LMFDB - Embedded newform 8007.2.a.j.1.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.32
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0482776 q^{2} -1.00000 q^{3} -1.99767 q^{4} +1.12713 q^{5} -0.0482776 q^{6} -3.19276 q^{7} -0.192998 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.0482776 q^{2} -1.00000 q^{3} -1.99767 q^{4} +1.12713 q^{5} -0.0482776 q^{6} -3.19276 q^{7} -0.192998 q^{8} +1.00000 q^{9} +0.0544150 q^{10} -5.55828 q^{11} +1.99767 q^{12} -2.12857 q^{13} -0.154139 q^{14} -1.12713 q^{15} +3.98602 q^{16} +1.00000 q^{17} +0.0482776 q^{18} +4.53670 q^{19} -2.25163 q^{20} +3.19276 q^{21} -0.268340 q^{22} -6.46999 q^{23} +0.192998 q^{24} -3.72958 q^{25} -0.102762 q^{26} -1.00000 q^{27} +6.37809 q^{28} -7.35503 q^{29} -0.0544150 q^{30} -3.74866 q^{31} +0.578431 q^{32} +5.55828 q^{33} +0.0482776 q^{34} -3.59866 q^{35} -1.99767 q^{36} +2.70621 q^{37} +0.219021 q^{38} +2.12857 q^{39} -0.217533 q^{40} -7.26988 q^{41} +0.154139 q^{42} +10.2025 q^{43} +11.1036 q^{44} +1.12713 q^{45} -0.312355 q^{46} -10.6309 q^{47} -3.98602 q^{48} +3.19374 q^{49} -0.180055 q^{50} -1.00000 q^{51} +4.25218 q^{52} -7.51252 q^{53} -0.0482776 q^{54} -6.26490 q^{55} +0.616196 q^{56} -4.53670 q^{57} -0.355083 q^{58} +3.99008 q^{59} +2.25163 q^{60} -3.71721 q^{61} -0.180976 q^{62} -3.19276 q^{63} -7.94412 q^{64} -2.39917 q^{65} +0.268340 q^{66} -9.30348 q^{67} -1.99767 q^{68} +6.46999 q^{69} -0.173734 q^{70} -14.7710 q^{71} -0.192998 q^{72} +14.0106 q^{73} +0.130649 q^{74} +3.72958 q^{75} -9.06283 q^{76} +17.7463 q^{77} +0.102762 q^{78} -7.54648 q^{79} +4.49276 q^{80} +1.00000 q^{81} -0.350972 q^{82} -17.8714 q^{83} -6.37809 q^{84} +1.12713 q^{85} +0.492551 q^{86} +7.35503 q^{87} +1.07274 q^{88} -15.0113 q^{89} +0.0544150 q^{90} +6.79603 q^{91} +12.9249 q^{92} +3.74866 q^{93} -0.513233 q^{94} +5.11345 q^{95} -0.578431 q^{96} -3.37810 q^{97} +0.154186 q^{98} -5.55828 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * 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 $

$2$	0.0482776	0.0341374	0.0170687	−	0.999854i	$-0.494567\pi$
$2$	0.0482776	0.0341374	0.0170687	+	0.999854i	$0.494567\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.99767	−0.998835
$5$	1.12713	0.504067	0.252034	−	0.967718i	$-0.418901\pi$
$5$	1.12713	0.504067	0.252034	+	0.967718i	$0.418901\pi$
$6$	−0.0482776	−0.0197092
$7$	−3.19276	−1.20675	−0.603376	−	0.797457i	$-0.706178\pi$
$7$	−3.19276	−1.20675	−0.603376	+	0.797457i	$0.706178\pi$
$8$	−0.192998	−0.0682350
$9$	1.00000	0.333333
$10$	0.0544150	0.0172075
$11$	−5.55828	−1.67589	−0.837943	−	0.545758i	$-0.816242\pi$
$11$	−5.55828	−1.67589	−0.837943	+	0.545758i	$0.816242\pi$
$12$	1.99767	0.576677
$13$	−2.12857	−0.590360	−0.295180	−	0.955442i	$-0.595380\pi$
$13$	−2.12857	−0.590360	−0.295180	+	0.955442i	$0.595380\pi$
$14$	−0.154139	−0.0411953
$15$	−1.12713	−0.291023
$16$	3.98602	0.996505
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.0482776	0.0113791
$19$	4.53670	1.04079	0.520395	−	0.853925i	$-0.325785\pi$
$19$	4.53670	1.04079	0.520395	+	0.853925i	$0.325785\pi$
$20$	−2.25163	−0.503480
$21$	3.19276	0.696718
$22$	−0.268340	−0.0572104
$23$	−6.46999	−1.34909	−0.674543	−	0.738236i	$-0.735659\pi$
$23$	−6.46999	−1.34909	−0.674543	+	0.738236i	$0.735659\pi$
$24$	0.192998	0.0393955
$25$	−3.72958	−0.745916
$26$	−0.102762	−0.0201533
$27$	−1.00000	−0.192450
$28$	6.37809	1.20534
$29$	−7.35503	−1.36579	−0.682897	−	0.730514i	$-0.739280\pi$
$29$	−7.35503	−1.36579	−0.682897	+	0.730514i	$0.739280\pi$
$30$	−0.0544150	−0.00993478
$31$	−3.74866	−0.673280	−0.336640	−	0.941633i	$-0.609291\pi$
$31$	−3.74866	−0.673280	−0.336640	+	0.941633i	$0.609291\pi$
$32$	0.578431	0.102253
$33$	5.55828	0.967573
$34$	0.0482776	0.00827953
$35$	−3.59866	−0.608284
$36$	−1.99767	−0.332945
$37$	2.70621	0.444899	0.222449	−	0.974944i	$-0.428595\pi$
$37$	2.70621	0.444899	0.222449	+	0.974944i	$0.428595\pi$
$38$	0.219021	0.0355299
$39$	2.12857	0.340844
$40$	−0.217533	−0.0343950
$41$	−7.26988	−1.13536	−0.567682	−	0.823248i	$-0.692160\pi$
$41$	−7.26988	−1.13536	−0.567682	+	0.823248i	$0.692160\pi$
$42$	0.154139	0.0237841
$43$	10.2025	1.55587	0.777933	−	0.628348i	$-0.216268\pi$
$43$	10.2025	1.55587	0.777933	+	0.628348i	$0.216268\pi$
$44$	11.1036	1.67393
$45$	1.12713	0.168022
$46$	−0.312355	−0.0460542
$47$	−10.6309	−1.55067	−0.775336	−	0.631549i	$-0.782420\pi$
$47$	−10.6309	−1.55067	−0.775336	+	0.631549i	$0.782420\pi$
$48$	−3.98602	−0.575333
$49$	3.19374	0.456248
$50$	−0.180055	−0.0254636
$51$	−1.00000	−0.140028
$52$	4.25218	0.589672
$53$	−7.51252	−1.03192	−0.515962	−	0.856611i	$-0.672565\pi$
$53$	−7.51252	−1.03192	−0.515962	+	0.856611i	$0.672565\pi$
$54$	−0.0482776	−0.00656974
$55$	−6.26490	−0.844759
$56$	0.616196	0.0823426
$57$	−4.53670	−0.600901
$58$	−0.355083	−0.0466246
$59$	3.99008	0.519464	0.259732	−	0.965681i	$-0.416366\pi$
$59$	3.99008	0.519464	0.259732	+	0.965681i	$0.416366\pi$
$60$	2.25163	0.290684
$61$	−3.71721	−0.475940	−0.237970	−	0.971273i	$-0.576482\pi$
$61$	−3.71721	−0.475940	−0.237970	+	0.971273i	$0.576482\pi$
$62$	−0.180976	−0.0229840
$63$	−3.19276	−0.402250
$64$	−7.94412	−0.993015
$65$	−2.39917	−0.297581
$66$	0.268340	0.0330304
$67$	−9.30348	−1.13660	−0.568300	−	0.822821i	$-0.692399\pi$
$67$	−9.30348	−1.13660	−0.568300	+	0.822821i	$0.692399\pi$
$68$	−1.99767	−0.242253
$69$	6.46999	0.778895
$70$	−0.173734	−0.0207652
$71$	−14.7710	−1.75300	−0.876500	−	0.481402i	$-0.840128\pi$
$71$	−14.7710	−1.75300	−0.876500	+	0.481402i	$0.840128\pi$
$72$	−0.192998	−0.0227450
$73$	14.0106	1.63982	0.819909	−	0.572494i	$-0.194024\pi$
$73$	14.0106	1.63982	0.819909	+	0.572494i	$0.194024\pi$
$74$	0.130649	0.0151877
$75$	3.72958	0.430655
$76$	−9.06283	−1.03958
$77$	17.7463	2.02238
$78$	0.102762	0.0116355
$79$	−7.54648	−0.849045	−0.424523	−	0.905417i	$-0.639558\pi$
$79$	−7.54648	−0.849045	−0.424523	+	0.905417i	$0.639558\pi$
$80$	4.49276	0.502306
$81$	1.00000	0.111111
$82$	−0.350972	−0.0387584
$83$	−17.8714	−1.96164	−0.980820	−	0.194915i	$-0.937557\pi$
$83$	−17.8714	−1.96164	−0.980820	+	0.194915i	$0.937557\pi$
$84$	−6.37809	−0.695906
$85$	1.12713	0.122254
$86$	0.492551	0.0531132
$87$	7.35503	0.788542
$88$	1.07274	0.114354
$89$	−15.0113	−1.59119	−0.795597	−	0.605826i	$-0.792843\pi$
$89$	−15.0113	−1.59119	−0.795597	+	0.605826i	$0.792843\pi$
$90$	0.0544150	0.00573585
$91$	6.79603	0.712417
$92$	12.9249	1.34751
$93$	3.74866	0.388718
$94$	−0.513233	−0.0529359
$95$	5.11345	0.524629
$96$	−0.578431	−0.0590358
$97$	−3.37810	−0.342994	−0.171497	−	0.985185i	$-0.554860\pi$
$97$	−3.37810	−0.342994	−0.171497	+	0.985185i	$0.554860\pi$
$98$	0.154186	0.0155751
$99$	−5.55828	−0.558629
$100$	7.45047	0.745047
$101$	9.91102	0.986183	0.493092	−	0.869977i	$-0.335867\pi$
$101$	9.91102	0.986183	0.493092	+	0.869977i	$0.335867\pi$
$102$	−0.0482776	−0.00478019
$103$	−20.0651	−1.97707	−0.988534	−	0.150997i	$-0.951752\pi$
$103$	−20.0651	−1.97707	−0.988534	+	0.150997i	$0.951752\pi$
$104$	0.410809	0.0402832
$105$	3.59866	0.351193
$106$	−0.362686	−0.0352272
$107$	15.6209	1.51013	0.755063	−	0.655652i	$-0.227606\pi$
$107$	15.6209	1.51013	0.755063	+	0.655652i	$0.227606\pi$
$108$	1.99767	0.192226
$109$	8.23887	0.789141	0.394570	−	0.918866i	$-0.370893\pi$
$109$	8.23887	0.789141	0.394570	+	0.918866i	$0.370893\pi$
$110$	−0.302454	−0.0288379
$111$	−2.70621	−0.256863
$112$	−12.7264	−1.20253
$113$	17.5315	1.64922	0.824612	−	0.565698i	$-0.191393\pi$
$113$	17.5315	1.64922	0.824612	+	0.565698i	$0.191393\pi$
$114$	−0.219021	−0.0205132
$115$	−7.29251	−0.680030
$116$	14.6929	1.36420
$117$	−2.12857	−0.196787
$118$	0.192631	0.0177332
$119$	−3.19276	−0.292680
$120$	0.217533	0.0198580
$121$	19.8945	1.80859
$122$	−0.179458	−0.0162473
$123$	7.26988	0.655503
$124$	7.48859	0.672495
$125$	−9.83936	−0.880059
$126$	−0.154139	−0.0137318
$127$	−0.697297	−0.0618751	−0.0309376	−	0.999521i	$-0.509849\pi$
$127$	−0.697297	−0.0618751	−0.0309376	+	0.999521i	$0.509849\pi$
$128$	−1.54038	−0.136152
$129$	−10.2025	−0.898279
$130$	−0.115826	−0.0101586
$131$	−21.8691	−1.91071	−0.955354	−	0.295462i	$-0.904526\pi$
$131$	−21.8691	−1.91071	−0.955354	+	0.295462i	$0.904526\pi$
$132$	−11.1036	−0.966446
$133$	−14.4846	−1.25598
$134$	−0.449149	−0.0388006
$135$	−1.12713	−0.0970078
$136$	−0.192998	−0.0165494
$137$	0.874438	0.0747083	0.0373542	−	0.999302i	$-0.488107\pi$
$137$	0.874438	0.0747083	0.0373542	+	0.999302i	$0.488107\pi$
$138$	0.312355	0.0265894
$139$	−2.30439	−0.195456	−0.0977279	−	0.995213i	$-0.531157\pi$
$139$	−2.30439	−0.195456	−0.0977279	+	0.995213i	$0.531157\pi$
$140$	7.18892	0.607575
$141$	10.6309	0.895281
$142$	−0.713109	−0.0598428
$143$	11.8312	0.989375
$144$	3.98602	0.332168
$145$	−8.29007	−0.688452
$146$	0.676398	0.0559791
$147$	−3.19374	−0.263415
$148$	−5.40612	−0.444380
$149$	19.4695	1.59500	0.797501	−	0.603317i	$-0.206155\pi$
$149$	19.4695	1.59500	0.797501	+	0.603317i	$0.206155\pi$
$150$	0.180055	0.0147014
$151$	21.7975	1.77386	0.886928	−	0.461908i	$-0.152835\pi$
$151$	21.7975	1.77386	0.886928	+	0.461908i	$0.152835\pi$
$152$	−0.875573	−0.0710183
$153$	1.00000	0.0808452
$154$	0.856747	0.0690387
$155$	−4.22523	−0.339378
$156$	−4.25218	−0.340447
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−0.364326	−0.0289842
$159$	7.51252	0.595782
$160$	0.651966	0.0515424
$161$	20.6571	1.62801
$162$	0.0482776	0.00379304
$163$	−9.69766	−0.759580	−0.379790	−	0.925073i	$-0.624004\pi$
$163$	−9.69766	−0.759580	−0.379790	+	0.925073i	$0.624004\pi$
$164$	14.5228	1.13404
$165$	6.26490	0.487722
$166$	−0.862787	−0.0669653
$167$	−7.50455	−0.580719	−0.290360	−	0.956918i	$-0.593775\pi$
$167$	−7.50455	−0.580719	−0.290360	+	0.956918i	$0.593775\pi$
$168$	−0.616196	−0.0475405
$169$	−8.46918	−0.651476
$170$	0.0544150	0.00417344
$171$	4.53670	0.346930
$172$	−20.3812	−1.55405
$173$	−20.3374	−1.54622	−0.773111	−	0.634271i	$-0.781300\pi$
$173$	−20.3374	−1.54622	−0.773111	+	0.634271i	$0.781300\pi$
$174$	0.355083	0.0269188
$175$	11.9077	0.900135
$176$	−22.1554	−1.67003
$177$	−3.99008	−0.299913
$178$	−0.724709	−0.0543192
$179$	−3.20576	−0.239610	−0.119805	−	0.992797i	$-0.538227\pi$
$179$	−3.20576	−0.239610	−0.119805	+	0.992797i	$0.538227\pi$
$180$	−2.25163	−0.167827
$181$	−0.511274	−0.0380027	−0.0190013	−	0.999819i	$-0.506049\pi$
$181$	−0.511274	−0.0380027	−0.0190013	+	0.999819i	$0.506049\pi$
$182$	0.328095	0.0243201
$183$	3.71721	0.274784
$184$	1.24869	0.0920548
$185$	3.05025	0.224259
$186$	0.180976	0.0132698
$187$	−5.55828	−0.406462
$188$	21.2370	1.54887
$189$	3.19276	0.232239
$190$	0.246865	0.0179094
$191$	14.2297	1.02963	0.514813	−	0.857303i	$-0.327862\pi$
$191$	14.2297	1.02963	0.514813	+	0.857303i	$0.327862\pi$
$192$	7.94412	0.573317
$193$	−13.5818	−0.977641	−0.488820	−	0.872384i	$-0.662573\pi$
$193$	−13.5818	−0.977641	−0.488820	+	0.872384i	$0.662573\pi$
$194$	−0.163086	−0.0117089
$195$	2.39917	0.171808
$196$	−6.38003	−0.455717
$197$	−14.3144	−1.01986	−0.509931	−	0.860215i	$-0.670329\pi$
$197$	−14.3144	−1.01986	−0.509931	+	0.860215i	$0.670329\pi$
$198$	−0.268340	−0.0190701
$199$	−4.03438	−0.285990	−0.142995	−	0.989723i	$-0.545673\pi$
$199$	−4.03438	−0.285990	−0.142995	+	0.989723i	$0.545673\pi$
$200$	0.719800	0.0508976
$201$	9.30348	0.656217
$202$	0.478480	0.0336657
$203$	23.4829	1.64817
$204$	1.99767	0.139865
$205$	−8.19409	−0.572300
$206$	−0.968692	−0.0674919
$207$	−6.46999	−0.449695
$208$	−8.48453	−0.588296
$209$	−25.2163	−1.74425
$210$	0.173734	0.0119888
$211$	7.30618	0.502978	0.251489	−	0.967860i	$-0.419080\pi$
$211$	7.30618	0.502978	0.251489	+	0.967860i	$0.419080\pi$
$212$	15.0075	1.03072
$213$	14.7710	1.01209
$214$	0.754137	0.0515517
$215$	11.4995	0.784261
$216$	0.192998	0.0131318
$217$	11.9686	0.812481
$218$	0.397753	0.0269392
$219$	−14.0106	−0.946749
$220$	12.5152	0.843775
$221$	−2.12857	−0.143183
$222$	−0.130649	−0.00876861
$223$	−16.1040	−1.07840	−0.539201	−	0.842177i	$-0.681274\pi$
$223$	−16.1040	−1.07840	−0.539201	+	0.842177i	$0.681274\pi$
$224$	−1.84679	−0.123394
$225$	−3.72958	−0.248639
$226$	0.846378	0.0563002
$227$	28.8267	1.91330	0.956649	−	0.291244i	$-0.0940693\pi$
$227$	28.8267	1.91330	0.956649	+	0.291244i	$0.0940693\pi$
$228$	9.06283	0.600200
$229$	24.3244	1.60740	0.803701	−	0.595033i	$-0.202861\pi$
$229$	24.3244	1.60740	0.803701	+	0.595033i	$0.202861\pi$
$230$	−0.352064	−0.0232144
$231$	−17.7463	−1.16762
$232$	1.41950	0.0931950
$233$	7.42336	0.486320	0.243160	−	0.969986i	$-0.421816\pi$
$233$	7.42336	0.486320	0.243160	+	0.969986i	$0.421816\pi$
$234$	−0.102762	−0.00671778
$235$	−11.9824	−0.781643
$236$	−7.97086	−0.518859
$237$	7.54648	0.490197
$238$	−0.154139	−0.00999133
$239$	25.5895	1.65524	0.827622	−	0.561286i	$-0.189693\pi$
$239$	25.5895	1.65524	0.827622	+	0.561286i	$0.189693\pi$
$240$	−4.49276	−0.290006
$241$	6.91001	0.445113	0.222556	−	0.974920i	$-0.428560\pi$
$241$	6.91001	0.445113	0.222556	+	0.974920i	$0.428560\pi$
$242$	0.960459	0.0617406
$243$	−1.00000	−0.0641500
$244$	7.42575	0.475385
$245$	3.59975	0.229980
$246$	0.350972	0.0223772
$247$	−9.65669	−0.614441
$248$	0.723483	0.0459412
$249$	17.8714	1.13255
$250$	−0.475020	−0.0300429
$251$	−17.4610	−1.10213	−0.551065	−	0.834462i	$-0.685778\pi$
$251$	−17.4610	−1.10213	−0.551065	+	0.834462i	$0.685778\pi$
$252$	6.37809	0.401782
$253$	35.9620	2.26091
$254$	−0.0336638	−0.00211226
$255$	−1.12713	−0.0705836
$256$	15.8139	0.988367
$257$	16.9499	1.05731	0.528653	−	0.848838i	$-0.322697\pi$
$257$	16.9499	1.05731	0.528653	+	0.848838i	$0.322697\pi$
$258$	−0.492551	−0.0306649
$259$	−8.64030	−0.536882
$260$	4.79276	0.297234
$261$	−7.35503	−0.455265
$262$	−1.05578	−0.0652266
$263$	−23.0443	−1.42097	−0.710485	−	0.703712i	$-0.751525\pi$
$263$	−23.0443	−1.42097	−0.710485	+	0.703712i	$0.751525\pi$
$264$	−1.07274	−0.0660223
$265$	−8.46758	−0.520159
$266$	−0.699282	−0.0428757
$267$	15.0113	0.918677
$268$	18.5853	1.13528
$269$	3.13370	0.191065	0.0955327	−	0.995426i	$-0.469545\pi$
$269$	3.13370	0.191065	0.0955327	+	0.995426i	$0.469545\pi$
$270$	−0.0544150	−0.00331159
$271$	13.0477	0.792592	0.396296	−	0.918123i	$-0.370295\pi$
$271$	13.0477	0.792592	0.396296	+	0.918123i	$0.370295\pi$
$272$	3.98602	0.241688
$273$	−6.79603	−0.411314
$274$	0.0422157	0.00255035
$275$	20.7301	1.25007
$276$	−12.9249	−0.777987
$277$	9.26595	0.556737	0.278369	−	0.960474i	$-0.410206\pi$
$277$	9.26595	0.556737	0.278369	+	0.960474i	$0.410206\pi$
$278$	−0.111250	−0.00667235
$279$	−3.74866	−0.224427
$280$	0.694532	0.0415062
$281$	−11.8994	−0.709859	−0.354930	−	0.934893i	$-0.615495\pi$
$281$	−11.8994	−0.709859	−0.354930	+	0.934893i	$0.615495\pi$
$282$	0.513233	0.0305626
$283$	12.3246	0.732623	0.366312	−	0.930492i	$-0.380620\pi$
$283$	12.3246	0.732623	0.366312	+	0.930492i	$0.380620\pi$
$284$	29.5076	1.75096
$285$	−5.11345	−0.302894
$286$	0.571182	0.0337747
$287$	23.2110	1.37010
$288$	0.578431	0.0340844
$289$	1.00000	0.0588235
$290$	−0.400224	−0.0235020
$291$	3.37810	0.198027
$292$	−27.9886	−1.63791
$293$	10.2048	0.596173	0.298087	−	0.954539i	$-0.403652\pi$
$293$	10.2048	0.596173	0.298087	+	0.954539i	$0.403652\pi$
$294$	−0.154186	−0.00899230
$295$	4.49734	0.261845
$296$	−0.522293	−0.0303577
$297$	5.55828	0.322524
$298$	0.939939	0.0544492
$299$	13.7718	0.796445
$300$	−7.45047	−0.430153
$301$	−32.5741	−1.87754
$302$	1.05233	0.0605548
$303$	−9.91102	−0.569373
$304$	18.0834	1.03715
$305$	−4.18977	−0.239906
$306$	0.0482776	0.00275984
$307$	26.8461	1.53219	0.766093	−	0.642730i	$-0.222198\pi$
$307$	26.8461	1.53219	0.766093	+	0.642730i	$0.222198\pi$
$308$	−35.4512	−2.02002
$309$	20.0651	1.14146
$310$	−0.203984	−0.0115855
$311$	−29.6208	−1.67964	−0.839822	−	0.542863i	$-0.817340\pi$
$311$	−29.6208	−1.67964	−0.839822	+	0.542863i	$0.817340\pi$
$312$	−0.410809	−0.0232575
$313$	−6.12245	−0.346062	−0.173031	−	0.984916i	$-0.555356\pi$
$313$	−6.12245	−0.346062	−0.173031	+	0.984916i	$0.555356\pi$
$314$	−0.0482776	−0.00272446
$315$	−3.59866	−0.202761
$316$	15.0754	0.848056
$317$	−15.0484	−0.845204	−0.422602	−	0.906315i	$-0.638883\pi$
$317$	−15.0484	−0.845204	−0.422602	+	0.906315i	$0.638883\pi$
$318$	0.362686	0.0203384
$319$	40.8813	2.28892
$320$	−8.95404	−0.500546
$321$	−15.6209	−0.871872
$322$	0.997276	0.0555760
$323$	4.53670	0.252429
$324$	−1.99767	−0.110982
$325$	7.93868	0.440359
$326$	−0.468179	−0.0259301
$327$	−8.23887	−0.455611
$328$	1.40307	0.0774716
$329$	33.9419	1.87128
$330$	0.302454	0.0166496
$331$	−18.7446	−1.03029	−0.515147	−	0.857102i	$-0.672263\pi$
$331$	−18.7446	−1.03029	−0.515147	+	0.857102i	$0.672263\pi$
$332$	35.7011	1.95935
$333$	2.70621	0.148300
$334$	−0.362301	−0.0198242
$335$	−10.4862	−0.572923
$336$	12.7264	0.694283
$337$	−32.5993	−1.77580	−0.887898	−	0.460040i	$-0.847835\pi$
$337$	−32.5993	−1.77580	−0.887898	+	0.460040i	$0.847835\pi$
$338$	−0.408871	−0.0222397
$339$	−17.5315	−0.952180
$340$	−2.25163	−0.122112
$341$	20.8361	1.12834
$342$	0.219021	0.0118433
$343$	12.1525	0.656173
$344$	−1.96906	−0.106164
$345$	7.29251	0.392615
$346$	−0.981838	−0.0527839
$347$	2.64674	0.142084	0.0710421	−	0.997473i	$-0.477368\pi$
$347$	2.64674	0.142084	0.0710421	+	0.997473i	$0.477368\pi$
$348$	−14.6929	−0.787623
$349$	−10.0065	−0.535637	−0.267819	−	0.963469i	$-0.586303\pi$
$349$	−10.0065	−0.535637	−0.267819	+	0.963469i	$0.586303\pi$
$350$	0.574873	0.0307283
$351$	2.12857	0.113615
$352$	−3.21508	−0.171364
$353$	21.4690	1.14268	0.571341	−	0.820713i	$-0.306424\pi$
$353$	21.4690	1.14268	0.571341	+	0.820713i	$0.306424\pi$
$354$	−0.192631	−0.0102382
$355$	−16.6489	−0.883630
$356$	29.9876	1.58934
$357$	3.19276	0.168979
$358$	−0.154766	−0.00817964
$359$	−1.65329	−0.0872574	−0.0436287	−	0.999048i	$-0.513892\pi$
$359$	−1.65329	−0.0872574	−0.0436287	+	0.999048i	$0.513892\pi$
$360$	−0.217533	−0.0114650
$361$	1.58166	0.0832451
$362$	−0.0246830	−0.00129731
$363$	−19.8945	−1.04419
$364$	−13.5762	−0.711587
$365$	15.7918	0.826579
$366$	0.179458	0.00938040
$367$	−8.38929	−0.437917	−0.218959	−	0.975734i	$-0.570266\pi$
$367$	−8.38929	−0.437917	−0.218959	+	0.975734i	$0.570266\pi$
$368$	−25.7895	−1.34437
$369$	−7.26988	−0.378455
$370$	0.147259	0.00765562
$371$	23.9857	1.24528
$372$	−7.48859	−0.388265
$373$	−4.28053	−0.221638	−0.110819	−	0.993841i	$-0.535347\pi$
$373$	−4.28053	−0.221638	−0.110819	+	0.993841i	$0.535347\pi$
$374$	−0.268340	−0.0138755
$375$	9.83936	0.508103
$376$	2.05173	0.105810
$377$	15.6557	0.806310
$378$	0.154139	0.00792804
$379$	1.66051	0.0852945	0.0426473	−	0.999090i	$-0.486421\pi$
$379$	1.66051	0.0852945	0.0426473	+	0.999090i	$0.486421\pi$
$380$	−10.2150	−0.524017
$381$	0.697297	0.0357236
$382$	0.686975	0.0351487
$383$	8.68130	0.443594	0.221797	−	0.975093i	$-0.428808\pi$
$383$	8.68130	0.443594	0.221797	+	0.975093i	$0.428808\pi$
$384$	1.54038	0.0786074
$385$	20.0024	1.01941
$386$	−0.655697	−0.0333741
$387$	10.2025	0.518622
$388$	6.74832	0.342594
$389$	−16.9518	−0.859490	−0.429745	−	0.902950i	$-0.641397\pi$
$389$	−16.9518	−0.859490	−0.429745	+	0.902950i	$0.641397\pi$
$390$	0.115826	0.00586509
$391$	−6.46999	−0.327201
$392$	−0.616384	−0.0311321
$393$	21.8691	1.10315
$394$	−0.691067	−0.0348154
$395$	−8.50586	−0.427976
$396$	11.1036	0.557978
$397$	2.22249	0.111544	0.0557719	−	0.998444i	$-0.482238\pi$
$397$	2.22249	0.111544	0.0557719	+	0.998444i	$0.482238\pi$
$398$	−0.194770	−0.00976294
$399$	14.4846	0.725138
$400$	−14.8662	−0.743309
$401$	−28.1420	−1.40535	−0.702673	−	0.711513i	$-0.748010\pi$
$401$	−28.1420	−1.40535	−0.702673	+	0.711513i	$0.748010\pi$
$402$	0.449149	0.0224015
$403$	7.97930	0.397477
$404$	−19.7989	−0.985034
$405$	1.12713	0.0560075
$406$	1.13370	0.0562643
$407$	−15.0419	−0.745600
$408$	0.192998	0.00955481
$409$	15.8128	0.781895	0.390948	−	0.920413i	$-0.372147\pi$
$409$	15.8128	0.781895	0.390948	+	0.920413i	$0.372147\pi$
$410$	−0.395591	−0.0195368
$411$	−0.874438	−0.0431329
$412$	40.0833	1.97476
$413$	−12.7394	−0.626864
$414$	−0.312355	−0.0153514
$415$	−20.1434	−0.988799
$416$	−1.23123	−0.0603661
$417$	2.30439	0.112846
$418$	−1.21738	−0.0595440
$419$	25.2893	1.23546	0.617731	−	0.786389i	$-0.288052\pi$
$419$	25.2893	1.23546	0.617731	+	0.786389i	$0.288052\pi$
$420$	−7.18892	−0.350784
$421$	−11.2006	−0.545883	−0.272942	−	0.962031i	$-0.587997\pi$
$421$	−11.2006	−0.545883	−0.272942	+	0.962031i	$0.587997\pi$
$422$	0.352725	0.0171704
$423$	−10.6309	−0.516891
$424$	1.44990	0.0704133
$425$	−3.72958	−0.180911
$426$	0.713109	0.0345503
$427$	11.8682	0.574341
$428$	−31.2053	−1.50837
$429$	−11.8312	−0.571216
$430$	0.555169	0.0267726
$431$	−24.6499	−1.18734	−0.593672	−	0.804707i	$-0.702322\pi$
$431$	−24.6499	−1.18734	−0.593672	+	0.804707i	$0.702322\pi$
$432$	−3.98602	−0.191778
$433$	4.89500	0.235239	0.117619	−	0.993059i	$-0.462474\pi$
$433$	4.89500	0.235239	0.117619	+	0.993059i	$0.462474\pi$
$434$	0.577815	0.0277360
$435$	8.29007	0.397478
$436$	−16.4585	−0.788221
$437$	−29.3524	−1.40412
$438$	−0.676398	−0.0323195
$439$	−11.0895	−0.529273	−0.264636	−	0.964348i	$-0.585252\pi$
$439$	−11.0895	−0.529273	−0.264636	+	0.964348i	$0.585252\pi$
$440$	1.20911	0.0576421
$441$	3.19374	0.152083
$442$	−0.102762	−0.00488790
$443$	28.7256	1.36479	0.682396	−	0.730983i	$-0.260938\pi$
$443$	28.7256	1.36479	0.682396	+	0.730983i	$0.260938\pi$
$444$	5.40612	0.256563
$445$	−16.9197	−0.802070
$446$	−0.777461	−0.0368139
$447$	−19.4695	−0.920875
$448$	25.3637	1.19832
$449$	13.7512	0.648960	0.324480	−	0.945893i	$-0.394811\pi$
$449$	13.7512	0.648960	0.324480	+	0.945893i	$0.394811\pi$
$450$	−0.180055	−0.00848787
$451$	40.4081	1.90274
$452$	−35.0221	−1.64730
$453$	−21.7975	−1.02414
$454$	1.39168	0.0653150
$455$	7.66000	0.359106
$456$	0.875573	0.0410025
$457$	−12.0689	−0.564559	−0.282279	−	0.959332i	$-0.591090\pi$
$457$	−12.0689	−0.564559	−0.282279	+	0.959332i	$0.591090\pi$
$458$	1.17432	0.0548725
$459$	−1.00000	−0.0466760
$460$	14.5680	0.679237
$461$	8.45221	0.393659	0.196829	−	0.980438i	$-0.436936\pi$
$461$	8.45221	0.393659	0.196829	+	0.980438i	$0.436936\pi$
$462$	−0.856747	−0.0398595
$463$	−7.90234	−0.367253	−0.183626	−	0.982996i	$-0.558784\pi$
$463$	−7.90234	−0.367253	−0.183626	+	0.982996i	$0.558784\pi$
$464$	−29.3173	−1.36102
$465$	4.22523	0.195940
$466$	0.358381	0.0166017
$467$	33.4844	1.54947	0.774737	−	0.632283i	$-0.217882\pi$
$467$	33.4844	1.54947	0.774737	+	0.632283i	$0.217882\pi$
$468$	4.25218	0.196557
$469$	29.7038	1.37159
$470$	−0.578479	−0.0266833
$471$	1.00000	0.0460776
$472$	−0.770077	−0.0354456
$473$	−56.7083	−2.60745
$474$	0.364326	0.0167340
$475$	−16.9200	−0.776342
$476$	6.37809	0.292339
$477$	−7.51252	−0.343975
$478$	1.23540	0.0565057
$479$	−8.97103	−0.409897	−0.204948	−	0.978773i	$-0.565703\pi$
$479$	−8.97103	−0.409897	−0.204948	+	0.978773i	$0.565703\pi$
$480$	−0.651966	−0.0297580
$481$	−5.76037	−0.262650
$482$	0.333598	0.0151950
$483$	−20.6571	−0.939932
$484$	−39.7427	−1.80649
$485$	−3.80755	−0.172892
$486$	−0.0482776	−0.00218991
$487$	−15.8123	−0.716525	−0.358262	−	0.933621i	$-0.616631\pi$
$487$	−15.8123	−0.716525	−0.358262	+	0.933621i	$0.616631\pi$
$488$	0.717412	0.0324757
$489$	9.69766	0.438544
$490$	0.173787	0.00785091
$491$	18.6461	0.841488	0.420744	−	0.907179i	$-0.361769\pi$
$491$	18.6461	0.841488	0.420744	+	0.907179i	$0.361769\pi$
$492$	−14.5228	−0.654739
$493$	−7.35503	−0.331254
$494$	−0.466202	−0.0209754
$495$	−6.26490	−0.281586
$496$	−14.9423	−0.670927
$497$	47.1604	2.11543
$498$	0.862787	0.0386624
$499$	7.41294	0.331849	0.165924	−	0.986138i	$-0.446939\pi$
$499$	7.41294	0.331849	0.165924	+	0.986138i	$0.446939\pi$
$500$	19.6558	0.879034
$501$	7.50455	0.335278
$502$	−0.842976	−0.0376239
$503$	20.6026	0.918626	0.459313	−	0.888275i	$-0.348096\pi$
$503$	20.6026	0.918626	0.459313	+	0.888275i	$0.348096\pi$
$504$	0.616196	0.0274475
$505$	11.1710	0.497103
$506$	1.73616	0.0771817
$507$	8.46918	0.376130
$508$	1.39297	0.0618030
$509$	20.1362	0.892522	0.446261	−	0.894903i	$-0.352755\pi$
$509$	20.1362	0.892522	0.446261	+	0.894903i	$0.352755\pi$
$510$	−0.0544150	−0.00240954
$511$	−44.7326	−1.97885
$512$	3.84422	0.169892
$513$	−4.53670	−0.200300
$514$	0.818300	0.0360937
$515$	−22.6159	−0.996576
$516$	20.3812	0.897232
$517$	59.0894	2.59875
$518$	−0.417133	−0.0183278
$519$	20.3374	0.892711
$520$	0.463035	0.0203054
$521$	8.25845	0.361809	0.180905	−	0.983501i	$-0.442097\pi$
$521$	8.25845	0.361809	0.180905	+	0.983501i	$0.442097\pi$
$522$	−0.355083	−0.0155415
$523$	−14.2563	−0.623384	−0.311692	−	0.950183i	$-0.600896\pi$
$523$	−14.2563	−0.623384	−0.311692	+	0.950183i	$0.600896\pi$
$524$	43.6872	1.90848
$525$	−11.9077	−0.519693
$526$	−1.11252	−0.0485082
$527$	−3.74866	−0.163294
$528$	22.1554	0.964192
$529$	18.8607	0.820031
$530$	−0.408794	−0.0177569
$531$	3.99008	0.173155
$532$	28.9355	1.25451
$533$	15.4745	0.670273
$534$	0.724709	0.0313612
$535$	17.6067	0.761205
$536$	1.79555	0.0775559
$537$	3.20576	0.138339
$538$	0.151288	0.00652247
$539$	−17.7517	−0.764620
$540$	2.25163	0.0968948
$541$	28.4079	1.22135	0.610676	−	0.791881i	$-0.290898\pi$
$541$	28.4079	1.22135	0.610676	+	0.791881i	$0.290898\pi$
$542$	0.629912	0.0270570
$543$	0.511274	0.0219409
$544$	0.578431	0.0248000
$545$	9.28627	0.397780
$546$	−0.328095	−0.0140412
$547$	−9.07033	−0.387819	−0.193910	−	0.981019i	$-0.562117\pi$
$547$	−9.07033	−0.387819	−0.193910	+	0.981019i	$0.562117\pi$
$548$	−1.74684	−0.0746212
$549$	−3.71721	−0.158647
$550$	1.00080	0.0426741
$551$	−33.3676	−1.42151
$552$	−1.24869	−0.0531479
$553$	24.0941	1.02459
$554$	0.447337	0.0190055
$555$	−3.05025	−0.129476
$556$	4.60341	0.195228
$557$	−1.50061	−0.0635829	−0.0317915	−	0.999495i	$-0.510121\pi$
$557$	−1.50061	−0.0635829	−0.0317915	+	0.999495i	$0.510121\pi$
$558$	−0.180976	−0.00766134
$559$	−21.7167	−0.918520
$560$	−14.3443	−0.606158
$561$	5.55828	0.234671
$562$	−0.574474	−0.0242327
$563$	−29.7529	−1.25394	−0.626968	−	0.779045i	$-0.715704\pi$
$563$	−29.7529	−1.25394	−0.626968	+	0.779045i	$0.715704\pi$
$564$	−21.2370	−0.894238
$565$	19.7603	0.831320
$566$	0.595003	0.0250098
$567$	−3.19276	−0.134083
$568$	2.85078	0.119616
$569$	4.34717	0.182243	0.0911214	−	0.995840i	$-0.470955\pi$
$569$	4.34717	0.182243	0.0911214	+	0.995840i	$0.470955\pi$
$570$	−0.246865	−0.0103400
$571$	41.4667	1.73533	0.867663	−	0.497153i	$-0.165621\pi$
$571$	41.4667	1.73533	0.867663	+	0.497153i	$0.165621\pi$
$572$	−23.6348	−0.988222
$573$	−14.2297	−0.594454
$574$	1.12057	0.0467717
$575$	24.1303	1.00630
$576$	−7.94412	−0.331005
$577$	46.2209	1.92420	0.962100	−	0.272698i	$-0.0879160\pi$
$577$	46.2209	1.92420	0.962100	+	0.272698i	$0.0879160\pi$
$578$	0.0482776	0.00200808
$579$	13.5818	0.564441
$580$	16.5608	0.687650
$581$	57.0591	2.36721
$582$	0.163086	0.00676014
$583$	41.7567	1.72939
$584$	−2.70402	−0.111893
$585$	−2.39917	−0.0991937
$586$	0.492665	0.0203518
$587$	4.75806	0.196386	0.0981930	−	0.995167i	$-0.468694\pi$
$587$	4.75806	0.196386	0.0981930	+	0.995167i	$0.468694\pi$
$588$	6.38003	0.263108
$589$	−17.0066	−0.700743
$590$	0.217120	0.00893871
$591$	14.3144	0.588818
$592$	10.7870	0.443344
$593$	0.515062	0.0211510	0.0105755	−	0.999944i	$-0.496634\pi$
$593$	0.515062	0.0211510	0.0105755	+	0.999944i	$0.496634\pi$
$594$	0.268340	0.0110101
$595$	−3.59866	−0.147531
$596$	−38.8936	−1.59314
$597$	4.03438	0.165116
$598$	0.664870	0.0271886
$599$	−33.9124	−1.38562	−0.692812	−	0.721119i	$-0.743628\pi$
$599$	−33.9124	−1.38562	−0.692812	+	0.721119i	$0.743628\pi$
$600$	−0.719800	−0.0293857
$601$	33.3256	1.35938	0.679689	−	0.733500i	$-0.262115\pi$
$601$	33.3256	1.35938	0.679689	+	0.733500i	$0.262115\pi$
$602$	−1.57260	−0.0640944
$603$	−9.30348	−0.378867
$604$	−43.5442	−1.77179
$605$	22.4237	0.911653
$606$	−0.478480	−0.0194369
$607$	−35.9358	−1.45859	−0.729295	−	0.684199i	$-0.760152\pi$
$607$	−35.9358	−1.45859	−0.729295	+	0.684199i	$0.760152\pi$
$608$	2.62417	0.106424
$609$	−23.4829	−0.951574
$610$	−0.202272	−0.00818975
$611$	22.6286	0.915454
$612$	−1.99767	−0.0807510
$613$	23.3909	0.944750	0.472375	−	0.881398i	$-0.343397\pi$
$613$	23.3909	0.944750	0.472375	+	0.881398i	$0.343397\pi$
$614$	1.29606	0.0523048
$615$	8.19409	0.330418
$616$	−3.42499	−0.137997
$617$	−12.6250	−0.508265	−0.254132	−	0.967169i	$-0.581790\pi$
$617$	−12.6250	−0.508265	−0.254132	+	0.967169i	$0.581790\pi$
$618$	0.968692	0.0389665
$619$	−38.5198	−1.54824	−0.774120	−	0.633039i	$-0.781807\pi$
$619$	−38.5198	−1.54824	−0.774120	+	0.633039i	$0.781807\pi$
$620$	8.44061	0.338983
$621$	6.46999	0.259632
$622$	−1.43002	−0.0573386
$623$	47.9275	1.92018
$624$	8.48453	0.339653
$625$	7.55767	0.302307
$626$	−0.295577	−0.0118136
$627$	25.2163	1.00704
$628$	1.99767	0.0797157
$629$	2.70621	0.107904
$630$	−0.173734	−0.00692174
$631$	−32.2894	−1.28542	−0.642711	−	0.766109i	$-0.722190\pi$
$631$	−32.2894	−1.28542	−0.642711	+	0.766109i	$0.722190\pi$
$632$	1.45645	0.0579346
$633$	−7.30618	−0.290395
$634$	−0.726501	−0.0288531
$635$	−0.785944	−0.0311892
$636$	−15.0075	−0.595087
$637$	−6.79810	−0.269351
$638$	1.97365	0.0781376
$639$	−14.7710	−0.584333
$640$	−1.73621	−0.0686298
$641$	−27.9025	−1.10208	−0.551042	−	0.834478i	$-0.685770\pi$
$641$	−27.9025	−1.10208	−0.551042	+	0.834478i	$0.685770\pi$
$642$	−0.754137	−0.0297634
$643$	43.0322	1.69703	0.848513	−	0.529175i	$-0.177498\pi$
$643$	43.0322	1.69703	0.848513	+	0.529175i	$0.177498\pi$
$644$	−41.2661	−1.62611
$645$	−11.4995	−0.452793
$646$	0.219021	0.00861726
$647$	−21.1178	−0.830226	−0.415113	−	0.909770i	$-0.636258\pi$
$647$	−21.1178	−0.830226	−0.415113	+	0.909770i	$0.636258\pi$
$648$	−0.192998	−0.00758167
$649$	−22.1780	−0.870563
$650$	0.383260	0.0150327
$651$	−11.9686	−0.469086
$652$	19.3727	0.758695
$653$	10.3526	0.405127	0.202563	−	0.979269i	$-0.435073\pi$
$653$	10.3526	0.405127	0.202563	+	0.979269i	$0.435073\pi$
$654$	−0.397753	−0.0155534
$655$	−24.6493	−0.963126
$656$	−28.9779	−1.13140
$657$	14.0106	0.546606
$658$	1.63863	0.0638805
$659$	3.58720	0.139737	0.0698686	−	0.997556i	$-0.477742\pi$
$659$	3.58720	0.139737	0.0698686	+	0.997556i	$0.477742\pi$
$660$	−12.5152	−0.487154
$661$	−7.17428	−0.279047	−0.139524	−	0.990219i	$-0.544557\pi$
$661$	−7.17428	−0.279047	−0.139524	+	0.990219i	$0.544557\pi$
$662$	−0.904941	−0.0351715
$663$	2.12857	0.0826669
$664$	3.44914	0.133853
$665$	−16.3260	−0.633096
$666$	0.130649	0.00506256
$667$	47.5869	1.84257
$668$	14.9916	0.580042
$669$	16.1040	0.622616
$670$	−0.506249	−0.0195581
$671$	20.6613	0.797620
$672$	1.84679	0.0712416
$673$	20.7744	0.800794	0.400397	−	0.916342i	$-0.368872\pi$
$673$	20.7744	0.800794	0.400397	+	0.916342i	$0.368872\pi$
$674$	−1.57381	−0.0606210
$675$	3.72958	0.143552
$676$	16.9186	0.650716
$677$	36.8455	1.41609	0.708043	−	0.706169i	$-0.249578\pi$
$677$	36.8455	1.41609	0.708043	+	0.706169i	$0.249578\pi$
$678$	−0.846378	−0.0325049
$679$	10.7855	0.413908
$680$	−0.217533	−0.00834202
$681$	−28.8267	−1.10464
$682$	1.00592	0.0385186
$683$	−0.685299	−0.0262222	−0.0131111	−	0.999914i	$-0.504174\pi$
$683$	−0.685299	−0.0262222	−0.0131111	+	0.999914i	$0.504174\pi$
$684$	−9.06283	−0.346526
$685$	0.985605	0.0376580
$686$	0.586693	0.0224000
$687$	−24.3244	−0.928034
$688$	40.6673	1.55043
$689$	15.9909	0.609206
$690$	0.352064	0.0134029
$691$	−9.39759	−0.357501	−0.178751	−	0.983894i	$-0.557206\pi$
$691$	−9.39759	−0.357501	−0.178751	+	0.983894i	$0.557206\pi$
$692$	40.6273	1.54442
$693$	17.7463	0.674126
$694$	0.127778	0.00485039
$695$	−2.59734	−0.0985229
$696$	−1.41950	−0.0538061
$697$	−7.26988	−0.275366
$698$	−0.483091	−0.0182853
$699$	−7.42336	−0.280777
$700$	−23.7876	−0.899086
$701$	−31.5824	−1.19285	−0.596426	−	0.802668i	$-0.703413\pi$
$701$	−31.5824	−1.19285	−0.596426	+	0.802668i	$0.703413\pi$
$702$	0.102762	0.00387851
$703$	12.2773	0.463047
$704$	44.1557	1.66418
$705$	11.9824	0.451282
$706$	1.03647	0.0390081
$707$	−31.6435	−1.19008
$708$	7.97086	0.299563
$709$	−39.6731	−1.48995	−0.744977	−	0.667090i	$-0.767540\pi$
$709$	−39.6731	−1.48995	−0.744977	+	0.667090i	$0.767540\pi$
$710$	−0.803766	−0.0301648
$711$	−7.54648	−0.283015
$712$	2.89715	0.108575
$713$	24.2538	0.908312
$714$	0.154139	0.00576850
$715$	13.3353	0.498712
$716$	6.40404	0.239330
$717$	−25.5895	−0.955656
$718$	−0.0798168	−0.00297874
$719$	2.88599	0.107629	0.0538146	−	0.998551i	$-0.482862\pi$
$719$	2.88599	0.107629	0.0538146	+	0.998551i	$0.482862\pi$
$720$	4.49276	0.167435
$721$	64.0630	2.38583
$722$	0.0763585	0.00284177
$723$	−6.91001	−0.256986
$724$	1.02136	0.0379584
$725$	27.4312	1.01877
$726$	−0.960459	−0.0356460
$727$	−33.4201	−1.23948	−0.619741	−	0.784806i	$-0.712763\pi$
$727$	−33.4201	−1.23948	−0.619741	+	0.784806i	$0.712763\pi$
$728$	−1.31162	−0.0486118
$729$	1.00000	0.0370370
$730$	0.762388	0.0282172
$731$	10.2025	0.377353
$732$	−7.42575	−0.274464
$733$	22.5587	0.833225	0.416613	−	0.909084i	$-0.363217\pi$
$733$	22.5587	0.833225	0.416613	+	0.909084i	$0.363217\pi$
$734$	−0.405014	−0.0149493
$735$	−3.59975	−0.132779
$736$	−3.74244	−0.137948
$737$	51.7114	1.90481
$738$	−0.350972	−0.0129195
$739$	13.9901	0.514633	0.257317	−	0.966327i	$-0.417162\pi$
$739$	13.9901	0.514633	0.257317	+	0.966327i	$0.417162\pi$
$740$	−6.09340	−0.223998
$741$	9.65669	0.354747
$742$	1.15797	0.0425104
$743$	13.6567	0.501016	0.250508	−	0.968115i	$-0.419402\pi$
$743$	13.6567	0.501016	0.250508	+	0.968115i	$0.419402\pi$
$744$	−0.723483	−0.0265242
$745$	21.9446	0.803989
$746$	−0.206654	−0.00756613
$747$	−17.8714	−0.653880
$748$	11.1036	0.405988
$749$	−49.8737	−1.82235
$750$	0.475020	0.0173453
$751$	−31.3852	−1.14526	−0.572630	−	0.819814i	$-0.694077\pi$
$751$	−31.3852	−1.14526	−0.572630	+	0.819814i	$0.694077\pi$
$752$	−42.3749	−1.54525
$753$	17.4610	0.636315
$754$	0.755819	0.0275253
$755$	24.5686	0.894143
$756$	−6.37809	−0.231969
$757$	46.5641	1.69240	0.846201	−	0.532864i	$-0.178884\pi$
$757$	46.5641	1.69240	0.846201	+	0.532864i	$0.178884\pi$
$758$	0.0801652	0.00291173
$759$	−35.9620	−1.30534
$760$	−0.986883	−0.0357980
$761$	17.5803	0.637286	0.318643	−	0.947875i	$-0.396773\pi$
$761$	17.5803	0.637286	0.318643	+	0.947875i	$0.396773\pi$
$762$	0.0336638	0.00121951
$763$	−26.3048	−0.952297
$764$	−28.4262	−1.02843
$765$	1.12713	0.0407514
$766$	0.419112	0.0151431
$767$	−8.49318	−0.306671
$768$	−15.8139	−0.570634
$769$	10.4817	0.377978	0.188989	−	0.981979i	$-0.439479\pi$
$769$	10.4817	0.377978	0.188989	+	0.981979i	$0.439479\pi$
$770$	0.965665	0.0348001
$771$	−16.9499	−0.610436
$772$	27.1320	0.976501
$773$	20.1521	0.724819	0.362410	−	0.932019i	$-0.381954\pi$
$773$	20.1521	0.724819	0.362410	+	0.932019i	$0.381954\pi$
$774$	0.492551	0.0177044
$775$	13.9809	0.502210
$776$	0.651965	0.0234042
$777$	8.64030	0.309969
$778$	−0.818391	−0.0293407
$779$	−32.9813	−1.18168
$780$	−4.79276	−0.171608
$781$	82.1016	2.93783
$782$	−0.312355	−0.0111698
$783$	7.35503	0.262847
$784$	12.7303	0.454654
$785$	−1.12713	−0.0402290
$786$	1.05578	0.0376586
$787$	12.5423	0.447083	0.223541	−	0.974694i	$-0.428238\pi$
$787$	12.5423	0.447083	0.223541	+	0.974694i	$0.428238\pi$
$788$	28.5955	1.01867
$789$	23.0443	0.820398
$790$	−0.410642	−0.0146100
$791$	−55.9739	−1.99020
$792$	1.07274	0.0381180
$793$	7.91234	0.280975
$794$	0.107297	0.00380781
$795$	8.46758	0.300314
$796$	8.05936	0.285656
$797$	22.0650	0.781584	0.390792	−	0.920479i	$-0.372201\pi$
$797$	22.0650	0.781584	0.390792	+	0.920479i	$0.372201\pi$
$798$	0.699282	0.0247543
$799$	−10.6309	−0.376093
$800$	−2.15730	−0.0762722
$801$	−15.0113	−0.530398
$802$	−1.35863	−0.0479748
$803$	−77.8750	−2.74815
$804$	−18.5853	−0.655452
$805$	23.2833	0.820627
$806$	0.385221	0.0135688
$807$	−3.13370	−0.110312
$808$	−1.91280	−0.0672922
$809$	−0.985278	−0.0346405	−0.0173203	−	0.999850i	$-0.505513\pi$
$809$	−0.985278	−0.0346405	−0.0173203	+	0.999850i	$0.505513\pi$
$810$	0.0544150	0.00191195
$811$	43.4771	1.52669	0.763344	−	0.645992i	$-0.223556\pi$
$811$	43.4771	1.52669	0.763344	+	0.645992i	$0.223556\pi$
$812$	−46.9110	−1.64625
$813$	−13.0477	−0.457603
$814$	−0.726187	−0.0254528
$815$	−10.9305	−0.382879
$816$	−3.98602	−0.139539
$817$	46.2856	1.61933
$818$	0.763406	0.0266919
$819$	6.79603	0.237472
$820$	16.3691	0.571633
$821$	−25.2807	−0.882301	−0.441151	−	0.897433i	$-0.645430\pi$
$821$	−25.2807	−0.882301	−0.441151	+	0.897433i	$0.645430\pi$
$822$	−0.0422157	−0.00147244
$823$	17.4066	0.606756	0.303378	−	0.952870i	$-0.401886\pi$
$823$	17.4066	0.606756	0.303378	+	0.952870i	$0.401886\pi$
$824$	3.87251	0.134905
$825$	−20.7301	−0.721728
$826$	−0.615026	−0.0213995
$827$	−10.1977	−0.354608	−0.177304	−	0.984156i	$-0.556738\pi$
$827$	−10.1977	−0.354608	−0.177304	+	0.984156i	$0.556738\pi$
$828$	12.9249	0.449171
$829$	−46.6270	−1.61942	−0.809711	−	0.586829i	$-0.800376\pi$
$829$	−46.6270	−1.61942	−0.809711	+	0.586829i	$0.800376\pi$
$830$	−0.972472	−0.0337550
$831$	−9.26595	−0.321432
$832$	16.9096	0.586236
$833$	3.19374	0.110656
$834$	0.111250	0.00385228
$835$	−8.45859	−0.292722
$836$	50.3738	1.74221
$837$	3.74866	0.129573
$838$	1.22090	0.0421754
$839$	−16.0115	−0.552778	−0.276389	−	0.961046i	$-0.589138\pi$
$839$	−16.0115	−0.552778	−0.276389	+	0.961046i	$0.589138\pi$
$840$	−0.694532	−0.0239636
$841$	25.0964	0.865394
$842$	−0.540737	−0.0186350
$843$	11.8994	0.409837
$844$	−14.5953	−0.502392
$845$	−9.54586	−0.328388
$846$	−0.513233	−0.0176453
$847$	−63.5185	−2.18252
$848$	−29.9451	−1.02832
$849$	−12.3246	−0.422980
$850$	−0.180055	−0.00617584
$851$	−17.5092	−0.600207
$852$	−29.5076	−1.01092
$853$	−1.80114	−0.0616697	−0.0308348	−	0.999524i	$-0.509817\pi$
$853$	−1.80114	−0.0616697	−0.0308348	+	0.999524i	$0.509817\pi$
$854$	0.572966	0.0196065
$855$	5.11345	0.174876
$856$	−3.01479	−0.103043
$857$	−43.3353	−1.48031	−0.740154	−	0.672438i	$-0.765247\pi$
$857$	−43.3353	−1.48031	−0.740154	+	0.672438i	$0.765247\pi$
$858$	−0.571182	−0.0194998
$859$	−22.3452	−0.762410	−0.381205	−	0.924491i	$-0.624491\pi$
$859$	−22.3452	−0.762410	−0.381205	+	0.924491i	$0.624491\pi$
$860$	−22.9722	−0.783347
$861$	−23.2110	−0.791029
$862$	−1.19004	−0.0405328
$863$	−43.7873	−1.49054	−0.745269	−	0.666764i	$-0.767679\pi$
$863$	−43.7873	−1.49054	−0.745269	+	0.666764i	$0.767679\pi$
$864$	−0.578431	−0.0196786
$865$	−22.9228	−0.779400
$866$	0.236319	0.00803043
$867$	−1.00000	−0.0339618
$868$	−23.9093	−0.811534
$869$	41.9455	1.42290
$870$	0.400224	0.0135689
$871$	19.8031	0.671003
$872$	−1.59008	−0.0538470
$873$	−3.37810	−0.114331
$874$	−1.41706	−0.0479328
$875$	31.4148	1.06201
$876$	27.9886	0.945646
$877$	−23.8886	−0.806659	−0.403330	−	0.915055i	$-0.632147\pi$
$877$	−23.8886	−0.806659	−0.403330	+	0.915055i	$0.632147\pi$
$878$	−0.535374	−0.0180680
$879$	−10.2048	−0.344201
$880$	−24.9720	−0.841807
$881$	15.2646	0.514278	0.257139	−	0.966374i	$-0.417220\pi$
$881$	15.2646	0.514278	0.257139	+	0.966374i	$0.417220\pi$
$882$	0.154186	0.00519171
$883$	−22.4006	−0.753839	−0.376920	−	0.926246i	$-0.623017\pi$
$883$	−22.4006	−0.753839	−0.376920	+	0.926246i	$0.623017\pi$
$884$	4.25218	0.143016
$885$	−4.49734	−0.151176
$886$	1.38680	0.0465904
$887$	−0.0897199	−0.00301250	−0.00150625	−	0.999999i	$-0.500479\pi$
$887$	−0.0897199	−0.00301250	−0.00150625	+	0.999999i	$0.500479\pi$
$888$	0.522293	0.0175270
$889$	2.22631	0.0746679
$890$	−0.816840	−0.0273806
$891$	−5.55828	−0.186210
$892$	32.1704	1.07715
$893$	−48.2291	−1.61393
$894$	−0.939939	−0.0314363
$895$	−3.61330	−0.120779
$896$	4.91808	0.164302
$897$	−13.7718	−0.459828
$898$	0.663875	0.0221538
$899$	27.5715	0.919562
$900$	7.45047	0.248349
$901$	−7.51252	−0.250278
$902$	1.95080	0.0649546
$903$	32.5741	1.08400
$904$	−3.38354	−0.112535
$905$	−0.576272	−0.0191559
$906$	−1.05233	−0.0349613
$907$	31.3279	1.04023	0.520113	−	0.854098i	$-0.325890\pi$
$907$	31.3279	1.04023	0.520113	+	0.854098i	$0.325890\pi$
$908$	−57.5863	−1.91107
$909$	9.91102	0.328728
$910$	0.369806	0.0122589
$911$	56.7986	1.88182	0.940910	−	0.338656i	$-0.109972\pi$
$911$	56.7986	1.88182	0.940910	+	0.338656i	$0.109972\pi$
$912$	−18.0834	−0.598801
$913$	99.3343	3.28749
$914$	−0.582656	−0.0192726
$915$	4.18977	0.138510
$916$	−48.5921	−1.60553
$917$	69.8227	2.30575
$918$	−0.0482776	−0.00159340
$919$	−7.10928	−0.234514	−0.117257	−	0.993102i	$-0.537410\pi$
$919$	−7.10928	−0.234514	−0.117257	+	0.993102i	$0.537410\pi$
$920$	1.40744	0.0464018
$921$	−26.8461	−0.884608
$922$	0.408052	0.0134385
$923$	31.4412	1.03490
$924$	35.4512	1.16626
$925$	−10.0930	−0.331857
$926$	−0.381506	−0.0125371
$927$	−20.0651	−0.659023
$928$	−4.25437	−0.139657
$929$	−12.1766	−0.399501	−0.199751	−	0.979847i	$-0.564013\pi$
$929$	−12.1766	−0.399501	−0.199751	+	0.979847i	$0.564013\pi$
$930$	0.203984	0.00668889
$931$	14.4890	0.474859
$932$	−14.8294	−0.485754
$933$	29.6208	0.969742
$934$	1.61655	0.0528950
$935$	−6.26490	−0.204884
$936$	0.410809	0.0134277
$937$	58.8140	1.92137	0.960685	−	0.277642i	$-0.0895529\pi$
$937$	58.8140	1.92137	0.960685	+	0.277642i	$0.0895529\pi$
$938$	1.43403	0.0468226
$939$	6.12245	0.199799
$940$	23.9368	0.780732
$941$	−26.5180	−0.864462	−0.432231	−	0.901763i	$-0.642273\pi$
$941$	−26.5180	−0.864462	−0.432231	+	0.901763i	$0.642273\pi$
$942$	0.0482776	0.00157297
$943$	47.0360	1.53170
$944$	15.9046	0.517649
$945$	3.59866	0.117064
$946$	−2.73774	−0.0890116
$947$	−52.7154	−1.71302	−0.856511	−	0.516129i	$-0.827372\pi$
$947$	−52.7154	−1.71302	−0.856511	+	0.516129i	$0.827372\pi$
$948$	−15.0754	−0.489625
$949$	−29.8226	−0.968082
$950$	−0.816856	−0.0265023
$951$	15.0484	0.487979
$952$	0.616196	0.0199710
$953$	16.5401	0.535787	0.267893	−	0.963449i	$-0.413673\pi$
$953$	16.5401	0.535787	0.267893	+	0.963449i	$0.413673\pi$
$954$	−0.362686	−0.0117424
$955$	16.0387	0.519000
$956$	−51.1193	−1.65332
$957$	−40.8813	−1.32151
$958$	−0.433099	−0.0139928
$959$	−2.79187	−0.0901543
$960$	8.95404	0.288991
$961$	−16.9475	−0.546694
$962$	−0.278097	−0.00896619
$963$	15.6209	0.503375
$964$	−13.8039	−0.444594
$965$	−15.3085	−0.492797
$966$	−0.997276	−0.0320868
$967$	−18.1876	−0.584872	−0.292436	−	0.956285i	$-0.594466\pi$
$967$	−18.1876	−0.584872	−0.292436	+	0.956285i	$0.594466\pi$
$968$	−3.83960	−0.123409
$969$	−4.53670	−0.145740
$970$	−0.183819	−0.00590208
$971$	−15.8629	−0.509066	−0.254533	−	0.967064i	$-0.581922\pi$
$971$	−15.8629	−0.509066	−0.254533	+	0.967064i	$0.581922\pi$
$972$	1.99767	0.0640753
$973$	7.35737	0.235867
$974$	−0.763380	−0.0244603
$975$	−7.93868	−0.254241
$976$	−14.8169	−0.474276
$977$	−25.9139	−0.829061	−0.414530	−	0.910035i	$-0.636054\pi$
$977$	−25.9139	−0.829061	−0.414530	+	0.910035i	$0.636054\pi$
$978$	0.468179	0.0149707
$979$	83.4371	2.66666
$980$	−7.19112	−0.229712
$981$	8.23887	0.263047
$982$	0.900189	0.0287262
$983$	−31.7217	−1.01176	−0.505882	−	0.862603i	$-0.668833\pi$
$983$	−31.7217	−1.01176	−0.505882	+	0.862603i	$0.668833\pi$
$984$	−1.40307	−0.0447283
$985$	−16.1342	−0.514079
$986$	−0.355083	−0.0113081
$987$	−33.9419	−1.08038
$988$	19.2909	0.613725
$989$	−66.0100	−2.09899
$990$	−0.302454	−0.00961263
$991$	21.9931	0.698635	0.349317	−	0.937004i	$-0.386414\pi$
$991$	21.9931	0.698635	0.349317	+	0.937004i	$0.386414\pi$
$992$	−2.16834	−0.0688449
$993$	18.7446	0.594841
$994$	2.27679	0.0722154
$995$	−4.54727	−0.144158
$996$	−35.7011	−1.13123
$997$	−39.8415	−1.26179	−0.630897	−	0.775867i	$-0.717313\pi$
$997$	−39.8415	−1.26179	−0.630897	+	0.775867i	$0.717313\pi$
$998$	0.357878	0.0113284
$999$	−2.70621	−0.0856208

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.32	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.32	✓	64	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q+0.0482776 q^{2} -1.00000 q^{3} -1.99767 q^{4} +1.12713 q^{5} -0.0482776 q^{6} -3.19276 q^{7} -0.192998 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.0482776 q^{2} -1.00000 q^{3} -1.99767 q^{4} +1.12713 q^{5} -0.0482776 q^{6} -3.19276 q^{7} -0.192998 q^{8} +1.00000 q^{9} +0.0544150 q^{10} -5.55828 q^{11} +1.99767 q^{12} -2.12857 q^{13} -0.154139 q^{14} -1.12713 q^{15} +3.98602 q^{16} +1.00000 q^{17} +0.0482776 q^{18} +4.53670 q^{19} -2.25163 q^{20} +3.19276 q^{21} -0.268340 q^{22} -6.46999 q^{23} +0.192998 q^{24} -3.72958 q^{25} -0.102762 q^{26} -1.00000 q^{27} +6.37809 q^{28} -7.35503 q^{29} -0.0544150 q^{30} -3.74866 q^{31} +0.578431 q^{32} +5.55828 q^{33} +0.0482776 q^{34} -3.59866 q^{35} -1.99767 q^{36} +2.70621 q^{37} +0.219021 q^{38} +2.12857 q^{39} -0.217533 q^{40} -7.26988 q^{41} +0.154139 q^{42} +10.2025 q^{43} +11.1036 q^{44} +1.12713 q^{45} -0.312355 q^{46} -10.6309 q^{47} -3.98602 q^{48} +3.19374 q^{49} -0.180055 q^{50} -1.00000 q^{51} +4.25218 q^{52} -7.51252 q^{53} -0.0482776 q^{54} -6.26490 q^{55} +0.616196 q^{56} -4.53670 q^{57} -0.355083 q^{58} +3.99008 q^{59} +2.25163 q^{60} -3.71721 q^{61} -0.180976 q^{62} -3.19276 q^{63} -7.94412 q^{64} -2.39917 q^{65} +0.268340 q^{66} -9.30348 q^{67} -1.99767 q^{68} +6.46999 q^{69} -0.173734 q^{70} -14.7710 q^{71} -0.192998 q^{72} +14.0106 q^{73} +0.130649 q^{74} +3.72958 q^{75} -9.06283 q^{76} +17.7463 q^{77} +0.102762 q^{78} -7.54648 q^{79} +4.49276 q^{80} +1.00000 q^{81} -0.350972 q^{82} -17.8714 q^{83} -6.37809 q^{84} +1.12713 q^{85} +0.492551 q^{86} +7.35503 q^{87} +1.07274 q^{88} -15.0113 q^{89} +0.0544150 q^{90} +6.79603 q^{91} +12.9249 q^{92} +3.74866 q^{93} -0.513233 q^{94} +5.11345 q^{95} -0.578431 q^{96} -3.37810 q^{97} +0.154186 q^{98} -5.55828 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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