LMFDB - Embedded newform 8007.2.a.f.1.20

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:	$1$
Dimension:	$48$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q-0.557584 q^{2} -1.00000 q^{3} -1.68910 q^{4} +2.57031 q^{5} +0.557584 q^{6} +2.28117 q^{7} +2.05698 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.557584 q^{2} -1.00000 q^{3} -1.68910 q^{4} +2.57031 q^{5} +0.557584 q^{6} +2.28117 q^{7} +2.05698 q^{8} +1.00000 q^{9} -1.43316 q^{10} -2.42518 q^{11} +1.68910 q^{12} +5.98863 q^{13} -1.27194 q^{14} -2.57031 q^{15} +2.23126 q^{16} -1.00000 q^{17} -0.557584 q^{18} +4.65582 q^{19} -4.34151 q^{20} -2.28117 q^{21} +1.35224 q^{22} +0.860875 q^{23} -2.05698 q^{24} +1.60649 q^{25} -3.33917 q^{26} -1.00000 q^{27} -3.85312 q^{28} -5.60357 q^{29} +1.43316 q^{30} -7.14237 q^{31} -5.35808 q^{32} +2.42518 q^{33} +0.557584 q^{34} +5.86331 q^{35} -1.68910 q^{36} -7.55997 q^{37} -2.59601 q^{38} -5.98863 q^{39} +5.28708 q^{40} +7.64575 q^{41} +1.27194 q^{42} -10.6920 q^{43} +4.09638 q^{44} +2.57031 q^{45} -0.480010 q^{46} -11.4803 q^{47} -2.23126 q^{48} -1.79626 q^{49} -0.895754 q^{50} +1.00000 q^{51} -10.1154 q^{52} -1.24871 q^{53} +0.557584 q^{54} -6.23347 q^{55} +4.69233 q^{56} -4.65582 q^{57} +3.12446 q^{58} +10.3301 q^{59} +4.34151 q^{60} -12.6616 q^{61} +3.98247 q^{62} +2.28117 q^{63} -1.47494 q^{64} +15.3926 q^{65} -1.35224 q^{66} +0.360054 q^{67} +1.68910 q^{68} -0.860875 q^{69} -3.26929 q^{70} -6.84154 q^{71} +2.05698 q^{72} -6.78327 q^{73} +4.21532 q^{74} -1.60649 q^{75} -7.86414 q^{76} -5.53226 q^{77} +3.33917 q^{78} -13.1176 q^{79} +5.73503 q^{80} +1.00000 q^{81} -4.26315 q^{82} -7.63054 q^{83} +3.85312 q^{84} -2.57031 q^{85} +5.96171 q^{86} +5.60357 q^{87} -4.98856 q^{88} -5.84324 q^{89} -1.43316 q^{90} +13.6611 q^{91} -1.45410 q^{92} +7.14237 q^{93} +6.40121 q^{94} +11.9669 q^{95} +5.35808 q^{96} -2.78593 q^{97} +1.00157 q^{98} -2.42518 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9}+O(q^{10}) $ 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9} - 20 q^{10} + 5 q^{11} - 45 q^{12} - 8 q^{13} + 4 q^{14} - q^{15} + 39 q^{16} - 48 q^{17} - q^{18} - 6 q^{19} + 6 q^{20} + 13 q^{21} - 35 q^{22} - 8 q^{23} + 6 q^{24} + 13 q^{25} + 17 q^{26} - 48 q^{27} - 38 q^{28} + q^{29} + 20 q^{30} - 21 q^{31} - 3 q^{32} - 5 q^{33} + q^{34} + 19 q^{35} + 45 q^{36} - 58 q^{37} - 14 q^{38} + 8 q^{39} - 54 q^{40} - 3 q^{41} - 4 q^{42} - 33 q^{43} + 2 q^{44} + q^{45} - 26 q^{46} + 9 q^{47} - 39 q^{48} + 11 q^{49} + 4 q^{50} + 48 q^{51} - 31 q^{52} - 33 q^{53} + q^{54} - 21 q^{55} + 6 q^{57} - 55 q^{58} + 77 q^{59} - 6 q^{60} - 29 q^{61} - 46 q^{62} - 13 q^{63} + 24 q^{64} - 49 q^{65} + 35 q^{66} - 44 q^{67} - 45 q^{68} + 8 q^{69} + 4 q^{70} + 22 q^{71} - 6 q^{72} - 63 q^{73} - 16 q^{74} - 13 q^{75} - 46 q^{76} - 30 q^{77} - 17 q^{78} - 46 q^{79} - 14 q^{80} + 48 q^{81} - 75 q^{82} + 11 q^{83} + 38 q^{84} - q^{85} + 8 q^{86} - q^{87} - 116 q^{88} + 10 q^{89} - 20 q^{90} - 67 q^{91} - 64 q^{92} + 21 q^{93} - 16 q^{94} - 8 q^{95} + 3 q^{96} - 96 q^{97} - 46 q^{98} + 5 q^{99}+O(q^{100}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9 - 20 * q^10 + 5 * q^11 - 45 * q^12 - 8 * q^13 + 4 * q^14 - q^15 + 39 * q^16 - 48 * q^17 - q^18 - 6 * q^19 + 6 * q^20 + 13 * q^21 - 35 * q^22 - 8 * q^23 + 6 * q^24 + 13 * q^25 + 17 * q^26 - 48 * q^27 - 38 * q^28 + q^29 + 20 * q^30 - 21 * q^31 - 3 * q^32 - 5 * q^33 + q^34 + 19 * q^35 + 45 * q^36 - 58 * q^37 - 14 * q^38 + 8 * q^39 - 54 * q^40 - 3 * q^41 - 4 * q^42 - 33 * q^43 + 2 * q^44 + q^45 - 26 * q^46 + 9 * q^47 - 39 * q^48 + 11 * q^49 + 4 * q^50 + 48 * q^51 - 31 * q^52 - 33 * q^53 + q^54 - 21 * q^55 + 6 * q^57 - 55 * q^58 + 77 * q^59 - 6 * q^60 - 29 * q^61 - 46 * q^62 - 13 * q^63 + 24 * q^64 - 49 * q^65 + 35 * q^66 - 44 * q^67 - 45 * q^68 + 8 * q^69 + 4 * q^70 + 22 * q^71 - 6 * q^72 - 63 * q^73 - 16 * q^74 - 13 * q^75 - 46 * q^76 - 30 * q^77 - 17 * q^78 - 46 * q^79 - 14 * q^80 + 48 * q^81 - 75 * q^82 + 11 * q^83 + 38 * q^84 - q^85 + 8 * q^86 - q^87 - 116 * q^88 + 10 * q^89 - 20 * q^90 - 67 * q^91 - 64 * q^92 + 21 * q^93 - 16 * q^94 - 8 * q^95 + 3 * q^96 - 96 * q^97 - 46 * q^98 + 5 * 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 $

$2$	−0.557584	−0.394271	−0.197136	−	0.980376i	$-0.563164\pi$
$2$	−0.557584	−0.394271	−0.197136	+	0.980376i	$0.563164\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.68910	−0.844550
$5$	2.57031	1.14948	0.574739	−	0.818337i	$-0.305104\pi$
$5$	2.57031	1.14948	0.574739	+	0.818337i	$0.305104\pi$
$6$	0.557584	0.227633
$7$	2.28117	0.862201	0.431101	−	0.902304i	$-0.358125\pi$
$7$	2.28117	0.862201	0.431101	+	0.902304i	$0.358125\pi$
$8$	2.05698	0.727253
$9$	1.00000	0.333333
$10$	−1.43316	−0.453206
$11$	−2.42518	−0.731220	−0.365610	−	0.930768i	$-0.619140\pi$
$11$	−2.42518	−0.731220	−0.365610	+	0.930768i	$0.619140\pi$
$12$	1.68910	0.487601
$13$	5.98863	1.66095	0.830474	−	0.557058i	$-0.188070\pi$
$13$	5.98863	1.66095	0.830474	+	0.557058i	$0.188070\pi$
$14$	−1.27194	−0.339941
$15$	−2.57031	−0.663651
$16$	2.23126	0.557815
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.557584	−0.131424
$19$	4.65582	1.06812	0.534059	−	0.845447i	$-0.320666\pi$
$19$	4.65582	1.06812	0.534059	+	0.845447i	$0.320666\pi$
$20$	−4.34151	−0.970791
$21$	−2.28117	−0.497792
$22$	1.35224	0.288299
$23$	0.860875	0.179505	0.0897524	−	0.995964i	$-0.471392\pi$
$23$	0.860875	0.179505	0.0897524	+	0.995964i	$0.471392\pi$
$24$	−2.05698	−0.419880
$25$	1.60649	0.321298
$26$	−3.33917	−0.654864
$27$	−1.00000	−0.192450
$28$	−3.85312	−0.728172
$29$	−5.60357	−1.04056	−0.520279	−	0.853997i	$-0.674172\pi$
$29$	−5.60357	−1.04056	−0.520279	+	0.853997i	$0.674172\pi$
$30$	1.43316	0.261659
$31$	−7.14237	−1.28281	−0.641404	−	0.767203i	$-0.721648\pi$
$31$	−7.14237	−1.28281	−0.641404	+	0.767203i	$0.721648\pi$
$32$	−5.35808	−0.947184
$33$	2.42518	0.422170
$34$	0.557584	0.0956249
$35$	5.86331	0.991081
$36$	−1.68910	−0.281517
$37$	−7.55997	−1.24285	−0.621426	−	0.783473i	$-0.713446\pi$
$37$	−7.55997	−1.24285	−0.621426	+	0.783473i	$0.713446\pi$
$38$	−2.59601	−0.421128
$39$	−5.98863	−0.958948
$40$	5.28708	0.835961
$41$	7.64575	1.19406	0.597032	−	0.802217i	$-0.296346\pi$
$41$	7.64575	1.19406	0.597032	+	0.802217i	$0.296346\pi$
$42$	1.27194	0.196265
$43$	−10.6920	−1.63052	−0.815260	−	0.579095i	$-0.803406\pi$
$43$	−10.6920	−1.63052	−0.815260	+	0.579095i	$0.803406\pi$
$44$	4.09638	0.617552
$45$	2.57031	0.383159
$46$	−0.480010	−0.0707736
$47$	−11.4803	−1.67457	−0.837284	−	0.546768i	$-0.815858\pi$
$47$	−11.4803	−1.67457	−0.837284	+	0.546768i	$0.815858\pi$
$48$	−2.23126	−0.322054
$49$	−1.79626	−0.256609
$50$	−0.895754	−0.126679
$51$	1.00000	0.140028
$52$	−10.1154	−1.40275
$53$	−1.24871	−0.171524	−0.0857618	−	0.996316i	$-0.527332\pi$
$53$	−1.24871	−0.171524	−0.0857618	+	0.996316i	$0.527332\pi$
$54$	0.557584	0.0758776
$55$	−6.23347	−0.840521
$56$	4.69233	0.627039
$57$	−4.65582	−0.616678
$58$	3.12446	0.410262
$59$	10.3301	1.34487	0.672435	−	0.740156i	$-0.265249\pi$
$59$	10.3301	1.34487	0.672435	+	0.740156i	$0.265249\pi$
$60$	4.34151	0.560487
$61$	−12.6616	−1.62115	−0.810576	−	0.585634i	$-0.800846\pi$
$61$	−12.6616	−1.62115	−0.810576	+	0.585634i	$0.800846\pi$
$62$	3.98247	0.505775
$63$	2.28117	0.287400
$64$	−1.47494	−0.184367
$65$	15.3926	1.90922
$66$	−1.35224	−0.166450
$67$	0.360054	0.0439875	0.0219938	−	0.999758i	$-0.492999\pi$
$67$	0.360054	0.0439875	0.0219938	+	0.999758i	$0.492999\pi$
$68$	1.68910	0.204833
$69$	−0.860875	−0.103637
$70$	−3.26929	−0.390755
$71$	−6.84154	−0.811941	−0.405970	−	0.913886i	$-0.633066\pi$
$71$	−6.84154	−0.811941	−0.405970	+	0.913886i	$0.633066\pi$
$72$	2.05698	0.242418
$73$	−6.78327	−0.793922	−0.396961	−	0.917836i	$-0.629935\pi$
$73$	−6.78327	−0.793922	−0.396961	+	0.917836i	$0.629935\pi$
$74$	4.21532	0.490021
$75$	−1.60649	−0.185502
$76$	−7.86414	−0.902079
$77$	−5.53226	−0.630459
$78$	3.33917	0.378086
$79$	−13.1176	−1.47584	−0.737921	−	0.674887i	$-0.764192\pi$
$79$	−13.1176	−1.47584	−0.737921	+	0.674887i	$0.764192\pi$
$80$	5.73503	0.641195
$81$	1.00000	0.111111
$82$	−4.26315	−0.470786
$83$	−7.63054	−0.837560	−0.418780	−	0.908088i	$-0.637542\pi$
$83$	−7.63054	−0.837560	−0.418780	+	0.908088i	$0.637542\pi$
$84$	3.85312	0.420410
$85$	−2.57031	−0.278789
$86$	5.96171	0.642868
$87$	5.60357	0.600766
$88$	−4.98856	−0.531783
$89$	−5.84324	−0.619382	−0.309691	−	0.950837i	$-0.600226\pi$
$89$	−5.84324	−0.619382	−0.309691	+	0.950837i	$0.600226\pi$
$90$	−1.43316	−0.151069
$91$	13.6611	1.43207
$92$	−1.45410	−0.151601
$93$	7.14237	0.740630
$94$	6.40121	0.660235
$95$	11.9669	1.22778
$96$	5.35808	0.546857
$97$	−2.78593	−0.282868	−0.141434	−	0.989948i	$-0.545171\pi$
$97$	−2.78593	−0.282868	−0.141434	+	0.989948i	$0.545171\pi$
$98$	1.00157	0.101174
$99$	−2.42518	−0.243740
$100$	−2.71353	−0.271353
$101$	−9.86245	−0.981350	−0.490675	−	0.871343i	$-0.663250\pi$
$101$	−9.86245	−0.981350	−0.490675	+	0.871343i	$0.663250\pi$
$102$	−0.557584	−0.0552091
$103$	10.6391	1.04830	0.524150	−	0.851626i	$-0.324383\pi$
$103$	10.6391	1.04830	0.524150	+	0.851626i	$0.324383\pi$
$104$	12.3185	1.20793
$105$	−5.86331	−0.572201
$106$	0.696261	0.0676268
$107$	4.70455	0.454806	0.227403	−	0.973801i	$-0.426977\pi$
$107$	4.70455	0.454806	0.227403	+	0.973801i	$0.426977\pi$
$108$	1.68910	0.162534
$109$	−14.6987	−1.40788	−0.703939	−	0.710261i	$-0.748577\pi$
$109$	−14.6987	−1.40788	−0.703939	+	0.710261i	$0.748577\pi$
$110$	3.47569	0.331394
$111$	7.55997	0.717561
$112$	5.08988	0.480949
$113$	−10.7705	−1.01320	−0.506599	−	0.862182i	$-0.669098\pi$
$113$	−10.7705	−1.01320	−0.506599	+	0.862182i	$0.669098\pi$
$114$	2.59601	0.243139
$115$	2.21271	0.206337
$116$	9.46499	0.878803
$117$	5.98863	0.553649
$118$	−5.75992	−0.530244
$119$	−2.28117	−0.209115
$120$	−5.28708	−0.482643
$121$	−5.11848	−0.465317
$122$	7.05990	0.639174
$123$	−7.64575	−0.689394
$124$	12.0642	1.08340
$125$	−8.72237	−0.780152
$126$	−1.27194	−0.113314
$127$	−18.7363	−1.66258	−0.831290	−	0.555839i	$-0.812397\pi$
$127$	−18.7363	−1.66258	−0.831290	+	0.555839i	$0.812397\pi$
$128$	11.5386	1.01987
$129$	10.6920	0.941381
$130$	−8.58269	−0.752752
$131$	15.2673	1.33391	0.666954	−	0.745099i	$-0.267598\pi$
$131$	15.2673	1.33391	0.666954	+	0.745099i	$0.267598\pi$
$132$	−4.09638	−0.356544
$133$	10.6207	0.920932
$134$	−0.200760	−0.0173430
$135$	−2.57031	−0.221217
$136$	−2.05698	−0.176385
$137$	−14.4760	−1.23677	−0.618383	−	0.785877i	$-0.712212\pi$
$137$	−14.4760	−1.23677	−0.618383	+	0.785877i	$0.712212\pi$
$138$	0.480010	0.0408612
$139$	20.2579	1.71825	0.859126	−	0.511764i	$-0.171008\pi$
$139$	20.2579	1.71825	0.859126	+	0.511764i	$0.171008\pi$
$140$	−9.90372	−0.837017
$141$	11.4803	0.966813
$142$	3.81473	0.320125
$143$	−14.5235	−1.21452
$144$	2.23126	0.185938
$145$	−14.4029	−1.19610
$146$	3.78224	0.313021
$147$	1.79626	0.148153
$148$	12.7696	1.04965
$149$	−0.913554	−0.0748413	−0.0374206	−	0.999300i	$-0.511914\pi$
$149$	−0.913554	−0.0748413	−0.0374206	+	0.999300i	$0.511914\pi$
$150$	0.895754	0.0731380
$151$	11.5558	0.940398	0.470199	−	0.882561i	$-0.344182\pi$
$151$	11.5558	0.940398	0.470199	+	0.882561i	$0.344182\pi$
$152$	9.57694	0.776792
$153$	−1.00000	−0.0808452
$154$	3.08470	0.248572
$155$	−18.3581	−1.47456
$156$	10.1154	0.809880
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	7.31415	0.581882
$159$	1.24871	0.0990292
$160$	−13.7719	−1.08877
$161$	1.96380	0.154769
$162$	−0.557584	−0.0438079
$163$	7.21230	0.564911	0.282455	−	0.959280i	$-0.408851\pi$
$163$	7.21230	0.564911	0.282455	+	0.959280i	$0.408851\pi$
$164$	−12.9144	−1.00845
$165$	6.23347	0.485275
$166$	4.25467	0.330226
$167$	22.2178	1.71926	0.859631	−	0.510916i	$-0.170694\pi$
$167$	22.2178	1.71926	0.859631	+	0.510916i	$0.170694\pi$
$168$	−4.69233	−0.362021
$169$	22.8637	1.75875
$170$	1.43316	0.109919
$171$	4.65582	0.356039
$172$	18.0599	1.37706
$173$	−5.66663	−0.430826	−0.215413	−	0.976523i	$-0.569110\pi$
$173$	−5.66663	−0.430826	−0.215413	+	0.976523i	$0.569110\pi$
$174$	−3.12446	−0.236865
$175$	3.66468	0.277024
$176$	−5.41121	−0.407885
$177$	−10.3301	−0.776461
$178$	3.25810	0.244205
$179$	−3.06701	−0.229239	−0.114619	−	0.993409i	$-0.536565\pi$
$179$	−3.06701	−0.229239	−0.114619	+	0.993409i	$0.536565\pi$
$180$	−4.34151	−0.323597
$181$	−23.2615	−1.72901	−0.864506	−	0.502623i	$-0.832368\pi$
$181$	−23.2615	−1.72901	−0.864506	+	0.502623i	$0.832368\pi$
$182$	−7.61721	−0.564625
$183$	12.6616	0.935972
$184$	1.77080	0.130545
$185$	−19.4315	−1.42863
$186$	−3.98247	−0.292009
$187$	2.42518	0.177347
$188$	19.3913	1.41426
$189$	−2.28117	−0.165931
$190$	−6.67255	−0.484078
$191$	16.4607	1.19106	0.595528	−	0.803334i	$-0.296943\pi$
$191$	16.4607	1.19106	0.595528	+	0.803334i	$0.296943\pi$
$192$	1.47494	0.106444
$193$	−10.7056	−0.770609	−0.385305	−	0.922789i	$-0.625904\pi$
$193$	−10.7056	−0.770609	−0.385305	+	0.922789i	$0.625904\pi$
$194$	1.55339	0.111527
$195$	−15.3926	−1.10229
$196$	3.03407	0.216719
$197$	2.97115	0.211686	0.105843	−	0.994383i	$-0.466246\pi$
$197$	2.97115	0.211686	0.105843	+	0.994383i	$0.466246\pi$
$198$	1.35224	0.0960998
$199$	0.00311595	0.000220884 0	0.000110442	−	1.00000i	$-0.499965\pi$
$199$	0.00311595	0.000220884 0	0.000110442		1.00000i	$0.499965\pi$
$200$	3.30453	0.233665
$201$	−0.360054	−0.0253962
$202$	5.49914	0.386918
$203$	−12.7827	−0.897170
$204$	−1.68910	−0.118261
$205$	19.6519	1.37255
$206$	−5.93218	−0.413315
$207$	0.860875	0.0598349
$208$	13.3622	0.926501
$209$	−11.2912	−0.781029
$210$	3.26929	0.225602
$211$	7.48494	0.515285	0.257642	−	0.966240i	$-0.417054\pi$
$211$	7.48494	0.515285	0.257642	+	0.966240i	$0.417054\pi$
$212$	2.10920	0.144860
$213$	6.84154	0.468774
$214$	−2.62318	−0.179317
$215$	−27.4818	−1.87425
$216$	−2.05698	−0.139960
$217$	−16.2930	−1.10604
$218$	8.19575	0.555086
$219$	6.78327	0.458371
$220$	10.5290	0.709862
$221$	−5.98863	−0.402839
$222$	−4.21532	−0.282914
$223$	21.5652	1.44411	0.722056	−	0.691835i	$-0.243197\pi$
$223$	21.5652	1.44411	0.722056	+	0.691835i	$0.243197\pi$
$224$	−12.2227	−0.816663
$225$	1.60649	0.107099
$226$	6.00543	0.399475
$227$	−2.09643	−0.139145	−0.0695726	−	0.997577i	$-0.522164\pi$
$227$	−2.09643	−0.139145	−0.0695726	+	0.997577i	$0.522164\pi$
$228$	7.86414	0.520815
$229$	7.93938	0.524649	0.262324	−	0.964980i	$-0.415511\pi$
$229$	7.93938	0.524649	0.262324	+	0.964980i	$0.415511\pi$
$230$	−1.23377	−0.0813527
$231$	5.53226	0.363996
$232$	−11.5265	−0.756749
$233$	10.4908	0.687276	0.343638	−	0.939102i	$-0.388341\pi$
$233$	10.4908	0.687276	0.343638	+	0.939102i	$0.388341\pi$
$234$	−3.33917	−0.218288
$235$	−29.5078	−1.92488
$236$	−17.4486	−1.13581
$237$	13.1176	0.852078
$238$	1.27194	0.0824479
$239$	−2.06358	−0.133482	−0.0667409	−	0.997770i	$-0.521260\pi$
$239$	−2.06358	−0.133482	−0.0667409	+	0.997770i	$0.521260\pi$
$240$	−5.73503	−0.370194
$241$	−17.6112	−1.13444	−0.567219	−	0.823567i	$-0.691981\pi$
$241$	−17.6112	−1.13444	−0.567219	+	0.823567i	$0.691981\pi$
$242$	2.85399	0.183461
$243$	−1.00000	−0.0641500
$244$	21.3867	1.36914
$245$	−4.61695	−0.294966
$246$	4.26315	0.271808
$247$	27.8820	1.77409
$248$	−14.6917	−0.932927
$249$	7.63054	0.483566
$250$	4.86345	0.307592
$251$	−24.4298	−1.54200	−0.770999	−	0.636837i	$-0.780242\pi$
$251$	−24.4298	−1.54200	−0.770999	+	0.636837i	$0.780242\pi$
$252$	−3.85312	−0.242724
$253$	−2.08778	−0.131258
$254$	10.4471	0.655508
$255$	2.57031	0.160959
$256$	−3.48385	−0.217740
$257$	0.168260	0.0104957	0.00524787	−	0.999986i	$-0.498330\pi$
$257$	0.168260	0.0104957	0.00524787	+	0.999986i	$0.498330\pi$
$258$	−5.96171	−0.371160
$259$	−17.2456	−1.07159
$260$	−25.9997	−1.61243
$261$	−5.60357	−0.346852
$262$	−8.51279	−0.525922
$263$	13.4461	0.829124	0.414562	−	0.910021i	$-0.363935\pi$
$263$	13.4461	0.829124	0.414562	+	0.910021i	$0.363935\pi$
$264$	4.98856	0.307025
$265$	−3.20957	−0.197162
$266$	−5.92194	−0.363097
$267$	5.84324	0.357600
$268$	−0.608166	−0.0371497
$269$	−11.1882	−0.682156	−0.341078	−	0.940035i	$-0.610792\pi$
$269$	−11.1882	−0.682156	−0.341078	+	0.940035i	$0.610792\pi$
$270$	1.43316	0.0872196
$271$	12.8358	0.779720	0.389860	−	0.920874i	$-0.372523\pi$
$271$	12.8358	0.779720	0.389860	+	0.920874i	$0.372523\pi$
$272$	−2.23126	−0.135290
$273$	−13.6611	−0.826807
$274$	8.07157	0.487621
$275$	−3.89604	−0.234940
$276$	1.45410	0.0875267
$277$	−12.8645	−0.772952	−0.386476	−	0.922299i	$-0.626308\pi$
$277$	−12.8645	−0.772952	−0.386476	+	0.922299i	$0.626308\pi$
$278$	−11.2955	−0.677458
$279$	−7.14237	−0.427603
$280$	12.0607	0.720767
$281$	26.9236	1.60613	0.803064	−	0.595893i	$-0.203202\pi$
$281$	26.9236	1.60613	0.803064	+	0.595893i	$0.203202\pi$
$282$	−6.40121	−0.381187
$283$	−16.5871	−0.986001	−0.493000	−	0.870029i	$-0.664100\pi$
$283$	−16.5871	−0.986001	−0.493000	+	0.870029i	$0.664100\pi$
$284$	11.5560	0.685725
$285$	−11.9669	−0.708857
$286$	8.09809	0.478850
$287$	17.4412	1.02952
$288$	−5.35808	−0.315728
$289$	1.00000	0.0588235
$290$	8.03084	0.471587
$291$	2.78593	0.163314
$292$	11.4576	0.670507
$293$	32.8754	1.92060	0.960299	−	0.278972i	$-0.0899935\pi$
$293$	32.8754	1.92060	0.960299	+	0.278972i	$0.0899935\pi$
$294$	−1.00157	−0.0584126
$295$	26.5517	1.54590
$296$	−15.5507	−0.903868
$297$	2.42518	0.140723
$298$	0.509383	0.0295078
$299$	5.15546	0.298148
$300$	2.71353	0.156665
$301$	−24.3904	−1.40584
$302$	−6.44333	−0.370772
$303$	9.86245	0.566583
$304$	10.3883	0.595812
$305$	−32.5442	−1.86348
$306$	0.557584	0.0318750
$307$	−9.51912	−0.543285	−0.271643	−	0.962398i	$-0.587567\pi$
$307$	−9.51912	−0.543285	−0.271643	+	0.962398i	$0.587567\pi$
$308$	9.34454	0.532454
$309$	−10.6391	−0.605236
$310$	10.2362	0.581377
$311$	5.96578	0.338288	0.169144	−	0.985591i	$-0.445900\pi$
$311$	5.96578	0.338288	0.169144	+	0.985591i	$0.445900\pi$
$312$	−12.3185	−0.697399
$313$	5.60364	0.316736	0.158368	−	0.987380i	$-0.449377\pi$
$313$	5.60364	0.316736	0.158368	+	0.987380i	$0.449377\pi$
$314$	0.557584	0.0314663
$315$	5.86331	0.330360
$316$	22.1569	1.24642
$317$	−17.3820	−0.976268	−0.488134	−	0.872769i	$-0.662322\pi$
$317$	−17.3820	−0.976268	−0.488134	+	0.872769i	$0.662322\pi$
$318$	−0.696261	−0.0390444
$319$	13.5897	0.760877
$320$	−3.79104	−0.211926
$321$	−4.70455	−0.262582
$322$	−1.09498	−0.0610211
$323$	−4.65582	−0.259057
$324$	−1.68910	−0.0938389
$325$	9.62069	0.533660
$326$	−4.02146	−0.222728
$327$	14.6987	0.812839
$328$	15.7272	0.868388
$329$	−26.1884	−1.44382
$330$	−3.47569	−0.191330
$331$	7.45842	0.409952	0.204976	−	0.978767i	$-0.434288\pi$
$331$	7.45842	0.409952	0.204976	+	0.978767i	$0.434288\pi$
$332$	12.8887	0.707362
$333$	−7.55997	−0.414284
$334$	−12.3883	−0.677856
$335$	0.925449	0.0505627
$336$	−5.08988	−0.277676
$337$	−15.2165	−0.828893	−0.414447	−	0.910074i	$-0.636025\pi$
$337$	−15.2165	−0.828893	−0.414447	+	0.910074i	$0.636025\pi$
$338$	−12.7484	−0.693424
$339$	10.7705	0.584971
$340$	4.34151	0.235451
$341$	17.3216	0.938015
$342$	−2.59601	−0.140376
$343$	−20.0658	−1.08345
$344$	−21.9933	−1.18580
$345$	−2.21271	−0.119129
$346$	3.15962	0.169862
$347$	16.3866	0.879680	0.439840	−	0.898076i	$-0.355035\pi$
$347$	16.3866	0.879680	0.439840	+	0.898076i	$0.355035\pi$
$348$	−9.46499	−0.507377
$349$	−24.0635	−1.28809	−0.644045	−	0.764988i	$-0.722745\pi$
$349$	−24.0635	−1.28809	−0.644045	+	0.764988i	$0.722745\pi$
$350$	−2.04337	−0.109223
$351$	−5.98863	−0.319649
$352$	12.9943	0.692600
$353$	19.1711	1.02038	0.510189	−	0.860063i	$-0.329576\pi$
$353$	19.1711	1.02038	0.510189	+	0.860063i	$0.329576\pi$
$354$	5.75992	0.306136
$355$	−17.5849	−0.933308
$356$	9.86981	0.523099
$357$	2.28117	0.120732
$358$	1.71011	0.0903823
$359$	13.0198	0.687157	0.343578	−	0.939124i	$-0.388361\pi$
$359$	13.0198	0.687157	0.343578	+	0.939124i	$0.388361\pi$
$360$	5.28708	0.278654
$361$	2.67663	0.140875
$362$	12.9702	0.681700
$363$	5.11848	0.268651
$364$	−23.0749	−1.20946
$365$	−17.4351	−0.912595
$366$	−7.05990	−0.369027
$367$	−0.448480	−0.0234105	−0.0117052	−	0.999931i	$-0.503726\pi$
$367$	−0.448480	−0.0234105	−0.0117052	+	0.999931i	$0.503726\pi$
$368$	1.92083	0.100130
$369$	7.64575	0.398022
$370$	10.8347	0.563268
$371$	−2.84852	−0.147888
$372$	−12.0642	−0.625499
$373$	25.1547	1.30246	0.651229	−	0.758881i	$-0.274254\pi$
$373$	25.1547	1.30246	0.651229	+	0.758881i	$0.274254\pi$
$374$	−1.35224	−0.0699229
$375$	8.72237	0.450421
$376$	−23.6147	−1.21784
$377$	−33.5577	−1.72831
$378$	1.27194	0.0654218
$379$	−8.21734	−0.422096	−0.211048	−	0.977476i	$-0.567688\pi$
$379$	−8.21734	−0.422096	−0.211048	+	0.977476i	$0.567688\pi$
$380$	−20.2133	−1.03692
$381$	18.7363	0.959891
$382$	−9.17824	−0.469600
$383$	−18.4339	−0.941927	−0.470963	−	0.882153i	$-0.656094\pi$
$383$	−18.4339	−0.941927	−0.470963	+	0.882153i	$0.656094\pi$
$384$	−11.5386	−0.588825
$385$	−14.2196	−0.724699
$386$	5.96930	0.303829
$387$	−10.6920	−0.543507
$388$	4.70571	0.238896
$389$	11.7237	0.594415	0.297207	−	0.954813i	$-0.403945\pi$
$389$	11.7237	0.594415	0.297207	+	0.954813i	$0.403945\pi$
$390$	8.58269	0.434601
$391$	−0.860875	−0.0435363
$392$	−3.69488	−0.186620
$393$	−15.2673	−0.770132
$394$	−1.65667	−0.0834616
$395$	−33.7162	−1.69645
$396$	4.09638	0.205851
$397$	−1.62892	−0.0817529	−0.0408765	−	0.999164i	$-0.513015\pi$
$397$	−1.62892	−0.0817529	−0.0408765	+	0.999164i	$0.513015\pi$
$398$	−0.00173740	−8.70882e−5 0
$399$	−10.6207	−0.531701
$400$	3.58450	0.179225
$401$	−7.92567	−0.395789	−0.197894	−	0.980223i	$-0.563410\pi$
$401$	−7.92567	−0.395789	−0.197894	+	0.980223i	$0.563410\pi$
$402$	0.200760	0.0100130
$403$	−42.7730	−2.13068
$404$	16.6587	0.828799
$405$	2.57031	0.127720
$406$	7.12743	0.353728
$407$	18.3343	0.908799
$408$	2.05698	0.101836
$409$	−7.49370	−0.370540	−0.185270	−	0.982688i	$-0.559316\pi$
$409$	−7.49370	−0.370540	−0.185270	+	0.982688i	$0.559316\pi$
$410$	−10.9576	−0.541158
$411$	14.4760	0.714047
$412$	−17.9705	−0.885342
$413$	23.5648	1.15955
$414$	−0.480010	−0.0235912
$415$	−19.6128	−0.962757
$416$	−32.0876	−1.57322
$417$	−20.2579	−0.992033
$418$	6.29580	0.307938
$419$	21.4723	1.04899	0.524496	−	0.851413i	$-0.324254\pi$
$419$	21.4723	1.04899	0.524496	+	0.851413i	$0.324254\pi$
$420$	9.90372	0.483252
$421$	15.7215	0.766221	0.383110	−	0.923703i	$-0.374853\pi$
$421$	15.7215	0.766221	0.383110	+	0.923703i	$0.374853\pi$
$422$	−4.17348	−0.203162
$423$	−11.4803	−0.558190
$424$	−2.56858	−0.124741
$425$	−1.60649	−0.0779263
$426$	−3.81473	−0.184824
$427$	−28.8833	−1.39776
$428$	−7.94645	−0.384106
$429$	14.5235	0.701203
$430$	15.3234	0.738962
$431$	22.3477	1.07645	0.538226	−	0.842801i	$-0.319095\pi$
$431$	22.3477	1.07645	0.538226	+	0.842801i	$0.319095\pi$
$432$	−2.23126	−0.107351
$433$	21.3451	1.02578	0.512890	−	0.858455i	$-0.328575\pi$
$433$	21.3451	1.02578	0.512890	+	0.858455i	$0.328575\pi$
$434$	9.08470	0.436080
$435$	14.4029	0.690567
$436$	24.8275	1.18902
$437$	4.00807	0.191732
$438$	−3.78224	−0.180723
$439$	25.4189	1.21318	0.606589	−	0.795015i	$-0.292537\pi$
$439$	25.4189	1.21318	0.606589	+	0.795015i	$0.292537\pi$
$440$	−12.8222	−0.611272
$441$	−1.79626	−0.0855363
$442$	3.33917	0.158828
$443$	7.98059	0.379169	0.189585	−	0.981864i	$-0.439286\pi$
$443$	7.98059	0.379169	0.189585	+	0.981864i	$0.439286\pi$
$444$	−12.7696	−0.606016
$445$	−15.0189	−0.711965
$446$	−12.0244	−0.569372
$447$	0.913554	0.0432096
$448$	−3.36458	−0.158962
$449$	−4.58022	−0.216154	−0.108077	−	0.994143i	$-0.534469\pi$
$449$	−4.58022	−0.216154	−0.108077	+	0.994143i	$0.534469\pi$
$450$	−0.895754	−0.0422263
$451$	−18.5423	−0.873125
$452$	18.1924	0.855697
$453$	−11.5558	−0.542939
$454$	1.16894	0.0548610
$455$	35.1132	1.64613
$456$	−9.57694	−0.448481
$457$	29.9508	1.40104	0.700520	−	0.713633i	$-0.252952\pi$
$457$	29.9508	1.40104	0.700520	+	0.713633i	$0.252952\pi$
$458$	−4.42687	−0.206854
$459$	1.00000	0.0466760
$460$	−3.73750	−0.174262
$461$	−23.1577	−1.07856	−0.539281	−	0.842126i	$-0.681304\pi$
$461$	−23.1577	−1.07856	−0.539281	+	0.842126i	$0.681304\pi$
$462$	−3.08470	−0.143513
$463$	1.97968	0.0920035	0.0460017	−	0.998941i	$-0.485352\pi$
$463$	1.97968	0.0920035	0.0460017	+	0.998941i	$0.485352\pi$
$464$	−12.5030	−0.580438
$465$	18.3581	0.851337
$466$	−5.84951	−0.270973
$467$	31.0397	1.43635	0.718173	−	0.695864i	$-0.244978\pi$
$467$	31.0397	1.43635	0.718173	+	0.695864i	$0.244978\pi$
$468$	−10.1154	−0.467584
$469$	0.821344	0.0379261
$470$	16.4531	0.758925
$471$	1.00000	0.0460776
$472$	21.2489	0.978061
$473$	25.9302	1.19227
$474$	−7.31415	−0.335950
$475$	7.47953	0.343184
$476$	3.85312	0.176608
$477$	−1.24871	−0.0571745
$478$	1.15062	0.0526280
$479$	−11.0544	−0.505090	−0.252545	−	0.967585i	$-0.581268\pi$
$479$	−11.0544	−0.505090	−0.252545	+	0.967585i	$0.581268\pi$
$480$	13.7719	0.628600
$481$	−45.2739	−2.06431
$482$	9.81973	0.447276
$483$	−1.96380	−0.0893561
$484$	8.64563	0.392983
$485$	−7.16069	−0.325150
$486$	0.557584	0.0252925
$487$	−31.8709	−1.44421	−0.722105	−	0.691784i	$-0.756825\pi$
$487$	−31.8709	−1.44421	−0.722105	+	0.691784i	$0.756825\pi$
$488$	−26.0447	−1.17899
$489$	−7.21230	−0.326151
$490$	2.57434	0.116297
$491$	−37.3317	−1.68476	−0.842379	−	0.538885i	$-0.818846\pi$
$491$	−37.3317	−1.68476	−0.842379	+	0.538885i	$0.818846\pi$
$492$	12.9144	0.582227
$493$	5.60357	0.252372
$494$	−15.5465	−0.699472
$495$	−6.23347	−0.280174
$496$	−15.9365	−0.715569
$497$	−15.6067	−0.700057
$498$	−4.25467	−0.190656
$499$	−27.8344	−1.24604	−0.623020	−	0.782206i	$-0.714095\pi$
$499$	−27.8344	−1.24604	−0.623020	+	0.782206i	$0.714095\pi$
$500$	14.7330	0.658878
$501$	−22.2178	−0.992616
$502$	13.6217	0.607966
$503$	43.3557	1.93314	0.966569	−	0.256408i	$-0.0825392\pi$
$503$	43.3557	1.93314	0.966569	+	0.256408i	$0.0825392\pi$
$504$	4.69233	0.209013
$505$	−25.3495	−1.12804
$506$	1.16411	0.0517511
$507$	−22.8637	−1.01541
$508$	31.6475	1.40413
$509$	4.03475	0.178837	0.0894187	−	0.995994i	$-0.471499\pi$
$509$	4.03475	0.178837	0.0894187	+	0.995994i	$0.471499\pi$
$510$	−1.43316	−0.0634616
$511$	−15.4738	−0.684520
$512$	−21.1346	−0.934026
$513$	−4.65582	−0.205559
$514$	−0.0938189	−0.00413817
$515$	27.3457	1.20500
$516$	−18.0599	−0.795044
$517$	27.8417	1.22448
$518$	9.61587	0.422497
$519$	5.66663	0.248738
$520$	31.6624	1.38849
$521$	1.75526	0.0768994	0.0384497	−	0.999261i	$-0.487758\pi$
$521$	1.75526	0.0768994	0.0384497	+	0.999261i	$0.487758\pi$
$522$	3.12446	0.136754
$523$	−3.12261	−0.136542	−0.0682711	−	0.997667i	$-0.521748\pi$
$523$	−3.12261	−0.136542	−0.0682711	+	0.997667i	$0.521748\pi$
$524$	−25.7880	−1.12655
$525$	−3.66468	−0.159940
$526$	−7.49735	−0.326900
$527$	7.14237	0.311127
$528$	5.41121	0.235493
$529$	−22.2589	−0.967778
$530$	1.78961	0.0777355
$531$	10.3301	0.448290
$532$	−17.9394	−0.777774
$533$	45.7876	1.98328
$534$	−3.25810	−0.140992
$535$	12.0921	0.522789
$536$	0.740624	0.0319901
$537$	3.06701	0.132351
$538$	6.23836	0.268955
$539$	4.35626	0.187638
$540$	4.34151	0.186829
$541$	22.3133	0.959325	0.479663	−	0.877453i	$-0.340759\pi$
$541$	22.3133	0.959325	0.479663	+	0.877453i	$0.340759\pi$
$542$	−7.15704	−0.307421
$543$	23.2615	0.998245
$544$	5.35808	0.229726
$545$	−37.7801	−1.61832
$546$	7.61721	0.325986
$547$	−6.96561	−0.297828	−0.148914	−	0.988850i	$-0.547578\pi$
$547$	−6.96561	−0.297828	−0.148914	+	0.988850i	$0.547578\pi$
$548$	24.4514	1.04451
$549$	−12.6616	−0.540384
$550$	2.17237	0.0926301
$551$	−26.0892	−1.11144
$552$	−1.77080	−0.0753704
$553$	−29.9234	−1.27247
$554$	7.17304	0.304753
$555$	19.4315	0.824820
$556$	−34.2176	−1.45115
$557$	21.4567	0.909150	0.454575	−	0.890708i	$-0.349791\pi$
$557$	21.4567	0.909150	0.454575	+	0.890708i	$0.349791\pi$
$558$	3.98247	0.168592
$559$	−64.0307	−2.70821
$560$	13.0826	0.552840
$561$	−2.42518	−0.102391
$562$	−15.0122	−0.633251
$563$	−44.8900	−1.89189	−0.945944	−	0.324329i	$-0.894861\pi$
$563$	−44.8900	−1.89189	−0.945944	+	0.324329i	$0.894861\pi$
$564$	−19.3913	−0.816522
$565$	−27.6834	−1.16465
$566$	9.24870	0.388752
$567$	2.28117	0.0958002
$568$	−14.0729	−0.590487
$569$	14.8993	0.624611	0.312305	−	0.949982i	$-0.398899\pi$
$569$	14.8993	0.624611	0.312305	+	0.949982i	$0.398899\pi$
$570$	6.67255	0.279482
$571$	20.4277	0.854872	0.427436	−	0.904046i	$-0.359417\pi$
$571$	20.4277	0.854872	0.427436	+	0.904046i	$0.359417\pi$
$572$	24.5317	1.02572
$573$	−16.4607	−0.687657
$574$	−9.72496	−0.405912
$575$	1.38299	0.0576746
$576$	−1.47494	−0.0614557
$577$	28.7380	1.19638	0.598188	−	0.801356i	$-0.295887\pi$
$577$	28.7380	1.19638	0.598188	+	0.801356i	$0.295887\pi$
$578$	−0.557584	−0.0231924
$579$	10.7056	0.444911
$580$	24.3280	1.01016
$581$	−17.4066	−0.722146
$582$	−1.55339	−0.0643900
$583$	3.02835	0.125422
$584$	−13.9531	−0.577382
$585$	15.3926	0.636407
$586$	−18.3308	−0.757237
$587$	−21.1509	−0.872989	−0.436495	−	0.899707i	$-0.643780\pi$
$587$	−21.1509	−0.872989	−0.436495	+	0.899707i	$0.643780\pi$
$588$	−3.03407	−0.125123
$589$	−33.2536	−1.37019
$590$	−14.8048	−0.609503
$591$	−2.97115	−0.122217
$592$	−16.8683	−0.693281
$593$	4.18862	0.172006	0.0860030	−	0.996295i	$-0.472591\pi$
$593$	4.18862	0.172006	0.0860030	+	0.996295i	$0.472591\pi$
$594$	−1.35224	−0.0554832
$595$	−5.86331	−0.240372
$596$	1.54308	0.0632072
$597$	−0.00311595	−0.000127527 0
$598$	−2.87460	−0.117551
$599$	−31.5329	−1.28840	−0.644200	−	0.764857i	$-0.722810\pi$
$599$	−31.5329	−1.28840	−0.644200	+	0.764857i	$0.722810\pi$
$600$	−3.30453	−0.134907
$601$	−0.898549	−0.0366526	−0.0183263	−	0.999832i	$-0.505834\pi$
$601$	−0.898549	−0.0366526	−0.0183263	+	0.999832i	$0.505834\pi$
$602$	13.5997	0.554281
$603$	0.360054	0.0146625
$604$	−19.5189	−0.794213
$605$	−13.1561	−0.534871
$606$	−5.49914	−0.223387
$607$	−2.27389	−0.0922943	−0.0461472	−	0.998935i	$-0.514694\pi$
$607$	−2.27389	−0.0922943	−0.0461472	+	0.998935i	$0.514694\pi$
$608$	−24.9462	−1.01170
$609$	12.7827	0.517981
$610$	18.1461	0.734716
$611$	−68.7511	−2.78137
$612$	1.68910	0.0682778
$613$	−17.4478	−0.704711	−0.352356	−	0.935866i	$-0.614619\pi$
$613$	−17.4478	−0.704711	−0.352356	+	0.935866i	$0.614619\pi$
$614$	5.30771	0.214202
$615$	−19.6519	−0.792442
$616$	−11.3798	−0.458504
$617$	11.7395	0.472616	0.236308	−	0.971678i	$-0.424063\pi$
$617$	11.7395	0.472616	0.236308	+	0.971678i	$0.424063\pi$
$618$	5.93218	0.238627
$619$	0.193779	0.00778865	0.00389433	−	0.999992i	$-0.498760\pi$
$619$	0.193779	0.00778865	0.00389433	+	0.999992i	$0.498760\pi$
$620$	31.0087	1.24534
$621$	−0.860875	−0.0345457
$622$	−3.32642	−0.133377
$623$	−13.3294	−0.534032
$624$	−13.3622	−0.534916
$625$	−30.4516	−1.21807
$626$	−3.12450	−0.124880
$627$	11.2912	0.450928
$628$	1.68910	0.0674024
$629$	7.55997	0.301436
$630$	−3.26929	−0.130252
$631$	−7.13757	−0.284142	−0.142071	−	0.989856i	$-0.545376\pi$
$631$	−7.13757	−0.284142	−0.142071	+	0.989856i	$0.545376\pi$
$632$	−26.9826	−1.07331
$633$	−7.48494	−0.297500
$634$	9.69190	0.384915
$635$	−48.1581	−1.91110
$636$	−2.10920	−0.0836351
$637$	−10.7571	−0.426214
$638$	−7.57740	−0.299992
$639$	−6.84154	−0.270647
$640$	29.6577	1.17232
$641$	−37.3037	−1.47341	−0.736703	−	0.676216i	$-0.763619\pi$
$641$	−37.3037	−1.47341	−0.736703	+	0.676216i	$0.763619\pi$
$642$	2.62318	0.103529
$643$	−15.5799	−0.614411	−0.307206	−	0.951643i	$-0.599394\pi$
$643$	−15.5799	−0.614411	−0.307206	+	0.951643i	$0.599394\pi$
$644$	−3.31706	−0.130710
$645$	27.4818	1.08210
$646$	2.59601	0.102139
$647$	8.41034	0.330645	0.165322	−	0.986240i	$-0.447134\pi$
$647$	8.41034	0.330645	0.165322	+	0.986240i	$0.447134\pi$
$648$	2.05698	0.0808059
$649$	−25.0525	−0.983396
$650$	−5.36434	−0.210407
$651$	16.2930	0.638572
$652$	−12.1823	−0.477095
$653$	1.19781	0.0468738	0.0234369	−	0.999725i	$-0.492539\pi$
$653$	1.19781	0.0468738	0.0234369	+	0.999725i	$0.492539\pi$
$654$	−8.19575	−0.320479
$655$	39.2416	1.53330
$656$	17.0596	0.666067
$657$	−6.78327	−0.264641
$658$	14.6023	0.569255
$659$	−12.0572	−0.469681	−0.234840	−	0.972034i	$-0.575457\pi$
$659$	−12.0572	−0.469681	−0.234840	+	0.972034i	$0.575457\pi$
$660$	−10.5290	−0.409839
$661$	19.4807	0.757711	0.378856	−	0.925456i	$-0.376318\pi$
$661$	19.4807	0.757711	0.378856	+	0.925456i	$0.376318\pi$
$662$	−4.15870	−0.161632
$663$	5.98863	0.232579
$664$	−15.6959	−0.609119
$665$	27.2985	1.05859
$666$	4.21532	0.163340
$667$	−4.82397	−0.186785
$668$	−37.5280	−1.45200
$669$	−21.5652	−0.833758
$670$	−0.516016	−0.0199354
$671$	30.7067	1.18542
$672$	12.2227	0.471501
$673$	−21.8095	−0.840693	−0.420346	−	0.907364i	$-0.638091\pi$
$673$	−21.8095	−0.840693	−0.420346	+	0.907364i	$0.638091\pi$
$674$	8.48446	0.326809
$675$	−1.60649	−0.0618339
$676$	−38.6191	−1.48535
$677$	−25.6392	−0.985395	−0.492698	−	0.870201i	$-0.663989\pi$
$677$	−25.6392	−0.985395	−0.492698	+	0.870201i	$0.663989\pi$
$678$	−6.00543	−0.230637
$679$	−6.35517	−0.243889
$680$	−5.28708	−0.202750
$681$	2.09643	0.0803355
$682$	−9.65823	−0.369833
$683$	25.6713	0.982284	0.491142	−	0.871079i	$-0.336580\pi$
$683$	25.6713	0.982284	0.491142	+	0.871079i	$0.336580\pi$
$684$	−7.86414	−0.300693
$685$	−37.2077	−1.42163
$686$	11.1884	0.427173
$687$	−7.93938	−0.302906
$688$	−23.8567	−0.909528
$689$	−7.47807	−0.284892
$690$	1.23377	0.0469690
$691$	−34.8985	−1.32760	−0.663800	−	0.747910i	$-0.731057\pi$
$691$	−34.8985	−1.32760	−0.663800	+	0.747910i	$0.731057\pi$
$692$	9.57151	0.363854
$693$	−5.53226	−0.210153
$694$	−9.13692	−0.346833
$695$	52.0691	1.97509
$696$	11.5265	0.436909
$697$	−7.64575	−0.289603
$698$	13.4174	0.507857
$699$	−10.4908	−0.396799
$700$	−6.19001	−0.233960
$701$	32.7128	1.23554	0.617772	−	0.786357i	$-0.288035\pi$
$701$	32.7128	1.23554	0.617772	+	0.786357i	$0.288035\pi$
$702$	3.33917	0.126029
$703$	−35.1979	−1.32751
$704$	3.57699	0.134813
$705$	29.5078	1.11133
$706$	−10.6895	−0.402306
$707$	−22.4979	−0.846121
$708$	17.4486	0.655760
$709$	25.2635	0.948789	0.474394	−	0.880312i	$-0.342667\pi$
$709$	25.2635	0.948789	0.474394	+	0.880312i	$0.342667\pi$
$710$	9.80504	0.367977
$711$	−13.1176	−0.491947
$712$	−12.0194	−0.450448
$713$	−6.14869	−0.230270
$714$	−1.27194	−0.0476013
$715$	−37.3300	−1.39606
$716$	5.18048	0.193604
$717$	2.06358	0.0770657
$718$	−7.25961	−0.270926
$719$	25.0704	0.934967	0.467483	−	0.884002i	$-0.345161\pi$
$719$	25.0704	0.934967	0.467483	+	0.884002i	$0.345161\pi$
$720$	5.73503	0.213732
$721$	24.2696	0.903846
$722$	−1.49245	−0.0555431
$723$	17.6112	0.654968
$724$	39.2910	1.46024
$725$	−9.00209	−0.334329
$726$	−2.85399	−0.105921
$727$	−28.0600	−1.04069	−0.520344	−	0.853957i	$-0.674196\pi$
$727$	−28.0600	−1.04069	−0.520344	+	0.853957i	$0.674196\pi$
$728$	28.1006	1.04148
$729$	1.00000	0.0370370
$730$	9.72154	0.359810
$731$	10.6920	0.395459
$732$	−21.3867	−0.790475
$733$	12.8857	0.475944	0.237972	−	0.971272i	$-0.423517\pi$
$733$	12.8857	0.475944	0.237972	+	0.971272i	$0.423517\pi$
$734$	0.250065	0.00923007
$735$	4.61695	0.170299
$736$	−4.61264	−0.170024
$737$	−0.873196	−0.0321646
$738$	−4.26315	−0.156929
$739$	−6.60328	−0.242906	−0.121453	−	0.992597i	$-0.538755\pi$
$739$	−6.60328	−0.242906	−0.121453	+	0.992597i	$0.538755\pi$
$740$	32.8217	1.20655
$741$	−27.8820	−1.02427
$742$	1.58829	0.0583080
$743$	−28.5658	−1.04798	−0.523990	−	0.851725i	$-0.675557\pi$
$743$	−28.5658	−1.04798	−0.523990	+	0.851725i	$0.675557\pi$
$744$	14.6917	0.538625
$745$	−2.34812	−0.0860284
$746$	−14.0258	−0.513522
$747$	−7.63054	−0.279187
$748$	−4.09638	−0.149778
$749$	10.7319	0.392134
$750$	−4.86345	−0.177588
$751$	8.20013	0.299227	0.149613	−	0.988745i	$-0.452197\pi$
$751$	8.20013	0.299227	0.149613	+	0.988745i	$0.452197\pi$
$752$	−25.6154	−0.934099
$753$	24.4298	0.890272
$754$	18.7113	0.681424
$755$	29.7020	1.08097
$756$	3.85312	0.140137
$757$	−38.8721	−1.41283	−0.706416	−	0.707797i	$-0.749689\pi$
$757$	−38.8721	−1.41283	−0.706416	+	0.707797i	$0.749689\pi$
$758$	4.58186	0.166420
$759$	2.08778	0.0757816
$760$	24.6157	0.892905
$761$	11.0561	0.400782	0.200391	−	0.979716i	$-0.435779\pi$
$761$	11.0561	0.400782	0.200391	+	0.979716i	$0.435779\pi$
$762$	−10.4471	−0.378458
$763$	−33.5302	−1.21387
$764$	−27.8038	−1.00591
$765$	−2.57031	−0.0929297
$766$	10.2784	0.371375
$767$	61.8634	2.23376
$768$	3.48385	0.125712
$769$	−1.74873	−0.0630609	−0.0315305	−	0.999503i	$-0.510038\pi$
$769$	−1.74873	−0.0630609	−0.0315305	+	0.999503i	$0.510038\pi$
$770$	7.92863	0.285728
$771$	−0.168260	−0.00605972
$772$	18.0829	0.650818
$773$	37.4020	1.34526	0.672628	−	0.739981i	$-0.265165\pi$
$773$	37.4020	1.34526	0.672628	+	0.739981i	$0.265165\pi$
$774$	5.96171	0.214289
$775$	−11.4742	−0.412164
$776$	−5.73060	−0.205717
$777$	17.2456	0.618682
$778$	−6.53694	−0.234361
$779$	35.5972	1.27540
$780$	25.9997	0.930939
$781$	16.5920	0.593708
$782$	0.480010	0.0171651
$783$	5.60357	0.200255
$784$	−4.00792	−0.143140
$785$	−2.57031	−0.0917383
$786$	8.51279	0.303641
$787$	44.4020	1.58276	0.791380	−	0.611324i	$-0.209363\pi$
$787$	44.4020	1.58276	0.791380	+	0.611324i	$0.209363\pi$
$788$	−5.01857	−0.178779
$789$	−13.4461	−0.478695
$790$	18.7996	0.668861
$791$	−24.5692	−0.873582
$792$	−4.98856	−0.177261
$793$	−75.8256	−2.69265
$794$	0.908257	0.0322328
$795$	3.20957	0.113832
$796$	−0.00526315	−0.000186547 0
$797$	23.3214	0.826085	0.413042	−	0.910712i	$-0.364466\pi$
$797$	23.3214	0.826085	0.413042	+	0.910712i	$0.364466\pi$
$798$	5.92194	0.209634
$799$	11.4803	0.406143
$800$	−8.60771	−0.304329
$801$	−5.84324	−0.206461
$802$	4.41923	0.156048
$803$	16.4507	0.580532
$804$	0.608166	0.0214484
$805$	5.04758	0.177904
$806$	23.8496	0.840065
$807$	11.1882	0.393843
$808$	−20.2869	−0.713690
$809$	36.3204	1.27696	0.638478	−	0.769640i	$-0.279564\pi$
$809$	36.3204	1.27696	0.638478	+	0.769640i	$0.279564\pi$
$810$	−1.43316	−0.0503562
$811$	−23.9469	−0.840891	−0.420445	−	0.907318i	$-0.638126\pi$
$811$	−23.9469	−0.840891	−0.420445	+	0.907318i	$0.638126\pi$
$812$	21.5913	0.757705
$813$	−12.8358	−0.450172
$814$	−10.2229	−0.358313
$815$	18.5378	0.649352
$816$	2.23126	0.0781097
$817$	−49.7802	−1.74159
$818$	4.17837	0.146093
$819$	13.6611	0.477357
$820$	−33.1941	−1.15919
$821$	−15.4203	−0.538171	−0.269086	−	0.963116i	$-0.586721\pi$
$821$	−15.4203	−0.538171	−0.269086	+	0.963116i	$0.586721\pi$
$822$	−8.07157	−0.281528
$823$	−41.3441	−1.44116	−0.720582	−	0.693370i	$-0.756125\pi$
$823$	−41.3441	−1.44116	−0.720582	+	0.693370i	$0.756125\pi$
$824$	21.8844	0.762380
$825$	3.89604	0.135643
$826$	−13.1394	−0.457177
$827$	−4.02627	−0.140007	−0.0700035	−	0.997547i	$-0.522301\pi$
$827$	−4.02627	−0.140007	−0.0700035	+	0.997547i	$0.522301\pi$
$828$	−1.45410	−0.0505336
$829$	13.2272	0.459401	0.229700	−	0.973261i	$-0.426225\pi$
$829$	13.2272	0.459401	0.229700	+	0.973261i	$0.426225\pi$
$830$	10.9358	0.379587
$831$	12.8645	0.446264
$832$	−8.83285	−0.306224
$833$	1.79626	0.0622368
$834$	11.2955	0.391130
$835$	57.1065	1.97625
$836$	19.0720	0.659618
$837$	7.14237	0.246877
$838$	−11.9726	−0.413587
$839$	−22.7731	−0.786216	−0.393108	−	0.919492i	$-0.628600\pi$
$839$	−22.7731	−0.786216	−0.393108	+	0.919492i	$0.628600\pi$
$840$	−12.0607	−0.416135
$841$	2.40002	0.0827592
$842$	−8.76608	−0.302099
$843$	−26.9236	−0.927299
$844$	−12.6428	−0.435184
$845$	58.7668	2.02164
$846$	6.40121	0.220078
$847$	−11.6761	−0.401197
$848$	−2.78620	−0.0956784
$849$	16.5871	0.569268
$850$	0.895754	0.0307241
$851$	−6.50819	−0.223098
$852$	−11.5560	−0.395903
$853$	−21.5422	−0.737592	−0.368796	−	0.929510i	$-0.620230\pi$
$853$	−21.5422	−0.737592	−0.368796	+	0.929510i	$0.620230\pi$
$854$	16.1048	0.551096
$855$	11.9669	0.409259
$856$	9.67717	0.330759
$857$	15.3627	0.524779	0.262389	−	0.964962i	$-0.415490\pi$
$857$	15.3627	0.524779	0.262389	+	0.964962i	$0.415490\pi$
$858$	−8.09809	−0.276464
$859$	27.6812	0.944471	0.472235	−	0.881473i	$-0.343447\pi$
$859$	27.6812	0.944471	0.472235	+	0.881473i	$0.343447\pi$
$860$	46.4196	1.58289
$861$	−17.4412	−0.594396
$862$	−12.4607	−0.424414
$863$	−1.19662	−0.0407335	−0.0203667	−	0.999793i	$-0.506483\pi$
$863$	−1.19662	−0.0407335	−0.0203667	+	0.999793i	$0.506483\pi$
$864$	5.35808	0.182286
$865$	−14.5650	−0.495225
$866$	−11.9017	−0.404435
$867$	−1.00000	−0.0339618
$868$	27.5205	0.934105
$869$	31.8125	1.07917
$870$	−8.03084	−0.272271
$871$	2.15623	0.0730610
$872$	−30.2349	−1.02388
$873$	−2.78593	−0.0942893
$874$	−2.23484	−0.0755945
$875$	−19.8972	−0.672648
$876$	−11.4576	−0.387117
$877$	3.50001	0.118187	0.0590935	−	0.998252i	$-0.481179\pi$
$877$	3.50001	0.118187	0.0590935	+	0.998252i	$0.481179\pi$
$878$	−14.1732	−0.478322
$879$	−32.8754	−1.10886
$880$	−13.9085	−0.468855
$881$	−56.9316	−1.91807	−0.959037	−	0.283282i	$-0.908577\pi$
$881$	−56.9316	−1.91807	−0.959037	+	0.283282i	$0.908577\pi$
$882$	1.00157	0.0337245
$883$	10.2254	0.344112	0.172056	−	0.985087i	$-0.444959\pi$
$883$	10.2254	0.344112	0.172056	+	0.985087i	$0.444959\pi$
$884$	10.1154	0.340218
$885$	−26.5517	−0.892524
$886$	−4.44985	−0.149496
$887$	−5.02440	−0.168703	−0.0843514	−	0.996436i	$-0.526882\pi$
$887$	−5.02440	−0.168703	−0.0843514	+	0.996436i	$0.526882\pi$
$888$	15.5507	0.521849
$889$	−42.7407	−1.43348
$890$	8.37431	0.280708
$891$	−2.42518	−0.0812467
$892$	−36.4258	−1.21962
$893$	−53.4500	−1.78864
$894$	−0.509383	−0.0170363
$895$	−7.88316	−0.263505
$896$	26.3214	0.879337
$897$	−5.15546	−0.172136
$898$	2.55386	0.0852233
$899$	40.0228	1.33484
$900$	−2.71353	−0.0904508
$901$	1.24871	0.0416006
$902$	10.3389	0.344248
$903$	24.3904	0.811660
$904$	−22.1546	−0.736852
$905$	−59.7892	−1.98746
$906$	6.44333	0.214065
$907$	58.1444	1.93065	0.965326	−	0.261048i	$-0.0840681\pi$
$907$	58.1444	1.93065	0.965326	+	0.261048i	$0.0840681\pi$
$908$	3.54109	0.117515
$909$	−9.86245	−0.327117
$910$	−19.5786	−0.649023
$911$	−13.1575	−0.435927	−0.217963	−	0.975957i	$-0.569941\pi$
$911$	−13.1575	−0.435927	−0.217963	+	0.975957i	$0.569941\pi$
$912$	−10.3883	−0.343992
$913$	18.5055	0.612441
$914$	−16.7001	−0.552390
$915$	32.5442	1.07588
$916$	−13.4104	−0.443092
$917$	34.8273	1.15010
$918$	−0.557584	−0.0184030
$919$	−15.0798	−0.497436	−0.248718	−	0.968576i	$-0.580009\pi$
$919$	−15.0798	−0.497436	−0.248718	+	0.968576i	$0.580009\pi$
$920$	4.55152	0.150059
$921$	9.51912	0.313666
$922$	12.9124	0.425246
$923$	−40.9714	−1.34859
$924$	−9.34454	−0.307413
$925$	−12.1450	−0.399326
$926$	−1.10384	−0.0362744
$927$	10.6391	0.349433
$928$	30.0244	0.985599
$929$	8.61431	0.282626	0.141313	−	0.989965i	$-0.454868\pi$
$929$	8.61431	0.282626	0.141313	+	0.989965i	$0.454868\pi$
$930$	−10.2362	−0.335658
$931$	−8.36307	−0.274088
$932$	−17.7200	−0.580439
$933$	−5.96578	−0.195311
$934$	−17.3073	−0.566311
$935$	6.23347	0.203856
$936$	12.3185	0.402643
$937$	−2.26912	−0.0741288	−0.0370644	−	0.999313i	$-0.511801\pi$
$937$	−2.26912	−0.0741288	−0.0370644	+	0.999313i	$0.511801\pi$
$938$	−0.457968	−0.0149532
$939$	−5.60364	−0.182868
$940$	49.8417	1.62566
$941$	−45.7976	−1.49296	−0.746479	−	0.665409i	$-0.768257\pi$
$941$	−45.7976	−1.49296	−0.746479	+	0.665409i	$0.768257\pi$
$942$	−0.557584	−0.0181671
$943$	6.58203	0.214340
$944$	23.0492	0.750188
$945$	−5.86331	−0.190734
$946$	−14.4582	−0.470078
$947$	44.2873	1.43914	0.719572	−	0.694418i	$-0.244338\pi$
$947$	44.2873	1.43914	0.719572	+	0.694418i	$0.244338\pi$
$948$	−22.1569	−0.719622
$949$	−40.6225	−1.31866
$950$	−4.17047	−0.135308
$951$	17.3820	0.563648
$952$	−4.69233	−0.152079
$953$	6.83616	0.221445	0.110722	−	0.993851i	$-0.464684\pi$
$953$	6.83616	0.221445	0.110722	+	0.993851i	$0.464684\pi$
$954$	0.696261	0.0225423
$955$	42.3092	1.36909
$956$	3.48559	0.112732
$957$	−13.5897	−0.439292
$958$	6.16377	0.199142
$959$	−33.0221	−1.06634
$960$	3.79104	0.122355
$961$	20.0135	0.645597
$962$	25.2440	0.813899
$963$	4.70455	0.151602
$964$	29.7471	0.958089
$965$	−27.5168	−0.885798
$966$	1.09498	0.0352305
$967$	1.54153	0.0495722	0.0247861	−	0.999693i	$-0.492110\pi$
$967$	1.54153	0.0495722	0.0247861	+	0.999693i	$0.492110\pi$
$968$	−10.5286	−0.338403
$969$	4.65582	0.149566
$970$	3.99269	0.128197
$971$	−56.6339	−1.81747	−0.908734	−	0.417375i	$-0.862950\pi$
$971$	−56.6339	−1.81747	−0.908734	+	0.417375i	$0.862950\pi$
$972$	1.68910	0.0541779
$973$	46.2117	1.48148
$974$	17.7707	0.569411
$975$	−9.62069	−0.308109
$976$	−28.2513	−0.904302
$977$	−8.93841	−0.285965	−0.142982	−	0.989725i	$-0.545669\pi$
$977$	−8.93841	−0.285965	−0.142982	+	0.989725i	$0.545669\pi$
$978$	4.02146	0.128592
$979$	14.1709	0.452905
$980$	7.79849	0.249114
$981$	−14.6987	−0.469293
$982$	20.8156	0.664252
$983$	−12.5330	−0.399741	−0.199870	−	0.979822i	$-0.564052\pi$
$983$	−12.5330	−0.399741	−0.199870	+	0.979822i	$0.564052\pi$
$984$	−15.7272	−0.501364
$985$	7.63678	0.243328
$986$	−3.12446	−0.0995032
$987$	26.1884	0.833587
$988$	−47.0954	−1.49831
$989$	−9.20450	−0.292686
$990$	3.47569	0.110465
$991$	58.0655	1.84451	0.922256	−	0.386581i	$-0.126344\pi$
$991$	58.0655	1.84451	0.922256	+	0.386581i	$0.126344\pi$
$992$	38.2694	1.21506
$993$	−7.45842	−0.236686
$994$	8.70205	0.276012
$995$	0.00800895	0.000253901 0
$996$	−12.8887	−0.408395
$997$	39.9132	1.26406	0.632032	−	0.774942i	$-0.282221\pi$
$997$	39.9132	1.26406	0.632032	+	0.774942i	$0.282221\pi$
$998$	15.5200	0.491278
$999$	7.55997	0.239187

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.f.1.20	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.f.1.20	✓	48	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)

\(f(q)\)	\(=\)	\(q-0.557584 q^{2} -1.00000 q^{3} -1.68910 q^{4} +2.57031 q^{5} +0.557584 q^{6} +2.28117 q^{7} +2.05698 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.557584 q^{2} -1.00000 q^{3} -1.68910 q^{4} +2.57031 q^{5} +0.557584 q^{6} +2.28117 q^{7} +2.05698 q^{8} +1.00000 q^{9} -1.43316 q^{10} -2.42518 q^{11} +1.68910 q^{12} +5.98863 q^{13} -1.27194 q^{14} -2.57031 q^{15} +2.23126 q^{16} -1.00000 q^{17} -0.557584 q^{18} +4.65582 q^{19} -4.34151 q^{20} -2.28117 q^{21} +1.35224 q^{22} +0.860875 q^{23} -2.05698 q^{24} +1.60649 q^{25} -3.33917 q^{26} -1.00000 q^{27} -3.85312 q^{28} -5.60357 q^{29} +1.43316 q^{30} -7.14237 q^{31} -5.35808 q^{32} +2.42518 q^{33} +0.557584 q^{34} +5.86331 q^{35} -1.68910 q^{36} -7.55997 q^{37} -2.59601 q^{38} -5.98863 q^{39} +5.28708 q^{40} +7.64575 q^{41} +1.27194 q^{42} -10.6920 q^{43} +4.09638 q^{44} +2.57031 q^{45} -0.480010 q^{46} -11.4803 q^{47} -2.23126 q^{48} -1.79626 q^{49} -0.895754 q^{50} +1.00000 q^{51} -10.1154 q^{52} -1.24871 q^{53} +0.557584 q^{54} -6.23347 q^{55} +4.69233 q^{56} -4.65582 q^{57} +3.12446 q^{58} +10.3301 q^{59} +4.34151 q^{60} -12.6616 q^{61} +3.98247 q^{62} +2.28117 q^{63} -1.47494 q^{64} +15.3926 q^{65} -1.35224 q^{66} +0.360054 q^{67} +1.68910 q^{68} -0.860875 q^{69} -3.26929 q^{70} -6.84154 q^{71} +2.05698 q^{72} -6.78327 q^{73} +4.21532 q^{74} -1.60649 q^{75} -7.86414 q^{76} -5.53226 q^{77} +3.33917 q^{78} -13.1176 q^{79} +5.73503 q^{80} +1.00000 q^{81} -4.26315 q^{82} -7.63054 q^{83} +3.85312 q^{84} -2.57031 q^{85} +5.96171 q^{86} +5.60357 q^{87} -4.98856 q^{88} -5.84324 q^{89} -1.43316 q^{90} +13.6611 q^{91} -1.45410 q^{92} +7.14237 q^{93} +6.40121 q^{94} +11.9669 q^{95} +5.35808 q^{96} -2.78593 q^{97} +1.00157 q^{98} -2.42518 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9}+O(q^{10}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9} - 20 q^{10} + 5 q^{11} - 45 q^{12} - 8 q^{13} + 4 q^{14} - q^{15} + 39 q^{16} - 48 q^{17} - q^{18} - 6 q^{19} + 6 q^{20} + 13 q^{21} - 35 q^{22} - 8 q^{23} + 6 q^{24} + 13 q^{25} + 17 q^{26} - 48 q^{27} - 38 q^{28} + q^{29} + 20 q^{30} - 21 q^{31} - 3 q^{32} - 5 q^{33} + q^{34} + 19 q^{35} + 45 q^{36} - 58 q^{37} - 14 q^{38} + 8 q^{39} - 54 q^{40} - 3 q^{41} - 4 q^{42} - 33 q^{43} + 2 q^{44} + q^{45} - 26 q^{46} + 9 q^{47} - 39 q^{48} + 11 q^{49} + 4 q^{50} + 48 q^{51} - 31 q^{52} - 33 q^{53} + q^{54} - 21 q^{55} + 6 q^{57} - 55 q^{58} + 77 q^{59} - 6 q^{60} - 29 q^{61} - 46 q^{62} - 13 q^{63} + 24 q^{64} - 49 q^{65} + 35 q^{66} - 44 q^{67} - 45 q^{68} + 8 q^{69} + 4 q^{70} + 22 q^{71} - 6 q^{72} - 63 q^{73} - 16 q^{74} - 13 q^{75} - 46 q^{76} - 30 q^{77} - 17 q^{78} - 46 q^{79} - 14 q^{80} + 48 q^{81} - 75 q^{82} + 11 q^{83} + 38 q^{84} - q^{85} + 8 q^{86} - q^{87} - 116 q^{88} + 10 q^{89} - 20 q^{90} - 67 q^{91} - 64 q^{92} + 21 q^{93} - 16 q^{94} - 8 q^{95} + 3 q^{96} - 96 q^{97} - 46 q^{98} + 5 q^{99}+O(q^{100}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9 - 20 * q^10 + 5 * q^11 - 45 * q^12 - 8 * q^13 + 4 * q^14 - q^15 + 39 * q^16 - 48 * q^17 - q^18 - 6 * q^19 + 6 * q^20 + 13 * q^21 - 35 * q^22 - 8 * q^23 + 6 * q^24 + 13 * q^25 + 17 * q^26 - 48 * q^27 - 38 * q^28 + q^29 + 20 * q^30 - 21 * q^31 - 3 * q^32 - 5 * q^33 + q^34 + 19 * q^35 + 45 * q^36 - 58 * q^37 - 14 * q^38 + 8 * q^39 - 54 * q^40 - 3 * q^41 - 4 * q^42 - 33 * q^43 + 2 * q^44 + q^45 - 26 * q^46 + 9 * q^47 - 39 * q^48 + 11 * q^49 + 4 * q^50 + 48 * q^51 - 31 * q^52 - 33 * q^53 + q^54 - 21 * q^55 + 6 * q^57 - 55 * q^58 + 77 * q^59 - 6 * q^60 - 29 * q^61 - 46 * q^62 - 13 * q^63 + 24 * q^64 - 49 * q^65 + 35 * q^66 - 44 * q^67 - 45 * q^68 + 8 * q^69 + 4 * q^70 + 22 * q^71 - 6 * q^72 - 63 * q^73 - 16 * q^74 - 13 * q^75 - 46 * q^76 - 30 * q^77 - 17 * q^78 - 46 * q^79 - 14 * q^80 + 48 * q^81 - 75 * q^82 + 11 * q^83 + 38 * q^84 - q^85 + 8 * q^86 - q^87 - 116 * q^88 + 10 * q^89 - 20 * q^90 - 67 * q^91 - 64 * q^92 + 21 * q^93 - 16 * q^94 - 8 * q^95 + 3 * q^96 - 96 * q^97 - 46 * q^98 + 5 * q^99

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