LMFDB - Embedded newform 8002.2.a.e.1.7

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			1.7
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.62668 q^{3} +1.00000 q^{4} +0.854809 q^{5} +2.62668 q^{6} +1.79286 q^{7} -1.00000 q^{8} +3.89945 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.62668 q^{3} +1.00000 q^{4} +0.854809 q^{5} +2.62668 q^{6} +1.79286 q^{7} -1.00000 q^{8} +3.89945 q^{9} -0.854809 q^{10} +1.39811 q^{11} -2.62668 q^{12} +4.58926 q^{13} -1.79286 q^{14} -2.24531 q^{15} +1.00000 q^{16} +4.16383 q^{17} -3.89945 q^{18} +7.03095 q^{19} +0.854809 q^{20} -4.70927 q^{21} -1.39811 q^{22} -6.43702 q^{23} +2.62668 q^{24} -4.26930 q^{25} -4.58926 q^{26} -2.36257 q^{27} +1.79286 q^{28} +4.33951 q^{29} +2.24531 q^{30} +3.24386 q^{31} -1.00000 q^{32} -3.67239 q^{33} -4.16383 q^{34} +1.53255 q^{35} +3.89945 q^{36} +3.51846 q^{37} -7.03095 q^{38} -12.0545 q^{39} -0.854809 q^{40} +7.42613 q^{41} +4.70927 q^{42} +5.43299 q^{43} +1.39811 q^{44} +3.33329 q^{45} +6.43702 q^{46} +9.18945 q^{47} -2.62668 q^{48} -3.78565 q^{49} +4.26930 q^{50} -10.9370 q^{51} +4.58926 q^{52} +13.3398 q^{53} +2.36257 q^{54} +1.19512 q^{55} -1.79286 q^{56} -18.4681 q^{57} -4.33951 q^{58} +15.0144 q^{59} -2.24531 q^{60} -10.2707 q^{61} -3.24386 q^{62} +6.99118 q^{63} +1.00000 q^{64} +3.92294 q^{65} +3.67239 q^{66} +3.19534 q^{67} +4.16383 q^{68} +16.9080 q^{69} -1.53255 q^{70} -5.20239 q^{71} -3.89945 q^{72} +4.59082 q^{73} -3.51846 q^{74} +11.2141 q^{75} +7.03095 q^{76} +2.50662 q^{77} +12.0545 q^{78} +12.9027 q^{79} +0.854809 q^{80} -5.49263 q^{81} -7.42613 q^{82} +8.96203 q^{83} -4.70927 q^{84} +3.55928 q^{85} -5.43299 q^{86} -11.3985 q^{87} -1.39811 q^{88} -2.56615 q^{89} -3.33329 q^{90} +8.22790 q^{91} -6.43702 q^{92} -8.52059 q^{93} -9.18945 q^{94} +6.01012 q^{95} +2.62668 q^{96} -13.9084 q^{97} +3.78565 q^{98} +5.45187 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.62668	−1.51651	−0.758257	−	0.651955i	$-0.773949\pi$
$3$	−2.62668	−1.51651	−0.758257	+	0.651955i	$0.773949\pi$
$4$	1.00000	0.500000
$5$	0.854809	0.382282	0.191141	−	0.981563i	$-0.438781\pi$
$5$	0.854809	0.382282	0.191141	+	0.981563i	$0.438781\pi$
$6$	2.62668	1.07234
$7$	1.79286	0.677638	0.338819	−	0.940852i	$-0.389973\pi$
$7$	1.79286	0.677638	0.338819	+	0.940852i	$0.389973\pi$
$8$	−1.00000	−0.353553
$9$	3.89945	1.29982
$10$	−0.854809	−0.270314
$11$	1.39811	0.421547	0.210773	−	0.977535i	$-0.432402\pi$
$11$	1.39811	0.421547	0.210773	+	0.977535i	$0.432402\pi$
$12$	−2.62668	−0.758257
$13$	4.58926	1.27283	0.636416	−	0.771346i	$-0.280416\pi$
$13$	4.58926	1.27283	0.636416	+	0.771346i	$0.280416\pi$
$14$	−1.79286	−0.479162
$15$	−2.24531	−0.579737
$16$	1.00000	0.250000
$17$	4.16383	1.00988	0.504938	−	0.863155i	$-0.331515\pi$
$17$	4.16383	1.00988	0.504938	+	0.863155i	$0.331515\pi$
$18$	−3.89945	−0.919110
$19$	7.03095	1.61301	0.806505	−	0.591228i	$-0.201356\pi$
$19$	7.03095	1.61301	0.806505	+	0.591228i	$0.201356\pi$
$20$	0.854809	0.191141
$21$	−4.70927	−1.02765
$22$	−1.39811	−0.298078
$23$	−6.43702	−1.34221	−0.671105	−	0.741362i	$-0.734180\pi$
$23$	−6.43702	−1.34221	−0.671105	+	0.741362i	$0.734180\pi$
$24$	2.62668	0.536169
$25$	−4.26930	−0.853860
$26$	−4.58926	−0.900028
$27$	−2.36257	−0.454677
$28$	1.79286	0.338819
$29$	4.33951	0.805827	0.402913	−	0.915238i	$-0.367998\pi$
$29$	4.33951	0.805827	0.402913	+	0.915238i	$0.367998\pi$
$30$	2.24531	0.409936
$31$	3.24386	0.582615	0.291307	−	0.956630i	$-0.405910\pi$
$31$	3.24386	0.582615	0.291307	+	0.956630i	$0.405910\pi$
$32$	−1.00000	−0.176777
$33$	−3.67239	−0.639282
$34$	−4.16383	−0.714090
$35$	1.53255	0.259049
$36$	3.89945	0.649909
$37$	3.51846	0.578431	0.289215	−	0.957264i	$-0.406606\pi$
$37$	3.51846	0.578431	0.289215	+	0.957264i	$0.406606\pi$
$38$	−7.03095	−1.14057
$39$	−12.0545	−1.93027
$40$	−0.854809	−0.135157
$41$	7.42613	1.15977	0.579883	−	0.814700i	$-0.303098\pi$
$41$	7.42613	1.15977	0.579883	+	0.814700i	$0.303098\pi$
$42$	4.70927	0.726657
$43$	5.43299	0.828523	0.414261	−	0.910158i	$-0.364040\pi$
$43$	5.43299	0.828523	0.414261	+	0.910158i	$0.364040\pi$
$44$	1.39811	0.210773
$45$	3.33329	0.496897
$46$	6.43702	0.949086
$47$	9.18945	1.34042	0.670210	−	0.742172i	$-0.266204\pi$
$47$	9.18945	1.34042	0.670210	+	0.742172i	$0.266204\pi$
$48$	−2.62668	−0.379129
$49$	−3.78565	−0.540807
$50$	4.26930	0.603770
$51$	−10.9370	−1.53149
$52$	4.58926	0.636416
$53$	13.3398	1.83236	0.916179	−	0.400769i	$-0.131257\pi$
$53$	13.3398	1.83236	0.916179	+	0.400769i	$0.131257\pi$
$54$	2.36257	0.321505
$55$	1.19512	0.161150
$56$	−1.79286	−0.239581
$57$	−18.4681	−2.44615
$58$	−4.33951	−0.569805
$59$	15.0144	1.95471	0.977353	−	0.211614i	$-0.0678721\pi$
$59$	15.0144	1.95471	0.977353	+	0.211614i	$0.0678721\pi$
$60$	−2.24531	−0.289868
$61$	−10.2707	−1.31503	−0.657514	−	0.753442i	$-0.728392\pi$
$61$	−10.2707	−1.31503	−0.657514	+	0.753442i	$0.728392\pi$
$62$	−3.24386	−0.411971
$63$	6.99118	0.880805
$64$	1.00000	0.125000
$65$	3.92294	0.486581
$66$	3.67239	0.452040
$67$	3.19534	0.390373	0.195187	−	0.980766i	$-0.437469\pi$
$67$	3.19534	0.390373	0.195187	+	0.980766i	$0.437469\pi$
$68$	4.16383	0.504938
$69$	16.9080	2.03548
$70$	−1.53255	−0.183175
$71$	−5.20239	−0.617411	−0.308705	−	0.951158i	$-0.599896\pi$
$71$	−5.20239	−0.617411	−0.308705	+	0.951158i	$0.599896\pi$
$72$	−3.89945	−0.459555
$73$	4.59082	0.537315	0.268657	−	0.963236i	$-0.413420\pi$
$73$	4.59082	0.537315	0.268657	+	0.963236i	$0.413420\pi$
$74$	−3.51846	−0.409012
$75$	11.2141	1.29489
$76$	7.03095	0.806505
$77$	2.50662	0.285656
$78$	12.0545	1.36491
$79$	12.9027	1.45166	0.725832	−	0.687872i	$-0.241455\pi$
$79$	12.9027	1.45166	0.725832	+	0.687872i	$0.241455\pi$
$80$	0.854809	0.0955706
$81$	−5.49263	−0.610292
$82$	−7.42613	−0.820079
$83$	8.96203	0.983710	0.491855	−	0.870677i	$-0.336319\pi$
$83$	8.96203	0.983710	0.491855	+	0.870677i	$0.336319\pi$
$84$	−4.70927	−0.513824
$85$	3.55928	0.386058
$86$	−5.43299	−0.585854
$87$	−11.3985	−1.22205
$88$	−1.39811	−0.149039
$89$	−2.56615	−0.272011	−0.136006	−	0.990708i	$-0.543426\pi$
$89$	−2.56615	−0.272011	−0.136006	+	0.990708i	$0.543426\pi$
$90$	−3.33329	−0.351359
$91$	8.22790	0.862519
$92$	−6.43702	−0.671105
$93$	−8.52059	−0.883544
$94$	−9.18945	−0.947819
$95$	6.01012	0.616625
$96$	2.62668	0.268084
$97$	−13.9084	−1.41219	−0.706095	−	0.708118i	$-0.749545\pi$
$97$	−13.9084	−1.41219	−0.706095	+	0.708118i	$0.749545\pi$
$98$	3.78565	0.382408
$99$	5.45187	0.547933
$100$	−4.26930	−0.426930
$101$	−18.6206	−1.85282	−0.926411	−	0.376514i	$-0.877123\pi$
$101$	−18.6206	−1.85282	−0.926411	+	0.376514i	$0.877123\pi$
$102$	10.9370	1.08293
$103$	−7.47862	−0.736890	−0.368445	−	0.929649i	$-0.620110\pi$
$103$	−7.47862	−0.736890	−0.368445	+	0.929649i	$0.620110\pi$
$104$	−4.58926	−0.450014
$105$	−4.02553	−0.392851
$106$	−13.3398	−1.29567
$107$	16.1348	1.55981	0.779906	−	0.625897i	$-0.215267\pi$
$107$	16.1348	1.55981	0.779906	+	0.625897i	$0.215267\pi$
$108$	−2.36257	−0.227339
$109$	14.6084	1.39923	0.699616	−	0.714519i	$-0.253354\pi$
$109$	14.6084	1.39923	0.699616	+	0.714519i	$0.253354\pi$
$110$	−1.19512	−0.113950
$111$	−9.24186	−0.877198
$112$	1.79286	0.169409
$113$	−11.4365	−1.07586	−0.537928	−	0.842991i	$-0.680793\pi$
$113$	−11.4365	−1.07586	−0.537928	+	0.842991i	$0.680793\pi$
$114$	18.4681	1.72969
$115$	−5.50242	−0.513103
$116$	4.33951	0.402913
$117$	17.8956	1.65445
$118$	−15.0144	−1.38219
$119$	7.46516	0.684330
$120$	2.24531	0.204968
$121$	−9.04528	−0.822298
$122$	10.2707	0.929866
$123$	−19.5061	−1.75880
$124$	3.24386	0.291307
$125$	−7.92348	−0.708698
$126$	−6.99118	−0.622823
$127$	9.05839	0.803802	0.401901	−	0.915683i	$-0.368350\pi$
$127$	9.05839	0.803802	0.401901	+	0.915683i	$0.368350\pi$
$128$	−1.00000	−0.0883883
$129$	−14.2707	−1.25647
$130$	−3.92294	−0.344065
$131$	−3.80330	−0.332296	−0.166148	−	0.986101i	$-0.553133\pi$
$131$	−3.80330	−0.332296	−0.166148	+	0.986101i	$0.553133\pi$
$132$	−3.67239	−0.319641
$133$	12.6055	1.09304
$134$	−3.19534	−0.276036
$135$	−2.01955	−0.173815
$136$	−4.16383	−0.357045
$137$	20.6547	1.76465	0.882326	−	0.470638i	$-0.155976\pi$
$137$	20.6547	1.76465	0.882326	+	0.470638i	$0.155976\pi$
$138$	−16.9080	−1.43930
$139$	6.77841	0.574937	0.287469	−	0.957790i	$-0.407186\pi$
$139$	6.77841	0.574937	0.287469	+	0.957790i	$0.407186\pi$
$140$	1.53255	0.129524
$141$	−24.1378	−2.03277
$142$	5.20239	0.436575
$143$	6.41630	0.536558
$144$	3.89945	0.324954
$145$	3.70945	0.308053
$146$	−4.59082	−0.379939
$147$	9.94369	0.820142
$148$	3.51846	0.289215
$149$	5.51127	0.451500	0.225750	−	0.974185i	$-0.427517\pi$
$149$	5.51127	0.451500	0.225750	+	0.974185i	$0.427517\pi$
$150$	−11.2141	−0.915627
$151$	−9.42711	−0.767167	−0.383584	−	0.923506i	$-0.625310\pi$
$151$	−9.42711	−0.767167	−0.383584	+	0.923506i	$0.625310\pi$
$152$	−7.03095	−0.570285
$153$	16.2366	1.31265
$154$	−2.50662	−0.201989
$155$	2.77288	0.222723
$156$	−12.0545	−0.965134
$157$	−14.6278	−1.16743	−0.583715	−	0.811959i	$-0.698401\pi$
$157$	−14.6278	−1.16743	−0.583715	+	0.811959i	$0.698401\pi$
$158$	−12.9027	−1.02648
$159$	−35.0393	−2.77880
$160$	−0.854809	−0.0675786
$161$	−11.5407	−0.909533
$162$	5.49263	0.431542
$163$	−1.17571	−0.0920884	−0.0460442	−	0.998939i	$-0.514662\pi$
$163$	−1.17571	−0.0920884	−0.0460442	+	0.998939i	$0.514662\pi$
$164$	7.42613	0.579883
$165$	−3.13919	−0.244386
$166$	−8.96203	−0.695588
$167$	6.13476	0.474722	0.237361	−	0.971422i	$-0.423718\pi$
$167$	6.13476	0.474722	0.237361	+	0.971422i	$0.423718\pi$
$168$	4.70927	0.363328
$169$	8.06129	0.620099
$170$	−3.55928	−0.272984
$171$	27.4168	2.09662
$172$	5.43299	0.414261
$173$	6.25113	0.475264	0.237632	−	0.971355i	$-0.423629\pi$
$173$	6.25113	0.475264	0.237632	+	0.971355i	$0.423629\pi$
$174$	11.3985	0.864118
$175$	−7.65426	−0.578608
$176$	1.39811	0.105387
$177$	−39.4380	−2.96434
$178$	2.56615	0.192341
$179$	−3.65995	−0.273557	−0.136779	−	0.990602i	$-0.543675\pi$
$179$	−3.65995	−0.273557	−0.136779	+	0.990602i	$0.543675\pi$
$180$	3.33329	0.248449
$181$	−17.3263	−1.28786	−0.643928	−	0.765086i	$-0.722696\pi$
$181$	−17.3263	−1.28786	−0.643928	+	0.765086i	$0.722696\pi$
$182$	−8.22790	−0.609893
$183$	26.9779	1.99426
$184$	6.43702	0.474543
$185$	3.00761	0.221124
$186$	8.52059	0.624760
$187$	5.82150	0.425710
$188$	9.18945	0.670210
$189$	−4.23576	−0.308106
$190$	−6.01012	−0.436020
$191$	17.2881	1.25092	0.625460	−	0.780256i	$-0.284911\pi$
$191$	17.2881	1.25092	0.625460	+	0.780256i	$0.284911\pi$
$192$	−2.62668	−0.189564
$193$	−15.8238	−1.13902	−0.569512	−	0.821983i	$-0.692868\pi$
$193$	−15.8238	−1.13902	−0.569512	+	0.821983i	$0.692868\pi$
$194$	13.9084	0.998569
$195$	−10.3043	−0.737907
$196$	−3.78565	−0.270404
$197$	−12.0973	−0.861899	−0.430950	−	0.902376i	$-0.641821\pi$
$197$	−12.0973	−0.861899	−0.430950	+	0.902376i	$0.641821\pi$
$198$	−5.45187	−0.387447
$199$	−18.1581	−1.28720	−0.643598	−	0.765364i	$-0.722559\pi$
$199$	−18.1581	−1.28720	−0.643598	+	0.765364i	$0.722559\pi$
$200$	4.26930	0.301885
$201$	−8.39314	−0.592007
$202$	18.6206	1.31014
$203$	7.78014	0.546059
$204$	−10.9370	−0.765746
$205$	6.34792	0.443358
$206$	7.47862	0.521060
$207$	−25.1008	−1.74463
$208$	4.58926	0.318208
$209$	9.83005	0.679959
$210$	4.02553	0.277788
$211$	−9.69641	−0.667529	−0.333764	−	0.942657i	$-0.608319\pi$
$211$	−9.69641	−0.667529	−0.333764	+	0.942657i	$0.608319\pi$
$212$	13.3398	0.916179
$213$	13.6650	0.936312
$214$	−16.1348	−1.10295
$215$	4.64417	0.316730
$216$	2.36257	0.160753
$217$	5.81579	0.394802
$218$	−14.6084	−0.989406
$219$	−12.0586	−0.814846
$220$	1.19512	0.0805749
$221$	19.1089	1.28540
$222$	9.24186	0.620273
$223$	−13.9655	−0.935200	−0.467600	−	0.883940i	$-0.654881\pi$
$223$	−13.9655	−0.935200	−0.467600	+	0.883940i	$0.654881\pi$
$224$	−1.79286	−0.119791
$225$	−16.6479	−1.10986
$226$	11.4365	0.760745
$227$	8.81918	0.585350	0.292675	−	0.956212i	$-0.405455\pi$
$227$	8.81918	0.585350	0.292675	+	0.956212i	$0.405455\pi$
$228$	−18.4681	−1.22308
$229$	−17.8260	−1.17797	−0.588986	−	0.808143i	$-0.700473\pi$
$229$	−17.8260	−1.17797	−0.588986	+	0.808143i	$0.700473\pi$
$230$	5.50242	0.362819
$231$	−6.58409	−0.433201
$232$	−4.33951	−0.284903
$233$	−13.1809	−0.863511	−0.431755	−	0.901991i	$-0.642106\pi$
$233$	−13.1809	−0.863511	−0.431755	+	0.901991i	$0.642106\pi$
$234$	−17.8956	−1.16987
$235$	7.85522	0.512418
$236$	15.0144	0.977353
$237$	−33.8912	−2.20147
$238$	−7.46516	−0.483895
$239$	13.2733	0.858579	0.429289	−	0.903167i	$-0.358764\pi$
$239$	13.2733	0.858579	0.429289	+	0.903167i	$0.358764\pi$
$240$	−2.24531	−0.144934
$241$	−9.51088	−0.612649	−0.306325	−	0.951927i	$-0.599099\pi$
$241$	−9.51088	−0.612649	−0.306325	+	0.951927i	$0.599099\pi$
$242$	9.04528	0.581453
$243$	21.5151	1.38019
$244$	−10.2707	−0.657514
$245$	−3.23601	−0.206741
$246$	19.5061	1.24366
$247$	32.2668	2.05309
$248$	−3.24386	−0.205985
$249$	−23.5404	−1.49181
$250$	7.92348	0.501125
$251$	−25.2709	−1.59508	−0.797542	−	0.603263i	$-0.793867\pi$
$251$	−25.2709	−1.59508	−0.797542	+	0.603263i	$0.793867\pi$
$252$	6.99118	0.440403
$253$	−8.99967	−0.565804
$254$	−9.05839	−0.568374
$255$	−9.34908	−0.585462
$256$	1.00000	0.0625000
$257$	0.815232	0.0508528	0.0254264	−	0.999677i	$-0.491906\pi$
$257$	0.815232	0.0508528	0.0254264	+	0.999677i	$0.491906\pi$
$258$	14.2707	0.888457
$259$	6.30810	0.391966
$260$	3.92294	0.243290
$261$	16.9217	1.04743
$262$	3.80330	0.234969
$263$	−25.4272	−1.56791	−0.783954	−	0.620819i	$-0.786800\pi$
$263$	−25.4272	−1.56791	−0.783954	+	0.620819i	$0.786800\pi$
$264$	3.67239	0.226020
$265$	11.4030	0.700478
$266$	−12.6055	−0.772893
$267$	6.74045	0.412509
$268$	3.19534	0.195187
$269$	−18.1899	−1.10906	−0.554530	−	0.832164i	$-0.687102\pi$
$269$	−18.1899	−1.10906	−0.554530	+	0.832164i	$0.687102\pi$
$270$	2.01955	0.122906
$271$	−9.42443	−0.572493	−0.286247	−	0.958156i	$-0.592408\pi$
$271$	−9.42443	−0.572493	−0.286247	+	0.958156i	$0.592408\pi$
$272$	4.16383	0.252469
$273$	−21.6121	−1.30802
$274$	−20.6547	−1.24780
$275$	−5.96896	−0.359942
$276$	16.9080	1.01774
$277$	22.4304	1.34771	0.673855	−	0.738864i	$-0.264637\pi$
$277$	22.4304	1.34771	0.673855	+	0.738864i	$0.264637\pi$
$278$	−6.77841	−0.406542
$279$	12.6493	0.757293
$280$	−1.53255	−0.0915876
$281$	9.63200	0.574597	0.287299	−	0.957841i	$-0.407243\pi$
$281$	9.63200	0.574597	0.287299	+	0.957841i	$0.407243\pi$
$282$	24.1378	1.43738
$283$	−18.2230	−1.08324	−0.541622	−	0.840622i	$-0.682189\pi$
$283$	−18.2230	−1.08324	−0.541622	+	0.840622i	$0.682189\pi$
$284$	−5.20239	−0.308705
$285$	−15.7867	−0.935121
$286$	−6.41630	−0.379404
$287$	13.3140	0.785901
$288$	−3.89945	−0.229777
$289$	0.337458	0.0198505
$290$	−3.70945	−0.217826
$291$	36.5331	2.14161
$292$	4.59082	0.268657
$293$	11.5816	0.676604	0.338302	−	0.941038i	$-0.390147\pi$
$293$	11.5816	0.676604	0.338302	+	0.941038i	$0.390147\pi$
$294$	−9.94369	−0.579928
$295$	12.8344	0.747250
$296$	−3.51846	−0.204506
$297$	−3.30314	−0.191668
$298$	−5.51127	−0.319259
$299$	−29.5411	−1.70841
$300$	11.2141	0.647446
$301$	9.74059	0.561438
$302$	9.42711	0.542469
$303$	48.9104	2.80983
$304$	7.03095	0.403252
$305$	−8.77949	−0.502712
$306$	−16.2366	−0.928187
$307$	−24.7384	−1.41189	−0.705947	−	0.708264i	$-0.749479\pi$
$307$	−24.7384	−1.41189	−0.705947	+	0.708264i	$0.749479\pi$
$308$	2.50662	0.142828
$309$	19.6440	1.11751
$310$	−2.77288	−0.157489
$311$	19.6832	1.11613	0.558066	−	0.829796i	$-0.311544\pi$
$311$	19.6832	1.11613	0.558066	+	0.829796i	$0.311544\pi$
$312$	12.0545	0.682453
$313$	26.9784	1.52491	0.762456	−	0.647040i	$-0.223993\pi$
$313$	26.9784	1.52491	0.762456	+	0.647040i	$0.223993\pi$
$314$	14.6278	0.825497
$315$	5.97612	0.336716
$316$	12.9027	0.725832
$317$	5.08898	0.285826	0.142913	−	0.989735i	$-0.454353\pi$
$317$	5.08898	0.285826	0.142913	+	0.989735i	$0.454353\pi$
$318$	35.0393	1.96491
$319$	6.06712	0.339693
$320$	0.854809	0.0477853
$321$	−42.3810	−2.36548
$322$	11.5407	0.643137
$323$	29.2756	1.62894
$324$	−5.49263	−0.305146
$325$	−19.5929	−1.08682
$326$	1.17571	0.0651163
$327$	−38.3716	−2.12196
$328$	−7.42613	−0.410039
$329$	16.4754	0.908319
$330$	3.13919	0.172807
$331$	−17.9887	−0.988749	−0.494374	−	0.869249i	$-0.664603\pi$
$331$	−17.9887	−0.988749	−0.494374	+	0.869249i	$0.664603\pi$
$332$	8.96203	0.491855
$333$	13.7200	0.751854
$334$	−6.13476	−0.335679
$335$	2.73141	0.149233
$336$	−4.70927	−0.256912
$337$	−12.0506	−0.656437	−0.328219	−	0.944602i	$-0.606448\pi$
$337$	−12.0506	−0.656437	−0.328219	+	0.944602i	$0.606448\pi$
$338$	−8.06129	−0.438477
$339$	30.0400	1.63155
$340$	3.55928	0.193029
$341$	4.53528	0.245599
$342$	−27.4168	−1.48253
$343$	−19.3372	−1.04411
$344$	−5.43299	−0.292927
$345$	14.4531	0.778129
$346$	−6.25113	−0.336063
$347$	4.32749	0.232312	0.116156	−	0.993231i	$-0.462943\pi$
$347$	4.32749	0.232312	0.116156	+	0.993231i	$0.462943\pi$
$348$	−11.3985	−0.611024
$349$	7.97325	0.426798	0.213399	−	0.976965i	$-0.431547\pi$
$349$	7.97325	0.426798	0.213399	+	0.976965i	$0.431547\pi$
$350$	7.65426	0.409138
$351$	−10.8425	−0.578727
$352$	−1.39811	−0.0745196
$353$	8.60601	0.458052	0.229026	−	0.973420i	$-0.426446\pi$
$353$	8.60601	0.458052	0.229026	+	0.973420i	$0.426446\pi$
$354$	39.4380	2.09611
$355$	−4.44705	−0.236025
$356$	−2.56615	−0.136006
$357$	−19.6086	−1.03780
$358$	3.65995	0.193434
$359$	−11.4828	−0.606040	−0.303020	−	0.952984i	$-0.597995\pi$
$359$	−11.4828	−0.606040	−0.303020	+	0.952984i	$0.597995\pi$
$360$	−3.33329	−0.175680
$361$	30.4342	1.60180
$362$	17.3263	0.910652
$363$	23.7591	1.24703
$364$	8.22790	0.431259
$365$	3.92427	0.205406
$366$	−26.9779	−1.41016
$367$	−26.0578	−1.36021	−0.680104	−	0.733115i	$-0.738065\pi$
$367$	−26.0578	−1.36021	−0.680104	+	0.733115i	$0.738065\pi$
$368$	−6.43702	−0.335553
$369$	28.9578	1.50748
$370$	−3.00761	−0.156358
$371$	23.9163	1.24168
$372$	−8.52059	−0.441772
$373$	−28.1289	−1.45646	−0.728230	−	0.685333i	$-0.759657\pi$
$373$	−28.1289	−1.45646	−0.728230	+	0.685333i	$0.759657\pi$
$374$	−5.82150	−0.301022
$375$	20.8125	1.07475
$376$	−9.18945	−0.473910
$377$	19.9151	1.02568
$378$	4.23576	0.217864
$379$	−21.9273	−1.12633	−0.563164	−	0.826345i	$-0.690416\pi$
$379$	−21.9273	−1.12633	−0.563164	+	0.826345i	$0.690416\pi$
$380$	6.01012	0.308312
$381$	−23.7935	−1.21898
$382$	−17.2881	−0.884534
$383$	−18.4116	−0.940790	−0.470395	−	0.882456i	$-0.655889\pi$
$383$	−18.4116	−0.940790	−0.470395	+	0.882456i	$0.655889\pi$
$384$	2.62668	0.134042
$385$	2.14268	0.109201
$386$	15.8238	0.805412
$387$	21.1857	1.07693
$388$	−13.9084	−0.706095
$389$	−14.2023	−0.720086	−0.360043	−	0.932936i	$-0.617238\pi$
$389$	−14.2023	−0.720086	−0.360043	+	0.932936i	$0.617238\pi$
$390$	10.3043	0.521779
$391$	−26.8026	−1.35547
$392$	3.78565	0.191204
$393$	9.99006	0.503932
$394$	12.0973	0.609455
$395$	11.0293	0.554945
$396$	5.45187	0.273967
$397$	12.4757	0.626140	0.313070	−	0.949730i	$-0.398643\pi$
$397$	12.4757	0.626140	0.313070	+	0.949730i	$0.398643\pi$
$398$	18.1581	0.910185
$399$	−33.1106	−1.65761
$400$	−4.26930	−0.213465
$401$	−14.5417	−0.726176	−0.363088	−	0.931755i	$-0.618278\pi$
$401$	−14.5417	−0.726176	−0.363088	+	0.931755i	$0.618278\pi$
$402$	8.39314	0.418612
$403$	14.8869	0.741570
$404$	−18.6206	−0.926411
$405$	−4.69515	−0.233304
$406$	−7.78014	−0.386122
$407$	4.91919	0.243835
$408$	10.9370	0.541464
$409$	−33.6657	−1.66466	−0.832332	−	0.554278i	$-0.812994\pi$
$409$	−33.6657	−1.66466	−0.832332	+	0.554278i	$0.812994\pi$
$410$	−6.34792	−0.313501
$411$	−54.2534	−2.67612
$412$	−7.47862	−0.368445
$413$	26.9187	1.32458
$414$	25.1008	1.23364
$415$	7.66082	0.376055
$416$	−4.58926	−0.225007
$417$	−17.8047	−0.871901
$418$	−9.83005	−0.480803
$419$	14.6756	0.716952	0.358476	−	0.933539i	$-0.383296\pi$
$419$	14.6756	0.716952	0.358476	+	0.933539i	$0.383296\pi$
$420$	−4.02553	−0.196426
$421$	8.02186	0.390962	0.195481	−	0.980708i	$-0.437373\pi$
$421$	8.02186	0.390962	0.195481	+	0.980708i	$0.437373\pi$
$422$	9.69641	0.472014
$423$	35.8338	1.74230
$424$	−13.3398	−0.647836
$425$	−17.7766	−0.862293
$426$	−13.6650	−0.662073
$427$	−18.4139	−0.891113
$428$	16.1348	0.779906
$429$	−16.8536	−0.813698
$430$	−4.64417	−0.223962
$431$	−7.96699	−0.383757	−0.191878	−	0.981419i	$-0.561458\pi$
$431$	−7.96699	−0.383757	−0.191878	+	0.981419i	$0.561458\pi$
$432$	−2.36257	−0.113669
$433$	11.7495	0.564647	0.282324	−	0.959319i	$-0.408895\pi$
$433$	11.7495	0.564647	0.282324	+	0.959319i	$0.408895\pi$
$434$	−5.81579	−0.279167
$435$	−9.74354	−0.467167
$436$	14.6084	0.699616
$437$	−45.2583	−2.16500
$438$	12.0586	0.576183
$439$	23.9236	1.14181	0.570906	−	0.821016i	$-0.306592\pi$
$439$	23.9236	1.14181	0.570906	+	0.821016i	$0.306592\pi$
$440$	−1.19512	−0.0569750
$441$	−14.7620	−0.702950
$442$	−19.1089	−0.908917
$443$	−14.5183	−0.689785	−0.344893	−	0.938642i	$-0.612085\pi$
$443$	−14.5183	−0.689785	−0.344893	+	0.938642i	$0.612085\pi$
$444$	−9.24186	−0.438599
$445$	−2.19357	−0.103985
$446$	13.9655	0.661286
$447$	−14.4763	−0.684707
$448$	1.79286	0.0847047
$449$	−13.9199	−0.656923	−0.328461	−	0.944517i	$-0.606530\pi$
$449$	−13.9199	−0.656923	−0.328461	+	0.944517i	$0.606530\pi$
$450$	16.6479	0.784791
$451$	10.3826	0.488895
$452$	−11.4365	−0.537928
$453$	24.7620	1.16342
$454$	−8.81918	−0.413905
$455$	7.03329	0.329726
$456$	18.4681	0.864846
$457$	34.2333	1.60137	0.800683	−	0.599088i	$-0.204470\pi$
$457$	34.2333	1.60137	0.800683	+	0.599088i	$0.204470\pi$
$458$	17.8260	0.832952
$459$	−9.83734	−0.459168
$460$	−5.50242	−0.256552
$461$	30.6217	1.42619	0.713097	−	0.701065i	$-0.247292\pi$
$461$	30.6217	1.42619	0.713097	+	0.701065i	$0.247292\pi$
$462$	6.58409	0.306320
$463$	2.79958	0.130107	0.0650537	−	0.997882i	$-0.479278\pi$
$463$	2.79958	0.130107	0.0650537	+	0.997882i	$0.479278\pi$
$464$	4.33951	0.201457
$465$	−7.28348	−0.337763
$466$	13.1809	0.610594
$467$	18.1898	0.841726	0.420863	−	0.907124i	$-0.361727\pi$
$467$	18.1898	0.841726	0.420863	+	0.907124i	$0.361727\pi$
$468$	17.8956	0.827224
$469$	5.72880	0.264532
$470$	−7.85522	−0.362334
$471$	38.4227	1.77042
$472$	−15.0144	−0.691093
$473$	7.59592	0.349261
$474$	33.8912	1.55667
$475$	−30.0172	−1.37728
$476$	7.46516	0.342165
$477$	52.0178	2.38173
$478$	−13.2733	−0.607107
$479$	11.2498	0.514014	0.257007	−	0.966409i	$-0.417264\pi$
$479$	11.2498	0.514014	0.257007	+	0.966409i	$0.417264\pi$
$480$	2.24531	0.102484
$481$	16.1471	0.736244
$482$	9.51088	0.433209
$483$	30.3137	1.37932
$484$	−9.04528	−0.411149
$485$	−11.8891	−0.539855
$486$	−21.5151	−0.975945
$487$	0.183892	0.00833294	0.00416647	−	0.999991i	$-0.498674\pi$
$487$	0.183892	0.00833294	0.00416647	+	0.999991i	$0.498674\pi$
$488$	10.2707	0.464933
$489$	3.08820	0.139653
$490$	3.23601	0.146188
$491$	−13.3053	−0.600461	−0.300230	−	0.953867i	$-0.597064\pi$
$491$	−13.3053	−0.600461	−0.300230	+	0.953867i	$0.597064\pi$
$492$	−19.5061	−0.879401
$493$	18.0690	0.813785
$494$	−32.2668	−1.45175
$495$	4.66031	0.209465
$496$	3.24386	0.145654
$497$	−9.32717	−0.418381
$498$	23.5404	1.05487
$499$	−12.7933	−0.572707	−0.286353	−	0.958124i	$-0.592443\pi$
$499$	−12.7933	−0.572707	−0.286353	+	0.958124i	$0.592443\pi$
$500$	−7.92348	−0.354349
$501$	−16.1141	−0.719923
$502$	25.2709	1.12789
$503$	30.8891	1.37728	0.688638	−	0.725105i	$-0.258209\pi$
$503$	30.8891	1.37728	0.688638	+	0.725105i	$0.258209\pi$
$504$	−6.99118	−0.311412
$505$	−15.9171	−0.708301
$506$	8.99967	0.400084
$507$	−21.1744	−0.940390
$508$	9.05839	0.401901
$509$	−1.90594	−0.0844795	−0.0422397	−	0.999108i	$-0.513449\pi$
$509$	−1.90594	−0.0844795	−0.0422397	+	0.999108i	$0.513449\pi$
$510$	9.34908	0.413984
$511$	8.23070	0.364105
$512$	−1.00000	−0.0441942
$513$	−16.6111	−0.733399
$514$	−0.815232	−0.0359583
$515$	−6.39279	−0.281700
$516$	−14.2707	−0.628234
$517$	12.8479	0.565049
$518$	−6.30810	−0.277162
$519$	−16.4197	−0.720745
$520$	−3.92294	−0.172032
$521$	−13.2261	−0.579445	−0.289722	−	0.957111i	$-0.593563\pi$
$521$	−13.2261	−0.579445	−0.289722	+	0.957111i	$0.593563\pi$
$522$	−16.9217	−0.740643
$523$	−15.3727	−0.672200	−0.336100	−	0.941826i	$-0.609108\pi$
$523$	−15.3727	−0.672200	−0.336100	+	0.941826i	$0.609108\pi$
$524$	−3.80330	−0.166148
$525$	20.1053	0.877468
$526$	25.4272	1.10868
$527$	13.5069	0.588369
$528$	−3.67239	−0.159820
$529$	18.4352	0.801530
$530$	−11.4030	−0.495313
$531$	58.5479	2.54076
$532$	12.6055	0.546518
$533$	34.0804	1.47619
$534$	−6.74045	−0.291688
$535$	13.7922	0.596288
$536$	−3.19534	−0.138018
$537$	9.61351	0.414853
$538$	18.1899	0.784223
$539$	−5.29276	−0.227975
$540$	−2.01955	−0.0869075
$541$	28.4009	1.22105	0.610525	−	0.791997i	$-0.290958\pi$
$541$	28.4009	1.22105	0.610525	+	0.791997i	$0.290958\pi$
$542$	9.42443	0.404814
$543$	45.5107	1.95305
$544$	−4.16383	−0.178523
$545$	12.4874	0.534901
$546$	21.6121	0.924911
$547$	34.5878	1.47887	0.739434	−	0.673229i	$-0.235093\pi$
$547$	34.5878	1.47887	0.739434	+	0.673229i	$0.235093\pi$
$548$	20.6547	0.882326
$549$	−40.0501	−1.70930
$550$	5.96896	0.254517
$551$	30.5109	1.29981
$552$	−16.9080	−0.719652
$553$	23.1327	0.983702
$554$	−22.4304	−0.952975
$555$	−7.90002	−0.335337
$556$	6.77841	0.287469
$557$	−24.9401	−1.05675	−0.528373	−	0.849012i	$-0.677198\pi$
$557$	−24.9401	−1.05675	−0.528373	+	0.849012i	$0.677198\pi$
$558$	−12.6493	−0.535487
$559$	24.9334	1.05457
$560$	1.53255	0.0647622
$561$	−15.2912	−0.645595
$562$	−9.63200	−0.406302
$563$	−26.1339	−1.10141	−0.550706	−	0.834699i	$-0.685642\pi$
$563$	−26.1339	−1.10141	−0.550706	+	0.834699i	$0.685642\pi$
$564$	−24.1378	−1.01638
$565$	−9.77603	−0.411280
$566$	18.2230	0.765969
$567$	−9.84753	−0.413557
$568$	5.20239	0.218288
$569$	−9.66767	−0.405290	−0.202645	−	0.979252i	$-0.564954\pi$
$569$	−9.66767	−0.405290	−0.202645	+	0.979252i	$0.564954\pi$
$570$	15.7867	0.661230
$571$	15.4616	0.647046	0.323523	−	0.946220i	$-0.395133\pi$
$571$	15.4616	0.647046	0.323523	+	0.946220i	$0.395133\pi$
$572$	6.41630	0.268279
$573$	−45.4102	−1.89704
$574$	−13.3140	−0.555716
$575$	27.4816	1.14606
$576$	3.89945	0.162477
$577$	26.6487	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$577$	26.6487	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$578$	−0.337458	−0.0140364
$579$	41.5641	1.72735
$580$	3.70945	0.154027
$581$	16.0677	0.666599
$582$	−36.5331	−1.51434
$583$	18.6505	0.772424
$584$	−4.59082	−0.189970
$585$	15.2973	0.632466
$586$	−11.5816	−0.478432
$587$	5.65942	0.233589	0.116795	−	0.993156i	$-0.462738\pi$
$587$	5.65942	0.233589	0.116795	+	0.993156i	$0.462738\pi$
$588$	9.94369	0.410071
$589$	22.8074	0.939763
$590$	−12.8344	−0.528385
$591$	31.7758	1.30708
$592$	3.51846	0.144608
$593$	18.9259	0.777195	0.388598	−	0.921408i	$-0.372960\pi$
$593$	18.9259	0.777195	0.388598	+	0.921408i	$0.372960\pi$
$594$	3.30314	0.135529
$595$	6.38129	0.261607
$596$	5.51127	0.225750
$597$	47.6956	1.95205
$598$	29.5411	1.20803
$599$	−6.03648	−0.246644	−0.123322	−	0.992367i	$-0.539355\pi$
$599$	−6.03648	−0.246644	−0.123322	+	0.992367i	$0.539355\pi$
$600$	−11.2141	−0.457813
$601$	13.7806	0.562122	0.281061	−	0.959690i	$-0.409314\pi$
$601$	13.7806	0.562122	0.281061	+	0.959690i	$0.409314\pi$
$602$	−9.74059	−0.396997
$603$	12.4601	0.507414
$604$	−9.42711	−0.383584
$605$	−7.73199	−0.314350
$606$	−48.9104	−1.98685
$607$	16.5217	0.670597	0.335298	−	0.942112i	$-0.391163\pi$
$607$	16.5217	0.670597	0.335298	+	0.942112i	$0.391163\pi$
$608$	−7.03095	−0.285143
$609$	−20.4359	−0.828106
$610$	8.77949	0.355471
$611$	42.1728	1.70613
$612$	16.2366	0.656327
$613$	−26.2590	−1.06059	−0.530295	−	0.847813i	$-0.677919\pi$
$613$	−26.2590	−1.06059	−0.530295	+	0.847813i	$0.677919\pi$
$614$	24.7384	0.998360
$615$	−16.6740	−0.672359
$616$	−2.50662	−0.100995
$617$	−32.8817	−1.32377	−0.661884	−	0.749607i	$-0.730243\pi$
$617$	−32.8817	−1.32377	−0.661884	+	0.749607i	$0.730243\pi$
$618$	−19.6440	−0.790196
$619$	−6.10571	−0.245409	−0.122705	−	0.992443i	$-0.539157\pi$
$619$	−6.10571	−0.245409	−0.122705	+	0.992443i	$0.539157\pi$
$620$	2.77288	0.111362
$621$	15.2079	0.610273
$622$	−19.6832	−0.789225
$623$	−4.60075	−0.184325
$624$	−12.0545	−0.482567
$625$	14.5734	0.582938
$626$	−26.9784	−1.07828
$627$	−25.8204	−1.03117
$628$	−14.6278	−0.583715
$629$	14.6502	0.584143
$630$	−5.97612	−0.238094
$631$	41.1629	1.63867	0.819335	−	0.573315i	$-0.194343\pi$
$631$	41.1629	1.63867	0.819335	+	0.573315i	$0.194343\pi$
$632$	−12.9027	−0.513241
$633$	25.4694	1.01232
$634$	−5.08898	−0.202109
$635$	7.74319	0.307279
$636$	−35.0393	−1.38940
$637$	−17.3733	−0.688356
$638$	−6.06712	−0.240200
$639$	−20.2865	−0.802521
$640$	−0.854809	−0.0337893
$641$	−32.4758	−1.28272	−0.641359	−	0.767241i	$-0.721629\pi$
$641$	−32.4758	−1.28272	−0.641359	+	0.767241i	$0.721629\pi$
$642$	42.3810	1.67265
$643$	20.5401	0.810022	0.405011	−	0.914312i	$-0.367268\pi$
$643$	20.5401	0.810022	0.405011	+	0.914312i	$0.367268\pi$
$644$	−11.5407	−0.454766
$645$	−12.1987	−0.480325
$646$	−29.2756	−1.15183
$647$	−30.1269	−1.18441	−0.592205	−	0.805787i	$-0.701742\pi$
$647$	−30.1269	−1.18441	−0.592205	+	0.805787i	$0.701742\pi$
$648$	5.49263	0.215771
$649$	20.9918	0.824000
$650$	19.5929	0.768498
$651$	−15.2762	−0.598723
$652$	−1.17571	−0.0460442
$653$	42.0664	1.64619	0.823093	−	0.567906i	$-0.192246\pi$
$653$	42.0664	1.64619	0.823093	+	0.567906i	$0.192246\pi$
$654$	38.3716	1.50045
$655$	−3.25110	−0.127031
$656$	7.42613	0.289942
$657$	17.9017	0.698411
$658$	−16.4754	−0.642278
$659$	−8.63696	−0.336448	−0.168224	−	0.985749i	$-0.553803\pi$
$659$	−8.63696	−0.336448	−0.168224	+	0.985749i	$0.553803\pi$
$660$	−3.13919	−0.122193
$661$	−46.9973	−1.82798	−0.913992	−	0.405733i	$-0.867016\pi$
$661$	−46.9973	−1.82798	−0.913992	+	0.405733i	$0.867016\pi$
$662$	17.9887	0.699151
$663$	−50.1929	−1.94933
$664$	−8.96203	−0.347794
$665$	10.7753	0.417848
$666$	−13.7200	−0.531641
$667$	−27.9335	−1.08159
$668$	6.13476	0.237361
$669$	36.6829	1.41824
$670$	−2.73141	−0.105523
$671$	−14.3596	−0.554346
$672$	4.70927	0.181664
$673$	−5.05267	−0.194766	−0.0973830	−	0.995247i	$-0.531047\pi$
$673$	−5.05267	−0.194766	−0.0973830	+	0.995247i	$0.531047\pi$
$674$	12.0506	0.464171
$675$	10.0865	0.388231
$676$	8.06129	0.310050
$677$	−8.93098	−0.343246	−0.171623	−	0.985163i	$-0.554901\pi$
$677$	−8.93098	−0.343246	−0.171623	+	0.985163i	$0.554901\pi$
$678$	−30.0400	−1.15368
$679$	−24.9359	−0.956953
$680$	−3.55928	−0.136492
$681$	−23.1652	−0.887691
$682$	−4.53528	−0.173665
$683$	26.7911	1.02513	0.512566	−	0.858648i	$-0.328695\pi$
$683$	26.7911	1.02513	0.512566	+	0.858648i	$0.328695\pi$
$684$	27.4168	1.04831
$685$	17.6558	0.674595
$686$	19.3372	0.738297
$687$	46.8231	1.78641
$688$	5.43299	0.207131
$689$	61.2196	2.33228
$690$	−14.4531	−0.550220
$691$	31.2062	1.18714	0.593571	−	0.804782i	$-0.297718\pi$
$691$	31.2062	1.18714	0.593571	+	0.804782i	$0.297718\pi$
$692$	6.25113	0.237632
$693$	9.77444	0.371300
$694$	−4.32749	−0.164269
$695$	5.79425	0.219788
$696$	11.3985	0.432059
$697$	30.9211	1.17122
$698$	−7.97325	−0.301792
$699$	34.6221	1.30953
$700$	−7.65426	−0.289304
$701$	−29.3651	−1.10910	−0.554552	−	0.832149i	$-0.687110\pi$
$701$	−29.3651	−1.10910	−0.554552	+	0.832149i	$0.687110\pi$
$702$	10.8425	0.409222
$703$	24.7381	0.933014
$704$	1.39811	0.0526933
$705$	−20.6332	−0.777090
$706$	−8.60601	−0.323892
$707$	−33.3842	−1.25554
$708$	−39.4380	−1.48217
$709$	19.6656	0.738558	0.369279	−	0.929319i	$-0.379605\pi$
$709$	19.6656	0.738558	0.369279	+	0.929319i	$0.379605\pi$
$710$	4.44705	0.166895
$711$	50.3133	1.88690
$712$	2.56615	0.0961704
$713$	−20.8808	−0.781992
$714$	19.6086	0.733833
$715$	5.48471	0.205116
$716$	−3.65995	−0.136779
$717$	−34.8647	−1.30205
$718$	11.4828	0.428535
$719$	−4.74756	−0.177054	−0.0885271	−	0.996074i	$-0.528216\pi$
$719$	−4.74756	−0.177054	−0.0885271	+	0.996074i	$0.528216\pi$
$720$	3.33329	0.124224
$721$	−13.4081	−0.499345
$722$	−30.4342	−1.13264
$723$	24.9820	0.929092
$724$	−17.3263	−0.643928
$725$	−18.5267	−0.688063
$726$	−23.7591	−0.881782
$727$	−3.26857	−0.121224	−0.0606122	−	0.998161i	$-0.519305\pi$
$727$	−3.26857	−0.121224	−0.0606122	+	0.998161i	$0.519305\pi$
$728$	−8.22790	−0.304946
$729$	−40.0354	−1.48279
$730$	−3.92427	−0.145244
$731$	22.6220	0.836706
$732$	26.9779	0.997130
$733$	−17.7987	−0.657411	−0.328706	−	0.944432i	$-0.606612\pi$
$733$	−17.7987	−0.657411	−0.328706	+	0.944432i	$0.606612\pi$
$734$	26.0578	0.961813
$735$	8.49996	0.313526
$736$	6.43702	0.237272
$737$	4.46745	0.164560
$738$	−28.9578	−1.06595
$739$	22.1082	0.813262	0.406631	−	0.913593i	$-0.366704\pi$
$739$	22.1082	0.813262	0.406631	+	0.913593i	$0.366704\pi$
$740$	3.00761	0.110562
$741$	−84.7547	−3.11354
$742$	−23.9163	−0.877997
$743$	36.2103	1.32843	0.664214	−	0.747543i	$-0.268766\pi$
$743$	36.2103	1.32843	0.664214	+	0.747543i	$0.268766\pi$
$744$	8.52059	0.312380
$745$	4.71108	0.172601
$746$	28.1289	1.02987
$747$	34.9470	1.27864
$748$	5.82150	0.212855
$749$	28.9275	1.05699
$750$	−20.8125	−0.759964
$751$	31.6501	1.15493	0.577465	−	0.816416i	$-0.304042\pi$
$751$	31.6501	1.15493	0.577465	+	0.816416i	$0.304042\pi$
$752$	9.18945	0.335105
$753$	66.3785	2.41897
$754$	−19.9151	−0.725266
$755$	−8.05838	−0.293274
$756$	−4.23576	−0.154053
$757$	32.2734	1.17300	0.586499	−	0.809950i	$-0.300506\pi$
$757$	32.2734	1.17300	0.586499	+	0.809950i	$0.300506\pi$
$758$	21.9273	0.796434
$759$	23.6393	0.858051
$760$	−6.01012	−0.218010
$761$	0.674180	0.0244390	0.0122195	−	0.999925i	$-0.496110\pi$
$761$	0.674180	0.0244390	0.0122195	+	0.999925i	$0.496110\pi$
$762$	23.7935	0.861948
$763$	26.1909	0.948172
$764$	17.2881	0.625460
$765$	13.8792	0.501805
$766$	18.4116	0.665239
$767$	68.9049	2.48801
$768$	−2.62668	−0.0947822
$769$	20.2062	0.728653	0.364326	−	0.931271i	$-0.381299\pi$
$769$	20.2062	0.728653	0.364326	+	0.931271i	$0.381299\pi$
$770$	−2.14268	−0.0772169
$771$	−2.14135	−0.0771190
$772$	−15.8238	−0.569512
$773$	−40.8794	−1.47033	−0.735165	−	0.677888i	$-0.762895\pi$
$773$	−40.8794	−1.47033	−0.735165	+	0.677888i	$0.762895\pi$
$774$	−21.1857	−0.761503
$775$	−13.8490	−0.497472
$776$	13.9084	0.499284
$777$	−16.5694	−0.594423
$778$	14.2023	0.509178
$779$	52.2127	1.87071
$780$	−10.3043	−0.368953
$781$	−7.27353	−0.260267
$782$	26.8026	0.958460
$783$	−10.2524	−0.366391
$784$	−3.78565	−0.135202
$785$	−12.5040	−0.446287
$786$	−9.99006	−0.356334
$787$	−0.586423	−0.0209037	−0.0104519	−	0.999945i	$-0.503327\pi$
$787$	−0.586423	−0.0209037	−0.0104519	+	0.999945i	$0.503327\pi$
$788$	−12.0973	−0.430950
$789$	66.7891	2.37776
$790$	−11.0293	−0.392406
$791$	−20.5041	−0.729040
$792$	−5.45187	−0.193724
$793$	−47.1349	−1.67381
$794$	−12.4757	−0.442748
$795$	−29.9519	−1.06229
$796$	−18.1581	−0.643598
$797$	40.4574	1.43307	0.716537	−	0.697549i	$-0.245726\pi$
$797$	40.4574	1.43307	0.716537	+	0.697549i	$0.245726\pi$
$798$	33.1106	1.17210
$799$	38.2633	1.35366
$800$	4.26930	0.150943
$801$	−10.0066	−0.353565
$802$	14.5417	0.513484
$803$	6.41848	0.226503
$804$	−8.39314	−0.296003
$805$	−9.86508	−0.347698
$806$	−14.8869	−0.524369
$807$	47.7791	1.68190
$808$	18.6206	0.655071
$809$	26.7279	0.939704	0.469852	−	0.882745i	$-0.344307\pi$
$809$	26.7279	0.939704	0.469852	+	0.882745i	$0.344307\pi$
$810$	4.69515	0.164971
$811$	−16.8999	−0.593435	−0.296717	−	0.954965i	$-0.595892\pi$
$811$	−16.8999	−0.593435	−0.296717	+	0.954965i	$0.595892\pi$
$812$	7.78014	0.273029
$813$	24.7550	0.868195
$814$	−4.91919	−0.172418
$815$	−1.00500	−0.0352038
$816$	−10.9370	−0.382873
$817$	38.1990	1.33642
$818$	33.6657	1.17709
$819$	32.0843	1.12112
$820$	6.34792	0.221679
$821$	−52.8740	−1.84532	−0.922658	−	0.385620i	$-0.873988\pi$
$821$	−52.8740	−1.84532	−0.922658	+	0.385620i	$0.873988\pi$
$822$	54.2534	1.89230
$823$	41.6115	1.45049	0.725243	−	0.688493i	$-0.241727\pi$
$823$	41.6115	1.45049	0.725243	+	0.688493i	$0.241727\pi$
$824$	7.47862	0.260530
$825$	15.6786	0.545857
$826$	−26.9187	−0.936622
$827$	−48.2422	−1.67754	−0.838772	−	0.544483i	$-0.816726\pi$
$827$	−48.2422	−1.67754	−0.838772	+	0.544483i	$0.816726\pi$
$828$	−25.1008	−0.872314
$829$	27.6293	0.959605	0.479802	−	0.877377i	$-0.340708\pi$
$829$	27.6293	0.959605	0.479802	+	0.877377i	$0.340708\pi$
$830$	−7.66082	−0.265911
$831$	−58.9174	−2.04382
$832$	4.58926	0.159104
$833$	−15.7628	−0.546148
$834$	17.8047	0.616527
$835$	5.24405	0.181478
$836$	9.83005	0.339979
$837$	−7.66386	−0.264902
$838$	−14.6756	−0.506962
$839$	38.7610	1.33818	0.669090	−	0.743182i	$-0.266684\pi$
$839$	38.7610	1.33818	0.669090	+	0.743182i	$0.266684\pi$
$840$	4.02553	0.138894
$841$	−10.1687	−0.350643
$842$	−8.02186	−0.276452
$843$	−25.3002	−0.871385
$844$	−9.69641	−0.333764
$845$	6.89087	0.237053
$846$	−35.8338	−1.23199
$847$	−16.2169	−0.557221
$848$	13.3398	0.458090
$849$	47.8659	1.64275
$850$	17.7766	0.609734
$851$	−22.6484	−0.776376
$852$	13.6650	0.468156
$853$	26.2095	0.897397	0.448698	−	0.893683i	$-0.351888\pi$
$853$	26.2095	0.897397	0.448698	+	0.893683i	$0.351888\pi$
$854$	18.4139	0.630112
$855$	23.4362	0.801500
$856$	−16.1348	−0.551477
$857$	−18.9087	−0.645908	−0.322954	−	0.946415i	$-0.604676\pi$
$857$	−18.9087	−0.645908	−0.322954	+	0.946415i	$0.604676\pi$
$858$	16.8536	0.575371
$859$	−44.9505	−1.53369	−0.766845	−	0.641832i	$-0.778175\pi$
$859$	−44.9505	−1.53369	−0.766845	+	0.641832i	$0.778175\pi$
$860$	4.64417	0.158365
$861$	−34.9717	−1.19183
$862$	7.96699	0.271357
$863$	13.5828	0.462362	0.231181	−	0.972911i	$-0.425741\pi$
$863$	13.5828	0.462362	0.231181	+	0.972911i	$0.425741\pi$
$864$	2.36257	0.0803763
$865$	5.34352	0.181685
$866$	−11.7495	−0.399266
$867$	−0.886394	−0.0301035
$868$	5.81579	0.197401
$869$	18.0394	0.611944
$870$	9.74354	0.330337
$871$	14.6643	0.496879
$872$	−14.6084	−0.494703
$873$	−54.2353	−1.83559
$874$	45.2583	1.53089
$875$	−14.2057	−0.480240
$876$	−12.0586	−0.407423
$877$	−21.6707	−0.731767	−0.365883	−	0.930661i	$-0.619233\pi$
$877$	−21.6707	−0.731767	−0.365883	+	0.930661i	$0.619233\pi$
$878$	−23.9236	−0.807382
$879$	−30.4212	−1.02608
$880$	1.19512	0.0402874
$881$	−51.9407	−1.74993	−0.874963	−	0.484190i	$-0.839114\pi$
$881$	−51.9407	−1.74993	−0.874963	+	0.484190i	$0.839114\pi$
$882$	14.7620	0.497061
$883$	−8.02180	−0.269955	−0.134978	−	0.990849i	$-0.543096\pi$
$883$	−8.02180	−0.269955	−0.134978	+	0.990849i	$0.543096\pi$
$884$	19.1089	0.642701
$885$	−33.7120	−1.13321
$886$	14.5183	0.487752
$887$	53.2708	1.78866	0.894330	−	0.447408i	$-0.147653\pi$
$887$	53.2708	1.78866	0.894330	+	0.447408i	$0.147653\pi$
$888$	9.24186	0.310136
$889$	16.2404	0.544687
$890$	2.19357	0.0735285
$891$	−7.67931	−0.257267
$892$	−13.9655	−0.467600
$893$	64.6105	2.16211
$894$	14.4763	0.484161
$895$	−3.12855	−0.104576
$896$	−1.79286	−0.0598953
$897$	77.5951	2.59083
$898$	13.9199	0.464515
$899$	14.0768	0.469486
$900$	−16.6479	−0.554931
$901$	55.5445	1.85046
$902$	−10.3826	−0.345701
$903$	−25.5854	−0.851430
$904$	11.4365	0.380372
$905$	−14.8107	−0.492324
$906$	−24.7620	−0.822663
$907$	35.1878	1.16839	0.584196	−	0.811613i	$-0.301410\pi$
$907$	35.1878	1.16839	0.584196	+	0.811613i	$0.301410\pi$
$908$	8.81918	0.292675
$909$	−72.6102	−2.40833
$910$	−7.03329	−0.233151
$911$	26.9190	0.891867	0.445934	−	0.895066i	$-0.352872\pi$
$911$	26.9190	0.891867	0.445934	+	0.895066i	$0.352872\pi$
$912$	−18.4681	−0.611538
$913$	12.5299	0.414680
$914$	−34.2333	−1.13234
$915$	23.0609	0.762370
$916$	−17.8260	−0.588986
$917$	−6.81879	−0.225176
$918$	9.83734	0.324681
$919$	−18.4655	−0.609121	−0.304560	−	0.952493i	$-0.598510\pi$
$919$	−18.4655	−0.609121	−0.304560	+	0.952493i	$0.598510\pi$
$920$	5.50242	0.181409
$921$	64.9799	2.14116
$922$	−30.6217	−1.00847
$923$	−23.8751	−0.785859
$924$	−6.58409	−0.216601
$925$	−15.0213	−0.493899
$926$	−2.79958	−0.0919998
$927$	−29.1625	−0.957823
$928$	−4.33951	−0.142451
$929$	−7.28308	−0.238950	−0.119475	−	0.992837i	$-0.538121\pi$
$929$	−7.28308	−0.238950	−0.119475	+	0.992837i	$0.538121\pi$
$930$	7.28348	0.238835
$931$	−26.6167	−0.872327
$932$	−13.1809	−0.431755
$933$	−51.7015	−1.69263
$934$	−18.1898	−0.595190
$935$	4.97627	0.162741
$936$	−17.8956	−0.584936
$937$	−39.8225	−1.30095	−0.650473	−	0.759529i	$-0.725429\pi$
$937$	−39.8225	−1.30095	−0.650473	+	0.759529i	$0.725429\pi$
$938$	−5.72880	−0.187052
$939$	−70.8638	−2.31255
$940$	7.85522	0.256209
$941$	−56.7318	−1.84940	−0.924702	−	0.380692i	$-0.875686\pi$
$941$	−56.7318	−1.84940	−0.924702	+	0.380692i	$0.875686\pi$
$942$	−38.4227	−1.25188
$943$	−47.8021	−1.55665
$944$	15.0144	0.488677
$945$	−3.62077	−0.117784
$946$	−7.59592	−0.246965
$947$	9.83411	0.319566	0.159783	−	0.987152i	$-0.448921\pi$
$947$	9.83411	0.319566	0.159783	+	0.987152i	$0.448921\pi$
$948$	−33.8912	−1.10073
$949$	21.0685	0.683911
$950$	30.0172	0.973888
$951$	−13.3671	−0.433459
$952$	−7.46516	−0.241947
$953$	46.4862	1.50584	0.752918	−	0.658114i	$-0.228646\pi$
$953$	46.4862	1.50584	0.752918	+	0.658114i	$0.228646\pi$
$954$	−52.0178	−1.68414
$955$	14.7780	0.478204
$956$	13.2733	0.429289
$957$	−15.9364	−0.515150
$958$	−11.2498	−0.363463
$959$	37.0311	1.19580
$960$	−2.24531	−0.0724671
$961$	−20.4774	−0.660560
$962$	−16.1471	−0.520603
$963$	62.9170	2.02747
$964$	−9.51088	−0.306325
$965$	−13.5263	−0.435429
$966$	−30.3137	−0.975327
$967$	−43.1669	−1.38816	−0.694078	−	0.719900i	$-0.744188\pi$
$967$	−43.1669	−1.38816	−0.694078	+	0.719900i	$0.744188\pi$
$968$	9.04528	0.290726
$969$	−76.8978	−2.47031
$970$	11.8891	0.381735
$971$	−21.1048	−0.677287	−0.338643	−	0.940915i	$-0.609968\pi$
$971$	−21.1048	−0.677287	−0.338643	+	0.940915i	$0.609968\pi$
$972$	21.5151	0.690097
$973$	12.1527	0.389599
$974$	−0.183892	−0.00589228
$975$	51.4644	1.64818
$976$	−10.2707	−0.328757
$977$	−55.5374	−1.77680	−0.888400	−	0.459070i	$-0.848183\pi$
$977$	−55.5374	−1.77680	−0.888400	+	0.459070i	$0.848183\pi$
$978$	−3.08820	−0.0987499
$979$	−3.58776	−0.114665
$980$	−3.23601	−0.103370
$981$	56.9648	1.81875
$982$	13.3053	0.424590
$983$	16.7990	0.535803	0.267902	−	0.963446i	$-0.413670\pi$
$983$	16.7990	0.535803	0.267902	+	0.963446i	$0.413670\pi$
$984$	19.5061	0.621831
$985$	−10.3409	−0.329489
$986$	−18.0690	−0.575433
$987$	−43.2756	−1.37748
$988$	32.2668	1.02654
$989$	−34.9722	−1.11205
$990$	−4.66031	−0.148114
$991$	36.2646	1.15198	0.575991	−	0.817456i	$-0.304616\pi$
$991$	36.2646	1.15198	0.575991	+	0.817456i	$0.304616\pi$
$992$	−3.24386	−0.102993
$993$	47.2506	1.49945
$994$	9.32717	0.295840
$995$	−15.5217	−0.492072
$996$	−23.5404	−0.745906
$997$	35.8129	1.13420	0.567102	−	0.823647i	$-0.308064\pi$
$997$	35.8129	1.13420	0.567102	+	0.823647i	$0.308064\pi$
$998$	12.7933	0.404965
$999$	−8.31261	−0.262999

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.e.1.7	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.e.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.62668 q^{3} +1.00000 q^{4} +0.854809 q^{5} +2.62668 q^{6} +1.79286 q^{7} -1.00000 q^{8} +3.89945 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.62668 q^{3} +1.00000 q^{4} +0.854809 q^{5} +2.62668 q^{6} +1.79286 q^{7} -1.00000 q^{8} +3.89945 q^{9} -0.854809 q^{10} +1.39811 q^{11} -2.62668 q^{12} +4.58926 q^{13} -1.79286 q^{14} -2.24531 q^{15} +1.00000 q^{16} +4.16383 q^{17} -3.89945 q^{18} +7.03095 q^{19} +0.854809 q^{20} -4.70927 q^{21} -1.39811 q^{22} -6.43702 q^{23} +2.62668 q^{24} -4.26930 q^{25} -4.58926 q^{26} -2.36257 q^{27} +1.79286 q^{28} +4.33951 q^{29} +2.24531 q^{30} +3.24386 q^{31} -1.00000 q^{32} -3.67239 q^{33} -4.16383 q^{34} +1.53255 q^{35} +3.89945 q^{36} +3.51846 q^{37} -7.03095 q^{38} -12.0545 q^{39} -0.854809 q^{40} +7.42613 q^{41} +4.70927 q^{42} +5.43299 q^{43} +1.39811 q^{44} +3.33329 q^{45} +6.43702 q^{46} +9.18945 q^{47} -2.62668 q^{48} -3.78565 q^{49} +4.26930 q^{50} -10.9370 q^{51} +4.58926 q^{52} +13.3398 q^{53} +2.36257 q^{54} +1.19512 q^{55} -1.79286 q^{56} -18.4681 q^{57} -4.33951 q^{58} +15.0144 q^{59} -2.24531 q^{60} -10.2707 q^{61} -3.24386 q^{62} +6.99118 q^{63} +1.00000 q^{64} +3.92294 q^{65} +3.67239 q^{66} +3.19534 q^{67} +4.16383 q^{68} +16.9080 q^{69} -1.53255 q^{70} -5.20239 q^{71} -3.89945 q^{72} +4.59082 q^{73} -3.51846 q^{74} +11.2141 q^{75} +7.03095 q^{76} +2.50662 q^{77} +12.0545 q^{78} +12.9027 q^{79} +0.854809 q^{80} -5.49263 q^{81} -7.42613 q^{82} +8.96203 q^{83} -4.70927 q^{84} +3.55928 q^{85} -5.43299 q^{86} -11.3985 q^{87} -1.39811 q^{88} -2.56615 q^{89} -3.33329 q^{90} +8.22790 q^{91} -6.43702 q^{92} -8.52059 q^{93} -9.18945 q^{94} +6.01012 q^{95} +2.62668 q^{96} -13.9084 q^{97} +3.78565 q^{98} +5.45187 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) 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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