LMFDB - Embedded newform 8005.2.a.f.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8005,2,Mod(1,8005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8005, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8005 = 5 \cdot 1601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8005.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:	$63.9202468180$
Analytic rank:	$1$
Dimension:	$127$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.42159 q^{2} +1.03210 q^{3} +3.86412 q^{4} -1.00000 q^{5} -2.49933 q^{6} -3.82183 q^{7} -4.51414 q^{8} -1.93477 q^{9} +O(q^{10})$	\(q-2.42159 q^{2} +1.03210 q^{3} +3.86412 q^{4} -1.00000 q^{5} -2.49933 q^{6} -3.82183 q^{7} -4.51414 q^{8} -1.93477 q^{9} +2.42159 q^{10} -4.68195 q^{11} +3.98816 q^{12} -5.13539 q^{13} +9.25493 q^{14} -1.03210 q^{15} +3.20318 q^{16} +4.11352 q^{17} +4.68523 q^{18} +2.79842 q^{19} -3.86412 q^{20} -3.94451 q^{21} +11.3378 q^{22} +2.09332 q^{23} -4.65904 q^{24} +1.00000 q^{25} +12.4358 q^{26} -5.09318 q^{27} -14.7680 q^{28} -0.178067 q^{29} +2.49933 q^{30} +1.79272 q^{31} +1.27148 q^{32} -4.83224 q^{33} -9.96128 q^{34} +3.82183 q^{35} -7.47618 q^{36} +9.36570 q^{37} -6.77665 q^{38} -5.30024 q^{39} +4.51414 q^{40} +10.1797 q^{41} +9.55201 q^{42} +5.87953 q^{43} -18.0916 q^{44} +1.93477 q^{45} -5.06916 q^{46} -3.17309 q^{47} +3.30600 q^{48} +7.60640 q^{49} -2.42159 q^{50} +4.24556 q^{51} -19.8438 q^{52} +3.45246 q^{53} +12.3336 q^{54} +4.68195 q^{55} +17.2523 q^{56} +2.88825 q^{57} +0.431206 q^{58} -12.9276 q^{59} -3.98816 q^{60} -4.03068 q^{61} -4.34125 q^{62} +7.39437 q^{63} -9.48537 q^{64} +5.13539 q^{65} +11.7017 q^{66} -4.08545 q^{67} +15.8951 q^{68} +2.16051 q^{69} -9.25493 q^{70} +0.315197 q^{71} +8.73382 q^{72} +15.1087 q^{73} -22.6799 q^{74} +1.03210 q^{75} +10.8134 q^{76} +17.8936 q^{77} +12.8350 q^{78} -8.71294 q^{79} -3.20318 q^{80} +0.547644 q^{81} -24.6511 q^{82} -5.99337 q^{83} -15.2421 q^{84} -4.11352 q^{85} -14.2378 q^{86} -0.183783 q^{87} +21.1350 q^{88} +5.80828 q^{89} -4.68523 q^{90} +19.6266 q^{91} +8.08882 q^{92} +1.85027 q^{93} +7.68394 q^{94} -2.79842 q^{95} +1.31229 q^{96} +7.99784 q^{97} -18.4196 q^{98} +9.05850 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 127 q - 6 q^{2} - 18 q^{3} + 114 q^{4} - 127 q^{5} - 20 q^{6} + 28 q^{7} - 18 q^{8} + 101 q^{9}+O(q^{10}) $ 127 * q - 6 * q^2 - 18 * q^3 + 114 * q^4 - 127 * q^5 - 20 * q^6 + 28 * q^7 - 18 * q^8 + 101 * q^9	\( 127 q - 6 q^{2} - 18 q^{3} + 114 q^{4} - 127 q^{5} - 20 q^{6} + 28 q^{7} - 18 q^{8} + 101 q^{9} + 6 q^{10} - 45 q^{11} - 30 q^{12} - 53 q^{14} + 18 q^{15} + 84 q^{16} - 36 q^{17} - 10 q^{18} - 49 q^{19} - 114 q^{20} - 48 q^{21} + 13 q^{22} - 29 q^{23} - 63 q^{24} + 127 q^{25} - 55 q^{26} - 75 q^{27} + 44 q^{28} - 45 q^{29} + 20 q^{30} - 49 q^{31} - 32 q^{32} - 8 q^{33} - 52 q^{34} - 28 q^{35} + 44 q^{36} + 36 q^{37} - 65 q^{38} - 52 q^{39} + 18 q^{40} - 66 q^{41} - 18 q^{42} - 5 q^{43} - 93 q^{44} - 101 q^{45} - 25 q^{46} - 32 q^{47} - 54 q^{48} + 77 q^{49} - 6 q^{50} - 102 q^{51} - 13 q^{52} - 67 q^{53} - 53 q^{54} + 45 q^{55} - 158 q^{56} + 16 q^{57} + 35 q^{58} - 213 q^{59} + 30 q^{60} - 62 q^{61} - 33 q^{62} + 59 q^{63} + 34 q^{64} - 60 q^{66} + 10 q^{67} - 94 q^{68} - 93 q^{69} + 53 q^{70} - 118 q^{71} - 24 q^{72} + 35 q^{73} - 107 q^{74} - 18 q^{75} - 98 q^{76} - 93 q^{77} + 21 q^{78} - 64 q^{79} - 84 q^{80} + 15 q^{81} + 15 q^{82} - 187 q^{83} - 118 q^{84} + 36 q^{85} - 126 q^{86} - 53 q^{87} + 15 q^{88} - 138 q^{89} + 10 q^{90} - 138 q^{91} - 86 q^{92} + 23 q^{93} - 60 q^{94} + 49 q^{95} - 92 q^{96} + 9 q^{97} - 67 q^{98} - 147 q^{99}+O(q^{100}) \) 127 * q - 6 * q^2 - 18 * q^3 + 114 * q^4 - 127 * q^5 - 20 * q^6 + 28 * q^7 - 18 * q^8 + 101 * q^9 + 6 * q^10 - 45 * q^11 - 30 * q^12 - 53 * q^14 + 18 * q^15 + 84 * q^16 - 36 * q^17 - 10 * q^18 - 49 * q^19 - 114 * q^20 - 48 * q^21 + 13 * q^22 - 29 * q^23 - 63 * q^24 + 127 * q^25 - 55 * q^26 - 75 * q^27 + 44 * q^28 - 45 * q^29 + 20 * q^30 - 49 * q^31 - 32 * q^32 - 8 * q^33 - 52 * q^34 - 28 * q^35 + 44 * q^36 + 36 * q^37 - 65 * q^38 - 52 * q^39 + 18 * q^40 - 66 * q^41 - 18 * q^42 - 5 * q^43 - 93 * q^44 - 101 * q^45 - 25 * q^46 - 32 * q^47 - 54 * q^48 + 77 * q^49 - 6 * q^50 - 102 * q^51 - 13 * q^52 - 67 * q^53 - 53 * q^54 + 45 * q^55 - 158 * q^56 + 16 * q^57 + 35 * q^58 - 213 * q^59 + 30 * q^60 - 62 * q^61 - 33 * q^62 + 59 * q^63 + 34 * q^64 - 60 * q^66 + 10 * q^67 - 94 * q^68 - 93 * q^69 + 53 * q^70 - 118 * q^71 - 24 * q^72 + 35 * q^73 - 107 * q^74 - 18 * q^75 - 98 * q^76 - 93 * q^77 + 21 * q^78 - 64 * q^79 - 84 * q^80 + 15 * q^81 + 15 * q^82 - 187 * q^83 - 118 * q^84 + 36 * q^85 - 126 * q^86 - 53 * q^87 + 15 * q^88 - 138 * q^89 + 10 * q^90 - 138 * q^91 - 86 * q^92 + 23 * q^93 - 60 * q^94 + 49 * q^95 - 92 * q^96 + 9 * q^97 - 67 * q^98 - 147 * 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 $

$2$	−2.42159	−1.71233	−0.856163	−	0.516706i	$-0.827158\pi$
$2$	−2.42159	−1.71233	−0.856163	+	0.516706i	$0.827158\pi$
$3$	1.03210	0.595883	0.297942	−	0.954584i	$-0.403700\pi$
$3$	1.03210	0.595883	0.297942	+	0.954584i	$0.403700\pi$
$4$	3.86412	1.93206
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.49933	−1.02035
$7$	−3.82183	−1.44452	−0.722258	−	0.691623i	$-0.756896\pi$
$7$	−3.82183	−1.44452	−0.722258	+	0.691623i	$0.756896\pi$
$8$	−4.51414	−1.59599
$9$	−1.93477	−0.644923
$10$	2.42159	0.765775
$11$	−4.68195	−1.41166	−0.705831	−	0.708380i	$-0.749426\pi$
$11$	−4.68195	−1.41166	−0.705831	+	0.708380i	$0.749426\pi$
$12$	3.98816	1.15128
$13$	−5.13539	−1.42430	−0.712151	−	0.702026i	$-0.752279\pi$
$13$	−5.13539	−1.42430	−0.712151	+	0.702026i	$0.752279\pi$
$14$	9.25493	2.47348
$15$	−1.03210	−0.266487
$16$	3.20318	0.800795
$17$	4.11352	0.997675	0.498838	−	0.866696i	$-0.333760\pi$
$17$	4.11352	0.997675	0.498838	+	0.866696i	$0.333760\pi$
$18$	4.68523	1.10432
$19$	2.79842	0.642003	0.321001	−	0.947079i	$-0.395981\pi$
$19$	2.79842	0.642003	0.321001	+	0.947079i	$0.395981\pi$
$20$	−3.86412	−0.864043
$21$	−3.94451	−0.860763
$22$	11.3378	2.41723
$23$	2.09332	0.436487	0.218243	−	0.975894i	$-0.429967\pi$
$23$	2.09332	0.436487	0.218243	+	0.975894i	$0.429967\pi$
$24$	−4.65904	−0.951023
$25$	1.00000	0.200000
$26$	12.4358	2.43887
$27$	−5.09318	−0.980182
$28$	−14.7680	−2.79089
$29$	−0.178067	−0.0330662	−0.0165331	−	0.999863i	$-0.505263\pi$
$29$	−0.178067	−0.0330662	−0.0165331	+	0.999863i	$0.505263\pi$
$30$	2.49933	0.456313
$31$	1.79272	0.321983	0.160991	−	0.986956i	$-0.448531\pi$
$31$	1.79272	0.321983	0.160991	+	0.986956i	$0.448531\pi$
$32$	1.27148	0.224768
$33$	−4.83224	−0.841185
$34$	−9.96128	−1.70834
$35$	3.82183	0.646008
$36$	−7.47618	−1.24603
$37$	9.36570	1.53971	0.769856	−	0.638218i	$-0.220328\pi$
$37$	9.36570	1.53971	0.769856	+	0.638218i	$0.220328\pi$
$38$	−6.77665	−1.09932
$39$	−5.30024	−0.848718
$40$	4.51414	0.713748
$41$	10.1797	1.58980	0.794900	−	0.606741i	$-0.207523\pi$
$41$	10.1797	1.58980	0.794900	+	0.606741i	$0.207523\pi$
$42$	9.55201	1.47391
$43$	5.87953	0.896619	0.448310	−	0.893878i	$-0.352026\pi$
$43$	5.87953	0.896619	0.448310	+	0.893878i	$0.352026\pi$
$44$	−18.0916	−2.72742
$45$	1.93477	0.288418
$46$	−5.06916	−0.747407
$47$	−3.17309	−0.462843	−0.231421	−	0.972854i	$-0.574338\pi$
$47$	−3.17309	−0.462843	−0.231421	+	0.972854i	$0.574338\pi$
$48$	3.30600	0.477180
$49$	7.60640	1.08663
$50$	−2.42159	−0.342465
$51$	4.24556	0.594498
$52$	−19.8438	−2.75184
$53$	3.45246	0.474232	0.237116	−	0.971481i	$-0.423798\pi$
$53$	3.45246	0.474232	0.237116	+	0.971481i	$0.423798\pi$
$54$	12.3336	1.67839
$55$	4.68195	0.631314
$56$	17.2523	2.30543
$57$	2.88825	0.382559
$58$	0.431206	0.0566202
$59$	−12.9276	−1.68304	−0.841518	−	0.540229i	$-0.818337\pi$
$59$	−12.9276	−1.68304	−0.841518	+	0.540229i	$0.818337\pi$
$60$	−3.98816	−0.514869
$61$	−4.03068	−0.516076	−0.258038	−	0.966135i	$-0.583076\pi$
$61$	−4.03068	−0.516076	−0.258038	+	0.966135i	$0.583076\pi$
$62$	−4.34125	−0.551339
$63$	7.39437	0.931602
$64$	−9.48537	−1.18567
$65$	5.13539	0.636967
$66$	11.7017	1.44038
$67$	−4.08545	−0.499117	−0.249559	−	0.968360i	$-0.580286\pi$
$67$	−4.08545	−0.499117	−0.249559	+	0.968360i	$0.580286\pi$
$68$	15.8951	1.92757
$69$	2.16051	0.260095
$70$	−9.25493	−1.10618
$71$	0.315197	0.0374070	0.0187035	−	0.999825i	$-0.494046\pi$
$71$	0.315197	0.0374070	0.0187035	+	0.999825i	$0.494046\pi$
$72$	8.73382	1.02929
$73$	15.1087	1.76833	0.884167	−	0.467171i	$-0.154727\pi$
$73$	15.1087	1.76833	0.884167	+	0.467171i	$0.154727\pi$
$74$	−22.6799	−2.63649
$75$	1.03210	0.119177
$76$	10.8134	1.24039
$77$	17.8936	2.03917
$78$	12.8350	1.45328
$79$	−8.71294	−0.980282	−0.490141	−	0.871643i	$-0.663055\pi$
$79$	−8.71294	−0.980282	−0.490141	+	0.871643i	$0.663055\pi$
$80$	−3.20318	−0.358126
$81$	0.547644	0.0608494
$82$	−24.6511	−2.72226
$83$	−5.99337	−0.657858	−0.328929	−	0.944355i	$-0.606688\pi$
$83$	−5.99337	−0.657858	−0.328929	+	0.944355i	$0.606688\pi$
$84$	−15.2421	−1.66305
$85$	−4.11352	−0.446174
$86$	−14.2378	−1.53530
$87$	−0.183783	−0.0197036
$88$	21.1350	2.25300
$89$	5.80828	0.615676	0.307838	−	0.951439i	$-0.400394\pi$
$89$	5.80828	0.615676	0.307838	+	0.951439i	$0.400394\pi$
$90$	−4.68523	−0.493866
$91$	19.6266	2.05743
$92$	8.08882	0.843318
$93$	1.85027	0.191864
$94$	7.68394	0.792538
$95$	−2.79842	−0.287112
$96$	1.31229	0.133935
$97$	7.99784	0.812058	0.406029	−	0.913860i	$-0.366913\pi$
$97$	7.99784	0.812058	0.406029	+	0.913860i	$0.366913\pi$
$98$	−18.4196	−1.86066
$99$	9.05850	0.910414
$100$	3.86412	0.386412
$101$	10.6016	1.05490	0.527450	−	0.849586i	$-0.323148\pi$
$101$	10.6016	1.05490	0.527450	+	0.849586i	$0.323148\pi$
$102$	−10.2810	−1.01797
$103$	13.6122	1.34125	0.670626	−	0.741795i	$-0.266025\pi$
$103$	13.6122	1.34125	0.670626	+	0.741795i	$0.266025\pi$
$104$	23.1819	2.27317
$105$	3.94451	0.384945
$106$	−8.36046	−0.812040
$107$	−2.46835	−0.238625	−0.119312	−	0.992857i	$-0.538069\pi$
$107$	−2.46835	−0.238625	−0.119312	+	0.992857i	$0.538069\pi$
$108$	−19.6806	−1.89377
$109$	15.7333	1.50697	0.753486	−	0.657464i	$-0.228371\pi$
$109$	15.7333	1.50697	0.753486	+	0.657464i	$0.228371\pi$
$110$	−11.3378	−1.08102
$111$	9.66634	0.917488
$112$	−12.2420	−1.15676
$113$	8.68630	0.817139	0.408569	−	0.912727i	$-0.366028\pi$
$113$	8.68630	0.817139	0.408569	+	0.912727i	$0.366028\pi$
$114$	−6.99418	−0.655065
$115$	−2.09332	−0.195203
$116$	−0.688073	−0.0638859
$117$	9.93581	0.918566
$118$	31.3055	2.88191
$119$	−15.7212	−1.44116
$120$	4.65904	0.425311
$121$	10.9207	0.992789
$122$	9.76067	0.883690
$123$	10.5065	0.947335
$124$	6.92730	0.622090
$125$	−1.00000	−0.0894427
$126$	−17.9062	−1.59521
$127$	−21.3491	−1.89442	−0.947211	−	0.320611i	$-0.896112\pi$
$127$	−21.3491	−1.89442	−0.947211	+	0.320611i	$0.896112\pi$
$128$	20.4268	1.80549
$129$	6.06826	0.534280
$130$	−12.4358	−1.09070
$131$	−20.6769	−1.80655	−0.903273	−	0.429066i	$-0.858843\pi$
$131$	−20.6769	−1.80655	−0.903273	+	0.429066i	$0.858843\pi$
$132$	−18.6724	−1.62522
$133$	−10.6951	−0.927384
$134$	9.89330	0.854651
$135$	5.09318	0.438351
$136$	−18.5690	−1.59228
$137$	−7.07090	−0.604108	−0.302054	−	0.953291i	$-0.597672\pi$
$137$	−7.07090	−0.604108	−0.302054	+	0.953291i	$0.597672\pi$
$138$	−5.23188	−0.445367
$139$	−16.2502	−1.37833	−0.689164	−	0.724605i	$-0.742022\pi$
$139$	−16.2502	−1.37833	−0.689164	+	0.724605i	$0.742022\pi$
$140$	14.7680	1.24813
$141$	−3.27495	−0.275800
$142$	−0.763280	−0.0640531
$143$	24.0437	2.01063
$144$	−6.19742	−0.516451
$145$	0.178067	0.0147877
$146$	−36.5870	−3.02796
$147$	7.85056	0.647504
$148$	36.1902	2.97481
$149$	11.7415	0.961898	0.480949	−	0.876749i	$-0.340292\pi$
$149$	11.7415	0.961898	0.480949	+	0.876749i	$0.340292\pi$
$150$	−2.49933	−0.204069
$151$	−12.2023	−0.993009	−0.496505	−	0.868034i	$-0.665383\pi$
$151$	−12.2023	−0.993009	−0.496505	+	0.868034i	$0.665383\pi$
$152$	−12.6325	−1.02463
$153$	−7.95871	−0.643424
$154$	−43.3311	−3.49172
$155$	−1.79272	−0.143995
$156$	−20.4808	−1.63977
$157$	−3.88455	−0.310021	−0.155010	−	0.987913i	$-0.549541\pi$
$157$	−3.88455	−0.310021	−0.155010	+	0.987913i	$0.549541\pi$
$158$	21.0992	1.67856
$159$	3.56329	0.282587
$160$	−1.27148	−0.100519
$161$	−8.00030	−0.630512
$162$	−1.32617	−0.104194
$163$	10.3599	0.811450	0.405725	−	0.913995i	$-0.367019\pi$
$163$	10.3599	0.811450	0.405725	+	0.913995i	$0.367019\pi$
$164$	39.3355	3.07159
$165$	4.83224	0.376190
$166$	14.5135	1.12647
$167$	22.0619	1.70720	0.853602	−	0.520926i	$-0.174413\pi$
$167$	22.0619	1.70720	0.853602	+	0.520926i	$0.174413\pi$
$168$	17.8061	1.37377
$169$	13.3723	1.02864
$170$	9.96128	0.763995
$171$	−5.41431	−0.414042
$172$	22.7192	1.73232
$173$	−10.0627	−0.765053	−0.382526	−	0.923945i	$-0.624946\pi$
$173$	−10.0627	−0.765053	−0.382526	+	0.923945i	$0.624946\pi$
$174$	0.445048	0.0337390
$175$	−3.82183	−0.288903
$176$	−14.9971	−1.13045
$177$	−13.3426	−1.00289
$178$	−14.0653	−1.05424
$179$	−10.2799	−0.768355	−0.384178	−	0.923259i	$-0.625515\pi$
$179$	−10.2799	−0.768355	−0.384178	+	0.923259i	$0.625515\pi$
$180$	7.47618	0.557242
$181$	2.30172	0.171085	0.0855426	−	0.996335i	$-0.472738\pi$
$181$	2.30172	0.171085	0.0855426	+	0.996335i	$0.472738\pi$
$182$	−47.5277	−3.52299
$183$	−4.16006	−0.307521
$184$	−9.44953	−0.696628
$185$	−9.36570	−0.688580
$186$	−4.48060	−0.328534
$187$	−19.2593	−1.40838
$188$	−12.2612	−0.894240
$189$	19.4653	1.41589
$190$	6.77665	0.491630
$191$	19.2302	1.39145	0.695726	−	0.718308i	$-0.255083\pi$
$191$	19.2302	1.39145	0.695726	+	0.718308i	$0.255083\pi$
$192$	−9.78985	−0.706521
$193$	10.6790	0.768695	0.384347	−	0.923189i	$-0.374427\pi$
$193$	10.6790	0.768695	0.384347	+	0.923189i	$0.374427\pi$
$194$	−19.3675	−1.39051
$195$	5.30024	0.379558
$196$	29.3920	2.09943
$197$	3.80171	0.270861	0.135430	−	0.990787i	$-0.456758\pi$
$197$	3.80171	0.270861	0.135430	+	0.990787i	$0.456758\pi$
$198$	−21.9360	−1.55892
$199$	−19.9564	−1.41467	−0.707335	−	0.706878i	$-0.750103\pi$
$199$	−19.9564	−1.41467	−0.707335	+	0.706878i	$0.750103\pi$
$200$	−4.51414	−0.319198
$201$	−4.21659	−0.297415
$202$	−25.6728	−1.80633
$203$	0.680542	0.0477647
$204$	16.4054	1.14861
$205$	−10.1797	−0.710980
$206$	−32.9633	−2.29666
$207$	−4.05009	−0.281500
$208$	−16.4496	−1.14057
$209$	−13.1021	−0.906291
$210$	−9.55201	−0.659151
$211$	−2.70145	−0.185975	−0.0929877	−	0.995667i	$-0.529642\pi$
$211$	−2.70145	−0.185975	−0.0929877	+	0.995667i	$0.529642\pi$
$212$	13.3407	0.916245
$213$	0.325315	0.0222902
$214$	5.97735	0.408603
$215$	−5.87953	−0.400980
$216$	22.9913	1.56436
$217$	−6.85149	−0.465109
$218$	−38.0996	−2.58043
$219$	15.5936	1.05372
$220$	18.0916	1.21974
$221$	−21.1245	−1.42099
$222$	−23.4079	−1.57104
$223$	9.72526	0.651252	0.325626	−	0.945499i	$-0.394425\pi$
$223$	9.72526	0.651252	0.325626	+	0.945499i	$0.394425\pi$
$224$	−4.85938	−0.324681
$225$	−1.93477	−0.128985
$226$	−21.0347	−1.39921
$227$	−22.0463	−1.46326	−0.731632	−	0.681700i	$-0.761241\pi$
$227$	−22.0463	−1.46326	−0.731632	+	0.681700i	$0.761241\pi$
$228$	11.1606	0.739126
$229$	−13.1933	−0.871838	−0.435919	−	0.899986i	$-0.643577\pi$
$229$	−13.1933	−0.871838	−0.435919	+	0.899986i	$0.643577\pi$
$230$	5.06916	0.334251
$231$	18.4680	1.21511
$232$	0.803820	0.0527734
$233$	−22.7717	−1.49182	−0.745911	−	0.666046i	$-0.767985\pi$
$233$	−22.7717	−1.49182	−0.745911	+	0.666046i	$0.767985\pi$
$234$	−24.0605	−1.57288
$235$	3.17309	0.206990
$236$	−49.9540	−3.25173
$237$	−8.99262	−0.584134
$238$	38.0703	2.46773
$239$	18.4321	1.19227	0.596136	−	0.802883i	$-0.296702\pi$
$239$	18.4321	1.19227	0.596136	+	0.802883i	$0.296702\pi$
$240$	−3.30600	−0.213402
$241$	−7.95089	−0.512162	−0.256081	−	0.966655i	$-0.582431\pi$
$241$	−7.95089	−0.512162	−0.256081	+	0.966655i	$0.582431\pi$
$242$	−26.4455	−1.69998
$243$	15.8447	1.01644
$244$	−15.5750	−0.997089
$245$	−7.60640	−0.485955
$246$	−25.4424	−1.62215
$247$	−14.3710	−0.914406
$248$	−8.09261	−0.513881
$249$	−6.18576	−0.392006
$250$	2.42159	0.153155
$251$	−18.6667	−1.17823	−0.589116	−	0.808049i	$-0.700524\pi$
$251$	−18.6667	−1.17823	−0.589116	+	0.808049i	$0.700524\pi$
$252$	28.5727	1.79991
$253$	−9.80081	−0.616172
$254$	51.6987	3.24387
$255$	−4.24556	−0.265867
$256$	−30.4946	−1.90591
$257$	−19.9161	−1.24233	−0.621167	−	0.783678i	$-0.713341\pi$
$257$	−19.9161	−1.24233	−0.621167	+	0.783678i	$0.713341\pi$
$258$	−14.6949	−0.914862
$259$	−35.7941	−2.22414
$260$	19.8438	1.23066
$261$	0.344519	0.0213252
$262$	50.0710	3.09340
$263$	−2.71520	−0.167427	−0.0837133	−	0.996490i	$-0.526678\pi$
$263$	−2.71520	−0.167427	−0.0837133	+	0.996490i	$0.526678\pi$
$264$	21.8134	1.34252
$265$	−3.45246	−0.212083
$266$	25.8992	1.58798
$267$	5.99472	0.366871
$268$	−15.7867	−0.964324
$269$	−23.7894	−1.45047	−0.725233	−	0.688503i	$-0.758268\pi$
$269$	−23.7894	−1.45047	−0.725233	+	0.688503i	$0.758268\pi$
$270$	−12.3336	−0.750599
$271$	2.61931	0.159112	0.0795560	−	0.996830i	$-0.474650\pi$
$271$	2.61931	0.159112	0.0795560	+	0.996830i	$0.474650\pi$
$272$	13.1763	0.798933
$273$	20.2566	1.22599
$274$	17.1229	1.03443
$275$	−4.68195	−0.282332
$276$	8.34847	0.502519
$277$	21.6213	1.29910	0.649548	−	0.760320i	$-0.274958\pi$
$277$	21.6213	1.29910	0.649548	+	0.760320i	$0.274958\pi$
$278$	39.3515	2.36015
$279$	−3.46851	−0.207654
$280$	−17.2523	−1.03102
$281$	−24.9174	−1.48645	−0.743224	−	0.669043i	$-0.766704\pi$
$281$	−24.9174	−1.48645	−0.743224	+	0.669043i	$0.766704\pi$
$282$	7.93059	0.472260
$283$	9.13721	0.543151	0.271575	−	0.962417i	$-0.412455\pi$
$283$	9.13721	0.543151	0.271575	+	0.962417i	$0.412455\pi$
$284$	1.21796	0.0722726
$285$	−2.88825	−0.171085
$286$	−58.2240	−3.44286
$287$	−38.9050	−2.29649
$288$	−2.46002	−0.144958
$289$	−0.0789561	−0.00464448
$290$	−0.431206	−0.0253213
$291$	8.25457	0.483892
$292$	58.3816	3.41653
$293$	−26.9919	−1.57689	−0.788443	−	0.615108i	$-0.789112\pi$
$293$	−26.9919	−1.57689	−0.788443	+	0.615108i	$0.789112\pi$
$294$	−19.0109	−1.10874
$295$	12.9276	0.752676
$296$	−42.2781	−2.45736
$297$	23.8460	1.38369
$298$	−28.4330	−1.64708
$299$	−10.7500	−0.621689
$300$	3.98816	0.230256
$301$	−22.4706	−1.29518
$302$	29.5490	1.70036
$303$	10.9419	0.628597
$304$	8.96386	0.514113
$305$	4.03068	0.230796
$306$	19.2728	1.10175
$307$	30.5714	1.74480	0.872402	−	0.488789i	$-0.162561\pi$
$307$	30.5714	1.74480	0.872402	+	0.488789i	$0.162561\pi$
$308$	69.1431	3.93980
$309$	14.0492	0.799230
$310$	4.34125	0.246566
$311$	12.9079	0.731942	0.365971	−	0.930626i	$-0.380737\pi$
$311$	12.9079	0.731942	0.365971	+	0.930626i	$0.380737\pi$
$312$	23.9260	1.35454
$313$	−7.54989	−0.426745	−0.213372	−	0.976971i	$-0.568445\pi$
$313$	−7.54989	−0.426745	−0.213372	+	0.976971i	$0.568445\pi$
$314$	9.40681	0.530857
$315$	−7.39437	−0.416625
$316$	−33.6678	−1.89396
$317$	14.9007	0.836908	0.418454	−	0.908238i	$-0.362572\pi$
$317$	14.9007	0.836908	0.418454	+	0.908238i	$0.362572\pi$
$318$	−8.62883	−0.483881
$319$	0.833702	0.0466783
$320$	9.48537	0.530248
$321$	−2.54759	−0.142192
$322$	19.3735	1.07964
$323$	11.5114	0.640510
$324$	2.11616	0.117565
$325$	−5.13539	−0.284860
$326$	−25.0875	−1.38947
$327$	16.2383	0.897980
$328$	−45.9525	−2.53730
$329$	12.1270	0.668584
$330$	−11.7017	−0.644159
$331$	−6.13231	−0.337062	−0.168531	−	0.985696i	$-0.553902\pi$
$331$	−6.13231	−0.337062	−0.168531	+	0.985696i	$0.553902\pi$
$332$	−23.1591	−1.27102
$333$	−18.1205	−0.992996
$334$	−53.4251	−2.92329
$335$	4.08545	0.223212
$336$	−12.6350	−0.689295
$337$	22.1265	1.20531	0.602655	−	0.798002i	$-0.294110\pi$
$337$	22.1265	1.20531	0.602655	+	0.798002i	$0.294110\pi$
$338$	−32.3822	−1.76136
$339$	8.96513	0.486919
$340$	−15.8951	−0.862035
$341$	−8.39345	−0.454531
$342$	13.1113	0.708976
$343$	−2.31756	−0.125136
$344$	−26.5410	−1.43100
$345$	−2.16051	−0.116318
$346$	24.3678	1.31002
$347$	−19.6731	−1.05611	−0.528054	−	0.849211i	$-0.677078\pi$
$347$	−19.6731	−1.05611	−0.528054	+	0.849211i	$0.677078\pi$
$348$	−0.710160	−0.0380685
$349$	6.32835	0.338749	0.169374	−	0.985552i	$-0.445825\pi$
$349$	6.32835	0.338749	0.169374	+	0.985552i	$0.445825\pi$
$350$	9.25493	0.494697
$351$	26.1555	1.39608
$352$	−5.95300	−0.317296
$353$	−2.70833	−0.144150	−0.0720750	−	0.997399i	$-0.522962\pi$
$353$	−2.70833	−0.144150	−0.0720750	+	0.997399i	$0.522962\pi$
$354$	32.3104	1.71728
$355$	−0.315197	−0.0167289
$356$	22.4439	1.18952
$357$	−16.2258	−0.858762
$358$	24.8937	1.31567
$359$	20.1084	1.06128	0.530641	−	0.847597i	$-0.321951\pi$
$359$	20.1084	1.06128	0.530641	+	0.847597i	$0.321951\pi$
$360$	−8.73382	−0.460313
$361$	−11.1688	−0.587833
$362$	−5.57382	−0.292954
$363$	11.2712	0.591586
$364$	75.8396	3.97507
$365$	−15.1087	−0.790823
$366$	10.0740	0.526576
$367$	4.26927	0.222854	0.111427	−	0.993773i	$-0.464458\pi$
$367$	4.26927	0.222854	0.111427	+	0.993773i	$0.464458\pi$
$368$	6.70527	0.349536
$369$	−19.6953	−1.02530
$370$	22.6799	1.17907
$371$	−13.1947	−0.685036
$372$	7.14966	0.370693
$373$	−9.09375	−0.470857	−0.235428	−	0.971892i	$-0.575649\pi$
$373$	−9.09375	−0.470857	−0.235428	+	0.971892i	$0.575649\pi$
$374$	46.6382	2.41161
$375$	−1.03210	−0.0532974
$376$	14.3238	0.738693
$377$	0.914445	0.0470963
$378$	−47.1370	−2.42446
$379$	14.2343	0.731166	0.365583	−	0.930779i	$-0.380870\pi$
$379$	14.2343	0.731166	0.365583	+	0.930779i	$0.380870\pi$
$380$	−10.8134	−0.554718
$381$	−22.0344	−1.12885
$382$	−46.5678	−2.38262
$383$	−27.8004	−1.42053	−0.710266	−	0.703934i	$-0.751425\pi$
$383$	−27.8004	−1.42053	−0.710266	+	0.703934i	$0.751425\pi$
$384$	21.0824	1.07586
$385$	−17.8936	−0.911944
$386$	−25.8603	−1.31626
$387$	−11.3755	−0.578251
$388$	30.9046	1.56894
$389$	−15.5579	−0.788818	−0.394409	−	0.918935i	$-0.629051\pi$
$389$	−15.5579	−0.788818	−0.394409	+	0.918935i	$0.629051\pi$
$390$	−12.8350	−0.649927
$391$	8.61090	0.435472
$392$	−34.3364	−1.73425
$393$	−21.3406	−1.07649
$394$	−9.20621	−0.463802
$395$	8.71294	0.438395
$396$	35.0031	1.75897
$397$	−3.36747	−0.169008	−0.0845042	−	0.996423i	$-0.526931\pi$
$397$	−3.36747	−0.169008	−0.0845042	+	0.996423i	$0.526931\pi$
$398$	48.3263	2.42238
$399$	−11.0384	−0.552612
$400$	3.20318	0.160159
$401$	25.7362	1.28520	0.642602	−	0.766200i	$-0.277855\pi$
$401$	25.7362	1.28520	0.642602	+	0.766200i	$0.277855\pi$
$402$	10.2109	0.509272
$403$	−9.20634	−0.458600
$404$	40.9659	2.03813
$405$	−0.547644	−0.0272127
$406$	−1.64800	−0.0817888
$407$	−43.8498	−2.17355
$408$	−19.1651	−0.948812
$409$	4.34493	0.214843	0.107421	−	0.994214i	$-0.465741\pi$
$409$	4.34493	0.214843	0.107421	+	0.994214i	$0.465741\pi$
$410$	24.6511	1.21743
$411$	−7.29788	−0.359978
$412$	52.5993	2.59138
$413$	49.4073	2.43117
$414$	9.80766	0.482020
$415$	5.99337	0.294203
$416$	−6.52955	−0.320137
$417$	−16.7719	−0.821322
$418$	31.7280	1.55186
$419$	3.72223	0.181843	0.0909215	−	0.995858i	$-0.471019\pi$
$419$	3.72223	0.181843	0.0909215	+	0.995858i	$0.471019\pi$
$420$	15.2421	0.743737
$421$	38.8432	1.89310	0.946551	−	0.322554i	$-0.104541\pi$
$421$	38.8432	1.89310	0.946551	+	0.322554i	$0.104541\pi$
$422$	6.54181	0.318450
$423$	6.13920	0.298498
$424$	−15.5849	−0.756870
$425$	4.11352	0.199535
$426$	−0.787781	−0.0381681
$427$	15.4046	0.745480
$428$	−9.53801	−0.461037
$429$	24.8155	1.19810
$430$	14.2378	0.686609
$431$	−25.7196	−1.23887	−0.619436	−	0.785047i	$-0.712639\pi$
$431$	−25.7196	−1.23887	−0.619436	+	0.785047i	$0.712639\pi$
$432$	−16.3144	−0.784925
$433$	31.9235	1.53415	0.767073	−	0.641560i	$-0.221713\pi$
$433$	31.9235	1.53415	0.767073	+	0.641560i	$0.221713\pi$
$434$	16.5915	0.796419
$435$	0.183783	0.00881172
$436$	60.7952	2.91156
$437$	5.85799	0.280226
$438$	−37.7615	−1.80431
$439$	16.6830	0.796234	0.398117	−	0.917335i	$-0.369664\pi$
$439$	16.6830	0.796234	0.398117	+	0.917335i	$0.369664\pi$
$440$	−21.1350	−1.00757
$441$	−14.7166	−0.700792
$442$	51.1551	2.43320
$443$	−21.0849	−1.00177	−0.500887	−	0.865512i	$-0.666993\pi$
$443$	−21.0849	−1.00177	−0.500887	+	0.865512i	$0.666993\pi$
$444$	37.3519	1.77264
$445$	−5.80828	−0.275339
$446$	−23.5506	−1.11516
$447$	12.1184	0.573178
$448$	36.2515	1.71272
$449$	−23.9253	−1.12911	−0.564553	−	0.825397i	$-0.690951\pi$
$449$	−23.9253	−1.12911	−0.564553	+	0.825397i	$0.690951\pi$
$450$	4.68523	0.220864
$451$	−47.6608	−2.24426
$452$	33.5649	1.57876
$453$	−12.5940	−0.591718
$454$	53.3872	2.50558
$455$	−19.6266	−0.920110
$456$	−13.0380	−0.610560
$457$	8.86338	0.414612	0.207306	−	0.978276i	$-0.433531\pi$
$457$	8.86338	0.414612	0.207306	+	0.978276i	$0.433531\pi$
$458$	31.9488	1.49287
$459$	−20.9509	−0.977903
$460$	−8.08882	−0.377143
$461$	24.6058	1.14601	0.573003	−	0.819553i	$-0.305778\pi$
$461$	24.6058	1.14601	0.573003	+	0.819553i	$0.305778\pi$
$462$	−44.7221	−2.08066
$463$	31.8749	1.48135	0.740676	−	0.671863i	$-0.234506\pi$
$463$	31.8749	1.48135	0.740676	+	0.671863i	$0.234506\pi$
$464$	−0.570381	−0.0264793
$465$	−1.85027	−0.0858042
$466$	55.1437	2.55448
$467$	−33.5269	−1.55144	−0.775721	−	0.631076i	$-0.782614\pi$
$467$	−33.5269	−1.55144	−0.775721	+	0.631076i	$0.782614\pi$
$468$	38.3931	1.77472
$469$	15.6139	0.720983
$470$	−7.68394	−0.354434
$471$	−4.00924	−0.184736
$472$	58.3572	2.68611
$473$	−27.5277	−1.26572
$474$	21.7765	1.00023
$475$	2.79842	0.128401
$476$	−60.7485	−2.78440
$477$	−6.67972	−0.305843
$478$	−44.6350	−2.04156
$479$	0.216465	0.00989055	0.00494528	−	0.999988i	$-0.498426\pi$
$479$	0.216465	0.00989055	0.00494528	+	0.999988i	$0.498426\pi$
$480$	−1.31229	−0.0598977
$481$	−48.0966	−2.19301
$482$	19.2538	0.876988
$483$	−8.25711	−0.375712
$484$	42.1988	1.91813
$485$	−7.99784	−0.363163
$486$	−38.3696	−1.74048
$487$	−11.2094	−0.507946	−0.253973	−	0.967211i	$-0.581737\pi$
$487$	−11.2094	−0.507946	−0.253973	+	0.967211i	$0.581737\pi$
$488$	18.1951	0.823652
$489$	10.6925	0.483530
$490$	18.4196	0.832113
$491$	−26.0923	−1.17753	−0.588765	−	0.808304i	$-0.700386\pi$
$491$	−26.0923	−1.17753	−0.588765	+	0.808304i	$0.700386\pi$
$492$	40.5982	1.83031
$493$	−0.732482	−0.0329894
$494$	34.8008	1.56576
$495$	−9.05850	−0.407149
$496$	5.74242	0.257842
$497$	−1.20463	−0.0540351
$498$	14.9794	0.671243
$499$	−3.16073	−0.141494	−0.0707468	−	0.997494i	$-0.522538\pi$
$499$	−3.16073	−0.141494	−0.0707468	+	0.997494i	$0.522538\pi$
$500$	−3.86412	−0.172809
$501$	22.7701	1.01729
$502$	45.2032	2.01752
$503$	24.5995	1.09684	0.548419	−	0.836204i	$-0.315230\pi$
$503$	24.5995	1.09684	0.548419	+	0.836204i	$0.315230\pi$
$504$	−33.3792	−1.48683
$505$	−10.6016	−0.471765
$506$	23.7336	1.05509
$507$	13.8015	0.612947
$508$	−82.4953	−3.66014
$509$	−18.4123	−0.816112	−0.408056	−	0.912957i	$-0.633793\pi$
$509$	−18.4123	−0.816112	−0.408056	+	0.912957i	$0.633793\pi$
$510$	10.2810	0.455252
$511$	−57.7427	−2.55439
$512$	32.9920	1.45805
$513$	−14.2529	−0.629279
$514$	48.2288	2.12728
$515$	−13.6122	−0.599826
$516$	23.4485	1.03226
$517$	14.8563	0.653378
$518$	86.6789	3.80845
$519$	−10.3857	−0.455882
$520$	−23.1819	−1.01659
$521$	−23.1009	−1.01207	−0.506035	−	0.862513i	$-0.668889\pi$
$521$	−23.1009	−1.01207	−0.506035	+	0.862513i	$0.668889\pi$
$522$	−0.834285	−0.0365157
$523$	15.7689	0.689524	0.344762	−	0.938690i	$-0.387960\pi$
$523$	15.7689	0.689524	0.344762	+	0.938690i	$0.387960\pi$
$524$	−79.8979	−3.49036
$525$	−3.94451	−0.172153
$526$	6.57512	0.286689
$527$	7.37440	0.321234
$528$	−15.4785	−0.673617
$529$	−18.6180	−0.809479
$530$	8.36046	0.363155
$531$	25.0120	1.08543
$532$	−41.3272	−1.79176
$533$	−52.2767	−2.26435
$534$	−14.5168	−0.628203
$535$	2.46835	0.106716
$536$	18.4423	0.796586
$537$	−10.6099	−0.457850
$538$	57.6083	2.48367
$539$	−35.6128	−1.53395
$540$	19.6806	0.846920
$541$	−0.690358	−0.0296808	−0.0148404	−	0.999890i	$-0.504724\pi$
$541$	−0.690358	−0.0296808	−0.0148404	+	0.999890i	$0.504724\pi$
$542$	−6.34292	−0.272452
$543$	2.37560	0.101947
$544$	5.23025	0.224245
$545$	−15.7333	−0.673939
$546$	−49.0533	−2.09929
$547$	36.9829	1.58127	0.790637	−	0.612285i	$-0.209750\pi$
$547$	36.9829	1.58127	0.790637	+	0.612285i	$0.209750\pi$
$548$	−27.3228	−1.16717
$549$	7.79844	0.332829
$550$	11.3378	0.483445
$551$	−0.498307	−0.0212286
$552$	−9.75285	−0.415109
$553$	33.2994	1.41603
$554$	−52.3580	−2.22448
$555$	−9.66634	−0.410313
$556$	−62.7929	−2.66301
$557$	0.926544	0.0392589	0.0196295	−	0.999807i	$-0.493751\pi$
$557$	0.926544	0.0392589	0.0196295	+	0.999807i	$0.493751\pi$
$558$	8.39932	0.355571
$559$	−30.1937	−1.27706
$560$	12.2420	0.517320
$561$	−19.8775	−0.839230
$562$	60.3398	2.54528
$563$	39.0808	1.64706	0.823530	−	0.567272i	$-0.192001\pi$
$563$	39.0808	1.64706	0.823530	+	0.567272i	$0.192001\pi$
$564$	−12.6548	−0.532863
$565$	−8.68630	−0.365436
$566$	−22.1266	−0.930051
$567$	−2.09300	−0.0878979
$568$	−1.42285	−0.0597013
$569$	−5.34824	−0.224210	−0.112105	−	0.993696i	$-0.535759\pi$
$569$	−5.34824	−0.224210	−0.112105	+	0.993696i	$0.535759\pi$
$570$	6.99418	0.292954
$571$	9.03796	0.378227	0.189113	−	0.981955i	$-0.439439\pi$
$571$	9.03796	0.378227	0.189113	+	0.981955i	$0.439439\pi$
$572$	92.9076	3.88466
$573$	19.8475	0.829142
$574$	94.2122	3.93234
$575$	2.09332	0.0872973
$576$	18.3520	0.764667
$577$	25.1633	1.04756	0.523781	−	0.851853i	$-0.324521\pi$
$577$	25.1633	1.04756	0.523781	+	0.851853i	$0.324521\pi$
$578$	0.191200	0.00795286
$579$	11.0218	0.458052
$580$	0.688073	0.0285707
$581$	22.9056	0.950286
$582$	−19.9892	−0.828580
$583$	−16.1643	−0.669455
$584$	−68.2026	−2.82224
$585$	−9.93581	−0.410795
$586$	65.3635	2.70014
$587$	−25.0445	−1.03370	−0.516849	−	0.856077i	$-0.672895\pi$
$587$	−25.0445	−1.03370	−0.516849	+	0.856077i	$0.672895\pi$
$588$	30.3355	1.25102
$589$	5.01680	0.206714
$590$	−31.3055	−1.28883
$591$	3.92375	0.161401
$592$	30.0000	1.23299
$593$	5.29835	0.217577	0.108789	−	0.994065i	$-0.465303\pi$
$593$	5.29835	0.217577	0.108789	+	0.994065i	$0.465303\pi$
$594$	−57.7454	−2.36932
$595$	15.7212	0.644506
$596$	45.3704	1.85844
$597$	−20.5970	−0.842978
$598$	26.0321	1.06453
$599$	7.69835	0.314546	0.157273	−	0.987555i	$-0.449730\pi$
$599$	7.69835	0.314546	0.157273	+	0.987555i	$0.449730\pi$
$600$	−4.65904	−0.190205
$601$	−3.06751	−0.125126	−0.0625631	−	0.998041i	$-0.519927\pi$
$601$	−3.06751	−0.125126	−0.0625631	+	0.998041i	$0.519927\pi$
$602$	54.4146	2.21777
$603$	7.90441	0.321892
$604$	−47.1512	−1.91855
$605$	−10.9207	−0.443989
$606$	−26.4969	−1.07636
$607$	11.3536	0.460828	0.230414	−	0.973093i	$-0.425992\pi$
$607$	11.3536	0.460828	0.230414	+	0.973093i	$0.425992\pi$
$608$	3.55814	0.144302
$609$	0.702388	0.0284622
$610$	−9.76067	−0.395198
$611$	16.2951	0.659228
$612$	−30.7534	−1.24313
$613$	20.2745	0.818880	0.409440	−	0.912337i	$-0.365724\pi$
$613$	20.2745	0.818880	0.409440	+	0.912337i	$0.365724\pi$
$614$	−74.0316	−2.98767
$615$	−10.5065	−0.423661
$616$	−80.7744	−3.25449
$617$	11.9844	0.482472	0.241236	−	0.970466i	$-0.422447\pi$
$617$	11.9844	0.482472	0.241236	+	0.970466i	$0.422447\pi$
$618$	−34.0214	−1.36854
$619$	−6.27985	−0.252409	−0.126204	−	0.992004i	$-0.540279\pi$
$619$	−6.27985	−0.252409	−0.126204	+	0.992004i	$0.540279\pi$
$620$	−6.92730	−0.278207
$621$	−10.6616	−0.427836
$622$	−31.2578	−1.25332
$623$	−22.1983	−0.889355
$624$	−16.9776	−0.679649
$625$	1.00000	0.0400000
$626$	18.2828	0.730726
$627$	−13.5227	−0.540043
$628$	−15.0104	−0.598979
$629$	38.5260	1.53613
$630$	17.9062	0.713398
$631$	37.7124	1.50131	0.750654	−	0.660695i	$-0.229738\pi$
$631$	37.7124	1.50131	0.750654	+	0.660695i	$0.229738\pi$
$632$	39.3314	1.56452
$633$	−2.78816	−0.110820
$634$	−36.0835	−1.43306
$635$	21.3491	0.847211
$636$	13.7690	0.545975
$637$	−39.0619	−1.54769
$638$	−2.01889	−0.0799285
$639$	−0.609834	−0.0241247
$640$	−20.4268	−0.807438
$641$	−20.1459	−0.795715	−0.397858	−	0.917447i	$-0.630246\pi$
$641$	−20.1459	−0.795715	−0.397858	+	0.917447i	$0.630246\pi$
$642$	6.16922	0.243480
$643$	−33.9533	−1.33899	−0.669494	−	0.742818i	$-0.733489\pi$
$643$	−33.9533	−1.33899	−0.669494	+	0.742818i	$0.733489\pi$
$644$	−30.9141	−1.21819
$645$	−6.06826	−0.238937
$646$	−27.8759	−1.09676
$647$	12.8149	0.503804	0.251902	−	0.967753i	$-0.418944\pi$
$647$	12.8149	0.503804	0.251902	+	0.967753i	$0.418944\pi$
$648$	−2.47214	−0.0971150
$649$	60.5266	2.37588
$650$	12.4358	0.487774
$651$	−7.07142	−0.277151
$652$	40.0319	1.56777
$653$	24.1840	0.946394	0.473197	−	0.880957i	$-0.343100\pi$
$653$	24.1840	0.946394	0.473197	+	0.880957i	$0.343100\pi$
$654$	−39.3226	−1.53763
$655$	20.6769	0.807912
$656$	32.6074	1.27310
$657$	−29.2318	−1.14044
$658$	−29.3667	−1.14483
$659$	40.3390	1.57138	0.785691	−	0.618619i	$-0.212307\pi$
$659$	40.3390	1.57138	0.785691	+	0.618619i	$0.212307\pi$
$660$	18.6724	0.726821
$661$	−0.187797	−0.00730445	−0.00365222	−	0.999993i	$-0.501163\pi$
$661$	−0.187797	−0.00730445	−0.00365222	+	0.999993i	$0.501163\pi$
$662$	14.8500	0.577160
$663$	−21.8026	−0.846744
$664$	27.0549	1.04993
$665$	10.6951	0.414739
$666$	43.8804	1.70033
$667$	−0.372751	−0.0144330
$668$	85.2500	3.29842
$669$	10.0374	0.388070
$670$	−9.89330	−0.382212
$671$	18.8715	0.728524
$672$	−5.01536	−0.193472
$673$	−11.8521	−0.456865	−0.228432	−	0.973560i	$-0.573360\pi$
$673$	−11.8521	−0.456865	−0.228432	+	0.973560i	$0.573360\pi$
$674$	−53.5815	−2.06388
$675$	−5.09318	−0.196036
$676$	51.6721	1.98739
$677$	−26.1523	−1.00512	−0.502558	−	0.864544i	$-0.667608\pi$
$677$	−26.1523	−1.00512	−0.502558	+	0.864544i	$0.667608\pi$
$678$	−21.7099	−0.833764
$679$	−30.5664	−1.17303
$680$	18.5690	0.712089
$681$	−22.7540	−0.871934
$682$	20.3255	0.778304
$683$	−23.8058	−0.910905	−0.455452	−	0.890260i	$-0.650522\pi$
$683$	−23.8058	−0.910905	−0.455452	+	0.890260i	$0.650522\pi$
$684$	−20.9215	−0.799955
$685$	7.07090	0.270165
$686$	5.61218	0.214274
$687$	−13.6168	−0.519513
$688$	18.8332	0.718008
$689$	−17.7298	−0.675450
$690$	5.23188	0.199174
$691$	−7.36499	−0.280177	−0.140089	−	0.990139i	$-0.544739\pi$
$691$	−7.36499	−0.280177	−0.140089	+	0.990139i	$0.544739\pi$
$692$	−38.8835	−1.47813
$693$	−34.6201	−1.31511
$694$	47.6403	1.80840
$695$	16.2502	0.616407
$696$	0.829622	0.0314468
$697$	41.8743	1.58610
$698$	−15.3247	−0.580049
$699$	−23.5026	−0.888951
$700$	−14.7680	−0.558179
$701$	−23.8530	−0.900914	−0.450457	−	0.892798i	$-0.648739\pi$
$701$	−23.8530	−0.900914	−0.450457	+	0.892798i	$0.648739\pi$
$702$	−63.3379	−2.39054
$703$	26.2092	0.988499
$704$	44.4100	1.67377
$705$	3.27495	0.123342
$706$	6.55848	0.246832
$707$	−40.5176	−1.52382
$708$	−51.5575	−1.93765
$709$	−14.7155	−0.552652	−0.276326	−	0.961064i	$-0.589117\pi$
$709$	−14.7155	−0.552652	−0.276326	+	0.961064i	$0.589117\pi$
$710$	0.763280	0.0286454
$711$	16.8575	0.632207
$712$	−26.2194	−0.982613
$713$	3.75274	0.140541
$714$	39.2924	1.47048
$715$	−24.0437	−0.899182
$716$	−39.7227	−1.48451
$717$	19.0238	0.710455
$718$	−48.6944	−1.81726
$719$	−32.8903	−1.22660	−0.613301	−	0.789849i	$-0.710159\pi$
$719$	−32.8903	−1.22660	−0.613301	+	0.789849i	$0.710159\pi$
$720$	6.19742	0.230964
$721$	−52.0236	−1.93746
$722$	27.0464	1.00656
$723$	−8.20612	−0.305189
$724$	8.89411	0.330547
$725$	−0.178067	−0.00661325
$726$	−27.2944	−1.01299
$727$	17.0847	0.633638	0.316819	−	0.948486i	$-0.397385\pi$
$727$	17.0847	0.633638	0.316819	+	0.948486i	$0.397385\pi$
$728$	−88.5973	−3.28363
$729$	14.7104	0.544831
$730$	36.5870	1.35415
$731$	24.1855	0.894535
$732$	−16.0750	−0.594148
$733$	9.05412	0.334422	0.167211	−	0.985921i	$-0.446524\pi$
$733$	9.05412	0.334422	0.167211	+	0.985921i	$0.446524\pi$
$734$	−10.3385	−0.381599
$735$	−7.85056	−0.289572
$736$	2.66161	0.0981082
$737$	19.1279	0.704585
$738$	47.6941	1.75565
$739$	−9.88400	−0.363589	−0.181794	−	0.983337i	$-0.558191\pi$
$739$	−9.88400	−0.363589	−0.181794	+	0.983337i	$0.558191\pi$
$740$	−36.1902	−1.33038
$741$	−14.8323	−0.544879
$742$	31.9523	1.17301
$743$	40.1017	1.47119	0.735594	−	0.677423i	$-0.236903\pi$
$743$	40.1017	1.47119	0.735594	+	0.677423i	$0.236903\pi$
$744$	−8.35238	−0.306213
$745$	−11.7415	−0.430174
$746$	22.0214	0.806260
$747$	11.5958	0.424268
$748$	−74.4203	−2.72107
$749$	9.43363	0.344697
$750$	2.49933	0.0912625
$751$	−1.30316	−0.0475529	−0.0237765	−	0.999717i	$-0.507569\pi$
$751$	−1.30316	−0.0475529	−0.0237765	+	0.999717i	$0.507569\pi$
$752$	−10.1640	−0.370642
$753$	−19.2659	−0.702088
$754$	−2.21441	−0.0806442
$755$	12.2023	0.444087
$756$	75.2161	2.73558
$757$	13.2843	0.482825	0.241412	−	0.970423i	$-0.422389\pi$
$757$	13.2843	0.482825	0.241412	+	0.970423i	$0.422389\pi$
$758$	−34.4697	−1.25200
$759$	−10.1154	−0.367166
$760$	12.6325	0.458228
$761$	44.2551	1.60425	0.802124	−	0.597158i	$-0.203703\pi$
$761$	44.2551	1.60425	0.802124	+	0.597158i	$0.203703\pi$
$762$	53.3583	1.93297
$763$	−60.1299	−2.17685
$764$	74.3079	2.68837
$765$	7.95871	0.287748
$766$	67.3212	2.43241
$767$	66.3885	2.39715
$768$	−31.4734	−1.13570
$769$	−5.67708	−0.204721	−0.102360	−	0.994747i	$-0.532639\pi$
$769$	−5.67708	−0.204721	−0.102360	+	0.994747i	$0.532639\pi$
$770$	43.3311	1.56155
$771$	−20.5554	−0.740286
$772$	41.2651	1.48516
$773$	42.4625	1.52727	0.763635	−	0.645648i	$-0.223413\pi$
$773$	42.4625	1.52727	0.763635	+	0.645648i	$0.223413\pi$
$774$	27.5469	0.990154
$775$	1.79272	0.0643965
$776$	−36.1034	−1.29604
$777$	−36.9431	−1.32533
$778$	37.6750	1.35071
$779$	28.4871	1.02066
$780$	20.4808	0.733329
$781$	−1.47574	−0.0528061
$782$	−20.8521	−0.745670
$783$	0.906927	0.0324109
$784$	24.3647	0.870167
$785$	3.88455	0.138646
$786$	51.6783	1.84330
$787$	22.2319	0.792480	0.396240	−	0.918147i	$-0.370315\pi$
$787$	22.2319	0.792480	0.396240	+	0.918147i	$0.370315\pi$
$788$	14.6903	0.523319
$789$	−2.80236	−0.0997667
$790$	−21.0992	−0.750676
$791$	−33.1976	−1.18037
$792$	−40.8914	−1.45301
$793$	20.6991	0.735048
$794$	8.15464	0.289397
$795$	−3.56329	−0.126377
$796$	−77.1139	−2.73323
$797$	10.3629	0.367073	0.183536	−	0.983013i	$-0.441245\pi$
$797$	10.3629	0.367073	0.183536	+	0.983013i	$0.441245\pi$
$798$	26.7306	0.946252
$799$	−13.0526	−0.461767
$800$	1.27148	0.0449536
$801$	−11.2377	−0.397064
$802$	−62.3226	−2.20069
$803$	−70.7380	−2.49629
$804$	−16.2934	−0.574624
$805$	8.00030	0.281974
$806$	22.2940	0.785273
$807$	−24.5531	−0.864308
$808$	−47.8572	−1.68361
$809$	−16.3965	−0.576469	−0.288234	−	0.957560i	$-0.593068\pi$
$809$	−16.3965	−0.576469	−0.288234	+	0.957560i	$0.593068\pi$
$810$	1.32617	0.0465970
$811$	−48.2285	−1.69353	−0.846766	−	0.531965i	$-0.821454\pi$
$811$	−48.2285	−1.69353	−0.846766	+	0.531965i	$0.821454\pi$
$812$	2.62970	0.0922843
$813$	2.70339	0.0948121
$814$	106.186	3.72183
$815$	−10.3599	−0.362892
$816$	13.5993	0.476071
$817$	16.4534	0.575632
$818$	−10.5216	−0.367881
$819$	−37.9730	−1.32688
$820$	−39.3355	−1.37366
$821$	−47.1145	−1.64431	−0.822155	−	0.569264i	$-0.807228\pi$
$821$	−47.1145	−1.64431	−0.822155	+	0.569264i	$0.807228\pi$
$822$	17.6725	0.616399
$823$	44.7947	1.56145	0.780723	−	0.624877i	$-0.214851\pi$
$823$	44.7947	1.56145	0.780723	+	0.624877i	$0.214851\pi$
$824$	−61.4475	−2.14063
$825$	−4.83224	−0.168237
$826$	−119.644	−4.16296
$827$	20.4752	0.711994	0.355997	−	0.934487i	$-0.384141\pi$
$827$	20.4752	0.711994	0.355997	+	0.934487i	$0.384141\pi$
$828$	−15.6500	−0.543876
$829$	24.3140	0.844462	0.422231	−	0.906488i	$-0.361247\pi$
$829$	24.3140	0.844462	0.422231	+	0.906488i	$0.361247\pi$
$830$	−14.5135	−0.503771
$831$	22.3153	0.774110
$832$	48.7111	1.68875
$833$	31.2891	1.08410
$834$	40.6147	1.40637
$835$	−22.0619	−0.763485
$836$	−50.6280	−1.75101
$837$	−9.13065	−0.315602
$838$	−9.01374	−0.311374
$839$	−31.2732	−1.07967	−0.539836	−	0.841770i	$-0.681514\pi$
$839$	−31.2732	−1.07967	−0.539836	+	0.841770i	$0.681514\pi$
$840$	−17.8061	−0.614368
$841$	−28.9683	−0.998907
$842$	−94.0625	−3.24161
$843$	−25.7172	−0.885749
$844$	−10.4387	−0.359316
$845$	−13.3723	−0.460020
$846$	−14.8667	−0.511126
$847$	−41.7370	−1.43410
$848$	11.0589	0.379763
$849$	9.43051	0.323654
$850$	−9.96128	−0.341669
$851$	19.6054	0.672064
$852$	1.25706	0.0430661
$853$	−43.1854	−1.47864	−0.739321	−	0.673354i	$-0.764853\pi$
$853$	−43.1854	−1.47864	−0.739321	+	0.673354i	$0.764853\pi$
$854$	−37.3036	−1.27650
$855$	5.41431	0.185165
$856$	11.1425	0.380842
$857$	−5.45630	−0.186384	−0.0931918	−	0.995648i	$-0.529707\pi$
$857$	−5.45630	−0.186384	−0.0931918	+	0.995648i	$0.529707\pi$
$858$	−60.0930	−2.05154
$859$	54.0364	1.84370	0.921849	−	0.387550i	$-0.126678\pi$
$859$	54.0364	1.84370	0.921849	+	0.387550i	$0.126678\pi$
$860$	−22.7192	−0.774718
$861$	−40.1539	−1.36844
$862$	62.2825	2.12135
$863$	23.4465	0.798128	0.399064	−	0.916923i	$-0.369335\pi$
$863$	23.4465	0.798128	0.399064	+	0.916923i	$0.369335\pi$
$864$	−6.47587	−0.220313
$865$	10.0627	0.342142
$866$	−77.3057	−2.62696
$867$	−0.0814906	−0.00276756
$868$	−26.4750	−0.898619
$869$	40.7936	1.38383
$870$	−0.445048	−0.0150885
$871$	20.9804	0.710894
$872$	−71.0221	−2.40511
$873$	−15.4740	−0.523715
$874$	−14.1857	−0.479837
$875$	3.82183	0.129202
$876$	60.2557	2.03585
$877$	−31.1577	−1.05212	−0.526060	−	0.850447i	$-0.676331\pi$
$877$	−31.1577	−1.05212	−0.526060	+	0.850447i	$0.676331\pi$
$878$	−40.3994	−1.36341
$879$	−27.8584	−0.939639
$880$	14.9971	0.505553
$881$	−10.4086	−0.350674	−0.175337	−	0.984508i	$-0.556102\pi$
$881$	−10.4086	−0.350674	−0.175337	+	0.984508i	$0.556102\pi$
$882$	35.6377	1.19998
$883$	−55.8243	−1.87864	−0.939319	−	0.343046i	$-0.888541\pi$
$883$	−55.8243	−1.87864	−0.939319	+	0.343046i	$0.888541\pi$
$884$	−81.6278	−2.74544
$885$	13.3426	0.448507
$886$	51.0591	1.71537
$887$	−38.8187	−1.30340	−0.651702	−	0.758475i	$-0.725945\pi$
$887$	−38.8187	−1.30340	−0.651702	+	0.758475i	$0.725945\pi$
$888$	−43.6352	−1.46430
$889$	81.5925	2.73652
$890$	14.0653	0.471470
$891$	−2.56405	−0.0858987
$892$	37.5796	1.25826
$893$	−8.87966	−0.297146
$894$	−29.3457	−0.981468
$895$	10.2799	0.343619
$896$	−78.0676	−2.60806
$897$	−11.0951	−0.370454
$898$	57.9374	1.93340
$899$	−0.319225	−0.0106468
$900$	−7.47618	−0.249206
$901$	14.2018	0.473130
$902$	115.415	3.84290
$903$	−23.1919	−0.771777
$904$	−39.2112	−1.30415
$905$	−2.30172	−0.0765117
$906$	30.4976	1.01321
$907$	−48.2531	−1.60222	−0.801109	−	0.598519i	$-0.795756\pi$
$907$	−48.2531	−1.60222	−0.801109	+	0.598519i	$0.795756\pi$
$908$	−85.1895	−2.82711
$909$	−20.5117	−0.680329
$910$	47.5277	1.57553
$911$	31.3429	1.03844	0.519219	−	0.854641i	$-0.326223\pi$
$911$	31.3429	1.03844	0.519219	+	0.854641i	$0.326223\pi$
$912$	9.25160	0.306351
$913$	28.0607	0.928673
$914$	−21.4635	−0.709950
$915$	4.16006	0.137527
$916$	−50.9805	−1.68444
$917$	79.0235	2.60959
$918$	50.7345	1.67449
$919$	36.8614	1.21595	0.607973	−	0.793958i	$-0.291983\pi$
$919$	36.8614	1.21595	0.607973	+	0.793958i	$0.291983\pi$
$920$	9.44953	0.311542
$921$	31.5528	1.03970
$922$	−59.5853	−1.96234
$923$	−1.61866	−0.0532789
$924$	71.3626	2.34766
$925$	9.36570	0.307942
$926$	−77.1880	−2.53656
$927$	−26.3365	−0.865005
$928$	−0.226409	−0.00743223
$929$	−7.87784	−0.258464	−0.129232	−	0.991614i	$-0.541251\pi$
$929$	−7.87784	−0.258464	−0.129232	+	0.991614i	$0.541251\pi$
$930$	4.48060	0.146925
$931$	21.2859	0.697618
$932$	−87.9924	−2.88229
$933$	13.3223	0.436152
$934$	81.1887	2.65657
$935$	19.2593	0.629847
$936$	−44.8516	−1.46602
$937$	−22.5208	−0.735723	−0.367862	−	0.929881i	$-0.619910\pi$
$937$	−22.5208	−0.735723	−0.367862	+	0.929881i	$0.619910\pi$
$938$	−37.8105	−1.23456
$939$	−7.79224	−0.254290
$940$	12.2612	0.399916
$941$	−28.2133	−0.919729	−0.459864	−	0.887989i	$-0.652102\pi$
$941$	−28.2133	−0.919729	−0.459864	+	0.887989i	$0.652102\pi$
$942$	9.70876	0.316329
$943$	21.3093	0.693926
$944$	−41.4096	−1.34777
$945$	−19.4653	−0.633205
$946$	66.6608	2.16733
$947$	−25.6350	−0.833027	−0.416513	−	0.909130i	$-0.636748\pi$
$947$	−25.6350	−0.833027	−0.416513	+	0.909130i	$0.636748\pi$
$948$	−34.7486	−1.12858
$949$	−77.5889	−2.51864
$950$	−6.77665	−0.219864
$951$	15.3790	0.498699
$952$	70.9676	2.30007
$953$	−5.44125	−0.176259	−0.0881296	−	0.996109i	$-0.528089\pi$
$953$	−5.44125	−0.176259	−0.0881296	+	0.996109i	$0.528089\pi$
$954$	16.1756	0.523703
$955$	−19.2302	−0.622276
$956$	71.2238	2.30354
$957$	0.860463	0.0278148
$958$	−0.524191	−0.0169358
$959$	27.0238	0.872644
$960$	9.78985	0.315966
$961$	−27.7861	−0.896327
$962$	116.470	3.75516
$963$	4.77569	0.153895
$964$	−30.7232	−0.989528
$965$	−10.6790	−0.343771
$966$	19.9954	0.643341
$967$	−46.2277	−1.48658	−0.743292	−	0.668967i	$-0.766737\pi$
$967$	−46.2277	−1.48658	−0.743292	+	0.668967i	$0.766737\pi$
$968$	−49.2975	−1.58448
$969$	11.8809	0.381669
$970$	19.3675	0.621854
$971$	−40.9211	−1.31322	−0.656610	−	0.754230i	$-0.728010\pi$
$971$	−40.9211	−1.31322	−0.656610	+	0.754230i	$0.728010\pi$
$972$	61.2260	1.96383
$973$	62.1057	1.99102
$974$	27.1446	0.869769
$975$	−5.30024	−0.169744
$976$	−12.9110	−0.413271
$977$	−59.4804	−1.90295	−0.951474	−	0.307730i	$-0.900431\pi$
$977$	−59.4804	−1.90295	−0.951474	+	0.307730i	$0.900431\pi$
$978$	−25.8928	−0.827960
$979$	−27.1941	−0.869127
$980$	−29.3920	−0.938894
$981$	−30.4402	−0.971882
$982$	63.1850	2.01631
$983$	15.1619	0.483591	0.241795	−	0.970327i	$-0.422264\pi$
$983$	15.1619	0.483591	0.241795	+	0.970327i	$0.422264\pi$
$984$	−47.4276	−1.51194
$985$	−3.80171	−0.121133
$986$	1.77378	0.0564885
$987$	12.5163	0.398398
$988$	−55.5313	−1.76669
$989$	12.3077	0.391362
$990$	21.9360	0.697172
$991$	−27.6538	−0.878451	−0.439225	−	0.898377i	$-0.644747\pi$
$991$	−27.6538	−0.878451	−0.439225	+	0.898377i	$0.644747\pi$
$992$	2.27941	0.0723713
$993$	−6.32915	−0.200850
$994$	2.91713	0.0925257
$995$	19.9564	0.632660
$996$	−23.9025	−0.757380
$997$	−4.52486	−0.143304	−0.0716519	−	0.997430i	$-0.522827\pi$
$997$	−4.52486	−0.143304	−0.0716519	+	0.997430i	$0.522827\pi$
$998$	7.65400	0.242283
$999$	−47.7012	−1.50920

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8005.2.a.f.1.13	✓	127

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8005.2.a.f.1.13	✓	127	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:	\( N \)	\(=\)	\( 8005 = 5 \cdot 1601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.42159 q^{2} +1.03210 q^{3} +3.86412 q^{4} -1.00000 q^{5} -2.49933 q^{6} -3.82183 q^{7} -4.51414 q^{8} -1.93477 q^{9} +O(q^{10})\)	\(q-2.42159 q^{2} +1.03210 q^{3} +3.86412 q^{4} -1.00000 q^{5} -2.49933 q^{6} -3.82183 q^{7} -4.51414 q^{8} -1.93477 q^{9} +2.42159 q^{10} -4.68195 q^{11} +3.98816 q^{12} -5.13539 q^{13} +9.25493 q^{14} -1.03210 q^{15} +3.20318 q^{16} +4.11352 q^{17} +4.68523 q^{18} +2.79842 q^{19} -3.86412 q^{20} -3.94451 q^{21} +11.3378 q^{22} +2.09332 q^{23} -4.65904 q^{24} +1.00000 q^{25} +12.4358 q^{26} -5.09318 q^{27} -14.7680 q^{28} -0.178067 q^{29} +2.49933 q^{30} +1.79272 q^{31} +1.27148 q^{32} -4.83224 q^{33} -9.96128 q^{34} +3.82183 q^{35} -7.47618 q^{36} +9.36570 q^{37} -6.77665 q^{38} -5.30024 q^{39} +4.51414 q^{40} +10.1797 q^{41} +9.55201 q^{42} +5.87953 q^{43} -18.0916 q^{44} +1.93477 q^{45} -5.06916 q^{46} -3.17309 q^{47} +3.30600 q^{48} +7.60640 q^{49} -2.42159 q^{50} +4.24556 q^{51} -19.8438 q^{52} +3.45246 q^{53} +12.3336 q^{54} +4.68195 q^{55} +17.2523 q^{56} +2.88825 q^{57} +0.431206 q^{58} -12.9276 q^{59} -3.98816 q^{60} -4.03068 q^{61} -4.34125 q^{62} +7.39437 q^{63} -9.48537 q^{64} +5.13539 q^{65} +11.7017 q^{66} -4.08545 q^{67} +15.8951 q^{68} +2.16051 q^{69} -9.25493 q^{70} +0.315197 q^{71} +8.73382 q^{72} +15.1087 q^{73} -22.6799 q^{74} +1.03210 q^{75} +10.8134 q^{76} +17.8936 q^{77} +12.8350 q^{78} -8.71294 q^{79} -3.20318 q^{80} +0.547644 q^{81} -24.6511 q^{82} -5.99337 q^{83} -15.2421 q^{84} -4.11352 q^{85} -14.2378 q^{86} -0.183783 q^{87} +21.1350 q^{88} +5.80828 q^{89} -4.68523 q^{90} +19.6266 q^{91} +8.08882 q^{92} +1.85027 q^{93} +7.68394 q^{94} -2.79842 q^{95} +1.31229 q^{96} +7.99784 q^{97} -18.4196 q^{98} +9.05850 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 127 q - 6 q^{2} - 18 q^{3} + 114 q^{4} - 127 q^{5} - 20 q^{6} + 28 q^{7} - 18 q^{8} + 101 q^{9}+O(q^{10}) \) 127 * q - 6 * q^2 - 18 * q^3 + 114 * q^4 - 127 * q^5 - 20 * q^6 + 28 * q^7 - 18 * q^8 + 101 * q^9	\( 127 q - 6 q^{2} - 18 q^{3} + 114 q^{4} - 127 q^{5} - 20 q^{6} + 28 q^{7} - 18 q^{8} + 101 q^{9} + 6 q^{10} - 45 q^{11} - 30 q^{12} - 53 q^{14} + 18 q^{15} + 84 q^{16} - 36 q^{17} - 10 q^{18} - 49 q^{19} - 114 q^{20} - 48 q^{21} + 13 q^{22} - 29 q^{23} - 63 q^{24} + 127 q^{25} - 55 q^{26} - 75 q^{27} + 44 q^{28} - 45 q^{29} + 20 q^{30} - 49 q^{31} - 32 q^{32} - 8 q^{33} - 52 q^{34} - 28 q^{35} + 44 q^{36} + 36 q^{37} - 65 q^{38} - 52 q^{39} + 18 q^{40} - 66 q^{41} - 18 q^{42} - 5 q^{43} - 93 q^{44} - 101 q^{45} - 25 q^{46} - 32 q^{47} - 54 q^{48} + 77 q^{49} - 6 q^{50} - 102 q^{51} - 13 q^{52} - 67 q^{53} - 53 q^{54} + 45 q^{55} - 158 q^{56} + 16 q^{57} + 35 q^{58} - 213 q^{59} + 30 q^{60} - 62 q^{61} - 33 q^{62} + 59 q^{63} + 34 q^{64} - 60 q^{66} + 10 q^{67} - 94 q^{68} - 93 q^{69} + 53 q^{70} - 118 q^{71} - 24 q^{72} + 35 q^{73} - 107 q^{74} - 18 q^{75} - 98 q^{76} - 93 q^{77} + 21 q^{78} - 64 q^{79} - 84 q^{80} + 15 q^{81} + 15 q^{82} - 187 q^{83} - 118 q^{84} + 36 q^{85} - 126 q^{86} - 53 q^{87} + 15 q^{88} - 138 q^{89} + 10 q^{90} - 138 q^{91} - 86 q^{92} + 23 q^{93} - 60 q^{94} + 49 q^{95} - 92 q^{96} + 9 q^{97} - 67 q^{98} - 147 q^{99}+O(q^{100}) \) 127 * q - 6 * q^2 - 18 * q^3 + 114 * q^4 - 127 * q^5 - 20 * q^6 + 28 * q^7 - 18 * q^8 + 101 * q^9 + 6 * q^10 - 45 * q^11 - 30 * q^12 - 53 * q^14 + 18 * q^15 + 84 * q^16 - 36 * q^17 - 10 * q^18 - 49 * q^19 - 114 * q^20 - 48 * q^21 + 13 * q^22 - 29 * q^23 - 63 * q^24 + 127 * q^25 - 55 * q^26 - 75 * q^27 + 44 * q^28 - 45 * q^29 + 20 * q^30 - 49 * q^31 - 32 * q^32 - 8 * q^33 - 52 * q^34 - 28 * q^35 + 44 * q^36 + 36 * q^37 - 65 * q^38 - 52 * q^39 + 18 * q^40 - 66 * q^41 - 18 * q^42 - 5 * q^43 - 93 * q^44 - 101 * q^45 - 25 * q^46 - 32 * q^47 - 54 * q^48 + 77 * q^49 - 6 * q^50 - 102 * q^51 - 13 * q^52 - 67 * q^53 - 53 * q^54 + 45 * q^55 - 158 * q^56 + 16 * q^57 + 35 * q^58 - 213 * q^59 + 30 * q^60 - 62 * q^61 - 33 * q^62 + 59 * q^63 + 34 * q^64 - 60 * q^66 + 10 * q^67 - 94 * q^68 - 93 * q^69 + 53 * q^70 - 118 * q^71 - 24 * q^72 + 35 * q^73 - 107 * q^74 - 18 * q^75 - 98 * q^76 - 93 * q^77 + 21 * q^78 - 64 * q^79 - 84 * q^80 + 15 * q^81 + 15 * q^82 - 187 * q^83 - 118 * q^84 + 36 * q^85 - 126 * q^86 - 53 * q^87 + 15 * q^88 - 138 * q^89 + 10 * q^90 - 138 * q^91 - 86 * q^92 + 23 * q^93 - 60 * q^94 + 49 * q^95 - 92 * q^96 + 9 * q^97 - 67 * q^98 - 147 * q^99

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