LMFDB - Embedded newform 8007.2.a.j.1.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.36
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.472051 q^{2} -1.00000 q^{3} -1.77717 q^{4} +3.15298 q^{5} -0.472051 q^{6} +4.34645 q^{7} -1.78302 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.472051 q^{2} -1.00000 q^{3} -1.77717 q^{4} +3.15298 q^{5} -0.472051 q^{6} +4.34645 q^{7} -1.78302 q^{8} +1.00000 q^{9} +1.48837 q^{10} -2.51251 q^{11} +1.77717 q^{12} +3.17852 q^{13} +2.05175 q^{14} -3.15298 q^{15} +2.71266 q^{16} +1.00000 q^{17} +0.472051 q^{18} +3.45142 q^{19} -5.60337 q^{20} -4.34645 q^{21} -1.18604 q^{22} +8.44505 q^{23} +1.78302 q^{24} +4.94127 q^{25} +1.50043 q^{26} -1.00000 q^{27} -7.72437 q^{28} +2.82399 q^{29} -1.48837 q^{30} -4.74608 q^{31} +4.84655 q^{32} +2.51251 q^{33} +0.472051 q^{34} +13.7043 q^{35} -1.77717 q^{36} +6.55035 q^{37} +1.62925 q^{38} -3.17852 q^{39} -5.62181 q^{40} -6.71735 q^{41} -2.05175 q^{42} -6.85331 q^{43} +4.46516 q^{44} +3.15298 q^{45} +3.98650 q^{46} +12.9234 q^{47} -2.71266 q^{48} +11.8916 q^{49} +2.33253 q^{50} -1.00000 q^{51} -5.64877 q^{52} -13.3590 q^{53} -0.472051 q^{54} -7.92190 q^{55} -7.74980 q^{56} -3.45142 q^{57} +1.33307 q^{58} +10.4404 q^{59} +5.60337 q^{60} -6.70593 q^{61} -2.24039 q^{62} +4.34645 q^{63} -3.13750 q^{64} +10.0218 q^{65} +1.18604 q^{66} +6.78065 q^{67} -1.77717 q^{68} -8.44505 q^{69} +6.46912 q^{70} -4.76584 q^{71} -1.78302 q^{72} +6.64953 q^{73} +3.09210 q^{74} -4.94127 q^{75} -6.13375 q^{76} -10.9205 q^{77} -1.50043 q^{78} +6.63091 q^{79} +8.55296 q^{80} +1.00000 q^{81} -3.17093 q^{82} -5.87355 q^{83} +7.72437 q^{84} +3.15298 q^{85} -3.23511 q^{86} -2.82399 q^{87} +4.47985 q^{88} -10.8218 q^{89} +1.48837 q^{90} +13.8153 q^{91} -15.0083 q^{92} +4.74608 q^{93} +6.10051 q^{94} +10.8822 q^{95} -4.84655 q^{96} -0.294768 q^{97} +5.61346 q^{98} -2.51251 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * 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 $

$2$	0.472051	0.333791	0.166895	−	0.985975i	$-0.446626\pi$
$2$	0.472051	0.333791	0.166895	+	0.985975i	$0.446626\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.77717	−0.888584
$5$	3.15298	1.41005	0.705027	−	0.709180i	$-0.250935\pi$
$5$	3.15298	1.41005	0.705027	+	0.709180i	$0.250935\pi$
$6$	−0.472051	−0.192714
$7$	4.34645	1.64280	0.821402	−	0.570350i	$-0.193192\pi$
$7$	4.34645	1.64280	0.821402	+	0.570350i	$0.193192\pi$
$8$	−1.78302	−0.630392
$9$	1.00000	0.333333
$10$	1.48837	0.470663
$11$	−2.51251	−0.757551	−0.378776	−	0.925489i	$-0.623655\pi$
$11$	−2.51251	−0.757551	−0.378776	+	0.925489i	$0.623655\pi$
$12$	1.77717	0.513024
$13$	3.17852	0.881564	0.440782	−	0.897614i	$-0.354701\pi$
$13$	3.17852	0.881564	0.440782	+	0.897614i	$0.354701\pi$
$14$	2.05175	0.548353
$15$	−3.15298	−0.814095
$16$	2.71266	0.678165
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.472051	0.111264
$19$	3.45142	0.791810	0.395905	−	0.918291i	$-0.370431\pi$
$19$	3.45142	0.791810	0.395905	+	0.918291i	$0.370431\pi$
$20$	−5.60337	−1.25295
$21$	−4.34645	−0.948473
$22$	−1.18604	−0.252864
$23$	8.44505	1.76091	0.880457	−	0.474125i	$-0.157236\pi$
$23$	8.44505	1.76091	0.880457	+	0.474125i	$0.157236\pi$
$24$	1.78302	0.363957
$25$	4.94127	0.988254
$26$	1.50043	0.294258
$27$	−1.00000	−0.192450
$28$	−7.72437	−1.45977
$29$	2.82399	0.524401	0.262201	−	0.965013i	$-0.415552\pi$
$29$	2.82399	0.524401	0.262201	+	0.965013i	$0.415552\pi$
$30$	−1.48837	−0.271737
$31$	−4.74608	−0.852421	−0.426210	−	0.904624i	$-0.640152\pi$
$31$	−4.74608	−0.852421	−0.426210	+	0.904624i	$0.640152\pi$
$32$	4.84655	0.856757
$33$	2.51251	0.437372
$34$	0.472051	0.0809561
$35$	13.7043	2.31644
$36$	−1.77717	−0.296195
$37$	6.55035	1.07687	0.538436	−	0.842667i	$-0.319015\pi$
$37$	6.55035	1.07687	0.538436	+	0.842667i	$0.319015\pi$
$38$	1.62925	0.264299
$39$	−3.17852	−0.508971
$40$	−5.62181	−0.888887
$41$	−6.71735	−1.04907	−0.524537	−	0.851388i	$-0.675762\pi$
$41$	−6.71735	−1.04907	−0.524537	+	0.851388i	$0.675762\pi$
$42$	−2.05175	−0.316592
$43$	−6.85331	−1.04512	−0.522560	−	0.852603i	$-0.675023\pi$
$43$	−6.85331	−1.04512	−0.522560	+	0.852603i	$0.675023\pi$
$44$	4.46516	0.673148
$45$	3.15298	0.470018
$46$	3.98650	0.587777
$47$	12.9234	1.88507	0.942537	−	0.334103i	$-0.108433\pi$
$47$	12.9234	1.88507	0.942537	+	0.334103i	$0.108433\pi$
$48$	−2.71266	−0.391539
$49$	11.8916	1.69880
$50$	2.33253	0.329870
$51$	−1.00000	−0.140028
$52$	−5.64877	−0.783343
$53$	−13.3590	−1.83500	−0.917498	−	0.397740i	$-0.869795\pi$
$53$	−13.3590	−1.83500	−0.917498	+	0.397740i	$0.869795\pi$
$54$	−0.472051	−0.0642381
$55$	−7.92190	−1.06819
$56$	−7.74980	−1.03561
$57$	−3.45142	−0.457152
$58$	1.33307	0.175040
$59$	10.4404	1.35922	0.679610	−	0.733574i	$-0.262149\pi$
$59$	10.4404	1.35922	0.679610	+	0.733574i	$0.262149\pi$
$60$	5.60337	0.723392
$61$	−6.70593	−0.858606	−0.429303	−	0.903161i	$-0.641241\pi$
$61$	−6.70593	−0.858606	−0.429303	+	0.903161i	$0.641241\pi$
$62$	−2.24039	−0.284530
$63$	4.34645	0.547601
$64$	−3.13750	−0.392187
$65$	10.0218	1.24305
$66$	1.18604	0.145991
$67$	6.78065	0.828388	0.414194	−	0.910189i	$-0.364064\pi$
$67$	6.78065	0.828388	0.414194	+	0.910189i	$0.364064\pi$
$68$	−1.77717	−0.215513
$69$	−8.44505	−1.01666
$70$	6.46912	0.773207
$71$	−4.76584	−0.565602	−0.282801	−	0.959179i	$-0.591264\pi$
$71$	−4.76584	−0.565602	−0.282801	+	0.959179i	$0.591264\pi$
$72$	−1.78302	−0.210131
$73$	6.64953	0.778269	0.389134	−	0.921181i	$-0.372774\pi$
$73$	6.64953	0.778269	0.389134	+	0.921181i	$0.372774\pi$
$74$	3.09210	0.359450
$75$	−4.94127	−0.570569
$76$	−6.13375	−0.703589
$77$	−10.9205	−1.24451
$78$	−1.50043	−0.169890
$79$	6.63091	0.746036	0.373018	−	0.927824i	$-0.378323\pi$
$79$	6.63091	0.746036	0.373018	+	0.927824i	$0.378323\pi$
$80$	8.55296	0.956249
$81$	1.00000	0.111111
$82$	−3.17093	−0.350171
$83$	−5.87355	−0.644706	−0.322353	−	0.946620i	$-0.604474\pi$
$83$	−5.87355	−0.644706	−0.322353	+	0.946620i	$0.604474\pi$
$84$	7.72437	0.842798
$85$	3.15298	0.341988
$86$	−3.23511	−0.348851
$87$	−2.82399	−0.302763
$88$	4.47985	0.477554
$89$	−10.8218	−1.14711	−0.573554	−	0.819168i	$-0.694436\pi$
$89$	−10.8218	−1.14711	−0.573554	+	0.819168i	$0.694436\pi$
$90$	1.48837	0.156888
$91$	13.8153	1.44824
$92$	−15.0083	−1.56472
$93$	4.74608	0.492145
$94$	6.10051	0.629220
$95$	10.8822	1.11650
$96$	−4.84655	−0.494649
$97$	−0.294768	−0.0299292	−0.0149646	−	0.999888i	$-0.504764\pi$
$97$	−0.294768	−0.0299292	−0.0149646	+	0.999888i	$0.504764\pi$
$98$	5.61346	0.567045
$99$	−2.51251	−0.252517
$100$	−8.78146	−0.878146
$101$	11.4071	1.13505	0.567524	−	0.823357i	$-0.307902\pi$
$101$	11.4071	1.13505	0.567524	+	0.823357i	$0.307902\pi$
$102$	−0.472051	−0.0467400
$103$	12.4283	1.22459	0.612297	−	0.790628i	$-0.290246\pi$
$103$	12.4283	1.22459	0.612297	+	0.790628i	$0.290246\pi$
$104$	−5.66736	−0.555730
$105$	−13.7043	−1.33740
$106$	−6.30612	−0.612505
$107$	−3.13878	−0.303438	−0.151719	−	0.988424i	$-0.548481\pi$
$107$	−3.13878	−0.303438	−0.151719	+	0.988424i	$0.548481\pi$
$108$	1.77717	0.171008
$109$	0.0407170	0.00389998	0.00194999	−	0.999998i	$-0.499379\pi$
$109$	0.0407170	0.00389998	0.00194999	+	0.999998i	$0.499379\pi$
$110$	−3.73954	−0.356551
$111$	−6.55035	−0.621732
$112$	11.7904	1.11409
$113$	−11.0775	−1.04208	−0.521042	−	0.853531i	$-0.674457\pi$
$113$	−11.0775	−1.04208	−0.521042	+	0.853531i	$0.674457\pi$
$114$	−1.62925	−0.152593
$115$	26.6271	2.48299
$116$	−5.01870	−0.465975
$117$	3.17852	0.293855
$118$	4.92839	0.453695
$119$	4.34645	0.398438
$120$	5.62181	0.513199
$121$	−4.68728	−0.426116
$122$	−3.16554	−0.286595
$123$	6.71735	0.605683
$124$	8.43457	0.757447
$125$	−0.185174	−0.0165625
$126$	2.05175	0.182784
$127$	16.9418	1.50334	0.751672	−	0.659537i	$-0.229248\pi$
$127$	16.9418	1.50334	0.751672	+	0.659537i	$0.229248\pi$
$128$	−11.1742	−0.987665
$129$	6.85331	0.603400
$130$	4.73081	0.414920
$131$	−5.11902	−0.447251	−0.223626	−	0.974675i	$-0.571789\pi$
$131$	−5.11902	−0.447251	−0.223626	+	0.974675i	$0.571789\pi$
$132$	−4.46516	−0.388642
$133$	15.0014	1.30079
$134$	3.20081	0.276508
$135$	−3.15298	−0.271365
$136$	−1.78302	−0.152892
$137$	17.8761	1.52726	0.763628	−	0.645656i	$-0.223416\pi$
$137$	17.8761	1.52726	0.763628	+	0.645656i	$0.223416\pi$
$138$	−3.98650	−0.339353
$139$	−10.5852	−0.897828	−0.448914	−	0.893575i	$-0.648189\pi$
$139$	−10.5852	−0.897828	−0.448914	+	0.893575i	$0.648189\pi$
$140$	−24.3548	−2.05835
$141$	−12.9234	−1.08835
$142$	−2.24972	−0.188793
$143$	−7.98608	−0.667830
$144$	2.71266	0.226055
$145$	8.90397	0.739435
$146$	3.13892	0.259779
$147$	−11.8916	−0.980805
$148$	−11.6411	−0.956891
$149$	−3.62333	−0.296834	−0.148417	−	0.988925i	$-0.547418\pi$
$149$	−3.62333	−0.296834	−0.148417	+	0.988925i	$0.547418\pi$
$150$	−2.33253	−0.190451
$151$	−14.5099	−1.18080	−0.590398	−	0.807112i	$-0.701029\pi$
$151$	−14.5099	−1.18080	−0.590398	+	0.807112i	$0.701029\pi$
$152$	−6.15394	−0.499150
$153$	1.00000	0.0808452
$154$	−5.15504	−0.415405
$155$	−14.9643	−1.20196
$156$	5.64877	0.452263
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	3.13013	0.249020
$159$	13.3590	1.05944
$160$	15.2811	1.20807
$161$	36.7060	2.89284
$162$	0.472051	0.0370879
$163$	−12.9942	−1.01778	−0.508892	−	0.860831i	$-0.669945\pi$
$163$	−12.9942	−1.01778	−0.508892	+	0.860831i	$0.669945\pi$
$164$	11.9379	0.932190
$165$	7.92190	0.616719
$166$	−2.77262	−0.215197
$167$	−24.5568	−1.90026	−0.950130	−	0.311854i	$-0.899050\pi$
$167$	−24.5568	−1.90026	−0.950130	+	0.311854i	$0.899050\pi$
$168$	7.74980	0.597910
$169$	−2.89699	−0.222846
$170$	1.48837	0.114153
$171$	3.45142	0.263937
$172$	12.1795	0.928676
$173$	−14.7252	−1.11954	−0.559769	−	0.828649i	$-0.689110\pi$
$173$	−14.7252	−1.11954	−0.559769	+	0.828649i	$0.689110\pi$
$174$	−1.33307	−0.101060
$175$	21.4770	1.62351
$176$	−6.81559	−0.513745
$177$	−10.4404	−0.784746
$178$	−5.10844	−0.382894
$179$	6.21817	0.464768	0.232384	−	0.972624i	$-0.425347\pi$
$179$	6.21817	0.464768	0.232384	+	0.972624i	$0.425347\pi$
$180$	−5.60337	−0.417651
$181$	5.79899	0.431035	0.215518	−	0.976500i	$-0.430856\pi$
$181$	5.79899	0.431035	0.215518	+	0.976500i	$0.430856\pi$
$182$	6.52153	0.483408
$183$	6.70593	0.495716
$184$	−15.0577	−1.11007
$185$	20.6531	1.51845
$186$	2.24039	0.164274
$187$	−2.51251	−0.183733
$188$	−22.9671	−1.67505
$189$	−4.34645	−0.316158
$190$	5.13698	0.372676
$191$	19.0886	1.38120	0.690602	−	0.723235i	$-0.257346\pi$
$191$	19.0886	1.38120	0.690602	+	0.723235i	$0.257346\pi$
$192$	3.13750	0.226429
$193$	15.7230	1.13176	0.565882	−	0.824486i	$-0.308536\pi$
$193$	15.7230	1.13176	0.565882	+	0.824486i	$0.308536\pi$
$194$	−0.139146	−0.00999009
$195$	−10.0218	−0.717677
$196$	−21.1334	−1.50953
$197$	−13.6976	−0.975912	−0.487956	−	0.872868i	$-0.662257\pi$
$197$	−13.6976	−0.975912	−0.487956	+	0.872868i	$0.662257\pi$
$198$	−1.18604	−0.0842879
$199$	2.43289	0.172463	0.0862315	−	0.996275i	$-0.472518\pi$
$199$	2.43289	0.172463	0.0862315	+	0.996275i	$0.472518\pi$
$200$	−8.81037	−0.622987
$201$	−6.78065	−0.478270
$202$	5.38473	0.378868
$203$	12.2743	0.861489
$204$	1.77717	0.124427
$205$	−21.1797	−1.47925
$206$	5.86678	0.408758
$207$	8.44505	0.586972
$208$	8.62225	0.597845
$209$	−8.67174	−0.599837
$210$	−6.46912	−0.446411
$211$	−19.8151	−1.36413	−0.682064	−	0.731292i	$-0.738917\pi$
$211$	−19.8151	−1.36413	−0.682064	+	0.731292i	$0.738917\pi$
$212$	23.7411	1.63055
$213$	4.76584	0.326550
$214$	−1.48167	−0.101285
$215$	−21.6083	−1.47368
$216$	1.78302	0.121319
$217$	−20.6286	−1.40036
$218$	0.0192205	0.00130178
$219$	−6.64953	−0.449334
$220$	14.0785	0.949175
$221$	3.17852	0.213811
$222$	−3.09210	−0.207528
$223$	−25.7185	−1.72224	−0.861119	−	0.508403i	$-0.830236\pi$
$223$	−25.7185	−1.72224	−0.861119	+	0.508403i	$0.830236\pi$
$224$	21.0653	1.40748
$225$	4.94127	0.329418
$226$	−5.22915	−0.347838
$227$	−26.8576	−1.78260	−0.891299	−	0.453415i	$-0.850206\pi$
$227$	−26.8576	−1.78260	−0.891299	+	0.453415i	$0.850206\pi$
$228$	6.13375	0.406218
$229$	−0.924614	−0.0611002	−0.0305501	−	0.999533i	$-0.509726\pi$
$229$	−0.924614	−0.0611002	−0.0305501	+	0.999533i	$0.509726\pi$
$230$	12.5693	0.828798
$231$	10.9205	0.718517
$232$	−5.03522	−0.330578
$233$	8.56217	0.560926	0.280463	−	0.959865i	$-0.409512\pi$
$233$	8.56217	0.560926	0.280463	+	0.959865i	$0.409512\pi$
$234$	1.50043	0.0980859
$235$	40.7472	2.65806
$236$	−18.5543	−1.20778
$237$	−6.63091	−0.430724
$238$	2.05175	0.132995
$239$	4.01866	0.259945	0.129973	−	0.991518i	$-0.458511\pi$
$239$	4.01866	0.259945	0.129973	+	0.991518i	$0.458511\pi$
$240$	−8.55296	−0.552091
$241$	8.80467	0.567158	0.283579	−	0.958949i	$-0.408478\pi$
$241$	8.80467	0.567158	0.283579	+	0.958949i	$0.408478\pi$
$242$	−2.21264	−0.142234
$243$	−1.00000	−0.0641500
$244$	11.9176	0.762943
$245$	37.4941	2.39541
$246$	3.17093	0.202171
$247$	10.9704	0.698031
$248$	8.46234	0.537359
$249$	5.87355	0.372221
$250$	−0.0874118	−0.00552840
$251$	−2.32516	−0.146763	−0.0733814	−	0.997304i	$-0.523379\pi$
$251$	−2.32516	−0.146763	−0.0733814	+	0.997304i	$0.523379\pi$
$252$	−7.72437	−0.486590
$253$	−21.2183	−1.33398
$254$	7.99741	0.501802
$255$	−3.15298	−0.197447
$256$	1.00022	0.0625139
$257$	22.8413	1.42480	0.712402	−	0.701772i	$-0.247608\pi$
$257$	22.8413	1.42480	0.712402	+	0.701772i	$0.247608\pi$
$258$	3.23511	0.201409
$259$	28.4708	1.76909
$260$	−17.8104	−1.10456
$261$	2.82399	0.174800
$262$	−2.41644	−0.149288
$263$	−31.8584	−1.96447	−0.982237	−	0.187645i	$-0.939915\pi$
$263$	−31.8584	−1.96447	−0.982237	+	0.187645i	$0.939915\pi$
$264$	−4.47985	−0.275716
$265$	−42.1205	−2.58744
$266$	7.08144	0.434191
$267$	10.8218	0.662283
$268$	−12.0503	−0.736092
$269$	23.8765	1.45577	0.727887	−	0.685697i	$-0.240503\pi$
$269$	23.8765	1.45577	0.727887	+	0.685697i	$0.240503\pi$
$270$	−1.48837	−0.0905792
$271$	−5.93408	−0.360470	−0.180235	−	0.983624i	$-0.557686\pi$
$271$	−5.93408	−0.360470	−0.180235	+	0.983624i	$0.557686\pi$
$272$	2.71266	0.164479
$273$	−13.8153	−0.836140
$274$	8.43843	0.509784
$275$	−12.4150	−0.748653
$276$	15.0083	0.903392
$277$	24.9584	1.49960	0.749802	−	0.661663i	$-0.230149\pi$
$277$	24.9584	1.49960	0.749802	+	0.661663i	$0.230149\pi$
$278$	−4.99677	−0.299687
$279$	−4.74608	−0.284140
$280$	−24.4349	−1.46027
$281$	−5.18302	−0.309193	−0.154596	−	0.987978i	$-0.549408\pi$
$281$	−5.18302	−0.309193	−0.154596	+	0.987978i	$0.549408\pi$
$282$	−6.10051	−0.363280
$283$	−26.7777	−1.59177	−0.795883	−	0.605450i	$-0.792993\pi$
$283$	−26.7777	−1.59177	−0.795883	+	0.605450i	$0.792993\pi$
$284$	8.46970	0.502584
$285$	−10.8822	−0.644609
$286$	−3.76984	−0.222915
$287$	−29.1966	−1.72342
$288$	4.84655	0.285586
$289$	1.00000	0.0588235
$290$	4.20313	0.246816
$291$	0.294768	0.0172796
$292$	−11.8173	−0.691557
$293$	7.84811	0.458492	0.229246	−	0.973369i	$-0.426374\pi$
$293$	7.84811	0.458492	0.229246	+	0.973369i	$0.426374\pi$
$294$	−5.61346	−0.327384
$295$	32.9182	1.91657
$296$	−11.6794	−0.678851
$297$	2.51251	0.145791
$298$	−1.71040	−0.0990806
$299$	26.8428	1.55236
$300$	8.78146	0.506998
$301$	−29.7876	−1.71693
$302$	−6.84941	−0.394139
$303$	−11.4071	−0.655320
$304$	9.36253	0.536978
$305$	−21.1436	−1.21068
$306$	0.472051	0.0269854
$307$	−3.36118	−0.191832	−0.0959162	−	0.995389i	$-0.530578\pi$
$307$	−3.36118	−0.191832	−0.0959162	+	0.995389i	$0.530578\pi$
$308$	19.4076	1.10585
$309$	−12.4283	−0.707020
$310$	−7.06391	−0.401203
$311$	−9.94127	−0.563718	−0.281859	−	0.959456i	$-0.590951\pi$
$311$	−9.94127	−0.563718	−0.281859	+	0.959456i	$0.590951\pi$
$312$	5.66736	0.320851
$313$	27.4120	1.54942	0.774710	−	0.632317i	$-0.217896\pi$
$313$	27.4120	1.54942	0.774710	+	0.632317i	$0.217896\pi$
$314$	−0.472051	−0.0266394
$315$	13.7043	0.772148
$316$	−11.7842	−0.662915
$317$	32.9107	1.84845	0.924224	−	0.381851i	$-0.124713\pi$
$317$	32.9107	1.84845	0.924224	+	0.381851i	$0.124713\pi$
$318$	6.30612	0.353630
$319$	−7.09531	−0.397261
$320$	−9.89247	−0.553006
$321$	3.13878	0.175190
$322$	17.3271	0.965602
$323$	3.45142	0.192042
$324$	−1.77717	−0.0987315
$325$	15.7059	0.871209
$326$	−6.13392	−0.339727
$327$	−0.0407170	−0.00225166
$328$	11.9772	0.661328
$329$	56.1710	3.09681
$330$	3.73954	0.205855
$331$	28.3491	1.55821	0.779104	−	0.626894i	$-0.215674\pi$
$331$	28.3491	1.55821	0.779104	+	0.626894i	$0.215674\pi$
$332$	10.4383	0.572875
$333$	6.55035	0.358957
$334$	−11.5921	−0.634289
$335$	21.3792	1.16807
$336$	−11.7904	−0.643221
$337$	6.85072	0.373182	0.186591	−	0.982438i	$-0.440256\pi$
$337$	6.85072	0.373182	0.186591	+	0.982438i	$0.440256\pi$
$338$	−1.36753	−0.0743838
$339$	11.0775	0.601648
$340$	−5.60337	−0.303885
$341$	11.9246	0.645752
$342$	1.62925	0.0880996
$343$	21.2612	1.14800
$344$	12.2196	0.658835
$345$	−26.6271	−1.43355
$346$	−6.95106	−0.373691
$347$	18.5589	0.996294	0.498147	−	0.867093i	$-0.334014\pi$
$347$	18.5589	0.996294	0.498147	+	0.867093i	$0.334014\pi$
$348$	5.01870	0.269031
$349$	14.1382	0.756802	0.378401	−	0.925642i	$-0.376474\pi$
$349$	14.1382	0.756802	0.378401	+	0.925642i	$0.376474\pi$
$350$	10.1382	0.541912
$351$	−3.17852	−0.169657
$352$	−12.1770	−0.649037
$353$	10.9500	0.582812	0.291406	−	0.956599i	$-0.405877\pi$
$353$	10.9500	0.582812	0.291406	+	0.956599i	$0.405877\pi$
$354$	−4.92839	−0.261941
$355$	−15.0266	−0.797529
$356$	19.2321	1.01930
$357$	−4.34645	−0.230039
$358$	2.93530	0.155135
$359$	18.3787	0.969991	0.484996	−	0.874517i	$-0.338821\pi$
$359$	18.3787	0.969991	0.484996	+	0.874517i	$0.338821\pi$
$360$	−5.62181	−0.296296
$361$	−7.08770	−0.373037
$362$	2.73742	0.143876
$363$	4.68728	0.246018
$364$	−24.5521	−1.28688
$365$	20.9658	1.09740
$366$	3.16554	0.165466
$367$	−0.420034	−0.0219256	−0.0109628	−	0.999940i	$-0.503490\pi$
$367$	−0.420034	−0.0219256	−0.0109628	+	0.999940i	$0.503490\pi$
$368$	22.9085	1.19419
$369$	−6.71735	−0.349691
$370$	9.74934	0.506844
$371$	−58.0641	−3.01454
$372$	−8.43457	−0.437312
$373$	−14.1555	−0.732942	−0.366471	−	0.930430i	$-0.619434\pi$
$373$	−14.1555	−0.732942	−0.366471	+	0.930430i	$0.619434\pi$
$374$	−1.18604	−0.0613284
$375$	0.185174	0.00956236
$376$	−23.0427	−1.18833
$377$	8.97611	0.462293
$378$	−2.05175	−0.105531
$379$	31.2637	1.60591	0.802955	−	0.596040i	$-0.203260\pi$
$379$	31.2637	1.60591	0.802955	+	0.596040i	$0.203260\pi$
$380$	−19.3396	−0.992100
$381$	−16.9418	−0.867956
$382$	9.01080	0.461033
$383$	−19.8311	−1.01332	−0.506661	−	0.862145i	$-0.669120\pi$
$383$	−19.8311	−1.01332	−0.506661	+	0.862145i	$0.669120\pi$
$384$	11.1742	0.570229
$385$	−34.4321	−1.75482
$386$	7.42205	0.377772
$387$	−6.85331	−0.348373
$388$	0.523853	0.0265946
$389$	−4.07064	−0.206390	−0.103195	−	0.994661i	$-0.532907\pi$
$389$	−4.07064	−0.206390	−0.103195	+	0.994661i	$0.532907\pi$
$390$	−4.73081	−0.239554
$391$	8.44505	0.427085
$392$	−21.2030	−1.07091
$393$	5.11902	0.258221
$394$	−6.46596	−0.325751
$395$	20.9071	1.05195
$396$	4.46516	0.224383
$397$	−0.408769	−0.0205155	−0.0102578	−	0.999947i	$-0.503265\pi$
$397$	−0.408769	−0.0205155	−0.0102578	+	0.999947i	$0.503265\pi$
$398$	1.14845	0.0575666
$399$	−15.0014	−0.751011
$400$	13.4040	0.670199
$401$	33.8628	1.69103	0.845513	−	0.533955i	$-0.179295\pi$
$401$	33.8628	1.69103	0.845513	+	0.533955i	$0.179295\pi$
$402$	−3.20081	−0.159642
$403$	−15.0855	−0.751463
$404$	−20.2723	−1.00858
$405$	3.15298	0.156673
$406$	5.79411	0.287557
$407$	−16.4579	−0.815786
$408$	1.78302	0.0882725
$409$	−12.2685	−0.606637	−0.303318	−	0.952889i	$-0.598095\pi$
$409$	−12.2685	−0.606637	−0.303318	+	0.952889i	$0.598095\pi$
$410$	−9.99789	−0.493760
$411$	−17.8761	−0.881762
$412$	−22.0871	−1.08815
$413$	45.3785	2.23293
$414$	3.98650	0.195926
$415$	−18.5192	−0.909070
$416$	15.4049	0.755286
$417$	10.5852	0.518361
$418$	−4.09351	−0.200220
$419$	−34.2979	−1.67556	−0.837782	−	0.546005i	$-0.816148\pi$
$419$	−34.2979	−1.67556	−0.837782	+	0.546005i	$0.816148\pi$
$420$	24.3548	1.18839
$421$	18.6864	0.910719	0.455360	−	0.890308i	$-0.349511\pi$
$421$	18.6864	0.910719	0.455360	+	0.890308i	$0.349511\pi$
$422$	−9.35375	−0.455333
$423$	12.9234	0.628358
$424$	23.8193	1.15677
$425$	4.94127	0.239687
$426$	2.24972	0.108999
$427$	−29.1470	−1.41052
$428$	5.57814	0.269630
$429$	7.98608	0.385572
$430$	−10.2002	−0.491899
$431$	−37.4292	−1.80290	−0.901451	−	0.432881i	$-0.857497\pi$
$431$	−37.4292	−1.80290	−0.901451	+	0.432881i	$0.857497\pi$
$432$	−2.71266	−0.130513
$433$	31.8602	1.53110	0.765551	−	0.643375i	$-0.222466\pi$
$433$	31.8602	1.53110	0.765551	+	0.643375i	$0.222466\pi$
$434$	−9.73775	−0.467427
$435$	−8.90397	−0.426913
$436$	−0.0723610	−0.00346546
$437$	29.1474	1.39431
$438$	−3.13892	−0.149983
$439$	11.4762	0.547730	0.273865	−	0.961768i	$-0.411698\pi$
$439$	11.4762	0.547730	0.273865	+	0.961768i	$0.411698\pi$
$440$	14.1249	0.673377
$441$	11.8916	0.566268
$442$	1.50043	0.0713680
$443$	21.3836	1.01596	0.507982	−	0.861368i	$-0.330392\pi$
$443$	21.3836	1.01596	0.507982	+	0.861368i	$0.330392\pi$
$444$	11.6411	0.552461
$445$	−34.1209	−1.61749
$446$	−12.1405	−0.574867
$447$	3.62333	0.171377
$448$	−13.6370	−0.644287
$449$	25.9329	1.22385	0.611924	−	0.790917i	$-0.290396\pi$
$449$	25.9329	1.22385	0.611924	+	0.790917i	$0.290396\pi$
$450$	2.33253	0.109957
$451$	16.8774	0.794727
$452$	19.6866	0.925979
$453$	14.5099	0.681733
$454$	−12.6781	−0.595015
$455$	43.5593	2.04209
$456$	6.15394	0.288185
$457$	12.5802	0.588477	0.294239	−	0.955732i	$-0.404934\pi$
$457$	12.5802	0.588477	0.294239	+	0.955732i	$0.404934\pi$
$458$	−0.436465	−0.0203947
$459$	−1.00000	−0.0466760
$460$	−47.3207	−2.20634
$461$	−3.60888	−0.168082	−0.0840412	−	0.996462i	$-0.526783\pi$
$461$	−3.60888	−0.168082	−0.0840412	+	0.996462i	$0.526783\pi$
$462$	5.15504	0.239834
$463$	28.2178	1.31139	0.655696	−	0.755025i	$-0.272375\pi$
$463$	28.2178	1.31139	0.655696	+	0.755025i	$0.272375\pi$
$464$	7.66052	0.355631
$465$	14.9643	0.693952
$466$	4.04178	0.187232
$467$	−35.4505	−1.64045	−0.820226	−	0.572040i	$-0.806152\pi$
$467$	−35.4505	−1.64045	−0.820226	+	0.572040i	$0.806152\pi$
$468$	−5.64877	−0.261114
$469$	29.4717	1.36088
$470$	19.2348	0.887234
$471$	1.00000	0.0460776
$472$	−18.6153	−0.856841
$473$	17.2190	0.791731
$474$	−3.13013	−0.143772
$475$	17.0544	0.782509
$476$	−7.72437	−0.354046
$477$	−13.3590	−0.611665
$478$	1.89701	0.0867673
$479$	−15.8152	−0.722617	−0.361309	−	0.932446i	$-0.617670\pi$
$479$	−15.8152	−0.722617	−0.361309	+	0.932446i	$0.617670\pi$
$480$	−15.2811	−0.697482
$481$	20.8205	0.949331
$482$	4.15625	0.189312
$483$	−36.7060	−1.67018
$484$	8.33008	0.378640
$485$	−0.929398	−0.0422018
$486$	−0.472051	−0.0214127
$487$	−18.7932	−0.851600	−0.425800	−	0.904817i	$-0.640007\pi$
$487$	−18.7932	−0.851600	−0.425800	+	0.904817i	$0.640007\pi$
$488$	11.9568	0.541258
$489$	12.9942	0.587617
$490$	17.6991	0.799565
$491$	−8.55045	−0.385876	−0.192938	−	0.981211i	$-0.561802\pi$
$491$	−8.55045	−0.385876	−0.192938	+	0.981211i	$0.561802\pi$
$492$	−11.9379	−0.538200
$493$	2.82399	0.127186
$494$	5.17860	0.232996
$495$	−7.92190	−0.356063
$496$	−12.8745	−0.578082
$497$	−20.7145	−0.929173
$498$	2.77262	0.124244
$499$	−21.3698	−0.956646	−0.478323	−	0.878184i	$-0.658755\pi$
$499$	−21.3698	−0.956646	−0.478323	+	0.878184i	$0.658755\pi$
$500$	0.329086	0.0147172
$501$	24.5568	1.09712
$502$	−1.09759	−0.0489881
$503$	25.9307	1.15619	0.578096	−	0.815969i	$-0.303796\pi$
$503$	25.9307	1.15619	0.578096	+	0.815969i	$0.303796\pi$
$504$	−7.74980	−0.345203
$505$	35.9663	1.60048
$506$	−10.0161	−0.445271
$507$	2.89699	0.128660
$508$	−30.1085	−1.33585
$509$	30.8466	1.36725	0.683625	−	0.729833i	$-0.260402\pi$
$509$	30.8466	1.36725	0.683625	+	0.729833i	$0.260402\pi$
$510$	−1.48837	−0.0659060
$511$	28.9019	1.27854
$512$	22.8205	1.00853
$513$	−3.45142	−0.152384
$514$	10.7823	0.475586
$515$	39.1861	1.72674
$516$	−12.1795	−0.536171
$517$	−32.4702	−1.42804
$518$	13.4397	0.590506
$519$	14.7252	0.646365
$520$	−17.8691	−0.783610
$521$	18.3873	0.805563	0.402782	−	0.915296i	$-0.368043\pi$
$521$	18.3873	0.805563	0.402782	+	0.915296i	$0.368043\pi$
$522$	1.33307	0.0583468
$523$	19.7725	0.864591	0.432296	−	0.901732i	$-0.357704\pi$
$523$	19.7725	0.864591	0.432296	+	0.901732i	$0.357704\pi$
$524$	9.09736	0.397420
$525$	−21.4770	−0.937333
$526$	−15.0388	−0.655723
$527$	−4.74608	−0.206742
$528$	6.81559	0.296611
$529$	48.3189	2.10082
$530$	−19.8831	−0.863665
$531$	10.4404	0.453073
$532$	−26.6600	−1.15586
$533$	−21.3513	−0.924825
$534$	5.10844	0.221064
$535$	−9.89651	−0.427864
$536$	−12.0900	−0.522209
$537$	−6.21817	−0.268334
$538$	11.2709	0.485924
$539$	−29.8779	−1.28693
$540$	5.60337	0.241131
$541$	27.8471	1.19724	0.598621	−	0.801032i	$-0.295716\pi$
$541$	27.8471	1.19724	0.598621	+	0.801032i	$0.295716\pi$
$542$	−2.80119	−0.120321
$543$	−5.79899	−0.248858
$544$	4.84655	0.207794
$545$	0.128380	0.00549919
$546$	−6.52153	−0.279096
$547$	−10.8919	−0.465705	−0.232853	−	0.972512i	$-0.574806\pi$
$547$	−10.8919	−0.465705	−0.232853	+	0.972512i	$0.574806\pi$
$548$	−31.7688	−1.35710
$549$	−6.70593	−0.286202
$550$	−5.86052	−0.249893
$551$	9.74677	0.415226
$552$	15.0577	0.640897
$553$	28.8209	1.22559
$554$	11.7816	0.500554
$555$	−20.6531	−0.876676
$556$	18.8117	0.797795
$557$	−33.4792	−1.41856	−0.709280	−	0.704927i	$-0.750980\pi$
$557$	−33.4792	−1.41856	−0.709280	+	0.704927i	$0.750980\pi$
$558$	−2.24039	−0.0948434
$559$	−21.7834	−0.921339
$560$	37.1750	1.57093
$561$	2.51251	0.106078
$562$	−2.44665	−0.103206
$563$	1.21785	0.0513262	0.0256631	−	0.999671i	$-0.491830\pi$
$563$	1.21785	0.0513262	0.0256631	+	0.999671i	$0.491830\pi$
$564$	22.9671	0.967088
$565$	−34.9271	−1.46940
$566$	−12.6404	−0.531317
$567$	4.34645	0.182534
$568$	8.49758	0.356551
$569$	−6.32390	−0.265112	−0.132556	−	0.991176i	$-0.542318\pi$
$569$	−6.32390	−0.265112	−0.132556	+	0.991176i	$0.542318\pi$
$570$	−5.13698	−0.215164
$571$	−18.3947	−0.769796	−0.384898	−	0.922959i	$-0.625763\pi$
$571$	−18.3947	−0.769796	−0.384898	+	0.922959i	$0.625763\pi$
$572$	14.1926	0.593423
$573$	−19.0886	−0.797438
$574$	−13.7823	−0.575263
$575$	41.7293	1.74023
$576$	−3.13750	−0.130729
$577$	−0.939133	−0.0390966	−0.0195483	−	0.999809i	$-0.506223\pi$
$577$	−0.939133	−0.0390966	−0.0195483	+	0.999809i	$0.506223\pi$
$578$	0.472051	0.0196347
$579$	−15.7230	−0.653424
$580$	−15.8239	−0.657050
$581$	−25.5291	−1.05913
$582$	0.139146	0.00576778
$583$	33.5646	1.39010
$584$	−11.8562	−0.490614
$585$	10.0218	0.414351
$586$	3.70471	0.153040
$587$	11.5846	0.478149	0.239075	−	0.971001i	$-0.423156\pi$
$587$	11.5846	0.478149	0.239075	+	0.971001i	$0.423156\pi$
$588$	21.1334	0.871528
$589$	−16.3807	−0.674955
$590$	15.5391	0.639735
$591$	13.6976	0.563443
$592$	17.7689	0.730297
$593$	−24.4734	−1.00500	−0.502500	−	0.864577i	$-0.667586\pi$
$593$	−24.4734	−1.00500	−0.502500	+	0.864577i	$0.667586\pi$
$594$	1.18604	0.0486636
$595$	13.7043	0.561820
$596$	6.43926	0.263762
$597$	−2.43289	−0.0995716
$598$	12.6712	0.518163
$599$	−31.4993	−1.28703	−0.643514	−	0.765434i	$-0.722524\pi$
$599$	−31.4993	−1.28703	−0.643514	+	0.765434i	$0.722524\pi$
$600$	8.81037	0.359682
$601$	8.26364	0.337081	0.168540	−	0.985695i	$-0.446095\pi$
$601$	8.26364	0.337081	0.168540	+	0.985695i	$0.446095\pi$
$602$	−14.0613	−0.573094
$603$	6.78065	0.276129
$604$	25.7865	1.04924
$605$	−14.7789	−0.600847
$606$	−5.38473	−0.218740
$607$	31.9683	1.29755	0.648777	−	0.760978i	$-0.275281\pi$
$607$	31.9683	1.29755	0.648777	+	0.760978i	$0.275281\pi$
$608$	16.7275	0.678389
$609$	−12.2743	−0.497381
$610$	−9.98088	−0.404114
$611$	41.0774	1.66181
$612$	−1.77717	−0.0718377
$613$	−37.0228	−1.49534	−0.747668	−	0.664073i	$-0.768826\pi$
$613$	−37.0228	−1.49534	−0.747668	+	0.664073i	$0.768826\pi$
$614$	−1.58665	−0.0640319
$615$	21.1797	0.854046
$616$	19.4715	0.784528
$617$	21.4553	0.863757	0.431879	−	0.901932i	$-0.357851\pi$
$617$	21.4553	0.863757	0.431879	+	0.901932i	$0.357851\pi$
$618$	−5.86678	−0.235997
$619$	28.4441	1.14326	0.571632	−	0.820510i	$-0.306311\pi$
$619$	28.4441	1.14326	0.571632	+	0.820510i	$0.306311\pi$
$620$	26.5940	1.06804
$621$	−8.44505	−0.338888
$622$	−4.69279	−0.188164
$623$	−47.0364	−1.88447
$624$	−8.62225	−0.345166
$625$	−25.2902	−1.01161
$626$	12.9399	0.517182
$627$	8.67174	0.346316
$628$	1.77717	0.0709167
$629$	6.55035	0.261180
$630$	6.46912	0.257736
$631$	8.43180	0.335665	0.167832	−	0.985816i	$-0.446323\pi$
$631$	8.43180	0.335665	0.167832	+	0.985816i	$0.446323\pi$
$632$	−11.8230	−0.470295
$633$	19.8151	0.787580
$634$	15.5355	0.616995
$635$	53.4172	2.11980
$636$	−23.7411	−0.941397
$637$	37.7978	1.49760
$638$	−3.34935	−0.132602
$639$	−4.76584	−0.188534
$640$	−35.2319	−1.39266
$641$	−46.5147	−1.83722	−0.918610	−	0.395165i	$-0.870687\pi$
$641$	−46.5147	−1.83722	−0.918610	+	0.395165i	$0.870687\pi$
$642$	1.48167	0.0584767
$643$	16.5543	0.652839	0.326419	−	0.945225i	$-0.394158\pi$
$643$	16.5543	0.652839	0.326419	+	0.945225i	$0.394158\pi$
$644$	−65.2327	−2.57053
$645$	21.6083	0.850827
$646$	1.62925	0.0641019
$647$	−5.18395	−0.203802	−0.101901	−	0.994795i	$-0.532493\pi$
$647$	−5.18395	−0.203802	−0.101901	+	0.994795i	$0.532493\pi$
$648$	−1.78302	−0.0700435
$649$	−26.2316	−1.02968
$650$	7.41401	0.290801
$651$	20.6286	0.808498
$652$	23.0928	0.904386
$653$	−41.6424	−1.62959	−0.814797	−	0.579746i	$-0.803152\pi$
$653$	−41.6424	−1.62959	−0.814797	+	0.579746i	$0.803152\pi$
$654$	−0.0192205	−0.000751582 0
$655$	−16.1402	−0.630649
$656$	−18.2219	−0.711445
$657$	6.64953	0.259423
$658$	26.5156	1.03368
$659$	−38.1950	−1.48787	−0.743933	−	0.668255i	$-0.767042\pi$
$659$	−38.1950	−1.48787	−0.743933	+	0.668255i	$0.767042\pi$
$660$	−14.0785	−0.548007
$661$	3.53452	0.137477	0.0687384	−	0.997635i	$-0.478103\pi$
$661$	3.53452	0.137477	0.0687384	+	0.997635i	$0.478103\pi$
$662$	13.3822	0.520116
$663$	−3.17852	−0.123444
$664$	10.4726	0.406417
$665$	47.2992	1.83418
$666$	3.09210	0.119817
$667$	23.8487	0.923426
$668$	43.6415	1.68854
$669$	25.7185	0.994335
$670$	10.0921	0.389892
$671$	16.8487	0.650438
$672$	−21.0653	−0.812611
$673$	14.0694	0.542335	0.271168	−	0.962532i	$-0.412590\pi$
$673$	14.0694	0.542335	0.271168	+	0.962532i	$0.412590\pi$
$674$	3.23389	0.124565
$675$	−4.94127	−0.190190
$676$	5.14844	0.198017
$677$	27.1214	1.04236	0.521180	−	0.853447i	$-0.325492\pi$
$677$	27.1214	1.04236	0.521180	+	0.853447i	$0.325492\pi$
$678$	5.22915	0.200824
$679$	−1.28120	−0.0491678
$680$	−5.62181	−0.215587
$681$	26.8576	1.02918
$682$	5.62902	0.215546
$683$	16.4889	0.630931	0.315465	−	0.948937i	$-0.397839\pi$
$683$	16.4889	0.630931	0.315465	+	0.948937i	$0.397839\pi$
$684$	−6.13375	−0.234530
$685$	56.3629	2.15352
$686$	10.0364	0.383192
$687$	0.924614	0.0352762
$688$	−18.5907	−0.708763
$689$	−42.4618	−1.61767
$690$	−12.5693	−0.478507
$691$	−18.9846	−0.722207	−0.361103	−	0.932526i	$-0.617600\pi$
$691$	−18.9846	−0.722207	−0.361103	+	0.932526i	$0.617600\pi$
$692$	26.1692	0.994803
$693$	−10.9205	−0.414836
$694$	8.76075	0.332554
$695$	−33.3750	−1.26599
$696$	5.03522	0.190859
$697$	−6.71735	−0.254438
$698$	6.67397	0.252614
$699$	−8.56217	−0.323851
$700$	−38.1682	−1.44262
$701$	22.5903	0.853223	0.426612	−	0.904435i	$-0.359707\pi$
$701$	22.5903	0.853223	0.426612	+	0.904435i	$0.359707\pi$
$702$	−1.50043	−0.0566299
$703$	22.6080	0.852678
$704$	7.88301	0.297102
$705$	−40.7472	−1.53463
$706$	5.16898	0.194537
$707$	49.5803	1.86466
$708$	18.5543	0.697312
$709$	−29.1803	−1.09589	−0.547944	−	0.836515i	$-0.684589\pi$
$709$	−29.1803	−1.09589	−0.547944	+	0.836515i	$0.684589\pi$
$710$	−7.09333	−0.266208
$711$	6.63091	0.248679
$712$	19.2955	0.723128
$713$	−40.0809	−1.50104
$714$	−2.05175	−0.0767847
$715$	−25.1799	−0.941676
$716$	−11.0507	−0.412985
$717$	−4.01866	−0.150079
$718$	8.67570	0.323774
$719$	47.6458	1.77689	0.888445	−	0.458983i	$-0.151786\pi$
$719$	47.6458	1.77689	0.888445	+	0.458983i	$0.151786\pi$
$720$	8.55296	0.318750
$721$	54.0189	2.01177
$722$	−3.34576	−0.124516
$723$	−8.80467	−0.327449
$724$	−10.3058	−0.383011
$725$	13.9541	0.518242
$726$	2.21264	0.0821186
$727$	−23.8830	−0.885772	−0.442886	−	0.896578i	$-0.646045\pi$
$727$	−23.8830	−0.885772	−0.442886	+	0.896578i	$0.646045\pi$
$728$	−24.6329	−0.912956
$729$	1.00000	0.0370370
$730$	9.89694	0.366302
$731$	−6.85331	−0.253479
$732$	−11.9176	−0.440486
$733$	−27.0202	−0.998012	−0.499006	−	0.866598i	$-0.666301\pi$
$733$	−27.0202	−0.998012	−0.499006	+	0.866598i	$0.666301\pi$
$734$	−0.198278	−0.00731857
$735$	−37.4941	−1.38299
$736$	40.9293	1.50868
$737$	−17.0365	−0.627546
$738$	−3.17093	−0.116724
$739$	35.9024	1.32069	0.660345	−	0.750963i	$-0.270410\pi$
$739$	35.9024	1.32069	0.660345	+	0.750963i	$0.270410\pi$
$740$	−36.7041	−1.34927
$741$	−10.9704	−0.403008
$742$	−27.4092	−1.00623
$743$	3.69145	0.135426	0.0677131	−	0.997705i	$-0.478430\pi$
$743$	3.69145	0.135426	0.0677131	+	0.997705i	$0.478430\pi$
$744$	−8.46234	−0.310244
$745$	−11.4243	−0.418553
$746$	−6.68210	−0.244649
$747$	−5.87355	−0.214902
$748$	4.46516	0.163262
$749$	−13.6426	−0.498488
$750$	0.0874118	0.00319183
$751$	34.0259	1.24162	0.620811	−	0.783960i	$-0.286803\pi$
$751$	34.0259	1.24162	0.620811	+	0.783960i	$0.286803\pi$
$752$	35.0568	1.27839
$753$	2.32516	0.0847335
$754$	4.23719	0.154309
$755$	−45.7493	−1.66499
$756$	7.72437	0.280933
$757$	−29.2067	−1.06154	−0.530768	−	0.847517i	$-0.678096\pi$
$757$	−29.2067	−1.06154	−0.530768	+	0.847517i	$0.678096\pi$
$758$	14.7581	0.536038
$759$	21.2183	0.770176
$760$	−19.4032	−0.703829
$761$	14.4204	0.522738	0.261369	−	0.965239i	$-0.415826\pi$
$761$	14.4204	0.522738	0.261369	+	0.965239i	$0.415826\pi$
$762$	−7.99741	−0.289716
$763$	0.176975	0.00640691
$764$	−33.9237	−1.22731
$765$	3.15298	0.113996
$766$	−9.36130	−0.338237
$767$	33.1849	1.19824
$768$	−1.00022	−0.0360924
$769$	16.5136	0.595497	0.297748	−	0.954644i	$-0.403764\pi$
$769$	16.5136	0.595497	0.297748	+	0.954644i	$0.403764\pi$
$770$	−16.2537	−0.585744
$771$	−22.8413	−0.822610
$772$	−27.9424	−1.00567
$773$	−12.2415	−0.440297	−0.220149	−	0.975466i	$-0.570654\pi$
$773$	−12.2415	−0.440297	−0.220149	+	0.975466i	$0.570654\pi$
$774$	−3.23511	−0.116284
$775$	−23.4517	−0.842408
$776$	0.525577	0.0188671
$777$	−28.4708	−1.02138
$778$	−1.92155	−0.0688910
$779$	−23.1844	−0.830667
$780$	17.8104	0.637716
$781$	11.9742	0.428472
$782$	3.98650	0.142557
$783$	−2.82399	−0.100921
$784$	32.2580	1.15207
$785$	−3.15298	−0.112535
$786$	2.41644	0.0861916
$787$	−27.8778	−0.993735	−0.496867	−	0.867826i	$-0.665516\pi$
$787$	−27.8778	−0.993735	−0.496867	+	0.867826i	$0.665516\pi$
$788$	24.3429	0.867180
$789$	31.8584	1.13419
$790$	9.86923	0.351132
$791$	−48.1479	−1.71194
$792$	4.47985	0.159185
$793$	−21.3149	−0.756916
$794$	−0.192960	−0.00684789
$795$	42.1205	1.49386
$796$	−4.32365	−0.153248
$797$	−0.644967	−0.0228459	−0.0114230	−	0.999935i	$-0.503636\pi$
$797$	−0.644967	−0.0228459	−0.0114230	+	0.999935i	$0.503636\pi$
$798$	−7.08144	−0.250680
$799$	12.9234	0.457197
$800$	23.9481	0.846693
$801$	−10.8218	−0.382369
$802$	15.9850	0.564449
$803$	−16.7070	−0.589578
$804$	12.0503	0.424983
$805$	115.733	4.07906
$806$	−7.12114	−0.250831
$807$	−23.8765	−0.840491
$808$	−20.3390	−0.715524
$809$	−2.80293	−0.0985459	−0.0492730	−	0.998785i	$-0.515690\pi$
$809$	−2.80293	−0.0985459	−0.0492730	+	0.998785i	$0.515690\pi$
$810$	1.48837	0.0522959
$811$	−20.1955	−0.709160	−0.354580	−	0.935026i	$-0.615376\pi$
$811$	−20.1955	−0.709160	−0.354580	+	0.935026i	$0.615376\pi$
$812$	−21.8135	−0.765505
$813$	5.93408	0.208117
$814$	−7.76895	−0.272302
$815$	−40.9704	−1.43513
$816$	−2.71266	−0.0949621
$817$	−23.6536	−0.827536
$818$	−5.79135	−0.202490
$819$	13.8153	0.482745
$820$	37.6398	1.31444
$821$	54.1605	1.89022	0.945108	−	0.326758i	$-0.105956\pi$
$821$	54.1605	1.89022	0.945108	+	0.326758i	$0.105956\pi$
$822$	−8.43843	−0.294324
$823$	−0.532925	−0.0185766	−0.00928830	−	0.999957i	$-0.502957\pi$
$823$	−0.532925	−0.0185766	−0.00928830	+	0.999957i	$0.502957\pi$
$824$	−22.1598	−0.771974
$825$	12.4150	0.432235
$826$	21.4210	0.745332
$827$	7.90955	0.275042	0.137521	−	0.990499i	$-0.456087\pi$
$827$	7.90955	0.275042	0.137521	+	0.990499i	$0.456087\pi$
$828$	−15.0083	−0.521573
$829$	22.8673	0.794215	0.397107	−	0.917772i	$-0.370014\pi$
$829$	22.8673	0.794215	0.397107	+	0.917772i	$0.370014\pi$
$830$	−8.74200	−0.303439
$831$	−24.9584	−0.865796
$832$	−9.97261	−0.345738
$833$	11.8916	0.412021
$834$	4.99677	0.173024
$835$	−77.4270	−2.67947
$836$	15.4111	0.533005
$837$	4.74608	0.164048
$838$	−16.1904	−0.559288
$839$	−17.4583	−0.602729	−0.301364	−	0.953509i	$-0.597442\pi$
$839$	−17.4583	−0.602729	−0.301364	+	0.953509i	$0.597442\pi$
$840$	24.4349	0.843085
$841$	−21.0251	−0.725003
$842$	8.82094	0.303990
$843$	5.18302	0.178513
$844$	35.2148	1.21214
$845$	−9.13415	−0.314224
$846$	6.10051	0.209740
$847$	−20.3730	−0.700025
$848$	−36.2383	−1.24443
$849$	26.7777	0.919007
$850$	2.33253	0.0800052
$851$	55.3181	1.89628
$852$	−8.46970	−0.290167
$853$	3.80023	0.130117	0.0650586	−	0.997881i	$-0.479277\pi$
$853$	3.80023	0.130117	0.0650586	+	0.997881i	$0.479277\pi$
$854$	−13.7589	−0.470819
$855$	10.8822	0.372165
$856$	5.59650	0.191285
$857$	−36.2326	−1.23768	−0.618841	−	0.785516i	$-0.712398\pi$
$857$	−36.2326	−1.23768	−0.618841	+	0.785516i	$0.712398\pi$
$858$	3.76984	0.128700
$859$	47.8023	1.63099	0.815496	−	0.578762i	$-0.196464\pi$
$859$	47.8023	1.63099	0.815496	+	0.578762i	$0.196464\pi$
$860$	38.4016	1.30948
$861$	29.1966	0.995019
$862$	−17.6685	−0.601792
$863$	−48.1658	−1.63958	−0.819791	−	0.572663i	$-0.805910\pi$
$863$	−48.1658	−1.63958	−0.819791	+	0.572663i	$0.805910\pi$
$864$	−4.84655	−0.164883
$865$	−46.4283	−1.57861
$866$	15.0396	0.511068
$867$	−1.00000	−0.0339618
$868$	36.6605	1.24434
$869$	−16.6603	−0.565160
$870$	−4.20313	−0.142500
$871$	21.5524	0.730277
$872$	−0.0725991	−0.00245852
$873$	−0.294768	−0.00997640
$874$	13.7591	0.465408
$875$	−0.804851	−0.0272089
$876$	11.8173	0.399271
$877$	−13.1669	−0.444613	−0.222307	−	0.974977i	$-0.571359\pi$
$877$	−13.1669	−0.444613	−0.222307	+	0.974977i	$0.571359\pi$
$878$	5.41737	0.182827
$879$	−7.84811	−0.264710
$880$	−21.4894	−0.724408
$881$	19.3053	0.650411	0.325205	−	0.945643i	$-0.394567\pi$
$881$	19.3053	0.650411	0.325205	+	0.945643i	$0.394567\pi$
$882$	5.61346	0.189015
$883$	48.9914	1.64869	0.824346	−	0.566086i	$-0.191543\pi$
$883$	48.9914	1.64869	0.824346	+	0.566086i	$0.191543\pi$
$884$	−5.64877	−0.189989
$885$	−32.9182	−1.10653
$886$	10.0941	0.339119
$887$	−19.7758	−0.664006	−0.332003	−	0.943278i	$-0.607724\pi$
$887$	−19.7758	−0.664006	−0.332003	+	0.943278i	$0.607724\pi$
$888$	11.6794	0.391935
$889$	73.6368	2.46970
$890$	−16.1068	−0.539902
$891$	−2.51251	−0.0841724
$892$	45.7061	1.53035
$893$	44.6041	1.49262
$894$	1.71040	0.0572042
$895$	19.6058	0.655348
$896$	−48.5679	−1.62254
$897$	−26.8428	−0.896255
$898$	12.2416	0.408509
$899$	−13.4029	−0.447011
$900$	−8.78146	−0.292715
$901$	−13.3590	−0.445052
$902$	7.96702	0.265273
$903$	29.7876	0.991268
$904$	19.7514	0.656921
$905$	18.2841	0.607783
$906$	6.84941	0.227556
$907$	2.28105	0.0757410	0.0378705	−	0.999283i	$-0.487943\pi$
$907$	2.28105	0.0757410	0.0378705	+	0.999283i	$0.487943\pi$
$908$	47.7304	1.58399
$909$	11.4071	0.378349
$910$	20.5622	0.681631
$911$	34.2795	1.13573	0.567865	−	0.823122i	$-0.307770\pi$
$911$	34.2795	1.13573	0.567865	+	0.823122i	$0.307770\pi$
$912$	−9.36253	−0.310024
$913$	14.7574	0.488398
$914$	5.93850	0.196428
$915$	21.1436	0.698987
$916$	1.64319	0.0542926
$917$	−22.2496	−0.734746
$918$	−0.472051	−0.0155800
$919$	2.38732	0.0787505	0.0393752	−	0.999224i	$-0.487463\pi$
$919$	2.38732	0.0787505	0.0393752	+	0.999224i	$0.487463\pi$
$920$	−47.4765	−1.56525
$921$	3.36118	0.110755
$922$	−1.70358	−0.0561043
$923$	−15.1483	−0.498614
$924$	−19.4076	−0.638463
$925$	32.3671	1.06422
$926$	13.3203	0.437731
$927$	12.4283	0.408198
$928$	13.6866	0.449285
$929$	−33.7012	−1.10570	−0.552849	−	0.833281i	$-0.686460\pi$
$929$	−33.7012	−1.10570	−0.552849	+	0.833281i	$0.686460\pi$
$930$	7.06391	0.231635
$931$	41.0430	1.34513
$932$	−15.2164	−0.498430
$933$	9.94127	0.325463
$934$	−16.7344	−0.547568
$935$	−7.92190	−0.259074
$936$	−5.66736	−0.185243
$937$	−47.2050	−1.54212	−0.771060	−	0.636762i	$-0.780273\pi$
$937$	−47.2050	−1.54212	−0.771060	+	0.636762i	$0.780273\pi$
$938$	13.9122	0.454249
$939$	−27.4120	−0.894558
$940$	−72.4146	−2.36191
$941$	52.6387	1.71597	0.857986	−	0.513674i	$-0.171716\pi$
$941$	52.6387	1.71597	0.857986	+	0.513674i	$0.171716\pi$
$942$	0.472051	0.0153803
$943$	−56.7284	−1.84733
$944$	28.3212	0.921775
$945$	−13.7043	−0.445800
$946$	8.12826	0.264273
$947$	−23.9246	−0.777445	−0.388723	−	0.921355i	$-0.627084\pi$
$947$	−23.9246	−0.777445	−0.388723	+	0.921355i	$0.627084\pi$
$948$	11.7842	0.382734
$949$	21.1357	0.686093
$950$	8.05055	0.261194
$951$	−32.9107	−1.06720
$952$	−7.74980	−0.251172
$953$	−31.7526	−1.02857	−0.514283	−	0.857620i	$-0.671942\pi$
$953$	−31.7526	−1.02857	−0.514283	+	0.857620i	$0.671942\pi$
$954$	−6.30612	−0.204168
$955$	60.1860	1.94757
$956$	−7.14183	−0.230983
$957$	7.09531	0.229359
$958$	−7.46561	−0.241203
$959$	77.6975	2.50898
$960$	9.89247	0.319278
$961$	−8.47475	−0.273379
$962$	9.82832	0.316878
$963$	−3.13878	−0.101146
$964$	−15.6474	−0.503968
$965$	49.5742	1.59585
$966$	−17.3271	−0.557491
$967$	2.40141	0.0772240	0.0386120	−	0.999254i	$-0.487706\pi$
$967$	2.40141	0.0772240	0.0386120	+	0.999254i	$0.487706\pi$
$968$	8.35749	0.268620
$969$	−3.45142	−0.110876
$970$	−0.438724	−0.0140866
$971$	−24.1135	−0.773839	−0.386919	−	0.922114i	$-0.626461\pi$
$971$	−24.1135	−0.773839	−0.386919	+	0.922114i	$0.626461\pi$
$972$	1.77717	0.0570027
$973$	−46.0082	−1.47496
$974$	−8.87134	−0.284256
$975$	−15.7059	−0.502993
$976$	−18.1909	−0.582276
$977$	−27.3508	−0.875029	−0.437514	−	0.899211i	$-0.644141\pi$
$977$	−27.3508	−0.875029	−0.437514	+	0.899211i	$0.644141\pi$
$978$	6.13392	0.196141
$979$	27.1899	0.868993
$980$	−66.6332	−2.12852
$981$	0.0407170	0.00129999
$982$	−4.03625	−0.128802
$983$	−47.6415	−1.51953	−0.759764	−	0.650200i	$-0.774685\pi$
$983$	−47.6415	−1.51953	−0.759764	+	0.650200i	$0.774685\pi$
$984$	−11.9772	−0.381818
$985$	−43.1882	−1.37609
$986$	1.33307	0.0424535
$987$	−56.1710	−1.78794
$988$	−19.4963	−0.620259
$989$	−57.8765	−1.84037
$990$	−3.73954	−0.118850
$991$	−2.53219	−0.0804376	−0.0402188	−	0.999191i	$-0.512805\pi$
$991$	−2.53219	−0.0804376	−0.0402188	+	0.999191i	$0.512805\pi$
$992$	−23.0021	−0.730317
$993$	−28.3491	−0.899632
$994$	−9.77831	−0.310149
$995$	7.67085	0.243182
$996$	−10.4383	−0.330750
$997$	14.8038	0.468840	0.234420	−	0.972135i	$-0.424681\pi$
$997$	14.8038	0.468840	0.234420	+	0.972135i	$0.424681\pi$
$998$	−10.0877	−0.319319
$999$	−6.55035	−0.207244

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.36	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.36	✓	64	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q+0.472051 q^{2} -1.00000 q^{3} -1.77717 q^{4} +3.15298 q^{5} -0.472051 q^{6} +4.34645 q^{7} -1.78302 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.472051 q^{2} -1.00000 q^{3} -1.77717 q^{4} +3.15298 q^{5} -0.472051 q^{6} +4.34645 q^{7} -1.78302 q^{8} +1.00000 q^{9} +1.48837 q^{10} -2.51251 q^{11} +1.77717 q^{12} +3.17852 q^{13} +2.05175 q^{14} -3.15298 q^{15} +2.71266 q^{16} +1.00000 q^{17} +0.472051 q^{18} +3.45142 q^{19} -5.60337 q^{20} -4.34645 q^{21} -1.18604 q^{22} +8.44505 q^{23} +1.78302 q^{24} +4.94127 q^{25} +1.50043 q^{26} -1.00000 q^{27} -7.72437 q^{28} +2.82399 q^{29} -1.48837 q^{30} -4.74608 q^{31} +4.84655 q^{32} +2.51251 q^{33} +0.472051 q^{34} +13.7043 q^{35} -1.77717 q^{36} +6.55035 q^{37} +1.62925 q^{38} -3.17852 q^{39} -5.62181 q^{40} -6.71735 q^{41} -2.05175 q^{42} -6.85331 q^{43} +4.46516 q^{44} +3.15298 q^{45} +3.98650 q^{46} +12.9234 q^{47} -2.71266 q^{48} +11.8916 q^{49} +2.33253 q^{50} -1.00000 q^{51} -5.64877 q^{52} -13.3590 q^{53} -0.472051 q^{54} -7.92190 q^{55} -7.74980 q^{56} -3.45142 q^{57} +1.33307 q^{58} +10.4404 q^{59} +5.60337 q^{60} -6.70593 q^{61} -2.24039 q^{62} +4.34645 q^{63} -3.13750 q^{64} +10.0218 q^{65} +1.18604 q^{66} +6.78065 q^{67} -1.77717 q^{68} -8.44505 q^{69} +6.46912 q^{70} -4.76584 q^{71} -1.78302 q^{72} +6.64953 q^{73} +3.09210 q^{74} -4.94127 q^{75} -6.13375 q^{76} -10.9205 q^{77} -1.50043 q^{78} +6.63091 q^{79} +8.55296 q^{80} +1.00000 q^{81} -3.17093 q^{82} -5.87355 q^{83} +7.72437 q^{84} +3.15298 q^{85} -3.23511 q^{86} -2.82399 q^{87} +4.47985 q^{88} -10.8218 q^{89} +1.48837 q^{90} +13.8153 q^{91} -15.0083 q^{92} +4.74608 q^{93} +6.10051 q^{94} +10.8822 q^{95} -4.84655 q^{96} -0.294768 q^{97} +5.61346 q^{98} -2.51251 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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