LMFDB - Embedded newform 8015.2.a.l.1.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.33
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.177306 q^{2} -1.77336 q^{3} -1.96856 q^{4} -1.00000 q^{5} -0.314428 q^{6} -1.00000 q^{7} -0.703651 q^{8} +0.144804 q^{9} +O(q^{10})$	\(q+0.177306 q^{2} -1.77336 q^{3} -1.96856 q^{4} -1.00000 q^{5} -0.314428 q^{6} -1.00000 q^{7} -0.703651 q^{8} +0.144804 q^{9} -0.177306 q^{10} -0.639776 q^{11} +3.49097 q^{12} -2.64003 q^{13} -0.177306 q^{14} +1.77336 q^{15} +3.81236 q^{16} +6.32556 q^{17} +0.0256746 q^{18} -6.95789 q^{19} +1.96856 q^{20} +1.77336 q^{21} -0.113436 q^{22} -3.01957 q^{23} +1.24783 q^{24} +1.00000 q^{25} -0.468094 q^{26} +5.06329 q^{27} +1.96856 q^{28} -1.66003 q^{29} +0.314428 q^{30} -5.14184 q^{31} +2.08326 q^{32} +1.13455 q^{33} +1.12156 q^{34} +1.00000 q^{35} -0.285055 q^{36} -0.896079 q^{37} -1.23368 q^{38} +4.68172 q^{39} +0.703651 q^{40} +1.25216 q^{41} +0.314428 q^{42} -9.47924 q^{43} +1.25944 q^{44} -0.144804 q^{45} -0.535389 q^{46} -7.01227 q^{47} -6.76069 q^{48} +1.00000 q^{49} +0.177306 q^{50} -11.2175 q^{51} +5.19706 q^{52} -9.00910 q^{53} +0.897753 q^{54} +0.639776 q^{55} +0.703651 q^{56} +12.3388 q^{57} -0.294334 q^{58} -10.4486 q^{59} -3.49097 q^{60} -4.57798 q^{61} -0.911681 q^{62} -0.144804 q^{63} -7.25535 q^{64} +2.64003 q^{65} +0.201163 q^{66} -5.16197 q^{67} -12.4523 q^{68} +5.35479 q^{69} +0.177306 q^{70} +9.51234 q^{71} -0.101891 q^{72} +5.65625 q^{73} -0.158880 q^{74} -1.77336 q^{75} +13.6971 q^{76} +0.639776 q^{77} +0.830098 q^{78} +1.21962 q^{79} -3.81236 q^{80} -9.41344 q^{81} +0.222015 q^{82} -17.2730 q^{83} -3.49097 q^{84} -6.32556 q^{85} -1.68073 q^{86} +2.94383 q^{87} +0.450179 q^{88} +7.76378 q^{89} -0.0256746 q^{90} +2.64003 q^{91} +5.94422 q^{92} +9.11834 q^{93} -1.24332 q^{94} +6.95789 q^{95} -3.69437 q^{96} -18.6292 q^{97} +0.177306 q^{98} -0.0926419 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * 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 $

$2$	0.177306	0.125375	0.0626873	−	0.998033i	$-0.480033\pi$
$2$	0.177306	0.125375	0.0626873	+	0.998033i	$0.480033\pi$
$3$	−1.77336	−1.02385	−0.511925	−	0.859030i	$-0.671067\pi$
$3$	−1.77336	−1.02385	−0.511925	+	0.859030i	$0.671067\pi$
$4$	−1.96856	−0.984281
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.314428	−0.128365
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.703651	−0.248778
$9$	0.144804	0.0482679
$10$	−0.177306	−0.0560692
$11$	−0.639776	−0.192900	−0.0964499	−	0.995338i	$-0.530749\pi$
$11$	−0.639776	−0.192900	−0.0964499	+	0.995338i	$0.530749\pi$
$12$	3.49097	1.00776
$13$	−2.64003	−0.732212	−0.366106	−	0.930573i	$-0.619309\pi$
$13$	−2.64003	−0.732212	−0.366106	+	0.930573i	$0.619309\pi$
$14$	−0.177306	−0.0473871
$15$	1.77336	0.457879
$16$	3.81236	0.953091
$17$	6.32556	1.53417	0.767087	−	0.641543i	$-0.221705\pi$
$17$	6.32556	1.53417	0.767087	+	0.641543i	$0.221705\pi$
$18$	0.0256746	0.00605156
$19$	−6.95789	−1.59625	−0.798125	−	0.602492i	$-0.794175\pi$
$19$	−6.95789	−1.59625	−0.798125	+	0.602492i	$0.794175\pi$
$20$	1.96856	0.440184
$21$	1.77336	0.386979
$22$	−0.113436	−0.0241847
$23$	−3.01957	−0.629624	−0.314812	−	0.949154i	$-0.601942\pi$
$23$	−3.01957	−0.629624	−0.314812	+	0.949154i	$0.601942\pi$
$24$	1.24783	0.254712
$25$	1.00000	0.200000
$26$	−0.468094	−0.0918007
$27$	5.06329	0.974430
$28$	1.96856	0.372023
$29$	−1.66003	−0.308260	−0.154130	−	0.988051i	$-0.549257\pi$
$29$	−1.66003	−0.308260	−0.154130	+	0.988051i	$0.549257\pi$
$30$	0.314428	0.0574064
$31$	−5.14184	−0.923502	−0.461751	−	0.887010i	$-0.652779\pi$
$31$	−5.14184	−0.923502	−0.461751	+	0.887010i	$0.652779\pi$
$32$	2.08326	0.368272
$33$	1.13455	0.197500
$34$	1.12156	0.192346
$35$	1.00000	0.169031
$36$	−0.285055	−0.0475092
$37$	−0.896079	−0.147314	−0.0736572	−	0.997284i	$-0.523467\pi$
$37$	−0.896079	−0.147314	−0.0736572	+	0.997284i	$0.523467\pi$
$38$	−1.23368	−0.200129
$39$	4.68172	0.749675
$40$	0.703651	0.111257
$41$	1.25216	0.195554	0.0977770	−	0.995208i	$-0.468827\pi$
$41$	1.25216	0.195554	0.0977770	+	0.995208i	$0.468827\pi$
$42$	0.314428	0.0485173
$43$	−9.47924	−1.44557	−0.722785	−	0.691073i	$-0.757138\pi$
$43$	−9.47924	−1.44557	−0.722785	+	0.691073i	$0.757138\pi$
$44$	1.25944	0.189868
$45$	−0.144804	−0.0215861
$46$	−0.535389	−0.0789388
$47$	−7.01227	−1.02284	−0.511422	−	0.859330i	$-0.670881\pi$
$47$	−7.01227	−1.02284	−0.511422	+	0.859330i	$0.670881\pi$
$48$	−6.76069	−0.975822
$49$	1.00000	0.142857
$50$	0.177306	0.0250749
$51$	−11.2175	−1.57076
$52$	5.19706	0.720703
$53$	−9.00910	−1.23749	−0.618747	−	0.785590i	$-0.712360\pi$
$53$	−9.00910	−1.23749	−0.618747	+	0.785590i	$0.712360\pi$
$54$	0.897753	0.122169
$55$	0.639776	0.0862674
$56$	0.703651	0.0940294
$57$	12.3388	1.63432
$58$	−0.294334	−0.0386480
$59$	−10.4486	−1.36029	−0.680144	−	0.733079i	$-0.738083\pi$
$59$	−10.4486	−1.36029	−0.680144	+	0.733079i	$0.738083\pi$
$60$	−3.49097	−0.450682
$61$	−4.57798	−0.586150	−0.293075	−	0.956090i	$-0.594679\pi$
$61$	−4.57798	−0.586150	−0.293075	+	0.956090i	$0.594679\pi$
$62$	−0.911681	−0.115784
$63$	−0.144804	−0.0182435
$64$	−7.25535	−0.906919
$65$	2.64003	0.327455
$66$	0.201163	0.0247615
$67$	−5.16197	−0.630635	−0.315317	−	0.948986i	$-0.602111\pi$
$67$	−5.16197	−0.630635	−0.315317	+	0.948986i	$0.602111\pi$
$68$	−12.4523	−1.51006
$69$	5.35479	0.644641
$70$	0.177306	0.0211922
$71$	9.51234	1.12891	0.564454	−	0.825465i	$-0.309087\pi$
$71$	9.51234	1.12891	0.564454	+	0.825465i	$0.309087\pi$
$72$	−0.101891	−0.0120080
$73$	5.65625	0.662015	0.331007	−	0.943628i	$-0.392612\pi$
$73$	5.65625	0.662015	0.331007	+	0.943628i	$0.392612\pi$
$74$	−0.158880	−0.0184695
$75$	−1.77336	−0.204770
$76$	13.6971	1.57116
$77$	0.639776	0.0729093
$78$	0.830098	0.0939901
$79$	1.21962	0.137218	0.0686091	−	0.997644i	$-0.478144\pi$
$79$	1.21962	0.137218	0.0686091	+	0.997644i	$0.478144\pi$
$80$	−3.81236	−0.426235
$81$	−9.41344	−1.04594
$82$	0.222015	0.0245175
$83$	−17.2730	−1.89595	−0.947977	−	0.318339i	$-0.896875\pi$
$83$	−17.2730	−1.89595	−0.947977	+	0.318339i	$0.896875\pi$
$84$	−3.49097	−0.380896
$85$	−6.32556	−0.686104
$86$	−1.68073	−0.181238
$87$	2.94383	0.315612
$88$	0.450179	0.0479893
$89$	7.76378	0.822959	0.411480	−	0.911419i	$-0.365012\pi$
$89$	7.76378	0.822959	0.411480	+	0.911419i	$0.365012\pi$
$90$	−0.0256746	−0.00270634
$91$	2.64003	0.276750
$92$	5.94422	0.619727
$93$	9.11834	0.945527
$94$	−1.24332	−0.128239
$95$	6.95789	0.713865
$96$	−3.69437	−0.377055
$97$	−18.6292	−1.89151	−0.945753	−	0.324885i	$-0.894674\pi$
$97$	−18.6292	−1.89151	−0.945753	+	0.324885i	$0.894674\pi$
$98$	0.177306	0.0179106
$99$	−0.0926419	−0.00931086
$100$	−1.96856	−0.196856
$101$	9.10274	0.905756	0.452878	−	0.891572i	$-0.350397\pi$
$101$	9.10274	0.905756	0.452878	+	0.891572i	$0.350397\pi$
$102$	−1.98893	−0.196934
$103$	−13.0303	−1.28391	−0.641957	−	0.766741i	$-0.721877\pi$
$103$	−13.0303	−1.28391	−0.641957	+	0.766741i	$0.721877\pi$
$104$	1.85766	0.182158
$105$	−1.77336	−0.173062
$106$	−1.59737	−0.155150
$107$	−7.46844	−0.722001	−0.361001	−	0.932566i	$-0.617565\pi$
$107$	−7.46844	−0.722001	−0.361001	+	0.932566i	$0.617565\pi$
$108$	−9.96740	−0.959114
$109$	−20.0020	−1.91585	−0.957923	−	0.287025i	$-0.907334\pi$
$109$	−20.0020	−1.91585	−0.957923	+	0.287025i	$0.907334\pi$
$110$	0.113436	0.0108157
$111$	1.58907	0.150828
$112$	−3.81236	−0.360234
$113$	−13.3848	−1.25914	−0.629570	−	0.776944i	$-0.716769\pi$
$113$	−13.3848	−1.25914	−0.629570	+	0.776944i	$0.716769\pi$
$114$	2.18776	0.204902
$115$	3.01957	0.281577
$116$	3.26788	0.303415
$117$	−0.382286	−0.0353423
$118$	−1.85260	−0.170545
$119$	−6.32556	−0.579863
$120$	−1.24783	−0.113910
$121$	−10.5907	−0.962790
$122$	−0.811704	−0.0734882
$123$	−2.22052	−0.200218
$124$	10.1220	0.908986
$125$	−1.00000	−0.0894427
$126$	−0.0256746	−0.00228728
$127$	−9.93366	−0.881469	−0.440735	−	0.897637i	$-0.645282\pi$
$127$	−9.93366	−0.881469	−0.440735	+	0.897637i	$0.645282\pi$
$128$	−5.45294	−0.481976
$129$	16.8101	1.48005
$130$	0.468094	0.0410545
$131$	5.00799	0.437551	0.218775	−	0.975775i	$-0.429794\pi$
$131$	5.00799	0.437551	0.218775	+	0.975775i	$0.429794\pi$
$132$	−2.23344	−0.194396
$133$	6.95789	0.603326
$134$	−0.915250	−0.0790655
$135$	−5.06329	−0.435779
$136$	−4.45099	−0.381669
$137$	22.7945	1.94746	0.973731	−	0.227701i	$-0.0731209\pi$
$137$	22.7945	1.94746	0.973731	+	0.227701i	$0.0731209\pi$
$138$	0.949438	0.0808215
$139$	21.9719	1.86363	0.931815	−	0.362935i	$-0.118225\pi$
$139$	21.9719	1.86363	0.931815	+	0.362935i	$0.118225\pi$
$140$	−1.96856	−0.166374
$141$	12.4353	1.04724
$142$	1.68660	0.141536
$143$	1.68903	0.141244
$144$	0.552044	0.0460037
$145$	1.66003	0.137858
$146$	1.00289	0.0829997
$147$	−1.77336	−0.146264
$148$	1.76399	0.144999
$149$	6.86559	0.562451	0.281226	−	0.959642i	$-0.409259\pi$
$149$	6.86559	0.562451	0.281226	+	0.959642i	$0.409259\pi$
$150$	−0.314428	−0.0256729
$151$	−1.72727	−0.140564	−0.0702818	−	0.997527i	$-0.522390\pi$
$151$	−1.72727	−0.140564	−0.0702818	+	0.997527i	$0.522390\pi$
$152$	4.89593	0.397112
$153$	0.915965	0.0740514
$154$	0.113436	0.00914096
$155$	5.14184	0.413003
$156$	−9.21626	−0.737891
$157$	7.85732	0.627082	0.313541	−	0.949575i	$-0.398485\pi$
$157$	7.85732	0.627082	0.313541	+	0.949575i	$0.398485\pi$
$158$	0.216247	0.0172037
$159$	15.9764	1.26701
$160$	−2.08326	−0.164696
$161$	3.01957	0.237976
$162$	−1.66906	−0.131134
$163$	10.9697	0.859212	0.429606	−	0.903016i	$-0.358652\pi$
$163$	10.9697	0.859212	0.429606	+	0.903016i	$0.358652\pi$
$164$	−2.46495	−0.192480
$165$	−1.13455	−0.0883248
$166$	−3.06261	−0.237704
$167$	−0.101144	−0.00782677	−0.00391339	−	0.999992i	$-0.501246\pi$
$167$	−0.101144	−0.00782677	−0.00391339	+	0.999992i	$0.501246\pi$
$168$	−1.24783	−0.0962719
$169$	−6.03025	−0.463865
$170$	−1.12156	−0.0860199
$171$	−1.00753	−0.0770476
$172$	18.6605	1.42285
$173$	−2.37379	−0.180476	−0.0902379	−	0.995920i	$-0.528763\pi$
$173$	−2.37379	−0.180476	−0.0902379	+	0.995920i	$0.528763\pi$
$174$	0.521960	0.0395697
$175$	−1.00000	−0.0755929
$176$	−2.43906	−0.183851
$177$	18.5291	1.39273
$178$	1.37657	0.103178
$179$	−16.7854	−1.25460	−0.627298	−	0.778779i	$-0.715839\pi$
$179$	−16.7854	−1.25460	−0.627298	+	0.778779i	$0.715839\pi$
$180$	0.285055	0.0212467
$181$	−14.2181	−1.05682	−0.528410	−	0.848989i	$-0.677212\pi$
$181$	−14.2181	−1.05682	−0.528410	+	0.848989i	$0.677212\pi$
$182$	0.468094	0.0346974
$183$	8.11840	0.600129
$184$	2.12473	0.156637
$185$	0.896079	0.0658810
$186$	1.61674	0.118545
$187$	−4.04694	−0.295942
$188$	13.8041	1.00677
$189$	−5.06329	−0.368300
$190$	1.23368	0.0895005
$191$	−9.13370	−0.660892	−0.330446	−	0.943825i	$-0.607199\pi$
$191$	−9.13370	−0.660892	−0.330446	+	0.943825i	$0.607199\pi$
$192$	12.8663	0.928549
$193$	22.3999	1.61238	0.806189	−	0.591658i	$-0.201526\pi$
$193$	22.3999	1.61238	0.806189	+	0.591658i	$0.201526\pi$
$194$	−3.30307	−0.237147
$195$	−4.68172	−0.335265
$196$	−1.96856	−0.140612
$197$	−10.5228	−0.749718	−0.374859	−	0.927082i	$-0.622309\pi$
$197$	−10.5228	−0.749718	−0.374859	+	0.927082i	$0.622309\pi$
$198$	−0.0164260	−0.00116734
$199$	−22.9550	−1.62724	−0.813619	−	0.581399i	$-0.802506\pi$
$199$	−22.9550	−1.62724	−0.813619	+	0.581399i	$0.802506\pi$
$200$	−0.703651	−0.0497557
$201$	9.15403	0.645675
$202$	1.61397	0.113559
$203$	1.66003	0.116511
$204$	22.0823	1.54607
$205$	−1.25216	−0.0874544
$206$	−2.31035	−0.160970
$207$	−0.437245	−0.0303906
$208$	−10.0647	−0.697865
$209$	4.45149	0.307916
$210$	−0.314428	−0.0216976
$211$	−21.4441	−1.47627	−0.738136	−	0.674651i	$-0.764294\pi$
$211$	−21.4441	−1.47627	−0.738136	+	0.674651i	$0.764294\pi$
$212$	17.7350	1.21804
$213$	−16.8688	−1.15583
$214$	−1.32420	−0.0905206
$215$	9.47924	0.646479
$216$	−3.56279	−0.242417
$217$	5.14184	0.349051
$218$	−3.54648	−0.240198
$219$	−10.0306	−0.677803
$220$	−1.25944	−0.0849114
$221$	−16.6997	−1.12334
$222$	0.281752	0.0189100
$223$	−11.6626	−0.780986	−0.390493	−	0.920606i	$-0.627695\pi$
$223$	−11.6626	−0.780986	−0.390493	+	0.920606i	$0.627695\pi$
$224$	−2.08326	−0.139194
$225$	0.144804	0.00965358
$226$	−2.37322	−0.157864
$227$	3.51032	0.232988	0.116494	−	0.993191i	$-0.462834\pi$
$227$	3.51032	0.232988	0.116494	+	0.993191i	$0.462834\pi$
$228$	−24.2898	−1.60863
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	0.535389	0.0353025
$231$	−1.13455	−0.0746481
$232$	1.16808	0.0766884
$233$	14.0683	0.921643	0.460821	−	0.887493i	$-0.347555\pi$
$233$	14.0683	0.921643	0.460821	+	0.887493i	$0.347555\pi$
$234$	−0.0677817	−0.00443103
$235$	7.01227	0.457430
$236$	20.5687	1.33891
$237$	−2.16283	−0.140491
$238$	−1.12156	−0.0727001
$239$	6.38400	0.412947	0.206473	−	0.978452i	$-0.433801\pi$
$239$	6.38400	0.412947	0.206473	+	0.978452i	$0.433801\pi$
$240$	6.76069	0.436401
$241$	1.06088	0.0683375	0.0341687	−	0.999416i	$-0.489122\pi$
$241$	1.06088	0.0683375	0.0341687	+	0.999416i	$0.489122\pi$
$242$	−1.87780	−0.120709
$243$	1.50355	0.0964528
$244$	9.01203	0.576936
$245$	−1.00000	−0.0638877
$246$	−0.393713	−0.0251022
$247$	18.3690	1.16879
$248$	3.61806	0.229747
$249$	30.6312	1.94117
$250$	−0.177306	−0.0112138
$251$	−26.1553	−1.65091	−0.825455	−	0.564468i	$-0.809081\pi$
$251$	−26.1553	−1.65091	−0.825455	+	0.564468i	$0.809081\pi$
$252$	0.285055	0.0179568
$253$	1.93185	0.121454
$254$	−1.76130	−0.110514
$255$	11.2175	0.702467
$256$	13.5439	0.846491
$257$	−1.74763	−0.109014	−0.0545071	−	0.998513i	$-0.517359\pi$
$257$	−1.74763	−0.109014	−0.0545071	+	0.998513i	$0.517359\pi$
$258$	2.98054	0.185560
$259$	0.896079	0.0556796
$260$	−5.19706	−0.322308
$261$	−0.240379	−0.0148791
$262$	0.887949	0.0548577
$263$	9.21353	0.568131	0.284065	−	0.958805i	$-0.408317\pi$
$263$	9.21353	0.568131	0.284065	+	0.958805i	$0.408317\pi$
$264$	−0.798330	−0.0491338
$265$	9.00910	0.553424
$266$	1.23368	0.0756417
$267$	−13.7680	−0.842586
$268$	10.1617	0.620722
$269$	18.3383	1.11811	0.559054	−	0.829131i	$-0.311164\pi$
$269$	18.3383	1.11811	0.559054	+	0.829131i	$0.311164\pi$
$270$	−0.897753	−0.0546355
$271$	−22.9608	−1.39477	−0.697386	−	0.716696i	$-0.745654\pi$
$271$	−22.9608	−1.39477	−0.697386	+	0.716696i	$0.745654\pi$
$272$	24.1153	1.46221
$273$	−4.68172	−0.283351
$274$	4.04160	0.244162
$275$	−0.639776	−0.0385800
$276$	−10.5412	−0.634508
$277$	−10.7662	−0.646877	−0.323439	−	0.946249i	$-0.604839\pi$
$277$	−10.7662	−0.646877	−0.323439	+	0.946249i	$0.604839\pi$
$278$	3.89575	0.233652
$279$	−0.744558	−0.0445755
$280$	−0.703651	−0.0420512
$281$	18.7391	1.11788	0.558940	−	0.829208i	$-0.311208\pi$
$281$	18.7391	1.11788	0.558940	+	0.829208i	$0.311208\pi$
$282$	2.20485	0.131297
$283$	24.7051	1.46857	0.734283	−	0.678843i	$-0.237519\pi$
$283$	24.7051	1.46857	0.734283	+	0.678843i	$0.237519\pi$
$284$	−18.7256	−1.11116
$285$	−12.3388	−0.730890
$286$	0.299475	0.0177083
$287$	−1.25216	−0.0739124
$288$	0.301663	0.0177757
$289$	23.0128	1.35369
$290$	0.294334	0.0172839
$291$	33.0362	1.93662
$292$	−11.1347	−0.651609
$293$	33.2001	1.93957	0.969784	−	0.243966i	$-0.0784484\pi$
$293$	33.2001	1.93957	0.969784	+	0.243966i	$0.0784484\pi$
$294$	−0.314428	−0.0183378
$295$	10.4486	0.608339
$296$	0.630527	0.0366486
$297$	−3.23937	−0.187967
$298$	1.21731	0.0705171
$299$	7.97176	0.461019
$300$	3.49097	0.201551
$301$	9.47924	0.546374
$302$	−0.306257	−0.0176231
$303$	−16.1424	−0.927358
$304$	−26.5260	−1.52137
$305$	4.57798	0.262134
$306$	0.162406	0.00928415
$307$	24.7066	1.41008	0.705039	−	0.709169i	$-0.250930\pi$
$307$	24.7066	1.41008	0.705039	+	0.709169i	$0.250930\pi$
$308$	−1.25944	−0.0717632
$309$	23.1074	1.31453
$310$	0.911681	0.0517800
$311$	18.8964	1.07152	0.535759	−	0.844371i	$-0.320026\pi$
$311$	18.8964	1.07152	0.535759	+	0.844371i	$0.320026\pi$
$312$	−3.29430	−0.186503
$313$	−24.5126	−1.38554	−0.692768	−	0.721160i	$-0.743609\pi$
$313$	−24.5126	−1.38554	−0.692768	+	0.721160i	$0.743609\pi$
$314$	1.39315	0.0786201
$315$	0.144804	0.00815876
$316$	−2.40090	−0.135061
$317$	7.11436	0.399582	0.199791	−	0.979839i	$-0.435974\pi$
$317$	7.11436	0.399582	0.199791	+	0.979839i	$0.435974\pi$
$318$	2.83271	0.158851
$319$	1.06205	0.0594633
$320$	7.25535	0.405586
$321$	13.2442	0.739221
$322$	0.535389	0.0298361
$323$	−44.0126	−2.44893
$324$	18.5310	1.02950
$325$	−2.64003	−0.146442
$326$	1.94499	0.107723
$327$	35.4708	1.96154
$328$	−0.881081	−0.0486496
$329$	7.01227	0.386599
$330$	−0.201163	−0.0110737
$331$	−26.6025	−1.46221	−0.731103	−	0.682267i	$-0.760994\pi$
$331$	−26.6025	−1.46221	−0.731103	+	0.682267i	$0.760994\pi$
$332$	34.0029	1.86615
$333$	−0.129756	−0.00711056
$334$	−0.0179335	−0.000981277 0
$335$	5.16197	0.282029
$336$	6.76069	0.368826
$337$	−20.5741	−1.12074	−0.560371	−	0.828242i	$-0.689342\pi$
$337$	−20.5741	−1.12074	−0.560371	+	0.828242i	$0.689342\pi$
$338$	−1.06920	−0.0581569
$339$	23.7361	1.28917
$340$	12.4523	0.675319
$341$	3.28963	0.178143
$342$	−0.178641	−0.00965981
$343$	−1.00000	−0.0539949
$344$	6.67008	0.359627
$345$	−5.35479	−0.288292
$346$	−0.420888	−0.0226271
$347$	19.1273	1.02681	0.513404	−	0.858147i	$-0.328384\pi$
$347$	19.1273	1.02681	0.513404	+	0.858147i	$0.328384\pi$
$348$	−5.79512	−0.310651
$349$	−22.1849	−1.18753	−0.593765	−	0.804638i	$-0.702359\pi$
$349$	−22.1849	−1.18753	−0.593765	+	0.804638i	$0.702359\pi$
$350$	−0.177306	−0.00947742
$351$	−13.3672	−0.713490
$352$	−1.33282	−0.0710395
$353$	2.55318	0.135892	0.0679462	−	0.997689i	$-0.478355\pi$
$353$	2.55318	0.135892	0.0679462	+	0.997689i	$0.478355\pi$
$354$	3.28532	0.174613
$355$	−9.51234	−0.504863
$356$	−15.2835	−0.810023
$357$	11.2175	0.593693
$358$	−2.97615	−0.157294
$359$	14.3040	0.754938	0.377469	−	0.926022i	$-0.376794\pi$
$359$	14.3040	0.754938	0.377469	+	0.926022i	$0.376794\pi$
$360$	0.101891	0.00537014
$361$	29.4123	1.54802
$362$	−2.52095	−0.132498
$363$	18.7811	0.985752
$364$	−5.19706	−0.272400
$365$	−5.65625	−0.296062
$366$	1.43944	0.0752409
$367$	3.02815	0.158068	0.0790341	−	0.996872i	$-0.474816\pi$
$367$	3.02815	0.158068	0.0790341	+	0.996872i	$0.474816\pi$
$368$	−11.5117	−0.600089
$369$	0.181317	0.00943898
$370$	0.158880	0.00825980
$371$	9.00910	0.467729
$372$	−17.9500	−0.930665
$373$	−20.0667	−1.03901	−0.519507	−	0.854466i	$-0.673884\pi$
$373$	−20.0667	−1.03901	−0.519507	+	0.854466i	$0.673884\pi$
$374$	−0.717549	−0.0371036
$375$	1.77336	0.0915759
$376$	4.93419	0.254461
$377$	4.38253	0.225712
$378$	−0.897753	−0.0461754
$379$	−31.0196	−1.59337	−0.796686	−	0.604394i	$-0.793415\pi$
$379$	−31.0196	−1.59337	−0.796686	+	0.604394i	$0.793415\pi$
$380$	−13.6971	−0.702644
$381$	17.6159	0.902492
$382$	−1.61946	−0.0828590
$383$	28.4889	1.45572	0.727858	−	0.685728i	$-0.240516\pi$
$383$	28.4889	1.45572	0.727858	+	0.685728i	$0.240516\pi$
$384$	9.67002	0.493471
$385$	−0.639776	−0.0326060
$386$	3.97164	0.202151
$387$	−1.37263	−0.0697746
$388$	36.6727	1.86177
$389$	−13.7177	−0.695517	−0.347759	−	0.937584i	$-0.613057\pi$
$389$	−13.7177	−0.695517	−0.347759	+	0.937584i	$0.613057\pi$
$390$	−0.830098	−0.0420337
$391$	−19.1005	−0.965954
$392$	−0.703651	−0.0355398
$393$	−8.88097	−0.447986
$394$	−1.86576	−0.0939955
$395$	−1.21962	−0.0613659
$396$	0.182371	0.00916451
$397$	14.8305	0.744323	0.372161	−	0.928168i	$-0.378617\pi$
$397$	14.8305	0.744323	0.372161	+	0.928168i	$0.378617\pi$
$398$	−4.07007	−0.204014
$399$	−12.3388	−0.617715
$400$	3.81236	0.190618
$401$	34.4861	1.72216	0.861078	−	0.508473i	$-0.169790\pi$
$401$	34.4861	1.72216	0.861078	+	0.508473i	$0.169790\pi$
$402$	1.62307	0.0809512
$403$	13.5746	0.676200
$404$	−17.9193	−0.891519
$405$	9.41344	0.467758
$406$	0.294334	0.0146076
$407$	0.573290	0.0284169
$408$	7.89321	0.390772
$409$	17.7653	0.878438	0.439219	−	0.898380i	$-0.355255\pi$
$409$	17.7653	0.878438	0.439219	+	0.898380i	$0.355255\pi$
$410$	−0.222015	−0.0109645
$411$	−40.4228	−1.99391
$412$	25.6509	1.26373
$413$	10.4486	0.514140
$414$	−0.0775263	−0.00381021
$415$	17.2730	0.847896
$416$	−5.49986	−0.269653
$417$	−38.9640	−1.90808
$418$	0.789278	0.0386049
$419$	−14.0985	−0.688758	−0.344379	−	0.938831i	$-0.611910\pi$
$419$	−14.0985	−0.688758	−0.344379	+	0.938831i	$0.611910\pi$
$420$	3.49097	0.170342
$421$	2.43136	0.118497	0.0592485	−	0.998243i	$-0.481130\pi$
$421$	2.43136	0.118497	0.0592485	+	0.998243i	$0.481130\pi$
$422$	−3.80217	−0.185087
$423$	−1.01540	−0.0493705
$424$	6.33926	0.307862
$425$	6.32556	0.306835
$426$	−2.99095	−0.144912
$427$	4.57798	0.221544
$428$	14.7021	0.710652
$429$	−2.99525	−0.144612
$430$	1.68073	0.0810520
$431$	11.5551	0.556592	0.278296	−	0.960495i	$-0.410230\pi$
$431$	11.5551	0.556592	0.278296	+	0.960495i	$0.410230\pi$
$432$	19.3031	0.928721
$433$	35.1114	1.68735	0.843673	−	0.536858i	$-0.180389\pi$
$433$	35.1114	1.68735	0.843673	+	0.536858i	$0.180389\pi$
$434$	0.911681	0.0437621
$435$	−2.94383	−0.141146
$436$	39.3752	1.88573
$437$	21.0099	1.00504
$438$	−1.77848	−0.0849793
$439$	8.10691	0.386922	0.193461	−	0.981108i	$-0.438029\pi$
$439$	8.10691	0.386922	0.193461	+	0.981108i	$0.438029\pi$
$440$	−0.450179	−0.0214615
$441$	0.144804	0.00689541
$442$	−2.96096	−0.140838
$443$	13.4712	0.640035	0.320018	−	0.947412i	$-0.396311\pi$
$443$	13.4712	0.640035	0.320018	+	0.947412i	$0.396311\pi$
$444$	−3.12818	−0.148457
$445$	−7.76378	−0.368038
$446$	−2.06785	−0.0979157
$447$	−12.1752	−0.575866
$448$	7.25535	0.342783
$449$	−35.2371	−1.66294	−0.831470	−	0.555570i	$-0.812500\pi$
$449$	−35.2371	−1.66294	−0.831470	+	0.555570i	$0.812500\pi$
$450$	0.0256746	0.00121031
$451$	−0.801100	−0.0377223
$452$	26.3489	1.23935
$453$	3.06308	0.143916
$454$	0.622402	0.0292108
$455$	−2.64003	−0.123766
$456$	−8.68225	−0.406583
$457$	−24.5476	−1.14829	−0.574145	−	0.818754i	$-0.694665\pi$
$457$	−24.5476	−1.14829	−0.574145	+	0.818754i	$0.694665\pi$
$458$	0.177306	0.00828498
$459$	32.0282	1.49495
$460$	−5.94422	−0.277151
$461$	6.05338	0.281934	0.140967	−	0.990014i	$-0.454979\pi$
$461$	6.05338	0.281934	0.140967	+	0.990014i	$0.454979\pi$
$462$	−0.201163	−0.00935897
$463$	−4.03738	−0.187633	−0.0938166	−	0.995590i	$-0.529907\pi$
$463$	−4.03738	−0.187633	−0.0938166	+	0.995590i	$0.529907\pi$
$464$	−6.32864	−0.293800
$465$	−9.11834	−0.422853
$466$	2.49439	0.115551
$467$	−21.9718	−1.01673	−0.508366	−	0.861141i	$-0.669750\pi$
$467$	−21.9718	−1.01673	−0.508366	+	0.861141i	$0.669750\pi$
$468$	0.752553	0.0347868
$469$	5.16197	0.238358
$470$	1.24332	0.0573500
$471$	−13.9338	−0.642038
$472$	7.35215	0.338410
$473$	6.06459	0.278850
$474$	−0.383483	−0.0176140
$475$	−6.95789	−0.319250
$476$	12.4523	0.570749
$477$	−1.30455	−0.0597313
$478$	1.13192	0.0517730
$479$	−6.64512	−0.303623	−0.151812	−	0.988409i	$-0.548511\pi$
$479$	−6.64512	−0.303623	−0.151812	+	0.988409i	$0.548511\pi$
$480$	3.69437	0.168624
$481$	2.36567	0.107865
$482$	0.188101	0.00856778
$483$	−5.35479	−0.243651
$484$	20.8484	0.947656
$485$	18.6292	0.845908
$486$	0.266589	0.0120927
$487$	12.7097	0.575933	0.287967	−	0.957640i	$-0.407021\pi$
$487$	12.7097	0.575933	0.287967	+	0.957640i	$0.407021\pi$
$488$	3.22130	0.145821
$489$	−19.4532	−0.879704
$490$	−0.177306	−0.00800988
$491$	−27.5861	−1.24494	−0.622472	−	0.782642i	$-0.713872\pi$
$491$	−27.5861	−1.24494	−0.622472	+	0.782642i	$0.713872\pi$
$492$	4.37124	0.197071
$493$	−10.5006	−0.472925
$494$	3.25695	0.146537
$495$	0.0926419	0.00416394
$496$	−19.6026	−0.880181
$497$	−9.51234	−0.426687
$498$	5.43110	0.243373
$499$	−37.3390	−1.67152	−0.835761	−	0.549094i	$-0.814973\pi$
$499$	−37.3390	−1.67152	−0.835761	+	0.549094i	$0.814973\pi$
$500$	1.96856	0.0880368
$501$	0.179365	0.00801344
$502$	−4.63750	−0.206982
$503$	24.5926	1.09653	0.548264	−	0.836305i	$-0.315289\pi$
$503$	24.5926	1.09653	0.548264	+	0.836305i	$0.315289\pi$
$504$	0.101891	0.00453860
$505$	−9.10274	−0.405067
$506$	0.342529	0.0152273
$507$	10.6938	0.474928
$508$	19.5550	0.867614
$509$	−17.4789	−0.774737	−0.387369	−	0.921925i	$-0.626616\pi$
$509$	−17.4789	−0.774737	−0.387369	+	0.921925i	$0.626616\pi$
$510$	1.98893	0.0880714
$511$	−5.65625	−0.250218
$512$	13.3073	0.588105
$513$	−35.2298	−1.55544
$514$	−0.309866	−0.0136676
$515$	13.0303	0.574183
$516$	−33.0917	−1.45678
$517$	4.48628	0.197306
$518$	0.158880	0.00698081
$519$	4.20958	0.184780
$520$	−1.85766	−0.0814637
$521$	−1.48819	−0.0651990	−0.0325995	−	0.999468i	$-0.510379\pi$
$521$	−1.48819	−0.0651990	−0.0325995	+	0.999468i	$0.510379\pi$
$522$	−0.0426207	−0.00186546
$523$	2.09180	0.0914679	0.0457339	−	0.998954i	$-0.485437\pi$
$523$	2.09180	0.0914679	0.0457339	+	0.998954i	$0.485437\pi$
$524$	−9.85855	−0.430673
$525$	1.77336	0.0773958
$526$	1.63362	0.0712291
$527$	−32.5251	−1.41681
$528$	4.32533	0.188236
$529$	−13.8822	−0.603573
$530$	1.59737	0.0693853
$531$	−1.51299	−0.0656582
$532$	−13.6971	−0.593842
$533$	−3.30573	−0.143187
$534$	−2.44115	−0.105639
$535$	7.46844	0.322889
$536$	3.63223	0.156888
$537$	29.7665	1.28452
$538$	3.25150	0.140182
$539$	−0.639776	−0.0275571
$540$	9.96740	0.428929
$541$	−14.6748	−0.630920	−0.315460	−	0.948939i	$-0.602159\pi$
$541$	−14.6748	−0.630920	−0.315460	+	0.948939i	$0.602159\pi$
$542$	−4.07110	−0.174869
$543$	25.2137	1.08202
$544$	13.1778	0.564993
$545$	20.0020	0.856792
$546$	−0.830098	−0.0355249
$547$	39.9747	1.70920	0.854598	−	0.519290i	$-0.173804\pi$
$547$	39.9747	1.70920	0.854598	+	0.519290i	$0.173804\pi$
$548$	−44.8723	−1.91685
$549$	−0.662908	−0.0282922
$550$	−0.113436	−0.00483694
$551$	11.5503	0.492060
$552$	−3.76790	−0.160373
$553$	−1.21962	−0.0518636
$554$	−1.90891	−0.0811019
$555$	−1.58907	−0.0674523
$556$	−43.2530	−1.83434
$557$	−25.7840	−1.09250	−0.546251	−	0.837621i	$-0.683946\pi$
$557$	−25.7840	−1.09250	−0.546251	+	0.837621i	$0.683946\pi$
$558$	−0.132015	−0.00558863
$559$	25.0255	1.05846
$560$	3.81236	0.161102
$561$	7.17669	0.303000
$562$	3.32256	0.140154
$563$	15.4832	0.652537	0.326269	−	0.945277i	$-0.394209\pi$
$563$	15.4832	0.652537	0.326269	+	0.945277i	$0.394209\pi$
$564$	−24.4796	−1.03078
$565$	13.3848	0.563104
$566$	4.38037	0.184121
$567$	9.41344	0.395327
$568$	−6.69337	−0.280848
$569$	−26.5208	−1.11181	−0.555906	−	0.831245i	$-0.687628\pi$
$569$	−26.5208	−1.11181	−0.555906	+	0.831245i	$0.687628\pi$
$570$	−2.18776	−0.0916350
$571$	27.6779	1.15828	0.579142	−	0.815227i	$-0.303388\pi$
$571$	27.6779	1.15828	0.579142	+	0.815227i	$0.303388\pi$
$572$	−3.32496	−0.139023
$573$	16.1973	0.676654
$574$	−0.222015	−0.00926674
$575$	−3.01957	−0.125925
$576$	−1.05060	−0.0437751
$577$	19.0810	0.794352	0.397176	−	0.917743i	$-0.369990\pi$
$577$	19.0810	0.794352	0.397176	+	0.917743i	$0.369990\pi$
$578$	4.08031	0.169718
$579$	−39.7230	−1.65083
$580$	−3.26788	−0.135691
$581$	17.2730	0.716603
$582$	5.85753	0.242803
$583$	5.76381	0.238712
$584$	−3.98003	−0.164695
$585$	0.382286	0.0158056
$586$	5.88658	0.243172
$587$	−34.9330	−1.44184	−0.720920	−	0.693018i	$-0.756281\pi$
$587$	−34.9330	−1.44184	−0.720920	+	0.693018i	$0.756281\pi$
$588$	3.49097	0.143965
$589$	35.7764	1.47414
$590$	1.85260	0.0762702
$591$	18.6607	0.767599
$592$	−3.41618	−0.140404
$593$	−3.83915	−0.157655	−0.0788275	−	0.996888i	$-0.525118\pi$
$593$	−3.83915	−0.157655	−0.0788275	+	0.996888i	$0.525118\pi$
$594$	−0.574361	−0.0235663
$595$	6.32556	0.259323
$596$	−13.5153	−0.553610
$597$	40.7075	1.66605
$598$	1.41344	0.0578000
$599$	40.6855	1.66237	0.831183	−	0.555999i	$-0.187664\pi$
$599$	40.6855	1.66237	0.831183	+	0.555999i	$0.187664\pi$
$600$	1.24783	0.0509423
$601$	22.7544	0.928170	0.464085	−	0.885791i	$-0.346383\pi$
$601$	22.7544	0.928170	0.464085	+	0.885791i	$0.346383\pi$
$602$	1.68073	0.0685014
$603$	−0.747472	−0.0304394
$604$	3.40025	0.138354
$605$	10.5907	0.430573
$606$	−2.86215	−0.116267
$607$	23.9724	0.973010	0.486505	−	0.873678i	$-0.338272\pi$
$607$	23.9724	0.973010	0.486505	+	0.873678i	$0.338272\pi$
$608$	−14.4951	−0.587854
$609$	−2.94383	−0.119290
$610$	0.811704	0.0328649
$611$	18.5126	0.748939
$612$	−1.80313	−0.0728874
$613$	3.34662	0.135169	0.0675845	−	0.997714i	$-0.478471\pi$
$613$	3.34662	0.135169	0.0675845	+	0.997714i	$0.478471\pi$
$614$	4.38063	0.176788
$615$	2.22052	0.0895401
$616$	−0.450179	−0.0181382
$617$	−10.9995	−0.442822	−0.221411	−	0.975181i	$-0.571066\pi$
$617$	−10.9995	−0.442822	−0.221411	+	0.975181i	$0.571066\pi$
$618$	4.09709	0.164809
$619$	16.3619	0.657640	0.328820	−	0.944393i	$-0.393349\pi$
$619$	16.3619	0.657640	0.328820	+	0.944393i	$0.393349\pi$
$620$	−10.1220	−0.406511
$621$	−15.2890	−0.613525
$622$	3.35046	0.134341
$623$	−7.76378	−0.311049
$624$	17.8484	0.714508
$625$	1.00000	0.0400000
$626$	−4.34625	−0.173711
$627$	−7.89410	−0.315260
$628$	−15.4676	−0.617225
$629$	−5.66820	−0.226006
$630$	0.0256746	0.00102290
$631$	36.1886	1.44065	0.720323	−	0.693639i	$-0.243994\pi$
$631$	36.1886	1.44065	0.720323	+	0.693639i	$0.243994\pi$
$632$	−0.858189	−0.0341369
$633$	38.0281	1.51148
$634$	1.26142	0.0500974
$635$	9.93366	0.394205
$636$	−31.4505	−1.24709
$637$	−2.64003	−0.104602
$638$	0.188308	0.00745518
$639$	1.37742	0.0544900
$640$	5.45294	0.215546
$641$	−25.6413	−1.01277	−0.506385	−	0.862308i	$-0.669018\pi$
$641$	−25.6413	−1.01277	−0.506385	+	0.862308i	$0.669018\pi$
$642$	2.34829	0.0926794
$643$	0.144796	0.00571018	0.00285509	−	0.999996i	$-0.499091\pi$
$643$	0.144796	0.00571018	0.00285509	+	0.999996i	$0.499091\pi$
$644$	−5.94422	−0.234235
$645$	−16.8101	−0.661897
$646$	−7.80371	−0.307033
$647$	−14.2312	−0.559486	−0.279743	−	0.960075i	$-0.590249\pi$
$647$	−14.2312	−0.559486	−0.279743	+	0.960075i	$0.590249\pi$
$648$	6.62378	0.260207
$649$	6.68474	0.262399
$650$	−0.468094	−0.0183601
$651$	−9.11834	−0.357376
$652$	−21.5945	−0.845706
$653$	−5.41349	−0.211846	−0.105923	−	0.994374i	$-0.533780\pi$
$653$	−5.41349	−0.211846	−0.105923	+	0.994374i	$0.533780\pi$
$654$	6.28919	0.245927
$655$	−5.00799	−0.195679
$656$	4.77367	0.186381
$657$	0.819046	0.0319540
$658$	1.24332	0.0484696
$659$	−32.2234	−1.25524	−0.627622	−	0.778518i	$-0.715972\pi$
$659$	−32.2234	−1.25524	−0.627622	+	0.778518i	$0.715972\pi$
$660$	2.23344	0.0869365
$661$	−29.6861	−1.15466	−0.577328	−	0.816513i	$-0.695904\pi$
$661$	−29.6861	−1.15466	−0.577328	+	0.816513i	$0.695904\pi$
$662$	−4.71679	−0.183323
$663$	29.6145	1.15013
$664$	12.1541	0.471672
$665$	−6.95789	−0.269816
$666$	−0.0230065	−0.000891483 0
$667$	5.01259	0.194088
$668$	0.199109	0.00770374
$669$	20.6820	0.799612
$670$	0.915250	0.0353592
$671$	2.92888	0.113068
$672$	3.69437	0.142513
$673$	−11.2206	−0.432523	−0.216262	−	0.976335i	$-0.569386\pi$
$673$	−11.2206	−0.432523	−0.216262	+	0.976335i	$0.569386\pi$
$674$	−3.64792	−0.140513
$675$	5.06329	0.194886
$676$	11.8709	0.456574
$677$	31.2202	1.19989	0.599944	−	0.800042i	$-0.295189\pi$
$677$	31.2202	1.19989	0.599944	+	0.800042i	$0.295189\pi$
$678$	4.20856	0.161629
$679$	18.6292	0.714922
$680$	4.45099	0.170688
$681$	−6.22506	−0.238545
$682$	0.583272	0.0223346
$683$	35.5516	1.36034	0.680172	−	0.733053i	$-0.261905\pi$
$683$	35.5516	1.36034	0.680172	+	0.733053i	$0.261905\pi$
$684$	1.98338	0.0758365
$685$	−22.7945	−0.870932
$686$	−0.177306	−0.00676959
$687$	−1.77336	−0.0676579
$688$	−36.1383	−1.37776
$689$	23.7843	0.906109
$690$	−0.949438	−0.0361445
$691$	−21.0442	−0.800560	−0.400280	−	0.916393i	$-0.631087\pi$
$691$	−21.0442	−0.800560	−0.400280	+	0.916393i	$0.631087\pi$
$692$	4.67295	0.177639
$693$	0.0926419	0.00351918
$694$	3.39139	0.128735
$695$	−21.9719	−0.833440
$696$	−2.07143	−0.0785174
$697$	7.92059	0.300014
$698$	−3.93352	−0.148886
$699$	−24.9481	−0.943624
$700$	1.96856	0.0744047
$701$	−22.3782	−0.845212	−0.422606	−	0.906313i	$-0.638885\pi$
$701$	−22.3782	−0.845212	−0.422606	+	0.906313i	$0.638885\pi$
$702$	−2.37009	−0.0894534
$703$	6.23482	0.235151
$704$	4.64180	0.174944
$705$	−12.4353	−0.468339
$706$	0.452696	0.0170374
$707$	−9.10274	−0.342344
$708$	−36.4756	−1.37084
$709$	45.5067	1.70904	0.854520	−	0.519419i	$-0.173851\pi$
$709$	45.5067	1.70904	0.854520	+	0.519419i	$0.173851\pi$
$710$	−1.68660	−0.0632969
$711$	0.176606	0.00662324
$712$	−5.46299	−0.204734
$713$	15.5262	0.581460
$714$	1.98893	0.0744340
$715$	−1.68903	−0.0631660
$716$	33.0430	1.23488
$717$	−11.3211	−0.422795
$718$	2.53620	0.0946500
$719$	18.7149	0.697950	0.348975	−	0.937132i	$-0.386530\pi$
$719$	18.7149	0.697950	0.348975	+	0.937132i	$0.386530\pi$
$720$	−0.552044	−0.0205735
$721$	13.0303	0.485274
$722$	5.21499	0.194082
$723$	−1.88133	−0.0699673
$724$	27.9891	1.04021
$725$	−1.66003	−0.0616520
$726$	3.33001	0.123588
$727$	−20.3001	−0.752888	−0.376444	−	0.926439i	$-0.622853\pi$
$727$	−20.3001	−0.752888	−0.376444	+	0.926439i	$0.622853\pi$
$728$	−1.85766	−0.0688494
$729$	25.5740	0.947185
$730$	−1.00289	−0.0371186
$731$	−59.9615	−2.21776
$732$	−15.9816	−0.590696
$733$	−5.90820	−0.218224	−0.109112	−	0.994029i	$-0.534801\pi$
$733$	−5.90820	−0.218224	−0.109112	+	0.994029i	$0.534801\pi$
$734$	0.536911	0.0198177
$735$	1.77336	0.0654113
$736$	−6.29055	−0.231873
$737$	3.30250	0.121649
$738$	0.0321486	0.00118341
$739$	25.3524	0.932604	0.466302	−	0.884625i	$-0.345586\pi$
$739$	25.3524	0.932604	0.466302	+	0.884625i	$0.345586\pi$
$740$	−1.76399	−0.0648455
$741$	−32.5749	−1.19667
$742$	1.59737	0.0586413
$743$	41.4168	1.51943	0.759717	−	0.650253i	$-0.225337\pi$
$743$	41.4168	1.51943	0.759717	+	0.650253i	$0.225337\pi$
$744$	−6.41613	−0.235227
$745$	−6.86559	−0.251536
$746$	−3.55795	−0.130266
$747$	−2.50119	−0.0915137
$748$	7.96666	0.291290
$749$	7.46844	0.272891
$750$	0.314428	0.0114813
$751$	11.5455	0.421300	0.210650	−	0.977562i	$-0.432442\pi$
$751$	11.5455	0.421300	0.210650	+	0.977562i	$0.432442\pi$
$752$	−26.7333	−0.974863
$753$	46.3828	1.69028
$754$	0.777050	0.0282985
$755$	1.72727	0.0628620
$756$	9.96740	0.362511
$757$	−14.3446	−0.521363	−0.260681	−	0.965425i	$-0.583947\pi$
$757$	−14.3446	−0.521363	−0.260681	+	0.965425i	$0.583947\pi$
$758$	−5.49998	−0.199768
$759$	−3.42587	−0.124351
$760$	−4.89593	−0.177594
$761$	3.31937	0.120327	0.0601635	−	0.998189i	$-0.480838\pi$
$761$	3.31937	0.120327	0.0601635	+	0.998189i	$0.480838\pi$
$762$	3.12342	0.113149
$763$	20.0020	0.724122
$764$	17.9803	0.650503
$765$	−0.915965	−0.0331168
$766$	5.05127	0.182510
$767$	27.5845	0.996019
$768$	−24.0181	−0.866680
$769$	−3.61887	−0.130500	−0.0652499	−	0.997869i	$-0.520784\pi$
$769$	−3.61887	−0.130500	−0.0652499	+	0.997869i	$0.520784\pi$
$770$	−0.113436	−0.00408796
$771$	3.09918	0.111614
$772$	−44.0956	−1.58703
$773$	−43.6956	−1.57162	−0.785810	−	0.618468i	$-0.787754\pi$
$773$	−43.6956	−1.57162	−0.785810	+	0.618468i	$0.787754\pi$
$774$	−0.243376	−0.00874796
$775$	−5.14184	−0.184700
$776$	13.1084	0.470566
$777$	−1.58907	−0.0570076
$778$	−2.43224	−0.0872001
$779$	−8.71237	−0.312153
$780$	9.21626	0.329995
$781$	−6.08577	−0.217766
$782$	−3.38664	−0.121106
$783$	−8.40522	−0.300378
$784$	3.81236	0.136156
$785$	−7.85732	−0.280440
$786$	−1.57465	−0.0561660
$787$	22.2010	0.791379	0.395689	−	0.918384i	$-0.370506\pi$
$787$	22.2010	0.791379	0.395689	+	0.918384i	$0.370506\pi$
$788$	20.7148	0.737933
$789$	−16.3389	−0.581680
$790$	−0.216247	−0.00769372
$791$	13.3848	0.475910
$792$	0.0651876	0.00231634
$793$	12.0860	0.429186
$794$	2.62955	0.0933191
$795$	−15.9764	−0.566623
$796$	45.1884	1.60166
$797$	0.552766	0.0195800	0.00978999	−	0.999952i	$-0.496884\pi$
$797$	0.552766	0.0195800	0.00978999	+	0.999952i	$0.496884\pi$
$798$	−2.18776	−0.0774457
$799$	−44.3565	−1.56922
$800$	2.08326	0.0736543
$801$	1.12422	0.0397225
$802$	6.11461	0.215914
$803$	−3.61874	−0.127702
$804$	−18.0203	−0.635526
$805$	−3.01957	−0.106426
$806$	2.40686	0.0847782
$807$	−32.5205	−1.14477
$808$	−6.40515	−0.225332
$809$	−23.4047	−0.822866	−0.411433	−	0.911440i	$-0.634972\pi$
$809$	−23.4047	−0.822866	−0.411433	+	0.911440i	$0.634972\pi$
$810$	1.66906	0.0586449
$811$	30.7889	1.08115	0.540573	−	0.841297i	$-0.318207\pi$
$811$	30.7889	1.08115	0.540573	+	0.841297i	$0.318207\pi$
$812$	−3.26788	−0.114680
$813$	40.7178	1.42804
$814$	0.101648	0.00356276
$815$	−10.9697	−0.384251
$816$	−42.7652	−1.49708
$817$	65.9556	2.30749
$818$	3.14990	0.110134
$819$	0.382286	0.0133581
$820$	2.46495	0.0860797
$821$	−53.9264	−1.88204	−0.941022	−	0.338344i	$-0.890133\pi$
$821$	−53.9264	−1.88204	−0.941022	+	0.338344i	$0.890133\pi$
$822$	−7.16721	−0.249985
$823$	−20.4217	−0.711856	−0.355928	−	0.934513i	$-0.615835\pi$
$823$	−20.4217	−0.711856	−0.355928	+	0.934513i	$0.615835\pi$
$824$	9.16878	0.319410
$825$	1.13455	0.0395001
$826$	1.85260	0.0644601
$827$	32.6957	1.13694	0.568470	−	0.822704i	$-0.307535\pi$
$827$	32.6957	1.13694	0.568470	+	0.822704i	$0.307535\pi$
$828$	0.860744	0.0299129
$829$	37.3968	1.29884	0.649422	−	0.760428i	$-0.275011\pi$
$829$	37.3968	1.29884	0.649422	+	0.760428i	$0.275011\pi$
$830$	3.06261	0.106305
$831$	19.0923	0.662305
$832$	19.1543	0.664057
$833$	6.32556	0.219168
$834$	−6.90857	−0.239224
$835$	0.101144	0.00350024
$836$	−8.76305	−0.303076
$837$	−26.0346	−0.899889
$838$	−2.49976	−0.0863527
$839$	−17.2708	−0.596254	−0.298127	−	0.954526i	$-0.596362\pi$
$839$	−17.2708	−0.596254	−0.298127	+	0.954526i	$0.596362\pi$
$840$	1.24783	0.0430541
$841$	−26.2443	−0.904976
$842$	0.431095	0.0148565
$843$	−33.2311	−1.14454
$844$	42.2141	1.45307
$845$	6.03025	0.207447
$846$	−0.180037	−0.00618981
$847$	10.5907	0.363900
$848$	−34.3459	−1.17944
$849$	−43.8110	−1.50359
$850$	1.12156	0.0384693
$851$	2.70578	0.0927528
$852$	33.2073	1.13766
$853$	−26.6556	−0.912672	−0.456336	−	0.889808i	$-0.650838\pi$
$853$	−26.6556	−0.912672	−0.456336	+	0.889808i	$0.650838\pi$
$854$	0.811704	0.0277759
$855$	1.00753	0.0344568
$856$	5.25518	0.179618
$857$	44.4595	1.51871	0.759354	−	0.650678i	$-0.225515\pi$
$857$	44.4595	1.51871	0.759354	+	0.650678i	$0.225515\pi$
$858$	−0.531077	−0.0181307
$859$	14.5481	0.496375	0.248187	−	0.968712i	$-0.420165\pi$
$859$	14.5481	0.496375	0.248187	+	0.968712i	$0.420165\pi$
$860$	−18.6605	−0.636317
$861$	2.22052	0.0756752
$862$	2.04880	0.0697824
$863$	−32.4779	−1.10556	−0.552780	−	0.833327i	$-0.686433\pi$
$863$	−32.4779	−1.10556	−0.552780	+	0.833327i	$0.686433\pi$
$864$	10.5481	0.358855
$865$	2.37379	0.0807112
$866$	6.22547	0.211550
$867$	−40.8099	−1.38598
$868$	−10.1220	−0.343564
$869$	−0.780286	−0.0264694
$870$	−0.521960	−0.0176961
$871$	13.6277	0.461759
$872$	14.0744	0.476621
$873$	−2.69757	−0.0912990
$874$	3.72518	0.126006
$875$	1.00000	0.0338062
$876$	19.7458	0.667149
$877$	29.5104	0.996495	0.498247	−	0.867035i	$-0.333977\pi$
$877$	29.5104	0.996495	0.498247	+	0.867035i	$0.333977\pi$
$878$	1.43741	0.0485101
$879$	−58.8756	−1.98583
$880$	2.43906	0.0822207
$881$	28.8388	0.971605	0.485802	−	0.874069i	$-0.338527\pi$
$881$	28.8388	0.971605	0.485802	+	0.874069i	$0.338527\pi$
$882$	0.0256746	0.000864509 0
$883$	−6.08332	−0.204720	−0.102360	−	0.994747i	$-0.532639\pi$
$883$	−6.08332	−0.204720	−0.102360	+	0.994747i	$0.532639\pi$
$884$	32.8743	1.10568
$885$	−18.5291	−0.622848
$886$	2.38853	0.0802441
$887$	4.67202	0.156871	0.0784355	−	0.996919i	$-0.475008\pi$
$887$	4.67202	0.156871	0.0784355	+	0.996919i	$0.475008\pi$
$888$	−1.11815	−0.0375227
$889$	9.93366	0.333164
$890$	−1.37657	−0.0461426
$891$	6.02250	0.201761
$892$	22.9586	0.768709
$893$	48.7906	1.63272
$894$	−2.15873	−0.0721989
$895$	16.7854	0.561073
$896$	5.45294	0.182170
$897$	−14.1368	−0.472014
$898$	−6.24775	−0.208490
$899$	8.53562	0.284679
$900$	−0.285055	−0.00950184
$901$	−56.9876	−1.89853
$902$	−0.142040	−0.00472942
$903$	−16.8101	−0.559405
$904$	9.41826	0.313247
$905$	14.2181	0.472624
$906$	0.543103	0.0180434
$907$	37.0421	1.22996	0.614981	−	0.788542i	$-0.289164\pi$
$907$	37.0421	1.22996	0.614981	+	0.788542i	$0.289164\pi$
$908$	−6.91028	−0.229326
$909$	1.31811	0.0437189
$910$	−0.468094	−0.0155172
$911$	3.87020	0.128226	0.0641128	−	0.997943i	$-0.479578\pi$
$911$	3.87020	0.128226	0.0641128	+	0.997943i	$0.479578\pi$
$912$	47.0402	1.55766
$913$	11.0508	0.365729
$914$	−4.35245	−0.143966
$915$	−8.11840	−0.268386
$916$	−1.96856	−0.0650431
$917$	−5.00799	−0.165379
$918$	5.67879	0.187428
$919$	−42.9788	−1.41774	−0.708870	−	0.705339i	$-0.750795\pi$
$919$	−42.9788	−1.41774	−0.708870	+	0.705339i	$0.750795\pi$
$920$	−2.12473	−0.0700501
$921$	−43.8136	−1.44371
$922$	1.07330	0.0353473
$923$	−25.1129	−0.826600
$924$	2.23344	0.0734747
$925$	−0.896079	−0.0294629
$926$	−0.715854	−0.0235244
$927$	−1.88683	−0.0619718
$928$	−3.45827	−0.113523
$929$	−17.7526	−0.582445	−0.291222	−	0.956655i	$-0.594062\pi$
$929$	−17.7526	−0.582445	−0.291222	+	0.956655i	$0.594062\pi$
$930$	−1.61674	−0.0530149
$931$	−6.95789	−0.228036
$932$	−27.6943	−0.907156
$933$	−33.5101	−1.09707
$934$	−3.89573	−0.127472
$935$	4.04694	0.132349
$936$	0.268996	0.00879240
$937$	45.9827	1.50219	0.751094	−	0.660195i	$-0.229526\pi$
$937$	45.9827	1.50219	0.751094	+	0.660195i	$0.229526\pi$
$938$	0.915250	0.0298840
$939$	43.4697	1.41858
$940$	−13.8041	−0.450240
$941$	18.7917	0.612591	0.306295	−	0.951937i	$-0.400910\pi$
$941$	18.7917	0.612591	0.306295	+	0.951937i	$0.400910\pi$
$942$	−2.47056	−0.0804952
$943$	−3.78098	−0.123126
$944$	−39.8337	−1.29648
$945$	5.06329	0.164709
$946$	1.07529	0.0349607
$947$	−21.7088	−0.705440	−0.352720	−	0.935729i	$-0.614743\pi$
$947$	−21.7088	−0.705440	−0.352720	+	0.935729i	$0.614743\pi$
$948$	4.25767	0.138283
$949$	−14.9327	−0.484735
$950$	−1.23368	−0.0400258
$951$	−12.6163	−0.409112
$952$	4.45099	0.144257
$953$	14.7668	0.478344	0.239172	−	0.970977i	$-0.423124\pi$
$953$	14.7668	0.478344	0.239172	+	0.970977i	$0.423124\pi$
$954$	−0.231305	−0.00748878
$955$	9.13370	0.295560
$956$	−12.5673	−0.406456
$957$	−1.88339	−0.0608815
$958$	−1.17822	−0.0380666
$959$	−22.7945	−0.736071
$960$	−12.8663	−0.415260
$961$	−4.56145	−0.147144
$962$	0.419449	0.0135236
$963$	−1.08146	−0.0348495
$964$	−2.08841	−0.0672633
$965$	−22.3999	−0.721077
$966$	−0.949438	−0.0305477
$967$	−47.7645	−1.53600	−0.768001	−	0.640449i	$-0.778748\pi$
$967$	−47.7645	−1.53600	−0.768001	+	0.640449i	$0.778748\pi$
$968$	7.45215	0.239521
$969$	78.0502	2.50733
$970$	3.30307	0.106055
$971$	−44.0116	−1.41240	−0.706199	−	0.708013i	$-0.749592\pi$
$971$	−44.0116	−1.41240	−0.706199	+	0.708013i	$0.749592\pi$
$972$	−2.95983	−0.0949366
$973$	−21.9719	−0.704386
$974$	2.25352	0.0722074
$975$	4.68172	0.149935
$976$	−17.4529	−0.558654
$977$	−3.25938	−0.104277	−0.0521384	−	0.998640i	$-0.516604\pi$
$977$	−3.25938	−0.104277	−0.0521384	+	0.998640i	$0.516604\pi$
$978$	−3.44917	−0.110292
$979$	−4.96708	−0.158749
$980$	1.96856	0.0628834
$981$	−2.89637	−0.0924738
$982$	−4.89119	−0.156084
$983$	−52.0093	−1.65884	−0.829419	−	0.558627i	$-0.811328\pi$
$983$	−52.0093	−1.65884	−0.829419	+	0.558627i	$0.811328\pi$
$984$	1.56247	0.0498098
$985$	10.5228	0.335284
$986$	−1.86183	−0.0592927
$987$	−12.4353	−0.395819
$988$	−36.1606	−1.15042
$989$	28.6233	0.910166
$990$	0.0164260	0.000522053 0
$991$	−59.0845	−1.87688	−0.938440	−	0.345441i	$-0.887729\pi$
$991$	−59.0845	−1.87688	−0.938440	+	0.345441i	$0.887729\pi$
$992$	−10.7118	−0.340100
$993$	47.1758	1.49708
$994$	−1.68660	−0.0534957
$995$	22.9550	0.727723
$996$	−60.2994	−1.91066
$997$	18.9426	0.599918	0.299959	−	0.953952i	$-0.403027\pi$
$997$	18.9426	0.599918	0.299959	+	0.953952i	$0.403027\pi$
$998$	−6.62044	−0.209566
$999$	−4.53711	−0.143548

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.33	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.33	✓	62	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q+0.177306 q^{2} -1.77336 q^{3} -1.96856 q^{4} -1.00000 q^{5} -0.314428 q^{6} -1.00000 q^{7} -0.703651 q^{8} +0.144804 q^{9} +O(q^{10})\)	\(q+0.177306 q^{2} -1.77336 q^{3} -1.96856 q^{4} -1.00000 q^{5} -0.314428 q^{6} -1.00000 q^{7} -0.703651 q^{8} +0.144804 q^{9} -0.177306 q^{10} -0.639776 q^{11} +3.49097 q^{12} -2.64003 q^{13} -0.177306 q^{14} +1.77336 q^{15} +3.81236 q^{16} +6.32556 q^{17} +0.0256746 q^{18} -6.95789 q^{19} +1.96856 q^{20} +1.77336 q^{21} -0.113436 q^{22} -3.01957 q^{23} +1.24783 q^{24} +1.00000 q^{25} -0.468094 q^{26} +5.06329 q^{27} +1.96856 q^{28} -1.66003 q^{29} +0.314428 q^{30} -5.14184 q^{31} +2.08326 q^{32} +1.13455 q^{33} +1.12156 q^{34} +1.00000 q^{35} -0.285055 q^{36} -0.896079 q^{37} -1.23368 q^{38} +4.68172 q^{39} +0.703651 q^{40} +1.25216 q^{41} +0.314428 q^{42} -9.47924 q^{43} +1.25944 q^{44} -0.144804 q^{45} -0.535389 q^{46} -7.01227 q^{47} -6.76069 q^{48} +1.00000 q^{49} +0.177306 q^{50} -11.2175 q^{51} +5.19706 q^{52} -9.00910 q^{53} +0.897753 q^{54} +0.639776 q^{55} +0.703651 q^{56} +12.3388 q^{57} -0.294334 q^{58} -10.4486 q^{59} -3.49097 q^{60} -4.57798 q^{61} -0.911681 q^{62} -0.144804 q^{63} -7.25535 q^{64} +2.64003 q^{65} +0.201163 q^{66} -5.16197 q^{67} -12.4523 q^{68} +5.35479 q^{69} +0.177306 q^{70} +9.51234 q^{71} -0.101891 q^{72} +5.65625 q^{73} -0.158880 q^{74} -1.77336 q^{75} +13.6971 q^{76} +0.639776 q^{77} +0.830098 q^{78} +1.21962 q^{79} -3.81236 q^{80} -9.41344 q^{81} +0.222015 q^{82} -17.2730 q^{83} -3.49097 q^{84} -6.32556 q^{85} -1.68073 q^{86} +2.94383 q^{87} +0.450179 q^{88} +7.76378 q^{89} -0.0256746 q^{90} +2.64003 q^{91} +5.94422 q^{92} +9.11834 q^{93} -1.24332 q^{94} +6.95789 q^{95} -3.69437 q^{96} -18.6292 q^{97} +0.177306 q^{98} -0.0926419 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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