LMFDB - Embedded newform 8002.2.a.e.1.65

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			1.65
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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.38683 q^{3} +1.00000 q^{4} -2.88254 q^{5} -2.38683 q^{6} -1.19657 q^{7} -1.00000 q^{8} +2.69696 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.38683 q^{3} +1.00000 q^{4} -2.88254 q^{5} -2.38683 q^{6} -1.19657 q^{7} -1.00000 q^{8} +2.69696 q^{9} +2.88254 q^{10} -1.32688 q^{11} +2.38683 q^{12} -5.89727 q^{13} +1.19657 q^{14} -6.88014 q^{15} +1.00000 q^{16} -2.38308 q^{17} -2.69696 q^{18} +3.16514 q^{19} -2.88254 q^{20} -2.85601 q^{21} +1.32688 q^{22} -3.48308 q^{23} -2.38683 q^{24} +3.30904 q^{25} +5.89727 q^{26} -0.723302 q^{27} -1.19657 q^{28} +0.502592 q^{29} +6.88014 q^{30} -4.42796 q^{31} -1.00000 q^{32} -3.16703 q^{33} +2.38308 q^{34} +3.44916 q^{35} +2.69696 q^{36} +6.76836 q^{37} -3.16514 q^{38} -14.0758 q^{39} +2.88254 q^{40} -3.08665 q^{41} +2.85601 q^{42} -3.51613 q^{43} -1.32688 q^{44} -7.77410 q^{45} +3.48308 q^{46} +10.7579 q^{47} +2.38683 q^{48} -5.56822 q^{49} -3.30904 q^{50} -5.68802 q^{51} -5.89727 q^{52} +5.89980 q^{53} +0.723302 q^{54} +3.82478 q^{55} +1.19657 q^{56} +7.55466 q^{57} -0.502592 q^{58} -5.76626 q^{59} -6.88014 q^{60} +6.41551 q^{61} +4.42796 q^{62} -3.22710 q^{63} +1.00000 q^{64} +16.9991 q^{65} +3.16703 q^{66} -2.99768 q^{67} -2.38308 q^{68} -8.31352 q^{69} -3.44916 q^{70} +13.7449 q^{71} -2.69696 q^{72} -2.94610 q^{73} -6.76836 q^{74} +7.89812 q^{75} +3.16514 q^{76} +1.58770 q^{77} +14.0758 q^{78} -1.03317 q^{79} -2.88254 q^{80} -9.81728 q^{81} +3.08665 q^{82} +10.4056 q^{83} -2.85601 q^{84} +6.86933 q^{85} +3.51613 q^{86} +1.19960 q^{87} +1.32688 q^{88} -13.6530 q^{89} +7.77410 q^{90} +7.05649 q^{91} -3.48308 q^{92} -10.5688 q^{93} -10.7579 q^{94} -9.12365 q^{95} -2.38683 q^{96} -14.2640 q^{97} +5.56822 q^{98} -3.57854 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.38683	1.37804	0.689019	−	0.724744i	$-0.258042\pi$
$3$	2.38683	1.37804	0.689019	+	0.724744i	$0.258042\pi$
$4$	1.00000	0.500000
$5$	−2.88254	−1.28911	−0.644556	−	0.764557i	$-0.722958\pi$
$5$	−2.88254	−1.28911	−0.644556	+	0.764557i	$0.722958\pi$
$6$	−2.38683	−0.974420
$7$	−1.19657	−0.452260	−0.226130	−	0.974097i	$-0.572607\pi$
$7$	−1.19657	−0.452260	−0.226130	+	0.974097i	$0.572607\pi$
$8$	−1.00000	−0.353553
$9$	2.69696	0.898987
$10$	2.88254	0.911539
$11$	−1.32688	−0.400069	−0.200034	−	0.979789i	$-0.564105\pi$
$11$	−1.32688	−0.400069	−0.200034	+	0.979789i	$0.564105\pi$
$12$	2.38683	0.689019
$13$	−5.89727	−1.63561	−0.817805	−	0.575496i	$-0.804809\pi$
$13$	−5.89727	−1.63561	−0.817805	+	0.575496i	$0.804809\pi$
$14$	1.19657	0.319796
$15$	−6.88014	−1.77644
$16$	1.00000	0.250000
$17$	−2.38308	−0.577983	−0.288991	−	0.957332i	$-0.593320\pi$
$17$	−2.38308	−0.577983	−0.288991	+	0.957332i	$0.593320\pi$
$18$	−2.69696	−0.635680
$19$	3.16514	0.726133	0.363067	−	0.931763i	$-0.381730\pi$
$19$	3.16514	0.726133	0.363067	+	0.931763i	$0.381730\pi$
$20$	−2.88254	−0.644556
$21$	−2.85601	−0.623232
$22$	1.32688	0.282891
$23$	−3.48308	−0.726273	−0.363136	−	0.931736i	$-0.618294\pi$
$23$	−3.48308	−0.726273	−0.363136	+	0.931736i	$0.618294\pi$
$24$	−2.38683	−0.487210
$25$	3.30904	0.661808
$26$	5.89727	1.15655
$27$	−0.723302	−0.139200
$28$	−1.19657	−0.226130
$29$	0.502592	0.0933290	0.0466645	−	0.998911i	$-0.485141\pi$
$29$	0.502592	0.0933290	0.0466645	+	0.998911i	$0.485141\pi$
$30$	6.88014	1.25614
$31$	−4.42796	−0.795286	−0.397643	−	0.917540i	$-0.630172\pi$
$31$	−4.42796	−0.795286	−0.397643	+	0.917540i	$0.630172\pi$
$32$	−1.00000	−0.176777
$33$	−3.16703	−0.551310
$34$	2.38308	0.408695
$35$	3.44916	0.583014
$36$	2.69696	0.449494
$37$	6.76836	1.11271	0.556356	−	0.830944i	$-0.312199\pi$
$37$	6.76836	1.11271	0.556356	+	0.830944i	$0.312199\pi$
$38$	−3.16514	−0.513454
$39$	−14.0758	−2.25393
$40$	2.88254	0.455770
$41$	−3.08665	−0.482053	−0.241027	−	0.970518i	$-0.577484\pi$
$41$	−3.08665	−0.482053	−0.241027	+	0.970518i	$0.577484\pi$
$42$	2.85601	0.440691
$43$	−3.51613	−0.536205	−0.268102	−	0.963390i	$-0.586397\pi$
$43$	−3.51613	−0.536205	−0.268102	+	0.963390i	$0.586397\pi$
$44$	−1.32688	−0.200034
$45$	−7.77410	−1.15889
$46$	3.48308	0.513552
$47$	10.7579	1.56920	0.784600	−	0.620003i	$-0.212868\pi$
$47$	10.7579	1.56920	0.784600	+	0.620003i	$0.212868\pi$
$48$	2.38683	0.344509
$49$	−5.56822	−0.795461
$50$	−3.30904	−0.467969
$51$	−5.68802	−0.796482
$52$	−5.89727	−0.817805
$53$	5.89980	0.810399	0.405200	−	0.914228i	$-0.367202\pi$
$53$	5.89980	0.810399	0.405200	+	0.914228i	$0.367202\pi$
$54$	0.723302	0.0984289
$55$	3.82478	0.515733
$56$	1.19657	0.159898
$57$	7.55466	1.00064
$58$	−0.502592	−0.0659936
$59$	−5.76626	−0.750703	−0.375352	−	0.926883i	$-0.622478\pi$
$59$	−5.76626	−0.750703	−0.375352	+	0.926883i	$0.622478\pi$
$60$	−6.88014	−0.888222
$61$	6.41551	0.821422	0.410711	−	0.911765i	$-0.365280\pi$
$61$	6.41551	0.821422	0.410711	+	0.911765i	$0.365280\pi$
$62$	4.42796	0.562352
$63$	−3.22710	−0.406576
$64$	1.00000	0.125000
$65$	16.9991	2.10848
$66$	3.16703	0.389835
$67$	−2.99768	−0.366225	−0.183112	−	0.983092i	$-0.558617\pi$
$67$	−2.99768	−0.366225	−0.183112	+	0.983092i	$0.558617\pi$
$68$	−2.38308	−0.288991
$69$	−8.31352	−1.00083
$70$	−3.44916	−0.412253
$71$	13.7449	1.63122	0.815611	−	0.578600i	$-0.196401\pi$
$71$	13.7449	1.63122	0.815611	+	0.578600i	$0.196401\pi$
$72$	−2.69696	−0.317840
$73$	−2.94610	−0.344815	−0.172408	−	0.985026i	$-0.555155\pi$
$73$	−2.94610	−0.344815	−0.172408	+	0.985026i	$0.555155\pi$
$74$	−6.76836	−0.786806
$75$	7.89812	0.911996
$76$	3.16514	0.363067
$77$	1.58770	0.180935
$78$	14.0758	1.59377
$79$	−1.03317	−0.116240	−0.0581202	−	0.998310i	$-0.518511\pi$
$79$	−1.03317	−0.116240	−0.0581202	+	0.998310i	$0.518511\pi$
$80$	−2.88254	−0.322278
$81$	−9.81728	−1.09081
$82$	3.08665	0.340863
$83$	10.4056	1.14216	0.571082	−	0.820893i	$-0.306524\pi$
$83$	10.4056	1.14216	0.571082	+	0.820893i	$0.306524\pi$
$84$	−2.85601	−0.311616
$85$	6.86933	0.745084
$86$	3.51613	0.379154
$87$	1.19960	0.128611
$88$	1.32688	0.141446
$89$	−13.6530	−1.44722	−0.723609	−	0.690210i	$-0.757518\pi$
$89$	−13.6530	−1.44722	−0.723609	+	0.690210i	$0.757518\pi$
$90$	7.77410	0.819462
$91$	7.05649	0.739721
$92$	−3.48308	−0.363136
$93$	−10.5688	−1.09593
$94$	−10.7579	−1.10959
$95$	−9.12365	−0.936067
$96$	−2.38683	−0.243605
$97$	−14.2640	−1.44829	−0.724145	−	0.689647i	$-0.757766\pi$
$97$	−14.2640	−1.44829	−0.724145	+	0.689647i	$0.757766\pi$
$98$	5.56822	0.562476
$99$	−3.57854	−0.359657
$100$	3.30904	0.330904
$101$	11.0359	1.09812	0.549058	−	0.835784i	$-0.314986\pi$
$101$	11.0359	1.09812	0.549058	+	0.835784i	$0.314986\pi$
$102$	5.68802	0.563198
$103$	7.34123	0.723353	0.361676	−	0.932304i	$-0.382205\pi$
$103$	7.34123	0.723353	0.361676	+	0.932304i	$0.382205\pi$
$104$	5.89727	0.578275
$105$	8.23255	0.803415
$106$	−5.89980	−0.573039
$107$	−1.02746	−0.0993281	−0.0496640	−	0.998766i	$-0.515815\pi$
$107$	−1.02746	−0.0993281	−0.0496640	+	0.998766i	$0.515815\pi$
$108$	−0.723302	−0.0695998
$109$	7.85823	0.752682	0.376341	−	0.926481i	$-0.377182\pi$
$109$	7.85823	0.752682	0.376341	+	0.926481i	$0.377182\pi$
$110$	−3.82478	−0.364679
$111$	16.1549	1.53336
$112$	−1.19657	−0.113065
$113$	12.7384	1.19833	0.599163	−	0.800627i	$-0.295500\pi$
$113$	12.7384	1.19833	0.599163	+	0.800627i	$0.295500\pi$
$114$	−7.55466	−0.707559
$115$	10.0401	0.936246
$116$	0.502592	0.0466645
$117$	−15.9047	−1.47039
$118$	5.76626	0.530827
$119$	2.85152	0.261399
$120$	6.88014	0.628068
$121$	−9.23939	−0.839945
$122$	−6.41551	−0.580833
$123$	−7.36731	−0.664288
$124$	−4.42796	−0.397643
$125$	4.87426	0.435967
$126$	3.22710	0.287493
$127$	2.88017	0.255574	0.127787	−	0.991802i	$-0.459213\pi$
$127$	2.88017	0.255574	0.127787	+	0.991802i	$0.459213\pi$
$128$	−1.00000	−0.0883883
$129$	−8.39241	−0.738910
$130$	−16.9991	−1.49092
$131$	14.4462	1.26217	0.631086	−	0.775713i	$-0.282610\pi$
$131$	14.4462	1.26217	0.631086	+	0.775713i	$0.282610\pi$
$132$	−3.16703	−0.275655
$133$	−3.78731	−0.328401
$134$	2.99768	0.258960
$135$	2.08495	0.179444
$136$	2.38308	0.204348
$137$	15.2517	1.30304	0.651518	−	0.758633i	$-0.274132\pi$
$137$	15.2517	1.30304	0.651518	+	0.758633i	$0.274132\pi$
$138$	8.31352	0.707694
$139$	10.3800	0.880424	0.440212	−	0.897894i	$-0.354903\pi$
$139$	10.3800	0.880424	0.440212	+	0.897894i	$0.354903\pi$
$140$	3.44916	0.291507
$141$	25.6773	2.16242
$142$	−13.7449	−1.15345
$143$	7.82497	0.654357
$144$	2.69696	0.224747
$145$	−1.44874	−0.120311
$146$	2.94610	0.243821
$147$	−13.2904	−1.09617
$148$	6.76836	0.556356
$149$	7.98538	0.654188	0.327094	−	0.944992i	$-0.393931\pi$
$149$	7.98538	0.654188	0.327094	+	0.944992i	$0.393931\pi$
$150$	−7.89812	−0.644879
$151$	−8.26134	−0.672299	−0.336149	−	0.941809i	$-0.609125\pi$
$151$	−8.26134	−0.672299	−0.336149	+	0.941809i	$0.609125\pi$
$152$	−3.16514	−0.256727
$153$	−6.42708	−0.519599
$154$	−1.58770	−0.127941
$155$	12.7638	1.02521
$156$	−14.0758	−1.12697
$157$	−10.3288	−0.824325	−0.412162	−	0.911110i	$-0.635226\pi$
$157$	−10.3288	−0.824325	−0.412162	+	0.911110i	$0.635226\pi$
$158$	1.03317	0.0821944
$159$	14.0818	1.11676
$160$	2.88254	0.227885
$161$	4.16774	0.328464
$162$	9.81728	0.771319
$163$	7.91772	0.620164	0.310082	−	0.950710i	$-0.399644\pi$
$163$	7.91772	0.620164	0.310082	+	0.950710i	$0.399644\pi$
$164$	−3.08665	−0.241027
$165$	9.12911	0.710700
$166$	−10.4056	−0.807631
$167$	−0.0998182	−0.00772416	−0.00386208	−	0.999993i	$-0.501229\pi$
$167$	−0.0998182	−0.00772416	−0.00386208	+	0.999993i	$0.501229\pi$
$168$	2.85601	0.220346
$169$	21.7778	1.67522
$170$	−6.86933	−0.526854
$171$	8.53627	0.652785
$172$	−3.51613	−0.268102
$173$	−3.49349	−0.265605	−0.132803	−	0.991142i	$-0.542398\pi$
$173$	−3.49349	−0.265605	−0.132803	+	0.991142i	$0.542398\pi$
$174$	−1.19960	−0.0909416
$175$	−3.95949	−0.299310
$176$	−1.32688	−0.100017
$177$	−13.7631	−1.03450
$178$	13.6530	1.02334
$179$	4.42042	0.330398	0.165199	−	0.986260i	$-0.447173\pi$
$179$	4.42042	0.330398	0.165199	+	0.986260i	$0.447173\pi$
$180$	−7.77410	−0.579447
$181$	13.1365	0.976426	0.488213	−	0.872725i	$-0.337649\pi$
$181$	13.1365	0.976426	0.488213	+	0.872725i	$0.337649\pi$
$182$	−7.05649	−0.523062
$183$	15.3127	1.13195
$184$	3.48308	0.256776
$185$	−19.5101	−1.43441
$186$	10.5688	0.774942
$187$	3.16206	0.231233
$188$	10.7579	0.784600
$189$	0.865480	0.0629544
$190$	9.12365	0.661899
$191$	−6.27979	−0.454389	−0.227195	−	0.973849i	$-0.572955\pi$
$191$	−6.27979	−0.454389	−0.227195	+	0.973849i	$0.572955\pi$
$192$	2.38683	0.172255
$193$	−18.8161	−1.35441	−0.677207	−	0.735793i	$-0.736810\pi$
$193$	−18.8161	−1.35441	−0.677207	+	0.735793i	$0.736810\pi$
$194$	14.2640	1.02410
$195$	40.5741	2.90557
$196$	−5.56822	−0.397730
$197$	−6.06199	−0.431899	−0.215950	−	0.976405i	$-0.569285\pi$
$197$	−6.06199	−0.431899	−0.215950	+	0.976405i	$0.569285\pi$
$198$	3.57854	0.254316
$199$	−10.5597	−0.748555	−0.374277	−	0.927317i	$-0.622109\pi$
$199$	−10.5597	−0.748555	−0.374277	+	0.927317i	$0.622109\pi$
$200$	−3.30904	−0.233984
$201$	−7.15496	−0.504672
$202$	−11.0359	−0.776486
$203$	−0.601386	−0.0422090
$204$	−5.68802	−0.398241
$205$	8.89739	0.621421
$206$	−7.34123	−0.511488
$207$	−9.39373	−0.652910
$208$	−5.89727	−0.408902
$209$	−4.19976	−0.290503
$210$	−8.23255	−0.568100
$211$	−17.1052	−1.17757	−0.588786	−	0.808289i	$-0.700394\pi$
$211$	−17.1052	−1.17757	−0.588786	+	0.808289i	$0.700394\pi$
$212$	5.89980	0.405200
$213$	32.8068	2.24789
$214$	1.02746	0.0702356
$215$	10.1354	0.691228
$216$	0.723302	0.0492145
$217$	5.29836	0.359676
$218$	−7.85823	−0.532226
$219$	−7.03185	−0.475168
$220$	3.82478	0.257867
$221$	14.0537	0.945354
$222$	−16.1549	−1.08425
$223$	4.42359	0.296225	0.148113	−	0.988971i	$-0.452680\pi$
$223$	4.42359	0.296225	0.148113	+	0.988971i	$0.452680\pi$
$224$	1.19657	0.0799491
$225$	8.92435	0.594957
$226$	−12.7384	−0.847344
$227$	−9.93767	−0.659587	−0.329793	−	0.944053i	$-0.606979\pi$
$227$	−9.93767	−0.659587	−0.329793	+	0.944053i	$0.606979\pi$
$228$	7.55466	0.500320
$229$	−4.54456	−0.300313	−0.150157	−	0.988662i	$-0.547978\pi$
$229$	−4.54456	−0.300313	−0.150157	+	0.988662i	$0.547978\pi$
$230$	−10.0401	−0.662026
$231$	3.78957	0.249336
$232$	−0.502592	−0.0329968
$233$	8.61402	0.564324	0.282162	−	0.959367i	$-0.408949\pi$
$233$	8.61402	0.564324	0.282162	+	0.959367i	$0.408949\pi$
$234$	15.9047	1.03972
$235$	−31.0101	−2.02287
$236$	−5.76626	−0.375352
$237$	−2.46600	−0.160184
$238$	−2.85152	−0.184837
$239$	−4.21837	−0.272864	−0.136432	−	0.990649i	$-0.543563\pi$
$239$	−4.21837	−0.272864	−0.136432	+	0.990649i	$0.543563\pi$
$240$	−6.88014	−0.444111
$241$	8.94629	0.576282	0.288141	−	0.957588i	$-0.406963\pi$
$241$	8.94629	0.576282	0.288141	+	0.957588i	$0.406963\pi$
$242$	9.23939	0.593931
$243$	−21.2623	−1.36398
$244$	6.41551	0.410711
$245$	16.0506	1.02544
$246$	7.36731	0.469722
$247$	−18.6657	−1.18767
$248$	4.42796	0.281176
$249$	24.8364	1.57394
$250$	−4.87426	−0.308275
$251$	−15.7548	−0.994432	−0.497216	−	0.867627i	$-0.665644\pi$
$251$	−15.7548	−0.994432	−0.497216	+	0.867627i	$0.665644\pi$
$252$	−3.22710	−0.203288
$253$	4.62163	0.290559
$254$	−2.88017	−0.180718
$255$	16.3959	1.02675
$256$	1.00000	0.0625000
$257$	14.4006	0.898283	0.449142	−	0.893461i	$-0.351730\pi$
$257$	14.4006	0.898283	0.449142	+	0.893461i	$0.351730\pi$
$258$	8.39241	0.522488
$259$	−8.09881	−0.503236
$260$	16.9991	1.05424
$261$	1.35547	0.0839016
$262$	−14.4462	−0.892490
$263$	−4.45866	−0.274933	−0.137466	−	0.990506i	$-0.543896\pi$
$263$	−4.45866	−0.274933	−0.137466	+	0.990506i	$0.543896\pi$
$264$	3.16703	0.194918
$265$	−17.0064	−1.04469
$266$	3.78731	0.232215
$267$	−32.5875	−1.99432
$268$	−2.99768	−0.183112
$269$	8.31642	0.507061	0.253531	−	0.967327i	$-0.418408\pi$
$269$	8.31642	0.507061	0.253531	+	0.967327i	$0.418408\pi$
$270$	−2.08495	−0.126886
$271$	26.1062	1.58584	0.792919	−	0.609327i	$-0.208560\pi$
$271$	26.1062	1.58584	0.792919	+	0.609327i	$0.208560\pi$
$272$	−2.38308	−0.144496
$273$	16.8427	1.01936
$274$	−15.2517	−0.921386
$275$	−4.39069	−0.264769
$276$	−8.31352	−0.500415
$277$	8.72063	0.523972	0.261986	−	0.965072i	$-0.415623\pi$
$277$	8.72063	0.523972	0.261986	+	0.965072i	$0.415623\pi$
$278$	−10.3800	−0.622554
$279$	−11.9420	−0.714952
$280$	−3.44916	−0.206127
$281$	1.64559	0.0981676	0.0490838	−	0.998795i	$-0.484370\pi$
$281$	1.64559	0.0981676	0.0490838	+	0.998795i	$0.484370\pi$
$282$	−25.6773	−1.52906
$283$	−6.86437	−0.408044	−0.204022	−	0.978966i	$-0.565401\pi$
$283$	−6.86437	−0.408044	−0.204022	+	0.978966i	$0.565401\pi$
$284$	13.7449	0.815611
$285$	−21.7766	−1.28994
$286$	−7.82497	−0.462700
$287$	3.69339	0.218014
$288$	−2.69696	−0.158920
$289$	−11.3209	−0.665936
$290$	1.44874	0.0850731
$291$	−34.0458	−1.99580
$292$	−2.94610	−0.172408
$293$	24.4721	1.42967	0.714837	−	0.699291i	$-0.246501\pi$
$293$	24.4721	1.42967	0.714837	+	0.699291i	$0.246501\pi$
$294$	13.2904	0.775112
$295$	16.6215	0.967740
$296$	−6.76836	−0.393403
$297$	0.959734	0.0556894
$298$	−7.98538	−0.462581
$299$	20.5407	1.18790
$300$	7.89812	0.455998
$301$	4.20729	0.242504
$302$	8.26134	0.475387
$303$	26.3409	1.51325
$304$	3.16514	0.181533
$305$	−18.4930	−1.05890
$306$	6.42708	0.367412
$307$	8.76155	0.500048	0.250024	−	0.968240i	$-0.419561\pi$
$307$	8.76155	0.500048	0.250024	+	0.968240i	$0.419561\pi$
$308$	1.58770	0.0904677
$309$	17.5223	0.996807
$310$	−12.7638	−0.724934
$311$	−14.1095	−0.800075	−0.400038	−	0.916499i	$-0.631003\pi$
$311$	−14.1095	−0.800075	−0.400038	+	0.916499i	$0.631003\pi$
$312$	14.0758	0.796885
$313$	10.5097	0.594042	0.297021	−	0.954871i	$-0.404007\pi$
$313$	10.5097	0.594042	0.297021	+	0.954871i	$0.404007\pi$
$314$	10.3288	0.582886
$315$	9.30224	0.524122
$316$	−1.03317	−0.0581202
$317$	−1.61506	−0.0907110	−0.0453555	−	0.998971i	$-0.514442\pi$
$317$	−1.61506	−0.0907110	−0.0453555	+	0.998971i	$0.514442\pi$
$318$	−14.0818	−0.789669
$319$	−0.666879	−0.0373380
$320$	−2.88254	−0.161139
$321$	−2.45237	−0.136878
$322$	−4.16774	−0.232259
$323$	−7.54280	−0.419692
$324$	−9.81728	−0.545405
$325$	−19.5143	−1.08246
$326$	−7.91772	−0.438522
$327$	18.7563	1.03722
$328$	3.08665	0.170432
$329$	−12.8726	−0.709687
$330$	−9.12911	−0.502541
$331$	4.95488	0.272345	0.136172	−	0.990685i	$-0.456520\pi$
$331$	4.95488	0.272345	0.136172	+	0.990685i	$0.456520\pi$
$332$	10.4056	0.571082
$333$	18.2540	1.00031
$334$	0.0998182	0.00546181
$335$	8.64093	0.472105
$336$	−2.85601	−0.155808
$337$	19.8672	1.08223	0.541117	−	0.840947i	$-0.318001\pi$
$337$	19.8672	1.08223	0.541117	+	0.840947i	$0.318001\pi$
$338$	−21.7778	−1.18456
$339$	30.4043	1.65134
$340$	6.86933	0.372542
$341$	5.87537	0.318169
$342$	−8.53627	−0.461588
$343$	15.0387	0.812016
$344$	3.51613	0.189577
$345$	23.9641	1.29018
$346$	3.49349	0.187811
$347$	30.0711	1.61430	0.807150	−	0.590346i	$-0.201009\pi$
$347$	30.0711	1.61430	0.807150	+	0.590346i	$0.201009\pi$
$348$	1.19960	0.0643054
$349$	31.4913	1.68569	0.842846	−	0.538154i	$-0.180878\pi$
$349$	31.4913	1.68569	0.842846	+	0.538154i	$0.180878\pi$
$350$	3.95949	0.211644
$351$	4.26551	0.227676
$352$	1.32688	0.0707229
$353$	15.9111	0.846860	0.423430	−	0.905929i	$-0.360826\pi$
$353$	15.9111	0.846860	0.423430	+	0.905929i	$0.360826\pi$
$354$	13.7631	0.731500
$355$	−39.6203	−2.10283
$356$	−13.6530	−0.723609
$357$	6.80610	0.360217
$358$	−4.42042	−0.233627
$359$	34.8866	1.84124	0.920621	−	0.390457i	$-0.127683\pi$
$359$	34.8866	1.84124	0.920621	+	0.390457i	$0.127683\pi$
$360$	7.77410	0.409731
$361$	−8.98187	−0.472730
$362$	−13.1365	−0.690437
$363$	−22.0529	−1.15748
$364$	7.05649	0.369861
$365$	8.49226	0.444505
$366$	−15.3127	−0.800410
$367$	8.84445	0.461676	0.230838	−	0.972992i	$-0.425853\pi$
$367$	8.84445	0.461676	0.230838	+	0.972992i	$0.425853\pi$
$368$	−3.48308	−0.181568
$369$	−8.32457	−0.433360
$370$	19.5101	1.01428
$371$	−7.05951	−0.366511
$372$	−10.5688	−0.547967
$373$	−6.67149	−0.345436	−0.172718	−	0.984971i	$-0.555255\pi$
$373$	−6.67149	−0.345436	−0.172718	+	0.984971i	$0.555255\pi$
$374$	−3.16206	−0.163506
$375$	11.6340	0.600779
$376$	−10.7579	−0.554796
$377$	−2.96392	−0.152650
$378$	−0.865480	−0.0445155
$379$	13.1426	0.675091	0.337546	−	0.941309i	$-0.390403\pi$
$379$	13.1426	0.675091	0.337546	+	0.941309i	$0.390403\pi$
$380$	−9.12365	−0.468033
$381$	6.87449	0.352191
$382$	6.27979	0.321302
$383$	16.5754	0.846963	0.423482	−	0.905905i	$-0.360808\pi$
$383$	16.5754	0.846963	0.423482	+	0.905905i	$0.360808\pi$
$384$	−2.38683	−0.121802
$385$	−4.57661	−0.233246
$386$	18.8161	0.957715
$387$	−9.48287	−0.482041
$388$	−14.2640	−0.724145
$389$	−16.0750	−0.815033	−0.407516	−	0.913198i	$-0.633605\pi$
$389$	−16.0750	−0.815033	−0.407516	+	0.913198i	$0.633605\pi$
$390$	−40.5741	−2.05455
$391$	8.30047	0.419773
$392$	5.56822	0.281238
$393$	34.4807	1.73932
$394$	6.06199	0.305399
$395$	2.97815	0.149847
$396$	−3.57854	−0.179828
$397$	1.43463	0.0720020	0.0360010	−	0.999352i	$-0.488538\pi$
$397$	1.43463	0.0720020	0.0360010	+	0.999352i	$0.488538\pi$
$398$	10.5597	0.529308
$399$	−9.03967	−0.452549
$400$	3.30904	0.165452
$401$	−21.2097	−1.05916	−0.529580	−	0.848260i	$-0.677650\pi$
$401$	−21.2097	−1.05916	−0.529580	+	0.848260i	$0.677650\pi$
$402$	7.15496	0.356857
$403$	26.1129	1.30078
$404$	11.0359	0.549058
$405$	28.2987	1.40617
$406$	0.601386	0.0298463
$407$	−8.98080	−0.445162
$408$	5.68802	0.281599
$409$	−15.6820	−0.775425	−0.387713	−	0.921780i	$-0.626735\pi$
$409$	−15.6820	−0.775425	−0.387713	+	0.921780i	$0.626735\pi$
$410$	−8.89739	−0.439411
$411$	36.4031	1.79563
$412$	7.34123	0.361676
$413$	6.89972	0.339513
$414$	9.39373	0.461677
$415$	−29.9946	−1.47238
$416$	5.89727	0.289138
$417$	24.7754	1.21326
$418$	4.19976	0.205417
$419$	12.1528	0.593703	0.296852	−	0.954924i	$-0.404063\pi$
$419$	12.1528	0.593703	0.296852	+	0.954924i	$0.404063\pi$
$420$	8.23255	0.401708
$421$	−4.32347	−0.210713	−0.105357	−	0.994435i	$-0.533598\pi$
$421$	−4.32347	−0.210713	−0.105357	+	0.994435i	$0.533598\pi$
$422$	17.1052	0.832669
$423$	29.0136	1.41069
$424$	−5.89980	−0.286519
$425$	−7.88572	−0.382514
$426$	−32.8068	−1.58950
$427$	−7.67660	−0.371497
$428$	−1.02746	−0.0496640
$429$	18.6769	0.901728
$430$	−10.1354	−0.488772
$431$	1.94604	0.0937374	0.0468687	−	0.998901i	$-0.485076\pi$
$431$	1.94604	0.0937374	0.0468687	+	0.998901i	$0.485076\pi$
$432$	−0.723302	−0.0347999
$433$	8.59554	0.413075	0.206538	−	0.978439i	$-0.433780\pi$
$433$	8.59554	0.413075	0.206538	+	0.978439i	$0.433780\pi$
$434$	−5.29836	−0.254330
$435$	−3.45790	−0.165794
$436$	7.85823	0.376341
$437$	−11.0244	−0.527371
$438$	7.03185	0.335995
$439$	−22.6101	−1.07912	−0.539560	−	0.841947i	$-0.681409\pi$
$439$	−22.6101	−1.07912	−0.539560	+	0.841947i	$0.681409\pi$
$440$	−3.82478	−0.182339
$441$	−15.0173	−0.715109
$442$	−14.0537	−0.668466
$443$	−10.8824	−0.517039	−0.258520	−	0.966006i	$-0.583235\pi$
$443$	−10.8824	−0.517039	−0.258520	+	0.966006i	$0.583235\pi$
$444$	16.1549	0.766680
$445$	39.3554	1.86562
$446$	−4.42359	−0.209463
$447$	19.0598	0.901496
$448$	−1.19657	−0.0565325
$449$	−9.72508	−0.458955	−0.229477	−	0.973314i	$-0.573702\pi$
$449$	−9.72508	−0.458955	−0.229477	+	0.973314i	$0.573702\pi$
$450$	−8.92435	−0.420698
$451$	4.09561	0.192855
$452$	12.7384	0.599163
$453$	−19.7184	−0.926453
$454$	9.93767	0.466398
$455$	−20.3406	−0.953583
$456$	−7.55466	−0.353779
$457$	31.1493	1.45710	0.728552	−	0.684990i	$-0.240194\pi$
$457$	31.1493	1.45710	0.728552	+	0.684990i	$0.240194\pi$
$458$	4.54456	0.212354
$459$	1.72369	0.0804549
$460$	10.0401	0.468123
$461$	−12.3031	−0.573014	−0.286507	−	0.958078i	$-0.592494\pi$
$461$	−12.3031	−0.573014	−0.286507	+	0.958078i	$0.592494\pi$
$462$	−3.78957	−0.176307
$463$	−13.7248	−0.637846	−0.318923	−	0.947781i	$-0.603321\pi$
$463$	−13.7248	−0.637846	−0.318923	+	0.947781i	$0.603321\pi$
$464$	0.502592	0.0233322
$465$	30.4650	1.41278
$466$	−8.61402	−0.399037
$467$	−2.03351	−0.0940995	−0.0470498	−	0.998893i	$-0.514982\pi$
$467$	−2.03351	−0.0940995	−0.0470498	+	0.998893i	$0.514982\pi$
$468$	−15.9047	−0.735196
$469$	3.58693	0.165629
$470$	31.0101	1.43039
$471$	−24.6530	−1.13595
$472$	5.76626	0.265414
$473$	4.66548	0.214519
$474$	2.46600	0.113267
$475$	10.4736	0.480561
$476$	2.85152	0.130699
$477$	15.9115	0.728539
$478$	4.21837	0.192944
$479$	1.62944	0.0744512	0.0372256	−	0.999307i	$-0.488148\pi$
$479$	1.62944	0.0744512	0.0372256	+	0.999307i	$0.488148\pi$
$480$	6.88014	0.314034
$481$	−39.9149	−1.81996
$482$	−8.94629	−0.407493
$483$	9.94770	0.452636
$484$	−9.23939	−0.419972
$485$	41.1166	1.86701
$486$	21.2623	0.964477
$487$	−11.0193	−0.499332	−0.249666	−	0.968332i	$-0.580321\pi$
$487$	−11.0193	−0.499332	−0.249666	+	0.968332i	$0.580321\pi$
$488$	−6.41551	−0.290417
$489$	18.8983	0.854609
$490$	−16.0506	−0.725094
$491$	−16.3113	−0.736117	−0.368059	−	0.929803i	$-0.619977\pi$
$491$	−16.3113	−0.736117	−0.368059	+	0.929803i	$0.619977\pi$
$492$	−7.36731	−0.332144
$493$	−1.19772	−0.0539425
$494$	18.6657	0.839810
$495$	10.3153	0.463638
$496$	−4.42796	−0.198821
$497$	−16.4467	−0.737737
$498$	−24.8364	−1.11295
$499$	−19.9754	−0.894222	−0.447111	−	0.894478i	$-0.647547\pi$
$499$	−19.9754	−0.894222	−0.447111	+	0.894478i	$0.647547\pi$
$500$	4.87426	0.217984
$501$	−0.238249	−0.0106442
$502$	15.7548	0.703170
$503$	−21.7380	−0.969247	−0.484624	−	0.874723i	$-0.661043\pi$
$503$	−21.7380	−0.969247	−0.484624	+	0.874723i	$0.661043\pi$
$504$	3.22710	0.143746
$505$	−31.8115	−1.41559
$506$	−4.62163	−0.205456
$507$	51.9800	2.30851
$508$	2.88017	0.127787
$509$	−14.4725	−0.641484	−0.320742	−	0.947167i	$-0.603932\pi$
$509$	−14.4725	−0.641484	−0.320742	+	0.947167i	$0.603932\pi$
$510$	−16.3959	−0.726024
$511$	3.52521	0.155946
$512$	−1.00000	−0.0441942
$513$	−2.28935	−0.101077
$514$	−14.4006	−0.635182
$515$	−21.1614	−0.932482
$516$	−8.39241	−0.369455
$517$	−14.2744	−0.627788
$518$	8.09881	0.355841
$519$	−8.33838	−0.366014
$520$	−16.9991	−0.745461
$521$	32.6820	1.43183	0.715913	−	0.698190i	$-0.246011\pi$
$521$	32.6820	1.43183	0.715913	+	0.698190i	$0.246011\pi$
$522$	−1.35547	−0.0593274
$523$	3.94263	0.172399	0.0861996	−	0.996278i	$-0.472528\pi$
$523$	3.94263	0.172399	0.0861996	+	0.996278i	$0.472528\pi$
$524$	14.4462	0.631086
$525$	−9.45064	−0.412460
$526$	4.45866	0.194407
$527$	10.5522	0.459661
$528$	−3.16703	−0.137827
$529$	−10.8681	−0.472528
$530$	17.0064	0.738711
$531$	−15.5514	−0.674872
$532$	−3.78731	−0.164201
$533$	18.2028	0.788451
$534$	32.5875	1.41020
$535$	2.96169	0.128045
$536$	2.99768	0.129480
$537$	10.5508	0.455301
$538$	−8.31642	−0.358546
$539$	7.38836	0.318239
$540$	2.08495	0.0897219
$541$	−23.8522	−1.02549	−0.512743	−	0.858542i	$-0.671371\pi$
$541$	−23.8522	−1.02549	−0.512743	+	0.858542i	$0.671371\pi$
$542$	−26.1062	−1.12136
$543$	31.3545	1.34555
$544$	2.38308	0.102174
$545$	−22.6517	−0.970291
$546$	−16.8427	−0.720799
$547$	9.23977	0.395064	0.197532	−	0.980296i	$-0.436707\pi$
$547$	9.23977	0.395064	0.197532	+	0.980296i	$0.436707\pi$
$548$	15.2517	0.651518
$549$	17.3024	0.738448
$550$	4.39069	0.187220
$551$	1.59078	0.0677693
$552$	8.31352	0.353847
$553$	1.23626	0.0525709
$554$	−8.72063	−0.370504
$555$	−46.5673	−1.97667
$556$	10.3800	0.440212
$557$	8.89552	0.376915	0.188458	−	0.982081i	$-0.439651\pi$
$557$	8.89552	0.376915	0.188458	+	0.982081i	$0.439651\pi$
$558$	11.9420	0.505547
$559$	20.7356	0.877022
$560$	3.44916	0.145753
$561$	7.54731	0.318648
$562$	−1.64559	−0.0694150
$563$	−5.62556	−0.237089	−0.118545	−	0.992949i	$-0.537823\pi$
$563$	−5.62556	−0.237089	−0.118545	+	0.992949i	$0.537823\pi$
$564$	25.6773	1.08121
$565$	−36.7189	−1.54477
$566$	6.86437	0.288531
$567$	11.7471	0.493330
$568$	−13.7449	−0.576724
$569$	−23.4208	−0.981849	−0.490925	−	0.871202i	$-0.663341\pi$
$569$	−23.4208	−0.981849	−0.490925	+	0.871202i	$0.663341\pi$
$570$	21.7766	0.912122
$571$	−37.5218	−1.57024	−0.785120	−	0.619344i	$-0.787399\pi$
$571$	−37.5218	−1.57024	−0.785120	+	0.619344i	$0.787399\pi$
$572$	7.82497	0.327178
$573$	−14.9888	−0.626166
$574$	−3.69339	−0.154159
$575$	−11.5257	−0.480653
$576$	2.69696	0.112373
$577$	29.9504	1.24685	0.623425	−	0.781883i	$-0.285741\pi$
$577$	29.9504	1.24685	0.623425	+	0.781883i	$0.285741\pi$
$578$	11.3209	0.470888
$579$	−44.9109	−1.86643
$580$	−1.44874	−0.0601557
$581$	−12.4510	−0.516555
$582$	34.0458	1.41124
$583$	−7.82831	−0.324216
$584$	2.94610	0.121911
$585$	45.8460	1.89550
$586$	−24.4721	−1.01093
$587$	10.0019	0.412824	0.206412	−	0.978465i	$-0.433821\pi$
$587$	10.0019	0.412824	0.206412	+	0.978465i	$0.433821\pi$
$588$	−13.2904	−0.548087
$589$	−14.0151	−0.577484
$590$	−16.6215	−0.684295
$591$	−14.4689	−0.595173
$592$	6.76836	0.278178
$593$	40.5535	1.66533	0.832666	−	0.553776i	$-0.186814\pi$
$593$	40.5535	1.66533	0.832666	+	0.553776i	$0.186814\pi$
$594$	−0.959734	−0.0393784
$595$	−8.21963	−0.336972
$596$	7.98538	0.327094
$597$	−25.2041	−1.03154
$598$	−20.5407	−0.839971
$599$	16.7126	0.682856	0.341428	−	0.939908i	$-0.389089\pi$
$599$	16.7126	0.682856	0.341428	+	0.939908i	$0.389089\pi$
$600$	−7.89812	−0.322439
$601$	14.7344	0.601028	0.300514	−	0.953777i	$-0.402842\pi$
$601$	14.7344	0.601028	0.300514	+	0.953777i	$0.402842\pi$
$602$	−4.20729	−0.171476
$603$	−8.08463	−0.329231
$604$	−8.26134	−0.336149
$605$	26.6329	1.08278
$606$	−26.3409	−1.07003
$607$	−11.1186	−0.451290	−0.225645	−	0.974210i	$-0.572449\pi$
$607$	−11.1186	−0.451290	−0.225645	+	0.974210i	$0.572449\pi$
$608$	−3.16514	−0.128363
$609$	−1.43541	−0.0581656
$610$	18.4930	0.748759
$611$	−63.4422	−2.56660
$612$	−6.42708	−0.259799
$613$	3.87031	0.156320	0.0781601	−	0.996941i	$-0.475095\pi$
$613$	3.87031	0.156320	0.0781601	+	0.996941i	$0.475095\pi$
$614$	−8.76155	−0.353587
$615$	21.2366	0.856341
$616$	−1.58770	−0.0639703
$617$	−18.1326	−0.729991	−0.364996	−	0.931009i	$-0.618930\pi$
$617$	−18.1326	−0.729991	−0.364996	+	0.931009i	$0.618930\pi$
$618$	−17.5223	−0.704849
$619$	9.51167	0.382306	0.191153	−	0.981560i	$-0.438777\pi$
$619$	9.51167	0.382306	0.191153	+	0.981560i	$0.438777\pi$
$620$	12.7638	0.512606
$621$	2.51932	0.101097
$622$	14.1095	0.565739
$623$	16.3368	0.654519
$624$	−14.0758	−0.563483
$625$	−30.5955	−1.22382
$626$	−10.5097	−0.420051
$627$	−10.0241	−0.400325
$628$	−10.3288	−0.412162
$629$	−16.1296	−0.643128
$630$	−9.30224	−0.370610
$631$	−37.6679	−1.49953	−0.749767	−	0.661702i	$-0.769834\pi$
$631$	−37.6679	−1.49953	−0.749767	+	0.661702i	$0.769834\pi$
$632$	1.03317	0.0410972
$633$	−40.8272	−1.62274
$634$	1.61506	0.0641424
$635$	−8.30222	−0.329463
$636$	14.0818	0.558380
$637$	32.8373	1.30106
$638$	0.666879	0.0264020
$639$	37.0695	1.46645
$640$	2.88254	0.113942
$641$	−6.12500	−0.241923	−0.120961	−	0.992657i	$-0.538598\pi$
$641$	−6.12500	−0.241923	−0.120961	+	0.992657i	$0.538598\pi$
$642$	2.45237	0.0967872
$643$	−41.6799	−1.64369	−0.821847	−	0.569708i	$-0.807056\pi$
$643$	−41.6799	−1.64369	−0.821847	+	0.569708i	$0.807056\pi$
$644$	4.16774	0.164232
$645$	24.1915	0.952537
$646$	7.54280	0.296767
$647$	3.89455	0.153111	0.0765553	−	0.997065i	$-0.475608\pi$
$647$	3.89455	0.153111	0.0765553	+	0.997065i	$0.475608\pi$
$648$	9.81728	0.385659
$649$	7.65113	0.300333
$650$	19.5143	0.765415
$651$	12.6463	0.495647
$652$	7.91772	0.310082
$653$	5.17091	0.202353	0.101177	−	0.994868i	$-0.467739\pi$
$653$	5.17091	0.202353	0.101177	+	0.994868i	$0.467739\pi$
$654$	−18.7563	−0.733428
$655$	−41.6418	−1.62708
$656$	−3.08665	−0.120513
$657$	−7.94552	−0.309984
$658$	12.8726	0.501824
$659$	−40.7509	−1.58743	−0.793715	−	0.608289i	$-0.791856\pi$
$659$	−40.7509	−1.58743	−0.793715	+	0.608289i	$0.791856\pi$
$660$	9.12911	0.355350
$661$	0.664206	0.0258346	0.0129173	−	0.999917i	$-0.495888\pi$
$661$	0.664206	0.0258346	0.0129173	+	0.999917i	$0.495888\pi$
$662$	−4.95488	−0.192577
$663$	33.5438	1.30273
$664$	−10.4056	−0.403816
$665$	10.9171	0.423346
$666$	−18.2540	−0.707329
$667$	−1.75057	−0.0677823
$668$	−0.0998182	−0.00386208
$669$	10.5584	0.408209
$670$	−8.64093	−0.333828
$671$	−8.51261	−0.328626
$672$	2.85601	0.110173
$673$	−32.3282	−1.24616	−0.623081	−	0.782158i	$-0.714119\pi$
$673$	−32.3282	−1.24616	−0.623081	+	0.782158i	$0.714119\pi$
$674$	−19.8672	−0.765256
$675$	−2.39344	−0.0921234
$676$	21.7778	0.837609
$677$	−14.6052	−0.561322	−0.280661	−	0.959807i	$-0.590554\pi$
$677$	−14.6052	−0.561322	−0.280661	+	0.959807i	$0.590554\pi$
$678$	−30.4043	−1.16767
$679$	17.0679	0.655005
$680$	−6.86933	−0.263427
$681$	−23.7195	−0.908935
$682$	−5.87537	−0.224980
$683$	4.05114	0.155012	0.0775062	−	0.996992i	$-0.475304\pi$
$683$	4.05114	0.155012	0.0775062	+	0.996992i	$0.475304\pi$
$684$	8.53627	0.326392
$685$	−43.9635	−1.67976
$686$	−15.0387	−0.574182
$687$	−10.8471	−0.413843
$688$	−3.51613	−0.134051
$689$	−34.7927	−1.32550
$690$	−23.9641	−0.912297
$691$	45.5251	1.73186	0.865928	−	0.500169i	$-0.166729\pi$
$691$	45.5251	1.73186	0.865928	+	0.500169i	$0.166729\pi$
$692$	−3.49349	−0.132803
$693$	4.28197	0.162659
$694$	−30.0711	−1.14148
$695$	−29.9209	−1.13496
$696$	−1.19960	−0.0454708
$697$	7.35574	0.278618
$698$	−31.4913	−1.19196
$699$	20.5602	0.777659
$700$	−3.95949	−0.149655
$701$	26.7978	1.01214	0.506069	−	0.862493i	$-0.331098\pi$
$701$	26.7978	1.01214	0.506069	+	0.862493i	$0.331098\pi$
$702$	−4.26551	−0.160991
$703$	21.4228	0.807978
$704$	−1.32688	−0.0500086
$705$	−74.0158	−2.78759
$706$	−15.9111	−0.598821
$707$	−13.2053	−0.496635
$708$	−13.7631	−0.517248
$709$	48.4532	1.81970	0.909849	−	0.414939i	$-0.136197\pi$
$709$	48.4532	1.81970	0.909849	+	0.414939i	$0.136197\pi$
$710$	39.6203	1.48692
$711$	−2.78641	−0.104499
$712$	13.6530	0.511669
$713$	15.4230	0.577594
$714$	−6.80610	−0.254712
$715$	−22.5558	−0.843539
$716$	4.42042	0.165199
$717$	−10.0685	−0.376017
$718$	−34.8866	−1.30196
$719$	−5.33060	−0.198798	−0.0993989	−	0.995048i	$-0.531692\pi$
$719$	−5.33060	−0.198798	−0.0993989	+	0.995048i	$0.531692\pi$
$720$	−7.77410	−0.289724
$721$	−8.78428	−0.327144
$722$	8.98187	0.334271
$723$	21.3533	0.794137
$724$	13.1365	0.488213
$725$	1.66310	0.0617659
$726$	22.0529	0.818459
$727$	35.8352	1.32906	0.664528	−	0.747263i	$-0.268633\pi$
$727$	35.8352	1.32906	0.664528	+	0.747263i	$0.268633\pi$
$728$	−7.05649	−0.261531
$729$	−21.2976	−0.788801
$730$	−8.49226	−0.314313
$731$	8.37923	0.309917
$732$	15.3127	0.565975
$733$	16.6524	0.615070	0.307535	−	0.951537i	$-0.400496\pi$
$733$	16.6524	0.615070	0.307535	+	0.951537i	$0.400496\pi$
$734$	−8.84445	−0.326455
$735$	38.3101	1.41309
$736$	3.48308	0.128388
$737$	3.97756	0.146515
$738$	8.32457	0.306432
$739$	30.1949	1.11074	0.555368	−	0.831604i	$-0.312577\pi$
$739$	30.1949	1.11074	0.555368	+	0.831604i	$0.312577\pi$
$740$	−19.5101	−0.717205
$741$	−44.5519	−1.63665
$742$	7.05951	0.259163
$743$	25.9595	0.952363	0.476181	−	0.879347i	$-0.342021\pi$
$743$	25.9595	0.952363	0.476181	+	0.879347i	$0.342021\pi$
$744$	10.5688	0.387471
$745$	−23.0182	−0.843321
$746$	6.67149	0.244260
$747$	28.0635	1.02679
$748$	3.16206	0.115616
$749$	1.22942	0.0449222
$750$	−11.6340	−0.424815
$751$	−8.34656	−0.304570	−0.152285	−	0.988337i	$-0.548663\pi$
$751$	−8.34656	−0.304570	−0.152285	+	0.988337i	$0.548663\pi$
$752$	10.7579	0.392300
$753$	−37.6040	−1.37037
$754$	2.96392	0.107940
$755$	23.8137	0.866668
$756$	0.865480	0.0314772
$757$	49.0549	1.78293	0.891465	−	0.453091i	$-0.149679\pi$
$757$	49.0549	1.78293	0.891465	+	0.453091i	$0.149679\pi$
$758$	−13.1426	−0.477362
$759$	11.0310	0.400401
$760$	9.12365	0.330950
$761$	−38.0135	−1.37799	−0.688993	−	0.724768i	$-0.741947\pi$
$761$	−38.0135	−1.37799	−0.688993	+	0.724768i	$0.741947\pi$
$762$	−6.87449	−0.249036
$763$	−9.40291	−0.340408
$764$	−6.27979	−0.227195
$765$	18.5263	0.669821
$766$	−16.5754	−0.598894
$767$	34.0052	1.22786
$768$	2.38683	0.0861273
$769$	7.43799	0.268221	0.134110	−	0.990966i	$-0.457182\pi$
$769$	7.43799	0.268221	0.134110	+	0.990966i	$0.457182\pi$
$770$	4.57661	0.164930
$771$	34.3717	1.23787
$772$	−18.8161	−0.677207
$773$	−8.13053	−0.292435	−0.146217	−	0.989252i	$-0.546710\pi$
$773$	−8.13053	−0.292435	−0.146217	+	0.989252i	$0.546710\pi$
$774$	9.48287	0.340855
$775$	−14.6523	−0.526327
$776$	14.2640	0.512048
$777$	−19.3305	−0.693478
$778$	16.0750	0.576315
$779$	−9.76968	−0.350035
$780$	40.5741	1.45278
$781$	−18.2378	−0.652601
$782$	−8.30047	−0.296824
$783$	−0.363526	−0.0129914
$784$	−5.56822	−0.198865
$785$	29.7731	1.06265
$786$	−34.4807	−1.22988
$787$	20.6766	0.737042	0.368521	−	0.929620i	$-0.379864\pi$
$787$	20.6766	0.737042	0.368521	+	0.929620i	$0.379864\pi$
$788$	−6.06199	−0.215950
$789$	−10.6421	−0.378868
$790$	−2.97815	−0.105958
$791$	−15.2423	−0.541955
$792$	3.57854	0.127158
$793$	−37.8340	−1.34353
$794$	−1.43463	−0.0509131
$795$	−40.5914	−1.43963
$796$	−10.5597	−0.374277
$797$	14.2837	0.505953	0.252976	−	0.967472i	$-0.418590\pi$
$797$	14.2837	0.505953	0.252976	+	0.967472i	$0.418590\pi$
$798$	9.03967	0.320001
$799$	−25.6369	−0.906970
$800$	−3.30904	−0.116992
$801$	−36.8217	−1.30103
$802$	21.2097	0.748939
$803$	3.90912	0.137950
$804$	−7.15496	−0.252336
$805$	−12.0137	−0.423427
$806$	−26.1129	−0.919788
$807$	19.8499	0.698749
$808$	−11.0359	−0.388243
$809$	28.5568	1.00401	0.502003	−	0.864866i	$-0.332597\pi$
$809$	28.5568	1.00401	0.502003	+	0.864866i	$0.332597\pi$
$810$	−28.2987	−0.994316
$811$	−5.28004	−0.185407	−0.0927037	−	0.995694i	$-0.529551\pi$
$811$	−5.28004	−0.185407	−0.0927037	+	0.995694i	$0.529551\pi$
$812$	−0.601386	−0.0211045
$813$	62.3111	2.18534
$814$	8.98080	0.314777
$815$	−22.8232	−0.799460
$816$	−5.68802	−0.199120
$817$	−11.1291	−0.389356
$818$	15.6820	0.548308
$819$	19.0311	0.665000
$820$	8.89739	0.310710
$821$	48.0287	1.67621	0.838106	−	0.545508i	$-0.183663\pi$
$821$	48.0287	1.67621	0.838106	+	0.545508i	$0.183663\pi$
$822$	−36.4031	−1.26970
$823$	36.2253	1.26274	0.631368	−	0.775483i	$-0.282494\pi$
$823$	36.2253	1.26274	0.631368	+	0.775483i	$0.282494\pi$
$824$	−7.34123	−0.255744
$825$	−10.4798	−0.364861
$826$	−6.89972	−0.240072
$827$	1.10116	0.0382909	0.0191455	−	0.999817i	$-0.493905\pi$
$827$	1.10116	0.0382909	0.0191455	+	0.999817i	$0.493905\pi$
$828$	−9.39373	−0.326455
$829$	−8.36394	−0.290492	−0.145246	−	0.989396i	$-0.546397\pi$
$829$	−8.36394	−0.290492	−0.145246	+	0.989396i	$0.546397\pi$
$830$	29.9946	1.04113
$831$	20.8147	0.722053
$832$	−5.89727	−0.204451
$833$	13.2695	0.459762
$834$	−24.7754	−0.857903
$835$	0.287730	0.00995731
$836$	−4.19976	−0.145252
$837$	3.20276	0.110703
$838$	−12.1528	−0.419812
$839$	−41.9149	−1.44706	−0.723532	−	0.690291i	$-0.757483\pi$
$839$	−41.9149	−1.44706	−0.723532	+	0.690291i	$0.757483\pi$
$840$	−8.23255	−0.284050
$841$	−28.7474	−0.991290
$842$	4.32347	0.148997
$843$	3.92774	0.135279
$844$	−17.1052	−0.588786
$845$	−62.7755	−2.15954
$846$	−29.0136	−0.997509
$847$	11.0556	0.379874
$848$	5.89980	0.202600
$849$	−16.3841	−0.562300
$850$	7.88572	0.270478
$851$	−23.5748	−0.808132
$852$	32.8068	1.12394
$853$	56.4350	1.93230	0.966149	−	0.257986i	$-0.0830588\pi$
$853$	56.4350	1.93230	0.966149	+	0.257986i	$0.0830588\pi$
$854$	7.67660	0.262688
$855$	−24.6061	−0.841512
$856$	1.02746	0.0351178
$857$	10.4692	0.357621	0.178811	−	0.983883i	$-0.442775\pi$
$857$	10.4692	0.357621	0.178811	+	0.983883i	$0.442775\pi$
$858$	−18.6769	−0.637618
$859$	−9.14248	−0.311937	−0.155969	−	0.987762i	$-0.549850\pi$
$859$	−9.14248	−0.311937	−0.155969	+	0.987762i	$0.549850\pi$
$860$	10.1354	0.345614
$861$	8.81549	0.300431
$862$	−1.94604	−0.0662823
$863$	−16.1236	−0.548853	−0.274426	−	0.961608i	$-0.588488\pi$
$863$	−16.1236	−0.548853	−0.274426	+	0.961608i	$0.588488\pi$
$864$	0.723302	0.0246072
$865$	10.0701	0.342395
$866$	−8.59554	−0.292088
$867$	−27.0211	−0.917685
$868$	5.29836	0.179838
$869$	1.37089	0.0465042
$870$	3.45790	0.117234
$871$	17.6781	0.599001
$872$	−7.85823	−0.266113
$873$	−38.4695	−1.30199
$874$	11.0244	0.372907
$875$	−5.83239	−0.197171
$876$	−7.03185	−0.237584
$877$	−15.1501	−0.511582	−0.255791	−	0.966732i	$-0.582336\pi$
$877$	−15.1501	−0.511582	−0.255791	+	0.966732i	$0.582336\pi$
$878$	22.6101	0.763053
$879$	58.4107	1.97014
$880$	3.82478	0.128933
$881$	−24.9827	−0.841688	−0.420844	−	0.907133i	$-0.638266\pi$
$881$	−24.9827	−0.841688	−0.420844	+	0.907133i	$0.638266\pi$
$882$	15.0173	0.505658
$883$	−50.8713	−1.71196	−0.855979	−	0.517011i	$-0.827044\pi$
$883$	−50.8713	−1.71196	−0.855979	+	0.517011i	$0.827044\pi$
$884$	14.0537	0.472677
$885$	39.6727	1.33358
$886$	10.8824	0.365602
$887$	31.0999	1.04423	0.522117	−	0.852874i	$-0.325143\pi$
$887$	31.0999	1.04423	0.522117	+	0.852874i	$0.325143\pi$
$888$	−16.1549	−0.542124
$889$	−3.44632	−0.115586
$890$	−39.3554	−1.31920
$891$	13.0263	0.436399
$892$	4.42359	0.148113
$893$	34.0503	1.13945
$894$	−19.0598	−0.637454
$895$	−12.7420	−0.425920
$896$	1.19657	0.0399745
$897$	49.0271	1.63697
$898$	9.72508	0.324530
$899$	−2.22546	−0.0742232
$900$	8.92435	0.297478
$901$	−14.0597	−0.468397
$902$	−4.09561	−0.136369
$903$	10.0421	0.334180
$904$	−12.7384	−0.423672
$905$	−37.8664	−1.25872
$906$	19.7184	0.655101
$907$	−34.4500	−1.14389	−0.571947	−	0.820291i	$-0.693812\pi$
$907$	−34.4500	−1.14389	−0.571947	+	0.820291i	$0.693812\pi$
$908$	−9.93767	−0.329793
$909$	29.7635	0.987193
$910$	20.3406	0.674285
$911$	−39.8603	−1.32063	−0.660315	−	0.750989i	$-0.729577\pi$
$911$	−39.8603	−1.32063	−0.660315	+	0.750989i	$0.729577\pi$
$912$	7.55466	0.250160
$913$	−13.8070	−0.456944
$914$	−31.1493	−1.03033
$915$	−44.1396	−1.45921
$916$	−4.54456	−0.150157
$917$	−17.2859	−0.570830
$918$	−1.72369	−0.0568902
$919$	−19.4991	−0.643217	−0.321609	−	0.946873i	$-0.604224\pi$
$919$	−19.4991	−0.643217	−0.321609	+	0.946873i	$0.604224\pi$
$920$	−10.0401	−0.331013
$921$	20.9123	0.689085
$922$	12.3031	0.405182
$923$	−81.0576	−2.66804
$924$	3.78957	0.124668
$925$	22.3968	0.736402
$926$	13.7248	0.451025
$927$	19.7990	0.650285
$928$	−0.502592	−0.0164984
$929$	1.34705	0.0441953	0.0220977	−	0.999756i	$-0.492966\pi$
$929$	1.34705	0.0441953	0.0220977	+	0.999756i	$0.492966\pi$
$930$	−30.4650	−0.998987
$931$	−17.6242	−0.577611
$932$	8.61402	0.282162
$933$	−33.6769	−1.10253
$934$	2.03351	0.0665384
$935$	−9.11477	−0.298085
$936$	15.9047	0.519862
$937$	−19.5206	−0.637709	−0.318855	−	0.947804i	$-0.603298\pi$
$937$	−19.5206	−0.637709	−0.318855	+	0.947804i	$0.603298\pi$
$938$	−3.58693	−0.117117
$939$	25.0848	0.818612
$940$	−31.0101	−1.01144
$941$	16.8178	0.548245	0.274123	−	0.961695i	$-0.411613\pi$
$941$	16.8178	0.548245	0.274123	+	0.961695i	$0.411613\pi$
$942$	24.6530	0.803238
$943$	10.7510	0.350102
$944$	−5.76626	−0.187676
$945$	−2.49478	−0.0811553
$946$	−4.66548	−0.151688
$947$	−3.34578	−0.108723	−0.0543616	−	0.998521i	$-0.517312\pi$
$947$	−3.34578	−0.108723	−0.0543616	+	0.998521i	$0.517312\pi$
$948$	−2.46600	−0.0800918
$949$	17.3740	0.563983
$950$	−10.4736	−0.339808
$951$	−3.85488	−0.125003
$952$	−2.85152	−0.0924184
$953$	45.0499	1.45931	0.729655	−	0.683816i	$-0.239681\pi$
$953$	45.0499	1.45931	0.729655	+	0.683816i	$0.239681\pi$
$954$	−15.9115	−0.515155
$955$	18.1017	0.585758
$956$	−4.21837	−0.136432
$957$	−1.59173	−0.0514532
$958$	−1.62944	−0.0526449
$959$	−18.2497	−0.589312
$960$	−6.88014	−0.222055
$961$	−11.3931	−0.367521
$962$	39.9149	1.28691
$963$	−2.77101	−0.0892947
$964$	8.94629	0.288141
$965$	54.2382	1.74599
$966$	−9.94770	−0.320062
$967$	−27.3762	−0.880361	−0.440180	−	0.897909i	$-0.645085\pi$
$967$	−27.3762	−0.880361	−0.440180	+	0.897909i	$0.645085\pi$
$968$	9.23939	0.296965
$969$	−18.0034	−0.578352
$970$	−41.1166	−1.32017
$971$	31.3089	1.00475	0.502375	−	0.864650i	$-0.332460\pi$
$971$	31.3089	1.00475	0.502375	+	0.864650i	$0.332460\pi$
$972$	−21.2623	−0.681988
$973$	−12.4204	−0.398181
$974$	11.0193	0.353081
$975$	−46.5774	−1.49167
$976$	6.41551	0.205356
$977$	−32.3888	−1.03621	−0.518105	−	0.855317i	$-0.673363\pi$
$977$	−32.3888	−1.03621	−0.518105	+	0.855317i	$0.673363\pi$
$978$	−18.8983	−0.604300
$979$	18.1159	0.578987
$980$	16.0506	0.512719
$981$	21.1933	0.676651
$982$	16.3113	0.520514
$983$	8.67202	0.276594	0.138297	−	0.990391i	$-0.455837\pi$
$983$	8.67202	0.276594	0.138297	+	0.990391i	$0.455837\pi$
$984$	7.36731	0.234861
$985$	17.4739	0.556766
$986$	1.19772	0.0381431
$987$	−30.7246	−0.977975
$988$	−18.6657	−0.593835
$989$	12.2470	0.389431
$990$	−10.3153	−0.327841
$991$	5.83910	0.185485	0.0927425	−	0.995690i	$-0.470437\pi$
$991$	5.83910	0.185485	0.0927425	+	0.995690i	$0.470437\pi$
$992$	4.42796	0.140588
$993$	11.8265	0.375301
$994$	16.4467	0.521659
$995$	30.4387	0.964970
$996$	24.8364	0.786972
$997$	6.98735	0.221291	0.110646	−	0.993860i	$-0.464708\pi$
$997$	6.98735	0.221291	0.110646	+	0.993860i	$0.464708\pi$
$998$	19.9754	0.632310
$999$	−4.89557	−0.154889

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.e.1.65	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.e.1.65	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.38683 q^{3} +1.00000 q^{4} -2.88254 q^{5} -2.38683 q^{6} -1.19657 q^{7} -1.00000 q^{8} +2.69696 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.38683 q^{3} +1.00000 q^{4} -2.88254 q^{5} -2.38683 q^{6} -1.19657 q^{7} -1.00000 q^{8} +2.69696 q^{9} +2.88254 q^{10} -1.32688 q^{11} +2.38683 q^{12} -5.89727 q^{13} +1.19657 q^{14} -6.88014 q^{15} +1.00000 q^{16} -2.38308 q^{17} -2.69696 q^{18} +3.16514 q^{19} -2.88254 q^{20} -2.85601 q^{21} +1.32688 q^{22} -3.48308 q^{23} -2.38683 q^{24} +3.30904 q^{25} +5.89727 q^{26} -0.723302 q^{27} -1.19657 q^{28} +0.502592 q^{29} +6.88014 q^{30} -4.42796 q^{31} -1.00000 q^{32} -3.16703 q^{33} +2.38308 q^{34} +3.44916 q^{35} +2.69696 q^{36} +6.76836 q^{37} -3.16514 q^{38} -14.0758 q^{39} +2.88254 q^{40} -3.08665 q^{41} +2.85601 q^{42} -3.51613 q^{43} -1.32688 q^{44} -7.77410 q^{45} +3.48308 q^{46} +10.7579 q^{47} +2.38683 q^{48} -5.56822 q^{49} -3.30904 q^{50} -5.68802 q^{51} -5.89727 q^{52} +5.89980 q^{53} +0.723302 q^{54} +3.82478 q^{55} +1.19657 q^{56} +7.55466 q^{57} -0.502592 q^{58} -5.76626 q^{59} -6.88014 q^{60} +6.41551 q^{61} +4.42796 q^{62} -3.22710 q^{63} +1.00000 q^{64} +16.9991 q^{65} +3.16703 q^{66} -2.99768 q^{67} -2.38308 q^{68} -8.31352 q^{69} -3.44916 q^{70} +13.7449 q^{71} -2.69696 q^{72} -2.94610 q^{73} -6.76836 q^{74} +7.89812 q^{75} +3.16514 q^{76} +1.58770 q^{77} +14.0758 q^{78} -1.03317 q^{79} -2.88254 q^{80} -9.81728 q^{81} +3.08665 q^{82} +10.4056 q^{83} -2.85601 q^{84} +6.86933 q^{85} +3.51613 q^{86} +1.19960 q^{87} +1.32688 q^{88} -13.6530 q^{89} +7.77410 q^{90} +7.05649 q^{91} -3.48308 q^{92} -10.5688 q^{93} -10.7579 q^{94} -9.12365 q^{95} -2.38683 q^{96} -14.2640 q^{97} +5.56822 q^{98} -3.57854 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) 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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