LMFDB - Embedded newform 8007.2.a.f.1.17

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			1.17
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)

$f(q)$	$=$	$q-0.980818 q^{2} -1.00000 q^{3} -1.03800 q^{4} +1.00436 q^{5} +0.980818 q^{6} -3.53145 q^{7} +2.97972 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.980818 q^{2} -1.00000 q^{3} -1.03800 q^{4} +1.00436 q^{5} +0.980818 q^{6} -3.53145 q^{7} +2.97972 q^{8} +1.00000 q^{9} -0.985094 q^{10} +6.32698 q^{11} +1.03800 q^{12} +3.86467 q^{13} +3.46371 q^{14} -1.00436 q^{15} -0.846572 q^{16} -1.00000 q^{17} -0.980818 q^{18} -2.59733 q^{19} -1.04252 q^{20} +3.53145 q^{21} -6.20562 q^{22} +6.45448 q^{23} -2.97972 q^{24} -3.99126 q^{25} -3.79054 q^{26} -1.00000 q^{27} +3.66564 q^{28} -7.53770 q^{29} +0.985094 q^{30} -4.09152 q^{31} -5.12911 q^{32} -6.32698 q^{33} +0.980818 q^{34} -3.54685 q^{35} -1.03800 q^{36} +6.50621 q^{37} +2.54751 q^{38} -3.86467 q^{39} +2.99271 q^{40} -9.61376 q^{41} -3.46371 q^{42} +7.33861 q^{43} -6.56738 q^{44} +1.00436 q^{45} -6.33067 q^{46} -4.71120 q^{47} +0.846572 q^{48} +5.47117 q^{49} +3.91470 q^{50} +1.00000 q^{51} -4.01151 q^{52} +2.16439 q^{53} +0.980818 q^{54} +6.35456 q^{55} -10.5227 q^{56} +2.59733 q^{57} +7.39311 q^{58} +3.64108 q^{59} +1.04252 q^{60} +7.27575 q^{61} +4.01303 q^{62} -3.53145 q^{63} +6.72387 q^{64} +3.88152 q^{65} +6.20562 q^{66} -6.61390 q^{67} +1.03800 q^{68} -6.45448 q^{69} +3.47881 q^{70} -11.6229 q^{71} +2.97972 q^{72} -10.8308 q^{73} -6.38141 q^{74} +3.99126 q^{75} +2.69602 q^{76} -22.3434 q^{77} +3.79054 q^{78} -16.2317 q^{79} -0.850263 q^{80} +1.00000 q^{81} +9.42935 q^{82} -8.05337 q^{83} -3.66564 q^{84} -1.00436 q^{85} -7.19784 q^{86} +7.53770 q^{87} +18.8526 q^{88} +2.16759 q^{89} -0.985094 q^{90} -13.6479 q^{91} -6.69972 q^{92} +4.09152 q^{93} +4.62082 q^{94} -2.60865 q^{95} +5.12911 q^{96} +3.94258 q^{97} -5.36622 q^{98} +6.32698 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.980818	−0.693543	−0.346772	−	0.937950i	$-0.612722\pi$
$2$	−0.980818	−0.693543	−0.346772	+	0.937950i	$0.612722\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.03800	−0.518998
$5$	1.00436	0.449163	0.224582	−	0.974455i	$-0.427898\pi$
$5$	1.00436	0.449163	0.224582	+	0.974455i	$0.427898\pi$
$6$	0.980818	0.400417
$7$	−3.53145	−1.33476	−0.667382	−	0.744716i	$-0.732585\pi$
$7$	−3.53145	−1.33476	−0.667382	+	0.744716i	$0.732585\pi$
$8$	2.97972	1.05349
$9$	1.00000	0.333333
$10$	−0.985094	−0.311514
$11$	6.32698	1.90766	0.953828	−	0.300353i	$-0.0971046\pi$
$11$	6.32698	1.90766	0.953828	+	0.300353i	$0.0971046\pi$
$12$	1.03800	0.299644
$13$	3.86467	1.07187	0.535933	−	0.844260i	$-0.319960\pi$
$13$	3.86467	1.07187	0.535933	+	0.844260i	$0.319960\pi$
$14$	3.46371	0.925716
$15$	−1.00436	−0.259325
$16$	−0.846572	−0.211643
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.980818	−0.231181
$19$	−2.59733	−0.595868	−0.297934	−	0.954586i	$-0.596298\pi$
$19$	−2.59733	−0.595868	−0.297934	+	0.954586i	$0.596298\pi$
$20$	−1.04252	−0.233115
$21$	3.53145	0.770626
$22$	−6.20562	−1.32304
$23$	6.45448	1.34585	0.672926	−	0.739710i	$-0.265037\pi$
$23$	6.45448	1.34585	0.672926	+	0.739710i	$0.265037\pi$
$24$	−2.97972	−0.608233
$25$	−3.99126	−0.798252
$26$	−3.79054	−0.743385
$27$	−1.00000	−0.192450
$28$	3.66564	0.692740
$29$	−7.53770	−1.39972	−0.699858	−	0.714282i	$-0.746753\pi$
$29$	−7.53770	−1.39972	−0.699858	+	0.714282i	$0.746753\pi$
$30$	0.985094	0.179853
$31$	−4.09152	−0.734858	−0.367429	−	0.930051i	$-0.619762\pi$
$31$	−4.09152	−0.734858	−0.367429	+	0.930051i	$0.619762\pi$
$32$	−5.12911	−0.906707
$33$	−6.32698	−1.10139
$34$	0.980818	0.168209
$35$	−3.54685	−0.599527
$36$	−1.03800	−0.172999
$37$	6.50621	1.06961	0.534807	−	0.844974i	$-0.320384\pi$
$37$	6.50621	1.06961	0.534807	+	0.844974i	$0.320384\pi$
$38$	2.54751	0.413260
$39$	−3.86467	−0.618842
$40$	2.99271	0.473189
$41$	−9.61376	−1.50142	−0.750709	−	0.660633i	$-0.770288\pi$
$41$	−9.61376	−1.50142	−0.750709	+	0.660633i	$0.770288\pi$
$42$	−3.46371	−0.534463
$43$	7.33861	1.11913	0.559564	−	0.828787i	$-0.310969\pi$
$43$	7.33861	1.11913	0.559564	+	0.828787i	$0.310969\pi$
$44$	−6.56738	−0.990070
$45$	1.00436	0.149721
$46$	−6.33067	−0.933406
$47$	−4.71120	−0.687198	−0.343599	−	0.939116i	$-0.611646\pi$
$47$	−4.71120	−0.687198	−0.343599	+	0.939116i	$0.611646\pi$
$48$	0.846572	0.122192
$49$	5.47117	0.781595
$50$	3.91470	0.553622
$51$	1.00000	0.140028
$52$	−4.01151	−0.556297
$53$	2.16439	0.297301	0.148651	−	0.988890i	$-0.452507\pi$
$53$	2.16439	0.297301	0.148651	+	0.988890i	$0.452507\pi$
$54$	0.980818	0.133472
$55$	6.35456	0.856849
$56$	−10.5227	−1.40616
$57$	2.59733	0.344025
$58$	7.39311	0.970764
$59$	3.64108	0.474028	0.237014	−	0.971506i	$-0.423831\pi$
$59$	3.64108	0.474028	0.237014	+	0.971506i	$0.423831\pi$
$60$	1.04252	0.134589
$61$	7.27575	0.931564	0.465782	−	0.884899i	$-0.345773\pi$
$61$	7.27575	0.931564	0.465782	+	0.884899i	$0.345773\pi$
$62$	4.01303	0.509656
$63$	−3.53145	−0.444921
$64$	6.72387	0.840483
$65$	3.88152	0.481443
$66$	6.20562	0.763858
$67$	−6.61390	−0.808016	−0.404008	−	0.914755i	$-0.632383\pi$
$67$	−6.61390	−0.808016	−0.404008	+	0.914755i	$0.632383\pi$
$68$	1.03800	0.125876
$69$	−6.45448	−0.777028
$70$	3.47881	0.415798
$71$	−11.6229	−1.37939	−0.689695	−	0.724100i	$-0.742255\pi$
$71$	−11.6229	−1.37939	−0.689695	+	0.724100i	$0.742255\pi$
$72$	2.97972	0.351164
$73$	−10.8308	−1.26765	−0.633826	−	0.773476i	$-0.718516\pi$
$73$	−10.8308	−1.26765	−0.633826	+	0.773476i	$0.718516\pi$
$74$	−6.38141	−0.741824
$75$	3.99126	0.460871
$76$	2.69602	0.309254
$77$	−22.3434	−2.54627
$78$	3.79054	0.429194
$79$	−16.2317	−1.82621	−0.913103	−	0.407728i	$-0.866321\pi$
$79$	−16.2317	−1.82621	−0.913103	+	0.407728i	$0.866321\pi$
$80$	−0.850263	−0.0950623
$81$	1.00000	0.111111
$82$	9.42935	1.04130
$83$	−8.05337	−0.883972	−0.441986	−	0.897022i	$-0.645726\pi$
$83$	−8.05337	−0.883972	−0.441986	+	0.897022i	$0.645726\pi$
$84$	−3.66564	−0.399954
$85$	−1.00436	−0.108938
$86$	−7.19784	−0.776163
$87$	7.53770	0.808127
$88$	18.8526	2.00970
$89$	2.16759	0.229764	0.114882	−	0.993379i	$-0.463351\pi$
$89$	2.16759	0.229764	0.114882	+	0.993379i	$0.463351\pi$
$90$	−0.985094	−0.103838
$91$	−13.6479	−1.43069
$92$	−6.69972	−0.698494
$93$	4.09152	0.424271
$94$	4.62082	0.476602
$95$	−2.60865	−0.267642
$96$	5.12911	0.523488
$97$	3.94258	0.400308	0.200154	−	0.979764i	$-0.435856\pi$
$97$	3.94258	0.400308	0.200154	+	0.979764i	$0.435856\pi$
$98$	−5.36622	−0.542070
$99$	6.32698	0.635885
$100$	4.14291	0.414291
$101$	−12.4762	−1.24143	−0.620715	−	0.784037i	$-0.713157\pi$
$101$	−12.4762	−1.24143	−0.620715	+	0.784037i	$0.713157\pi$
$102$	−0.980818	−0.0971155
$103$	5.58186	0.549997	0.274998	−	0.961445i	$-0.411323\pi$
$103$	5.58186	0.549997	0.274998	+	0.961445i	$0.411323\pi$
$104$	11.5156	1.12920
$105$	3.54685	0.346137
$106$	−2.12287	−0.206191
$107$	8.77058	0.847884	0.423942	−	0.905689i	$-0.360646\pi$
$107$	8.77058	0.847884	0.423942	+	0.905689i	$0.360646\pi$
$108$	1.03800	0.0998812
$109$	8.70332	0.833626	0.416813	−	0.908992i	$-0.363147\pi$
$109$	8.70332	0.833626	0.416813	+	0.908992i	$0.363147\pi$
$110$	−6.23267	−0.594262
$111$	−6.50621	−0.617542
$112$	2.98963	0.282494
$113$	−8.93732	−0.840753	−0.420376	−	0.907350i	$-0.638102\pi$
$113$	−8.93732	−0.840753	−0.420376	+	0.907350i	$0.638102\pi$
$114$	−2.54751	−0.238596
$115$	6.48262	0.604507
$116$	7.82411	0.726450
$117$	3.86467	0.357289
$118$	−3.57124	−0.328759
$119$	3.53145	0.323728
$120$	−2.99271	−0.273196
$121$	29.0307	2.63915
$122$	−7.13619	−0.646080
$123$	9.61376	0.866844
$124$	4.24698	0.381390
$125$	−9.03046	−0.807709
$126$	3.46371	0.308572
$127$	7.22565	0.641173	0.320587	−	0.947219i	$-0.396120\pi$
$127$	7.22565	0.641173	0.320587	+	0.947219i	$0.396120\pi$
$128$	3.66333	0.323796
$129$	−7.33861	−0.646129
$130$	−3.80706	−0.333901
$131$	15.2193	1.32971	0.664856	−	0.746971i	$-0.268493\pi$
$131$	15.2193	1.32971	0.664856	+	0.746971i	$0.268493\pi$
$132$	6.56738	0.571617
$133$	9.17235	0.795343
$134$	6.48703	0.560394
$135$	−1.00436	−0.0864415
$136$	−2.97972	−0.255509
$137$	17.4584	1.49157	0.745787	−	0.666185i	$-0.232074\pi$
$137$	17.4584	1.49157	0.745787	+	0.666185i	$0.232074\pi$
$138$	6.33067	0.538902
$139$	23.1304	1.96189	0.980946	−	0.194278i	$-0.0622365\pi$
$139$	23.1304	1.96189	0.980946	+	0.194278i	$0.0622365\pi$
$140$	3.68162	0.311153
$141$	4.71120	0.396754
$142$	11.4000	0.956666
$143$	24.4517	2.04475
$144$	−0.846572	−0.0705477
$145$	−7.57056	−0.628701
$146$	10.6231	0.879171
$147$	−5.47117	−0.451254
$148$	−6.75342	−0.555128
$149$	7.85577	0.643570	0.321785	−	0.946813i	$-0.395717\pi$
$149$	7.85577	0.643570	0.321785	+	0.946813i	$0.395717\pi$
$150$	−3.91470	−0.319634
$151$	−1.61453	−0.131388	−0.0656941	−	0.997840i	$-0.520926\pi$
$151$	−1.61453	−0.131388	−0.0656941	+	0.997840i	$0.520926\pi$
$152$	−7.73932	−0.627741
$153$	−1.00000	−0.0808452
$154$	21.9148	1.76595
$155$	−4.10936	−0.330071
$156$	4.01151	0.321178
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	15.9203	1.26655
$159$	−2.16439	−0.171647
$160$	−5.15147	−0.407259
$161$	−22.7937	−1.79639
$162$	−0.980818	−0.0770603
$163$	−21.9925	−1.72258	−0.861291	−	0.508112i	$-0.830344\pi$
$163$	−21.9925	−1.72258	−0.861291	+	0.508112i	$0.830344\pi$
$164$	9.97905	0.779233
$165$	−6.35456	−0.494702
$166$	7.89889	0.613073
$167$	0.0214142	0.00165708	0.000828541	−	1.00000i	$-0.499736\pi$
$167$	0.0214142	0.00165708	0.000828541		1.00000i	$0.499736\pi$
$168$	10.5227	0.811848
$169$	1.93567	0.148897
$170$	0.985094	0.0755533
$171$	−2.59733	−0.198623
$172$	−7.61745	−0.580825
$173$	5.93545	0.451264	0.225632	−	0.974213i	$-0.427555\pi$
$173$	5.93545	0.451264	0.225632	+	0.974213i	$0.427555\pi$
$174$	−7.39311	−0.560471
$175$	14.0950	1.06548
$176$	−5.35624	−0.403742
$177$	−3.64108	−0.273680
$178$	−2.12601	−0.159351
$179$	−14.6954	−1.09838	−0.549191	−	0.835697i	$-0.685064\pi$
$179$	−14.6954	−1.09838	−0.549191	+	0.835697i	$0.685064\pi$
$180$	−1.04252	−0.0777050
$181$	−4.11606	−0.305944	−0.152972	−	0.988230i	$-0.548885\pi$
$181$	−4.11606	−0.305944	−0.152972	+	0.988230i	$0.548885\pi$
$182$	13.3861	0.992244
$183$	−7.27575	−0.537839
$184$	19.2325	1.41784
$185$	6.53457	0.480431
$186$	−4.01303	−0.294250
$187$	−6.32698	−0.462675
$188$	4.89020	0.356655
$189$	3.53145	0.256875
$190$	2.55861	0.185621
$191$	−7.47583	−0.540932	−0.270466	−	0.962730i	$-0.587178\pi$
$191$	−7.47583	−0.540932	−0.270466	+	0.962730i	$0.587178\pi$
$192$	−6.72387	−0.485253
$193$	2.58077	0.185768	0.0928839	−	0.995677i	$-0.470391\pi$
$193$	2.58077	0.185768	0.0928839	+	0.995677i	$0.470391\pi$
$194$	−3.86695	−0.277631
$195$	−3.88152	−0.277961
$196$	−5.67905	−0.405646
$197$	−20.6346	−1.47016	−0.735079	−	0.677982i	$-0.762855\pi$
$197$	−20.6346	−1.47016	−0.735079	+	0.677982i	$0.762855\pi$
$198$	−6.20562	−0.441014
$199$	−13.6167	−0.965264	−0.482632	−	0.875823i	$-0.660319\pi$
$199$	−13.6167	−0.965264	−0.482632	+	0.875823i	$0.660319\pi$
$200$	−11.8928	−0.840951
$201$	6.61390	0.466508
$202$	12.2369	0.860984
$203$	26.6191	1.86829
$204$	−1.03800	−0.0726743
$205$	−9.65568	−0.674382
$206$	−5.47478	−0.381446
$207$	6.45448	0.448617
$208$	−3.27172	−0.226853
$209$	−16.4332	−1.13671
$210$	−3.47881	−0.240061
$211$	−22.0131	−1.51544	−0.757722	−	0.652578i	$-0.773688\pi$
$211$	−22.0131	−1.51544	−0.757722	+	0.652578i	$0.773688\pi$
$212$	−2.24662	−0.154299
$213$	11.6229	0.796391
$214$	−8.60234	−0.588044
$215$	7.37061	0.502671
$216$	−2.97972	−0.202744
$217$	14.4490	0.980863
$218$	−8.53637	−0.578156
$219$	10.8308	0.731879
$220$	−6.59601	−0.444703
$221$	−3.86467	−0.259966
$222$	6.38141	0.428292
$223$	17.6054	1.17895	0.589474	−	0.807787i	$-0.299335\pi$
$223$	17.6054	1.17895	0.589474	+	0.807787i	$0.299335\pi$
$224$	18.1132	1.21024
$225$	−3.99126	−0.266084
$226$	8.76589	0.583098
$227$	−21.1832	−1.40598	−0.702991	−	0.711199i	$-0.748152\pi$
$227$	−21.1832	−1.40598	−0.702991	+	0.711199i	$0.748152\pi$
$228$	−2.69602	−0.178548
$229$	−18.7107	−1.23644	−0.618220	−	0.786005i	$-0.712146\pi$
$229$	−18.7107	−1.23644	−0.618220	+	0.786005i	$0.712146\pi$
$230$	−6.35827	−0.419252
$231$	22.3434	1.47009
$232$	−22.4603	−1.47459
$233$	−1.35758	−0.0889379	−0.0444689	−	0.999011i	$-0.514160\pi$
$233$	−1.35758	−0.0889379	−0.0444689	+	0.999011i	$0.514160\pi$
$234$	−3.79054	−0.247795
$235$	−4.73173	−0.308664
$236$	−3.77943	−0.246020
$237$	16.2317	1.05436
$238$	−3.46371	−0.224519
$239$	15.1210	0.978094	0.489047	−	0.872257i	$-0.337345\pi$
$239$	15.1210	0.978094	0.489047	+	0.872257i	$0.337345\pi$
$240$	0.850263	0.0548842
$241$	16.4242	1.05797	0.528987	−	0.848630i	$-0.322572\pi$
$241$	16.4242	1.05797	0.528987	+	0.848630i	$0.322572\pi$
$242$	−28.4738	−1.83037
$243$	−1.00000	−0.0641500
$244$	−7.55220	−0.483480
$245$	5.49502	0.351064
$246$	−9.42935	−0.601193
$247$	−10.0378	−0.638691
$248$	−12.1916	−0.774166
$249$	8.05337	0.510361
$250$	8.85724	0.560181
$251$	7.14002	0.450674	0.225337	−	0.974281i	$-0.427652\pi$
$251$	7.14002	0.450674	0.225337	+	0.974281i	$0.427652\pi$
$252$	3.66564	0.230913
$253$	40.8373	2.56742
$254$	−7.08705	−0.444681
$255$	1.00436	0.0628954
$256$	−17.0408	−1.06505
$257$	−9.05691	−0.564955	−0.282477	−	0.959274i	$-0.591156\pi$
$257$	−9.05691	−0.564955	−0.282477	+	0.959274i	$0.591156\pi$
$258$	7.19784	0.448118
$259$	−22.9764	−1.42768
$260$	−4.02900	−0.249868
$261$	−7.53770	−0.466572
$262$	−14.9273	−0.922213
$263$	5.55816	0.342731	0.171365	−	0.985208i	$-0.445182\pi$
$263$	5.55816	0.342731	0.171365	+	0.985208i	$0.445182\pi$
$264$	−18.8526	−1.16030
$265$	2.17382	0.133537
$266$	−8.99640	−0.551605
$267$	−2.16759	−0.132654
$268$	6.86520	0.419359
$269$	12.5220	0.763478	0.381739	−	0.924270i	$-0.375325\pi$
$269$	12.5220	0.763478	0.381739	+	0.924270i	$0.375325\pi$
$270$	0.985094	0.0599509
$271$	2.37609	0.144337	0.0721686	−	0.997392i	$-0.477008\pi$
$271$	2.37609	0.144337	0.0721686	+	0.997392i	$0.477008\pi$
$272$	0.846572	0.0513310
$273$	13.6479	0.826009
$274$	−17.1235	−1.03447
$275$	−25.2526	−1.52279
$276$	6.69972	0.403276
$277$	−21.2558	−1.27714	−0.638569	−	0.769564i	$-0.720473\pi$
$277$	−21.2558	−1.27714	−0.638569	+	0.769564i	$0.720473\pi$
$278$	−22.6867	−1.36066
$279$	−4.09152	−0.244953
$280$	−10.5686	−0.631596
$281$	−8.43216	−0.503020	−0.251510	−	0.967855i	$-0.580927\pi$
$281$	−8.43216	−0.503020	−0.251510	+	0.967855i	$0.580927\pi$
$282$	−4.62082	−0.275166
$283$	5.80167	0.344873	0.172437	−	0.985021i	$-0.444836\pi$
$283$	5.80167	0.344873	0.172437	+	0.985021i	$0.444836\pi$
$284$	12.0646	0.715900
$285$	2.60865	0.154523
$286$	−23.9826	−1.41812
$287$	33.9506	2.00404
$288$	−5.12911	−0.302236
$289$	1.00000	0.0588235
$290$	7.42535	0.436031
$291$	−3.94258	−0.231118
$292$	11.2424	0.657909
$293$	−25.3292	−1.47975	−0.739874	−	0.672745i	$-0.765115\pi$
$293$	−25.3292	−1.47975	−0.739874	+	0.672745i	$0.765115\pi$
$294$	5.36622	0.312964
$295$	3.65695	0.212916
$296$	19.3867	1.12683
$297$	−6.32698	−0.367129
$298$	−7.70508	−0.446343
$299$	24.9444	1.44257
$300$	−4.14291	−0.239191
$301$	−25.9160	−1.49377
$302$	1.58356	0.0911234
$303$	12.4762	0.716739
$304$	2.19883	0.126111
$305$	7.30747	0.418424
$306$	0.980818	0.0560696
$307$	−8.84271	−0.504680	−0.252340	−	0.967639i	$-0.581200\pi$
$307$	−8.84271	−0.504680	−0.252340	+	0.967639i	$0.581200\pi$
$308$	23.1924	1.32151
$309$	−5.58186	−0.317541
$310$	4.03053	0.228919
$311$	11.1415	0.631776	0.315888	−	0.948796i	$-0.397698\pi$
$311$	11.1415	0.631776	0.315888	+	0.948796i	$0.397698\pi$
$312$	−11.5156	−0.651945
$313$	−17.4045	−0.983760	−0.491880	−	0.870663i	$-0.663690\pi$
$313$	−17.4045	−0.983760	−0.491880	+	0.870663i	$0.663690\pi$
$314$	0.980818	0.0553508
$315$	−3.54685	−0.199842
$316$	16.8484	0.947798
$317$	30.5137	1.71382	0.856910	−	0.515466i	$-0.172381\pi$
$317$	30.5137	1.71382	0.856910	+	0.515466i	$0.172381\pi$
$318$	2.12287	0.119045
$319$	−47.6909	−2.67018
$320$	6.75318	0.377514
$321$	−8.77058	−0.489526
$322$	22.3565	1.24588
$323$	2.59733	0.144519
$324$	−1.03800	−0.0576664
$325$	−15.4249	−0.855620
$326$	21.5706	1.19468
$327$	−8.70332	−0.481294
$328$	−28.6463	−1.58173
$329$	16.6374	0.917248
$330$	6.23267	0.343097
$331$	18.7043	1.02808	0.514040	−	0.857766i	$-0.328148\pi$
$331$	18.7043	1.02808	0.514040	+	0.857766i	$0.328148\pi$
$332$	8.35936	0.458780
$333$	6.50621	0.356538
$334$	−0.0210034	−0.00114926
$335$	−6.64273	−0.362931
$336$	−2.98963	−0.163098
$337$	−18.1160	−0.986842	−0.493421	−	0.869791i	$-0.664254\pi$
$337$	−18.1160	−0.986842	−0.493421	+	0.869791i	$0.664254\pi$
$338$	−1.89854	−0.103267
$339$	8.93732	0.485409
$340$	1.04252	0.0565387
$341$	−25.8870	−1.40186
$342$	2.54751	0.137753
$343$	5.39900	0.291519
$344$	21.8670	1.17899
$345$	−6.48262	−0.349012
$346$	−5.82159	−0.312971
$347$	−12.5427	−0.673325	−0.336663	−	0.941625i	$-0.609298\pi$
$347$	−12.5427	−0.673325	−0.336663	+	0.941625i	$0.609298\pi$
$348$	−7.82411	−0.419416
$349$	−6.54338	−0.350259	−0.175129	−	0.984545i	$-0.556034\pi$
$349$	−6.54338	−0.350259	−0.175129	+	0.984545i	$0.556034\pi$
$350$	−13.8246	−0.738955
$351$	−3.86467	−0.206281
$352$	−32.4518	−1.72969
$353$	7.74439	0.412192	0.206096	−	0.978532i	$-0.433924\pi$
$353$	7.74439	0.412192	0.206096	+	0.978532i	$0.433924\pi$
$354$	3.57124	0.189809
$355$	−11.6736	−0.619571
$356$	−2.24995	−0.119247
$357$	−3.53145	−0.186904
$358$	14.4135	0.761776
$359$	−5.80074	−0.306151	−0.153076	−	0.988214i	$-0.548918\pi$
$359$	−5.80074	−0.306151	−0.153076	+	0.988214i	$0.548918\pi$
$360$	2.99271	0.157730
$361$	−12.2539	−0.644941
$362$	4.03711	0.212186
$363$	−29.0307	−1.52371
$364$	14.1665	0.742525
$365$	−10.8780	−0.569383
$366$	7.13619	0.373014
$367$	−9.02968	−0.471345	−0.235673	−	0.971832i	$-0.575729\pi$
$367$	−9.02968	−0.471345	−0.235673	+	0.971832i	$0.575729\pi$
$368$	−5.46418	−0.284840
$369$	−9.61376	−0.500472
$370$	−6.40923	−0.333200
$371$	−7.64343	−0.396827
$372$	−4.24698	−0.220196
$373$	−1.15360	−0.0597310	−0.0298655	−	0.999554i	$-0.509508\pi$
$373$	−1.15360	−0.0597310	−0.0298655	+	0.999554i	$0.509508\pi$
$374$	6.20562	0.320885
$375$	9.03046	0.466331
$376$	−14.0380	−0.723957
$377$	−29.1307	−1.50031
$378$	−3.46371	−0.178154
$379$	18.2491	0.937394	0.468697	−	0.883359i	$-0.344724\pi$
$379$	18.2491	0.937394	0.468697	+	0.883359i	$0.344724\pi$
$380$	2.70777	0.138906
$381$	−7.22565	−0.370181
$382$	7.33242	0.375159
$383$	−23.5927	−1.20553	−0.602764	−	0.797919i	$-0.705934\pi$
$383$	−23.5927	−1.20553	−0.602764	+	0.797919i	$0.705934\pi$
$384$	−3.66333	−0.186943
$385$	−22.4408	−1.14369
$386$	−2.53126	−0.128838
$387$	7.33861	0.373043
$388$	−4.09238	−0.207759
$389$	13.8726	0.703370	0.351685	−	0.936118i	$-0.385609\pi$
$389$	13.8726	0.703370	0.351685	+	0.936118i	$0.385609\pi$
$390$	3.80706	0.192778
$391$	−6.45448	−0.326417
$392$	16.3026	0.823403
$393$	−15.2193	−0.767710
$394$	20.2388	1.01962
$395$	−16.3024	−0.820265
$396$	−6.56738	−0.330023
$397$	19.8767	0.997581	0.498791	−	0.866722i	$-0.333778\pi$
$397$	19.8767	0.997581	0.498791	+	0.866722i	$0.333778\pi$
$398$	13.3555	0.669452
$399$	−9.17235	−0.459192
$400$	3.37889	0.168945
$401$	−23.1378	−1.15544	−0.577722	−	0.816233i	$-0.696058\pi$
$401$	−23.1378	−1.15544	−0.577722	+	0.816233i	$0.696058\pi$
$402$	−6.48703	−0.323544
$403$	−15.8124	−0.787670
$404$	12.9503	0.644299
$405$	1.00436	0.0499070
$406$	−26.1084	−1.29574
$407$	41.1647	2.04046
$408$	2.97972	0.147518
$409$	30.7047	1.51825	0.759125	−	0.650945i	$-0.225627\pi$
$409$	30.7047	1.51825	0.759125	+	0.650945i	$0.225627\pi$
$410$	9.47046	0.467713
$411$	−17.4584	−0.861160
$412$	−5.79394	−0.285447
$413$	−12.8583	−0.632716
$414$	−6.33067	−0.311135
$415$	−8.08848	−0.397048
$416$	−19.8223	−0.971869
$417$	−23.1304	−1.13270
$418$	16.1180	0.788358
$419$	27.4810	1.34254	0.671268	−	0.741215i	$-0.265750\pi$
$419$	27.4810	1.34254	0.671268	+	0.741215i	$0.265750\pi$
$420$	−3.68162	−0.179644
$421$	−32.6641	−1.59195	−0.795975	−	0.605329i	$-0.793041\pi$
$421$	−32.6641	−1.59195	−0.795975	+	0.605329i	$0.793041\pi$
$422$	21.5908	1.05103
$423$	−4.71120	−0.229066
$424$	6.44926	0.313204
$425$	3.99126	0.193605
$426$	−11.4000	−0.552331
$427$	−25.6940	−1.24342
$428$	−9.10382	−0.440050
$429$	−24.4517	−1.18054
$430$	−7.22922	−0.348624
$431$	−0.416855	−0.0200792	−0.0100396	−	0.999950i	$-0.503196\pi$
$431$	−0.416855	−0.0200792	−0.0100396	+	0.999950i	$0.503196\pi$
$432$	0.846572	0.0407307
$433$	6.04143	0.290332	0.145166	−	0.989407i	$-0.453628\pi$
$433$	6.04143	0.290332	0.145166	+	0.989407i	$0.453628\pi$
$434$	−14.1718	−0.680270
$435$	7.57056	0.362981
$436$	−9.03401	−0.432650
$437$	−16.7644	−0.801950
$438$	−10.6231	−0.507590
$439$	−5.79669	−0.276661	−0.138330	−	0.990386i	$-0.544174\pi$
$439$	−5.79669	−0.276661	−0.138330	+	0.990386i	$0.544174\pi$
$440$	18.9348	0.902682
$441$	5.47117	0.260532
$442$	3.79054	0.180297
$443$	−18.3239	−0.870596	−0.435298	−	0.900287i	$-0.643357\pi$
$443$	−18.3239	−0.870596	−0.435298	+	0.900287i	$0.643357\pi$
$444$	6.75342	0.320503
$445$	2.17704	0.103202
$446$	−17.2677	−0.817651
$447$	−7.85577	−0.371565
$448$	−23.7450	−1.12185
$449$	−30.6524	−1.44658	−0.723289	−	0.690546i	$-0.757370\pi$
$449$	−30.6524	−1.44658	−0.723289	+	0.690546i	$0.757370\pi$
$450$	3.91470	0.184541
$451$	−60.8261	−2.86419
$452$	9.27691	0.436349
$453$	1.61453	0.0758570
$454$	20.7769	0.975109
$455$	−13.7074	−0.642613
$456$	7.73932	0.362427
$457$	−40.9890	−1.91739	−0.958693	−	0.284444i	$-0.908191\pi$
$457$	−40.9890	−1.91739	−0.958693	+	0.284444i	$0.908191\pi$
$458$	18.3518	0.857524
$459$	1.00000	0.0466760
$460$	−6.72893	−0.313738
$461$	29.9443	1.39465	0.697323	−	0.716757i	$-0.254375\pi$
$461$	29.9443	1.39465	0.697323	+	0.716757i	$0.254375\pi$
$462$	−21.9148	−1.01957
$463$	−1.03311	−0.0480129	−0.0240065	−	0.999712i	$-0.507642\pi$
$463$	−1.03311	−0.0480129	−0.0240065	+	0.999712i	$0.507642\pi$
$464$	6.38121	0.296240
$465$	4.10936	0.190567
$466$	1.33154	0.0616822
$467$	−29.8673	−1.38209	−0.691046	−	0.722811i	$-0.742850\pi$
$467$	−29.8673	−1.38209	−0.691046	+	0.722811i	$0.742850\pi$
$468$	−4.01151	−0.185432
$469$	23.3567	1.07851
$470$	4.64097	0.214072
$471$	1.00000	0.0460776
$472$	10.8494	0.499384
$473$	46.4312	2.13491
$474$	−15.9203	−0.731245
$475$	10.3666	0.475653
$476$	−3.66564	−0.168014
$477$	2.16439	0.0991004
$478$	−14.8309	−0.678350
$479$	18.3559	0.838701	0.419350	−	0.907824i	$-0.362258\pi$
$479$	18.3559	0.838701	0.419350	+	0.907824i	$0.362258\pi$
$480$	5.15147	0.235131
$481$	25.1443	1.14648
$482$	−16.1091	−0.733751
$483$	22.7937	1.03715
$484$	−30.1337	−1.36971
$485$	3.95977	0.179804
$486$	0.980818	0.0444908
$487$	6.50618	0.294823	0.147412	−	0.989075i	$-0.452906\pi$
$487$	6.50618	0.294823	0.147412	+	0.989075i	$0.452906\pi$
$488$	21.6797	0.981394
$489$	21.9925	0.994533
$490$	−5.38961	−0.243478
$491$	−34.8722	−1.57376	−0.786880	−	0.617106i	$-0.788305\pi$
$491$	−34.8722	−1.57376	−0.786880	+	0.617106i	$0.788305\pi$
$492$	−9.97905	−0.449890
$493$	7.53770	0.339481
$494$	9.84527	0.442960
$495$	6.35456	0.285616
$496$	3.46377	0.155528
$497$	41.0459	1.84116
$498$	−7.89889	−0.353958
$499$	31.2012	1.39676	0.698379	−	0.715728i	$-0.253905\pi$
$499$	31.2012	1.39676	0.698379	+	0.715728i	$0.253905\pi$
$500$	9.37358	0.419199
$501$	−0.0214142	−0.000956716 0
$502$	−7.00306	−0.312562
$503$	32.9316	1.46835	0.734173	−	0.678963i	$-0.237570\pi$
$503$	32.9316	1.46835	0.734173	+	0.678963i	$0.237570\pi$
$504$	−10.5227	−0.468720
$505$	−12.5306	−0.557604
$506$	−40.0540	−1.78062
$507$	−1.93567	−0.0859660
$508$	−7.50020	−0.332768
$509$	13.7677	0.610243	0.305121	−	0.952313i	$-0.401303\pi$
$509$	13.7677	0.610243	0.305121	+	0.952313i	$0.401303\pi$
$510$	−0.985094	−0.0436207
$511$	38.2486	1.69202
$512$	9.38726	0.414862
$513$	2.59733	0.114675
$514$	8.88319	0.391821
$515$	5.60619	0.247038
$516$	7.61745	0.335340
$517$	−29.8076	−1.31094
$518$	22.5356	0.990160
$519$	−5.93545	−0.260537
$520$	11.5658	0.507196
$521$	10.9548	0.479940	0.239970	−	0.970780i	$-0.422862\pi$
$521$	10.9548	0.479940	0.239970	+	0.970780i	$0.422862\pi$
$522$	7.39311	0.323588
$523$	28.5644	1.24903	0.624516	−	0.781012i	$-0.285296\pi$
$523$	28.5644	1.24903	0.624516	+	0.781012i	$0.285296\pi$
$524$	−15.7975	−0.690118
$525$	−14.0950	−0.615154
$526$	−5.45155	−0.237699
$527$	4.09152	0.178229
$528$	5.35624	0.233101
$529$	18.6603	0.811316
$530$	−2.13212	−0.0926135
$531$	3.64108	0.158009
$532$	−9.52086	−0.412782
$533$	−37.1540	−1.60932
$534$	2.12601	0.0920015
$535$	8.80881	0.380838
$536$	−19.7076	−0.851237
$537$	14.6954	0.634151
$538$	−12.2818	−0.529505
$539$	34.6160	1.49101
$540$	1.04252	0.0448630
$541$	3.26376	0.140320	0.0701599	−	0.997536i	$-0.477649\pi$
$541$	3.26376	0.140320	0.0701599	+	0.997536i	$0.477649\pi$
$542$	−2.33051	−0.100104
$543$	4.11606	0.176637
$544$	5.12911	0.219909
$545$	8.74126	0.374434
$546$	−13.3861	−0.572872
$547$	−15.6784	−0.670361	−0.335180	−	0.942154i	$-0.608797\pi$
$547$	−15.6784	−0.670361	−0.335180	+	0.942154i	$0.608797\pi$
$548$	−18.1218	−0.774124
$549$	7.27575	0.310521
$550$	24.7682	1.05612
$551$	19.5779	0.834046
$552$	−19.2325	−0.818591
$553$	57.3214	2.43756
$554$	20.8481	0.885751
$555$	−6.53457	−0.277377
$556$	−24.0092	−1.01822
$557$	−44.5967	−1.88962	−0.944811	−	0.327615i	$-0.893755\pi$
$557$	−44.5967	−1.88962	−0.944811	+	0.327615i	$0.893755\pi$
$558$	4.01303	0.169885
$559$	28.3613	1.19956
$560$	3.00266	0.126886
$561$	6.32698	0.267125
$562$	8.27041	0.348866
$563$	18.1585	0.765290	0.382645	−	0.923895i	$-0.375013\pi$
$563$	18.1585	0.765290	0.382645	+	0.923895i	$0.375013\pi$
$564$	−4.89020	−0.205915
$565$	−8.97629	−0.377635
$566$	−5.69038	−0.239184
$567$	−3.53145	−0.148307
$568$	−34.6331	−1.45317
$569$	−17.4367	−0.730984	−0.365492	−	0.930814i	$-0.619099\pi$
$569$	−17.4367	−0.730984	−0.365492	+	0.930814i	$0.619099\pi$
$570$	−2.55861	−0.107169
$571$	20.6732	0.865147	0.432574	−	0.901599i	$-0.357606\pi$
$571$	20.6732	0.865147	0.432574	+	0.901599i	$0.357606\pi$
$572$	−25.3807	−1.06122
$573$	7.47583	0.312307
$574$	−33.2993	−1.38989
$575$	−25.7615	−1.07433
$576$	6.72387	0.280161
$577$	−33.5049	−1.39483	−0.697413	−	0.716669i	$-0.745666\pi$
$577$	−33.5049	−1.39483	−0.697413	+	0.716669i	$0.745666\pi$
$578$	−0.980818	−0.0407967
$579$	−2.58077	−0.107253
$580$	7.85822	0.326295
$581$	28.4401	1.17989
$582$	3.86695	0.160290
$583$	13.6940	0.567148
$584$	−32.2728	−1.33546
$585$	3.88152	0.160481
$586$	24.8433	1.02627
$587$	−14.9112	−0.615452	−0.307726	−	0.951475i	$-0.599568\pi$
$587$	−14.9112	−0.615452	−0.307726	+	0.951475i	$0.599568\pi$
$588$	5.67905	0.234200
$589$	10.6270	0.437879
$590$	−3.58681	−0.147666
$591$	20.6346	0.848796
$592$	−5.50798	−0.226376
$593$	−22.1437	−0.909332	−0.454666	−	0.890662i	$-0.650241\pi$
$593$	−22.1437	−0.909332	−0.454666	+	0.890662i	$0.650241\pi$
$594$	6.20562	0.254619
$595$	3.54685	0.145407
$596$	−8.15426	−0.334011
$597$	13.6167	0.557295
$598$	−24.4659	−1.00049
$599$	11.8283	0.483289	0.241645	−	0.970365i	$-0.422313\pi$
$599$	11.8283	0.483289	0.241645	+	0.970365i	$0.422313\pi$
$600$	11.8928	0.485523
$601$	−9.44203	−0.385149	−0.192574	−	0.981282i	$-0.561684\pi$
$601$	−9.44203	−0.385149	−0.192574	+	0.981282i	$0.561684\pi$
$602$	25.4189	1.03599
$603$	−6.61390	−0.269339
$604$	1.67587	0.0681902
$605$	29.1572	1.18541
$606$	−12.2369	−0.497090
$607$	−22.1184	−0.897756	−0.448878	−	0.893593i	$-0.648176\pi$
$607$	−22.1184	−0.897756	−0.448878	+	0.893593i	$0.648176\pi$
$608$	13.3220	0.540278
$609$	−26.6191	−1.07866
$610$	−7.16730	−0.290195
$611$	−18.2072	−0.736585
$612$	1.03800	0.0419585
$613$	−0.434638	−0.0175549	−0.00877744	−	0.999961i	$-0.502794\pi$
$613$	−0.434638	−0.0175549	−0.00877744	+	0.999961i	$0.502794\pi$
$614$	8.67309	0.350017
$615$	9.65568	0.389354
$616$	−66.5772	−2.68247
$617$	−13.4147	−0.540056	−0.270028	−	0.962853i	$-0.587033\pi$
$617$	−13.4147	−0.540056	−0.270028	+	0.962853i	$0.587033\pi$
$618$	5.47478	0.220228
$619$	−38.8737	−1.56246	−0.781232	−	0.624241i	$-0.785409\pi$
$619$	−38.8737	−1.56246	−0.781232	+	0.624241i	$0.785409\pi$
$620$	4.26550	0.171306
$621$	−6.45448	−0.259009
$622$	−10.9278	−0.438164
$623$	−7.65475	−0.306681
$624$	3.27172	0.130974
$625$	10.8865	0.435459
$626$	17.0706	0.682280
$627$	16.4332	0.656281
$628$	1.03800	0.0414206
$629$	−6.50621	−0.259420
$630$	3.47881	0.138599
$631$	−43.6469	−1.73755	−0.868777	−	0.495204i	$-0.835093\pi$
$631$	−43.6469	−1.73755	−0.868777	+	0.495204i	$0.835093\pi$
$632$	−48.3659	−1.92389
$633$	22.0131	0.874942
$634$	−29.9284	−1.18861
$635$	7.25716	0.287991
$636$	2.24662	0.0890844
$637$	21.1442	0.837766
$638$	46.7761	1.85188
$639$	−11.6229	−0.459796
$640$	3.67930	0.145437
$641$	−7.34221	−0.290000	−0.145000	−	0.989432i	$-0.546318\pi$
$641$	−7.34221	−0.290000	−0.145000	+	0.989432i	$0.546318\pi$
$642$	8.60234	0.339507
$643$	1.32896	0.0524089	0.0262044	−	0.999657i	$-0.491658\pi$
$643$	1.32896	0.0524089	0.0262044	+	0.999657i	$0.491658\pi$
$644$	23.6598	0.932325
$645$	−7.37061	−0.290217
$646$	−2.54751	−0.100230
$647$	−30.2272	−1.18835	−0.594177	−	0.804334i	$-0.702522\pi$
$647$	−30.2272	−1.18835	−0.594177	+	0.804334i	$0.702522\pi$
$648$	2.97972	0.117055
$649$	23.0370	0.904283
$650$	15.1290	0.593409
$651$	−14.4490	−0.566301
$652$	22.8281	0.894017
$653$	−42.1752	−1.65044	−0.825222	−	0.564809i	$-0.808950\pi$
$653$	−42.1752	−1.65044	−0.825222	+	0.564809i	$0.808950\pi$
$654$	8.53637	0.333798
$655$	15.2856	0.597258
$656$	8.13874	0.317765
$657$	−10.8308	−0.422551
$658$	−16.3182	−0.636151
$659$	2.87875	0.112140	0.0560701	−	0.998427i	$-0.482143\pi$
$659$	2.87875	0.112140	0.0560701	+	0.998427i	$0.482143\pi$
$660$	6.59601	0.256749
$661$	−4.30998	−0.167639	−0.0838193	−	0.996481i	$-0.526712\pi$
$661$	−4.30998	−0.167639	−0.0838193	+	0.996481i	$0.526712\pi$
$662$	−18.3455	−0.713017
$663$	3.86467	0.150091
$664$	−23.9968	−0.931256
$665$	9.21233	0.357239
$666$	−6.38141	−0.247275
$667$	−48.6519	−1.88381
$668$	−0.0222279	−0.000860022 0
$669$	−17.6054	−0.680666
$670$	6.51531	0.251708
$671$	46.0335	1.77710
$672$	−18.1132	−0.698732
$673$	−36.1438	−1.39324	−0.696620	−	0.717440i	$-0.745314\pi$
$673$	−36.1438	−1.39324	−0.696620	+	0.717440i	$0.745314\pi$
$674$	17.7685	0.684417
$675$	3.99126	0.153624
$676$	−2.00921	−0.0772775
$677$	0.978831	0.0376195	0.0188098	−	0.999823i	$-0.494012\pi$
$677$	0.978831	0.0376195	0.0188098	+	0.999823i	$0.494012\pi$
$678$	−8.76589	−0.336652
$679$	−13.9230	−0.534317
$680$	−2.99271	−0.114765
$681$	21.1832	0.811744
$682$	25.3904	0.972248
$683$	−20.5167	−0.785048	−0.392524	−	0.919742i	$-0.628398\pi$
$683$	−20.5167	−0.785048	−0.392524	+	0.919742i	$0.628398\pi$
$684$	2.69602	0.103085
$685$	17.5345	0.669960
$686$	−5.29544	−0.202181
$687$	18.7107	0.713859
$688$	−6.21266	−0.236856
$689$	8.36463	0.318667
$690$	6.35827	0.242055
$691$	8.25164	0.313907	0.156954	−	0.987606i	$-0.449833\pi$
$691$	8.25164	0.313907	0.156954	+	0.987606i	$0.449833\pi$
$692$	−6.16097	−0.234205
$693$	−22.3434	−0.848757
$694$	12.3021	0.466980
$695$	23.2312	0.881210
$696$	22.4603	0.851354
$697$	9.61376	0.364147
$698$	6.41786	0.242920
$699$	1.35758	0.0513483
$700$	−14.6305	−0.552981
$701$	−10.3876	−0.392333	−0.196166	−	0.980571i	$-0.562849\pi$
$701$	−10.3876	−0.392333	−0.196166	+	0.980571i	$0.562849\pi$
$702$	3.79054	0.143065
$703$	−16.8988	−0.637349
$704$	42.5418	1.60335
$705$	4.73173	0.178207
$706$	−7.59584	−0.285873
$707$	44.0592	1.65701
$708$	3.77943	0.142040
$709$	−7.12066	−0.267422	−0.133711	−	0.991020i	$-0.542689\pi$
$709$	−7.12066	−0.267422	−0.133711	+	0.991020i	$0.542689\pi$
$710$	11.4497	0.429699
$711$	−16.2317	−0.608736
$712$	6.45882	0.242054
$713$	−26.4086	−0.989010
$714$	3.46371	0.129626
$715$	24.5583	0.918428
$716$	15.2537	0.570058
$717$	−15.1210	−0.564703
$718$	5.68947	0.212329
$719$	23.3538	0.870948	0.435474	−	0.900201i	$-0.356581\pi$
$719$	23.3538	0.870948	0.435474	+	0.900201i	$0.356581\pi$
$720$	−0.850263	−0.0316874
$721$	−19.7121	−0.734116
$722$	12.0188	0.447295
$723$	−16.4242	−0.610822
$724$	4.27246	0.158785
$725$	30.0849	1.11733
$726$	28.4738	1.05676
$727$	23.5558	0.873636	0.436818	−	0.899550i	$-0.356105\pi$
$727$	23.5558	0.873636	0.436818	+	0.899550i	$0.356105\pi$
$728$	−40.6669	−1.50722
$729$	1.00000	0.0370370
$730$	10.6694	0.394891
$731$	−7.33861	−0.271428
$732$	7.55220	0.279137
$733$	−17.3075	−0.639266	−0.319633	−	0.947541i	$-0.603560\pi$
$733$	−17.3075	−0.639266	−0.319633	+	0.947541i	$0.603560\pi$
$734$	8.85647	0.326898
$735$	−5.49502	−0.202687
$736$	−33.1057	−1.22029
$737$	−41.8460	−1.54142
$738$	9.42935	0.347099
$739$	35.2270	1.29584	0.647922	−	0.761706i	$-0.275638\pi$
$739$	35.2270	1.29584	0.647922	+	0.761706i	$0.275638\pi$
$740$	−6.78286	−0.249343
$741$	10.0378	0.368748
$742$	7.49681	0.275217
$743$	30.3847	1.11471	0.557353	−	0.830275i	$-0.311817\pi$
$743$	30.3847	1.11471	0.557353	+	0.830275i	$0.311817\pi$
$744$	12.1916	0.446965
$745$	7.89002	0.289068
$746$	1.13147	0.0414260
$747$	−8.05337	−0.294657
$748$	6.56738	0.240127
$749$	−30.9729	−1.13172
$750$	−8.85724	−0.323421
$751$	−22.9662	−0.838047	−0.419024	−	0.907975i	$-0.637628\pi$
$751$	−22.9662	−0.838047	−0.419024	+	0.907975i	$0.637628\pi$
$752$	3.98837	0.145441
$753$	−7.14002	−0.260197
$754$	28.5719	1.04053
$755$	−1.62156	−0.0590148
$756$	−3.66564	−0.133318
$757$	−52.4501	−1.90633	−0.953165	−	0.302451i	$-0.902195\pi$
$757$	−52.4501	−1.90633	−0.953165	+	0.302451i	$0.902195\pi$
$758$	−17.8991	−0.650123
$759$	−40.8373	−1.48230
$760$	−7.77306	−0.281958
$761$	21.3685	0.774609	0.387304	−	0.921952i	$-0.373406\pi$
$761$	21.3685	0.774609	0.387304	+	0.921952i	$0.373406\pi$
$762$	7.08705	0.256737
$763$	−30.7354	−1.11269
$764$	7.75988	0.280743
$765$	−1.00436	−0.0363127
$766$	23.1401	0.836086
$767$	14.0716	0.508095
$768$	17.0408	0.614907
$769$	6.12609	0.220913	0.110456	−	0.993881i	$-0.464769\pi$
$769$	6.12609	0.220913	0.110456	+	0.993881i	$0.464769\pi$
$770$	22.0104	0.793199
$771$	9.05691	0.326177
$772$	−2.67883	−0.0964131
$773$	−6.32525	−0.227504	−0.113752	−	0.993509i	$-0.536287\pi$
$773$	−6.32525	−0.227504	−0.113752	+	0.993509i	$0.536287\pi$
$774$	−7.19784	−0.258721
$775$	16.3303	0.586602
$776$	11.7478	0.421721
$777$	22.9764	0.824273
$778$	−13.6065	−0.487818
$779$	24.9701	0.894647
$780$	4.02900	0.144261
$781$	−73.5381	−2.63140
$782$	6.33067	0.226384
$783$	7.53770	0.269376
$784$	−4.63174	−0.165419
$785$	−1.00436	−0.0358471
$786$	14.9273	0.532440
$787$	26.4440	0.942626	0.471313	−	0.881966i	$-0.343780\pi$
$787$	26.4440	0.942626	0.471313	+	0.881966i	$0.343780\pi$
$788$	21.4187	0.763009
$789$	−5.55816	−0.197876
$790$	15.9897	0.568889
$791$	31.5617	1.12221
$792$	18.8526	0.669899
$793$	28.1184	0.998512
$794$	−19.4954	−0.691866
$795$	−2.17382	−0.0770975
$796$	14.1341	0.500970
$797$	−44.0474	−1.56024	−0.780119	−	0.625631i	$-0.784841\pi$
$797$	−44.0474	−1.56024	−0.780119	+	0.625631i	$0.784841\pi$
$798$	8.99640	0.318469
$799$	4.71120	0.166670
$800$	20.4716	0.723781
$801$	2.16759	0.0765881
$802$	22.6939	0.801351
$803$	−68.5264	−2.41824
$804$	−6.86520	−0.242117
$805$	−22.8931	−0.806874
$806$	15.5091	0.546283
$807$	−12.5220	−0.440794
$808$	−37.1756	−1.30783
$809$	−2.28286	−0.0802612	−0.0401306	−	0.999194i	$-0.512777\pi$
$809$	−2.28286	−0.0802612	−0.0401306	+	0.999194i	$0.512777\pi$
$810$	−0.985094	−0.0346127
$811$	30.9797	1.08784	0.543922	−	0.839136i	$-0.316939\pi$
$811$	30.9797	1.08784	0.543922	+	0.839136i	$0.316939\pi$
$812$	−27.6305	−0.969639
$813$	−2.37609	−0.0833332
$814$	−40.3750	−1.41514
$815$	−22.0883	−0.773721
$816$	−0.846572	−0.0296360
$817$	−19.0608	−0.666853
$818$	−30.1157	−1.05297
$819$	−13.6479	−0.476896
$820$	10.0226	0.350003
$821$	14.3457	0.500669	0.250334	−	0.968159i	$-0.419459\pi$
$821$	14.3457	0.500669	0.250334	+	0.968159i	$0.419459\pi$
$822$	17.1235	0.597252
$823$	−17.0771	−0.595272	−0.297636	−	0.954679i	$-0.596198\pi$
$823$	−17.0771	−0.595272	−0.297636	+	0.954679i	$0.596198\pi$
$824$	16.6324	0.579416
$825$	25.2526	0.879184
$826$	12.6117	0.438816
$827$	17.7657	0.617774	0.308887	−	0.951099i	$-0.400043\pi$
$827$	17.7657	0.617774	0.308887	+	0.951099i	$0.400043\pi$
$828$	−6.69972	−0.232831
$829$	54.5361	1.89412	0.947058	−	0.321063i	$-0.104040\pi$
$829$	54.5361	1.89412	0.947058	+	0.321063i	$0.104040\pi$
$830$	7.93332	0.275370
$831$	21.2558	0.737356
$832$	25.9855	0.900886
$833$	−5.47117	−0.189565
$834$	22.6867	0.785576
$835$	0.0215076	0.000744300 0
$836$	17.0576	0.589951
$837$	4.09152	0.141424
$838$	−26.9539	−0.931106
$839$	−8.42316	−0.290800	−0.145400	−	0.989373i	$-0.546447\pi$
$839$	−8.42316	−0.290800	−0.145400	+	0.989373i	$0.546447\pi$
$840$	10.5686	0.364652
$841$	27.8170	0.959206
$842$	32.0375	1.10409
$843$	8.43216	0.290419
$844$	22.8495	0.786512
$845$	1.94411	0.0668793
$846$	4.62082	0.158867
$847$	−102.520	−3.52264
$848$	−1.83231	−0.0629217
$849$	−5.80167	−0.199113
$850$	−3.91470	−0.134273
$851$	41.9942	1.43954
$852$	−12.0646	−0.413325
$853$	−26.0950	−0.893476	−0.446738	−	0.894665i	$-0.647414\pi$
$853$	−26.0950	−0.893476	−0.446738	+	0.894665i	$0.647414\pi$
$854$	25.2011	0.862364
$855$	−2.60865	−0.0892140
$856$	26.1339	0.893237
$857$	−36.1183	−1.23378	−0.616889	−	0.787051i	$-0.711607\pi$
$857$	−36.1183	−1.23378	−0.616889	+	0.787051i	$0.711607\pi$
$858$	23.9826	0.818754
$859$	−16.6305	−0.567425	−0.283712	−	0.958909i	$-0.591566\pi$
$859$	−16.6305	−0.567425	−0.283712	+	0.958909i	$0.591566\pi$
$860$	−7.65066	−0.260885
$861$	−33.9506	−1.15703
$862$	0.408859	0.0139258
$863$	25.9834	0.884485	0.442243	−	0.896895i	$-0.354183\pi$
$863$	25.9834	0.884485	0.442243	+	0.896895i	$0.354183\pi$
$864$	5.12911	0.174496
$865$	5.96132	0.202691
$866$	−5.92554	−0.201358
$867$	−1.00000	−0.0339618
$868$	−14.9980	−0.509066
$869$	−102.698	−3.48377
$870$	−7.42535	−0.251743
$871$	−25.5605	−0.866085
$872$	25.9335	0.878218
$873$	3.94258	0.133436
$874$	16.4428	0.556187
$875$	31.8907	1.07810
$876$	−11.2424	−0.379844
$877$	3.16815	0.106981	0.0534904	−	0.998568i	$-0.482965\pi$
$877$	3.16815	0.106981	0.0534904	+	0.998568i	$0.482965\pi$
$878$	5.68550	0.191876
$879$	25.3292	0.854333
$880$	−5.37960	−0.181346
$881$	−42.5202	−1.43254	−0.716271	−	0.697822i	$-0.754153\pi$
$881$	−42.5202	−1.43254	−0.716271	+	0.697822i	$0.754153\pi$
$882$	−5.36622	−0.180690
$883$	−37.8272	−1.27299	−0.636493	−	0.771283i	$-0.719616\pi$
$883$	−37.8272	−1.27299	−0.636493	+	0.771283i	$0.719616\pi$
$884$	4.01151	0.134922
$885$	−3.65695	−0.122927
$886$	17.9724	0.603796
$887$	1.25871	0.0422633	0.0211317	−	0.999777i	$-0.493273\pi$
$887$	1.25871	0.0422633	0.0211317	+	0.999777i	$0.493273\pi$
$888$	−19.3867	−0.650575
$889$	−25.5171	−0.855815
$890$	−2.13528	−0.0715748
$891$	6.32698	0.211962
$892$	−18.2744	−0.611872
$893$	12.2365	0.409480
$894$	7.70508	0.257696
$895$	−14.7594	−0.493353
$896$	−12.9369	−0.432191
$897$	−24.9444	−0.832870
$898$	30.0645	1.00326
$899$	30.8406	1.02859
$900$	4.14291	0.138097
$901$	−2.16439	−0.0721061
$902$	59.6593	1.98644
$903$	25.9160	0.862429
$904$	−26.6307	−0.885725
$905$	−4.13401	−0.137419
$906$	−1.58356	−0.0526101
$907$	0.600796	0.0199491	0.00997455	−	0.999950i	$-0.496825\pi$
$907$	0.600796	0.0199491	0.00997455	+	0.999950i	$0.496825\pi$
$908$	21.9881	0.729702
$909$	−12.4762	−0.413810
$910$	13.4445	0.445680
$911$	45.7317	1.51516	0.757580	−	0.652743i	$-0.226382\pi$
$911$	45.7317	1.51516	0.757580	+	0.652743i	$0.226382\pi$
$912$	−2.19883	−0.0728104
$913$	−50.9535	−1.68631
$914$	40.2028	1.32979
$915$	−7.30747	−0.241577
$916$	19.4217	0.641710
$917$	−53.7461	−1.77485
$918$	−0.980818	−0.0323718
$919$	8.86669	0.292485	0.146243	−	0.989249i	$-0.453282\pi$
$919$	8.86669	0.292485	0.146243	+	0.989249i	$0.453282\pi$
$920$	19.3164	0.636842
$921$	8.84271	0.291377
$922$	−29.3699	−0.967246
$923$	−44.9188	−1.47852
$924$	−23.1924	−0.762974
$925$	−25.9680	−0.853822
$926$	1.01330	0.0332990
$927$	5.58186	0.183332
$928$	38.6617	1.26913
$929$	14.2950	0.469004	0.234502	−	0.972116i	$-0.424654\pi$
$929$	14.2950	0.469004	0.234502	+	0.972116i	$0.424654\pi$
$930$	−4.03053	−0.132166
$931$	−14.2104	−0.465728
$932$	1.40916	0.0461586
$933$	−11.1415	−0.364756
$934$	29.2944	0.958541
$935$	−6.35456	−0.207816
$936$	11.5156	0.376400
$937$	10.1695	0.332222	0.166111	−	0.986107i	$-0.446879\pi$
$937$	10.1695	0.332222	0.166111	+	0.986107i	$0.446879\pi$
$938$	−22.9086	−0.747994
$939$	17.4045	0.567974
$940$	4.91152	0.160196
$941$	53.2669	1.73645	0.868225	−	0.496170i	$-0.165261\pi$
$941$	53.2669	1.73645	0.868225	+	0.496170i	$0.165261\pi$
$942$	−0.980818	−0.0319568
$943$	−62.0518	−2.02068
$944$	−3.08244	−0.100325
$945$	3.54685	0.115379
$946$	−45.5406	−1.48065
$947$	−6.12953	−0.199183	−0.0995915	−	0.995028i	$-0.531754\pi$
$947$	−6.12953	−0.199183	−0.0995915	+	0.995028i	$0.531754\pi$
$948$	−16.8484	−0.547211
$949$	−41.8575	−1.35875
$950$	−10.1678	−0.329886
$951$	−30.5137	−0.989474
$952$	10.5227	0.341044
$953$	20.2026	0.654426	0.327213	−	0.944951i	$-0.393890\pi$
$953$	20.2026	0.654426	0.327213	+	0.944951i	$0.393890\pi$
$954$	−2.12287	−0.0687304
$955$	−7.50842	−0.242967
$956$	−15.6955	−0.507629
$957$	47.6909	1.54163
$958$	−18.0038	−0.581675
$959$	−61.6536	−1.99090
$960$	−6.75318	−0.217958
$961$	−14.2595	−0.459983
$962$	−24.6620	−0.795136
$963$	8.77058	0.282628
$964$	−17.0482	−0.549087
$965$	2.59202	0.0834401
$966$	−22.3565	−0.719307
$967$	51.5095	1.65644	0.828218	−	0.560407i	$-0.189355\pi$
$967$	51.5095	1.65644	0.828218	+	0.560407i	$0.189355\pi$
$968$	86.5033	2.78032
$969$	−2.59733	−0.0834382
$970$	−3.88381	−0.124702
$971$	4.84236	0.155399	0.0776993	−	0.996977i	$-0.475243\pi$
$971$	4.84236	0.155399	0.0776993	+	0.996977i	$0.475243\pi$
$972$	1.03800	0.0332937
$973$	−81.6839	−2.61866
$974$	−6.38138	−0.204473
$975$	15.4249	0.493992
$976$	−6.15945	−0.197159
$977$	8.04118	0.257260	0.128630	−	0.991693i	$-0.458942\pi$
$977$	8.04118	0.257260	0.128630	+	0.991693i	$0.458942\pi$
$978$	−21.5706	−0.689752
$979$	13.7143	0.438311
$980$	−5.70381	−0.182201
$981$	8.70332	0.277875
$982$	34.2033	1.09147
$983$	58.1175	1.85366	0.926830	−	0.375481i	$-0.122523\pi$
$983$	58.1175	1.85366	0.926830	+	0.375481i	$0.122523\pi$
$984$	28.6463	0.913212
$985$	−20.7246	−0.660341
$986$	−7.39311	−0.235445
$987$	−16.6374	−0.529573
$988$	10.4192	0.331479
$989$	47.3669	1.50618
$990$	−6.23267	−0.198087
$991$	−53.8212	−1.70969	−0.854843	−	0.518887i	$-0.826347\pi$
$991$	−53.8212	−1.70969	−0.854843	+	0.518887i	$0.826347\pi$
$992$	20.9858	0.666301
$993$	−18.7043	−0.593562
$994$	−40.2585	−1.27692
$995$	−13.6761	−0.433561
$996$	−8.35936	−0.264877
$997$	−46.4864	−1.47224	−0.736119	−	0.676852i	$-0.763344\pi$
$997$	−46.4864	−1.47224	−0.736119	+	0.676852i	$0.763344\pi$
$998$	−30.6027	−0.968712
$999$	−6.50621	−0.205847

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.f.1.17	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.f.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-0.980818 q^{2} -1.00000 q^{3} -1.03800 q^{4} +1.00436 q^{5} +0.980818 q^{6} -3.53145 q^{7} +2.97972 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.980818 q^{2} -1.00000 q^{3} -1.03800 q^{4} +1.00436 q^{5} +0.980818 q^{6} -3.53145 q^{7} +2.97972 q^{8} +1.00000 q^{9} -0.985094 q^{10} +6.32698 q^{11} +1.03800 q^{12} +3.86467 q^{13} +3.46371 q^{14} -1.00436 q^{15} -0.846572 q^{16} -1.00000 q^{17} -0.980818 q^{18} -2.59733 q^{19} -1.04252 q^{20} +3.53145 q^{21} -6.20562 q^{22} +6.45448 q^{23} -2.97972 q^{24} -3.99126 q^{25} -3.79054 q^{26} -1.00000 q^{27} +3.66564 q^{28} -7.53770 q^{29} +0.985094 q^{30} -4.09152 q^{31} -5.12911 q^{32} -6.32698 q^{33} +0.980818 q^{34} -3.54685 q^{35} -1.03800 q^{36} +6.50621 q^{37} +2.54751 q^{38} -3.86467 q^{39} +2.99271 q^{40} -9.61376 q^{41} -3.46371 q^{42} +7.33861 q^{43} -6.56738 q^{44} +1.00436 q^{45} -6.33067 q^{46} -4.71120 q^{47} +0.846572 q^{48} +5.47117 q^{49} +3.91470 q^{50} +1.00000 q^{51} -4.01151 q^{52} +2.16439 q^{53} +0.980818 q^{54} +6.35456 q^{55} -10.5227 q^{56} +2.59733 q^{57} +7.39311 q^{58} +3.64108 q^{59} +1.04252 q^{60} +7.27575 q^{61} +4.01303 q^{62} -3.53145 q^{63} +6.72387 q^{64} +3.88152 q^{65} +6.20562 q^{66} -6.61390 q^{67} +1.03800 q^{68} -6.45448 q^{69} +3.47881 q^{70} -11.6229 q^{71} +2.97972 q^{72} -10.8308 q^{73} -6.38141 q^{74} +3.99126 q^{75} +2.69602 q^{76} -22.3434 q^{77} +3.79054 q^{78} -16.2317 q^{79} -0.850263 q^{80} +1.00000 q^{81} +9.42935 q^{82} -8.05337 q^{83} -3.66564 q^{84} -1.00436 q^{85} -7.19784 q^{86} +7.53770 q^{87} +18.8526 q^{88} +2.16759 q^{89} -0.985094 q^{90} -13.6479 q^{91} -6.69972 q^{92} +4.09152 q^{93} +4.62082 q^{94} -2.60865 q^{95} +5.12911 q^{96} +3.94258 q^{97} -5.36622 q^{98} +6.32698 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9}+O(q^{10}) \) 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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