LMFDB - Embedded newform 8002.2.a.e.1.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$0$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.23
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.50560 q^{3} +1.00000 q^{4} -3.94222 q^{5} +1.50560 q^{6} -0.919611 q^{7} -1.00000 q^{8} -0.733164 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.50560 q^{3} +1.00000 q^{4} -3.94222 q^{5} +1.50560 q^{6} -0.919611 q^{7} -1.00000 q^{8} -0.733164 q^{9} +3.94222 q^{10} +0.400837 q^{11} -1.50560 q^{12} -0.361388 q^{13} +0.919611 q^{14} +5.93541 q^{15} +1.00000 q^{16} +3.01452 q^{17} +0.733164 q^{18} -7.05442 q^{19} -3.94222 q^{20} +1.38457 q^{21} -0.400837 q^{22} +4.28375 q^{23} +1.50560 q^{24} +10.5411 q^{25} +0.361388 q^{26} +5.62066 q^{27} -0.919611 q^{28} -2.24284 q^{29} -5.93541 q^{30} +6.77509 q^{31} -1.00000 q^{32} -0.603501 q^{33} -3.01452 q^{34} +3.62531 q^{35} -0.733164 q^{36} +3.39431 q^{37} +7.05442 q^{38} +0.544106 q^{39} +3.94222 q^{40} +1.33461 q^{41} -1.38457 q^{42} -7.28688 q^{43} +0.400837 q^{44} +2.89029 q^{45} -4.28375 q^{46} -11.1053 q^{47} -1.50560 q^{48} -6.15432 q^{49} -10.5411 q^{50} -4.53866 q^{51} -0.361388 q^{52} -10.4711 q^{53} -5.62066 q^{54} -1.58019 q^{55} +0.919611 q^{56} +10.6211 q^{57} +2.24284 q^{58} +7.52462 q^{59} +5.93541 q^{60} -9.80405 q^{61} -6.77509 q^{62} +0.674226 q^{63} +1.00000 q^{64} +1.42467 q^{65} +0.603501 q^{66} -5.11475 q^{67} +3.01452 q^{68} -6.44961 q^{69} -3.62531 q^{70} -9.38384 q^{71} +0.733164 q^{72} -9.90907 q^{73} -3.39431 q^{74} -15.8707 q^{75} -7.05442 q^{76} -0.368614 q^{77} -0.544106 q^{78} +4.77706 q^{79} -3.94222 q^{80} -6.26298 q^{81} -1.33461 q^{82} -10.8315 q^{83} +1.38457 q^{84} -11.8839 q^{85} +7.28688 q^{86} +3.37683 q^{87} -0.400837 q^{88} +3.20331 q^{89} -2.89029 q^{90} +0.332336 q^{91} +4.28375 q^{92} -10.2006 q^{93} +11.1053 q^{94} +27.8100 q^{95} +1.50560 q^{96} -10.0346 q^{97} +6.15432 q^{98} -0.293879 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) $ 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9 - 18 * q^10 + 30 * q^11 + 10 * q^12 - 2 * q^13 - 21 * q^14 + 21 * q^15 + 77 * q^16 + 60 * q^17 - 71 * q^18 - 3 * q^19 + 18 * q^20 + 10 * q^21 - 30 * q^22 + 53 * q^23 - 10 * q^24 + 59 * q^25 + 2 * q^26 + 43 * q^27 + 21 * q^28 + 30 * q^29 - 21 * q^30 + 22 * q^31 - 77 * q^32 + 31 * q^33 - 60 * q^34 + 41 * q^35 + 71 * q^36 - 3 * q^37 + 3 * q^38 + 44 * q^39 - 18 * q^40 + 48 * q^41 - 10 * q^42 + 21 * q^43 + 30 * q^44 + 33 * q^45 - 53 * q^46 + 107 * q^47 + 10 * q^48 + 24 * q^49 - 59 * q^50 + 18 * q^51 - 2 * q^52 + 42 * q^53 - 43 * q^54 + 49 * q^55 - 21 * q^56 + 32 * q^57 - 30 * q^58 + 42 * q^59 + 21 * q^60 - 31 * q^61 - 22 * q^62 + 109 * q^63 + 77 * q^64 + 39 * q^65 - 31 * q^66 - q^67 + 60 * q^68 - 33 * q^69 - 41 * q^70 + 58 * q^71 - 71 * q^72 + 35 * q^73 + 3 * q^74 + 34 * q^75 - 3 * q^76 + 86 * q^77 - 44 * q^78 + 25 * q^79 + 18 * q^80 + 53 * q^81 - 48 * q^82 + 107 * q^83 + 10 * q^84 + 21 * q^85 - 21 * q^86 + 100 * q^87 - 30 * q^88 + 34 * q^89 - 33 * q^90 - 51 * q^91 + 53 * q^92 + 48 * q^93 - 107 * q^94 + 118 * q^95 - 10 * q^96 - 13 * q^97 - 24 * q^98 + 63 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.50560	−0.869259	−0.434630	−	0.900609i	$-0.643121\pi$
$3$	−1.50560	−0.869259	−0.434630	+	0.900609i	$0.643121\pi$
$4$	1.00000	0.500000
$5$	−3.94222	−1.76301	−0.881507	−	0.472171i	$-0.843470\pi$
$5$	−3.94222	−1.76301	−0.881507	+	0.472171i	$0.843470\pi$
$6$	1.50560	0.614659
$7$	−0.919611	−0.347580	−0.173790	−	0.984783i	$-0.555601\pi$
$7$	−0.919611	−0.347580	−0.173790	+	0.984783i	$0.555601\pi$
$8$	−1.00000	−0.353553
$9$	−0.733164	−0.244388
$10$	3.94222	1.24664
$11$	0.400837	0.120857	0.0604284	−	0.998173i	$-0.480753\pi$
$11$	0.400837	0.120857	0.0604284	+	0.998173i	$0.480753\pi$
$12$	−1.50560	−0.434630
$13$	−0.361388	−0.100231	−0.0501155	−	0.998743i	$-0.515959\pi$
$13$	−0.361388	−0.100231	−0.0501155	+	0.998743i	$0.515959\pi$
$14$	0.919611	0.245776
$15$	5.93541	1.53252
$16$	1.00000	0.250000
$17$	3.01452	0.731127	0.365564	−	0.930786i	$-0.380876\pi$
$17$	3.01452	0.731127	0.365564	+	0.930786i	$0.380876\pi$
$18$	0.733164	0.172808
$19$	−7.05442	−1.61839	−0.809197	−	0.587538i	$-0.800097\pi$
$19$	−7.05442	−1.61839	−0.809197	+	0.587538i	$0.800097\pi$
$20$	−3.94222	−0.881507
$21$	1.38457	0.302137
$22$	−0.400837	−0.0854587
$23$	4.28375	0.893223	0.446611	−	0.894728i	$-0.352631\pi$
$23$	4.28375	0.893223	0.446611	+	0.894728i	$0.352631\pi$
$24$	1.50560	0.307330
$25$	10.5411	2.10822
$26$	0.361388	0.0708740
$27$	5.62066	1.08170
$28$	−0.919611	−0.173790
$29$	−2.24284	−0.416485	−0.208243	−	0.978077i	$-0.566774\pi$
$29$	−2.24284	−0.416485	−0.208243	+	0.978077i	$0.566774\pi$
$30$	−5.93541	−1.08365
$31$	6.77509	1.21684	0.608421	−	0.793615i	$-0.291803\pi$
$31$	6.77509	1.21684	0.608421	+	0.793615i	$0.291803\pi$
$32$	−1.00000	−0.176777
$33$	−0.603501	−0.105056
$34$	−3.01452	−0.516985
$35$	3.62531	0.612789
$36$	−0.733164	−0.122194
$37$	3.39431	0.558022	0.279011	−	0.960288i	$-0.409993\pi$
$37$	3.39431	0.558022	0.279011	+	0.960288i	$0.409993\pi$
$38$	7.05442	1.14438
$39$	0.544106	0.0871267
$40$	3.94222	0.623320
$41$	1.33461	0.208431	0.104215	−	0.994555i	$-0.466767\pi$
$41$	1.33461	0.208431	0.104215	+	0.994555i	$0.466767\pi$
$42$	−1.38457	−0.213643
$43$	−7.28688	−1.11124	−0.555620	−	0.831437i	$-0.687519\pi$
$43$	−7.28688	−1.11124	−0.555620	+	0.831437i	$0.687519\pi$
$44$	0.400837	0.0604284
$45$	2.89029	0.430860
$46$	−4.28375	−0.631604
$47$	−11.1053	−1.61987	−0.809936	−	0.586518i	$-0.800498\pi$
$47$	−11.1053	−1.61987	−0.809936	+	0.586518i	$0.800498\pi$
$48$	−1.50560	−0.217315
$49$	−6.15432	−0.879188
$50$	−10.5411	−1.49074
$51$	−4.53866	−0.635539
$52$	−0.361388	−0.0501155
$53$	−10.4711	−1.43832	−0.719158	−	0.694847i	$-0.755472\pi$
$53$	−10.4711	−1.43832	−0.719158	+	0.694847i	$0.755472\pi$
$54$	−5.62066	−0.764875
$55$	−1.58019	−0.213072
$56$	0.919611	0.122888
$57$	10.6211	1.40680
$58$	2.24284	0.294500
$59$	7.52462	0.979622	0.489811	−	0.871829i	$-0.337066\pi$
$59$	7.52462	0.979622	0.489811	+	0.871829i	$0.337066\pi$
$60$	5.93541	0.766258
$61$	−9.80405	−1.25528	−0.627640	−	0.778504i	$-0.715979\pi$
$61$	−9.80405	−1.25528	−0.627640	+	0.778504i	$0.715979\pi$
$62$	−6.77509	−0.860437
$63$	0.674226	0.0849445
$64$	1.00000	0.125000
$65$	1.42467	0.176709
$66$	0.603501	0.0742858
$67$	−5.11475	−0.624866	−0.312433	−	0.949940i	$-0.601144\pi$
$67$	−5.11475	−0.624866	−0.312433	+	0.949940i	$0.601144\pi$
$68$	3.01452	0.365564
$69$	−6.44961	−0.776442
$70$	−3.62531	−0.433307
$71$	−9.38384	−1.11366	−0.556828	−	0.830627i	$-0.687982\pi$
$71$	−9.38384	−1.11366	−0.556828	+	0.830627i	$0.687982\pi$
$72$	0.733164	0.0864042
$73$	−9.90907	−1.15977	−0.579884	−	0.814699i	$-0.696902\pi$
$73$	−9.90907	−1.15977	−0.579884	+	0.814699i	$0.696902\pi$
$74$	−3.39431	−0.394581
$75$	−15.8707	−1.83259
$76$	−7.05442	−0.809197
$77$	−0.368614	−0.0420075
$78$	−0.544106	−0.0616079
$79$	4.77706	0.537462	0.268731	−	0.963215i	$-0.413396\pi$
$79$	4.77706	0.537462	0.268731	+	0.963215i	$0.413396\pi$
$80$	−3.94222	−0.440753
$81$	−6.26298	−0.695886
$82$	−1.33461	−0.147383
$83$	−10.8315	−1.18891	−0.594455	−	0.804129i	$-0.702632\pi$
$83$	−10.8315	−1.18891	−0.594455	+	0.804129i	$0.702632\pi$
$84$	1.38457	0.151069
$85$	−11.8839	−1.28899
$86$	7.28688	0.785765
$87$	3.37683	0.362034
$88$	−0.400837	−0.0427294
$89$	3.20331	0.339550	0.169775	−	0.985483i	$-0.445696\pi$
$89$	3.20331	0.339550	0.169775	+	0.985483i	$0.445696\pi$
$90$	−2.89029	−0.304664
$91$	0.332336	0.0348383
$92$	4.28375	0.446611
$93$	−10.2006	−1.05775
$94$	11.1053	1.14542
$95$	27.8100	2.85325
$96$	1.50560	0.153665
$97$	−10.0346	−1.01886	−0.509431	−	0.860511i	$-0.670144\pi$
$97$	−10.0346	−1.01886	−0.509431	+	0.860511i	$0.670144\pi$
$98$	6.15432	0.621680
$99$	−0.293879	−0.0295360
$100$	10.5411	1.05411
$101$	9.45293	0.940602	0.470301	−	0.882506i	$-0.344145\pi$
$101$	9.45293	0.940602	0.470301	+	0.882506i	$0.344145\pi$
$102$	4.53866	0.449394
$103$	7.81072	0.769613	0.384807	−	0.922997i	$-0.374268\pi$
$103$	7.81072	0.769613	0.384807	+	0.922997i	$0.374268\pi$
$104$	0.361388	0.0354370
$105$	−5.45827	−0.532672
$106$	10.4711	1.01704
$107$	−10.3645	−1.00197	−0.500986	−	0.865456i	$-0.667029\pi$
$107$	−10.3645	−1.00197	−0.500986	+	0.865456i	$0.667029\pi$
$108$	5.62066	0.540848
$109$	−5.51240	−0.527992	−0.263996	−	0.964524i	$-0.585041\pi$
$109$	−5.51240	−0.527992	−0.263996	+	0.964524i	$0.585041\pi$
$110$	1.58019	0.150665
$111$	−5.11048	−0.485066
$112$	−0.919611	−0.0868950
$113$	9.79347	0.921292	0.460646	−	0.887584i	$-0.347618\pi$
$113$	9.79347	0.921292	0.460646	+	0.887584i	$0.347618\pi$
$114$	−10.6211	−0.994761
$115$	−16.8875	−1.57476
$116$	−2.24284	−0.208243
$117$	0.264957	0.0244953
$118$	−7.52462	−0.692697
$119$	−2.77218	−0.254125
$120$	−5.93541	−0.541826
$121$	−10.8393	−0.985394
$122$	9.80405	0.887617
$123$	−2.00939	−0.181180
$124$	6.77509	0.608421
$125$	−21.8442	−1.95380
$126$	−0.674226	−0.0600648
$127$	−17.8657	−1.58532	−0.792660	−	0.609664i	$-0.791305\pi$
$127$	−17.8657	−1.58532	−0.792660	+	0.609664i	$0.791305\pi$
$128$	−1.00000	−0.0883883
$129$	10.9711	0.965955
$130$	−1.42467	−0.124952
$131$	17.0677	1.49121	0.745606	−	0.666387i	$-0.232160\pi$
$131$	17.0677	1.49121	0.745606	+	0.666387i	$0.232160\pi$
$132$	−0.603501	−0.0525280
$133$	6.48732	0.562522
$134$	5.11475	0.441847
$135$	−22.1579	−1.90705
$136$	−3.01452	−0.258493
$137$	16.8700	1.44130	0.720652	−	0.693297i	$-0.243842\pi$
$137$	16.8700	1.44130	0.720652	+	0.693297i	$0.243842\pi$
$138$	6.44961	0.549028
$139$	−16.1862	−1.37290	−0.686448	−	0.727179i	$-0.740831\pi$
$139$	−16.1862	−1.37290	−0.686448	+	0.727179i	$0.740831\pi$
$140$	3.62531	0.306394
$141$	16.7201	1.40809
$142$	9.38384	0.787474
$143$	−0.144858	−0.0121136
$144$	−0.733164	−0.0610970
$145$	8.84178	0.734270
$146$	9.90907	0.820080
$147$	9.26595	0.764242
$148$	3.39431	0.279011
$149$	5.31679	0.435568	0.217784	−	0.975997i	$-0.430117\pi$
$149$	5.31679	0.435568	0.217784	+	0.975997i	$0.430117\pi$
$150$	15.8707	1.29584
$151$	−7.99345	−0.650497	−0.325249	−	0.945629i	$-0.605448\pi$
$151$	−7.99345	−0.650497	−0.325249	+	0.945629i	$0.605448\pi$
$152$	7.05442	0.572189
$153$	−2.21013	−0.178679
$154$	0.368614	0.0297038
$155$	−26.7089	−2.14531
$156$	0.544106	0.0435633
$157$	8.98238	0.716872	0.358436	−	0.933554i	$-0.383310\pi$
$157$	8.98238	0.716872	0.358436	+	0.933554i	$0.383310\pi$
$158$	−4.77706	−0.380043
$159$	15.7653	1.25027
$160$	3.94222	0.311660
$161$	−3.93938	−0.310467
$162$	6.26298	0.492066
$163$	17.3191	1.35653	0.678267	−	0.734816i	$-0.262731\pi$
$163$	17.3191	1.35653	0.678267	+	0.734816i	$0.262731\pi$
$164$	1.33461	0.104215
$165$	2.37913	0.185215
$166$	10.8315	0.840686
$167$	−7.80414	−0.603903	−0.301951	−	0.953323i	$-0.597638\pi$
$167$	−7.80414	−0.603903	−0.301951	+	0.953323i	$0.597638\pi$
$168$	−1.38457	−0.106822
$169$	−12.8694	−0.989954
$170$	11.8839	0.911452
$171$	5.17205	0.395516
$172$	−7.28688	−0.555620
$173$	7.50789	0.570814	0.285407	−	0.958406i	$-0.407871\pi$
$173$	7.50789	0.570814	0.285407	+	0.958406i	$0.407871\pi$
$174$	−3.37683	−0.255997
$175$	−9.69370	−0.732775
$176$	0.400837	0.0302142
$177$	−11.3291	−0.851546
$178$	−3.20331	−0.240098
$179$	4.23869	0.316814	0.158407	−	0.987374i	$-0.449364\pi$
$179$	4.23869	0.316814	0.158407	+	0.987374i	$0.449364\pi$
$180$	2.89029	0.215430
$181$	−7.19666	−0.534924	−0.267462	−	0.963568i	$-0.586185\pi$
$181$	−7.19666	−0.534924	−0.267462	+	0.963568i	$0.586185\pi$
$182$	−0.332336	−0.0246344
$183$	14.7610	1.09116
$184$	−4.28375	−0.315802
$185$	−13.3811	−0.983800
$186$	10.2006	0.747943
$187$	1.20833	0.0883618
$188$	−11.1053	−0.809936
$189$	−5.16882	−0.375976
$190$	−27.8100	−2.01755
$191$	−14.4982	−1.04905	−0.524526	−	0.851395i	$-0.675757\pi$
$191$	−14.4982	−1.04905	−0.524526	+	0.851395i	$0.675757\pi$
$192$	−1.50560	−0.108657
$193$	11.2547	0.810133	0.405067	−	0.914287i	$-0.367248\pi$
$193$	11.2547	0.810133	0.405067	+	0.914287i	$0.367248\pi$
$194$	10.0346	0.720444
$195$	−2.14499	−0.153606
$196$	−6.15432	−0.439594
$197$	−23.4104	−1.66792	−0.833962	−	0.551822i	$-0.813933\pi$
$197$	−23.4104	−1.66792	−0.833962	+	0.551822i	$0.813933\pi$
$198$	0.293879	0.0208851
$199$	−5.58797	−0.396121	−0.198060	−	0.980190i	$-0.563464\pi$
$199$	−5.58797	−0.396121	−0.198060	+	0.980190i	$0.563464\pi$
$200$	−10.5411	−0.745368
$201$	7.70078	0.543171
$202$	−9.45293	−0.665106
$203$	2.06254	0.144762
$204$	−4.53866	−0.317770
$205$	−5.26131	−0.367466
$206$	−7.81072	−0.544199
$207$	−3.14069	−0.218293
$208$	−0.361388	−0.0250577
$209$	−2.82767	−0.195594
$210$	5.45827	0.376656
$211$	−26.6826	−1.83690	−0.918452	−	0.395533i	$-0.870560\pi$
$211$	−26.6826	−1.83690	−0.918452	+	0.395533i	$0.870560\pi$
$212$	−10.4711	−0.719158
$213$	14.1283	0.968057
$214$	10.3645	0.708501
$215$	28.7265	1.95913
$216$	−5.62066	−0.382437
$217$	−6.23044	−0.422950
$218$	5.51240	0.373347
$219$	14.9191	1.00814
$220$	−1.58019	−0.106536
$221$	−1.08941	−0.0732816
$222$	5.11048	0.342993
$223$	17.9102	1.19936	0.599679	−	0.800241i	$-0.295295\pi$
$223$	17.9102	1.19936	0.599679	+	0.800241i	$0.295295\pi$
$224$	0.919611	0.0614441
$225$	−7.72835	−0.515223
$226$	−9.79347	−0.651452
$227$	−10.0339	−0.665975	−0.332987	−	0.942931i	$-0.608057\pi$
$227$	−10.0339	−0.665975	−0.332987	+	0.942931i	$0.608057\pi$
$228$	10.6211	0.703402
$229$	−20.9726	−1.38591	−0.692953	−	0.720983i	$-0.743691\pi$
$229$	−20.9726	−1.38591	−0.692953	+	0.720983i	$0.743691\pi$
$230$	16.8875	1.11353
$231$	0.554986	0.0365154
$232$	2.24284	0.147250
$233$	−9.80102	−0.642086	−0.321043	−	0.947065i	$-0.604033\pi$
$233$	−9.80102	−0.642086	−0.321043	+	0.947065i	$0.604033\pi$
$234$	−0.264957	−0.0173208
$235$	43.7795	2.85586
$236$	7.52462	0.489811
$237$	−7.19235	−0.467194
$238$	2.77218	0.179694
$239$	17.2200	1.11387	0.556936	−	0.830556i	$-0.311977\pi$
$239$	17.2200	1.11387	0.556936	+	0.830556i	$0.311977\pi$
$240$	5.93541	0.383129
$241$	−10.5308	−0.678351	−0.339176	−	0.940723i	$-0.610148\pi$
$241$	−10.5308	−0.678351	−0.339176	+	0.940723i	$0.610148\pi$
$242$	10.8393	0.696779
$243$	−7.43243	−0.476790
$244$	−9.80405	−0.627640
$245$	24.2617	1.55002
$246$	2.00939	0.128114
$247$	2.54938	0.162213
$248$	−6.77509	−0.430219
$249$	16.3079	1.03347
$250$	21.8442	1.38155
$251$	−0.988815	−0.0624135	−0.0312067	−	0.999513i	$-0.509935\pi$
$251$	−0.988815	−0.0624135	−0.0312067	+	0.999513i	$0.509935\pi$
$252$	0.674226	0.0424722
$253$	1.71708	0.107952
$254$	17.8657	1.12099
$255$	17.8924	1.12046
$256$	1.00000	0.0625000
$257$	14.4425	0.900897	0.450449	−	0.892802i	$-0.351264\pi$
$257$	14.4425	0.900897	0.450449	+	0.892802i	$0.351264\pi$
$258$	−10.9711	−0.683033
$259$	−3.12145	−0.193957
$260$	1.42467	0.0883543
$261$	1.64437	0.101784
$262$	−17.0677	−1.05445
$263$	16.4426	1.01389	0.506946	−	0.861978i	$-0.330774\pi$
$263$	16.4426	1.01389	0.506946	+	0.861978i	$0.330774\pi$
$264$	0.603501	0.0371429
$265$	41.2794	2.53577
$266$	−6.48732	−0.397763
$267$	−4.82291	−0.295157
$268$	−5.11475	−0.312433
$269$	−18.9477	−1.15526	−0.577630	−	0.816299i	$-0.696022\pi$
$269$	−18.9477	−1.15526	−0.577630	+	0.816299i	$0.696022\pi$
$270$	22.1579	1.34848
$271$	19.0310	1.15605	0.578027	−	0.816018i	$-0.303823\pi$
$271$	19.0310	1.15605	0.578027	+	0.816018i	$0.303823\pi$
$272$	3.01452	0.182782
$273$	−0.500366	−0.0302835
$274$	−16.8700	−1.01916
$275$	4.22526	0.254793
$276$	−6.44961	−0.388221
$277$	−21.4179	−1.28688	−0.643439	−	0.765498i	$-0.722493\pi$
$277$	−21.4179	−1.28688	−0.643439	+	0.765498i	$0.722493\pi$
$278$	16.1862	0.970783
$279$	−4.96725	−0.297382
$280$	−3.62531	−0.216654
$281$	16.8524	1.00533	0.502665	−	0.864481i	$-0.332353\pi$
$281$	16.8524	1.00533	0.502665	+	0.864481i	$0.332353\pi$
$282$	−16.7201	−0.995670
$283$	−14.6033	−0.868076	−0.434038	−	0.900895i	$-0.642912\pi$
$283$	−14.6033	−0.868076	−0.434038	+	0.900895i	$0.642912\pi$
$284$	−9.38384	−0.556828
$285$	−41.8708	−2.48021
$286$	0.144858	0.00856561
$287$	−1.22732	−0.0724463
$288$	0.733164	0.0432021
$289$	−7.91270	−0.465453
$290$	−8.84178	−0.519207
$291$	15.1082	0.885655
$292$	−9.90907	−0.579884
$293$	11.0215	0.643881	0.321940	−	0.946760i	$-0.395665\pi$
$293$	11.0215	0.643881	0.321940	+	0.946760i	$0.395665\pi$
$294$	−9.26595	−0.540401
$295$	−29.6637	−1.72709
$296$	−3.39431	−0.197291
$297$	2.25297	0.130730
$298$	−5.31679	−0.307993
$299$	−1.54809	−0.0895286
$300$	−15.8707	−0.916294
$301$	6.70110	0.386245
$302$	7.99345	0.459971
$303$	−14.2323	−0.817627
$304$	−7.05442	−0.404598
$305$	38.6497	2.21308
$306$	2.21013	0.126345
$307$	22.4949	1.28385	0.641926	−	0.766767i	$-0.278136\pi$
$307$	22.4949	1.28385	0.641926	+	0.766767i	$0.278136\pi$
$308$	−0.368614	−0.0210037
$309$	−11.7598	−0.668993
$310$	26.7089	1.51696
$311$	5.84917	0.331676	0.165838	−	0.986153i	$-0.446967\pi$
$311$	5.84917	0.331676	0.165838	+	0.986153i	$0.446967\pi$
$312$	−0.544106	−0.0308039
$313$	6.95578	0.393164	0.196582	−	0.980487i	$-0.437016\pi$
$313$	6.95578	0.393164	0.196582	+	0.980487i	$0.437016\pi$
$314$	−8.98238	−0.506905
$315$	−2.65795	−0.149758
$316$	4.77706	0.268731
$317$	−9.71251	−0.545509	−0.272755	−	0.962084i	$-0.587935\pi$
$317$	−9.71251	−0.545509	−0.272755	+	0.962084i	$0.587935\pi$
$318$	−15.7653	−0.884074
$319$	−0.899014	−0.0503351
$320$	−3.94222	−0.220377
$321$	15.6048	0.870973
$322$	3.93938	0.219533
$323$	−21.2656	−1.18325
$324$	−6.26298	−0.347943
$325$	−3.80942	−0.211309
$326$	−17.3191	−0.959214
$327$	8.29948	0.458962
$328$	−1.33461	−0.0736913
$329$	10.2125	0.563036
$330$	−2.37913	−0.130967
$331$	−3.35198	−0.184241	−0.0921207	−	0.995748i	$-0.529365\pi$
$331$	−3.35198	−0.184241	−0.0921207	+	0.995748i	$0.529365\pi$
$332$	−10.8315	−0.594455
$333$	−2.48859	−0.136374
$334$	7.80414	0.427024
$335$	20.1635	1.10165
$336$	1.38457	0.0755343
$337$	−8.18215	−0.445710	−0.222855	−	0.974852i	$-0.571538\pi$
$337$	−8.18215	−0.445710	−0.222855	+	0.974852i	$0.571538\pi$
$338$	12.8694	0.700003
$339$	−14.7451	−0.800842
$340$	−11.8839	−0.644494
$341$	2.71571	0.147064
$342$	−5.17205	−0.279672
$343$	12.0969	0.653169
$344$	7.28688	0.392882
$345$	25.4258	1.36888
$346$	−7.50789	−0.403626
$347$	−16.5637	−0.889186	−0.444593	−	0.895733i	$-0.646652\pi$
$347$	−16.5637	−0.889186	−0.444593	+	0.895733i	$0.646652\pi$
$348$	3.37683	0.181017
$349$	6.45045	0.345284	0.172642	−	0.984985i	$-0.444770\pi$
$349$	6.45045	0.345284	0.172642	+	0.984985i	$0.444770\pi$
$350$	9.69370	0.518150
$351$	−2.03124	−0.108419
$352$	−0.400837	−0.0213647
$353$	10.0877	0.536916	0.268458	−	0.963291i	$-0.413486\pi$
$353$	10.0877	0.536916	0.268458	+	0.963291i	$0.413486\pi$
$354$	11.3291	0.602134
$355$	36.9932	1.96339
$356$	3.20331	0.169775
$357$	4.17380	0.220901
$358$	−4.23869	−0.224022
$359$	−25.9333	−1.36871	−0.684353	−	0.729151i	$-0.739915\pi$
$359$	−25.9333	−1.36871	−0.684353	+	0.729151i	$0.739915\pi$
$360$	−2.89029	−0.152332
$361$	30.7648	1.61920
$362$	7.19666	0.378248
$363$	16.3197	0.856563
$364$	0.332336	0.0174191
$365$	39.0637	2.04469
$366$	−14.7610	−0.771569
$367$	−19.0143	−0.992539	−0.496269	−	0.868169i	$-0.665297\pi$
$367$	−19.0143	−0.992539	−0.496269	+	0.868169i	$0.665297\pi$
$368$	4.28375	0.223306
$369$	−0.978486	−0.0509379
$370$	13.3811	0.695652
$371$	9.62933	0.499930
$372$	−10.2006	−0.528876
$373$	21.9969	1.13896	0.569478	−	0.822007i	$-0.307145\pi$
$373$	21.9969	1.13896	0.569478	+	0.822007i	$0.307145\pi$
$374$	−1.20833	−0.0624812
$375$	32.8886	1.69836
$376$	11.1053	0.572712
$377$	0.810536	0.0417447
$378$	5.16882	0.265855
$379$	−19.1999	−0.986231	−0.493115	−	0.869964i	$-0.664142\pi$
$379$	−19.1999	−0.986231	−0.493115	+	0.869964i	$0.664142\pi$
$380$	27.8100	1.42663
$381$	26.8986	1.37805
$382$	14.4982	0.741791
$383$	21.6416	1.10583	0.552916	−	0.833237i	$-0.313515\pi$
$383$	21.6416	1.10583	0.552916	+	0.833237i	$0.313515\pi$
$384$	1.50560	0.0768324
$385$	1.45316	0.0740597
$386$	−11.2547	−0.572851
$387$	5.34248	0.271574
$388$	−10.0346	−0.509431
$389$	−31.4697	−1.59558	−0.797788	−	0.602939i	$-0.793996\pi$
$389$	−31.4697	−1.59558	−0.797788	+	0.602939i	$0.793996\pi$
$390$	2.14499	0.108616
$391$	12.9134	0.653060
$392$	6.15432	0.310840
$393$	−25.6971	−1.29625
$394$	23.4104	1.17940
$395$	−18.8322	−0.947552
$396$	−0.293879	−0.0147680
$397$	32.9657	1.65450	0.827251	−	0.561832i	$-0.189903\pi$
$397$	32.9657	1.65450	0.827251	+	0.561832i	$0.189903\pi$
$398$	5.58797	0.280100
$399$	−9.76731	−0.488977
$400$	10.5411	0.527054
$401$	17.8306	0.890417	0.445208	−	0.895427i	$-0.353130\pi$
$401$	17.8306	0.890417	0.445208	+	0.895427i	$0.353130\pi$
$402$	−7.70078	−0.384080
$403$	−2.44843	−0.121965
$404$	9.45293	0.470301
$405$	24.6900	1.22686
$406$	−2.06254	−0.102362
$407$	1.36057	0.0674408
$408$	4.53866	0.224697
$409$	5.14444	0.254376	0.127188	−	0.991879i	$-0.459405\pi$
$409$	5.14444	0.254376	0.127188	+	0.991879i	$0.459405\pi$
$410$	5.26131	0.259838
$411$	−25.3996	−1.25287
$412$	7.81072	0.384807
$413$	−6.91972	−0.340497
$414$	3.14069	0.154356
$415$	42.7001	2.09606
$416$	0.361388	0.0177185
$417$	24.3700	1.19340
$418$	2.82767	0.138306
$419$	28.8217	1.40803	0.704017	−	0.710183i	$-0.251388\pi$
$419$	28.8217	1.40803	0.704017	+	0.710183i	$0.251388\pi$
$420$	−5.45827	−0.266336
$421$	25.5619	1.24581	0.622907	−	0.782296i	$-0.285952\pi$
$421$	25.5619	1.24581	0.622907	+	0.782296i	$0.285952\pi$
$422$	26.6826	1.29889
$423$	8.14200	0.395878
$424$	10.4711	0.508521
$425$	31.7763	1.54138
$426$	−14.1283	−0.684520
$427$	9.01591	0.436310
$428$	−10.3645	−0.500986
$429$	0.218098	0.0105299
$430$	−28.7265	−1.38531
$431$	11.3093	0.544751	0.272375	−	0.962191i	$-0.412191\pi$
$431$	11.3093	0.544751	0.272375	+	0.962191i	$0.412191\pi$
$432$	5.62066	0.270424
$433$	−26.6116	−1.27887	−0.639436	−	0.768844i	$-0.720832\pi$
$433$	−26.6116	−1.27887	−0.639436	+	0.768844i	$0.720832\pi$
$434$	6.23044	0.299071
$435$	−13.3122	−0.638271
$436$	−5.51240	−0.263996
$437$	−30.2193	−1.44559
$438$	−14.9191	−0.712863
$439$	5.83372	0.278428	0.139214	−	0.990262i	$-0.455542\pi$
$439$	5.83372	0.278428	0.139214	+	0.990262i	$0.455542\pi$
$440$	1.58019	0.0753324
$441$	4.51213	0.214863
$442$	1.08941	0.0518179
$443$	−35.4540	−1.68447	−0.842234	−	0.539112i	$-0.818760\pi$
$443$	−35.4540	−1.68447	−0.842234	+	0.539112i	$0.818760\pi$
$444$	−5.11048	−0.242533
$445$	−12.6282	−0.598632
$446$	−17.9102	−0.848074
$447$	−8.00496	−0.378622
$448$	−0.919611	−0.0434475
$449$	−25.8741	−1.22107	−0.610536	−	0.791988i	$-0.709046\pi$
$449$	−25.8741	−1.22107	−0.610536	+	0.791988i	$0.709046\pi$
$450$	7.72835	0.364318
$451$	0.534960	0.0251903
$452$	9.79347	0.460646
$453$	12.0349	0.565451
$454$	10.0339	0.470915
$455$	−1.31014	−0.0614204
$456$	−10.6211	−0.497380
$457$	24.8602	1.16291	0.581456	−	0.813578i	$-0.302483\pi$
$457$	24.8602	1.16291	0.581456	+	0.813578i	$0.302483\pi$
$458$	20.9726	0.979983
$459$	16.9436	0.790857
$460$	−16.8875	−0.787382
$461$	29.2023	1.36008	0.680042	−	0.733173i	$-0.261961\pi$
$461$	29.2023	1.36008	0.680042	+	0.733173i	$0.261961\pi$
$462$	−0.554986	−0.0258203
$463$	23.3713	1.08615	0.543077	−	0.839683i	$-0.317259\pi$
$463$	23.3713	1.08615	0.543077	+	0.839683i	$0.317259\pi$
$464$	−2.24284	−0.104121
$465$	40.2129	1.86483
$466$	9.80102	0.454024
$467$	17.3858	0.804517	0.402259	−	0.915526i	$-0.368225\pi$
$467$	17.3858	0.804517	0.402259	+	0.915526i	$0.368225\pi$
$468$	0.264957	0.0122476
$469$	4.70358	0.217191
$470$	−43.7795	−2.01940
$471$	−13.5239	−0.623148
$472$	−7.52462	−0.346349
$473$	−2.92085	−0.134301
$474$	7.19235	0.330356
$475$	−74.3612	−3.41193
$476$	−2.77218	−0.127063
$477$	7.67703	0.351507
$478$	−17.2200	−0.787626
$479$	−1.47800	−0.0675316	−0.0337658	−	0.999430i	$-0.510750\pi$
$479$	−1.47800	−0.0675316	−0.0337658	+	0.999430i	$0.510750\pi$
$480$	−5.93541	−0.270913
$481$	−1.22666	−0.0559311
$482$	10.5308	0.479667
$483$	5.93113	0.269876
$484$	−10.8393	−0.492697
$485$	39.5587	1.79627
$486$	7.43243	0.337142
$487$	−32.4713	−1.47142	−0.735708	−	0.677299i	$-0.763151\pi$
$487$	−32.4713	−1.47142	−0.735708	+	0.677299i	$0.763151\pi$
$488$	9.80405	0.443808
$489$	−26.0756	−1.17918
$490$	−24.2617	−1.09603
$491$	−10.2131	−0.460913	−0.230456	−	0.973083i	$-0.574022\pi$
$491$	−10.2131	−0.460913	−0.230456	+	0.973083i	$0.574022\pi$
$492$	−2.00939	−0.0905901
$493$	−6.76108	−0.304504
$494$	−2.54938	−0.114702
$495$	1.15854	0.0520723
$496$	6.77509	0.304210
$497$	8.62948	0.387085
$498$	−16.3079	−0.730774
$499$	−42.1989	−1.88908	−0.944541	−	0.328393i	$-0.893493\pi$
$499$	−42.1989	−1.88908	−0.944541	+	0.328393i	$0.893493\pi$
$500$	−21.8442	−0.976902
$501$	11.7499	0.524948
$502$	0.988815	0.0441330
$503$	11.6276	0.518449	0.259224	−	0.965817i	$-0.416533\pi$
$503$	11.6276	0.518449	0.259224	+	0.965817i	$0.416533\pi$
$504$	−0.674226	−0.0300324
$505$	−37.2655	−1.65829
$506$	−1.71708	−0.0763337
$507$	19.3762	0.860527
$508$	−17.8657	−0.792660
$509$	−2.07009	−0.0917552	−0.0458776	−	0.998947i	$-0.514608\pi$
$509$	−2.07009	−0.0917552	−0.0458776	+	0.998947i	$0.514608\pi$
$510$	−17.8924	−0.792288
$511$	9.11249	0.403113
$512$	−1.00000	−0.0441942
$513$	−39.6505	−1.75061
$514$	−14.4425	−0.637030
$515$	−30.7916	−1.35684
$516$	10.9711	0.482978
$517$	−4.45141	−0.195773
$518$	3.12145	0.137149
$519$	−11.3039	−0.496185
$520$	−1.42467	−0.0624759
$521$	−25.7343	−1.12744	−0.563721	−	0.825966i	$-0.690630\pi$
$521$	−25.7343	−1.12744	−0.563721	+	0.825966i	$0.690630\pi$
$522$	−1.64437	−0.0719722
$523$	4.08553	0.178648	0.0893239	−	0.996003i	$-0.471529\pi$
$523$	4.08553	0.178648	0.0893239	+	0.996003i	$0.471529\pi$
$524$	17.0677	0.745606
$525$	14.5948	0.636971
$526$	−16.4426	−0.716930
$527$	20.4236	0.889666
$528$	−0.603501	−0.0262640
$529$	−4.64952	−0.202153
$530$	−41.2794	−1.79306
$531$	−5.51678	−0.239408
$532$	6.48732	0.281261
$533$	−0.482311	−0.0208912
$534$	4.82291	0.208708
$535$	40.8590	1.76649
$536$	5.11475	0.220924
$537$	−6.38177	−0.275394
$538$	18.9477	0.816891
$539$	−2.46688	−0.106256
$540$	−22.1579	−0.953523
$541$	9.73043	0.418344	0.209172	−	0.977879i	$-0.432923\pi$
$541$	9.73043	0.418344	0.209172	+	0.977879i	$0.432923\pi$
$542$	−19.0310	−0.817453
$543$	10.8353	0.464988
$544$	−3.01452	−0.129246
$545$	21.7311	0.930857
$546$	0.500366	0.0214137
$547$	13.6218	0.582428	0.291214	−	0.956658i	$-0.405941\pi$
$547$	13.6218	0.582428	0.291214	+	0.956658i	$0.405941\pi$
$548$	16.8700	0.720652
$549$	7.18798	0.306775
$550$	−4.22526	−0.180166
$551$	15.8219	0.674038
$552$	6.44961	0.274514
$553$	−4.39304	−0.186811
$554$	21.4179	0.909960
$555$	20.1466	0.855178
$556$	−16.1862	−0.686448
$557$	−18.1590	−0.769424	−0.384712	−	0.923037i	$-0.625699\pi$
$557$	−18.1590	−0.769424	−0.384712	+	0.923037i	$0.625699\pi$
$558$	4.96725	0.210281
$559$	2.63339	0.111381
$560$	3.62531	0.153197
$561$	−1.81926	−0.0768093
$562$	−16.8524	−0.710875
$563$	−44.0313	−1.85570	−0.927850	−	0.372953i	$-0.878345\pi$
$563$	−44.0313	−1.85570	−0.927850	+	0.372953i	$0.878345\pi$
$564$	16.7201	0.704045
$565$	−38.6080	−1.62425
$566$	14.6033	0.613822
$567$	5.75950	0.241876
$568$	9.38384	0.393737
$569$	20.8978	0.876082	0.438041	−	0.898955i	$-0.355672\pi$
$569$	20.8978	0.876082	0.438041	+	0.898955i	$0.355672\pi$
$570$	41.8708	1.75378
$571$	−14.8838	−0.622867	−0.311434	−	0.950268i	$-0.600809\pi$
$571$	−14.8838	−0.622867	−0.311434	+	0.950268i	$0.600809\pi$
$572$	−0.144858	−0.00605680
$573$	21.8285	0.911898
$574$	1.22732	0.0512273
$575$	45.1553	1.88311
$576$	−0.733164	−0.0305485
$577$	−10.8960	−0.453606	−0.226803	−	0.973941i	$-0.572827\pi$
$577$	−10.8960	−0.453606	−0.226803	+	0.973941i	$0.572827\pi$
$578$	7.91270	0.329125
$579$	−16.9451	−0.704216
$580$	8.84178	0.367135
$581$	9.96074	0.413241
$582$	−15.1082	−0.626253
$583$	−4.19720	−0.173830
$584$	9.90907	0.410040
$585$	−1.04452	−0.0431855
$586$	−11.0215	−0.455292
$587$	26.2007	1.08142	0.540710	−	0.841209i	$-0.318156\pi$
$587$	26.2007	1.08142	0.540710	+	0.841209i	$0.318156\pi$
$588$	9.26595	0.382121
$589$	−47.7943	−1.96933
$590$	29.6637	1.22123
$591$	35.2468	1.44986
$592$	3.39431	0.139505
$593$	12.0940	0.496641	0.248321	−	0.968678i	$-0.420121\pi$
$593$	12.0940	0.496641	0.248321	+	0.968678i	$0.420121\pi$
$594$	−2.25297	−0.0924404
$595$	10.9285	0.448027
$596$	5.31679	0.217784
$597$	8.41326	0.344332
$598$	1.54809	0.0633063
$599$	17.7464	0.725099	0.362549	−	0.931965i	$-0.381906\pi$
$599$	17.7464	0.725099	0.362549	+	0.931965i	$0.381906\pi$
$600$	15.8707	0.647918
$601$	−5.06201	−0.206484	−0.103242	−	0.994656i	$-0.532922\pi$
$601$	−5.06201	−0.206484	−0.103242	+	0.994656i	$0.532922\pi$
$602$	−6.70110	−0.273116
$603$	3.74995	0.152710
$604$	−7.99345	−0.325249
$605$	42.7310	1.73726
$606$	14.2323	0.578150
$607$	25.6336	1.04044	0.520218	−	0.854034i	$-0.325851\pi$
$607$	25.6336	1.04044	0.520218	+	0.854034i	$0.325851\pi$
$608$	7.05442	0.286094
$609$	−3.10537	−0.125836
$610$	−38.6497	−1.56488
$611$	4.01332	0.162361
$612$	−2.21013	−0.0893394
$613$	−38.4483	−1.55291	−0.776455	−	0.630172i	$-0.782984\pi$
$613$	−38.4483	−1.55291	−0.776455	+	0.630172i	$0.782984\pi$
$614$	−22.4949	−0.907821
$615$	7.92144	0.319423
$616$	0.368614	0.0148519
$617$	−29.2086	−1.17589	−0.587947	−	0.808899i	$-0.700064\pi$
$617$	−29.2086	−1.17589	−0.587947	+	0.808899i	$0.700064\pi$
$618$	11.7598	0.473050
$619$	7.35298	0.295541	0.147771	−	0.989022i	$-0.452790\pi$
$619$	7.35298	0.295541	0.147771	+	0.989022i	$0.452790\pi$
$620$	−26.7089	−1.07265
$621$	24.0775	0.966196
$622$	−5.84917	−0.234530
$623$	−2.94580	−0.118021
$624$	0.544106	0.0217817
$625$	33.4091	1.33636
$626$	−6.95578	−0.278009
$627$	4.25734	0.170022
$628$	8.98238	0.358436
$629$	10.2322	0.407985
$630$	2.65795	0.105895
$631$	0.489003	0.0194669	0.00973344	−	0.999953i	$-0.496902\pi$
$631$	0.489003	0.0194669	0.00973344	+	0.999953i	$0.496902\pi$
$632$	−4.77706	−0.190021
$633$	40.1733	1.59675
$634$	9.71251	0.385733
$635$	70.4303	2.79494
$636$	15.7653	0.625135
$637$	2.22410	0.0881219
$638$	0.899014	0.0355923
$639$	6.87990	0.272165
$640$	3.94222	0.155830
$641$	9.99950	0.394956	0.197478	−	0.980307i	$-0.436725\pi$
$641$	9.99950	0.394956	0.197478	+	0.980307i	$0.436725\pi$
$642$	−15.6048	−0.615871
$643$	39.7031	1.56574	0.782868	−	0.622188i	$-0.213756\pi$
$643$	39.7031	1.56574	0.782868	+	0.622188i	$0.213756\pi$
$644$	−3.93938	−0.155233
$645$	−43.2506	−1.70299
$646$	21.2656	0.836685
$647$	−16.2399	−0.638457	−0.319228	−	0.947678i	$-0.603424\pi$
$647$	−16.2399	−0.638457	−0.319228	+	0.947678i	$0.603424\pi$
$648$	6.26298	0.246033
$649$	3.01615	0.118394
$650$	3.80942	0.149418
$651$	9.38057	0.367653
$652$	17.3191	0.678267
$653$	−39.1284	−1.53121	−0.765606	−	0.643310i	$-0.777561\pi$
$653$	−39.1284	−1.53121	−0.765606	+	0.643310i	$0.777561\pi$
$654$	−8.29948	−0.324535
$655$	−67.2846	−2.62903
$656$	1.33461	0.0521076
$657$	7.26498	0.283434
$658$	−10.2125	−0.398126
$659$	−2.36403	−0.0920895	−0.0460447	−	0.998939i	$-0.514662\pi$
$659$	−2.36403	−0.0920895	−0.0460447	+	0.998939i	$0.514662\pi$
$660$	2.37913	0.0926076
$661$	5.68293	0.221040	0.110520	−	0.993874i	$-0.464748\pi$
$661$	5.68293	0.221040	0.110520	+	0.993874i	$0.464748\pi$
$662$	3.35198	0.130278
$663$	1.64022	0.0637007
$664$	10.8315	0.420343
$665$	−25.5744	−0.991733
$666$	2.48859	0.0964309
$667$	−9.60777	−0.372014
$668$	−7.80414	−0.301951
$669$	−26.9657	−1.04255
$670$	−20.1635	−0.778983
$671$	−3.92983	−0.151709
$672$	−1.38457	−0.0534108
$673$	35.2014	1.35691	0.678457	−	0.734640i	$-0.262649\pi$
$673$	35.2014	1.35691	0.678457	+	0.734640i	$0.262649\pi$
$674$	8.18215	0.315165
$675$	59.2478	2.28045
$676$	−12.8694	−0.494977
$677$	8.20806	0.315461	0.157731	−	0.987482i	$-0.449582\pi$
$677$	8.20806	0.315461	0.157731	+	0.987482i	$0.449582\pi$
$678$	14.7451	0.566281
$679$	9.22795	0.354136
$680$	11.8839	0.455726
$681$	15.1071	0.578905
$682$	−2.71571	−0.103990
$683$	3.59385	0.137515	0.0687575	−	0.997633i	$-0.478097\pi$
$683$	3.59385	0.137515	0.0687575	+	0.997633i	$0.478097\pi$
$684$	5.17205	0.197758
$685$	−66.5054	−2.54104
$686$	−12.0969	−0.461860
$687$	31.5763	1.20471
$688$	−7.28688	−0.277810
$689$	3.78413	0.144164
$690$	−25.4258	−0.967943
$691$	−5.36091	−0.203939	−0.101969	−	0.994788i	$-0.532514\pi$
$691$	−5.36091	−0.203939	−0.101969	+	0.994788i	$0.532514\pi$
$692$	7.50789	0.285407
$693$	0.270255	0.0102661
$694$	16.5637	0.628749
$695$	63.8095	2.42043
$696$	−3.37683	−0.127998
$697$	4.02319	0.152389
$698$	−6.45045	−0.244153
$699$	14.7564	0.558139
$700$	−9.69370	−0.366387
$701$	41.0708	1.55122	0.775610	−	0.631212i	$-0.217442\pi$
$701$	41.0708	1.55122	0.775610	+	0.631212i	$0.217442\pi$
$702$	2.03124	0.0766641
$703$	−23.9449	−0.903099
$704$	0.400837	0.0151071
$705$	−65.9144	−2.48248
$706$	−10.0877	−0.379657
$707$	−8.69302	−0.326935
$708$	−11.3291	−0.425773
$709$	20.1942	0.758409	0.379205	−	0.925313i	$-0.376198\pi$
$709$	20.1942	0.758409	0.379205	+	0.925313i	$0.376198\pi$
$710$	−36.9932	−1.38833
$711$	−3.50237	−0.131349
$712$	−3.20331	−0.120049
$713$	29.0228	1.08691
$714$	−4.17380	−0.156200
$715$	0.571060	0.0213564
$716$	4.23869	0.158407
$717$	−25.9265	−0.968243
$718$	25.9333	0.967821
$719$	−42.3486	−1.57934	−0.789668	−	0.613535i	$-0.789747\pi$
$719$	−42.3486	−1.57934	−0.789668	+	0.613535i	$0.789747\pi$
$720$	2.89029	0.107715
$721$	−7.18282	−0.267502
$722$	−30.7648	−1.14495
$723$	15.8552	0.589663
$724$	−7.19666	−0.267462
$725$	−23.6420	−0.878042
$726$	−16.3197	−0.605681
$727$	−15.1194	−0.560747	−0.280373	−	0.959891i	$-0.590458\pi$
$727$	−15.1194	−0.560747	−0.280373	+	0.959891i	$0.590458\pi$
$728$	−0.332336	−0.0123172
$729$	29.9792	1.11034
$730$	−39.0637	−1.44581
$731$	−21.9664	−0.812457
$732$	14.7610	0.545582
$733$	−10.3598	−0.382647	−0.191323	−	0.981527i	$-0.561278\pi$
$733$	−10.3598	−0.382647	−0.191323	+	0.981527i	$0.561278\pi$
$734$	19.0143	0.701831
$735$	−36.5284	−1.34737
$736$	−4.28375	−0.157901
$737$	−2.05018	−0.0755194
$738$	0.978486	0.0360186
$739$	18.1108	0.666218	0.333109	−	0.942888i	$-0.391902\pi$
$739$	18.1108	0.666218	0.333109	+	0.942888i	$0.391902\pi$
$740$	−13.3811	−0.491900
$741$	−3.83835	−0.141005
$742$	−9.62933	−0.353504
$743$	44.6308	1.63734	0.818672	−	0.574262i	$-0.194711\pi$
$743$	44.6308	1.63734	0.818672	+	0.574262i	$0.194711\pi$
$744$	10.2006	0.373972
$745$	−20.9599	−0.767912
$746$	−21.9969	−0.805364
$747$	7.94125	0.290555
$748$	1.20833	0.0441809
$749$	9.53128	0.348265
$750$	−32.8886	−1.20092
$751$	−24.6760	−0.900438	−0.450219	−	0.892918i	$-0.648654\pi$
$751$	−24.6760	−0.900438	−0.450219	+	0.892918i	$0.648654\pi$
$752$	−11.1053	−0.404968
$753$	1.48876	0.0542535
$754$	−0.810536	−0.0295180
$755$	31.5119	1.14684
$756$	−5.16882	−0.187988
$757$	−19.8072	−0.719907	−0.359953	−	0.932970i	$-0.617207\pi$
$757$	−19.8072	−0.719907	−0.359953	+	0.932970i	$0.617207\pi$
$758$	19.1999	0.697371
$759$	−2.58524	−0.0938384
$760$	−27.8100	−1.00878
$761$	41.0957	1.48972	0.744859	−	0.667222i	$-0.232517\pi$
$761$	41.0957	1.48972	0.744859	+	0.667222i	$0.232517\pi$
$762$	−26.8986	−0.974432
$763$	5.06926	0.183520
$764$	−14.4982	−0.524526
$765$	8.71284	0.315013
$766$	−21.6416	−0.781941
$767$	−2.71931	−0.0981884
$768$	−1.50560	−0.0543287
$769$	−49.3109	−1.77820	−0.889099	−	0.457715i	$-0.848668\pi$
$769$	−49.3109	−1.77820	−0.889099	+	0.457715i	$0.848668\pi$
$770$	−1.45316	−0.0523681
$771$	−21.7446	−0.783113
$772$	11.2547	0.405067
$773$	49.8336	1.79239	0.896195	−	0.443660i	$-0.146320\pi$
$773$	49.8336	1.79239	0.896195	+	0.443660i	$0.146320\pi$
$774$	−5.34248	−0.192032
$775$	71.4168	2.56537
$776$	10.0346	0.360222
$777$	4.69966	0.168599
$778$	31.4697	1.12824
$779$	−9.41487	−0.337323
$780$	−2.14499	−0.0768028
$781$	−3.76139	−0.134593
$782$	−12.9134	−0.461783
$783$	−12.6063	−0.450511
$784$	−6.15432	−0.219797
$785$	−35.4105	−1.26385
$786$	25.6971	0.916587
$787$	30.1726	1.07554	0.537768	−	0.843093i	$-0.319268\pi$
$787$	30.1726	1.07554	0.537768	+	0.843093i	$0.319268\pi$
$788$	−23.4104	−0.833962
$789$	−24.7560	−0.881335
$790$	18.8322	0.670021
$791$	−9.00618	−0.320223
$792$	0.293879	0.0104425
$793$	3.54306	0.125818
$794$	−32.9657	−1.16991
$795$	−62.1503	−2.20424
$796$	−5.58797	−0.198060
$797$	−13.5809	−0.481060	−0.240530	−	0.970642i	$-0.577321\pi$
$797$	−13.5809	−0.481060	−0.240530	+	0.970642i	$0.577321\pi$
$798$	9.76731	0.345759
$799$	−33.4771	−1.18433
$800$	−10.5411	−0.372684
$801$	−2.34855	−0.0829820
$802$	−17.8306	−0.629620
$803$	−3.97192	−0.140166
$804$	7.70078	0.271585
$805$	15.5299	0.547357
$806$	2.44843	0.0862424
$807$	28.5276	1.00422
$808$	−9.45293	−0.332553
$809$	43.3367	1.52364	0.761819	−	0.647790i	$-0.224306\pi$
$809$	43.3367	1.52364	0.761819	+	0.647790i	$0.224306\pi$
$810$	−24.6900	−0.867519
$811$	35.3304	1.24062	0.620310	−	0.784357i	$-0.287007\pi$
$811$	35.3304	1.24062	0.620310	+	0.784357i	$0.287007\pi$
$812$	2.06254	0.0723811
$813$	−28.6532	−1.00491
$814$	−1.36057	−0.0476878
$815$	−68.2755	−2.39159
$816$	−4.53866	−0.158885
$817$	51.4047	1.79842
$818$	−5.14444	−0.179871
$819$	−0.243657	−0.00851406
$820$	−5.26131	−0.183733
$821$	40.7056	1.42063	0.710317	−	0.703882i	$-0.248551\pi$
$821$	40.7056	1.42063	0.710317	+	0.703882i	$0.248551\pi$
$822$	25.3996	0.885911
$823$	18.4708	0.643850	0.321925	−	0.946765i	$-0.395670\pi$
$823$	18.4708	0.643850	0.321925	+	0.946765i	$0.395670\pi$
$824$	−7.81072	−0.272099
$825$	−6.36155	−0.221481
$826$	6.91972	0.240768
$827$	50.9584	1.77200	0.885999	−	0.463687i	$-0.153474\pi$
$827$	50.9584	1.77200	0.885999	+	0.463687i	$0.153474\pi$
$828$	−3.14069	−0.109147
$829$	−19.9055	−0.691348	−0.345674	−	0.938355i	$-0.612350\pi$
$829$	−19.9055	−0.691348	−0.345674	+	0.938355i	$0.612350\pi$
$830$	−42.7001	−1.48214
$831$	32.2468	1.11863
$832$	−0.361388	−0.0125289
$833$	−18.5523	−0.642798
$834$	−24.3700	−0.843863
$835$	30.7656	1.06469
$836$	−2.82767	−0.0977970
$837$	38.0805	1.31625
$838$	−28.8217	−0.995630
$839$	20.6276	0.712145	0.356073	−	0.934458i	$-0.384116\pi$
$839$	20.6276	0.712145	0.356073	+	0.934458i	$0.384116\pi$
$840$	5.45827	0.188328
$841$	−23.9697	−0.826540
$842$	−25.5619	−0.880923
$843$	−25.3730	−0.873892
$844$	−26.6826	−0.918452
$845$	50.7340	1.74530
$846$	−8.14200	−0.279928
$847$	9.96796	0.342503
$848$	−10.4711	−0.359579
$849$	21.9867	0.754583
$850$	−31.7763	−1.08992
$851$	14.5404	0.498438
$852$	14.1283	0.484028
$853$	26.6638	0.912950	0.456475	−	0.889736i	$-0.349112\pi$
$853$	26.6638	0.912950	0.456475	+	0.889736i	$0.349112\pi$
$854$	−9.01591	−0.308518
$855$	−20.3893	−0.697301
$856$	10.3645	0.354250
$857$	22.6617	0.774108	0.387054	−	0.922057i	$-0.373493\pi$
$857$	22.6617	0.774108	0.387054	+	0.922057i	$0.373493\pi$
$858$	−0.218098	−0.00744574
$859$	4.51321	0.153989	0.0769943	−	0.997032i	$-0.475468\pi$
$859$	4.51321	0.153989	0.0769943	+	0.997032i	$0.475468\pi$
$860$	28.7265	0.979565
$861$	1.84785	0.0629746
$862$	−11.3093	−0.385197
$863$	25.6268	0.872347	0.436173	−	0.899863i	$-0.356333\pi$
$863$	25.6268	0.872347	0.436173	+	0.899863i	$0.356333\pi$
$864$	−5.62066	−0.191219
$865$	−29.5977	−1.00635
$866$	26.6116	0.904299
$867$	11.9134	0.404599
$868$	−6.23044	−0.211475
$869$	1.91482	0.0649559
$870$	13.3122	0.451326
$871$	1.84841	0.0626309
$872$	5.51240	0.186673
$873$	7.35703	0.248998
$874$	30.2193	1.02218
$875$	20.0881	0.679103
$876$	14.9191	0.504070
$877$	−47.1137	−1.59092	−0.795458	−	0.606009i	$-0.792770\pi$
$877$	−47.1137	−1.59092	−0.795458	+	0.606009i	$0.792770\pi$
$878$	−5.83372	−0.196879
$879$	−16.5939	−0.559699
$880$	−1.58019	−0.0532681
$881$	9.17031	0.308956	0.154478	−	0.987996i	$-0.450630\pi$
$881$	9.17031	0.308956	0.154478	+	0.987996i	$0.450630\pi$
$882$	−4.51213	−0.151931
$883$	12.9304	0.435144	0.217572	−	0.976044i	$-0.430186\pi$
$883$	12.9304	0.435144	0.217572	+	0.976044i	$0.430186\pi$
$884$	−1.08941	−0.0366408
$885$	44.6617	1.50129
$886$	35.4540	1.19110
$887$	19.3261	0.648908	0.324454	−	0.945901i	$-0.394819\pi$
$887$	19.3261	0.648908	0.324454	+	0.945901i	$0.394819\pi$
$888$	5.11048	0.171497
$889$	16.4294	0.551026
$890$	12.6282	0.423297
$891$	−2.51043	−0.0841027
$892$	17.9102	0.599679
$893$	78.3413	2.62159
$894$	8.00496	0.267726
$895$	−16.7098	−0.558548
$896$	0.919611	0.0307220
$897$	2.33081	0.0778236
$898$	25.8741	0.863428
$899$	−15.1955	−0.506797
$900$	−7.72835	−0.257612
$901$	−31.5653	−1.05159
$902$	−0.534960	−0.0178122
$903$	−10.0892	−0.335747
$904$	−9.79347	−0.325726
$905$	28.3708	0.943078
$906$	−12.0349	−0.399834
$907$	3.59885	0.119498	0.0597489	−	0.998213i	$-0.480970\pi$
$907$	3.59885	0.119498	0.0597489	+	0.998213i	$0.480970\pi$
$908$	−10.0339	−0.332987
$909$	−6.93055	−0.229872
$910$	1.31014	0.0434308
$911$	−12.1845	−0.403691	−0.201846	−	0.979417i	$-0.564694\pi$
$911$	−12.1845	−0.403691	−0.201846	+	0.979417i	$0.564694\pi$
$912$	10.6211	0.351701
$913$	−4.34166	−0.143688
$914$	−24.8602	−0.822303
$915$	−58.1911	−1.92374
$916$	−20.9726	−0.692953
$917$	−15.6956	−0.518316
$918$	−16.9436	−0.559221
$919$	−49.4614	−1.63158	−0.815791	−	0.578347i	$-0.803698\pi$
$919$	−49.4614	−1.63158	−0.815791	+	0.578347i	$0.803698\pi$
$920$	16.8875	0.556763
$921$	−33.8684	−1.11600
$922$	−29.2023	−0.961725
$923$	3.39121	0.111623
$924$	0.554986	0.0182577
$925$	35.7798	1.17643
$926$	−23.3713	−0.768027
$927$	−5.72654	−0.188084
$928$	2.24284	0.0736249
$929$	2.89453	0.0949666	0.0474833	−	0.998872i	$-0.484880\pi$
$929$	2.89453	0.0949666	0.0474833	+	0.998872i	$0.484880\pi$
$930$	−40.2129	−1.31863
$931$	43.4151	1.42287
$932$	−9.80102	−0.321043
$933$	−8.80652	−0.288313
$934$	−17.3858	−0.568880
$935$	−4.76350	−0.155783
$936$	−0.264957	−0.00866038
$937$	−35.6254	−1.16383	−0.581916	−	0.813249i	$-0.697697\pi$
$937$	−35.6254	−1.16383	−0.581916	+	0.813249i	$0.697697\pi$
$938$	−4.70358	−0.153577
$939$	−10.4726	−0.341761
$940$	43.7795	1.42793
$941$	8.21347	0.267752	0.133876	−	0.990998i	$-0.457258\pi$
$941$	8.21347	0.267752	0.133876	+	0.990998i	$0.457258\pi$
$942$	13.5239	0.440632
$943$	5.71712	0.186175
$944$	7.52462	0.244905
$945$	20.3766	0.662851
$946$	2.92085	0.0949651
$947$	2.46557	0.0801203	0.0400602	−	0.999197i	$-0.487245\pi$
$947$	2.46557	0.0801203	0.0400602	+	0.999197i	$0.487245\pi$
$948$	−7.19235	−0.233597
$949$	3.58102	0.116245
$950$	74.3612	2.41260
$951$	14.6232	0.474189
$952$	2.77218	0.0898469
$953$	−12.1712	−0.394265	−0.197133	−	0.980377i	$-0.563163\pi$
$953$	−12.1712	−0.394265	−0.197133	+	0.980377i	$0.563163\pi$
$954$	−7.67703	−0.248553
$955$	57.1550	1.84949
$956$	17.2200	0.556936
$957$	1.35356	0.0437543
$958$	1.47800	0.0477520
$959$	−15.5139	−0.500969
$960$	5.93541	0.191565
$961$	14.9018	0.480704
$962$	1.22666	0.0395492
$963$	7.59886	0.244870
$964$	−10.5308	−0.339176
$965$	−44.3686	−1.42828
$966$	−5.93113	−0.190831
$967$	−31.8145	−1.02309	−0.511543	−	0.859258i	$-0.670926\pi$
$967$	−31.8145	−1.02309	−0.511543	+	0.859258i	$0.670926\pi$
$968$	10.8393	0.348389
$969$	32.0176	1.02855
$970$	−39.5587	−1.27015
$971$	−26.8379	−0.861270	−0.430635	−	0.902526i	$-0.641710\pi$
$971$	−26.8379	−0.861270	−0.430635	+	0.902526i	$0.641710\pi$
$972$	−7.43243	−0.238395
$973$	14.8850	0.477191
$974$	32.4713	1.04045
$975$	5.73547	0.183682
$976$	−9.80405	−0.313820
$977$	4.93325	0.157829	0.0789144	−	0.996881i	$-0.474855\pi$
$977$	4.93325	0.157829	0.0789144	+	0.996881i	$0.474855\pi$
$978$	26.0756	0.833806
$979$	1.28401	0.0410370
$980$	24.2617	0.775010
$981$	4.04149	0.129035
$982$	10.2131	0.325915
$983$	1.54879	0.0493989	0.0246994	−	0.999695i	$-0.492137\pi$
$983$	1.54879	0.0493989	0.0246994	+	0.999695i	$0.492137\pi$
$984$	2.00939	0.0640569
$985$	92.2890	2.94057
$986$	6.76108	0.215317
$987$	−15.3760	−0.489424
$988$	2.54938	0.0811066
$989$	−31.2152	−0.992584
$990$	−1.15854	−0.0368207
$991$	8.93110	0.283706	0.141853	−	0.989888i	$-0.454694\pi$
$991$	8.93110	0.283706	0.141853	+	0.989888i	$0.454694\pi$
$992$	−6.77509	−0.215109
$993$	5.04674	0.160154
$994$	−8.62948	−0.273711
$995$	22.0290	0.698366
$996$	16.3079	0.516735
$997$	14.4867	0.458799	0.229400	−	0.973332i	$-0.426324\pi$
$997$	14.4867	0.458799	0.229400	+	0.973332i	$0.426324\pi$
$998$	42.1989	1.33578
$999$	19.0783	0.603610

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.e.1.23	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.e.1.23	✓	77	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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.50560 q^{3} +1.00000 q^{4} -3.94222 q^{5} +1.50560 q^{6} -0.919611 q^{7} -1.00000 q^{8} -0.733164 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.50560 q^{3} +1.00000 q^{4} -3.94222 q^{5} +1.50560 q^{6} -0.919611 q^{7} -1.00000 q^{8} -0.733164 q^{9} +3.94222 q^{10} +0.400837 q^{11} -1.50560 q^{12} -0.361388 q^{13} +0.919611 q^{14} +5.93541 q^{15} +1.00000 q^{16} +3.01452 q^{17} +0.733164 q^{18} -7.05442 q^{19} -3.94222 q^{20} +1.38457 q^{21} -0.400837 q^{22} +4.28375 q^{23} +1.50560 q^{24} +10.5411 q^{25} +0.361388 q^{26} +5.62066 q^{27} -0.919611 q^{28} -2.24284 q^{29} -5.93541 q^{30} +6.77509 q^{31} -1.00000 q^{32} -0.603501 q^{33} -3.01452 q^{34} +3.62531 q^{35} -0.733164 q^{36} +3.39431 q^{37} +7.05442 q^{38} +0.544106 q^{39} +3.94222 q^{40} +1.33461 q^{41} -1.38457 q^{42} -7.28688 q^{43} +0.400837 q^{44} +2.89029 q^{45} -4.28375 q^{46} -11.1053 q^{47} -1.50560 q^{48} -6.15432 q^{49} -10.5411 q^{50} -4.53866 q^{51} -0.361388 q^{52} -10.4711 q^{53} -5.62066 q^{54} -1.58019 q^{55} +0.919611 q^{56} +10.6211 q^{57} +2.24284 q^{58} +7.52462 q^{59} +5.93541 q^{60} -9.80405 q^{61} -6.77509 q^{62} +0.674226 q^{63} +1.00000 q^{64} +1.42467 q^{65} +0.603501 q^{66} -5.11475 q^{67} +3.01452 q^{68} -6.44961 q^{69} -3.62531 q^{70} -9.38384 q^{71} +0.733164 q^{72} -9.90907 q^{73} -3.39431 q^{74} -15.8707 q^{75} -7.05442 q^{76} -0.368614 q^{77} -0.544106 q^{78} +4.77706 q^{79} -3.94222 q^{80} -6.26298 q^{81} -1.33461 q^{82} -10.8315 q^{83} +1.38457 q^{84} -11.8839 q^{85} +7.28688 q^{86} +3.37683 q^{87} -0.400837 q^{88} +3.20331 q^{89} -2.89029 q^{90} +0.332336 q^{91} +4.28375 q^{92} -10.2006 q^{93} +11.1053 q^{94} +27.8100 q^{95} +1.50560 q^{96} -10.0346 q^{97} +6.15432 q^{98} -0.293879 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9 - 18 * q^10 + 30 * q^11 + 10 * q^12 - 2 * q^13 - 21 * q^14 + 21 * q^15 + 77 * q^16 + 60 * q^17 - 71 * q^18 - 3 * q^19 + 18 * q^20 + 10 * q^21 - 30 * q^22 + 53 * q^23 - 10 * q^24 + 59 * q^25 + 2 * q^26 + 43 * q^27 + 21 * q^28 + 30 * q^29 - 21 * q^30 + 22 * q^31 - 77 * q^32 + 31 * q^33 - 60 * q^34 + 41 * q^35 + 71 * q^36 - 3 * q^37 + 3 * q^38 + 44 * q^39 - 18 * q^40 + 48 * q^41 - 10 * q^42 + 21 * q^43 + 30 * q^44 + 33 * q^45 - 53 * q^46 + 107 * q^47 + 10 * q^48 + 24 * q^49 - 59 * q^50 + 18 * q^51 - 2 * q^52 + 42 * q^53 - 43 * q^54 + 49 * q^55 - 21 * q^56 + 32 * q^57 - 30 * q^58 + 42 * q^59 + 21 * q^60 - 31 * q^61 - 22 * q^62 + 109 * q^63 + 77 * q^64 + 39 * q^65 - 31 * q^66 - q^67 + 60 * q^68 - 33 * q^69 - 41 * q^70 + 58 * q^71 - 71 * q^72 + 35 * q^73 + 3 * q^74 + 34 * q^75 - 3 * q^76 + 86 * q^77 - 44 * q^78 + 25 * q^79 + 18 * q^80 + 53 * q^81 - 48 * q^82 + 107 * q^83 + 10 * q^84 + 21 * q^85 - 21 * q^86 + 100 * q^87 - 30 * q^88 + 34 * q^89 - 33 * q^90 - 51 * q^91 + 53 * q^92 + 48 * q^93 - 107 * q^94 + 118 * q^95 - 10 * q^96 - 13 * q^97 - 24 * q^98 + 63 * q^99

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