LMFDB - Embedded newform 8014.2.a.d.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8014,2,Mod(1,8014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8014, 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("8014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8014 = 2 \cdot 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8014.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:	$63.9921121799$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.85388 q^{3} +1.00000 q^{4} +2.67388 q^{5} -2.85388 q^{6} -3.36481 q^{7} +1.00000 q^{8} +5.14465 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.85388 q^{3} +1.00000 q^{4} +2.67388 q^{5} -2.85388 q^{6} -3.36481 q^{7} +1.00000 q^{8} +5.14465 q^{9} +2.67388 q^{10} +4.50027 q^{11} -2.85388 q^{12} +1.97898 q^{13} -3.36481 q^{14} -7.63093 q^{15} +1.00000 q^{16} -1.53307 q^{17} +5.14465 q^{18} +6.89648 q^{19} +2.67388 q^{20} +9.60279 q^{21} +4.50027 q^{22} +7.08504 q^{23} -2.85388 q^{24} +2.14961 q^{25} +1.97898 q^{26} -6.12058 q^{27} -3.36481 q^{28} +4.81953 q^{29} -7.63093 q^{30} +3.11028 q^{31} +1.00000 q^{32} -12.8432 q^{33} -1.53307 q^{34} -8.99710 q^{35} +5.14465 q^{36} -9.98092 q^{37} +6.89648 q^{38} -5.64778 q^{39} +2.67388 q^{40} +4.60874 q^{41} +9.60279 q^{42} +6.09350 q^{43} +4.50027 q^{44} +13.7562 q^{45} +7.08504 q^{46} -3.54032 q^{47} -2.85388 q^{48} +4.32198 q^{49} +2.14961 q^{50} +4.37520 q^{51} +1.97898 q^{52} -10.6675 q^{53} -6.12058 q^{54} +12.0332 q^{55} -3.36481 q^{56} -19.6817 q^{57} +4.81953 q^{58} +6.14507 q^{59} -7.63093 q^{60} +5.50936 q^{61} +3.11028 q^{62} -17.3108 q^{63} +1.00000 q^{64} +5.29155 q^{65} -12.8432 q^{66} +2.00982 q^{67} -1.53307 q^{68} -20.2199 q^{69} -8.99710 q^{70} +8.43901 q^{71} +5.14465 q^{72} -11.0364 q^{73} -9.98092 q^{74} -6.13474 q^{75} +6.89648 q^{76} -15.1426 q^{77} -5.64778 q^{78} -1.74334 q^{79} +2.67388 q^{80} +2.03347 q^{81} +4.60874 q^{82} -1.12983 q^{83} +9.60279 q^{84} -4.09924 q^{85} +6.09350 q^{86} -13.7544 q^{87} +4.50027 q^{88} -12.5329 q^{89} +13.7562 q^{90} -6.65891 q^{91} +7.08504 q^{92} -8.87639 q^{93} -3.54032 q^{94} +18.4403 q^{95} -2.85388 q^{96} +4.36230 q^{97} +4.32198 q^{98} +23.1523 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9}+O(q^{10}) $ 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9	\( 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9} + 25 q^{10} + 70 q^{11} + 22 q^{12} + 31 q^{13} + 33 q^{14} + 47 q^{15} + 88 q^{16} + 19 q^{17} + 108 q^{18} + 33 q^{19} + 25 q^{20} + 48 q^{21} + 70 q^{22} + 77 q^{23} + 22 q^{24} + 109 q^{25} + 31 q^{26} + 88 q^{27} + 33 q^{28} + 83 q^{29} + 47 q^{30} + 51 q^{31} + 88 q^{32} + 30 q^{33} + 19 q^{34} + 40 q^{35} + 108 q^{36} + 45 q^{37} + 33 q^{38} + 82 q^{39} + 25 q^{40} + 35 q^{41} + 48 q^{42} + 78 q^{43} + 70 q^{44} + 37 q^{45} + 77 q^{46} + 59 q^{47} + 22 q^{48} + 103 q^{49} + 109 q^{50} + 21 q^{51} + 31 q^{52} + 58 q^{53} + 88 q^{54} + 35 q^{55} + 33 q^{56} - 16 q^{57} + 83 q^{58} + 54 q^{59} + 47 q^{60} + 18 q^{61} + 51 q^{62} + 47 q^{63} + 88 q^{64} + 34 q^{65} + 30 q^{66} + 88 q^{67} + 19 q^{68} + 62 q^{69} + 40 q^{70} + 139 q^{71} + 108 q^{72} - 6 q^{73} + 45 q^{74} + 45 q^{75} + 33 q^{76} + 37 q^{77} + 82 q^{78} + 94 q^{79} + 25 q^{80} + 112 q^{81} + 35 q^{82} + 58 q^{83} + 48 q^{84} + 83 q^{85} + 78 q^{86} + 21 q^{87} + 70 q^{88} + 99 q^{89} + 37 q^{90} + 53 q^{91} + 77 q^{92} + 57 q^{93} + 59 q^{94} + 92 q^{95} + 22 q^{96} + 16 q^{97} + 103 q^{98} + 150 q^{99}+O(q^{100}) \) 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9 + 25 * q^10 + 70 * q^11 + 22 * q^12 + 31 * q^13 + 33 * q^14 + 47 * q^15 + 88 * q^16 + 19 * q^17 + 108 * q^18 + 33 * q^19 + 25 * q^20 + 48 * q^21 + 70 * q^22 + 77 * q^23 + 22 * q^24 + 109 * q^25 + 31 * q^26 + 88 * q^27 + 33 * q^28 + 83 * q^29 + 47 * q^30 + 51 * q^31 + 88 * q^32 + 30 * q^33 + 19 * q^34 + 40 * q^35 + 108 * q^36 + 45 * q^37 + 33 * q^38 + 82 * q^39 + 25 * q^40 + 35 * q^41 + 48 * q^42 + 78 * q^43 + 70 * q^44 + 37 * q^45 + 77 * q^46 + 59 * q^47 + 22 * q^48 + 103 * q^49 + 109 * q^50 + 21 * q^51 + 31 * q^52 + 58 * q^53 + 88 * q^54 + 35 * q^55 + 33 * q^56 - 16 * q^57 + 83 * q^58 + 54 * q^59 + 47 * q^60 + 18 * q^61 + 51 * q^62 + 47 * q^63 + 88 * q^64 + 34 * q^65 + 30 * q^66 + 88 * q^67 + 19 * q^68 + 62 * q^69 + 40 * q^70 + 139 * q^71 + 108 * q^72 - 6 * q^73 + 45 * q^74 + 45 * q^75 + 33 * q^76 + 37 * q^77 + 82 * q^78 + 94 * q^79 + 25 * q^80 + 112 * q^81 + 35 * q^82 + 58 * q^83 + 48 * q^84 + 83 * q^85 + 78 * q^86 + 21 * q^87 + 70 * q^88 + 99 * q^89 + 37 * q^90 + 53 * q^91 + 77 * q^92 + 57 * q^93 + 59 * q^94 + 92 * q^95 + 22 * q^96 + 16 * q^97 + 103 * q^98 + 150 * 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
$3$	−2.85388	−1.64769	−0.823845	−	0.566815i	$-0.808175\pi$
$3$	−2.85388	−1.64769	−0.823845	+	0.566815i	$0.808175\pi$
$4$	1.00000	0.500000
$5$	2.67388	1.19579	0.597897	−	0.801573i	$-0.296003\pi$
$5$	2.67388	1.19579	0.597897	+	0.801573i	$0.296003\pi$
$6$	−2.85388	−1.16509
$7$	−3.36481	−1.27178	−0.635890	−	0.771780i	$-0.719367\pi$
$7$	−3.36481	−1.27178	−0.635890	+	0.771780i	$0.719367\pi$
$8$	1.00000	0.353553
$9$	5.14465	1.71488
$10$	2.67388	0.845554
$11$	4.50027	1.35688	0.678441	−	0.734655i	$-0.262656\pi$
$11$	4.50027	1.35688	0.678441	+	0.734655i	$0.262656\pi$
$12$	−2.85388	−0.823845
$13$	1.97898	0.548871	0.274435	−	0.961606i	$-0.411509\pi$
$13$	1.97898	0.548871	0.274435	+	0.961606i	$0.411509\pi$
$14$	−3.36481	−0.899284
$15$	−7.63093	−1.97030
$16$	1.00000	0.250000
$17$	−1.53307	−0.371824	−0.185912	−	0.982566i	$-0.559524\pi$
$17$	−1.53307	−0.371824	−0.185912	+	0.982566i	$0.559524\pi$
$18$	5.14465	1.21261
$19$	6.89648	1.58216	0.791081	−	0.611712i	$-0.209519\pi$
$19$	6.89648	1.58216	0.791081	+	0.611712i	$0.209519\pi$
$20$	2.67388	0.597897
$21$	9.60279	2.09550
$22$	4.50027	0.959461
$23$	7.08504	1.47733	0.738666	−	0.674072i	$-0.235456\pi$
$23$	7.08504	1.47733	0.738666	+	0.674072i	$0.235456\pi$
$24$	−2.85388	−0.582546
$25$	2.14961	0.429922
$26$	1.97898	0.388110
$27$	−6.12058	−1.17791
$28$	−3.36481	−0.635890
$29$	4.81953	0.894964	0.447482	−	0.894293i	$-0.352321\pi$
$29$	4.81953	0.894964	0.447482	+	0.894293i	$0.352321\pi$
$30$	−7.63093	−1.39321
$31$	3.11028	0.558624	0.279312	−	0.960200i	$-0.409894\pi$
$31$	3.11028	0.558624	0.279312	+	0.960200i	$0.409894\pi$
$32$	1.00000	0.176777
$33$	−12.8432	−2.23572
$34$	−1.53307	−0.262919
$35$	−8.99710	−1.52079
$36$	5.14465	0.857442
$37$	−9.98092	−1.64085	−0.820426	−	0.571752i	$-0.806264\pi$
$37$	−9.98092	−1.64085	−0.820426	+	0.571752i	$0.806264\pi$
$38$	6.89648	1.11876
$39$	−5.64778	−0.904369
$40$	2.67388	0.422777
$41$	4.60874	0.719764	0.359882	−	0.932998i	$-0.382817\pi$
$41$	4.60874	0.719764	0.359882	+	0.932998i	$0.382817\pi$
$42$	9.60279	1.48174
$43$	6.09350	0.929250	0.464625	−	0.885508i	$-0.346189\pi$
$43$	6.09350	0.929250	0.464625	+	0.885508i	$0.346189\pi$
$44$	4.50027	0.678441
$45$	13.7562	2.05065
$46$	7.08504	1.04463
$47$	−3.54032	−0.516409	−0.258204	−	0.966090i	$-0.583131\pi$
$47$	−3.54032	−0.516409	−0.258204	+	0.966090i	$0.583131\pi$
$48$	−2.85388	−0.411923
$49$	4.32198	0.617425
$50$	2.14961	0.304001
$51$	4.37520	0.612651
$52$	1.97898	0.274435
$53$	−10.6675	−1.46530	−0.732650	−	0.680606i	$-0.761717\pi$
$53$	−10.6675	−1.46530	−0.732650	+	0.680606i	$0.761717\pi$
$54$	−6.12058	−0.832905
$55$	12.0332	1.62255
$56$	−3.36481	−0.449642
$57$	−19.6817	−2.60691
$58$	4.81953	0.632835
$59$	6.14507	0.800021	0.400010	−	0.916511i	$-0.369007\pi$
$59$	6.14507	0.800021	0.400010	+	0.916511i	$0.369007\pi$
$60$	−7.63093	−0.985149
$61$	5.50936	0.705401	0.352701	−	0.935736i	$-0.385263\pi$
$61$	5.50936	0.705401	0.352701	+	0.935736i	$0.385263\pi$
$62$	3.11028	0.395006
$63$	−17.3108	−2.18095
$64$	1.00000	0.125000
$65$	5.29155	0.656336
$66$	−12.8432	−1.58089
$67$	2.00982	0.245538	0.122769	−	0.992435i	$-0.460823\pi$
$67$	2.00982	0.245538	0.122769	+	0.992435i	$0.460823\pi$
$68$	−1.53307	−0.185912
$69$	−20.2199	−2.43419
$70$	−8.99710	−1.07536
$71$	8.43901	1.00153	0.500763	−	0.865584i	$-0.333053\pi$
$71$	8.43901	1.00153	0.500763	+	0.865584i	$0.333053\pi$
$72$	5.14465	0.606303
$73$	−11.0364	−1.29171	−0.645857	−	0.763458i	$-0.723500\pi$
$73$	−11.0364	−1.29171	−0.645857	+	0.763458i	$0.723500\pi$
$74$	−9.98092	−1.16026
$75$	−6.13474	−0.708379
$76$	6.89648	0.791081
$77$	−15.1426	−1.72566
$78$	−5.64778	−0.639486
$79$	−1.74334	−0.196141	−0.0980705	−	0.995179i	$-0.531267\pi$
$79$	−1.74334	−0.196141	−0.0980705	+	0.995179i	$0.531267\pi$
$80$	2.67388	0.298948
$81$	2.03347	0.225941
$82$	4.60874	0.508950
$83$	−1.12983	−0.124015	−0.0620077	−	0.998076i	$-0.519750\pi$
$83$	−1.12983	−0.124015	−0.0620077	+	0.998076i	$0.519750\pi$
$84$	9.60279	1.04775
$85$	−4.09924	−0.444625
$86$	6.09350	0.657079
$87$	−13.7544	−1.47462
$88$	4.50027	0.479730
$89$	−12.5329	−1.32849	−0.664243	−	0.747517i	$-0.731246\pi$
$89$	−12.5329	−1.32849	−0.664243	+	0.747517i	$0.731246\pi$
$90$	13.7562	1.45003
$91$	−6.65891	−0.698043
$92$	7.08504	0.738666
$93$	−8.87639	−0.920439
$94$	−3.54032	−0.365156
$95$	18.4403	1.89194
$96$	−2.85388	−0.291273
$97$	4.36230	0.442925	0.221462	−	0.975169i	$-0.428917\pi$
$97$	4.36230	0.442925	0.221462	+	0.975169i	$0.428917\pi$
$98$	4.32198	0.436586
$99$	23.1523	2.32689
$100$	2.14961	0.214961
$101$	4.07803	0.405779	0.202889	−	0.979202i	$-0.434967\pi$
$101$	4.07803	0.405779	0.202889	+	0.979202i	$0.434967\pi$
$102$	4.37520	0.433210
$103$	−7.98979	−0.787258	−0.393629	−	0.919269i	$-0.628780\pi$
$103$	−7.98979	−0.787258	−0.393629	+	0.919269i	$0.628780\pi$
$104$	1.97898	0.194055
$105$	25.6767	2.50579
$106$	−10.6675	−1.03612
$107$	3.61535	0.349509	0.174754	−	0.984612i	$-0.444087\pi$
$107$	3.61535	0.349509	0.174754	+	0.984612i	$0.444087\pi$
$108$	−6.12058	−0.588953
$109$	0.433218	0.0414947	0.0207474	−	0.999785i	$-0.493395\pi$
$109$	0.433218	0.0414947	0.0207474	+	0.999785i	$0.493395\pi$
$110$	12.0332	1.14732
$111$	28.4844	2.70362
$112$	−3.36481	−0.317945
$113$	1.82508	0.171689	0.0858447	−	0.996309i	$-0.472641\pi$
$113$	1.82508	0.171689	0.0858447	+	0.996309i	$0.472641\pi$
$114$	−19.6817	−1.84336
$115$	18.9445	1.76658
$116$	4.81953	0.447482
$117$	10.1812	0.941249
$118$	6.14507	0.565700
$119$	5.15850	0.472879
$120$	−7.63093	−0.696605
$121$	9.25243	0.841130
$122$	5.50936	0.498794
$123$	−13.1528	−1.18595
$124$	3.11028	0.279312
$125$	−7.62159	−0.681695
$126$	−17.3108	−1.54217
$127$	−9.60785	−0.852559	−0.426280	−	0.904591i	$-0.640176\pi$
$127$	−9.60785	−0.852559	−0.426280	+	0.904591i	$0.640176\pi$
$128$	1.00000	0.0883883
$129$	−17.3901	−1.53112
$130$	5.29155	0.464100
$131$	3.08067	0.269159	0.134580	−	0.990903i	$-0.457032\pi$
$131$	3.08067	0.269159	0.134580	+	0.990903i	$0.457032\pi$
$132$	−12.8432	−1.11786
$133$	−23.2054	−2.01216
$134$	2.00982	0.173622
$135$	−16.3657	−1.40853
$136$	−1.53307	−0.131460
$137$	15.0470	1.28555	0.642776	−	0.766055i	$-0.277783\pi$
$137$	15.0470	1.28555	0.642776	+	0.766055i	$0.277783\pi$
$138$	−20.2199	−1.72123
$139$	−5.08029	−0.430905	−0.215452	−	0.976514i	$-0.569123\pi$
$139$	−5.08029	−0.430905	−0.215452	+	0.976514i	$0.569123\pi$
$140$	−8.99710	−0.760393
$141$	10.1037	0.850882
$142$	8.43901	0.708186
$143$	8.90595	0.744753
$144$	5.14465	0.428721
$145$	12.8868	1.07019
$146$	−11.0364	−0.913380
$147$	−12.3344	−1.01733
$148$	−9.98092	−0.820426
$149$	17.5464	1.43746	0.718729	−	0.695290i	$-0.244724\pi$
$149$	17.5464	1.43746	0.718729	+	0.695290i	$0.244724\pi$
$150$	−6.13474	−0.500899
$151$	7.57414	0.616375	0.308188	−	0.951326i	$-0.400278\pi$
$151$	7.57414	0.616375	0.308188	+	0.951326i	$0.400278\pi$
$152$	6.89648	0.559378
$153$	−7.88711	−0.637635
$154$	−15.1426	−1.22022
$155$	8.31651	0.667998
$156$	−5.64778	−0.452185
$157$	3.76064	0.300132	0.150066	−	0.988676i	$-0.452051\pi$
$157$	3.76064	0.300132	0.150066	+	0.988676i	$0.452051\pi$
$158$	−1.74334	−0.138693
$159$	30.4439	2.41436
$160$	2.67388	0.211388
$161$	−23.8398	−1.87884
$162$	2.03347	0.159764
$163$	5.94597	0.465724	0.232862	−	0.972510i	$-0.425191\pi$
$163$	5.94597	0.465724	0.232862	+	0.972510i	$0.425191\pi$
$164$	4.60874	0.359882
$165$	−34.3412	−2.67346
$166$	−1.12983	−0.0876922
$167$	8.04062	0.622202	0.311101	−	0.950377i	$-0.399302\pi$
$167$	8.04062	0.622202	0.311101	+	0.950377i	$0.399302\pi$
$168$	9.60279	0.740871
$169$	−9.08363	−0.698741
$170$	−4.09924	−0.314397
$171$	35.4800	2.71322
$172$	6.09350	0.464625
$173$	−10.9508	−0.832573	−0.416286	−	0.909234i	$-0.636669\pi$
$173$	−10.9508	−0.832573	−0.416286	+	0.909234i	$0.636669\pi$
$174$	−13.7544	−1.04272
$175$	−7.23304	−0.546767
$176$	4.50027	0.339221
$177$	−17.5373	−1.31819
$178$	−12.5329	−0.939381
$179$	−23.6398	−1.76692	−0.883459	−	0.468508i	$-0.844792\pi$
$179$	−23.6398	−1.76692	−0.883459	+	0.468508i	$0.844792\pi$
$180$	13.7562	1.02532
$181$	−11.1120	−0.825949	−0.412975	−	0.910742i	$-0.635510\pi$
$181$	−11.1120	−0.825949	−0.412975	+	0.910742i	$0.635510\pi$
$182$	−6.65891	−0.493591
$183$	−15.7231	−1.16228
$184$	7.08504	0.522316
$185$	−26.6877	−1.96212
$186$	−8.87639	−0.650848
$187$	−6.89923	−0.504522
$188$	−3.54032	−0.258204
$189$	20.5946	1.49804
$190$	18.4403	1.33780
$191$	−5.81186	−0.420531	−0.210266	−	0.977644i	$-0.567433\pi$
$191$	−5.81186	−0.420531	−0.210266	+	0.977644i	$0.567433\pi$
$192$	−2.85388	−0.205961
$193$	7.42528	0.534483	0.267242	−	0.963630i	$-0.413888\pi$
$193$	7.42528	0.534483	0.267242	+	0.963630i	$0.413888\pi$
$194$	4.36230	0.313195
$195$	−15.1015	−1.08144
$196$	4.32198	0.308713
$197$	15.7231	1.12022	0.560112	−	0.828417i	$-0.310758\pi$
$197$	15.7231	1.12022	0.560112	+	0.828417i	$0.310758\pi$
$198$	23.1523	1.64536
$199$	13.4116	0.950723	0.475362	−	0.879791i	$-0.342317\pi$
$199$	13.4116	0.950723	0.475362	+	0.879791i	$0.342317\pi$
$200$	2.14961	0.152000
$201$	−5.73579	−0.404571
$202$	4.07803	0.286929
$203$	−16.2168	−1.13820
$204$	4.37520	0.306326
$205$	12.3232	0.860689
$206$	−7.98979	−0.556675
$207$	36.4500	2.53345
$208$	1.97898	0.137218
$209$	31.0360	2.14681
$210$	25.6767	1.77186
$211$	−8.52755	−0.587060	−0.293530	−	0.955950i	$-0.594830\pi$
$211$	−8.52755	−0.587060	−0.293530	+	0.955950i	$0.594830\pi$
$212$	−10.6675	−0.732650
$213$	−24.0840	−1.65021
$214$	3.61535	0.247140
$215$	16.2933	1.11119
$216$	−6.12058	−0.416453
$217$	−10.4655	−0.710446
$218$	0.433218	0.0293412
$219$	31.4966	2.12834
$220$	12.0332	0.811276
$221$	−3.03392	−0.204083
$222$	28.4844	1.91175
$223$	7.11519	0.476468	0.238234	−	0.971208i	$-0.423431\pi$
$223$	7.11519	0.476468	0.238234	+	0.971208i	$0.423431\pi$
$224$	−3.36481	−0.224821
$225$	11.0590	0.737266
$226$	1.82508	0.121403
$227$	−9.96858	−0.661638	−0.330819	−	0.943694i	$-0.607325\pi$
$227$	−9.96858	−0.661638	−0.330819	+	0.943694i	$0.607325\pi$
$228$	−19.6817	−1.30346
$229$	−19.4360	−1.28437	−0.642183	−	0.766551i	$-0.721971\pi$
$229$	−19.4360	−1.28437	−0.642183	+	0.766551i	$0.721971\pi$
$230$	18.9445	1.24916
$231$	43.2151	2.84335
$232$	4.81953	0.316418
$233$	−12.8550	−0.842161	−0.421081	−	0.907023i	$-0.638349\pi$
$233$	−12.8550	−0.842161	−0.421081	+	0.907023i	$0.638349\pi$
$234$	10.1812	0.665564
$235$	−9.46638	−0.617518
$236$	6.14507	0.400010
$237$	4.97529	0.323180
$238$	5.15850	0.334376
$239$	17.5116	1.13273	0.566366	−	0.824154i	$-0.308349\pi$
$239$	17.5116	1.13273	0.566366	+	0.824154i	$0.308349\pi$
$240$	−7.63093	−0.492574
$241$	14.5839	0.939429	0.469714	−	0.882818i	$-0.344357\pi$
$241$	14.5839	0.939429	0.469714	+	0.882818i	$0.344357\pi$
$242$	9.25243	0.594769
$243$	12.5585	0.805625
$244$	5.50936	0.352701
$245$	11.5564	0.738313
$246$	−13.1528	−0.838592
$247$	13.6480	0.868402
$248$	3.11028	0.197503
$249$	3.22442	0.204339
$250$	−7.62159	−0.482031
$251$	22.5704	1.42463	0.712315	−	0.701860i	$-0.247647\pi$
$251$	22.5704	1.42463	0.712315	+	0.701860i	$0.247647\pi$
$252$	−17.3108	−1.09048
$253$	31.8846	2.00457
$254$	−9.60785	−0.602850
$255$	11.6988	0.732604
$256$	1.00000	0.0625000
$257$	11.8073	0.736521	0.368260	−	0.929723i	$-0.379953\pi$
$257$	11.8073	0.736521	0.368260	+	0.929723i	$0.379953\pi$
$258$	−17.3901	−1.08266
$259$	33.5839	2.08680
$260$	5.29155	0.328168
$261$	24.7948	1.53476
$262$	3.08067	0.190324
$263$	11.8503	0.730721	0.365360	−	0.930866i	$-0.380946\pi$
$263$	11.8503	0.730721	0.365360	+	0.930866i	$0.380946\pi$
$264$	−12.8432	−0.790447
$265$	−28.5237	−1.75220
$266$	−23.2054	−1.42281
$267$	35.7674	2.18893
$268$	2.00982	0.122769
$269$	−19.7602	−1.20480	−0.602400	−	0.798194i	$-0.705789\pi$
$269$	−19.7602	−1.20480	−0.602400	+	0.798194i	$0.705789\pi$
$270$	−16.3657	−0.995983
$271$	32.2012	1.95608	0.978041	−	0.208412i	$-0.0668295\pi$
$271$	32.2012	1.95608	0.978041	+	0.208412i	$0.0668295\pi$
$272$	−1.53307	−0.0929561
$273$	19.0037	1.15016
$274$	15.0470	0.909022
$275$	9.67383	0.583354
$276$	−20.2199	−1.21709
$277$	16.9589	1.01896	0.509480	−	0.860483i	$-0.329838\pi$
$277$	16.9589	1.01896	0.509480	+	0.860483i	$0.329838\pi$
$278$	−5.08029	−0.304696
$279$	16.0013	0.957974
$280$	−8.99710	−0.537679
$281$	18.8229	1.12288	0.561440	−	0.827517i	$-0.310247\pi$
$281$	18.8229	1.12288	0.561440	+	0.827517i	$0.310247\pi$
$282$	10.1037	0.601664
$283$	−2.47407	−0.147068	−0.0735341	−	0.997293i	$-0.523428\pi$
$283$	−2.47407	−0.147068	−0.0735341	+	0.997293i	$0.523428\pi$
$284$	8.43901	0.500763
$285$	−52.6265	−3.11733
$286$	8.90595	0.526620
$287$	−15.5075	−0.915382
$288$	5.14465	0.303151
$289$	−14.6497	−0.861747
$290$	12.8868	0.756740
$291$	−12.4495	−0.729803
$292$	−11.0364	−0.645857
$293$	−22.0065	−1.28563	−0.642816	−	0.766021i	$-0.722234\pi$
$293$	−22.0065	−1.28563	−0.642816	+	0.766021i	$0.722234\pi$
$294$	−12.3344	−0.719358
$295$	16.4312	0.956659
$296$	−9.98092	−0.580129
$297$	−27.5443	−1.59828
$298$	17.5464	1.01644
$299$	14.0212	0.810864
$300$	−6.13474	−0.354189
$301$	−20.5035	−1.18180
$302$	7.57414	0.435843
$303$	−11.6382	−0.668598
$304$	6.89648	0.395540
$305$	14.7313	0.843514
$306$	−7.88711	−0.450876
$307$	−15.6236	−0.891684	−0.445842	−	0.895112i	$-0.647096\pi$
$307$	−15.6236	−0.891684	−0.445842	+	0.895112i	$0.647096\pi$
$308$	−15.1426	−0.862828
$309$	22.8019	1.29716
$310$	8.31651	0.472346
$311$	−27.4209	−1.55490	−0.777449	−	0.628946i	$-0.783487\pi$
$311$	−27.4209	−1.55490	−0.777449	+	0.628946i	$0.783487\pi$
$312$	−5.64778	−0.319743
$313$	−22.0501	−1.24634	−0.623172	−	0.782085i	$-0.714156\pi$
$313$	−22.0501	−1.24634	−0.623172	+	0.782085i	$0.714156\pi$
$314$	3.76064	0.212225
$315$	−46.2869	−2.60797
$316$	−1.74334	−0.0980705
$317$	−20.6192	−1.15809	−0.579046	−	0.815295i	$-0.696575\pi$
$317$	−20.6192	−1.15809	−0.579046	+	0.815295i	$0.696575\pi$
$318$	30.4439	1.70721
$319$	21.6892	1.21436
$320$	2.67388	0.149474
$321$	−10.3178	−0.575882
$322$	−23.8398	−1.32854
$323$	−10.5728	−0.588286
$324$	2.03347	0.112970
$325$	4.25404	0.235972
$326$	5.94597	0.329317
$327$	−1.23635	−0.0683705
$328$	4.60874	0.254475
$329$	11.9125	0.656759
$330$	−34.3412	−1.89042
$331$	12.1230	0.666342	0.333171	−	0.942866i	$-0.391881\pi$
$331$	12.1230	0.666342	0.333171	+	0.942866i	$0.391881\pi$
$332$	−1.12983	−0.0620077
$333$	−51.3483	−2.81387
$334$	8.04062	0.439963
$335$	5.37400	0.293613
$336$	9.60279	0.523875
$337$	25.7820	1.40444	0.702218	−	0.711962i	$-0.252193\pi$
$337$	25.7820	1.40444	0.702218	+	0.711962i	$0.252193\pi$
$338$	−9.08363	−0.494084
$339$	−5.20858	−0.282891
$340$	−4.09924	−0.222312
$341$	13.9971	0.757986
$342$	35.4800	1.91854
$343$	9.01105	0.486551
$344$	6.09350	0.328539
$345$	−54.0654	−2.91078
$346$	−10.9508	−0.588718
$347$	−18.8353	−1.01113	−0.505566	−	0.862788i	$-0.668716\pi$
$347$	−18.8353	−1.01113	−0.505566	+	0.862788i	$0.668716\pi$
$348$	−13.7544	−0.737312
$349$	17.3425	0.928324	0.464162	−	0.885750i	$-0.346356\pi$
$349$	17.3425	0.928324	0.464162	+	0.885750i	$0.346356\pi$
$350$	−7.23304	−0.386622
$351$	−12.1125	−0.646518
$352$	4.50027	0.239865
$353$	6.54159	0.348174	0.174087	−	0.984730i	$-0.444303\pi$
$353$	6.54159	0.348174	0.174087	+	0.984730i	$0.444303\pi$
$354$	−17.5373	−0.932098
$355$	22.5649	1.19762
$356$	−12.5329	−0.664243
$357$	−14.7217	−0.779158
$358$	−23.6398	−1.24940
$359$	−27.6857	−1.46120	−0.730599	−	0.682807i	$-0.760759\pi$
$359$	−27.6857	−1.46120	−0.730599	+	0.682807i	$0.760759\pi$
$360$	13.7562	0.725013
$361$	28.5614	1.50323
$362$	−11.1120	−0.584034
$363$	−26.4053	−1.38592
$364$	−6.65891	−0.349022
$365$	−29.5100	−1.54462
$366$	−15.7231	−0.821858
$367$	16.2010	0.845687	0.422844	−	0.906203i	$-0.361032\pi$
$367$	16.2010	0.845687	0.422844	+	0.906203i	$0.361032\pi$
$368$	7.08504	0.369333
$369$	23.7103	1.23431
$370$	−26.6877	−1.38743
$371$	35.8943	1.86354
$372$	−8.87639	−0.460219
$373$	21.1063	1.09284	0.546421	−	0.837511i	$-0.315990\pi$
$373$	21.1063	1.09284	0.546421	+	0.837511i	$0.315990\pi$
$374$	−6.89923	−0.356751
$375$	21.7511	1.12322
$376$	−3.54032	−0.182578
$377$	9.53776	0.491220
$378$	20.5946	1.05927
$379$	−30.9867	−1.59168	−0.795839	−	0.605508i	$-0.792970\pi$
$379$	−30.9867	−1.59168	−0.795839	+	0.605508i	$0.792970\pi$
$380$	18.4403	0.945969
$381$	27.4197	1.40475
$382$	−5.81186	−0.297361
$383$	−12.1521	−0.620941	−0.310471	−	0.950583i	$-0.600487\pi$
$383$	−12.1521	−0.620941	−0.310471	+	0.950583i	$0.600487\pi$
$384$	−2.85388	−0.145637
$385$	−40.4894	−2.06353
$386$	7.42528	0.377937
$387$	31.3489	1.59355
$388$	4.36230	0.221462
$389$	−11.0813	−0.561843	−0.280922	−	0.959731i	$-0.590640\pi$
$389$	−11.0813	−0.561843	−0.280922	+	0.959731i	$0.590640\pi$
$390$	−15.1015	−0.764693
$391$	−10.8619	−0.549308
$392$	4.32198	0.218293
$393$	−8.79187	−0.443491
$394$	15.7231	0.792118
$395$	−4.66147	−0.234544
$396$	23.1523	1.16345
$397$	20.5512	1.03144	0.515719	−	0.856758i	$-0.327525\pi$
$397$	20.5512	1.03144	0.515719	+	0.856758i	$0.327525\pi$
$398$	13.4116	0.672263
$399$	66.2254	3.31542
$400$	2.14961	0.107481
$401$	−11.9556	−0.597035	−0.298518	−	0.954404i	$-0.596492\pi$
$401$	−11.9556	−0.597035	−0.298518	+	0.954404i	$0.596492\pi$
$402$	−5.73579	−0.286075
$403$	6.15520	0.306612
$404$	4.07803	0.202889
$405$	5.43724	0.270179
$406$	−16.2168	−0.804827
$407$	−44.9168	−2.22644
$408$	4.37520	0.216605
$409$	35.9049	1.77539	0.887693	−	0.460436i	$-0.152307\pi$
$409$	35.9049	1.77539	0.887693	+	0.460436i	$0.152307\pi$
$410$	12.3232	0.608599
$411$	−42.9423	−2.11819
$412$	−7.98979	−0.393629
$413$	−20.6770	−1.01745
$414$	36.4500	1.79142
$415$	−3.02104	−0.148297
$416$	1.97898	0.0970276
$417$	14.4986	0.709998
$418$	31.0360	1.51802
$419$	−22.2619	−1.08756	−0.543782	−	0.839227i	$-0.683008\pi$
$419$	−22.2619	−1.08756	−0.543782	+	0.839227i	$0.683008\pi$
$420$	25.6767	1.25289
$421$	−2.98481	−0.145471	−0.0727354	−	0.997351i	$-0.523173\pi$
$421$	−2.98481	−0.145471	−0.0727354	+	0.997351i	$0.523173\pi$
$422$	−8.52755	−0.415114
$423$	−18.2137	−0.885581
$424$	−10.6675	−0.518062
$425$	−3.29551	−0.159855
$426$	−24.0840	−1.16687
$427$	−18.5380	−0.897115
$428$	3.61535	0.174754
$429$	−25.4165	−1.22712
$430$	16.2933	0.785730
$431$	10.0382	0.483525	0.241763	−	0.970335i	$-0.422274\pi$
$431$	10.0382	0.483525	0.241763	+	0.970335i	$0.422274\pi$
$432$	−6.12058	−0.294476
$433$	9.68433	0.465399	0.232700	−	0.972549i	$-0.425244\pi$
$433$	9.68433	0.465399	0.232700	+	0.972549i	$0.425244\pi$
$434$	−10.4655	−0.502361
$435$	−36.7775	−1.76335
$436$	0.433218	0.0207474
$437$	48.8618	2.33738
$438$	31.4966	1.50497
$439$	15.1954	0.725235	0.362617	−	0.931938i	$-0.381883\pi$
$439$	15.1954	0.725235	0.362617	+	0.931938i	$0.381883\pi$
$440$	12.0332	0.573658
$441$	22.2351	1.05881
$442$	−3.03392	−0.144309
$443$	26.0570	1.23801	0.619003	−	0.785389i	$-0.287537\pi$
$443$	26.0570	1.23801	0.619003	+	0.785389i	$0.287537\pi$
$444$	28.4844	1.35181
$445$	−33.5114	−1.58859
$446$	7.11519	0.336914
$447$	−50.0754	−2.36849
$448$	−3.36481	−0.158973
$449$	−15.1786	−0.716320	−0.358160	−	0.933660i	$-0.616596\pi$
$449$	−15.1786	−0.716320	−0.358160	+	0.933660i	$0.616596\pi$
$450$	11.0590	0.521326
$451$	20.7406	0.976635
$452$	1.82508	0.0858447
$453$	−21.6157	−1.01560
$454$	−9.96858	−0.467849
$455$	−17.8051	−0.834715
$456$	−19.6817	−0.921682
$457$	19.7799	0.925267	0.462633	−	0.886550i	$-0.346905\pi$
$457$	19.7799	0.925267	0.462633	+	0.886550i	$0.346905\pi$
$458$	−19.4360	−0.908184
$459$	9.38328	0.437974
$460$	18.9445	0.883292
$461$	−17.3493	−0.808035	−0.404018	−	0.914751i	$-0.632387\pi$
$461$	−17.3493	−0.808035	−0.404018	+	0.914751i	$0.632387\pi$
$462$	43.2151	2.01055
$463$	−6.37081	−0.296077	−0.148038	−	0.988982i	$-0.547296\pi$
$463$	−6.37081	−0.296077	−0.148038	+	0.988982i	$0.547296\pi$
$464$	4.81953	0.223741
$465$	−23.7344	−1.10065
$466$	−12.8550	−0.595498
$467$	16.7083	0.773167	0.386584	−	0.922254i	$-0.373655\pi$
$467$	16.7083	0.773167	0.386584	+	0.922254i	$0.373655\pi$
$468$	10.1812	0.470625
$469$	−6.76267	−0.312271
$470$	−9.46638	−0.436651
$471$	−10.7324	−0.494524
$472$	6.14507	0.282850
$473$	27.4224	1.26088
$474$	4.97529	0.228522
$475$	14.8247	0.680206
$476$	5.15850	0.236439
$477$	−54.8808	−2.51282
$478$	17.5116	0.800963
$479$	21.2267	0.969872	0.484936	−	0.874550i	$-0.338843\pi$
$479$	21.2267	0.969872	0.484936	+	0.874550i	$0.338843\pi$
$480$	−7.63093	−0.348303
$481$	−19.7521	−0.900616
$482$	14.5839	0.664276
$483$	68.0361	3.09575
$484$	9.25243	0.420565
$485$	11.6643	0.529647
$486$	12.5585	0.569663
$487$	4.97355	0.225373	0.112687	−	0.993631i	$-0.464054\pi$
$487$	4.97355	0.225373	0.112687	+	0.993631i	$0.464054\pi$
$488$	5.50936	0.249397
$489$	−16.9691	−0.767369
$490$	11.5564	0.522066
$491$	34.5108	1.55745	0.778726	−	0.627365i	$-0.215866\pi$
$491$	34.5108	1.55745	0.778726	+	0.627365i	$0.215866\pi$
$492$	−13.1528	−0.592974
$493$	−7.38868	−0.332769
$494$	13.6480	0.614053
$495$	61.9064	2.78249
$496$	3.11028	0.139656
$497$	−28.3957	−1.27372
$498$	3.22442	0.144490
$499$	−12.6177	−0.564846	−0.282423	−	0.959290i	$-0.591138\pi$
$499$	−12.6177	−0.564846	−0.282423	+	0.959290i	$0.591138\pi$
$500$	−7.62159	−0.340848
$501$	−22.9470	−1.02520
$502$	22.5704	1.00737
$503$	−13.7740	−0.614151	−0.307076	−	0.951685i	$-0.599350\pi$
$503$	−13.7740	−0.614151	−0.307076	+	0.951685i	$0.599350\pi$
$504$	−17.3108	−0.771084
$505$	10.9041	0.485228
$506$	31.8846	1.41744
$507$	25.9236	1.15131
$508$	−9.60785	−0.426280
$509$	21.6633	0.960207	0.480103	−	0.877212i	$-0.340599\pi$
$509$	21.6633	0.960207	0.480103	+	0.877212i	$0.340599\pi$
$510$	11.6988	0.518029
$511$	37.1355	1.64278
$512$	1.00000	0.0441942
$513$	−42.2104	−1.86364
$514$	11.8073	0.520799
$515$	−21.3637	−0.941398
$516$	−17.3901	−0.765558
$517$	−15.9324	−0.700706
$518$	33.5839	1.47559
$519$	31.2523	1.37182
$520$	5.29155	0.232050
$521$	17.8862	0.783610	0.391805	−	0.920048i	$-0.371851\pi$
$521$	17.8862	0.783610	0.391805	+	0.920048i	$0.371851\pi$
$522$	24.7948	1.08524
$523$	0.780231	0.0341171	0.0170586	−	0.999854i	$-0.494570\pi$
$523$	0.780231	0.0341171	0.0170586	+	0.999854i	$0.494570\pi$
$524$	3.08067	0.134580
$525$	20.6423	0.900902
$526$	11.8503	0.516698
$527$	−4.76828	−0.207710
$528$	−12.8432	−0.558930
$529$	27.1977	1.18251
$530$	−28.5237	−1.23899
$531$	31.6143	1.37194
$532$	−23.2054	−1.00608
$533$	9.12061	0.395057
$534$	35.7674	1.54781
$535$	9.66698	0.417940
$536$	2.00982	0.0868109
$537$	67.4651	2.91133
$538$	−19.7602	−0.851922
$539$	19.4501	0.837773
$540$	−16.3657	−0.704266
$541$	−3.34259	−0.143709	−0.0718545	−	0.997415i	$-0.522892\pi$
$541$	−3.34259	−0.143709	−0.0718545	+	0.997415i	$0.522892\pi$
$542$	32.2012	1.38316
$543$	31.7124	1.36091
$544$	−1.53307	−0.0657299
$545$	1.15837	0.0496191
$546$	19.0037	0.813285
$547$	28.4122	1.21482	0.607409	−	0.794389i	$-0.292209\pi$
$547$	28.4122	1.21482	0.607409	+	0.794389i	$0.292209\pi$
$548$	15.0470	0.642776
$549$	28.3437	1.20968
$550$	9.67383	0.412493
$551$	33.2378	1.41598
$552$	−20.2199	−0.860615
$553$	5.86601	0.249448
$554$	16.9589	0.720513
$555$	76.1637	3.23297
$556$	−5.08029	−0.215452
$557$	27.8137	1.17850	0.589252	−	0.807949i	$-0.299422\pi$
$557$	27.8137	1.17850	0.589252	+	0.807949i	$0.299422\pi$
$558$	16.0013	0.677390
$559$	12.0589	0.510038
$560$	−8.99710	−0.380197
$561$	19.6896	0.831296
$562$	18.8229	0.793997
$563$	4.75166	0.200259	0.100129	−	0.994974i	$-0.468074\pi$
$563$	4.75166	0.200259	0.100129	+	0.994974i	$0.468074\pi$
$564$	10.1037	0.425441
$565$	4.88005	0.205305
$566$	−2.47407	−0.103993
$567$	−6.84224	−0.287347
$568$	8.43901	0.354093
$569$	31.9537	1.33957	0.669783	−	0.742557i	$-0.266387\pi$
$569$	31.9537	1.33957	0.669783	+	0.742557i	$0.266387\pi$
$570$	−52.6265	−2.20428
$571$	19.2358	0.804994	0.402497	−	0.915421i	$-0.368142\pi$
$571$	19.2358	0.804994	0.402497	+	0.915421i	$0.368142\pi$
$572$	8.90595	0.372377
$573$	16.5864	0.692905
$574$	−15.5075	−0.647273
$575$	15.2301	0.635138
$576$	5.14465	0.214360
$577$	26.4805	1.10240	0.551198	−	0.834374i	$-0.314171\pi$
$577$	26.4805	1.10240	0.551198	+	0.834374i	$0.314171\pi$
$578$	−14.6497	−0.609347
$579$	−21.1909	−0.880663
$580$	12.8868	0.535096
$581$	3.80168	0.157720
$582$	−12.4495	−0.516049
$583$	−48.0068	−1.98824
$584$	−11.0364	−0.456690
$585$	27.2232	1.12554
$586$	−22.0065	−0.909079
$587$	−14.5705	−0.601391	−0.300695	−	0.953720i	$-0.597219\pi$
$587$	−14.5705	−0.601391	−0.300695	+	0.953720i	$0.597219\pi$
$588$	−12.3344	−0.508663
$589$	21.4500	0.883832
$590$	16.4312	0.676460
$591$	−44.8719	−1.84578
$592$	−9.98092	−0.410213
$593$	−23.6347	−0.970560	−0.485280	−	0.874359i	$-0.661282\pi$
$593$	−23.6347	−0.970560	−0.485280	+	0.874359i	$0.661282\pi$
$594$	−27.5443	−1.13015
$595$	13.7932	0.565465
$596$	17.5464	0.718729
$597$	−38.2751	−1.56650
$598$	14.0212	0.573368
$599$	−21.5310	−0.879732	−0.439866	−	0.898064i	$-0.644974\pi$
$599$	−21.5310	−0.879732	−0.439866	+	0.898064i	$0.644974\pi$
$600$	−6.13474	−0.250450
$601$	0.321981	0.0131339	0.00656694	−	0.999978i	$-0.497910\pi$
$601$	0.321981	0.0131339	0.00656694	+	0.999978i	$0.497910\pi$
$602$	−20.5035	−0.835660
$603$	10.3398	0.421070
$604$	7.57414	0.308188
$605$	24.7398	1.00582
$606$	−11.6382	−0.472770
$607$	−26.0490	−1.05730	−0.528649	−	0.848841i	$-0.677301\pi$
$607$	−26.0490	−1.05730	−0.528649	+	0.848841i	$0.677301\pi$
$608$	6.89648	0.279689
$609$	46.2809	1.87540
$610$	14.7313	0.596455
$611$	−7.00623	−0.283442
$612$	−7.88711	−0.318818
$613$	7.34895	0.296821	0.148411	−	0.988926i	$-0.452584\pi$
$613$	7.34895	0.296821	0.148411	+	0.988926i	$0.452584\pi$
$614$	−15.6236	−0.630516
$615$	−35.1690	−1.41815
$616$	−15.1426	−0.610112
$617$	−16.3155	−0.656837	−0.328419	−	0.944532i	$-0.606516\pi$
$617$	−16.3155	−0.656837	−0.328419	+	0.944532i	$0.606516\pi$
$618$	22.8019	0.917228
$619$	13.5823	0.545918	0.272959	−	0.962026i	$-0.411998\pi$
$619$	13.5823	0.545918	0.272959	+	0.962026i	$0.411998\pi$
$620$	8.31651	0.333999
$621$	−43.3645	−1.74016
$622$	−27.4209	−1.09948
$623$	42.1709	1.68954
$624$	−5.64778	−0.226092
$625$	−31.1272	−1.24509
$626$	−22.0501	−0.881298
$627$	−88.5732	−3.53727
$628$	3.76064	0.150066
$629$	15.3014	0.610109
$630$	−46.2869	−1.84411
$631$	21.9306	0.873044	0.436522	−	0.899694i	$-0.356210\pi$
$631$	21.9306	0.873044	0.436522	+	0.899694i	$0.356210\pi$
$632$	−1.74334	−0.0693463
$633$	24.3366	0.967294
$634$	−20.6192	−0.818895
$635$	−25.6902	−1.01948
$636$	30.4439	1.20718
$637$	8.55311	0.338887
$638$	21.6892	0.858683
$639$	43.4158	1.71750
$640$	2.67388	0.105694
$641$	26.3515	1.04082	0.520411	−	0.853916i	$-0.325779\pi$
$641$	26.3515	1.04082	0.520411	+	0.853916i	$0.325779\pi$
$642$	−10.3178	−0.407210
$643$	−37.1315	−1.46433	−0.732163	−	0.681130i	$-0.761489\pi$
$643$	−37.1315	−1.46433	−0.732163	+	0.681130i	$0.761489\pi$
$644$	−23.8398	−0.939421
$645$	−46.4990	−1.83090
$646$	−10.5728	−0.415981
$647$	20.0277	0.787371	0.393686	−	0.919245i	$-0.371200\pi$
$647$	20.0277	0.787371	0.393686	+	0.919245i	$0.371200\pi$
$648$	2.03347	0.0798822
$649$	27.6545	1.08553
$650$	4.25404	0.166857
$651$	29.8674	1.17060
$652$	5.94597	0.232862
$653$	8.91716	0.348955	0.174478	−	0.984661i	$-0.444176\pi$
$653$	8.91716	0.348955	0.174478	+	0.984661i	$0.444176\pi$
$654$	−1.23635	−0.0483452
$655$	8.23733	0.321859
$656$	4.60874	0.179941
$657$	−56.7785	−2.21514
$658$	11.9125	0.464399
$659$	−11.2256	−0.437287	−0.218644	−	0.975805i	$-0.570163\pi$
$659$	−11.2256	−0.437287	−0.218644	+	0.975805i	$0.570163\pi$
$660$	−34.3412	−1.33673
$661$	−40.4544	−1.57350	−0.786748	−	0.617275i	$-0.788237\pi$
$661$	−40.4544	−1.57350	−0.786748	+	0.617275i	$0.788237\pi$
$662$	12.1230	0.471175
$663$	8.65845	0.336266
$664$	−1.12983	−0.0438461
$665$	−62.0483	−2.40613
$666$	−51.3483	−1.98971
$667$	34.1465	1.32216
$668$	8.04062	0.311101
$669$	−20.3059	−0.785072
$670$	5.37400	0.207616
$671$	24.7936	0.957146
$672$	9.60279	0.370436
$673$	−8.66308	−0.333937	−0.166969	−	0.985962i	$-0.553398\pi$
$673$	−8.66308	−0.333937	−0.166969	+	0.985962i	$0.553398\pi$
$674$	25.7820	0.993086
$675$	−13.1569	−0.506408
$676$	−9.08363	−0.349370
$677$	15.7891	0.606824	0.303412	−	0.952860i	$-0.401874\pi$
$677$	15.7891	0.606824	0.303412	+	0.952860i	$0.401874\pi$
$678$	−5.20858	−0.200034
$679$	−14.6783	−0.563303
$680$	−4.09924	−0.157199
$681$	28.4492	1.09017
$682$	13.9971	0.535977
$683$	35.7940	1.36962	0.684810	−	0.728722i	$-0.259885\pi$
$683$	35.7940	1.36962	0.684810	+	0.728722i	$0.259885\pi$
$684$	35.4800	1.35661
$685$	40.2338	1.53725
$686$	9.01105	0.344044
$687$	55.4680	2.11624
$688$	6.09350	0.232312
$689$	−21.1109	−0.804260
$690$	−54.0654	−2.05823
$691$	−45.5055	−1.73111	−0.865556	−	0.500813i	$-0.833035\pi$
$691$	−45.5055	−1.73111	−0.865556	+	0.500813i	$0.833035\pi$
$692$	−10.9508	−0.416286
$693$	−77.9032	−2.95930
$694$	−18.8353	−0.714978
$695$	−13.5841	−0.515273
$696$	−13.7544	−0.521358
$697$	−7.06552	−0.267626
$698$	17.3425	0.656424
$699$	36.6868	1.38762
$700$	−7.23304	−0.273383
$701$	3.12540	0.118045	0.0590223	−	0.998257i	$-0.481202\pi$
$701$	3.12540	0.118045	0.0590223	+	0.998257i	$0.481202\pi$
$702$	−12.1125	−0.457157
$703$	−68.8332	−2.59609
$704$	4.50027	0.169610
$705$	27.0159	1.01748
$706$	6.54159	0.246196
$707$	−13.7218	−0.516062
$708$	−17.5373	−0.659093
$709$	−6.03783	−0.226755	−0.113378	−	0.993552i	$-0.536167\pi$
$709$	−6.03783	−0.226755	−0.113378	+	0.993552i	$0.536167\pi$
$710$	22.5649	0.846844
$711$	−8.96887	−0.336359
$712$	−12.5329	−0.469690
$713$	22.0365	0.825272
$714$	−14.7217	−0.550948
$715$	23.8134	0.890571
$716$	−23.6398	−0.883459
$717$	−49.9761	−1.86639
$718$	−27.6857	−1.03322
$719$	−25.4704	−0.949884	−0.474942	−	0.880017i	$-0.657531\pi$
$719$	−25.4704	−0.949884	−0.474942	+	0.880017i	$0.657531\pi$
$720$	13.7562	0.512662
$721$	26.8842	1.00122
$722$	28.5614	1.06295
$723$	−41.6206	−1.54789
$724$	−11.1120	−0.412975
$725$	10.3601	0.384765
$726$	−26.4053	−0.979994
$727$	24.9843	0.926616	0.463308	−	0.886197i	$-0.346662\pi$
$727$	24.9843	0.926616	0.463308	+	0.886197i	$0.346662\pi$
$728$	−6.65891	−0.246796
$729$	−41.9408	−1.55336
$730$	−29.5100	−1.09221
$731$	−9.34176	−0.345517
$732$	−15.7231	−0.581141
$733$	53.9147	1.99138	0.995692	−	0.0927246i	$-0.0295576\pi$
$733$	53.9147	1.99138	0.995692	+	0.0927246i	$0.0295576\pi$
$734$	16.2010	0.597991
$735$	−32.9807	−1.21651
$736$	7.08504	0.261158
$737$	9.04472	0.333167
$738$	23.7103	0.872790
$739$	−14.8688	−0.546958	−0.273479	−	0.961878i	$-0.588174\pi$
$739$	−14.8688	−0.546958	−0.273479	+	0.961878i	$0.588174\pi$
$740$	−26.6877	−0.981061
$741$	−38.9498	−1.43086
$742$	35.8943	1.31772
$743$	21.1498	0.775912	0.387956	−	0.921678i	$-0.373181\pi$
$743$	21.1498	0.775912	0.387956	+	0.921678i	$0.373181\pi$
$744$	−8.87639	−0.325424
$745$	46.9169	1.71890
$746$	21.1063	0.772756
$747$	−5.81260	−0.212672
$748$	−6.89923	−0.252261
$749$	−12.1650	−0.444498
$750$	21.7511	0.794238
$751$	21.9107	0.799532	0.399766	−	0.916617i	$-0.369091\pi$
$751$	21.9107	0.799532	0.399766	+	0.916617i	$0.369091\pi$
$752$	−3.54032	−0.129102
$753$	−64.4133	−2.34735
$754$	9.53776	0.347345
$755$	20.2523	0.737057
$756$	20.5946	0.749019
$757$	13.6552	0.496306	0.248153	−	0.968721i	$-0.420176\pi$
$757$	13.6552	0.496306	0.248153	+	0.968721i	$0.420176\pi$
$758$	−30.9867	−1.12549
$759$	−90.9948	−3.30290
$760$	18.4403	0.668901
$761$	−46.4663	−1.68440	−0.842202	−	0.539163i	$-0.818741\pi$
$761$	−46.4663	−1.68440	−0.842202	+	0.539163i	$0.818741\pi$
$762$	27.4197	0.993311
$763$	−1.45770	−0.0527722
$764$	−5.81186	−0.210266
$765$	−21.0892	−0.762480
$766$	−12.1521	−0.439072
$767$	12.1610	0.439108
$768$	−2.85388	−0.102981
$769$	−34.1715	−1.23226	−0.616128	−	0.787646i	$-0.711300\pi$
$769$	−34.1715	−1.23226	−0.616128	+	0.787646i	$0.711300\pi$
$770$	−40.4894	−1.45914
$771$	−33.6967	−1.21356
$772$	7.42528	0.267242
$773$	−25.3398	−0.911410	−0.455705	−	0.890131i	$-0.650613\pi$
$773$	−25.3398	−0.911410	−0.455705	+	0.890131i	$0.650613\pi$
$774$	31.3489	1.12681
$775$	6.68590	0.240165
$776$	4.36230	0.156598
$777$	−95.8446	−3.43841
$778$	−11.0813	−0.397283
$779$	31.7841	1.13878
$780$	−15.1015	−0.540719
$781$	37.9778	1.35895
$782$	−10.8619	−0.388419
$783$	−29.4983	−1.05418
$784$	4.32198	0.154356
$785$	10.0555	0.358896
$786$	−8.79187	−0.313596
$787$	−31.7260	−1.13091	−0.565455	−	0.824779i	$-0.691299\pi$
$787$	−31.7260	−1.13091	−0.565455	+	0.824779i	$0.691299\pi$
$788$	15.7231	0.560112
$789$	−33.8194	−1.20400
$790$	−4.66147	−0.165848
$791$	−6.14107	−0.218351
$792$	23.1523	0.822681
$793$	10.9029	0.387174
$794$	20.5512	0.729336
$795$	81.4032	2.88708
$796$	13.4116	0.475362
$797$	−49.2575	−1.74479	−0.872395	−	0.488802i	$-0.837434\pi$
$797$	−49.2575	−1.74479	−0.872395	+	0.488802i	$0.837434\pi$
$798$	66.2254	2.34435
$799$	5.42756	0.192013
$800$	2.14961	0.0760002
$801$	−64.4774	−2.27820
$802$	−11.9556	−0.422168
$803$	−49.6668	−1.75270
$804$	−5.73579	−0.202286
$805$	−63.7447	−2.24671
$806$	6.15520	0.216808
$807$	56.3933	1.98514
$808$	4.07803	0.143464
$809$	2.10757	0.0740984	0.0370492	−	0.999313i	$-0.488204\pi$
$809$	2.10757	0.0740984	0.0370492	+	0.999313i	$0.488204\pi$
$810$	5.43724	0.191045
$811$	11.4686	0.402716	0.201358	−	0.979518i	$-0.435465\pi$
$811$	11.4686	0.402716	0.201358	+	0.979518i	$0.435465\pi$
$812$	−16.2168	−0.569099
$813$	−91.8984	−3.22302
$814$	−44.9168	−1.57433
$815$	15.8988	0.556910
$816$	4.37520	0.153163
$817$	42.0237	1.47022
$818$	35.9049	1.25539
$819$	−34.2577	−1.19706
$820$	12.3232	0.430345
$821$	−50.3526	−1.75732	−0.878659	−	0.477451i	$-0.841561\pi$
$821$	−50.3526	−1.75732	−0.878659	+	0.477451i	$0.841561\pi$
$822$	−42.9423	−1.49779
$823$	54.7792	1.90948	0.954741	−	0.297437i	$-0.0961320\pi$
$823$	54.7792	1.90948	0.954741	+	0.297437i	$0.0961320\pi$
$824$	−7.98979	−0.278338
$825$	−27.6080	−0.961186
$826$	−20.6770	−0.719446
$827$	−14.0182	−0.487460	−0.243730	−	0.969843i	$-0.578371\pi$
$827$	−14.0182	−0.487460	−0.243730	+	0.969843i	$0.578371\pi$
$828$	36.4500	1.26673
$829$	−20.8208	−0.723138	−0.361569	−	0.932345i	$-0.617759\pi$
$829$	−20.8208	−0.723138	−0.361569	+	0.932345i	$0.617759\pi$
$830$	−3.02104	−0.104862
$831$	−48.3986	−1.67893
$832$	1.97898	0.0686089
$833$	−6.62589	−0.229574
$834$	14.4986	0.502044
$835$	21.4996	0.744025
$836$	31.0360	1.07340
$837$	−19.0367	−0.658006
$838$	−22.2619	−0.769023
$839$	−39.9760	−1.38012	−0.690062	−	0.723751i	$-0.742417\pi$
$839$	−39.9760	−1.38012	−0.690062	+	0.723751i	$0.742417\pi$
$840$	25.6767	0.885929
$841$	−5.77214	−0.199039
$842$	−2.98481	−0.102863
$843$	−53.7184	−1.85016
$844$	−8.52755	−0.293530
$845$	−24.2885	−0.835550
$846$	−18.2137	−0.626200
$847$	−31.1327	−1.06973
$848$	−10.6675	−0.366325
$849$	7.06070	0.242323
$850$	−3.29551	−0.113035
$851$	−70.7152	−2.42408
$852$	−24.0840	−0.825103
$853$	22.8514	0.782417	0.391208	−	0.920302i	$-0.372057\pi$
$853$	22.8514	0.782417	0.391208	+	0.920302i	$0.372057\pi$
$854$	−18.5380	−0.634356
$855$	94.8690	3.24445
$856$	3.61535	0.123570
$857$	53.0949	1.81369	0.906843	−	0.421469i	$-0.138485\pi$
$857$	53.0949	1.81369	0.906843	+	0.421469i	$0.138485\pi$
$858$	−25.4165	−0.867707
$859$	−11.4956	−0.392225	−0.196112	−	0.980581i	$-0.562832\pi$
$859$	−11.4956	−0.392225	−0.196112	+	0.980581i	$0.562832\pi$
$860$	16.2933	0.555595
$861$	44.2567	1.50827
$862$	10.0382	0.341904
$863$	13.8398	0.471113	0.235556	−	0.971861i	$-0.424309\pi$
$863$	13.8398	0.471113	0.235556	+	0.971861i	$0.424309\pi$
$864$	−6.12058	−0.208226
$865$	−29.2810	−0.995585
$866$	9.68433	0.329087
$867$	41.8085	1.41989
$868$	−10.4655	−0.355223
$869$	−7.84550	−0.266140
$870$	−36.7775	−1.24687
$871$	3.97739	0.134769
$872$	0.433218	0.0146706
$873$	22.4425	0.759564
$874$	48.8618	1.65278
$875$	25.6452	0.866967
$876$	31.4966	1.06417
$877$	6.02018	0.203287	0.101644	−	0.994821i	$-0.467590\pi$
$877$	6.02018	0.203287	0.101644	+	0.994821i	$0.467590\pi$
$878$	15.1954	0.512818
$879$	62.8039	2.11832
$880$	12.0332	0.405638
$881$	−44.6870	−1.50554	−0.752771	−	0.658282i	$-0.771283\pi$
$881$	−44.6870	−1.50554	−0.752771	+	0.658282i	$0.771283\pi$
$882$	22.2351	0.748693
$883$	−0.624858	−0.0210281	−0.0105141	−	0.999945i	$-0.503347\pi$
$883$	−0.624858	−0.0210281	−0.0105141	+	0.999945i	$0.503347\pi$
$884$	−3.03392	−0.102042
$885$	−46.8926	−1.57628
$886$	26.0570	0.875402
$887$	−32.4094	−1.08820	−0.544100	−	0.839020i	$-0.683129\pi$
$887$	−32.4094	−1.08820	−0.544100	+	0.839020i	$0.683129\pi$
$888$	28.4844	0.955873
$889$	32.3286	1.08427
$890$	−33.5114	−1.12331
$891$	9.15115	0.306575
$892$	7.11519	0.238234
$893$	−24.4158	−0.817042
$894$	−50.0754	−1.67477
$895$	−63.2098	−2.11287
$896$	−3.36481	−0.112411
$897$	−40.0147	−1.33605
$898$	−15.1786	−0.506515
$899$	14.9901	0.499948
$900$	11.0590	0.368633
$901$	16.3541	0.544834
$902$	20.7406	0.690585
$903$	58.5146	1.94724
$904$	1.82508	0.0607014
$905$	−29.7121	−0.987665
$906$	−21.6157	−0.718134
$907$	−30.8861	−1.02555	−0.512777	−	0.858522i	$-0.671383\pi$
$907$	−30.8861	−1.02555	−0.512777	+	0.858522i	$0.671383\pi$
$908$	−9.96858	−0.330819
$909$	20.9800	0.695863
$910$	−17.8051	−0.590233
$911$	34.3000	1.13641	0.568204	−	0.822888i	$-0.307638\pi$
$911$	34.3000	1.13641	0.568204	+	0.822888i	$0.307638\pi$
$912$	−19.6817	−0.651728
$913$	−5.08456	−0.168274
$914$	19.7799	0.654262
$915$	−42.0415	−1.38985
$916$	−19.4360	−0.642183
$917$	−10.3659	−0.342312
$918$	9.38328	0.309694
$919$	19.9451	0.657927	0.328964	−	0.944343i	$-0.393301\pi$
$919$	19.9451	0.657927	0.328964	+	0.944343i	$0.393301\pi$
$920$	18.9445	0.624582
$921$	44.5878	1.46922
$922$	−17.3493	−0.571367
$923$	16.7007	0.549709
$924$	43.2151	1.42167
$925$	−21.4551	−0.705439
$926$	−6.37081	−0.209358
$927$	−41.1047	−1.35005
$928$	4.81953	0.158209
$929$	−26.3296	−0.863845	−0.431923	−	0.901911i	$-0.642165\pi$
$929$	−26.3296	−0.863845	−0.431923	+	0.901911i	$0.642165\pi$
$930$	−23.7344	−0.778280
$931$	29.8064	0.976866
$932$	−12.8550	−0.421081
$933$	78.2561	2.56199
$934$	16.7083	0.546712
$935$	−18.4477	−0.603304
$936$	10.1812	0.332782
$937$	−26.2446	−0.857374	−0.428687	−	0.903453i	$-0.641024\pi$
$937$	−26.2446	−0.857374	−0.428687	+	0.903453i	$0.641024\pi$
$938$	−6.76267	−0.220809
$939$	62.9283	2.05359
$940$	−9.46638	−0.308759
$941$	47.8747	1.56067	0.780336	−	0.625361i	$-0.215048\pi$
$941$	47.8747	1.56067	0.780336	+	0.625361i	$0.215048\pi$
$942$	−10.7324	−0.349682
$943$	32.6531	1.06333
$944$	6.14507	0.200005
$945$	55.0674	1.79134
$946$	27.4224	0.891579
$947$	48.3182	1.57013	0.785065	−	0.619413i	$-0.212629\pi$
$947$	48.3182	1.57013	0.785065	+	0.619413i	$0.212629\pi$
$948$	4.97529	0.161590
$949$	−21.8409	−0.708984
$950$	14.8247	0.480978
$951$	58.8449	1.90818
$952$	5.15850	0.167188
$953$	−53.3985	−1.72975	−0.864874	−	0.501989i	$-0.832602\pi$
$953$	−53.3985	−1.72975	−0.864874	+	0.501989i	$0.832602\pi$
$954$	−54.8808	−1.77683
$955$	−15.5402	−0.502869
$956$	17.5116	0.566366
$957$	−61.8984	−2.00089
$958$	21.2267	0.685803
$959$	−50.6303	−1.63494
$960$	−7.63093	−0.246287
$961$	−21.3261	−0.687940
$962$	−19.7521	−0.636832
$963$	18.5997	0.599366
$964$	14.5839	0.469714
$965$	19.8543	0.639132
$966$	68.0361	2.18903
$967$	9.21417	0.296308	0.148154	−	0.988964i	$-0.452667\pi$
$967$	9.21417	0.296308	0.148154	+	0.988964i	$0.452667\pi$
$968$	9.25243	0.297384
$969$	30.1735	0.969313
$970$	11.6643	0.374517
$971$	−1.23290	−0.0395658	−0.0197829	−	0.999804i	$-0.506297\pi$
$971$	−1.23290	−0.0395658	−0.0197829	+	0.999804i	$0.506297\pi$
$972$	12.5585	0.402813
$973$	17.0942	0.548016
$974$	4.97355	0.159363
$975$	−12.1405	−0.388808
$976$	5.50936	0.176350
$977$	−28.2842	−0.904890	−0.452445	−	0.891792i	$-0.649448\pi$
$977$	−28.2842	−0.904890	−0.452445	+	0.891792i	$0.649448\pi$
$978$	−16.9691	−0.542612
$979$	−56.4015	−1.80260
$980$	11.5564	0.369157
$981$	2.22875	0.0711586
$982$	34.5108	1.10128
$983$	−47.9961	−1.53084	−0.765419	−	0.643533i	$-0.777468\pi$
$983$	−47.9961	−1.53084	−0.765419	+	0.643533i	$0.777468\pi$
$984$	−13.1528	−0.419296
$985$	42.0416	1.33956
$986$	−7.38868	−0.235303
$987$	−33.9970	−1.08213
$988$	13.6480	0.434201
$989$	43.1726	1.37281
$990$	61.9064	1.96751
$991$	60.6178	1.92559	0.962794	−	0.270235i	$-0.0871015\pi$
$991$	60.6178	1.92559	0.962794	+	0.270235i	$0.0871015\pi$
$992$	3.11028	0.0987516
$993$	−34.5977	−1.09792
$994$	−28.3957	−0.900657
$995$	35.8610	1.13687
$996$	3.22442	0.102170
$997$	46.7970	1.48208	0.741038	−	0.671463i	$-0.234334\pi$
$997$	46.7970	1.48208	0.741038	+	0.671463i	$0.234334\pi$
$998$	−12.6177	−0.399406
$999$	61.0890	1.93277

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8014.2.a.d.1.7	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8014.2.a.d.1.7	✓	88	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:	\( N \)	\(=\)	\( 8014 = 2 \cdot 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.85388 q^{3} +1.00000 q^{4} +2.67388 q^{5} -2.85388 q^{6} -3.36481 q^{7} +1.00000 q^{8} +5.14465 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.85388 q^{3} +1.00000 q^{4} +2.67388 q^{5} -2.85388 q^{6} -3.36481 q^{7} +1.00000 q^{8} +5.14465 q^{9} +2.67388 q^{10} +4.50027 q^{11} -2.85388 q^{12} +1.97898 q^{13} -3.36481 q^{14} -7.63093 q^{15} +1.00000 q^{16} -1.53307 q^{17} +5.14465 q^{18} +6.89648 q^{19} +2.67388 q^{20} +9.60279 q^{21} +4.50027 q^{22} +7.08504 q^{23} -2.85388 q^{24} +2.14961 q^{25} +1.97898 q^{26} -6.12058 q^{27} -3.36481 q^{28} +4.81953 q^{29} -7.63093 q^{30} +3.11028 q^{31} +1.00000 q^{32} -12.8432 q^{33} -1.53307 q^{34} -8.99710 q^{35} +5.14465 q^{36} -9.98092 q^{37} +6.89648 q^{38} -5.64778 q^{39} +2.67388 q^{40} +4.60874 q^{41} +9.60279 q^{42} +6.09350 q^{43} +4.50027 q^{44} +13.7562 q^{45} +7.08504 q^{46} -3.54032 q^{47} -2.85388 q^{48} +4.32198 q^{49} +2.14961 q^{50} +4.37520 q^{51} +1.97898 q^{52} -10.6675 q^{53} -6.12058 q^{54} +12.0332 q^{55} -3.36481 q^{56} -19.6817 q^{57} +4.81953 q^{58} +6.14507 q^{59} -7.63093 q^{60} +5.50936 q^{61} +3.11028 q^{62} -17.3108 q^{63} +1.00000 q^{64} +5.29155 q^{65} -12.8432 q^{66} +2.00982 q^{67} -1.53307 q^{68} -20.2199 q^{69} -8.99710 q^{70} +8.43901 q^{71} +5.14465 q^{72} -11.0364 q^{73} -9.98092 q^{74} -6.13474 q^{75} +6.89648 q^{76} -15.1426 q^{77} -5.64778 q^{78} -1.74334 q^{79} +2.67388 q^{80} +2.03347 q^{81} +4.60874 q^{82} -1.12983 q^{83} +9.60279 q^{84} -4.09924 q^{85} +6.09350 q^{86} -13.7544 q^{87} +4.50027 q^{88} -12.5329 q^{89} +13.7562 q^{90} -6.65891 q^{91} +7.08504 q^{92} -8.87639 q^{93} -3.54032 q^{94} +18.4403 q^{95} -2.85388 q^{96} +4.36230 q^{97} +4.32198 q^{98} +23.1523 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9}+O(q^{10}) \) 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9	\( 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9} + 25 q^{10} + 70 q^{11} + 22 q^{12} + 31 q^{13} + 33 q^{14} + 47 q^{15} + 88 q^{16} + 19 q^{17} + 108 q^{18} + 33 q^{19} + 25 q^{20} + 48 q^{21} + 70 q^{22} + 77 q^{23} + 22 q^{24} + 109 q^{25} + 31 q^{26} + 88 q^{27} + 33 q^{28} + 83 q^{29} + 47 q^{30} + 51 q^{31} + 88 q^{32} + 30 q^{33} + 19 q^{34} + 40 q^{35} + 108 q^{36} + 45 q^{37} + 33 q^{38} + 82 q^{39} + 25 q^{40} + 35 q^{41} + 48 q^{42} + 78 q^{43} + 70 q^{44} + 37 q^{45} + 77 q^{46} + 59 q^{47} + 22 q^{48} + 103 q^{49} + 109 q^{50} + 21 q^{51} + 31 q^{52} + 58 q^{53} + 88 q^{54} + 35 q^{55} + 33 q^{56} - 16 q^{57} + 83 q^{58} + 54 q^{59} + 47 q^{60} + 18 q^{61} + 51 q^{62} + 47 q^{63} + 88 q^{64} + 34 q^{65} + 30 q^{66} + 88 q^{67} + 19 q^{68} + 62 q^{69} + 40 q^{70} + 139 q^{71} + 108 q^{72} - 6 q^{73} + 45 q^{74} + 45 q^{75} + 33 q^{76} + 37 q^{77} + 82 q^{78} + 94 q^{79} + 25 q^{80} + 112 q^{81} + 35 q^{82} + 58 q^{83} + 48 q^{84} + 83 q^{85} + 78 q^{86} + 21 q^{87} + 70 q^{88} + 99 q^{89} + 37 q^{90} + 53 q^{91} + 77 q^{92} + 57 q^{93} + 59 q^{94} + 92 q^{95} + 22 q^{96} + 16 q^{97} + 103 q^{98} + 150 q^{99}+O(q^{100}) \) 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9 + 25 * q^10 + 70 * q^11 + 22 * q^12 + 31 * q^13 + 33 * q^14 + 47 * q^15 + 88 * q^16 + 19 * q^17 + 108 * q^18 + 33 * q^19 + 25 * q^20 + 48 * q^21 + 70 * q^22 + 77 * q^23 + 22 * q^24 + 109 * q^25 + 31 * q^26 + 88 * q^27 + 33 * q^28 + 83 * q^29 + 47 * q^30 + 51 * q^31 + 88 * q^32 + 30 * q^33 + 19 * q^34 + 40 * q^35 + 108 * q^36 + 45 * q^37 + 33 * q^38 + 82 * q^39 + 25 * q^40 + 35 * q^41 + 48 * q^42 + 78 * q^43 + 70 * q^44 + 37 * q^45 + 77 * q^46 + 59 * q^47 + 22 * q^48 + 103 * q^49 + 109 * q^50 + 21 * q^51 + 31 * q^52 + 58 * q^53 + 88 * q^54 + 35 * q^55 + 33 * q^56 - 16 * q^57 + 83 * q^58 + 54 * q^59 + 47 * q^60 + 18 * q^61 + 51 * q^62 + 47 * q^63 + 88 * q^64 + 34 * q^65 + 30 * q^66 + 88 * q^67 + 19 * q^68 + 62 * q^69 + 40 * q^70 + 139 * q^71 + 108 * q^72 - 6 * q^73 + 45 * q^74 + 45 * q^75 + 33 * q^76 + 37 * q^77 + 82 * q^78 + 94 * q^79 + 25 * q^80 + 112 * q^81 + 35 * q^82 + 58 * q^83 + 48 * q^84 + 83 * q^85 + 78 * q^86 + 21 * q^87 + 70 * q^88 + 99 * q^89 + 37 * q^90 + 53 * q^91 + 77 * q^92 + 57 * q^93 + 59 * q^94 + 92 * q^95 + 22 * q^96 + 16 * q^97 + 103 * q^98 + 150 * q^99

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