\pi$
$109$	4.16929	0.399345	0.199673	+	0.979863i	$0.436012\pi$
$110$	−0.669273	−0.0638127
$111$	−20.5084	−1.94657
$112$	−2.80268	−0.264828
$113$	−5.75243	−0.541143	−0.270572	−	0.962700i	$-0.587213\pi$
$113$	−5.75243	−0.541143	−0.270572	+	0.962700i	$0.587213\pi$
$114$	12.1127	1.13446
$115$	1.41292	0.131755
$116$	−3.36352	−0.312295
$117$	1.24847	0.115421
$118$	−6.17307	−0.568278
$119$	3.14659	0.288447
$120$	−0.533696	−0.0487196
$121$	−5.08093	−0.461903
$122$	−2.40011	−0.217296
$123$	16.0358	1.44590
$124$	7.35325	0.660341
$125$	2.73009	0.244187
$126$	2.14089	0.190726
$127$	16.7212	1.48376	0.741882	−	0.670531i	$-0.233934\pi$
$127$	16.7212	1.48376	0.741882	+	0.670531i	$0.233934\pi$
$128$	−1.00000	−0.0883883
$129$	−21.5942	−1.90127
$130$	0.449609	0.0394333
$131$	−6.26032	−0.546967	−0.273483	−	0.961877i	$-0.588176\pi$
$131$	−6.26032	−0.546967	−0.273483	+	0.961877i	$0.588176\pi$
$132$	4.72002	0.410825
$133$	−17.4984	−1.51731
$134$	3.85137	0.332708
$135$	−1.19341	−0.102713
$136$	1.12271	0.0962712
$137$	8.90358	0.760684	0.380342	−	0.924846i	$-0.375806\pi$
$137$	8.90358	0.760684	0.380342	+	0.924846i	$0.375806\pi$
$138$	−9.96455	−0.848239
$139$	2.89358	0.245430	0.122715	−	0.992442i	$-0.460840\pi$
$139$	2.89358	0.245430	0.122715	+	0.992442i	$0.460840\pi$
$140$	0.770993	0.0651608
$141$	3.62255	0.305073
$142$	4.38439	0.367930
$143$	−3.97635	−0.332519
$144$	0.763873	0.0636561
$145$	0.925273	0.0768398
$146$	0.249004	0.0206077
$147$	−1.65880	−0.136815
$148$	10.5709	0.868926
$149$	−10.3303	−0.846291	−0.423145	−	0.906062i	$-0.639074\pi$
$149$	−10.3303	−0.846291	−0.423145	+	0.906062i	$0.639074\pi$
$150$	−9.55354	−0.780043
$151$	−18.8141	−1.53107	−0.765536	−	0.643393i	$-0.777526\pi$
$151$	−18.8141	−1.53107	−0.765536	+	0.643393i	$0.777526\pi$
$152$	−6.24346	−0.506411
$153$	−0.857604	−0.0693332
$154$	−6.81868	−0.549465
$155$	−2.02281	−0.162476
$156$	−3.17085	−0.253871
$157$	−2.56362	−0.204599	−0.102300	−	0.994754i	$-0.532620\pi$
$157$	−2.56362	−0.204599	−0.102300	+	0.994754i	$0.532620\pi$
$158$	12.4573	0.991053
$159$	−12.6284	−1.00149
$160$	0.275091	0.0217479
$161$	14.3951	1.13449
$162$	10.7081	0.841309
$163$	−11.8007	−0.924302	−0.462151	−	0.886801i	$-0.652922\pi$
$163$	−11.8007	−0.924302	−0.462151	+	0.886801i	$0.652922\pi$
$164$	−8.26556	−0.645432
$165$	−1.29844	−0.101083
$166$	−16.6569	−1.29283
$167$	7.22991	0.559468	0.279734	−	0.960078i	$-0.409754\pi$
$167$	7.22991	0.559468	0.279734	+	0.960078i	$0.409754\pi$
$168$	−5.43740	−0.419504
$169$	−10.3287	−0.794519
$170$	−0.308846	−0.0236874
$171$	4.76921	0.364710
$172$	11.1306	0.848703
$173$	12.8262	0.975155	0.487577	−	0.873080i	$-0.337881\pi$
$173$	12.8262	0.975155	0.487577	+	0.873080i	$0.337881\pi$
$174$	−6.52546	−0.494694
$175$	13.8013	1.04328
$176$	−2.43291	−0.183388
$177$	−11.9762	−0.900186
$178$	8.22939	0.616819
$179$	16.7297	1.25044	0.625218	−	0.780450i	$-0.285010\pi$
$179$	16.7297	1.25044	0.625218	+	0.780450i	$0.285010\pi$
$180$	−0.210135	−0.0156625
$181$	−11.0599	−0.822075	−0.411038	−	0.911618i	$-0.634833\pi$
$181$	−11.0599	−0.822075	−0.411038	+	0.911618i	$0.634833\pi$
$182$	4.58070	0.339544
$183$	−4.65638	−0.344210
$184$	5.13618	0.378644
$185$	−2.90797	−0.213798
$186$	14.2658	1.04602
$187$	2.73145	0.199743
$188$	−1.86722	−0.136181
$189$	−12.1587	−0.884416
$190$	1.71752	0.124602
$191$	16.5160	1.19505	0.597526	−	0.801849i	$-0.296150\pi$
$191$	16.5160	1.19505	0.597526	+	0.801849i	$0.296150\pi$
$192$	−1.94007	−0.140013
$193$	8.13814	0.585796	0.292898	−	0.956144i	$-0.405380\pi$
$193$	8.13814	0.585796	0.292898	+	0.956144i	$0.405380\pi$
$194$	−1.29351	−0.0928687
$195$	0.872272	0.0624647
$196$	0.855018	0.0610727
$197$	−15.3167	−1.09127	−0.545633	−	0.838024i	$-0.683711\pi$
$197$	−15.3167	−1.09127	−0.545633	+	0.838024i	$0.683711\pi$
$198$	1.85844	0.132073
$199$	10.5399	0.747154	0.373577	−	0.927599i	$-0.378131\pi$
$199$	10.5399	0.747154	0.373577	+	0.927599i	$0.378131\pi$
$200$	4.92432	0.348202
$201$	7.47193	0.527029
$202$	0.460574	0.0324059
$203$	9.42686	0.661636
$204$	2.17813	0.152499
$205$	2.27378	0.158808
$206$	−5.21367	−0.363253
$207$	−3.92339	−0.272694
$208$	1.63440	0.113325
$209$	−15.1898	−1.05070
$210$	1.49578	0.103219
$211$	−15.7812	−1.08642	−0.543210	−	0.839597i	$-0.682791\pi$
$211$	−15.7812	−1.08642	−0.543210	+	0.839597i	$0.682791\pi$
$212$	6.50923	0.447056
$213$	8.50603	0.582824
$214$	−3.51857	−0.240525
$215$	−3.06194	−0.208823
$216$	−4.33824	−0.295180
$217$	−20.6088	−1.39902
$218$	−4.16929	−0.282380
$219$	0.483085	0.0326439
$220$	0.669273	0.0451224
$221$	−1.83495	−0.123432
$222$	20.5084	1.37643
$223$	19.7771	1.32437	0.662187	−	0.749339i	$-0.269629\pi$
$223$	19.7771	1.32437	0.662187	+	0.749339i	$0.269629\pi$
$224$	2.80268	0.187262
$225$	−3.76156	−0.250770
$226$	5.75243	0.382646
$227$	2.17483	0.144349	0.0721744	−	0.997392i	$-0.477006\pi$
$227$	2.17483	0.144349	0.0721744	+	0.997392i	$0.477006\pi$
$228$	−12.1127	−0.802186
$229$	−16.7118	−1.10435	−0.552173	−	0.833730i	$-0.686201\pi$
$229$	−16.7118	−1.10435	−0.552173	+	0.833730i	$0.686201\pi$
$230$	−1.41292	−0.0931650
$231$	−13.2287	−0.870386
$232$	3.36352	0.220826
$233$	−23.9078	−1.56625	−0.783127	−	0.621862i	$-0.786377\pi$
$233$	−23.9078	−1.56625	−0.783127	+	0.621862i	$0.786377\pi$
$234$	−1.24847	−0.0816152
$235$	0.513657	0.0335073
$236$	6.17307	0.401833
$237$	24.1681	1.56989
$238$	−3.14659	−0.203963
$239$	−5.15820	−0.333656	−0.166828	−	0.985986i	$-0.553352\pi$
$239$	−5.15820	−0.333656	−0.166828	+	0.985986i	$0.553352\pi$
$240$	0.533696	0.0344499
$241$	13.3436	0.859539	0.429769	−	0.902939i	$-0.358595\pi$
$241$	13.3436	0.859539	0.429769	+	0.902939i	$0.358595\pi$
$242$	5.08093	0.326615
$243$	7.75977	0.497789
$244$	2.40011	0.153651
$245$	−0.235208	−0.0150269
$246$	−16.0358	−1.02240
$247$	10.2043	0.649284
$248$	−7.35325	−0.466932
$249$	−32.3156	−2.04792
$250$	−2.73009	−0.172666
$251$	0.882907	0.0557286	0.0278643	−	0.999612i	$-0.491129\pi$
$251$	0.882907	0.0557286	0.0278643	+	0.999612i	$0.491129\pi$
$252$	−2.14089	−0.134863
$253$	12.4959	0.785610
$254$	−16.7212	−1.04918
$255$	−0.599184	−0.0375223
$256$	1.00000	0.0625000
$257$	−15.9481	−0.994814	−0.497407	−	0.867517i	$-0.665714\pi$
$257$	−15.9481	−0.994814	−0.497407	+	0.867517i	$0.665714\pi$
$258$	21.5942	1.34440
$259$	−29.6270	−1.84093
$260$	−0.449609	−0.0278835
$261$	−2.56930	−0.159036
$262$	6.26032	0.386764
$263$	−29.6222	−1.82658	−0.913291	−	0.407307i	$-0.866468\pi$
$263$	−29.6222	−1.82658	−0.913291	+	0.407307i	$0.866468\pi$
$264$	−4.72002	−0.290497
$265$	−1.79063	−0.109998
$266$	17.4984	1.07290
$267$	15.9656	0.977078
$268$	−3.85137	−0.235260
$269$	29.2664	1.78440	0.892201	−	0.451638i	$-0.149160\pi$
$269$	29.2664	1.78440	0.892201	+	0.451638i	$0.149160\pi$
$270$	1.19341	0.0726288
$271$	−0.771400	−0.0468592	−0.0234296	−	0.999725i	$-0.507459\pi$
$271$	−0.771400	−0.0468592	−0.0234296	+	0.999725i	$0.507459\pi$
$272$	−1.12271	−0.0680740
$273$	8.88687	0.537858
$274$	−8.90358	−0.537885
$275$	11.9805	0.722449
$276$	9.96455	0.599795
$277$	−12.0783	−0.725712	−0.362856	−	0.931845i	$-0.618198\pi$
$277$	−12.0783	−0.725712	−0.362856	+	0.931845i	$0.618198\pi$
$278$	−2.89358	−0.173545
$279$	5.61694	0.336278
$280$	−0.770993	−0.0460756
$281$	8.91242	0.531671	0.265835	−	0.964018i	$-0.414352\pi$
$281$	8.91242	0.531671	0.265835	+	0.964018i	$0.414352\pi$
$282$	−3.62255	−0.215719
$283$	−2.71737	−0.161531	−0.0807656	−	0.996733i	$-0.525737\pi$
$283$	−2.71737	−0.161531	−0.0807656	+	0.996733i	$0.525737\pi$
$284$	−4.38439	−0.260166
$285$	3.33211	0.197377
$286$	3.97635	0.235127
$287$	23.1657	1.36743
$288$	−0.763873	−0.0450116
$289$	−15.7395	−0.925855
$290$	−0.925273	−0.0543339
$291$	−2.50950	−0.147110
$292$	−0.249004	−0.0145719
$293$	−16.5724	−0.968169	−0.484085	−	0.875021i	$-0.660847\pi$
$293$	−16.5724	−0.968169	−0.484085	+	0.875021i	$0.660847\pi$
$294$	1.65880	0.0967429
$295$	−1.69816	−0.0988706
$296$	−10.5709	−0.614423
$297$	−10.5546	−0.612439
$298$	10.3303	0.598418
$299$	−8.39456	−0.485470
$300$	9.55354	0.551574
$301$	−31.1956	−1.79809
$302$	18.8141	1.08263
$303$	0.893546	0.0513328
$304$	6.24346	0.358087
$305$	−0.660249	−0.0378057
$306$	0.857604	0.0490260
$307$	19.8726	1.13419	0.567094	−	0.823653i	$-0.308068\pi$
$307$	19.8726	1.13419	0.567094	+	0.823653i	$0.308068\pi$
$308$	6.81868	0.388530
$309$	−10.1149	−0.575415
$310$	2.02281	0.114888
$311$	−20.3156	−1.15199	−0.575996	−	0.817452i	$-0.695386\pi$
$311$	−20.3156	−1.15199	−0.575996	+	0.817452i	$0.695386\pi$
$312$	3.17085	0.179514
$313$	−32.1642	−1.81803	−0.909014	−	0.416766i	$-0.863164\pi$
$313$	−32.1642	−1.81803	−0.909014	+	0.416766i	$0.863164\pi$
$314$	2.56362	0.144673
$315$	0.588940	0.0331830
$316$	−12.4573	−0.700781
$317$	−25.1758	−1.41401	−0.707007	−	0.707207i	$-0.749955\pi$
$317$	−25.1758	−1.41401	−0.707007	+	0.707207i	$0.749955\pi$
$318$	12.6284	0.708163
$319$	8.18314	0.458168
$320$	−0.275091	−0.0153781
$321$	−6.82628	−0.381006
$322$	−14.3951	−0.802206
$323$	−7.00957	−0.390023
$324$	−10.7081	−0.594895
$325$	−8.04831	−0.446440
$326$	11.8007	0.653580
$327$	−8.08871	−0.447307
$328$	8.26556	0.456389
$329$	5.23323	0.288517
$330$	1.29844	0.0714766
$331$	−25.2843	−1.38975	−0.694876	−	0.719129i	$-0.744541\pi$
$331$	−25.2843	−1.38975	−0.694876	+	0.719129i	$0.744541\pi$
$332$	16.6569	0.914168
$333$	8.07485	0.442499
$334$	−7.22991	−0.395603
$335$	1.05948	0.0578855
$336$	5.43740	0.296634
$337$	−2.32522	−0.126663	−0.0633314	−	0.997993i	$-0.520173\pi$
$337$	−2.32522	−0.126663	−0.0633314	+	0.997993i	$0.520173\pi$
$338$	10.3287	0.561809
$339$	11.1601	0.606135
$340$	0.308846	0.0167495
$341$	−17.8898	−0.968788
$342$	−4.76921	−0.257889
$343$	17.2224	0.929923
$344$	−11.1306	−0.600124
$345$	−2.74116	−0.147579
$346$	−12.8262	−0.689539
$347$	−25.4324	−1.36528	−0.682640	−	0.730755i	$-0.739168\pi$
$347$	−25.4324	−1.36528	−0.682640	+	0.730755i	$0.739168\pi$
$348$	6.52546	0.349801
$349$	−25.8002	−1.38105	−0.690527	−	0.723307i	$-0.742621\pi$
$349$	−25.8002	−1.38105	−0.690527	+	0.723307i	$0.742621\pi$
$350$	−13.8013	−0.737711
$351$	7.09042	0.378459
$352$	2.43291	0.129675
$353$	5.96967	0.317734	0.158867	−	0.987300i	$-0.449216\pi$
$353$	5.96967	0.317734	0.158867	+	0.987300i	$0.449216\pi$
$354$	11.9762	0.636528
$355$	1.20611	0.0640136
$356$	−8.22939	−0.436157
$357$	−6.10460	−0.323089
$358$	−16.7297	−0.884192
$359$	−27.3006	−1.44087	−0.720435	−	0.693522i	$-0.756058\pi$
$359$	−27.3006	−1.44087	−0.720435	+	0.693522i	$0.756058\pi$
$360$	0.210135	0.0110751
$361$	19.9808	1.05162
$362$	11.0599	0.581295
$363$	9.85736	0.517377
$364$	−4.58070	−0.240094
$365$	0.0684988	0.00358539
$366$	4.65638	0.243393
$367$	−15.3449	−0.800999	−0.400499	−	0.916297i	$-0.631163\pi$
$367$	−15.3449	−0.800999	−0.400499	+	0.916297i	$0.631163\pi$
$368$	−5.13618	−0.267742
$369$	−6.31384	−0.328685
$370$	2.90797	0.151178
$371$	−18.2433	−0.947144
$372$	−14.2658	−0.739648
$373$	7.52956	0.389866	0.194933	−	0.980817i	$-0.437551\pi$
$373$	7.52956	0.389866	0.194933	+	0.980817i	$0.437551\pi$
$374$	−2.73145	−0.141240
$375$	−5.29657	−0.273514
$376$	1.86722	0.0962947
$377$	−5.49732	−0.283127
$378$	12.1587	0.625377
$379$	−32.0958	−1.64865	−0.824324	−	0.566118i	$-0.808445\pi$
$379$	−32.0958	−1.64865	−0.824324	+	0.566118i	$0.808445\pi$
$380$	−1.71752	−0.0881069
$381$	−32.4402	−1.66196
$382$	−16.5160	−0.845030
$383$	17.1137	0.874468	0.437234	−	0.899348i	$-0.355958\pi$
$383$	17.1137	0.874468	0.437234	+	0.899348i	$0.355958\pi$
$384$	1.94007	0.0990038
$385$	−1.87576	−0.0955975
$386$	−8.13814	−0.414220
$387$	8.50239	0.432201
$388$	1.29351	0.0656681
$389$	−21.6713	−1.09878	−0.549390	−	0.835566i	$-0.685140\pi$
$389$	−21.6713	−1.09878	−0.549390	+	0.835566i	$0.685140\pi$
$390$	−0.872272	−0.0441692
$391$	5.76642	0.291620
$392$	−0.855018	−0.0431849
$393$	12.1455	0.612658
$394$	15.3167	0.771642
$395$	3.42691	0.172426
$396$	−1.85844	−0.0933899
$397$	−22.8325	−1.14593	−0.572966	−	0.819579i	$-0.694207\pi$
$397$	−22.8325	−1.14593	−0.572966	+	0.819579i	$0.694207\pi$
$398$	−10.5399	−0.528317
$399$	33.9482	1.69953
$400$	−4.92432	−0.246216
$401$	−18.5160	−0.924646	−0.462323	−	0.886712i	$-0.652984\pi$
$401$	−18.5160	−0.924646	−0.462323	+	0.886712i	$0.652984\pi$
$402$	−7.47193	−0.372666
$403$	12.0181	0.598666
$404$	−0.460574	−0.0229144
$405$	2.94571	0.146373
$406$	−9.42686	−0.467847
$407$	−25.7182	−1.27480
$408$	−2.17813	−0.107833
$409$	4.45069	0.220072	0.110036	−	0.993928i	$-0.464903\pi$
$409$	4.45069	0.220072	0.110036	+	0.993928i	$0.464903\pi$
$410$	−2.27378	−0.112294
$411$	−17.2736	−0.852043
$412$	5.21367	0.256859
$413$	−17.3012	−0.851334
$414$	3.92339	0.192824
$415$	−4.58218	−0.224930
$416$	−1.63440	−0.0801330
$417$	−5.61374	−0.274906
$418$	15.1898	0.742957
$419$	15.6752	0.765785	0.382892	−	0.923793i	$-0.374928\pi$
$419$	15.6752	0.765785	0.382892	+	0.923793i	$0.374928\pi$
$420$	−1.49578	−0.0729866
$421$	24.5106	1.19457	0.597287	−	0.802028i	$-0.296245\pi$
$421$	24.5106	1.19457	0.597287	+	0.802028i	$0.296245\pi$
$422$	15.7812	0.768216
$423$	−1.42632	−0.0693501
$424$	−6.50923	−0.316116
$425$	5.52857	0.268175
$426$	−8.50603	−0.412119
$427$	−6.72674	−0.325530
$428$	3.51857	0.170077
$429$	7.71440	0.372455
$430$	3.06194	0.147660
$431$	15.5408	0.748575	0.374287	−	0.927313i	$-0.377887\pi$
$431$	15.5408	0.748575	0.374287	+	0.927313i	$0.377887\pi$
$432$	4.33824	0.208724
$433$	34.5338	1.65959	0.829794	−	0.558071i	$-0.188458\pi$
$433$	34.5338	1.65959	0.829794	+	0.558071i	$0.188458\pi$
$434$	20.6088	0.989254
$435$	−1.79510	−0.0860682
$436$	4.16929	0.199673
$437$	−32.0675	−1.53400
$438$	−0.483085	−0.0230827
$439$	13.1241	0.626379	0.313189	−	0.949691i	$-0.398603\pi$
$439$	13.1241	0.626379	0.313189	+	0.949691i	$0.398603\pi$
$440$	−0.669273	−0.0319063
$441$	0.653125	0.0311012
$442$	1.83495	0.0872796
$443$	−18.1521	−0.862430	−0.431215	−	0.902249i	$-0.641915\pi$
$443$	−18.1521	−0.862430	−0.431215	+	0.902249i	$0.641915\pi$
$444$	−20.5084	−0.973284
$445$	2.26383	0.107316
$446$	−19.7771	−0.936473
$447$	20.0415	0.947930
$448$	−2.80268	−0.132414
$449$	−2.68659	−0.126788	−0.0633941	−	0.997989i	$-0.520192\pi$
$449$	−2.68659	−0.126788	−0.0633941	+	0.997989i	$0.520192\pi$
$450$	3.76156	0.177321
$451$	20.1094	0.946915
$452$	−5.75243	−0.270572
$453$	36.5007	1.71495
$454$	−2.17483	−0.102070
$455$	1.26011	0.0590748
$456$	12.1127	0.567231
$457$	27.5313	1.28786	0.643930	−	0.765085i	$-0.277303\pi$
$457$	27.5313	1.28786	0.643930	+	0.765085i	$0.277303\pi$
$458$	16.7118	0.780891
$459$	−4.87057	−0.227339
$460$	1.41292	0.0658776
$461$	−3.54762	−0.165229	−0.0826146	−	0.996582i	$-0.526327\pi$
$461$	−3.54762	−0.165229	−0.0826146	+	0.996582i	$0.526327\pi$
$462$	13.2287	0.615456
$463$	−19.5632	−0.909180	−0.454590	−	0.890701i	$-0.650214\pi$
$463$	−19.5632	−0.909180	−0.454590	+	0.890701i	$0.650214\pi$
$464$	−3.36352	−0.156147
$465$	3.92440	0.181990
$466$	23.9078	1.10751
$467$	9.56141	0.442449	0.221225	−	0.975223i	$-0.428995\pi$
$467$	9.56141	0.442449	0.221225	+	0.975223i	$0.428995\pi$
$468$	1.24847	0.0577106
$469$	10.7942	0.498428
$470$	−0.513657	−0.0236932
$471$	4.97360	0.229171
$472$	−6.17307	−0.284139
$473$	−27.0799	−1.24513
$474$	−24.1681	−1.11008
$475$	−30.7448	−1.41067
$476$	3.14659	0.144223
$477$	4.97222	0.227662
$478$	5.15820	0.235930
$479$	−18.8832	−0.862796	−0.431398	−	0.902162i	$-0.641980\pi$
$479$	−18.8832	−0.862796	−0.431398	+	0.902162i	$0.641980\pi$
$480$	−0.533696	−0.0243598
$481$	17.2771	0.787769
$482$	−13.3436	−0.607786
$483$	−27.9275	−1.27074
$484$	−5.08093	−0.230951
$485$	−0.355834	−0.0161576
$486$	−7.75977	−0.351990
$487$	11.2812	0.511202	0.255601	−	0.966782i	$-0.417727\pi$
$487$	11.2812	0.511202	0.255601	+	0.966782i	$0.417727\pi$
$488$	−2.40011	−0.108648
$489$	22.8942	1.03531
$490$	0.235208	0.0106256
$491$	2.40116	0.108363	0.0541814	−	0.998531i	$-0.482745\pi$
$491$	2.40116	0.108363	0.0541814	+	0.998531i	$0.482745\pi$
$492$	16.0358	0.722949
$493$	3.77624	0.170073
$494$	−10.2043	−0.459113
$495$	0.511239	0.0229785
$496$	7.35325	0.330171
$497$	12.2881	0.551195
$498$	32.3156	1.44810
$499$	27.1221	1.21415	0.607075	−	0.794644i	$-0.292343\pi$
$499$	27.1221	1.21415	0.607075	+	0.794644i	$0.292343\pi$
$500$	2.73009	0.122094
$501$	−14.0265	−0.626660
$502$	−0.882907	−0.0394061
$503$	−2.05143	−0.0914686	−0.0457343	−	0.998954i	$-0.514563\pi$
$503$	−2.05143	−0.0914686	−0.0457343	+	0.998954i	$0.514563\pi$
$504$	2.14089	0.0953629
$505$	0.126700	0.00563807
$506$	−12.4959	−0.555510
$507$	20.0385	0.889940
$508$	16.7212	0.741882
$509$	6.34162	0.281088	0.140544	−	0.990074i	$-0.455115\pi$
$509$	6.34162	0.281088	0.140544	+	0.990074i	$0.455115\pi$
$510$	0.599184	0.0265323
$511$	0.697878	0.0308723
$512$	−1.00000	−0.0441942
$513$	27.0856	1.19586
$514$	15.9481	0.703440
$515$	−1.43423	−0.0631999
$516$	−21.5942	−0.950633
$517$	4.54280	0.199792
$518$	29.6270	1.30173
$519$	−24.8837	−1.09227
$520$	0.449609	0.0197166
$521$	−20.7037	−0.907048	−0.453524	−	0.891244i	$-0.649833\pi$
$521$	−20.7037	−0.907048	−0.453524	+	0.891244i	$0.649833\pi$
$522$	2.56930	0.112455
$523$	1.39716	0.0610934	0.0305467	−	0.999533i	$-0.490275\pi$
$523$	1.39716	0.0610934	0.0305467	+	0.999533i	$0.490275\pi$
$524$	−6.26032	−0.273483
$525$	−26.7755	−1.16858
$526$	29.6222	1.29159
$527$	−8.25553	−0.359617
$528$	4.72002	0.205413
$529$	3.38035	0.146972
$530$	1.79063	0.0777801
$531$	4.71544	0.204633
$532$	−17.4984	−0.758653
$533$	−13.5092	−0.585150
$534$	−15.9656	−0.690898
$535$	−0.967928	−0.0418472
$536$	3.85137	0.166354
$537$	−32.4568	−1.40061
$538$	−29.2664	−1.26176
$539$	−2.08019	−0.0895999
$540$	−1.19341	−0.0513563
$541$	−23.8933	−1.02725	−0.513626	−	0.858014i	$-0.671698\pi$
$541$	−23.8933	−1.02725	−0.513626	+	0.858014i	$0.671698\pi$
$542$	0.771400	0.0331345
$543$	21.4570	0.920806
$544$	1.12271	0.0481356
$545$	−1.14693	−0.0491292
$546$	−8.88687	−0.380323
$547$	7.15810	0.306058	0.153029	−	0.988222i	$-0.451097\pi$
$547$	7.15810	0.306058	0.153029	+	0.988222i	$0.451097\pi$
$548$	8.90358	0.380342
$549$	1.83338	0.0782467
$550$	−11.9805	−0.510848
$551$	−21.0000	−0.894629
$552$	−9.96455	−0.424119
$553$	34.9140	1.48469
$554$	12.0783	0.513156
$555$	5.64167	0.239476
$556$	2.89358	0.122715
$557$	1.21106	0.0513143	0.0256572	−	0.999671i	$-0.491832\pi$
$557$	1.21106	0.0513143	0.0256572	+	0.999671i	$0.491832\pi$
$558$	−5.61694	−0.237784
$559$	18.1919	0.769435
$560$	0.770993	0.0325804
$561$	−5.29920	−0.223732
$562$	−8.91242	−0.375948
$563$	−19.2792	−0.812521	−0.406261	−	0.913757i	$-0.633167\pi$
$563$	−19.2792	−0.812521	−0.406261	+	0.913757i	$0.633167\pi$
$564$	3.62255	0.152537
$565$	1.58244	0.0665739
$566$	2.71737	0.114220
$567$	30.0114	1.26036
$568$	4.38439	0.183965
$569$	6.01657	0.252228	0.126114	−	0.992016i	$-0.459750\pi$
$569$	6.01657	0.252228	0.126114	+	0.992016i	$0.459750\pi$
$570$	−3.33211	−0.139567
$571$	16.9092	0.707626	0.353813	−	0.935316i	$-0.384885\pi$
$571$	16.9092	0.707626	0.353813	+	0.935316i	$0.384885\pi$
$572$	−3.97635	−0.166260
$573$	−32.0421	−1.33858
$574$	−23.1657	−0.966919
$575$	25.2922	1.05476
$576$	0.763873	0.0318280
$577$	−12.5210	−0.521257	−0.260628	−	0.965439i	$-0.583930\pi$
$577$	−12.5210	−0.521257	−0.260628	+	0.965439i	$0.583930\pi$
$578$	15.7395	0.654678
$579$	−15.7886	−0.656150
$580$	0.925273	0.0384199
$581$	−46.6841	−1.93678
$582$	2.50950	0.104022
$583$	−15.8364	−0.655876
$584$	0.249004	0.0103039
$585$	−0.343444	−0.0141996
$586$	16.5724	0.684599
$587$	−22.3235	−0.921389	−0.460694	−	0.887559i	$-0.652400\pi$
$587$	−22.3235	−0.921389	−0.460694	+	0.887559i	$0.652400\pi$
$588$	−1.65880	−0.0684076
$589$	45.9097	1.89168
$590$	1.69816	0.0699121
$591$	29.7154	1.22233
$592$	10.5709	0.434463
$593$	20.7240	0.851033	0.425517	−	0.904951i	$-0.360092\pi$
$593$	20.7240	0.851033	0.425517	+	0.904951i	$0.360092\pi$
$594$	10.5546	0.433059
$595$	−0.865598	−0.0354860
$596$	−10.3303	−0.423145
$597$	−20.4481	−0.836887
$598$	8.39456	0.343279
$599$	−8.81251	−0.360069	−0.180035	−	0.983660i	$-0.557621\pi$
$599$	−8.81251	−0.360069	−0.180035	+	0.983660i	$0.557621\pi$
$600$	−9.55354	−0.390021
$601$	1.45283	0.0592623	0.0296311	−	0.999561i	$-0.490567\pi$
$601$	1.45283	0.0592623	0.0296311	+	0.999561i	$0.490567\pi$
$602$	31.1956	1.27144
$603$	−2.94196	−0.119806
$604$	−18.8141	−0.765536
$605$	1.39772	0.0568253
$606$	−0.893546	−0.0362978
$607$	−26.1434	−1.06113	−0.530564	−	0.847645i	$-0.678020\pi$
$607$	−26.1434	−1.06113	−0.530564	+	0.847645i	$0.678020\pi$
$608$	−6.24346	−0.253206
$609$	−18.2888	−0.741098
$610$	0.660249	0.0267327
$611$	−3.05179	−0.123462
$612$	−0.857604	−0.0346666
$613$	−12.2985	−0.496730	−0.248365	−	0.968667i	$-0.579893\pi$
$613$	−12.2985	−0.496730	−0.248365	+	0.968667i	$0.579893\pi$
$614$	−19.8726	−0.801992
$615$	−4.41130	−0.177881
$616$	−6.81868	−0.274732
$617$	28.0317	1.12851	0.564257	−	0.825599i	$-0.309163\pi$
$617$	28.0317	1.12851	0.564257	+	0.825599i	$0.309163\pi$
$618$	10.1149	0.406880
$619$	−25.9021	−1.04109	−0.520547	−	0.853833i	$-0.674272\pi$
$619$	−25.9021	−1.04109	−0.520547	+	0.853833i	$0.674272\pi$
$620$	−2.02281	−0.0812381
$621$	−22.2820	−0.894146
$622$	20.3156	0.814582
$623$	23.0643	0.924053
$624$	−3.17085	−0.126935
$625$	23.8706	0.954824
$626$	32.1642	1.28554
$627$	29.4693	1.17689
$628$	−2.56362	−0.102300
$629$	−11.8681	−0.473210
$630$	−0.588940	−0.0234639
$631$	22.4846	0.895100	0.447550	−	0.894259i	$-0.352297\pi$
$631$	22.4846	0.895100	0.447550	+	0.894259i	$0.352297\pi$
$632$	12.4573	0.495527
$633$	30.6166	1.21690
$634$	25.1758	0.999858
$635$	−4.59984	−0.182539
$636$	−12.6284	−0.500747
$637$	1.39744	0.0553686
$638$	−8.18314	−0.323974
$639$	−3.34912	−0.132489
$640$	0.275091	0.0108739
$641$	−30.0448	−1.18670	−0.593349	−	0.804945i	$-0.702195\pi$
$641$	−30.0448	−1.18670	−0.593349	+	0.804945i	$0.702195\pi$
$642$	6.82628	0.269412
$643$	−15.0181	−0.592257	−0.296129	−	0.955148i	$-0.595696\pi$
$643$	−15.0181	−0.592257	−0.296129	+	0.955148i	$0.595696\pi$
$644$	14.3951	0.567245
$645$	5.94038	0.233902
$646$	7.00957	0.275788
$647$	−48.2366	−1.89638	−0.948188	−	0.317711i	$-0.897086\pi$
$647$	−48.2366	−1.89638	−0.948188	+	0.317711i	$0.897086\pi$
$648$	10.7081	0.420655
$649$	−15.0186	−0.589530
$650$	8.04831	0.315681
$651$	39.9825	1.56704
$652$	−11.8007	−0.462151
$653$	−2.97201	−0.116304	−0.0581518	−	0.998308i	$-0.518521\pi$
$653$	−2.97201	−0.116304	−0.0581518	+	0.998308i	$0.518521\pi$
$654$	8.08871	0.316294
$655$	1.72216	0.0672903
$656$	−8.26556	−0.322716
$657$	−0.190207	−0.00742069
$658$	−5.23323	−0.204013
$659$	23.1266	0.900885	0.450442	−	0.892806i	$-0.351266\pi$
$659$	23.1266	0.900885	0.450442	+	0.892806i	$0.351266\pi$
$660$	−1.29844	−0.0505416
$661$	23.8625	0.928145	0.464072	−	0.885797i	$-0.346388\pi$
$661$	23.8625	0.928145	0.464072	+	0.885797i	$0.346388\pi$
$662$	25.2843	0.982704
$663$	3.55993	0.138256
$664$	−16.6569	−0.646415
$665$	4.81366	0.186666
$666$	−8.07485	−0.312894
$667$	17.2756	0.668915
$668$	7.22991	0.279734
$669$	−38.3690	−1.48343
$670$	−1.05948	−0.0409312
$671$	−5.83926	−0.225422
$672$	−5.43740	−0.209752
$673$	−37.6477	−1.45121	−0.725606	−	0.688110i	$-0.758441\pi$
$673$	−37.6477	−1.45121	−0.725606	+	0.688110i	$0.758441\pi$
$674$	2.32522	0.0895641
$675$	−21.3629	−0.822259
$676$	−10.3287	−0.397259
$677$	24.2085	0.930407	0.465204	−	0.885204i	$-0.345981\pi$
$677$	24.2085	0.930407	0.465204	+	0.885204i	$0.345981\pi$
$678$	−11.1601	−0.428602
$679$	−3.62530	−0.139126
$680$	−0.308846	−0.0118437
$681$	−4.21933	−0.161685
$682$	17.8898	0.685037
$683$	−0.966306	−0.0369747	−0.0184873	−	0.999829i	$-0.505885\pi$
$683$	−0.966306	−0.0369747	−0.0184873	+	0.999829i	$0.505885\pi$
$684$	4.76921	0.182355
$685$	−2.44930	−0.0935828
$686$	−17.2224	−0.657555
$687$	32.4220	1.23698
$688$	11.1306	0.424352
$689$	10.6387	0.405301
$690$	2.74116	0.104354
$691$	16.2000	0.616275	0.308138	−	0.951342i	$-0.400294\pi$
$691$	16.2000	0.616275	0.308138	+	0.951342i	$0.400294\pi$
$692$	12.8262	0.487577
$693$	5.20860	0.197858
$694$	25.4324	0.965399
$695$	−0.795998	−0.0301939
$696$	−6.52546	−0.247347
$697$	9.27980	0.351497
$698$	25.8002	0.976552
$699$	46.3829	1.75436
$700$	13.8013	0.521640
$701$	−0.649950	−0.0245483	−0.0122741	−	0.999925i	$-0.503907\pi$
$701$	−0.649950	−0.0245483	−0.0122741	+	0.999925i	$0.503907\pi$
$702$	−7.09042	−0.267611
$703$	65.9992	2.48921
$704$	−2.43291	−0.0916939
$705$	−0.996530	−0.0375315
$706$	−5.96967	−0.224672
$707$	1.29084	0.0485471
$708$	−11.9762	−0.450093
$709$	41.2234	1.54818	0.774089	−	0.633077i	$-0.218208\pi$
$709$	41.2234	1.54818	0.774089	+	0.633077i	$0.218208\pi$
$710$	−1.20611	−0.0452644
$711$	−9.51583	−0.356871
$712$	8.22939	0.308409
$713$	−37.7676	−1.41441
$714$	6.10460	0.228459
$715$	1.09386	0.0409080
$716$	16.7297	0.625218
$717$	10.0073	0.373728
$718$	27.3006	1.01885
$719$	33.0929	1.23416	0.617078	−	0.786902i	$-0.288316\pi$
$719$	33.0929	1.23416	0.617078	+	0.786902i	$0.288316\pi$
$720$	−0.210135	−0.00783125
$721$	−14.6122	−0.544188
$722$	−19.9808	−0.743607
$723$	−25.8876	−0.962769
$724$	−11.0599	−0.411038
$725$	16.5630	0.615136
$726$	−9.85736	−0.365841
$727$	2.56353	0.0950762	0.0475381	−	0.998869i	$-0.484862\pi$
$727$	2.56353	0.0950762	0.0475381	+	0.998869i	$0.484862\pi$
$728$	4.58070	0.169772
$729$	17.0699	0.632217
$730$	−0.0684988	−0.00253525
$731$	−12.4964	−0.462197
$732$	−4.65638	−0.172105
$733$	−10.6829	−0.394582	−0.197291	−	0.980345i	$-0.563214\pi$
$733$	−10.6829	−0.394582	−0.197291	+	0.980345i	$0.563214\pi$
$734$	15.3449	0.566391
$735$	0.456320	0.0168316
$736$	5.13618	0.189322
$737$	9.37005	0.345150
$738$	6.31384	0.232416
$739$	16.6718	0.613281	0.306640	−	0.951825i	$-0.400795\pi$
$739$	16.6718	0.613281	0.306640	+	0.951825i	$0.400795\pi$
$740$	−2.90797	−0.106899
$741$	−19.7971	−0.727263
$742$	18.2433	0.669732
$743$	42.6923	1.56623	0.783115	−	0.621877i	$-0.213630\pi$
$743$	42.6923	1.56623	0.783115	+	0.621877i	$0.213630\pi$
$744$	14.2658	0.523010
$745$	2.84177	0.104115
$746$	−7.52956	−0.275677
$747$	12.7238	0.465539
$748$	2.73145	0.0998716
$749$	−9.86143	−0.360329
$750$	5.29657	0.193404
$751$	−29.6088	−1.08044	−0.540220	−	0.841524i	$-0.681659\pi$
$751$	−29.6088	−1.08044	−0.540220	+	0.841524i	$0.681659\pi$
$752$	−1.86722	−0.0680907
$753$	−1.71290	−0.0624216
$754$	5.49732	0.200201
$755$	5.17560	0.188359
$756$	−12.1587	−0.442208
$757$	46.2049	1.67935	0.839673	−	0.543092i	$-0.182746\pi$
$757$	46.2049	1.67935	0.839673	+	0.543092i	$0.182746\pi$
$758$	32.0958	1.16577
$759$	−24.2429	−0.879961
$760$	1.71752	0.0623010
$761$	−19.5516	−0.708746	−0.354373	−	0.935104i	$-0.615306\pi$
$761$	−19.5516	−0.708746	−0.354373	+	0.935104i	$0.615306\pi$
$762$	32.4402	1.17519
$763$	−11.6852	−0.423032
$764$	16.5160	0.597526
$765$	0.235919	0.00852968
$766$	−17.1137	−0.618342
$767$	10.0893	0.364302
$768$	−1.94007	−0.0700063
$769$	9.21475	0.332292	0.166146	−	0.986101i	$-0.446868\pi$
$769$	9.21475	0.332292	0.166146	+	0.986101i	$0.446868\pi$
$770$	1.87576	0.0675977
$771$	30.9404	1.11429
$772$	8.13814	0.292898
$773$	30.9269	1.11236	0.556181	−	0.831061i	$-0.312266\pi$
$773$	30.9269	1.11236	0.556181	+	0.831061i	$0.312266\pi$
$774$	−8.50239	−0.305612
$775$	−36.2098	−1.30069
$776$	−1.29351	−0.0464344
$777$	57.4784	2.06203
$778$	21.6713	0.776954
$779$	−51.6057	−1.84897
$780$	0.872272	0.0312324
$781$	10.6669	0.381690
$782$	−5.76642	−0.206207
$783$	−14.5918	−0.521467
$784$	0.855018	0.0305364
$785$	0.705229	0.0251707
$786$	−12.1455	−0.433214
$787$	18.2309	0.649861	0.324930	−	0.945738i	$-0.394659\pi$
$787$	18.2309	0.649861	0.324930	+	0.945738i	$0.394659\pi$
$788$	−15.3167	−0.545633
$789$	57.4691	2.04596
$790$	−3.42691	−0.121924
$791$	16.1222	0.573241
$792$	1.85844	0.0660367
$793$	3.92274	0.139300
$794$	22.8325	0.810296
$795$	3.47395	0.123208
$796$	10.5399	0.373577
$797$	0.247791	0.00877722	0.00438861	−	0.999990i	$-0.498603\pi$
$797$	0.247791	0.00877722	0.00438861	+	0.999990i	$0.498603\pi$
$798$	−33.9482	−1.20175
$799$	2.09634	0.0741633
$800$	4.92432	0.174101
$801$	−6.28620	−0.222112
$802$	18.5160	0.653824
$803$	0.605805	0.0213784
$804$	7.47193	0.263515
$805$	−3.95996	−0.139570
$806$	−12.0181	−0.423321
$807$	−56.7788	−1.99871
$808$	0.460574	0.0162029
$809$	3.85660	0.135591	0.0677954	−	0.997699i	$-0.478403\pi$
$809$	3.85660	0.135591	0.0677954	+	0.997699i	$0.478403\pi$
$810$	−2.94571	−0.103502
$811$	18.6514	0.654939	0.327470	−	0.944862i	$-0.393804\pi$
$811$	18.6514	0.654939	0.327470	+	0.944862i	$0.393804\pi$
$812$	9.42686	0.330818
$813$	1.49657	0.0524870
$814$	25.7182	0.901422
$815$	3.24627	0.113712
$816$	2.17813	0.0762497
$817$	69.4937	2.43128
$818$	−4.45069	−0.155615
$819$	−3.49907	−0.122267
$820$	2.27378	0.0794040
$821$	−2.35684	−0.0822544	−0.0411272	−	0.999154i	$-0.513095\pi$
$821$	−2.35684	−0.0822544	−0.0411272	+	0.999154i	$0.513095\pi$
$822$	17.2736	0.602485
$823$	−32.0784	−1.11818	−0.559092	−	0.829106i	$-0.688850\pi$
$823$	−32.0784	−1.11818	−0.559092	+	0.829106i	$0.688850\pi$
$824$	−5.21367	−0.181627
$825$	−23.2429	−0.809215
$826$	17.3012	0.601984
$827$	33.3082	1.15824	0.579120	−	0.815242i	$-0.303396\pi$
$827$	33.3082	1.15824	0.579120	+	0.815242i	$0.303396\pi$
$828$	−3.92339	−0.136347
$829$	37.8284	1.31383	0.656917	−	0.753963i	$-0.271860\pi$
$829$	37.8284	1.31383	0.656917	+	0.753963i	$0.271860\pi$
$830$	4.58218	0.159050
$831$	23.4327	0.812871
$832$	1.63440	0.0566626
$833$	−0.959934	−0.0332597
$834$	5.61374	0.194388
$835$	−1.98889	−0.0688282
$836$	−15.1898	−0.525350
$837$	31.9002	1.10263
$838$	−15.6752	−0.541491
$839$	25.2002	0.870008	0.435004	−	0.900429i	$-0.356747\pi$
$839$	25.2002	0.870008	0.435004	+	0.900429i	$0.356747\pi$
$840$	1.49578	0.0516093
$841$	−17.6868	−0.609888
$842$	−24.5106	−0.844691
$843$	−17.2907	−0.595524
$844$	−15.7812	−0.543210
$845$	2.84135	0.0977453
$846$	1.42632	0.0490379
$847$	14.2402	0.489300
$848$	6.50923	0.223528
$849$	5.27190	0.180931
$850$	−5.52857	−0.189628
$851$	−54.2943	−1.86118
$852$	8.50603	0.291412
$853$	−17.9826	−0.615714	−0.307857	−	0.951433i	$-0.599612\pi$
$853$	−17.9826	−0.615714	−0.307857	+	0.951433i	$0.599612\pi$
$854$	6.72674	0.230184
$855$	−1.31197	−0.0448683
$856$	−3.51857	−0.120262
$857$	12.0180	0.410526	0.205263	−	0.978707i	$-0.434195\pi$
$857$	12.0180	0.410526	0.205263	+	0.978707i	$0.434195\pi$
$858$	−7.71440	−0.263365
$859$	10.9243	0.372734	0.186367	−	0.982480i	$-0.440329\pi$
$859$	10.9243	0.372734	0.186367	+	0.982480i	$0.440329\pi$
$860$	−3.06194	−0.104411
$861$	−44.9432	−1.53166
$862$	−15.5408	−0.529322
$863$	19.5829	0.666611	0.333305	−	0.942819i	$-0.391836\pi$
$863$	19.5829	0.666611	0.333305	+	0.942819i	$0.391836\pi$
$864$	−4.33824	−0.147590
$865$	−3.52836	−0.119968
$866$	−34.5338	−1.17351
$867$	30.5358	1.03705
$868$	−20.6088	−0.699508
$869$	30.3077	1.02812
$870$	1.79510	0.0608594
$871$	−6.29467	−0.213287
$872$	−4.16929	−0.141190
$873$	0.988078	0.0334414
$874$	32.0675	1.08470
$875$	−7.65158	−0.258671
$876$	0.483085	0.0163219
$877$	−10.5926	−0.357686	−0.178843	−	0.983878i	$-0.557235\pi$
$877$	−10.5926	−0.357686	−0.178843	+	0.983878i	$0.557235\pi$
$878$	−13.1241	−0.442917
$879$	32.1516	1.08445
$880$	0.669273	0.0225612
$881$	0.183373	0.00617799	0.00308899	−	0.999995i	$-0.499017\pi$
$881$	0.183373	0.00617799	0.00308899	+	0.999995i	$0.499017\pi$
$882$	−0.653125	−0.0219919
$883$	−16.4433	−0.553363	−0.276681	−	0.960962i	$-0.589235\pi$
$883$	−16.4433	−0.553363	−0.276681	+	0.960962i	$0.589235\pi$
$884$	−1.83495	−0.0617160
$885$	3.29455	0.110745
$886$	18.1521	0.609830
$887$	−9.45852	−0.317586	−0.158793	−	0.987312i	$-0.550760\pi$
$887$	−9.45852	−0.317586	−0.158793	+	0.987312i	$0.550760\pi$
$888$	20.5084	0.688216
$889$	−46.8641	−1.57177
$890$	−2.26383	−0.0758838
$891$	26.0519	0.872772
$892$	19.7771	0.662187
$893$	−11.6579	−0.390118
$894$	−20.0415	−0.670288
$895$	−4.60219	−0.153834
$896$	2.80268	0.0936310
$897$	16.2860	0.543775
$898$	2.68659	0.0896528
$899$	−24.7328	−0.824884
$900$	−3.76156	−0.125385
$901$	−7.30795	−0.243463
$902$	−20.1094	−0.669570
$903$	60.5217	2.01404
$904$	5.75243	0.191323
$905$	3.04248	0.101135
$906$	−36.5007	−1.21266
$907$	−12.8173	−0.425591	−0.212796	−	0.977097i	$-0.568257\pi$
$907$	−12.8173	−0.425591	−0.212796	+	0.977097i	$0.568257\pi$
$908$	2.17483	0.0721744
$909$	−0.351820	−0.0116691
$910$	−1.26011	−0.0417722
$911$	20.2926	0.672323	0.336161	−	0.941804i	$-0.390871\pi$
$911$	20.2926	0.672323	0.336161	+	0.941804i	$0.390871\pi$
$912$	−12.1127	−0.401093
$913$	−40.5249	−1.34118
$914$	−27.5313	−0.910654
$915$	1.28093	0.0423462
$916$	−16.7118	−0.552173
$917$	17.5457	0.579410
$918$	4.87057	0.160753
$919$	−9.33957	−0.308084	−0.154042	−	0.988064i	$-0.549229\pi$
$919$	−9.33957	−0.308084	−0.154042	+	0.988064i	$0.549229\pi$
$920$	−1.41292	−0.0465825
$921$	−38.5542	−1.27040
$922$	3.54762	0.116835
$923$	−7.16585	−0.235867
$924$	−13.2287	−0.435193
$925$	−52.0547	−1.71155
$926$	19.5632	0.642887
$927$	3.98258	0.130805
$928$	3.36352	0.110413
$929$	−23.9109	−0.784491	−0.392245	−	0.919861i	$-0.628302\pi$
$929$	−23.9109	−0.784491	−0.392245	+	0.919861i	$0.628302\pi$
$930$	−3.92440	−0.128686
$931$	5.33827	0.174955
$932$	−23.9078	−0.783127
$933$	39.4137	1.29035
$934$	−9.56141	−0.312859
$935$	−0.751397	−0.0245733
$936$	−1.24847	−0.0408076
$937$	−12.1991	−0.398527	−0.199264	−	0.979946i	$-0.563855\pi$
$937$	−12.1991	−0.398527	−0.199264	+	0.979946i	$0.563855\pi$
$938$	−10.7942	−0.352442
$939$	62.4008	2.03637
$940$	0.513657	0.0167536
$941$	40.0558	1.30578	0.652891	−	0.757452i	$-0.273556\pi$
$941$	40.0558	1.30578	0.652891	+	0.757452i	$0.273556\pi$
$942$	−4.97360	−0.162049
$943$	42.4534	1.38247
$944$	6.17307	0.200916
$945$	3.34475	0.108805
$946$	27.0799	0.880443
$947$	48.3544	1.57131	0.785653	−	0.618667i	$-0.212327\pi$
$947$	48.3544	1.57131	0.785653	+	0.618667i	$0.212327\pi$
$948$	24.1681	0.784944
$949$	−0.406972	−0.0132109
$950$	30.7448	0.997494
$951$	48.8428	1.58384
$952$	−3.14659	−0.101981
$953$	2.27188	0.0735933	0.0367967	−	0.999323i	$-0.488285\pi$
$953$	2.27188	0.0735933	0.0367967	+	0.999323i	$0.488285\pi$
$954$	−4.97222	−0.160982
$955$	−4.54339	−0.147021
$956$	−5.15820	−0.166828
$957$	−15.8759	−0.513194
$958$	18.8832	0.610089
$959$	−24.9539	−0.805803
$960$	0.533696	0.0172250
$961$	23.0703	0.744202
$962$	−17.2771	−0.557037
$963$	2.68774	0.0866112
$964$	13.3436	0.429769
$965$	−2.23873	−0.0720672
$966$	27.9275	0.898551
$967$	−20.4777	−0.658519	−0.329260	−	0.944239i	$-0.606799\pi$
$967$	−20.4777	−0.658519	−0.329260	+	0.944239i	$0.606799\pi$
$968$	5.08093	0.163307
$969$	13.5990	0.436864
$970$	0.355834	0.0114251
$971$	−16.7850	−0.538656	−0.269328	−	0.963049i	$-0.586802\pi$
$971$	−16.7850	−0.538656	−0.269328	+	0.963049i	$0.586802\pi$
$972$	7.75977	0.248895
$973$	−8.10977	−0.259987
$974$	−11.2812	−0.361474
$975$	15.6143	0.500057
$976$	2.40011	0.0768256
$977$	35.9953	1.15159	0.575796	−	0.817594i	$-0.304692\pi$
$977$	35.9953	1.15159	0.575796	+	0.817594i	$0.304692\pi$
$978$	−22.8942	−0.732075
$979$	20.0214	0.639886
$980$	−0.235208	−0.00751344
$981$	3.18480	0.101683
$982$	−2.40116	−0.0766240
$983$	−23.3866	−0.745915	−0.372958	−	0.927848i	$-0.621656\pi$
$983$	−23.3866	−0.745915	−0.372958	+	0.927848i	$0.621656\pi$
$984$	−16.0358	−0.511202
$985$	4.21348	0.134253
$986$	−3.77624	−0.120260
$987$	−10.1528	−0.323168
$988$	10.2043	0.324642
$989$	−57.1690	−1.81787
$990$	−0.511239	−0.0162483
$991$	4.45132	0.141401	0.0707004	−	0.997498i	$-0.477477\pi$
$991$	4.45132	0.141401	0.0707004	+	0.997498i	$0.477477\pi$
$992$	−7.35325	−0.233466
$993$	49.0534	1.55666
$994$	−12.2881	−0.389753
$995$	−2.89943	−0.0919182
$996$	−32.3156	−1.02396
$997$	−36.5925	−1.15890	−0.579448	−	0.815009i	$-0.696732\pi$
$997$	−36.5925	−1.15890	−0.579448	+	0.815009i	$0.696732\pi$
$998$	−27.1221	−0.858534
$999$	45.8593	1.45092

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.g.1.8	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.g.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.94007 q^{3} +1.00000 q^{4} -0.275091 q^{5} +1.94007 q^{6} -2.80268 q^{7} -1.00000 q^{8} +0.763873 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.94007 q^{3} +1.00000 q^{4} -0.275091 q^{5} +1.94007 q^{6} -2.80268 q^{7} -1.00000 q^{8} +0.763873 q^{9} +0.275091 q^{10} -2.43291 q^{11} -1.94007 q^{12} +1.63440 q^{13} +2.80268 q^{14} +0.533696 q^{15} +1.00000 q^{16} -1.12271 q^{17} -0.763873 q^{18} +6.24346 q^{19} -0.275091 q^{20} +5.43740 q^{21} +2.43291 q^{22} -5.13618 q^{23} +1.94007 q^{24} -4.92432 q^{25} -1.63440 q^{26} +4.33824 q^{27} -2.80268 q^{28} -3.36352 q^{29} -0.533696 q^{30} +7.35325 q^{31} -1.00000 q^{32} +4.72002 q^{33} +1.12271 q^{34} +0.770993 q^{35} +0.763873 q^{36} +10.5709 q^{37} -6.24346 q^{38} -3.17085 q^{39} +0.275091 q^{40} -8.26556 q^{41} -5.43740 q^{42} +11.1306 q^{43} -2.43291 q^{44} -0.210135 q^{45} +5.13618 q^{46} -1.86722 q^{47} -1.94007 q^{48} +0.855018 q^{49} +4.92432 q^{50} +2.17813 q^{51} +1.63440 q^{52} +6.50923 q^{53} -4.33824 q^{54} +0.669273 q^{55} +2.80268 q^{56} -12.1127 q^{57} +3.36352 q^{58} +6.17307 q^{59} +0.533696 q^{60} +2.40011 q^{61} -7.35325 q^{62} -2.14089 q^{63} +1.00000 q^{64} -0.449609 q^{65} -4.72002 q^{66} -3.85137 q^{67} -1.12271 q^{68} +9.96455 q^{69} -0.770993 q^{70} -4.38439 q^{71} -0.763873 q^{72} -0.249004 q^{73} -10.5709 q^{74} +9.55354 q^{75} +6.24346 q^{76} +6.81868 q^{77} +3.17085 q^{78} -12.4573 q^{79} -0.275091 q^{80} -10.7081 q^{81} +8.26556 q^{82} +16.6569 q^{83} +5.43740 q^{84} +0.308846 q^{85} -11.1306 q^{86} +6.52546 q^{87} +2.43291 q^{88} -8.22939 q^{89} +0.210135 q^{90} -4.58070 q^{91} -5.13618 q^{92} -14.2658 q^{93} +1.86722 q^{94} -1.71752 q^{95} +1.94007 q^{96} +1.29351 q^{97} -0.855018 q^{98} -1.85844 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) \) 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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