LMFDB - Embedded newform 8015.2.a.o.1.20

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:	$73$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q-1.40112 q^{2} +2.16021 q^{3} -0.0368596 q^{4} +1.00000 q^{5} -3.02672 q^{6} +1.00000 q^{7} +2.85389 q^{8} +1.66651 q^{9} +O(q^{10})$	\(q-1.40112 q^{2} +2.16021 q^{3} -0.0368596 q^{4} +1.00000 q^{5} -3.02672 q^{6} +1.00000 q^{7} +2.85389 q^{8} +1.66651 q^{9} -1.40112 q^{10} -2.82761 q^{11} -0.0796246 q^{12} -0.871253 q^{13} -1.40112 q^{14} +2.16021 q^{15} -3.92492 q^{16} -1.89642 q^{17} -2.33498 q^{18} +4.42553 q^{19} -0.0368596 q^{20} +2.16021 q^{21} +3.96182 q^{22} -4.27037 q^{23} +6.16500 q^{24} +1.00000 q^{25} +1.22073 q^{26} -2.88062 q^{27} -0.0368596 q^{28} +0.283667 q^{29} -3.02672 q^{30} +8.68762 q^{31} -0.208483 q^{32} -6.10823 q^{33} +2.65711 q^{34} +1.00000 q^{35} -0.0614269 q^{36} +4.34253 q^{37} -6.20071 q^{38} -1.88209 q^{39} +2.85389 q^{40} +1.23011 q^{41} -3.02672 q^{42} +9.14173 q^{43} +0.104225 q^{44} +1.66651 q^{45} +5.98330 q^{46} -6.22271 q^{47} -8.47866 q^{48} +1.00000 q^{49} -1.40112 q^{50} -4.09666 q^{51} +0.0321141 q^{52} -12.7847 q^{53} +4.03610 q^{54} -2.82761 q^{55} +2.85389 q^{56} +9.56008 q^{57} -0.397452 q^{58} -2.39875 q^{59} -0.0796246 q^{60} +10.5720 q^{61} -12.1724 q^{62} +1.66651 q^{63} +8.14195 q^{64} -0.871253 q^{65} +8.55837 q^{66} +2.14826 q^{67} +0.0699012 q^{68} -9.22489 q^{69} -1.40112 q^{70} -15.5147 q^{71} +4.75602 q^{72} +15.0864 q^{73} -6.08441 q^{74} +2.16021 q^{75} -0.163124 q^{76} -2.82761 q^{77} +2.63703 q^{78} +7.57190 q^{79} -3.92492 q^{80} -11.2223 q^{81} -1.72353 q^{82} +10.2139 q^{83} -0.0796246 q^{84} -1.89642 q^{85} -12.8087 q^{86} +0.612781 q^{87} -8.06968 q^{88} +16.1263 q^{89} -2.33498 q^{90} -0.871253 q^{91} +0.157404 q^{92} +18.7671 q^{93} +8.71877 q^{94} +4.42553 q^{95} -0.450367 q^{96} -14.6647 q^{97} -1.40112 q^{98} -4.71223 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) $ 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9 + 7 * q^10 + 27 * q^11 + 21 * q^12 + 21 * q^13 + 7 * q^14 + 14 * q^15 + 135 * q^16 + 23 * q^17 + 41 * q^18 + 26 * q^19 + 95 * q^20 + 14 * q^21 + 48 * q^22 + 16 * q^23 - q^24 + 73 * q^25 + 7 * q^26 + 44 * q^27 + 95 * q^28 + 66 * q^29 - q^30 + 23 * q^31 + 3 * q^32 + 77 * q^33 + 29 * q^34 + 73 * q^35 + 142 * q^36 + 66 * q^37 - 12 * q^38 + 53 * q^39 + 18 * q^40 + 50 * q^41 - q^42 + 43 * q^43 + 37 * q^44 + 111 * q^45 + 65 * q^46 + 28 * q^47 - 20 * q^48 + 73 * q^49 + 7 * q^50 + 71 * q^51 + 29 * q^52 - 7 * q^53 - 16 * q^54 + 27 * q^55 + 18 * q^56 + 33 * q^57 + 48 * q^58 + 16 * q^59 + 21 * q^60 + 42 * q^61 - 3 * q^62 + 111 * q^63 + 216 * q^64 + 21 * q^65 - 53 * q^66 + 48 * q^67 + 13 * q^68 + 73 * q^69 + 7 * q^70 + 68 * q^71 + 18 * q^72 + 65 * q^73 + 4 * q^74 + 14 * q^75 + 37 * q^76 + 27 * q^77 + 60 * q^78 + 116 * q^79 + 135 * q^80 + 177 * q^81 + 20 * q^82 + 40 * q^83 + 21 * q^84 + 23 * q^85 + 35 * q^86 - 14 * q^87 + 47 * q^88 + 59 * q^89 + 41 * q^90 + 21 * q^91 + 3 * q^92 + 37 * q^93 - 11 * q^94 + 26 * q^95 - 23 * q^96 + 70 * q^97 + 7 * q^98 + 49 * 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 $

$2$	−1.40112	−0.990742	−0.495371	−	0.868681i	$-0.664968\pi$
$2$	−1.40112	−0.990742	−0.495371	+	0.868681i	$0.664968\pi$
$3$	2.16021	1.24720	0.623599	−	0.781744i	$-0.285670\pi$
$3$	2.16021	1.24720	0.623599	+	0.781744i	$0.285670\pi$
$4$	−0.0368596	−0.0184298
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.02672	−1.23565
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.85389	1.00900
$9$	1.66651	0.555503
$10$	−1.40112	−0.443073
$11$	−2.82761	−0.852556	−0.426278	−	0.904592i	$-0.640175\pi$
$11$	−2.82761	−0.852556	−0.426278	+	0.904592i	$0.640175\pi$
$12$	−0.0796246	−0.0229856
$13$	−0.871253	−0.241642	−0.120821	−	0.992674i	$-0.538553\pi$
$13$	−0.871253	−0.241642	−0.120821	+	0.992674i	$0.538553\pi$
$14$	−1.40112	−0.374465
$15$	2.16021	0.557764
$16$	−3.92492	−0.981231
$17$	−1.89642	−0.459949	−0.229974	−	0.973197i	$-0.573864\pi$
$17$	−1.89642	−0.459949	−0.229974	+	0.973197i	$0.573864\pi$
$18$	−2.33498	−0.550360
$19$	4.42553	1.01529	0.507644	−	0.861567i	$-0.330517\pi$
$19$	4.42553	1.01529	0.507644	+	0.861567i	$0.330517\pi$
$20$	−0.0368596	−0.00824207
$21$	2.16021	0.471396
$22$	3.96182	0.844663
$23$	−4.27037	−0.890433	−0.445217	−	0.895423i	$-0.646873\pi$
$23$	−4.27037	−0.890433	−0.445217	+	0.895423i	$0.646873\pi$
$24$	6.16500	1.25842
$25$	1.00000	0.200000
$26$	1.22073	0.239405
$27$	−2.88062	−0.554376
$28$	−0.0368596	−0.00696582
$29$	0.283667	0.0526757	0.0263379	−	0.999653i	$-0.491615\pi$
$29$	0.283667	0.0526757	0.0263379	+	0.999653i	$0.491615\pi$
$30$	−3.02672	−0.552600
$31$	8.68762	1.56034	0.780172	−	0.625565i	$-0.215132\pi$
$31$	8.68762	1.56034	0.780172	+	0.625565i	$0.215132\pi$
$32$	−0.208483	−0.0368549
$33$	−6.10823	−1.06331
$34$	2.65711	0.455691
$35$	1.00000	0.169031
$36$	−0.0614269	−0.0102378
$37$	4.34253	0.713908	0.356954	−	0.934122i	$-0.383815\pi$
$37$	4.34253	0.713908	0.356954	+	0.934122i	$0.383815\pi$
$38$	−6.20071	−1.00589
$39$	−1.88209	−0.301375
$40$	2.85389	0.451239
$41$	1.23011	0.192111	0.0960554	−	0.995376i	$-0.469377\pi$
$41$	1.23011	0.192111	0.0960554	+	0.995376i	$0.469377\pi$
$42$	−3.02672	−0.467032
$43$	9.14173	1.39410	0.697050	−	0.717022i	$-0.254495\pi$
$43$	9.14173	1.39410	0.697050	+	0.717022i	$0.254495\pi$
$44$	0.104225	0.0157125
$45$	1.66651	0.248428
$46$	5.98330	0.882190
$47$	−6.22271	−0.907675	−0.453838	−	0.891084i	$-0.649945\pi$
$47$	−6.22271	−0.907675	−0.453838	+	0.891084i	$0.649945\pi$
$48$	−8.47866	−1.22379
$49$	1.00000	0.142857
$50$	−1.40112	−0.198148
$51$	−4.09666	−0.573647
$52$	0.0321141	0.00445342
$53$	−12.7847	−1.75612	−0.878058	−	0.478554i	$-0.841161\pi$
$53$	−12.7847	−1.75612	−0.878058	+	0.478554i	$0.841161\pi$
$54$	4.03610	0.549244
$55$	−2.82761	−0.381275
$56$	2.85389	0.381367
$57$	9.56008	1.26626
$58$	−0.397452	−0.0521881
$59$	−2.39875	−0.312291	−0.156145	−	0.987734i	$-0.549907\pi$
$59$	−2.39875	−0.312291	−0.156145	+	0.987734i	$0.549907\pi$
$60$	−0.0796246	−0.0102795
$61$	10.5720	1.35361	0.676803	−	0.736164i	$-0.263365\pi$
$61$	10.5720	1.35361	0.676803	+	0.736164i	$0.263365\pi$
$62$	−12.1724	−1.54590
$63$	1.66651	0.209960
$64$	8.14195	1.01774
$65$	−0.871253	−0.108066
$66$	8.55837	1.05346
$67$	2.14826	0.262452	0.131226	−	0.991353i	$-0.458109\pi$
$67$	2.14826	0.262452	0.131226	+	0.991353i	$0.458109\pi$
$68$	0.0699012	0.00847677
$69$	−9.22489	−1.11055
$70$	−1.40112	−0.167466
$71$	−15.5147	−1.84126	−0.920628	−	0.390440i	$-0.872323\pi$
$71$	−15.5147	−1.84126	−0.920628	+	0.390440i	$0.872323\pi$
$72$	4.75602	0.560503
$73$	15.0864	1.76573	0.882863	−	0.469631i	$-0.155613\pi$
$73$	15.0864	1.76573	0.882863	+	0.469631i	$0.155613\pi$
$74$	−6.08441	−0.707298
$75$	2.16021	0.249440
$76$	−0.163124	−0.0187116
$77$	−2.82761	−0.322236
$78$	2.63703	0.298585
$79$	7.57190	0.851906	0.425953	−	0.904745i	$-0.359939\pi$
$79$	7.57190	0.851906	0.425953	+	0.904745i	$0.359939\pi$
$80$	−3.92492	−0.438820
$81$	−11.2223	−1.24692
$82$	−1.72353	−0.190332
$83$	10.2139	1.12112	0.560559	−	0.828115i	$-0.310586\pi$
$83$	10.2139	1.12112	0.560559	+	0.828115i	$0.310586\pi$
$84$	−0.0796246	−0.00868775
$85$	−1.89642	−0.205695
$86$	−12.8087	−1.38119
$87$	0.612781	0.0656971
$88$	−8.06968	−0.860230
$89$	16.1263	1.70939	0.854694	−	0.519132i	$-0.173745\pi$
$89$	16.1263	1.70939	0.854694	+	0.519132i	$0.173745\pi$
$90$	−2.33498	−0.246128
$91$	−0.871253	−0.0913321
$92$	0.157404	0.0164105
$93$	18.7671	1.94606
$94$	8.71877	0.899272
$95$	4.42553	0.454050
$96$	−0.450367	−0.0459654
$97$	−14.6647	−1.48897	−0.744486	−	0.667638i	$-0.767305\pi$
$97$	−14.6647	−1.48897	−0.744486	+	0.667638i	$0.767305\pi$
$98$	−1.40112	−0.141535
$99$	−4.71223	−0.473597
$100$	−0.0368596	−0.00368596
$101$	−2.12691	−0.211636	−0.105818	−	0.994386i	$-0.533746\pi$
$101$	−2.12691	−0.211636	−0.105818	+	0.994386i	$0.533746\pi$
$102$	5.73992	0.568336
$103$	−7.46115	−0.735169	−0.367584	−	0.929990i	$-0.619815\pi$
$103$	−7.46115	−0.735169	−0.367584	+	0.929990i	$0.619815\pi$
$104$	−2.48646	−0.243817
$105$	2.16021	0.210815
$106$	17.9129	1.73986
$107$	9.09887	0.879621	0.439810	−	0.898091i	$-0.355046\pi$
$107$	9.09887	0.879621	0.439810	+	0.898091i	$0.355046\pi$
$108$	0.106179	0.0102171
$109$	16.7483	1.60419	0.802096	−	0.597195i	$-0.203718\pi$
$109$	16.7483	1.60419	0.802096	+	0.597195i	$0.203718\pi$
$110$	3.96182	0.377745
$111$	9.38078	0.890384
$112$	−3.92492	−0.370870
$113$	−8.28524	−0.779410	−0.389705	−	0.920940i	$-0.627423\pi$
$113$	−8.28524	−0.779410	−0.389705	+	0.920940i	$0.627423\pi$
$114$	−13.3948	−1.25454
$115$	−4.27037	−0.398214
$116$	−0.0104559	−0.000970804 0
$117$	−1.45195	−0.134233
$118$	3.36094	0.309400
$119$	−1.89642	−0.173844
$120$	6.16500	0.562785
$121$	−3.00463	−0.273148
$122$	−14.8126	−1.34107
$123$	2.65729	0.239600
$124$	−0.320223	−0.0287568
$125$	1.00000	0.0894427
$126$	−2.33498	−0.208016
$127$	9.82293	0.871644	0.435822	−	0.900033i	$-0.356458\pi$
$127$	9.82293	0.871644	0.435822	+	0.900033i	$0.356458\pi$
$128$	−10.9909	−0.971467
$129$	19.7481	1.73872
$130$	1.22073	0.107065
$131$	18.0617	1.57806	0.789030	−	0.614354i	$-0.210584\pi$
$131$	18.0617	1.57806	0.789030	+	0.614354i	$0.210584\pi$
$132$	0.225147	0.0195965
$133$	4.42553	0.383742
$134$	−3.00997	−0.260022
$135$	−2.88062	−0.247925
$136$	−5.41216	−0.464089
$137$	9.81693	0.838717	0.419358	−	0.907821i	$-0.362255\pi$
$137$	9.81693	0.838717	0.419358	+	0.907821i	$0.362255\pi$
$138$	12.9252	1.10027
$139$	6.58562	0.558585	0.279293	−	0.960206i	$-0.409900\pi$
$139$	6.58562	0.558585	0.279293	+	0.960206i	$0.409900\pi$
$140$	−0.0368596	−0.00311521
$141$	−13.4424	−1.13205
$142$	21.7380	1.82421
$143$	2.46356	0.206013
$144$	−6.54091	−0.545076
$145$	0.283667	0.0235573
$146$	−21.1378	−1.74938
$147$	2.16021	0.178171
$148$	−0.160064	−0.0131572
$149$	4.92107	0.403150	0.201575	−	0.979473i	$-0.435394\pi$
$149$	4.92107	0.403150	0.201575	+	0.979473i	$0.435394\pi$
$150$	−3.02672	−0.247130
$151$	−10.8544	−0.883317	−0.441658	−	0.897183i	$-0.645610\pi$
$151$	−10.8544	−0.883317	−0.441658	+	0.897183i	$0.645610\pi$
$152$	12.6300	1.02443
$153$	−3.16039	−0.255503
$154$	3.96182	0.319253
$155$	8.68762	0.697807
$156$	0.0693731	0.00555429
$157$	23.3978	1.86735	0.933673	−	0.358126i	$-0.116584\pi$
$157$	23.3978	1.86735	0.933673	+	0.358126i	$0.116584\pi$
$158$	−10.6092	−0.844019
$159$	−27.6177	−2.19023
$160$	−0.208483	−0.0164820
$161$	−4.27037	−0.336552
$162$	15.7238	1.23538
$163$	6.88714	0.539443	0.269721	−	0.962938i	$-0.413068\pi$
$163$	6.88714	0.539443	0.269721	+	0.962938i	$0.413068\pi$
$164$	−0.0453414	−0.00354057
$165$	−6.10823	−0.475525
$166$	−14.3109	−1.11074
$167$	7.02712	0.543775	0.271888	−	0.962329i	$-0.412352\pi$
$167$	7.02712	0.543775	0.271888	+	0.962329i	$0.412352\pi$
$168$	6.16500	0.475640
$169$	−12.2409	−0.941609
$170$	2.65711	0.203791
$171$	7.37519	0.563995
$172$	−0.336961	−0.0256930
$173$	11.5864	0.880900	0.440450	−	0.897777i	$-0.354819\pi$
$173$	11.5864	0.880900	0.440450	+	0.897777i	$0.354819\pi$
$174$	−0.858581	−0.0650888
$175$	1.00000	0.0755929
$176$	11.0981	0.836554
$177$	−5.18181	−0.389488
$178$	−22.5950	−1.69356
$179$	17.6782	1.32133	0.660664	−	0.750682i	$-0.270275\pi$
$179$	17.6782	1.32133	0.660664	+	0.750682i	$0.270275\pi$
$180$	−0.0614269	−0.00457849
$181$	−1.36240	−0.101266	−0.0506332	−	0.998717i	$-0.516124\pi$
$181$	−1.36240	−0.101266	−0.0506332	+	0.998717i	$0.516124\pi$
$182$	1.22073	0.0904866
$183$	22.8377	1.68821
$184$	−12.1871	−0.898449
$185$	4.34253	0.319269
$186$	−26.2950	−1.92804
$187$	5.36232	0.392132
$188$	0.229367	0.0167283
$189$	−2.88062	−0.209535
$190$	−6.20071	−0.449847
$191$	3.42320	0.247694	0.123847	−	0.992301i	$-0.460477\pi$
$191$	3.42320	0.247694	0.123847	+	0.992301i	$0.460477\pi$
$192$	17.5883	1.26933
$193$	−1.10855	−0.0797953	−0.0398976	−	0.999204i	$-0.512703\pi$
$193$	−1.10855	−0.0797953	−0.0398976	+	0.999204i	$0.512703\pi$
$194$	20.5470	1.47519
$195$	−1.88209	−0.134779
$196$	−0.0368596	−0.00263283
$197$	21.1922	1.50988	0.754940	−	0.655794i	$-0.227666\pi$
$197$	21.1922	1.50988	0.754940	+	0.655794i	$0.227666\pi$
$198$	6.60241	0.469213
$199$	−4.65508	−0.329990	−0.164995	−	0.986294i	$-0.552761\pi$
$199$	−4.65508	−0.329990	−0.164995	+	0.986294i	$0.552761\pi$
$200$	2.85389	0.201800
$201$	4.64069	0.327329
$202$	2.98007	0.209677
$203$	0.283667	0.0199096
$204$	0.151001	0.0105722
$205$	1.23011	0.0859145
$206$	10.4540	0.728363
$207$	−7.11660	−0.494638
$208$	3.41960	0.237107
$209$	−12.5137	−0.865589
$210$	−3.02672	−0.208863
$211$	−11.9172	−0.820412	−0.410206	−	0.911993i	$-0.634543\pi$
$211$	−11.9172	−0.820412	−0.410206	+	0.911993i	$0.634543\pi$
$212$	0.471240	0.0323649
$213$	−33.5150	−2.29641
$214$	−12.7486	−0.871478
$215$	9.14173	0.623461
$216$	−8.22097	−0.559366
$217$	8.68762	0.589754
$218$	−23.4663	−1.58934
$219$	32.5897	2.20221
$220$	0.104225	0.00702682
$221$	1.65226	0.111143
$222$	−13.1436	−0.882141
$223$	−23.4269	−1.56878	−0.784390	−	0.620268i	$-0.787024\pi$
$223$	−23.4269	−1.56878	−0.784390	+	0.620268i	$0.787024\pi$
$224$	−0.208483	−0.0139298
$225$	1.66651	0.111101
$226$	11.6086	0.772194
$227$	17.5094	1.16214	0.581071	−	0.813853i	$-0.302634\pi$
$227$	17.5094	1.16214	0.581071	+	0.813853i	$0.302634\pi$
$228$	−0.352381	−0.0233370
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	5.98330	0.394527
$231$	−6.10823	−0.401892
$232$	0.809555	0.0531499
$233$	−3.27087	−0.214282	−0.107141	−	0.994244i	$-0.534170\pi$
$233$	−3.27087	−0.214282	−0.107141	+	0.994244i	$0.534170\pi$
$234$	2.03436	0.132990
$235$	−6.22271	−0.405925
$236$	0.0884171	0.00575546
$237$	16.3569	1.06249
$238$	2.65711	0.172235
$239$	−27.6271	−1.78705	−0.893524	−	0.449016i	$-0.851775\pi$
$239$	−27.6271	−1.78705	−0.893524	+	0.449016i	$0.851775\pi$
$240$	−8.47866	−0.547295
$241$	19.1584	1.23410	0.617050	−	0.786924i	$-0.288328\pi$
$241$	19.1584	1.23410	0.617050	+	0.786924i	$0.288328\pi$
$242$	4.20985	0.270619
$243$	−15.6006	−1.00078
$244$	−0.389680	−0.0249467
$245$	1.00000	0.0638877
$246$	−3.72319	−0.237382
$247$	−3.85576	−0.245336
$248$	24.7935	1.57439
$249$	22.0641	1.39826
$250$	−1.40112	−0.0886147
$251$	30.8339	1.94622	0.973110	−	0.230340i	$-0.0739839\pi$
$251$	30.8339	1.94622	0.973110	+	0.230340i	$0.0739839\pi$
$252$	−0.0614269	−0.00386953
$253$	12.0749	0.759144
$254$	−13.7631	−0.863574
$255$	−4.09666	−0.256543
$256$	−0.884329	−0.0552706
$257$	−15.1957	−0.947884	−0.473942	−	0.880556i	$-0.657169\pi$
$257$	−15.1957	−0.947884	−0.473942	+	0.880556i	$0.657169\pi$
$258$	−27.6694	−1.72262
$259$	4.34253	0.269832
$260$	0.0321141	0.00199163
$261$	0.472734	0.0292615
$262$	−25.3067	−1.56345
$263$	−15.8165	−0.975288	−0.487644	−	0.873042i	$-0.662144\pi$
$263$	−15.8165	−0.975288	−0.487644	+	0.873042i	$0.662144\pi$
$264$	−17.4322	−1.07288
$265$	−12.7847	−0.785359
$266$	−6.20071	−0.380190
$267$	34.8363	2.13195
$268$	−0.0791840	−0.00483693
$269$	2.44832	0.149277	0.0746384	−	0.997211i	$-0.476220\pi$
$269$	2.44832	0.149277	0.0746384	+	0.997211i	$0.476220\pi$
$270$	4.03610	0.245629
$271$	−0.417319	−0.0253503	−0.0126752	−	0.999920i	$-0.504035\pi$
$271$	−0.417319	−0.0253503	−0.0126752	+	0.999920i	$0.504035\pi$
$272$	7.44329	0.451316
$273$	−1.88209	−0.113909
$274$	−13.7547	−0.830952
$275$	−2.82761	−0.170511
$276$	0.340026	0.0204672
$277$	5.43106	0.326320	0.163160	−	0.986600i	$-0.447831\pi$
$277$	5.43106	0.326320	0.163160	+	0.986600i	$0.447831\pi$
$278$	−9.22725	−0.553414
$279$	14.4780	0.866775
$280$	2.85389	0.170552
$281$	−19.3313	−1.15321	−0.576605	−	0.817023i	$-0.695623\pi$
$281$	−19.3313	−1.15321	−0.576605	+	0.817023i	$0.695623\pi$
$282$	18.8344	1.12157
$283$	−0.964592	−0.0573391	−0.0286695	−	0.999589i	$-0.509127\pi$
$283$	−0.964592	−0.0573391	−0.0286695	+	0.999589i	$0.509127\pi$
$284$	0.571866	0.0339340
$285$	9.56008	0.566291
$286$	−3.45175	−0.204106
$287$	1.23011	0.0726110
$288$	−0.347438	−0.0204730
$289$	−13.4036	−0.788447
$290$	−0.397452	−0.0233392
$291$	−31.6788	−1.85704
$292$	−0.556078	−0.0325420
$293$	−3.73026	−0.217924	−0.108962	−	0.994046i	$-0.534753\pi$
$293$	−3.73026	−0.217924	−0.108962	+	0.994046i	$0.534753\pi$
$294$	−3.02672	−0.176522
$295$	−2.39875	−0.139661
$296$	12.3931	0.720334
$297$	8.14528	0.472637
$298$	−6.89501	−0.399417
$299$	3.72057	0.215166
$300$	−0.0796246	−0.00459713
$301$	9.14173	0.526921
$302$	15.2083	0.875139
$303$	−4.59458	−0.263952
$304$	−17.3699	−0.996231
$305$	10.5720	0.605351
$306$	4.42809	0.253137
$307$	−0.305512	−0.0174365	−0.00871826	−	0.999962i	$-0.502775\pi$
$307$	−0.305512	−0.0174365	−0.00871826	+	0.999962i	$0.502775\pi$
$308$	0.104225	0.00593875
$309$	−16.1176	−0.916901
$310$	−12.1724	−0.691347
$311$	−5.13416	−0.291131	−0.145566	−	0.989349i	$-0.546500\pi$
$311$	−5.13416	−0.291131	−0.145566	+	0.989349i	$0.546500\pi$
$312$	−5.37127	−0.304088
$313$	5.20955	0.294461	0.147231	−	0.989102i	$-0.452964\pi$
$313$	5.20955	0.294461	0.147231	+	0.989102i	$0.452964\pi$
$314$	−32.7831	−1.85006
$315$	1.66651	0.0938971
$316$	−0.279098	−0.0157005
$317$	−15.7027	−0.881951	−0.440975	−	0.897519i	$-0.645367\pi$
$317$	−15.7027	−0.881951	−0.440975	+	0.897519i	$0.645367\pi$
$318$	38.6957	2.16995
$319$	−0.802101	−0.0449090
$320$	8.14195	0.455149
$321$	19.6555	1.09706
$322$	5.98330	0.333436
$323$	−8.39266	−0.466980
$324$	0.413649	0.0229805
$325$	−0.871253	−0.0483284
$326$	−9.64972	−0.534449
$327$	36.1798	2.00075
$328$	3.51059	0.193840
$329$	−6.22271	−0.343069
$330$	8.55837	0.471123
$331$	−3.89793	−0.214250	−0.107125	−	0.994246i	$-0.534164\pi$
$331$	−3.89793	−0.214250	−0.107125	+	0.994246i	$0.534164\pi$
$332$	−0.376479	−0.0206620
$333$	7.23686	0.396578
$334$	−9.84585	−0.538741
$335$	2.14826	0.117372
$336$	−8.47866	−0.462549
$337$	24.8288	1.35251	0.676254	−	0.736668i	$-0.263602\pi$
$337$	24.8288	1.35251	0.676254	+	0.736668i	$0.263602\pi$
$338$	17.1510	0.932892
$339$	−17.8979	−0.972078
$340$	0.0699012	0.00379093
$341$	−24.5652	−1.33028
$342$	−10.3335	−0.558773
$343$	1.00000	0.0539949
$344$	26.0895	1.40665
$345$	−9.22489	−0.496652
$346$	−16.2340	−0.872745
$347$	17.2270	0.924792	0.462396	−	0.886674i	$-0.346990\pi$
$347$	17.2270	0.924792	0.462396	+	0.886674i	$0.346990\pi$
$348$	−0.0225869	−0.00121078
$349$	27.8317	1.48979	0.744897	−	0.667179i	$-0.232499\pi$
$349$	27.8317	1.48979	0.744897	+	0.667179i	$0.232499\pi$
$350$	−1.40112	−0.0748931
$351$	2.50975	0.133961
$352$	0.589508	0.0314209
$353$	−9.82280	−0.522815	−0.261407	−	0.965229i	$-0.584187\pi$
$353$	−9.82280	−0.522815	−0.261407	+	0.965229i	$0.584187\pi$
$354$	7.26034	0.385883
$355$	−15.5147	−0.823435
$356$	−0.594411	−0.0315037
$357$	−4.09666	−0.216818
$358$	−24.7692	−1.30910
$359$	−19.5512	−1.03187	−0.515937	−	0.856627i	$-0.672556\pi$
$359$	−19.5512	−1.03187	−0.515937	+	0.856627i	$0.672556\pi$
$360$	4.75602	0.250665
$361$	0.585355	0.0308081
$362$	1.90889	0.100329
$363$	−6.49063	−0.340670
$364$	0.0321141	0.00168323
$365$	15.0864	0.789657
$366$	−31.9984	−1.67258
$367$	36.8685	1.92452	0.962261	−	0.272129i	$-0.0877279\pi$
$367$	36.8685	1.92452	0.962261	+	0.272129i	$0.0877279\pi$
$368$	16.7609	0.873720
$369$	2.04999	0.106718
$370$	−6.08441	−0.316313
$371$	−12.7847	−0.663750
$372$	−0.691748	−0.0358655
$373$	−9.19117	−0.475901	−0.237950	−	0.971277i	$-0.576476\pi$
$373$	−9.19117	−0.475901	−0.237950	+	0.971277i	$0.576476\pi$
$374$	−7.51327	−0.388502
$375$	2.16021	0.111553
$376$	−17.7589	−0.915846
$377$	−0.247146	−0.0127287
$378$	4.03610	0.207595
$379$	11.3955	0.585348	0.292674	−	0.956212i	$-0.405455\pi$
$379$	11.3955	0.585348	0.292674	+	0.956212i	$0.405455\pi$
$380$	−0.163124	−0.00836806
$381$	21.2196	1.08711
$382$	−4.79632	−0.245401
$383$	17.1362	0.875619	0.437809	−	0.899068i	$-0.355754\pi$
$383$	17.1362	0.875619	0.437809	+	0.899068i	$0.355754\pi$
$384$	−23.7426	−1.21161
$385$	−2.82761	−0.144108
$386$	1.55321	0.0790566
$387$	15.2348	0.774427
$388$	0.540535	0.0274415
$389$	−6.60253	−0.334761	−0.167381	−	0.985892i	$-0.553531\pi$
$389$	−6.60253	−0.334761	−0.167381	+	0.985892i	$0.553531\pi$
$390$	2.63703	0.133531
$391$	8.09840	0.409554
$392$	2.85389	0.144143
$393$	39.0171	1.96815
$394$	−29.6928	−1.49590
$395$	7.57190	0.380984
$396$	0.173691	0.00872831
$397$	−34.8613	−1.74964	−0.874819	−	0.484450i	$-0.839020\pi$
$397$	−34.8613	−1.74964	−0.874819	+	0.484450i	$0.839020\pi$
$398$	6.52234	0.326935
$399$	9.56008	0.478603
$400$	−3.92492	−0.196246
$401$	−10.4101	−0.519854	−0.259927	−	0.965628i	$-0.583699\pi$
$401$	−10.4101	−0.519854	−0.259927	+	0.965628i	$0.583699\pi$
$402$	−6.50217	−0.324299
$403$	−7.56912	−0.377044
$404$	0.0783973	0.00390041
$405$	−11.2223	−0.557639
$406$	−0.397452	−0.0197252
$407$	−12.2790	−0.608646
$408$	−11.6914	−0.578811
$409$	−0.0604969	−0.00299138	−0.00149569	−	0.999999i	$-0.500476\pi$
$409$	−0.0604969	−0.00299138	−0.00149569	+	0.999999i	$0.500476\pi$
$410$	−1.72353	−0.0851192
$411$	21.2066	1.04605
$412$	0.275015	0.0135490
$413$	−2.39875	−0.118035
$414$	9.97122	0.490059
$415$	10.2139	0.501379
$416$	0.181641	0.00890569
$417$	14.2263	0.696666
$418$	17.5332	0.857576
$419$	−6.66666	−0.325688	−0.162844	−	0.986652i	$-0.552067\pi$
$419$	−6.66666	−0.325688	−0.162844	+	0.986652i	$0.552067\pi$
$420$	−0.0796246	−0.00388528
$421$	34.8106	1.69657	0.848283	−	0.529543i	$-0.177637\pi$
$421$	34.8106	1.69657	0.848283	+	0.529543i	$0.177637\pi$
$422$	16.6974	0.812817
$423$	−10.3702	−0.504216
$424$	−36.4862	−1.77192
$425$	−1.89642	−0.0919897
$426$	46.9586	2.27515
$427$	10.5720	0.511615
$428$	−0.335381	−0.0162113
$429$	5.32181	0.256939
$430$	−12.8087	−0.617689
$431$	17.4452	0.840308	0.420154	−	0.907453i	$-0.361976\pi$
$431$	17.4452	0.840308	0.420154	+	0.907453i	$0.361976\pi$
$432$	11.3062	0.543971
$433$	10.4134	0.500435	0.250217	−	0.968190i	$-0.419498\pi$
$433$	10.4134	0.500435	0.250217	+	0.968190i	$0.419498\pi$
$434$	−12.1724	−0.584295
$435$	0.612781	0.0293806
$436$	−0.617335	−0.0295650
$437$	−18.8987	−0.904046
$438$	−45.6622	−2.18182
$439$	29.0242	1.38525	0.692624	−	0.721299i	$-0.256455\pi$
$439$	29.0242	1.38525	0.692624	+	0.721299i	$0.256455\pi$
$440$	−8.06968	−0.384707
$441$	1.66651	0.0793575
$442$	−2.31501	−0.110114
$443$	23.0424	1.09478	0.547388	−	0.836879i	$-0.315622\pi$
$443$	23.0424	1.09478	0.547388	+	0.836879i	$0.315622\pi$
$444$	−0.345772	−0.0164096
$445$	16.1263	0.764462
$446$	32.8239	1.55426
$447$	10.6305	0.502807
$448$	8.14195	0.384671
$449$	−5.96299	−0.281411	−0.140705	−	0.990052i	$-0.544937\pi$
$449$	−5.96299	−0.281411	−0.140705	+	0.990052i	$0.544937\pi$
$450$	−2.33498	−0.110072
$451$	−3.47827	−0.163785
$452$	0.305391	0.0143644
$453$	−23.4477	−1.10167
$454$	−24.5328	−1.15138
$455$	−0.871253	−0.0408450
$456$	27.2834	1.27766
$457$	−35.0083	−1.63762	−0.818810	−	0.574064i	$-0.805366\pi$
$457$	−35.0083	−1.63762	−0.818810	+	0.574064i	$0.805366\pi$
$458$	−1.40112	−0.0654701
$459$	5.46286	0.254985
$460$	0.157404	0.00733901
$461$	−34.3855	−1.60149	−0.800746	−	0.599005i	$-0.795563\pi$
$461$	−34.3855	−1.60149	−0.800746	+	0.599005i	$0.795563\pi$
$462$	8.55837	0.398171
$463$	21.3949	0.994305	0.497153	−	0.867663i	$-0.334379\pi$
$463$	21.3949	0.994305	0.497153	+	0.867663i	$0.334379\pi$
$464$	−1.11337	−0.0516870
$465$	18.7671	0.870303
$466$	4.58288	0.212298
$467$	−2.97770	−0.137792	−0.0688959	−	0.997624i	$-0.521948\pi$
$467$	−2.97770	−0.137792	−0.0688959	+	0.997624i	$0.521948\pi$
$468$	0.0535183	0.00247389
$469$	2.14826	0.0991973
$470$	8.71877	0.402167
$471$	50.5441	2.32895
$472$	−6.84576	−0.315102
$473$	−25.8492	−1.18855
$474$	−22.9180	−1.05266
$475$	4.42553	0.203057
$476$	0.0699012	0.00320392
$477$	−21.3058	−0.975527
$478$	38.7089	1.77050
$479$	12.0196	0.549191	0.274596	−	0.961560i	$-0.411456\pi$
$479$	12.0196	0.549191	0.274596	+	0.961560i	$0.411456\pi$
$480$	−0.450367	−0.0205563
$481$	−3.78344	−0.172510
$482$	−26.8432	−1.22268
$483$	−9.22489	−0.419747
$484$	0.110750	0.00503407
$485$	−14.6647	−0.665889
$486$	21.8583	0.991514
$487$	−13.8667	−0.628359	−0.314180	−	0.949364i	$-0.601729\pi$
$487$	−13.8667	−0.628359	−0.314180	+	0.949364i	$0.601729\pi$
$488$	30.1713	1.36579
$489$	14.8777	0.672792
$490$	−1.40112	−0.0632962
$491$	23.4182	1.05685	0.528424	−	0.848980i	$-0.322783\pi$
$491$	23.4182	1.05685	0.528424	+	0.848980i	$0.322783\pi$
$492$	−0.0979469	−0.00441579
$493$	−0.537952	−0.0242281
$494$	5.40238	0.243065
$495$	−4.71223	−0.211799
$496$	−34.0982	−1.53106
$497$	−15.5147	−0.695930
$498$	−30.9145	−1.38531
$499$	−18.1091	−0.810675	−0.405337	−	0.914167i	$-0.632846\pi$
$499$	−18.1091	−0.810675	−0.405337	+	0.914167i	$0.632846\pi$
$500$	−0.0368596	−0.00164841
$501$	15.1801	0.678195
$502$	−43.2021	−1.92820
$503$	−39.7019	−1.77022	−0.885111	−	0.465380i	$-0.845918\pi$
$503$	−39.7019	−1.77022	−0.885111	+	0.465380i	$0.845918\pi$
$504$	4.75602	0.211850
$505$	−2.12691	−0.0946465
$506$	−16.9184	−0.752116
$507$	−26.4430	−1.17437
$508$	−0.362069	−0.0160642
$509$	29.2780	1.29772	0.648862	−	0.760906i	$-0.275245\pi$
$509$	29.2780	1.29772	0.648862	+	0.760906i	$0.275245\pi$
$510$	5.73992	0.254168
$511$	15.0864	0.667382
$512$	23.2208	1.02623
$513$	−12.7483	−0.562851
$514$	21.2911	0.939108
$515$	−7.46115	−0.328777
$516$	−0.727906	−0.0320443
$517$	17.5954	0.773844
$518$	−6.08441	−0.267334
$519$	25.0291	1.09866
$520$	−2.48646	−0.109038
$521$	30.9180	1.35454	0.677272	−	0.735733i	$-0.263162\pi$
$521$	30.9180	1.35454	0.677272	+	0.735733i	$0.263162\pi$
$522$	−0.662358	−0.0289906
$523$	−9.10914	−0.398315	−0.199157	−	0.979968i	$-0.563820\pi$
$523$	−9.10914	−0.398315	−0.199157	+	0.979968i	$0.563820\pi$
$524$	−0.665749	−0.0290834
$525$	2.16021	0.0942793
$526$	22.1609	0.966259
$527$	−16.4754	−0.717678
$528$	23.9743	1.04335
$529$	−4.76395	−0.207128
$530$	17.9129	0.778089
$531$	−3.99754	−0.173478
$532$	−0.163124	−0.00707230
$533$	−1.07174	−0.0464220
$534$	−48.8099	−2.11221
$535$	9.09887	0.393378
$536$	6.13089	0.264814
$537$	38.1885	1.64796
$538$	−3.43039	−0.147895
$539$	−2.82761	−0.121794
$540$	0.106179	0.00456921
$541$	−16.5203	−0.710264	−0.355132	−	0.934816i	$-0.615564\pi$
$541$	−16.5203	−0.710264	−0.355132	+	0.934816i	$0.615564\pi$
$542$	0.584714	0.0251156
$543$	−2.94307	−0.126299
$544$	0.395370	0.0169514
$545$	16.7483	0.717417
$546$	2.63703	0.112855
$547$	−4.28651	−0.183278	−0.0916389	−	0.995792i	$-0.529211\pi$
$547$	−4.28651	−0.183278	−0.0916389	+	0.995792i	$0.529211\pi$
$548$	−0.361848	−0.0154574
$549$	17.6183	0.751931
$550$	3.96182	0.168933
$551$	1.25538	0.0534810
$552$	−26.3268	−1.12054
$553$	7.57190	0.321990
$554$	−7.60957	−0.323299
$555$	9.38078	0.398192
$556$	−0.242744	−0.0102946
$557$	13.7920	0.584385	0.292192	−	0.956360i	$-0.405615\pi$
$557$	13.7920	0.584385	0.292192	+	0.956360i	$0.405615\pi$
$558$	−20.2854	−0.858750
$559$	−7.96476	−0.336873
$560$	−3.92492	−0.165858
$561$	11.5837	0.489066
$562$	27.0855	1.14253
$563$	−43.4883	−1.83281	−0.916406	−	0.400249i	$-0.868924\pi$
$563$	−43.4883	−1.83281	−0.916406	+	0.400249i	$0.868924\pi$
$564$	0.495480	0.0208635
$565$	−8.28524	−0.348563
$566$	1.35151	0.0568082
$567$	−11.2223	−0.471291
$568$	−44.2772	−1.85783
$569$	25.1189	1.05304	0.526519	−	0.850164i	$-0.323497\pi$
$569$	25.1189	1.05304	0.526519	+	0.850164i	$0.323497\pi$
$570$	−13.3948	−0.561048
$571$	27.2323	1.13964	0.569819	−	0.821770i	$-0.307013\pi$
$571$	27.2323	1.13964	0.569819	+	0.821770i	$0.307013\pi$
$572$	−0.0908060	−0.00379679
$573$	7.39484	0.308924
$574$	−1.72353	−0.0719388
$575$	−4.27037	−0.178087
$576$	13.5686	0.565360
$577$	0.141814	0.00590380	0.00295190	−	0.999996i	$-0.499060\pi$
$577$	0.141814	0.00590380	0.00295190	+	0.999996i	$0.499060\pi$
$578$	18.7801	0.781148
$579$	−2.39470	−0.0995205
$580$	−0.0104559	−0.000434157 0
$581$	10.2139	0.423743
$582$	44.3858	1.83985
$583$	36.1502	1.49719
$584$	43.0548	1.78162
$585$	−1.45195	−0.0600307
$586$	5.22654	0.215907
$587$	31.4263	1.29710	0.648550	−	0.761172i	$-0.275376\pi$
$587$	31.4263	1.29710	0.648550	+	0.761172i	$0.275376\pi$
$588$	−0.0796246	−0.00328366
$589$	38.4474	1.58420
$590$	3.36094	0.138368
$591$	45.7796	1.88312
$592$	−17.0441	−0.700508
$593$	−3.71716	−0.152645	−0.0763227	−	0.997083i	$-0.524318\pi$
$593$	−3.71716	−0.152645	−0.0763227	+	0.997083i	$0.524318\pi$
$594$	−11.4125	−0.468261
$595$	−1.89642	−0.0777455
$596$	−0.181389	−0.00742997
$597$	−10.0560	−0.411563
$598$	−5.21297	−0.213174
$599$	5.77438	0.235935	0.117967	−	0.993017i	$-0.462362\pi$
$599$	5.77438	0.235935	0.117967	+	0.993017i	$0.462362\pi$
$600$	6.16500	0.251685
$601$	−31.4793	−1.28407	−0.642035	−	0.766676i	$-0.721909\pi$
$601$	−31.4793	−1.28407	−0.642035	+	0.766676i	$0.721909\pi$
$602$	−12.8087	−0.522043
$603$	3.58009	0.145792
$604$	0.400088	0.0162794
$605$	−3.00463	−0.122156
$606$	6.43757	0.261508
$607$	19.3452	0.785197	0.392599	−	0.919710i	$-0.371576\pi$
$607$	19.3452	0.785197	0.392599	+	0.919710i	$0.371576\pi$
$608$	−0.922648	−0.0374183
$609$	0.612781	0.0248312
$610$	−14.8126	−0.599747
$611$	5.42155	0.219332
$612$	0.116491	0.00470887
$613$	26.5489	1.07230	0.536149	−	0.844123i	$-0.319879\pi$
$613$	26.5489	1.07230	0.536149	+	0.844123i	$0.319879\pi$
$614$	0.428060	0.0172751
$615$	2.65729	0.107152
$616$	−8.06968	−0.325136
$617$	−3.45571	−0.139121	−0.0695607	−	0.997578i	$-0.522160\pi$
$617$	−3.45571	−0.139121	−0.0695607	+	0.997578i	$0.522160\pi$
$618$	22.5828	0.908412
$619$	−2.88910	−0.116123	−0.0580613	−	0.998313i	$-0.518492\pi$
$619$	−2.88910	−0.116123	−0.0580613	+	0.998313i	$0.518492\pi$
$620$	−0.320223	−0.0128605
$621$	12.3013	0.493635
$622$	7.19357	0.288436
$623$	16.1263	0.646088
$624$	7.38705	0.295719
$625$	1.00000	0.0400000
$626$	−7.29921	−0.291735
$627$	−27.0322	−1.07956
$628$	−0.862434	−0.0344149
$629$	−8.23525	−0.328361
$630$	−2.33498	−0.0930278
$631$	5.94654	0.236728	0.118364	−	0.992970i	$-0.462235\pi$
$631$	5.94654	0.236728	0.118364	+	0.992970i	$0.462235\pi$
$632$	21.6094	0.859574
$633$	−25.7436	−1.02322
$634$	22.0014	0.873786
$635$	9.82293	0.389811
$636$	1.01798	0.0403655
$637$	−0.871253	−0.0345203
$638$	1.12384	0.0444933
$639$	−25.8554	−1.02282
$640$	−10.9909	−0.434453
$641$	38.7473	1.53042	0.765212	−	0.643778i	$-0.222634\pi$
$641$	38.7473	1.53042	0.765212	+	0.643778i	$0.222634\pi$
$642$	−27.5397	−1.08691
$643$	−28.6415	−1.12951	−0.564755	−	0.825259i	$-0.691029\pi$
$643$	−28.6415	−1.12951	−0.564755	+	0.825259i	$0.691029\pi$
$644$	0.157404	0.00620260
$645$	19.7481	0.777579
$646$	11.7591	0.462657
$647$	−20.2781	−0.797216	−0.398608	−	0.917121i	$-0.630507\pi$
$647$	−20.2781	−0.797216	−0.398608	+	0.917121i	$0.630507\pi$
$648$	−32.0271	−1.25814
$649$	6.78273	0.266245
$650$	1.22073	0.0478810
$651$	18.7671	0.735540
$652$	−0.253858	−0.00994183
$653$	14.8245	0.580127	0.290064	−	0.957007i	$-0.406324\pi$
$653$	14.8245	0.580127	0.290064	+	0.957007i	$0.406324\pi$
$654$	−50.6922	−1.98222
$655$	18.0617	0.705730
$656$	−4.82808	−0.188505
$657$	25.1416	0.980865
$658$	8.71877	0.339893
$659$	−32.8283	−1.27881	−0.639404	−	0.768871i	$-0.720819\pi$
$659$	−32.8283	−1.27881	−0.639404	+	0.768871i	$0.720819\pi$
$660$	0.225147	0.00876384
$661$	20.4071	0.793745	0.396872	−	0.917874i	$-0.370096\pi$
$661$	20.4071	0.793745	0.396872	+	0.917874i	$0.370096\pi$
$662$	5.46148	0.212266
$663$	3.56923	0.138617
$664$	29.1492	1.13121
$665$	4.42553	0.171615
$666$	−10.1397	−0.392906
$667$	−1.21136	−0.0469042
$668$	−0.259017	−0.0100217
$669$	−50.6070	−1.95658
$670$	−3.00997	−0.116285
$671$	−29.8935	−1.15402
$672$	−0.450367	−0.0173733
$673$	−13.1903	−0.508449	−0.254225	−	0.967145i	$-0.581820\pi$
$673$	−13.1903	−0.508449	−0.254225	+	0.967145i	$0.581820\pi$
$674$	−34.7881	−1.33999
$675$	−2.88062	−0.110875
$676$	0.451196	0.0173537
$677$	35.9738	1.38258	0.691292	−	0.722575i	$-0.257042\pi$
$677$	35.9738	1.38258	0.691292	+	0.722575i	$0.257042\pi$
$678$	25.0771	0.963079
$679$	−14.6647	−0.562779
$680$	−5.41216	−0.207547
$681$	37.8241	1.44942
$682$	34.4188	1.31796
$683$	−12.9176	−0.494280	−0.247140	−	0.968980i	$-0.579491\pi$
$683$	−12.9176	−0.494280	−0.247140	+	0.968980i	$0.579491\pi$
$684$	−0.271847	−0.0103943
$685$	9.81693	0.375086
$686$	−1.40112	−0.0534951
$687$	2.16021	0.0824172
$688$	−35.8806	−1.36793
$689$	11.1387	0.424352
$690$	12.9252	0.492054
$691$	−28.3662	−1.07910	−0.539550	−	0.841953i	$-0.681406\pi$
$691$	−28.3662	−1.07910	−0.539550	+	0.841953i	$0.681406\pi$
$692$	−0.427072	−0.0162348
$693$	−4.71223	−0.179003
$694$	−24.1371	−0.916230
$695$	6.58562	0.249807
$696$	1.74881	0.0662884
$697$	−2.33280	−0.0883611
$698$	−38.9955	−1.47600
$699$	−7.06576	−0.267252
$700$	−0.0368596	−0.00139316
$701$	−30.8093	−1.16365	−0.581825	−	0.813314i	$-0.697661\pi$
$701$	−30.8093	−1.16365	−0.581825	+	0.813314i	$0.697661\pi$
$702$	−3.51646	−0.132720
$703$	19.2180	0.724821
$704$	−23.0223	−0.867684
$705$	−13.4424	−0.506268
$706$	13.7629	0.517975
$707$	−2.12691	−0.0799909
$708$	0.190999	0.00717820
$709$	37.4073	1.40486	0.702431	−	0.711752i	$-0.252098\pi$
$709$	37.4073	1.40486	0.702431	+	0.711752i	$0.252098\pi$
$710$	21.7380	0.815812
$711$	12.6186	0.473236
$712$	46.0228	1.72478
$713$	−37.0994	−1.38938
$714$	5.73992	0.214811
$715$	2.46356	0.0921320
$716$	−0.651611	−0.0243518
$717$	−59.6803	−2.22880
$718$	27.3936	1.02232
$719$	−24.6415	−0.918973	−0.459487	−	0.888185i	$-0.651967\pi$
$719$	−24.6415	−0.918973	−0.459487	+	0.888185i	$0.651967\pi$
$720$	−6.54091	−0.243765
$721$	−7.46115	−0.277868
$722$	−0.820153	−0.0305229
$723$	41.3862	1.53917
$724$	0.0502176	0.00186632
$725$	0.283667	0.0105351
$726$	9.09416	0.337516
$727$	2.16792	0.0804036	0.0402018	−	0.999192i	$-0.487200\pi$
$727$	2.16792	0.0804036	0.0402018	+	0.999192i	$0.487200\pi$
$728$	−2.48646	−0.0921542
$729$	−0.0337536	−0.00125013
$730$	−21.1378	−0.782346
$731$	−17.3365	−0.641215
$732$	−0.841791	−0.0311135
$733$	−44.2602	−1.63479	−0.817394	−	0.576079i	$-0.804582\pi$
$733$	−44.2602	−1.63479	−0.817394	+	0.576079i	$0.804582\pi$
$734$	−51.6573	−1.90670
$735$	2.16021	0.0796806
$736$	0.890299	0.0328168
$737$	−6.07443	−0.223755
$738$	−2.87228	−0.105730
$739$	8.43026	0.310112	0.155056	−	0.987906i	$-0.450444\pi$
$739$	8.43026	0.310112	0.155056	+	0.987906i	$0.450444\pi$
$740$	−0.160064	−0.00588407
$741$	−8.32925	−0.305983
$742$	17.9129	0.657605
$743$	−47.2471	−1.73333	−0.866664	−	0.498892i	$-0.833741\pi$
$743$	−47.2471	−1.73333	−0.866664	+	0.498892i	$0.833741\pi$
$744$	53.5592	1.96357
$745$	4.92107	0.180294
$746$	12.8779	0.471495
$747$	17.0215	0.622784
$748$	−0.197653	−0.00722692
$749$	9.09887	0.332465
$750$	−3.02672	−0.110520
$751$	−15.2018	−0.554722	−0.277361	−	0.960766i	$-0.589460\pi$
$751$	−15.2018	−0.554722	−0.277361	+	0.960766i	$0.589460\pi$
$752$	24.4236	0.890639
$753$	66.6078	2.42732
$754$	0.346282	0.0126108
$755$	−10.8544	−0.395031
$756$	0.106179	0.00386168
$757$	−54.0340	−1.96390	−0.981949	−	0.189147i	$-0.939428\pi$
$757$	−54.0340	−1.96390	−0.981949	+	0.189147i	$0.939428\pi$
$758$	−15.9665	−0.579929
$759$	26.0844	0.946803
$760$	12.6300	0.458137
$761$	−20.0117	−0.725424	−0.362712	−	0.931901i	$-0.618149\pi$
$761$	−20.0117	−0.725424	−0.362712	+	0.931901i	$0.618149\pi$
$762$	−29.7312	−1.07705
$763$	16.7483	0.606328
$764$	−0.126178	−0.00456496
$765$	−3.16039	−0.114264
$766$	−24.0099	−0.867513
$767$	2.08992	0.0754626
$768$	−1.91034	−0.0689333
$769$	−24.7722	−0.893308	−0.446654	−	0.894707i	$-0.647385\pi$
$769$	−24.7722	−0.893308	−0.446654	+	0.894707i	$0.647385\pi$
$770$	3.96182	0.142774
$771$	−32.8260	−1.18220
$772$	0.0408608	0.00147061
$773$	35.3517	1.27151	0.635756	−	0.771890i	$-0.280688\pi$
$773$	35.3517	1.27151	0.635756	+	0.771890i	$0.280688\pi$
$774$	−21.3458	−0.767257
$775$	8.68762	0.312069
$776$	−41.8513	−1.50238
$777$	9.38078	0.336534
$778$	9.25094	0.331662
$779$	5.44389	0.195048
$780$	0.0693731	0.00248396
$781$	43.8695	1.56977
$782$	−11.3468	−0.405762
$783$	−0.817139	−0.0292022
$784$	−3.92492	−0.140176
$785$	23.3978	0.835103
$786$	−54.6677	−1.94993
$787$	35.0971	1.25108	0.625538	−	0.780194i	$-0.284880\pi$
$787$	35.0971	1.25108	0.625538	+	0.780194i	$0.284880\pi$
$788$	−0.781136	−0.0278268
$789$	−34.1670	−1.21638
$790$	−10.6092	−0.377457
$791$	−8.28524	−0.294589
$792$	−13.4482	−0.477860
$793$	−9.21088	−0.327088
$794$	48.8449	1.73344
$795$	−27.6177	−0.979498
$796$	0.171585	0.00608166
$797$	−5.55795	−0.196873	−0.0984364	−	0.995143i	$-0.531384\pi$
$797$	−5.55795	−0.196873	−0.0984364	+	0.995143i	$0.531384\pi$
$798$	−13.3948	−0.474172
$799$	11.8008	0.417484
$800$	−0.208483	−0.00737098
$801$	26.8747	0.949570
$802$	14.5858	0.515041
$803$	−42.6583	−1.50538
$804$	−0.171054	−0.00603261
$805$	−4.27037	−0.150511
$806$	10.6052	0.373554
$807$	5.28889	0.186178
$808$	−6.06997	−0.213541
$809$	−10.7590	−0.378266	−0.189133	−	0.981951i	$-0.560568\pi$
$809$	−10.7590	−0.378266	−0.189133	+	0.981951i	$0.560568\pi$
$810$	15.7238	0.552477
$811$	22.9872	0.807191	0.403596	−	0.914937i	$-0.367760\pi$
$811$	22.9872	0.807191	0.403596	+	0.914937i	$0.367760\pi$
$812$	−0.0104559	−0.000366929 0
$813$	−0.901497	−0.0316169
$814$	17.2043	0.603012
$815$	6.88714	0.241246
$816$	16.0791	0.562880
$817$	40.4570	1.41541
$818$	0.0847634	0.00296368
$819$	−1.45195	−0.0507352
$820$	−0.0453414	−0.00158339
$821$	22.3830	0.781173	0.390587	−	0.920566i	$-0.372272\pi$
$821$	22.3830	0.781173	0.390587	+	0.920566i	$0.372272\pi$
$822$	−29.7131	−1.03636
$823$	−37.8925	−1.32085	−0.660425	−	0.750892i	$-0.729624\pi$
$823$	−37.8925	−1.32085	−0.660425	+	0.750892i	$0.729624\pi$
$824$	−21.2933	−0.741786
$825$	−6.10823	−0.212661
$826$	3.36094	0.116942
$827$	19.1136	0.664647	0.332323	−	0.943166i	$-0.392167\pi$
$827$	19.1136	0.664647	0.332323	+	0.943166i	$0.392167\pi$
$828$	0.262315	0.00911609
$829$	4.83194	0.167820	0.0839102	−	0.996473i	$-0.473259\pi$
$829$	4.83194	0.167820	0.0839102	+	0.996473i	$0.473259\pi$
$830$	−14.3109	−0.496737
$831$	11.7322	0.406986
$832$	−7.09370	−0.245930
$833$	−1.89642	−0.0657070
$834$	−19.9328	−0.690217
$835$	7.02712	0.243184
$836$	0.461250	0.0159527
$837$	−25.0258	−0.865017
$838$	9.34080	0.322672
$839$	−50.9520	−1.75906	−0.879529	−	0.475845i	$-0.842142\pi$
$839$	−50.9520	−1.75906	−0.879529	+	0.475845i	$0.842142\pi$
$840$	6.16500	0.212713
$841$	−28.9195	−0.997225
$842$	−48.7739	−1.68086
$843$	−41.7597	−1.43828
$844$	0.439263	0.0151201
$845$	−12.2409	−0.421100
$846$	14.5299	0.499548
$847$	−3.00463	−0.103240
$848$	50.1790	1.72316
$849$	−2.08372	−0.0715132
$850$	2.65711	0.0911381
$851$	−18.5442	−0.635687
$852$	1.23535	0.0423224
$853$	49.2247	1.68542	0.842710	−	0.538367i	$-0.180959\pi$
$853$	49.2247	1.68542	0.842710	+	0.538367i	$0.180959\pi$
$854$	−14.8126	−0.506878
$855$	7.37519	0.252226
$856$	25.9671	0.887539
$857$	−13.6008	−0.464595	−0.232298	−	0.972645i	$-0.574624\pi$
$857$	−13.6008	−0.464595	−0.232298	+	0.972645i	$0.574624\pi$
$858$	−7.45650	−0.254561
$859$	50.1312	1.71045	0.855227	−	0.518254i	$-0.173418\pi$
$859$	50.1312	1.71045	0.855227	+	0.518254i	$0.173418\pi$
$860$	−0.336961	−0.0114903
$861$	2.65729	0.0905603
$862$	−24.4429	−0.832528
$863$	1.50443	0.0512113	0.0256056	−	0.999672i	$-0.491849\pi$
$863$	1.50443	0.0512113	0.0256056	+	0.999672i	$0.491849\pi$
$864$	0.600561	0.0204315
$865$	11.5864	0.393950
$866$	−14.5904	−0.495802
$867$	−28.9546	−0.983350
$868$	−0.320223	−0.0108691
$869$	−21.4104	−0.726297
$870$	−0.858581	−0.0291086
$871$	−1.87168	−0.0634193
$872$	47.7977	1.61863
$873$	−24.4388	−0.827128
$874$	26.4793	0.895676
$875$	1.00000	0.0338062
$876$	−1.20125	−0.0405863
$877$	−41.0217	−1.38521	−0.692603	−	0.721319i	$-0.743536\pi$
$877$	−41.0217	−1.38521	−0.692603	+	0.721319i	$0.743536\pi$
$878$	−40.6664	−1.37242
$879$	−8.05814	−0.271794
$880$	11.0981	0.374118
$881$	34.4249	1.15981	0.579903	−	0.814686i	$-0.303091\pi$
$881$	34.4249	1.15981	0.579903	+	0.814686i	$0.303091\pi$
$882$	−2.33498	−0.0786228
$883$	−22.2472	−0.748679	−0.374339	−	0.927292i	$-0.622131\pi$
$883$	−22.2472	−0.748679	−0.374339	+	0.927292i	$0.622131\pi$
$884$	−0.0609016	−0.00204834
$885$	−5.18181	−0.174184
$886$	−32.2851	−1.08464
$887$	39.0076	1.30975	0.654874	−	0.755738i	$-0.272722\pi$
$887$	39.0076	1.30975	0.654874	+	0.755738i	$0.272722\pi$
$888$	26.7717	0.898399
$889$	9.82293	0.329450
$890$	−22.5950	−0.757385
$891$	31.7322	1.06307
$892$	0.863506	0.0289123
$893$	−27.5388	−0.921551
$894$	−14.8947	−0.498152
$895$	17.6782	0.590916
$896$	−10.9909	−0.367180
$897$	8.03721	0.268355
$898$	8.35487	0.278806
$899$	2.46440	0.0821922
$900$	−0.0614269	−0.00204756
$901$	24.2452	0.807724
$902$	4.87347	0.162269
$903$	19.7481	0.657174
$904$	−23.6451	−0.786425
$905$	−1.36240	−0.0452877
$906$	32.8531	1.09147
$907$	10.1260	0.336230	0.168115	−	0.985767i	$-0.446232\pi$
$907$	10.1260	0.336230	0.168115	+	0.985767i	$0.446232\pi$
$908$	−0.645392	−0.0214181
$909$	−3.54452	−0.117564
$910$	1.22073	0.0404668
$911$	40.4715	1.34088	0.670440	−	0.741963i	$-0.266105\pi$
$911$	40.4715	1.34088	0.670440	+	0.741963i	$0.266105\pi$
$912$	−37.5226	−1.24250
$913$	−28.8808	−0.955816
$914$	49.0509	1.62246
$915$	22.8377	0.754992
$916$	−0.0368596	−0.00121788
$917$	18.0617	0.596451
$918$	−7.65413	−0.252624
$919$	45.2033	1.49112	0.745560	−	0.666438i	$-0.232182\pi$
$919$	45.2033	1.49112	0.745560	+	0.666438i	$0.232182\pi$
$920$	−12.1871	−0.401798
$921$	−0.659971	−0.0217468
$922$	48.1782	1.58667
$923$	13.5172	0.444925
$924$	0.225147	0.00740680
$925$	4.34253	0.142782
$926$	−29.9768	−0.985100
$927$	−12.4341	−0.408388
$928$	−0.0591398	−0.00194136
$929$	−13.6887	−0.449111	−0.224556	−	0.974461i	$-0.572093\pi$
$929$	−13.6887	−0.449111	−0.224556	+	0.974461i	$0.572093\pi$
$930$	−26.2950	−0.862246
$931$	4.42553	0.145041
$932$	0.120563	0.00394917
$933$	−11.0909	−0.363098
$934$	4.17212	0.136516
$935$	5.36232	0.175367
$936$	−4.14370	−0.135441
$937$	15.2618	0.498580	0.249290	−	0.968429i	$-0.419803\pi$
$937$	15.2618	0.498580	0.249290	+	0.968429i	$0.419803\pi$
$938$	−3.00997	−0.0982790
$939$	11.2537	0.367251
$940$	0.229367	0.00748112
$941$	56.8696	1.85390	0.926948	−	0.375190i	$-0.122423\pi$
$941$	56.8696	1.85390	0.926948	+	0.375190i	$0.122423\pi$
$942$	−70.8185	−2.30739
$943$	−5.25302	−0.171062
$944$	9.41491	0.306429
$945$	−2.88062	−0.0937067
$946$	36.2179	1.17755
$947$	−8.31829	−0.270308	−0.135154	−	0.990825i	$-0.543153\pi$
$947$	−8.31829	−0.270308	−0.135154	+	0.990825i	$0.543153\pi$
$948$	−0.602909	−0.0195816
$949$	−13.1440	−0.426674
$950$	−6.20071	−0.201178
$951$	−33.9211	−1.09997
$952$	−5.41216	−0.175409
$953$	1.09097	0.0353401	0.0176701	−	0.999844i	$-0.494375\pi$
$953$	1.09097	0.0353401	0.0176701	+	0.999844i	$0.494375\pi$
$954$	29.8521	0.966496
$955$	3.42320	0.110772
$956$	1.01832	0.0329350
$957$	−1.73271	−0.0560104
$958$	−16.8410	−0.544107
$959$	9.81693	0.317005
$960$	17.5883	0.567661
$961$	44.4748	1.43467
$962$	5.30106	0.170913
$963$	15.1633	0.488632
$964$	−0.706171	−0.0227442
$965$	−1.10855	−0.0356855
$966$	12.9252	0.415861
$967$	−45.4108	−1.46031	−0.730156	−	0.683281i	$-0.760553\pi$
$967$	−45.4108	−1.46031	−0.730156	+	0.683281i	$0.760553\pi$
$968$	−8.57488	−0.275607
$969$	−18.1299	−0.582417
$970$	20.5470	0.659724
$971$	4.06559	0.130471	0.0652355	−	0.997870i	$-0.479220\pi$
$971$	4.06559	0.130471	0.0652355	+	0.997870i	$0.479220\pi$
$972$	0.575033	0.0184442
$973$	6.58562	0.211125
$974$	19.4289	0.622542
$975$	−1.88209	−0.0602751
$976$	−41.4943	−1.32820
$977$	−21.9208	−0.701307	−0.350654	−	0.936505i	$-0.614041\pi$
$977$	−21.9208	−0.701307	−0.350654	+	0.936505i	$0.614041\pi$
$978$	−20.8454	−0.666563
$979$	−45.5990	−1.45735
$980$	−0.0368596	−0.00117744
$981$	27.9111	0.891133
$982$	−32.8117	−1.04706
$983$	40.1430	1.28036	0.640181	−	0.768224i	$-0.278859\pi$
$983$	40.1430	1.28036	0.640181	+	0.768224i	$0.278859\pi$
$984$	7.58362	0.241757
$985$	21.1922	0.675239
$986$	0.753736	0.0240038
$987$	−13.4424	−0.427875
$988$	0.142122	0.00452150
$989$	−39.0386	−1.24135
$990$	6.60241	0.209838
$991$	−11.2841	−0.358450	−0.179225	−	0.983808i	$-0.557359\pi$
$991$	−11.2841	−0.358450	−0.179225	+	0.983808i	$0.557359\pi$
$992$	−1.81122	−0.0575063
$993$	−8.42035	−0.267212
$994$	21.7380	0.689487
$995$	−4.65508	−0.147576
$996$	−0.813275	−0.0257696
$997$	3.20555	0.101521	0.0507604	−	0.998711i	$-0.483836\pi$
$997$	3.20555	0.101521	0.0507604	+	0.998711i	$0.483836\pi$
$998$	25.3730	0.803170
$999$	−12.5092	−0.395773

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.o.1.20	✓	73

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.o.1.20	✓	73	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)

\(f(q)\)	\(=\)	\(q-1.40112 q^{2} +2.16021 q^{3} -0.0368596 q^{4} +1.00000 q^{5} -3.02672 q^{6} +1.00000 q^{7} +2.85389 q^{8} +1.66651 q^{9} +O(q^{10})\)	\(q-1.40112 q^{2} +2.16021 q^{3} -0.0368596 q^{4} +1.00000 q^{5} -3.02672 q^{6} +1.00000 q^{7} +2.85389 q^{8} +1.66651 q^{9} -1.40112 q^{10} -2.82761 q^{11} -0.0796246 q^{12} -0.871253 q^{13} -1.40112 q^{14} +2.16021 q^{15} -3.92492 q^{16} -1.89642 q^{17} -2.33498 q^{18} +4.42553 q^{19} -0.0368596 q^{20} +2.16021 q^{21} +3.96182 q^{22} -4.27037 q^{23} +6.16500 q^{24} +1.00000 q^{25} +1.22073 q^{26} -2.88062 q^{27} -0.0368596 q^{28} +0.283667 q^{29} -3.02672 q^{30} +8.68762 q^{31} -0.208483 q^{32} -6.10823 q^{33} +2.65711 q^{34} +1.00000 q^{35} -0.0614269 q^{36} +4.34253 q^{37} -6.20071 q^{38} -1.88209 q^{39} +2.85389 q^{40} +1.23011 q^{41} -3.02672 q^{42} +9.14173 q^{43} +0.104225 q^{44} +1.66651 q^{45} +5.98330 q^{46} -6.22271 q^{47} -8.47866 q^{48} +1.00000 q^{49} -1.40112 q^{50} -4.09666 q^{51} +0.0321141 q^{52} -12.7847 q^{53} +4.03610 q^{54} -2.82761 q^{55} +2.85389 q^{56} +9.56008 q^{57} -0.397452 q^{58} -2.39875 q^{59} -0.0796246 q^{60} +10.5720 q^{61} -12.1724 q^{62} +1.66651 q^{63} +8.14195 q^{64} -0.871253 q^{65} +8.55837 q^{66} +2.14826 q^{67} +0.0699012 q^{68} -9.22489 q^{69} -1.40112 q^{70} -15.5147 q^{71} +4.75602 q^{72} +15.0864 q^{73} -6.08441 q^{74} +2.16021 q^{75} -0.163124 q^{76} -2.82761 q^{77} +2.63703 q^{78} +7.57190 q^{79} -3.92492 q^{80} -11.2223 q^{81} -1.72353 q^{82} +10.2139 q^{83} -0.0796246 q^{84} -1.89642 q^{85} -12.8087 q^{86} +0.612781 q^{87} -8.06968 q^{88} +16.1263 q^{89} -2.33498 q^{90} -0.871253 q^{91} +0.157404 q^{92} +18.7671 q^{93} +8.71877 q^{94} +4.42553 q^{95} -0.450367 q^{96} -14.6647 q^{97} -1.40112 q^{98} -4.71223 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9 + 7 * q^10 + 27 * q^11 + 21 * q^12 + 21 * q^13 + 7 * q^14 + 14 * q^15 + 135 * q^16 + 23 * q^17 + 41 * q^18 + 26 * q^19 + 95 * q^20 + 14 * q^21 + 48 * q^22 + 16 * q^23 - q^24 + 73 * q^25 + 7 * q^26 + 44 * q^27 + 95 * q^28 + 66 * q^29 - q^30 + 23 * q^31 + 3 * q^32 + 77 * q^33 + 29 * q^34 + 73 * q^35 + 142 * q^36 + 66 * q^37 - 12 * q^38 + 53 * q^39 + 18 * q^40 + 50 * q^41 - q^42 + 43 * q^43 + 37 * q^44 + 111 * q^45 + 65 * q^46 + 28 * q^47 - 20 * q^48 + 73 * q^49 + 7 * q^50 + 71 * q^51 + 29 * q^52 - 7 * q^53 - 16 * q^54 + 27 * q^55 + 18 * q^56 + 33 * q^57 + 48 * q^58 + 16 * q^59 + 21 * q^60 + 42 * q^61 - 3 * q^62 + 111 * q^63 + 216 * q^64 + 21 * q^65 - 53 * q^66 + 48 * q^67 + 13 * q^68 + 73 * q^69 + 7 * q^70 + 68 * q^71 + 18 * q^72 + 65 * q^73 + 4 * q^74 + 14 * q^75 + 37 * q^76 + 27 * q^77 + 60 * q^78 + 116 * q^79 + 135 * q^80 + 177 * q^81 + 20 * q^82 + 40 * q^83 + 21 * q^84 + 23 * q^85 + 35 * q^86 - 14 * q^87 + 47 * q^88 + 59 * q^89 + 41 * q^90 + 21 * q^91 + 3 * q^92 + 37 * q^93 - 11 * q^94 + 26 * q^95 - 23 * q^96 + 70 * q^97 + 7 * q^98 + 49 * q^99

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