Open in CoCalc
1\\apmod_run16.gp
2\\Compute Hecke eigenvalues for a basis of newforms of
3\\S_k(Gamma_0(N); Fp).  This is really computed using modular symbols
4\\so in some special cases the computation may fail, e.g., maybe, if p divides
5\\the discriminant of the Hecke algebra.
6\\It is also possible, but very unlikely if p>3, that the dimension
7\\of the modp reduction will go up because of "spurious torsion."
8
9\\ Notation: This table is destined to be input into PARI.
10\\ Unfortunately, PARI doesn't support n-dimensional arrays.
11\\ Thus for now the output format is
12\\    apmod_k7p13[N,i] = [g(x), [a2(x), a3(x), a5(x), ...]].
13\\ where k=7,p=13 are examples,
14\\ i is the conjugacy class (in no particular order),
15\\ g(x) is an irreducible poly over Fp, and the Hecke eigenvalues a2, a3, ...
16\\ are expressed as polynomials in a fixed root of g(x).
17
18\\ William Stein ([email protected])
19\\ Fri May 21 23:23:09 1999
20
21
22apmod_k16p7[288,1] = [x^2+2, [0,0,4*x,0,6,3,x,6*x,3,6*x,5*x,1,2*x,2*x,2,x,5,5,5*x,5,5,4*x,3,3*x,3]];
23apmod_k16p7[288,2] = [x^2+2, [0,0,4*x,0,1,3,x,x,4,6*x,2*x,1,2*x,5*x,5,x,2,5,2*x,2,5,3*x,4,3*x,3]];
24apmod_k16p7[288,3] = [x^2+x+3, [0,0,2*x+6,0,x,3*x,x+2,x,3*x+6,6*x,2*x+6,4,3*x+2,2*x+5,4*x+4,x+1,x+5,5*x,2*x+1,5*x+1,6*x+2,2*x+4,x+3,3*x+3,5*x]];
25apmod_k16p7[288,4] = [x^2+6*x+3, [0,0,5*x+6,0,x,4*x,6*x+2,x,3*x+1,x,2*x+1,4,4*x+2,2*x+2,4*x+3,6*x+1,x+2,2*x,2*x+6,5*x+6,x+2,2*x+3,x+4,4*x+3,2*x]];
26apmod_k16p7[288,5] = [x^2+2, [0,0,x,2*x,4,0,x,3*x,3,0,0,0,x,0,0,0,0,0,0,4,0,0,0,6*x,0]];
27apmod_k16p7[288,6] = [x^2+2, [0,0,x,5*x,3,0,x,4*x,4,0,0,0,x,0,0,0,0,0,0,3,0,0,0,6*x,0]];
28apmod_k16p7[288,7] = [x^2+x+6, [0,0,4*x,0,x,4*x+2,6*x+5,6*x+6,2*x+6,4*x+1,2*x+2,x+4,2*x+3,6*x,6*x+5,4,5*x,6*x+3,4,5*x+4,3*x+1,2*x,x,2*x+4,6*x+1]];
29apmod_k16p7[288,8] = [x^2+6*x+6, [0,0,3*x,0,x,3*x+2,x+5,6*x+1,2*x+1,3*x+1,2*x+5,6*x+4,5*x+3,6*x,6*x+2,4,5*x,x+3,3,5*x+3,4*x+1,2*x,x,5*x+4,x+1]];
30apmod_k16p7[288,9] = [x^2+2*x+5, [0,0,4*x+4,0,x,5,6*x+1,6*x+6,4*x,4*x+2,2*x+4,3,2*x+3,6,x+2,1,2*x+5,x+5,5*x,5*x+6,5*x+2,6*x+5,3,4*x+4,4*x+6]];
31apmod_k16p7[288,10] = [x^2+5*x+5, [0,0,3*x+4,0,x,5,x+1,6*x+1,4*x,3*x+2,2*x+3,3,5*x+3,1,x+5,1,2*x+2,6*x+5,5*x,5*x+1,2*x+2,6*x+2,4,3*x+4,3*x+6]];
32apmod_k16p7[288,11] = [x, [0,0,5,2,4,0,4,1,1,5,0,2,3,4,5,4,1,3,6,6,1,4,4,5,6]];
33apmod_k16p7[288,12] = [x, [0,0,5,5,3,0,4,6,6,5,0,2,3,3,2,4,6,3,1,1,1,3,3,5,6]];
34apmod_k16p7[288,13] = [x^2+2, [0,0,5,0,x,0,1,x,x,6,4*x,4,3,2*x,2*x,4,5*x,1,0,4*x,4,6*x,5*x,0,5]];
35apmod_k16p7[288,14] = [x^2+6*x+6, [0,0,4*x,0,x,3*x+2,6*x+2,x+6,2*x+1,4*x+6,5*x+2,6*x+4,2*x+4,x,6*x+2,3,5*x,x+3,4,5*x+3,4*x+1,5*x,x,2*x+3,x+1]];
36apmod_k16p7[288,15] = [x^2+x+6, [0,0,3*x,0,x,4*x+2,x+2,x+1,2*x+6,3*x+6,5*x+5,x+4,5*x+4,x,6*x+5,3,5*x,6*x+3,3,5*x+4,3*x+1,5*x,x,5*x+3,6*x+1]];
37apmod_k16p7[288,16] = [x^2+2*x+3, [0,0,5*x,0,x,6*x+3,6*x+6,2*x+4,1,5*x+5,x+2,4*x+4,2*x+5,2*x,4*x+6,5,3*x+3,2*x+5,5,4*x+1,5*x+2,x,6*x+6,2,2*x+1]];
38apmod_k16p7[288,17] = [x^2+5*x+3, [0,0,2*x,0,x,x+3,x+6,2*x+3,6,2*x+5,x+5,3*x+4,5*x+5,2*x,4*x+1,5,3*x+4,5*x+5,2,4*x+6,2*x+2,x,6*x+1,2,5*x+1]];
39apmod_k16p7[288,18] = [x, [0,0,4,4,6,0,1,0,4,1,5,5,5,0,0,3,1,4,6,4,1,4,2,0,5]];
40apmod_k16p7[288,19] = [x, [0,0,4,3,1,0,1,0,3,1,2,5,5,0,0,3,6,4,1,3,1,3,5,0,5]];
41apmod_k16p7[288,20] = [x, [0,0,4,0,5,2,4,1,0,5,5,3,2,4,2,2,5,2,2,2,3,1,5,6,0]];
42apmod_k16p7[288,21] = [x, [0,0,4,0,2,2,4,6,0,5,2,3,2,3,5,2,2,2,5,5,3,6,2,6,0]];
43apmod_k16p7[288,22] = [x, [0,0,4,0,0,4,6,0,0,4,0,4,3,0,0,5,0,4,0,0,1,0,0,6,1]];
44apmod_k16p7[288,23] = [x, [0,0,4,0,0,5,1,1,0,1,0,5,1,6,5,4,6,1,6,6,3,5,5,0,6]];
45apmod_k16p7[288,24] = [x, [0,0,4,0,0,5,1,6,0,1,0,5,1,1,2,4,1,1,1,1,3,2,2,0,6]];
46apmod_k16p7[288,25] = [x, [0,0,3,2,5,6,2,5,1,6,5,2,3,5,3,4,4,2,6,6,0,0,1,4,2]];
47apmod_k16p7[288,26] = [x, [0,0,3,5,2,6,2,2,6,6,2,2,3,2,4,4,3,2,1,1,0,0,6,4,2]];
48apmod_k16p7[288,27] = [x, [0,0,3,0,2,6,6,6,1,2,3,1,5,1,0,5,1,1,3,2,6,0,5,5,5]];
49apmod_k16p7[288,28] = [x, [0,0,3,0,5,6,6,1,6,2,4,1,5,6,0,5,6,1,4,5,6,0,2,5,5]];
50apmod_k16p7[288,29] = [x, [0,0,3,0,0,1,1,0,0,3,0,3,3,0,0,0,0,6,0,0,3,0,0,6,3]];
51apmod_k16p7[288,30] = [x, [0,0,3,0,0,4,1,0,0,3,0,4,4,0,0,2,0,4,0,0,1,0,0,1,1]];
52apmod_k16p7[288,31] = [x, [0,0,1,0,6,2,6,2,4,6,3,6,3,4,5,1,3,5,0,2,4,1,0,5,5]];
53apmod_k16p7[288,32] = [x, [0,0,1,0,1,2,6,5,3,6,4,6,3,3,2,1,4,5,0,5,4,6,0,5,5]];
54apmod_k16p7[288,33] = [x, [0,0,1,0,0,6,4,0,0,4,0,3,6,0,0,2,0,6,0,0,4,0,0,4,4]];
55apmod_k16p7[288,34] = [x, [0,0,1,0,3,3,5,0,2,0,5,1,4,2,3,2,0,6,2,6,4,6,4,2,0]];
56apmod_k16p7[288,35] = [x, [0,0,1,0,3,5,6,5,2,0,5,6,6,2,6,3,4,3,0,2,2,6,5,6,1]];
57apmod_k16p7[288,36] = [x, [0,0,1,0,4,3,5,0,5,0,2,1,4,5,4,2,0,6,5,1,4,1,3,2,0]];
58apmod_k16p7[288,37] = [x, [0,0,1,0,4,5,6,2,5,0,2,6,6,5,1,3,3,3,0,5,2,1,2,6,1]];
59apmod_k16p7[288,38] = [x, [0,0,6,0,0,6,3,0,0,3,0,3,1,0,0,5,0,6,0,0,4,0,0,3,4]];
60apmod_k16p7[288,39] = [x, [0,0,6,0,0,3,3,0,0,4,0,4,6,0,0,0,0,4,0,0,6,0,0,4,6]];
61apmod_k16p7[288,40] = [x, [0,0,6,0,6,2,0,6,2,3,3,6,3,1,1,2,3,5,5,0,4,6,5,1,2]];
62apmod_k16p7[288,41] = [x, [0,0,6,0,6,2,1,5,4,1,4,6,4,3,5,6,3,5,0,2,4,6,0,2,5]];
63apmod_k16p7[288,42] = [x, [0,0,6,0,1,2,0,1,5,3,4,6,3,6,6,2,4,5,2,0,4,1,2,1,2]];
64apmod_k16p7[288,43] = [x, [0,0,6,0,1,2,1,2,3,1,3,6,4,4,2,6,4,5,0,5,4,1,0,2,5]];
65apmod_k16p7[288,44] = [x, [0,0,0,6,1,5,1,1,4,6,4,4,5,0,5,1,5,3,2,5,2,1,5,4,0]];
66apmod_k16p7[288,45] = [x, [0,0,0,1,6,5,1,6,3,6,3,4,5,0,2,1,2,3,5,2,2,6,2,4,0]];
67apmod_k16p7[288,46] = [x, [0,0,0,0,6,2,2,6,2,2,0,2,1,1,1,3,0,0,5,5,1,6,2,0,1]];
68apmod_k16p7[288,47] = [x, [0,0,0,0,6,1,1,4,5,1,5,3,5,6,2,4,3,3,6,4,5,3,0,4,4]];
69apmod_k16p7[288,48] = [x, [0,0,0,0,1,2,2,1,5,2,0,2,1,6,6,3,0,0,2,2,1,1,5,0,1]];
70apmod_k16p7[288,49] = [x, [0,0,0,0,1,1,1,3,2,1,2,3,5,1,5,4,4,3,1,3,5,4,0,4,4]];
71apmod_k16p7[288,50] = [x, [0,0,0,0,5,4,6,2,2,5,5,6,4,3,6,1,2,2,4,0,3,4,5,1,2]];
72apmod_k16p7[288,51] = [x, [0,0,0,0,5,5,2,0,6,4,4,3,3,1,2,5,4,4,4,2,4,5,2,4,2]];
73apmod_k16p7[288,52] = [x, [0,0,0,0,5,5,5,0,6,3,3,3,4,6,2,2,4,4,3,2,4,2,2,3,2]];
74apmod_k16p7[288,53] = [x, [0,0,0,0,2,4,6,5,5,5,2,6,4,4,1,1,5,2,3,0,3,3,2,1,2]];
75apmod_k16p7[288,54] = [x, [0,0,0,0,2,5,2,0,1,4,3,3,3,6,5,5,3,4,3,5,4,2,5,4,2]];
76apmod_k16p7[288,55] = [x, [0,0,0,0,2,5,5,0,1,3,4,3,4,1,5,2,3,4,4,5,4,5,5,3,2]];
77
78apmod_k16p11[288,1] = [x, [0,0,10,0,0,6,6,0,0,6,0,1,9,0,0,6,0,8,0,0,3,0,0,5,6]];
79apmod_k16p11[288,2] = [x, [0,0,4,10,0,9,0,9,10,2,4,9,4,10,7,0,3,9,4,9,7,8,10,6,2]];
80apmod_k16p11[288,3] = [x, [0,0,4,1,0,9,0,2,1,2,7,9,4,1,4,0,8,9,7,2,7,3,1,6,2]];
81apmod_k16p11[288,4] = [x, [0,0,7,8,4,10,5,5,7,6,2,7,4,5,6,10,8,10,9,4,8,1,10,8,1]];
82apmod_k16p11[288,5] = [x, [0,0,7,3,7,10,5,6,4,6,9,7,4,6,5,10,3,10,2,7,8,10,1,8,1]];
83apmod_k16p11[288,6] = [x^2+4*x+5, [0,0,3*x+2,x,0,3*x+4,2*x+9,9*x,9*x,10,7,x+6,7*x+7,9*x+1,4*x+8,7*x+3,2*x+4,4,10*x+10,2,8*x+8,2*x+7,x+2,x+8,3*x+2]];
84apmod_k16p11[288,7] = [x^2+7*x+5, [0,0,8*x+2,x,0,8*x+4,9*x+9,9*x,9*x,10,4,10*x+6,4*x+7,9*x+10,4*x+3,4*x+3,2*x+7,4,10*x+1,9,3*x+8,2*x+4,x+9,10*x+8,8*x+2]];
85apmod_k16p11[288,8] = [x^2+3*x+8, [0,0,6*x+3,x,0,10*x+5,6*x+8,5*x+6,x+4,x+6,5*x+1,4,7*x+10,6*x+3,3,8*x+9,x+7,x+3,6*x+8,8*x,2*x+10,9*x,2*x+1,5*x+1,6*x+2]];
86apmod_k16p11[288,9] = [x^2+8*x+8, [0,0,5*x+3,x,0,x+5,5*x+8,5*x+5,x+7,10*x+6,5*x+10,4,4*x+10,6*x+8,8,3*x+9,x+4,10*x+3,6*x+3,8*x,9*x+10,9*x,2*x+10,6*x+1,5*x+2]];
87apmod_k16p11[288,10] = [x^2+5*x+2, [0,0,x+6,x,0,5*x+8,4*x+2,x+4,3*x+5,0,9*x+3,3*x+3,2*x+1,7*x+9,10*x+5,6,7*x+6,3*x+10,3*x+1,9*x+5,6*x+9,4*x+2,10,6*x+1,x+4]];
88apmod_k16p11[288,11] = [x^2+6*x+2, [0,0,10*x+6,x,0,6*x+8,7*x+2,x+7,3*x+6,0,9*x+8,8*x+3,9*x+1,7*x+2,10*x+6,6,7*x+5,8*x+10,3*x+10,9*x+6,5*x+9,4*x+9,1,5*x+1,10*x+4]];
89apmod_k16p11[288,12] = [x^2+3, [0,0,x,6*x,0,5,6*x,2*x,6,x,x,3,0,10*x,9,2*x,1,2,9*x,7,10,10*x,6,4*x,4]];
90apmod_k16p11[288,13] = [x^2+3, [0,0,x,5*x,0,5,6*x,9*x,5,x,10*x,3,0,x,2,2*x,10,2,2*x,4,10,x,5,4*x,4]];
91apmod_k16p11[288,14] = [x^4+6*x^2+10, [0,0,10*x^3+x,x^3+5*x,0,7*x^2+9,3*x^3+4*x,6*x^3+4*x,7*x^2+3,x,6*x^3,9*x^2+2,x^3+5*x,4*x^3+4*x,4*x^2+9,4*x^3,9*x^2+9,7*x^2+10,3*x^3+8*x,6*x^2+5,7*x^2+6,5*x^3,6*x^2+10,8*x^3+7*x,4]];
92apmod_k16p11[288,15] = [x^4+6*x^2+10, [0,0,10*x^3+x,10*x^3+6*x,0,7*x^2+9,3*x^3+4*x,5*x^3+7*x,4*x^2+8,x,5*x^3,9*x^2+2,x^3+5*x,7*x^3+7*x,7*x^2+2,4*x^3,2*x^2+2,7*x^2+10,8*x^3+3*x,5*x^2+6,7*x^2+6,6*x^3,5*x^2+1,8*x^3+7*x,4]];
93apmod_k16p11[288,16] = [x, [0,0,2,1,0,7,3,0,9,2,5,7,4,5,9,3,8,4,2,3,7,10,1,10,9]];
94apmod_k16p11[288,17] = [x, [0,0,2,10,0,7,3,0,2,2,6,7,4,6,2,3,3,4,9,8,7,1,10,10,9]];
95apmod_k16p11[288,18] = [x, [0,0,2,0,0,3,3,0,0,3,0,9,8,0,0,0,0,8,0,0,3,0,0,0,0]];
96apmod_k16p11[288,19] = [x, [0,0,1,7,0,4,6,0,4,2,9,4,4,8,3,10,1,9,6,0,0,3,4,3,0]];
97apmod_k16p11[288,20] = [x, [0,0,1,4,0,4,6,0,7,2,2,4,4,3,8,10,10,9,5,0,0,8,7,3,0]];
98apmod_k16p11[288,21] = [x, [0,0,1,0,0,6,5,0,0,5,0,1,2,0,0,5,0,8,0,0,3,0,0,6,6]];
99apmod_k16p11[288,22] = [x, [0,0,3,10,0,7,4,6,5,4,5,0,6,9,8,10,3,8,9,4,10,0,8,9,8]];
100apmod_k16p11[288,23] = [x, [0,0,3,1,0,7,4,5,6,4,6,0,6,2,3,10,8,8,2,7,10,0,3,9,8]];
101apmod_k16p11[288,24] = [x, [0,0,9,4,2,2,6,6,1,2,7,4,7,5,10,2,6,3,1,1,8,9,0,7,10]];
102apmod_k16p11[288,25] = [x, [0,0,9,7,9,2,6,5,10,2,4,4,7,6,1,2,5,3,10,10,8,2,0,7,10]];
103apmod_k16p11[288,26] = [x, [0,0,9,0,0,3,8,0,0,8,0,9,3,0,0,0,0,8,0,0,3,0,0,0,0]];
104apmod_k16p11[288,27] = [x, [0,0,8,10,0,7,9,7,5,5,4,7,0,1,2,8,2,4,2,9,6,3,9,1,0]];
105apmod_k16p11[288,28] = [x, [0,0,8,10,3,1,2,10,4,8,6,2,6,7,10,2,10,7,9,3,10,6,7,9,8]];
106apmod_k16p11[288,29] = [x, [0,0,8,1,0,7,9,4,6,5,7,7,0,10,9,8,9,4,9,2,6,8,2,1,0]];
107apmod_k16p11[288,30] = [x, [0,0,8,1,8,1,2,1,7,8,5,2,6,4,1,2,1,7,2,8,10,5,4,9,8]];
108apmod_k16p11[288,31] = [x, [0,0,0,0,0,8,3,0,0,8,0,9,3,0,0,2,0,8,0,0,8,0,0,9,0]];
109apmod_k16p11[288,32] = [x, [0,0,0,2,10,8,6,7,6,10,10,1,10,2,10,6,9,8,10,8,5,1,2,9,4]];
110apmod_k16p11[288,33] = [x, [0,0,0,9,1,8,6,4,5,10,1,1,10,9,1,6,2,8,1,3,5,10,9,9,4]];
111apmod_k16p11[288,34] = [x, [0,0,0,8,10,0,3,8,2,8,0,0,8,8,0,0,9,0,0,0,0,8,0,0,0]];
112apmod_k16p11[288,35] = [x, [0,0,0,8,1,0,8,8,9,3,0,0,3,8,0,0,2,0,0,0,0,8,0,0,0]];
113apmod_k16p11[288,36] = [x, [0,0,0,3,10,0,8,3,2,3,0,0,3,3,0,0,9,0,0,0,0,3,0,0,0]];
114apmod_k16p11[288,37] = [x, [0,0,0,3,1,0,3,3,9,8,0,0,8,3,0,0,2,0,0,0,0,3,0,0,0]];
115apmod_k16p11[288,38] = [x, [0,0,6,4,0,9,10,10,9,10,7,2,3,4,5,9,8,5,9,8,0,8,1,3,5]];
116apmod_k16p11[288,39] = [x, [0,0,6,2,0,10,4,1,7,7,9,8,9,2,5,5,8,4,6,2,1,4,10,7,0]];
117apmod_k16p11[288,40] = [x, [0,0,6,9,0,10,4,10,4,7,2,8,9,9,6,5,3,4,5,9,1,7,1,7,0]];
118apmod_k16p11[288,41] = [x, [0,0,6,10,1,10,9,0,8,4,9,1,5,7,5,9,8,9,5,5,0,4,10,0,3]];
119apmod_k16p11[288,42] = [x, [0,0,6,1,10,10,9,0,3,4,2,1,5,4,6,9,3,9,6,6,0,7,1,0,3]];
120apmod_k16p11[288,43] = [x, [0,0,6,7,0,9,10,1,2,10,4,2,3,7,6,9,3,5,2,3,0,3,10,3,5]];
121apmod_k16p11[288,44] = [x^2+5, [0,0,6,x,0,8,0,4*x,0,9,3*x,4,7,0,8*x,0,4*x,2,9*x,10*x,2,8*x,x,9,5]];
122apmod_k16p11[288,45] = [x, [0,0,5,6,0,8,10,2,6,3,2,2,0,4,8,9,8,3,7,7,0,3,0,2,3]];
123apmod_k16p11[288,46] = [x, [0,0,5,5,0,8,10,9,5,3,9,2,0,7,3,9,3,3,4,4,0,8,0,2,3]];
124apmod_k16p11[288,47] = [x, [0,0,5,10,10,10,2,0,3,7,9,1,6,7,6,2,3,9,5,6,0,4,1,0,3]];
125apmod_k16p11[288,48] = [x, [0,0,5,1,1,10,2,0,8,7,2,1,6,4,5,2,8,9,6,5,0,7,10,0,3]];
126apmod_k16p11[288,49] = [x^2+5, [0,0,5,x,0,8,0,4*x,0,2,3*x,4,4,0,3*x,0,7*x,2,9*x,x,2,8*x,10*x,2,5]];
127apmod_k16p11[288,50] = [x, [0,0,5,0,0,5,2,0,0,9,0,1,6,0,0,10,0,8,0,0,8,0,0,1,5]];
128
129apmod_k16p13[288,1] = [x, [0,0,9,0,0,5,0,0,0,2,0,6,9,0,0,0,0,11,0,0,7,0,0,7,4]];
130apmod_k16p13[288,2] = [x, [0,0,4,0,0,5,0,0,0,11,0,6,4,0,0,0,0,11,0,0,7,0,0,6,4]];
131apmod_k16p13[288,3] = [x, [0,0,4,0,0,8,3,0,0,0,0,6,9,0,0,2,0,11,0,0,6,0,0,6,9]];
132apmod_k16p13[288,4] = [x, [0,0,6,0,0,0,7,0,0,12,0,4,3,0,0,4,0,1,0,0,9,0,0,6,9]];
133apmod_k16p13[288,5] = [x^2+11, [0,0,8,x,10*x,0,10,x,6*x,12,6*x,8,10,6*x,12*x,11,0,1,9*x,4*x,8,3*x,10*x,2,0]];
134apmod_k16p13[288,6] = [x, [0,0,11,12,5,10,3,2,9,8,8,2,3,6,5,5,1,2,9,10,5,1,8,2,9]];
135apmod_k16p13[288,7] = [x, [0,0,11,1,8,10,3,11,4,8,5,2,3,7,8,5,12,2,4,3,5,12,5,2,9]];
136apmod_k16p13[288,8] = [x, [0,0,7,0,0,0,6,0,0,1,0,4,10,0,0,9,0,1,0,0,9,0,0,7,9]];
137apmod_k16p13[288,9] = [x^2+11, [0,0,5,x,3*x,0,3,x,7*x,1,6*x,8,3,6*x,x,2,0,1,9*x,9*x,8,3*x,3*x,11,0]];
138apmod_k16p13[288,10] = [x, [0,0,12,4,11,0,7,0,1,2,7,1,5,5,9,12,4,1,10,4,8,6,5,7,0]];
139apmod_k16p13[288,11] = [x, [0,0,12,9,2,0,7,0,12,2,6,1,5,8,4,12,9,1,3,9,8,7,8,7,0]];
140apmod_k16p13[288,12] = [x^2+6*x+1, [0,0,12*x+8,x,11*x+1,0,7*x+2,x+11,5*x+2,5*x+8,10*x+6,6*x+2,10*x+11,3*x+1,6*x+12,8*x+2,2*x+4,2*x+4,3*x+5,4*x+9,9*x+5,5*x+4,5*x+11,11,7*x+8]];
141apmod_k16p13[288,13] = [x^2+7*x+1, [0,0,x+8,x,11*x+12,0,6*x+2,x+2,5*x+11,8*x+8,10*x+7,7*x+2,3*x+11,3*x+12,6*x+1,5*x+2,2*x+9,11*x+4,3*x+8,4*x+4,4*x+5,5*x+9,5*x+2,11,6*x+8]];
142apmod_k16p13[288,14] = [x^2+6*x+11, [0,0,4*x+7,x,10*x+11,0,9*x,3,11*x,8*x+9,5*x+3,x+12,2*x+1,11*x+5,9*x,x+7,3*x+1,3*x+8,10*x+7,12*x+10,6*x+11,7*x+9,10*x+1,4*x+1,12*x+11]];
143apmod_k16p13[288,15] = [x^2+7*x+11, [0,0,9*x+7,x,10*x+2,0,4*x,10,11*x,5*x+9,5*x+10,12*x+12,11*x+1,11*x+8,9*x,12*x+7,3*x+12,10*x+8,10*x+6,12*x+3,7*x+11,7*x+4,10*x+12,9*x+1,x+11]];
144apmod_k16p13[288,16] = [x^2+8*x+8, [0,0,8*x+7,x,9*x,0,4,2*x+10,3*x+11,5*x+5,4*x+3,8*x+11,9*x+1,x+1,3*x+10,4*x+12,5*x+7,8*x+9,4,2*x+12,5*x+11,7*x+7,7*x+12,5*x+7,4*x+8]];
145apmod_k16p13[288,17] = [x^2+5*x+8, [0,0,5*x+7,x,9*x,0,4,2*x+3,3*x+2,8*x+5,4*x+10,5*x+11,4*x+1,x+12,3*x+3,9*x+12,5*x+6,5*x+9,9,2*x+1,8*x+11,7*x+6,7*x+1,8*x+7,9*x+8]];
146apmod_k16p13[288,18] = [x^2+12*x+5, [0,0,5*x+4,x,10*x+3,0,7*x+3,8*x+11,9*x+6,4*x+1,12*x+6,9*x+11,2*x,3,x+11,9*x,9*x+11,x+12,7*x+8,5*x+6,0,2*x+10,3*x+10,2*x+10,6*x+6]];
147apmod_k16p13[288,19] = [x^2+x+5, [0,0,8*x+4,x,10*x+10,0,6*x+3,8*x+2,9*x+7,9*x+1,12*x+7,4*x+11,11*x,10,x+2,4*x,9*x+2,12*x+12,7*x+5,5*x+7,0,2*x+3,3*x+3,11*x+10,7*x+6]];
148apmod_k16p13[288,20] = [x^3+4*x^2+3*x+8, [0,0,x^2+10*x+5,x,6*x^2+12*x+5,0,x^2+4*x+10,3*x^2+11*x+2,5*x^2+3*x+3,12*x^2+6*x+3,5*x+7,2*x^2+4*x+8,9*x^2+9*x+4,8*x^2+7*x+6,8*x^2+9*x+10,11*x^2+7*x+11,3*x^2+x+5,8*x^2+12*x+1,5*x^2+5*x+4,4*x^2+x+12,10*x^2+2*x+5,12*x^2+3*x+6,12*x^2+9,x^2+4*x+9,5*x^2+10*x+11]];
149apmod_k16p13[288,21] = [x^3+9*x^2+3*x+5, [0,0,x^2+3*x+5,x,7*x^2+12*x+8,0,x^2+9*x+10,10*x^2+11*x+11,8*x^2+3*x+10,12*x^2+7*x+3,5*x+6,2*x^2+9*x+8,9*x^2+4*x+4,5*x^2+7*x+7,5*x^2+9*x+3,11*x^2+6*x+11,10*x^2+x+8,8*x^2+x+1,8*x^2+5*x+9,9*x^2+x+1,10*x^2+11*x+5,x^2+3*x+7,x^2+4,x^2+9*x+9,5*x^2+3*x+11]];
150apmod_k16p13[288,22] = [x^3+4*x^2+8*x+11, [0,0,x+10,x,x^2+6*x+7,0,9*x^2+7*x,8*x^2+11*x+5,4*x^2+5*x+7,12*x^2+4,8*x^2+5*x+12,x^2+5*x+7,11*x^2+4*x+11,x^2+4,3*x^2+7*x,4*x^2+4*x+10,x^2+7*x+3,12*x^2+12*x+6,9*x^2+x+9,7*x^2+12*x+11,12*x^2+4*x+8,4*x^2+3*x+11,12*x^2+8*x+7,12*x+8,x^2+11*x+12]];
151apmod_k16p13[288,23] = [x^3+9*x^2+8*x+2, [0,0,12*x+10,x,12*x^2+6*x+6,0,9*x^2+6*x,5*x^2+11*x+8,9*x^2+5*x+6,12*x^2+4,5*x^2+5*x+1,x^2+8*x+7,11*x^2+9*x+11,12*x^2+9,10*x^2+7*x,4*x^2+9*x+10,12*x^2+7*x+10,12*x^2+x+6,4*x^2+x+4,6*x^2+12*x+2,12*x^2+9*x+8,9*x^2+3*x+2,x^2+8*x+6,x+8,x^2+2*x+12]];
152apmod_k16p13[288,24] = [x^3+9*x^2+8*x+2, [0,0,x+3,x,x^2+7*x+7,0,4*x^2+7*x,5*x^2+11*x+8,4*x^2+8*x+7,x^2+9,5*x^2+5*x+1,x^2+8*x+7,2*x^2+4*x+2,12*x^2+9,3*x^2+6*x,9*x^2+4*x+3,x^2+6*x+3,12*x^2+x+6,4*x^2+x+4,7*x^2+x+11,12*x^2+9*x+8,9*x^2+3*x+2,12*x^2+5*x+7,12*x+5,x^2+2*x+12]];
153apmod_k16p13[288,25] = [x^3+4*x^2+8*x+11, [0,0,12*x+3,x,12*x^2+7*x+6,0,4*x^2+6*x,8*x^2+11*x+5,9*x^2+8*x+6,x^2+9,8*x^2+5*x+12,x^2+5*x+7,2*x^2+9*x+2,x^2+4,10*x^2+6*x,9*x^2+9*x+3,12*x^2+6*x+10,12*x^2+12*x+6,9*x^2+x+9,6*x^2+x+2,12*x^2+4*x+8,4*x^2+3*x+11,x^2+5*x+6,x+5,x^2+11*x+12]];
154apmod_k16p13[288,26] = [x, [0,0,0,0,6,12,0,0,10,0,0,7,0,0,6,0,6,0,0,9,6,0,4,0,9]];
155apmod_k16p13[288,27] = [x, [0,0,0,0,7,12,0,0,3,0,0,7,0,0,7,0,7,0,0,4,6,0,9,0,9]];
156apmod_k16p13[288,28] = [x, [0,0,1,3,10,2,9,10,1,2,9,6,4,5,6,9,8,2,2,9,11,3,8,5,10]];
157apmod_k16p13[288,29] = [x, [0,0,1,5,3,0,11,9,10,2,3,2,5,9,7,9,10,1,6,3,12,5,8,8,3]];
158apmod_k16p13[288,30] = [x, [0,0,1,10,3,2,9,3,12,2,4,6,4,8,7,9,5,2,11,4,11,10,5,5,10]];
159apmod_k16p13[288,31] = [x, [0,0,1,8,10,0,11,4,3,2,10,2,5,4,6,9,3,1,7,10,12,8,5,8,3]];
160apmod_k16p13[288,32] = [x, [0,0,3,11,8,0,11,2,0,7,7,4,9,3,1,3,2,2,8,5,4,4,5,7,7]];
161apmod_k16p13[288,33] = [x, [0,0,3,5,9,0,6,5,6,4,4,6,11,7,9,2,9,1,6,10,9,4,7,10,5]];
162apmod_k16p13[288,34] = [x, [0,0,3,4,7,5,1,3,3,4,4,12,6,1,9,1,6,10,4,11,5,6,8,0,8]];
163apmod_k16p13[288,35] = [x, [0,0,3,2,5,0,11,11,0,7,6,4,9,10,12,3,11,2,5,8,4,9,8,7,7]];
164apmod_k16p13[288,36] = [x, [0,0,3,9,6,5,1,10,10,4,9,12,6,12,4,1,7,10,9,2,5,7,5,0,8]];
165apmod_k16p13[288,37] = [x, [0,0,3,8,4,0,6,8,7,4,9,6,11,6,4,2,4,1,7,3,9,9,6,10,5]];
166apmod_k16p13[288,38] = [x^2+7, [0,0,3,x,0,0,7,11*x,12*x,2,10*x,0,8,7*x,0,0,8*x,12,9*x,5*x,5,5*x,11*x,7,3]];
167apmod_k16p13[288,39] = [x, [0,0,10,10,12,2,4,12,9,8,5,11,6,4,0,7,8,4,4,10,7,2,6,1,7]];
168apmod_k16p13[288,40] = [x, [0,0,10,3,1,2,4,1,4,8,8,11,6,9,0,7,5,4,9,3,7,11,7,1,7]];
169apmod_k16p13[288,41] = [x^2+7, [0,0,10,x,0,0,6,11*x,x,11,10*x,0,5,7*x,0,0,5*x,12,9*x,8*x,5,5*x,2*x,6,3]];
170apmod_k16p13[288,42] = [x, [0,0,10,0,0,0,5,0,0,4,0,4,6,0,0,12,0,1,0,0,4,0,0,7,4]];
171
172apmod_k16p17[288,1] = [x, [0,0,6,0,0,10,2,0,0,6,0,5,6,0,0,2,0,16,0,0,8,0,0,13,7]];
173apmod_k16p17[288,2] = [x, [0,0,11,0,0,10,15,0,0,11,0,5,11,0,0,15,0,16,0,0,8,0,0,4,7]];
174apmod_k16p17[288,3] = [x, [0,0,14,0,0,7,8,0,0,15,0,5,1,0,0,10,0,16,0,0,9,0,0,6,10]];
175apmod_k16p17[288,4] = [x, [0,0,2,1,4,5,5,11,12,15,0,14,14,0,5,11,5,6,4,7,11,12,8,8,6]];
176apmod_k16p17[288,5] = [x, [0,0,2,16,13,5,5,6,5,15,0,14,14,0,12,11,12,6,13,10,11,5,9,8,6]];
177apmod_k16p17[288,6] = [x, [0,0,12,13,11,12,7,1,15,1,7,4,6,6,14,10,14,2,2,8,14,7,3,5,0]];
178apmod_k16p17[288,7] = [x, [0,0,12,4,6,12,7,16,2,1,10,4,6,11,3,10,3,2,15,9,14,10,14,5,0]];
179apmod_k16p17[288,8] = [x, [0,0,4,2,14,15,5,10,16,10,9,16,7,2,13,9,10,8,10,8,3,4,7,6,4]];
180apmod_k16p17[288,9] = [x, [0,0,4,15,3,15,5,7,1,10,8,16,7,15,4,9,7,8,7,9,3,13,10,6,4]];
181apmod_k16p17[288,10] = [x, [0,0,15,1,14,10,16,2,2,7,3,2,6,14,6,2,14,4,5,8,14,5,8,7,4]];
182apmod_k16p17[288,11] = [x, [0,0,15,16,3,10,16,15,15,7,14,2,6,3,11,2,3,4,12,9,14,12,9,7,4]];
183apmod_k16p17[288,12] = [x, [0,0,1,5,7,6,6,6,5,15,14,7,12,5,10,14,15,0,8,11,5,2,13,9,7]];
184apmod_k16p17[288,13] = [x, [0,0,1,12,10,6,6,11,12,15,3,7,12,12,7,14,2,0,9,6,5,15,4,9,7]];
185apmod_k16p17[288,14] = [x, [0,0,5,13,6,12,10,1,2,16,7,4,11,6,3,7,3,2,2,9,14,7,14,12,0]];
186apmod_k16p17[288,15] = [x, [0,0,5,4,11,12,10,16,15,16,10,4,11,11,14,7,14,2,15,8,14,10,3,12,0]];
187apmod_k16p17[288,16] = [x^2+15*x+11, [0,0,3*x+6,x,12*x+2,11,13*x+2,3*x+7,16*x+11,12*x+2,12*x,11*x+8,5*x+3,9*x+9,16*x,12*x+9,14*x+2,8*x+5,10*x+2,16*x+1,7*x+14,13*x+13,11*x+9,2*x+1,8*x+1]];
188apmod_k16p17[288,17] = [x^2+2*x+11, [0,0,14*x+6,x,12*x+15,11,4*x+2,3*x+10,16*x+6,5*x+2,12*x,6*x+8,12*x+3,9*x+8,16*x,5*x+9,14*x+15,9*x+5,10*x+15,16*x+16,10*x+14,13*x+4,11*x+8,15*x+1,9*x+1]];
189apmod_k16p17[288,18] = [x^4+11*x^2+6, [0,0,11*x^2+2,x,7*x^3+10*x,3,8*x^2+6,x^3+15*x,2*x^3+15*x,3*x^2+4,2*x,16*x^2,12*x^2+1,13*x^3,x,14*x^2+16,12*x^3+8*x,8*x^2+9,5*x,16*x^3+13*x,3*x^2+16,14*x^3+6*x,11*x^3+3*x,13*x^2+8,16*x^2+10]];
190apmod_k16p17[288,19] = [x^4+11*x^2+6, [0,0,6*x^2+15,x,10*x^3+7*x,3,9*x^2+11,x^3+15*x,15*x^3+2*x,14*x^2+13,2*x,16*x^2,5*x^2+16,13*x^3,16*x,3*x^2+1,5*x^3+9*x,8*x^2+9,5*x,x^3+4*x,3*x^2+16,14*x^3+6*x,6*x^3+14*x,4*x^2+9,16*x^2+10]];
191apmod_k16p17[288,20] = [x^2+13*x+15, [0,0,3*x+12,x,7*x+4,10*x+4,9*x+13,4*x+2,15*x+3,14*x+2,13*x+6,10*x,15*x+12,14,14*x+13,8*x+3,10*x+6,8*x+6,3*x+4,11*x+6,14*x,15*x+1,x,3*x+6,3*x+9]];
192apmod_k16p17[288,21] = [x^2+4*x+15, [0,0,14*x+12,x,7*x+13,7*x+4,8*x+13,4*x+15,15*x+14,3*x+2,13*x+11,7*x,2*x+12,3,14*x+4,9*x+3,10*x+11,9*x+6,3*x+13,11*x+11,3*x,15*x+16,x,14*x+6,14*x+9]];
193apmod_k16p17[288,22] = [x^2+6*x+4, [0,0,3*x+15,x,2*x+10,8*x+2,13*x+13,15*x+16,6*x+2,3*x+6,14*x+10,6*x+14,8*x+8,4*x+7,15*x+16,14*x+16,3*x+13,9*x+2,11*x+11,16*x+13,13*x+5,12*x+6,10*x+2,3*x+4,8*x+5]];
194apmod_k16p17[288,23] = [x^2+11*x+4, [0,0,14*x+15,x,2*x+7,9*x+2,4*x+13,15*x+1,6*x+15,14*x+6,14*x+7,11*x+14,9*x+8,4*x+10,15*x+1,3*x+16,3*x+4,8*x+2,11*x+6,16*x+4,4*x+5,12*x+11,10*x+15,14*x+4,9*x+5]];
195apmod_k16p17[288,24] = [x^3+9*x^2+13*x+14, [0,0,9*x^2+12*x+13,x,3*x^2+14*x+8,8*x^2+7*x+11,10*x^2+8*x+4,5*x^2+10*x+10,8*x^2+15*x+12,11*x^2+9*x+9,4*x^2+6*x+16,13*x^2+5*x+2,16*x+15,5*x^2+14*x+6,5*x^2+4*x+6,14*x^2+3,7*x^2+6*x+11,15*x^2+16*x+8,4*x^2+14*x+2,16*x^2+9*x+13,6*x^2+9*x+9,2*x^2+4*x+7,3*x^2+x+15,16*x^2+9*x+3,13*x^2+6*x+15]];
196apmod_k16p17[288,25] = [x^3+8*x^2+13*x+3, [0,0,9*x^2+5*x+13,x,14*x^2+14*x+9,8*x^2+10*x+11,10*x^2+9*x+4,12*x^2+10*x+7,9*x^2+15*x+5,11*x^2+8*x+9,13*x^2+6*x+1,13*x^2+12*x+2,x+15,12*x^2+14*x+11,12*x^2+4*x+11,14*x^2+3,10*x^2+6*x+6,15*x^2+x+8,13*x^2+14*x+15,x^2+9*x+4,6*x^2+8*x+9,15*x^2+4*x+10,14*x^2+x+2,16*x^2+8*x+3,13*x^2+11*x+15]];
197apmod_k16p17[288,26] = [x^3+9*x^2+16*x+6, [0,0,9*x^2+5,x,14*x^2+12*x+9,7*x^2+6*x+9,13*x^2+x+6,11*x^2+9*x+4,10*x^2+15*x+7,6*x^2+3*x+15,7*x+13,15*x^2+x+16,3*x^2+16*x+1,12*x^2+3*x+14,12*x^2+11*x+16,15*x^2+13*x+7,5*x^2+2*x+16,3*x^2+6*x+7,14*x^2+9*x+9,13*x^2+6*x+13,16*x^2+16*x+8,14*x^2+14*x+12,2*x^2+11*x+4,14*x^2+8*x+5,15*x^2+12*x+14]];
198apmod_k16p17[288,27] = [x^3+8*x^2+16*x+11, [0,0,9*x^2+5,x,3*x^2+12*x+8,7*x^2+11*x+9,13*x^2+16*x+6,6*x^2+9*x+13,7*x^2+15*x+10,6*x^2+14*x+15,7*x+4,15*x^2+16*x+16,3*x^2+x+1,5*x^2+3*x+3,5*x^2+11*x+1,15*x^2+4*x+7,12*x^2+2*x+1,3*x^2+11*x+7,3*x^2+9*x+8,4*x^2+6*x+4,16*x^2+x+8,3*x^2+14*x+5,15*x^2+11*x+13,14*x^2+9*x+5,15*x^2+5*x+14]];
199apmod_k16p17[288,28] = [x^3+2*x^2+4, [0,0,9*x^2+8*x+3,x,5*x^2+11*x+15,6*x^2+9*x+5,15*x^2+9*x+5,9*x^2+9*x+13,6*x^2+15*x+11,3*x^2+14*x+9,3*x^2+5*x+1,3*x^2+13,11*x^2+10*x+11,8*x^2+14*x+8,8*x^2+1,3*x^2+x+3,9*x^2+6*x+6,10*x^2+3*x+9,2*x^2+14*x+12,13*x^2+6,2*x^2+x+2,4*x^2+10*x+15,3*x^2+11*x,8*x^2+4*x+13,5*x^2+13*x+9]];
200apmod_k16p17[288,29] = [x^3+15*x^2+13, [0,0,9*x^2+9*x+3,x,12*x^2+11*x+2,6*x^2+8*x+5,15*x^2+8*x+5,8*x^2+9*x+4,11*x^2+15*x+6,3*x^2+3*x+9,14*x^2+5*x+16,3*x^2+13,11*x^2+7*x+11,9*x^2+14*x+9,9*x^2+16,3*x^2+16*x+3,8*x^2+6*x+11,10*x^2+14*x+9,15*x^2+14*x+5,4*x^2+11,2*x^2+16*x+2,13*x^2+10*x+2,14*x^2+11*x,8*x^2+13*x+13,5*x^2+4*x+9]];
201apmod_k16p17[288,30] = [x^3+5*x^2+16*x+7, [0,0,16*x^2+15*x,x,11*x^2+7*x+15,8*x^2+14*x+7,3*x^2+12*x,9*x^2+8*x+11,14*x^2,12*x^2+7*x,11*x^2+13*x+15,11*x^2+4*x+7,10*x^2+7*x+12,14*x^2+x+12,x^2+9,5*x^2+15,4*x^2+10*x+16,12*x^2+10*x+4,4*x^2+7*x,3*x^2+13*x+3,6*x+1,8*x^2+2*x+10,10*x^2+3*x+14,x^2+3*x+2,5*x^2+2]];
202apmod_k16p17[288,31] = [x^3+12*x^2+16*x+10, [0,0,16*x^2+2*x,x,6*x^2+7*x+2,8*x^2+3*x+7,3*x^2+5*x,8*x^2+8*x+6,3*x^2,12*x^2+10*x,6*x^2+13*x+2,11*x^2+13*x+7,10*x^2+10*x+12,3*x^2+x+5,16*x^2+8,5*x^2+15,13*x^2+10*x+1,12*x^2+7*x+4,13*x^2+7*x,14*x^2+13*x+14,11*x+1,9*x^2+2*x+7,7*x^2+3*x+3,x^2+14*x+2,5*x^2+2]];
203apmod_k16p17[288,32] = [x^3+8*x^2+16*x+11, [0,0,8*x^2+12,x,14*x^2+5*x+9,7*x^2+11*x+9,4*x^2+x+11,6*x^2+9*x+13,10*x^2+2*x+7,11*x^2+3*x+2,7*x+4,15*x^2+16*x+16,14*x^2+16*x+16,5*x^2+3*x+3,12*x^2+6*x+16,2*x^2+13*x+10,5*x^2+15*x+16,3*x^2+11*x+7,3*x^2+9*x+8,13*x^2+11*x+13,16*x^2+x+8,3*x^2+14*x+5,2*x^2+6*x+4,3*x^2+8*x+12,15*x^2+5*x+14]];
204apmod_k16p17[288,33] = [x^3+9*x^2+16*x+6, [0,0,8*x^2+12,x,3*x^2+5*x+8,7*x^2+6*x+9,4*x^2+16*x+11,11*x^2+9*x+4,7*x^2+2*x+10,11*x^2+14*x+2,7*x+13,15*x^2+x+16,14*x^2+x+16,12*x^2+3*x+14,5*x^2+6*x+1,2*x^2+4*x+10,12*x^2+15*x+1,3*x^2+6*x+7,14*x^2+9*x+9,4*x^2+11*x+4,16*x^2+16*x+8,14*x^2+14*x+12,15*x^2+6*x+13,3*x^2+9*x+12,15*x^2+12*x+14]];
205apmod_k16p17[288,34] = [x^3+7*x^2+4*x+8, [0,0,9*x^2+15*x+15,x,6*x^2+x+8,15*x^2+3*x+11,2*x^2+3*x+9,6*x^2+6*x+3,7*x^2+12*x+9,16*x^2+12*x+4,12*x^2+10*x+3,5*x^2+11*x+11,6*x^2+x+10,8*x^2+2*x+13,8*x^2+7*x+6,11*x^2+7,16*x^2+8*x+5,5*x^2+x+15,6*x^2+4*x+10,6*x^2+x+12,5*x^2+5*x+7,15*x^2+x+8,7*x^2+12*x+6,15*x^2+7*x+8,13*x^2+11]];
206apmod_k16p17[288,35] = [x^3+10*x^2+4*x+9, [0,0,9*x^2+2*x+15,x,11*x^2+x+9,15*x^2+14*x+11,2*x^2+14*x+9,11*x^2+6*x+14,10*x^2+12*x+8,16*x^2+5*x+4,5*x^2+10*x+14,5*x^2+6*x+11,6*x^2+16*x+10,9*x^2+2*x+4,9*x^2+7*x+11,11*x^2+7,x^2+8*x+12,5*x^2+16*x+15,11*x^2+4*x+7,11*x^2+x+5,5*x^2+12*x+7,2*x^2+x+9,10*x^2+12*x+11,15*x^2+10*x+8,13*x^2+11]];
207apmod_k16p17[288,36] = [x, [0,0,16,5,10,6,11,6,12,2,14,7,5,5,7,3,2,0,8,6,5,2,4,8,7]];
208apmod_k16p17[288,37] = [x, [0,0,16,10,4,12,11,12,13,14,15,11,14,0,8,2,6,7,2,4,16,6,0,14,9]];
209apmod_k16p17[288,38] = [x, [0,0,16,12,7,6,11,11,5,2,3,7,5,12,10,3,15,0,9,11,5,15,13,8,7]];
210apmod_k16p17[288,39] = [x, [0,0,16,7,13,12,11,5,4,14,2,11,14,0,9,2,11,7,15,13,16,11,0,14,9]];
211
212apmod_k16p19[288,1] = [x, [0,0,7,1,17,4,0,1,10,13,4,5,18,14,14,9,0,8,8,15,6,17,0,9,5]];
213apmod_k16p19[288,2] = [x, [0,0,7,18,2,4,0,18,9,13,15,5,18,5,5,9,0,8,11,4,6,2,0,9,5]];
214apmod_k16p19[288,3] = [x, [0,0,14,18,3,3,18,15,1,17,6,4,0,9,10,13,6,15,5,11,13,16,15,1,11]];
215apmod_k16p19[288,4] = [x, [0,0,14,1,16,3,18,4,18,17,13,4,0,10,9,13,13,15,14,8,13,3,4,1,11]];
216apmod_k16p19[288,5] = [x, [0,0,15,16,17,10,12,14,0,16,2,5,10,18,7,13,12,2,13,3,18,14,15,14,11]];
217apmod_k16p19[288,6] = [x, [0,0,15,3,2,10,12,5,0,16,17,5,10,1,12,13,7,2,6,16,18,5,4,14,11]];
218apmod_k16p19[288,7] = [x, [0,0,6,12,17,10,12,17,2,1,8,4,15,1,1,16,17,14,15,17,17,4,6,9,8]];
219apmod_k16p19[288,8] = [x, [0,0,6,7,2,10,12,2,17,1,11,4,15,18,18,16,2,14,4,2,17,15,13,9,8]];
220apmod_k16p19[288,9] = [x, [0,0,5,18,16,3,1,15,18,2,6,4,0,9,9,6,13,15,5,8,13,16,4,18,11]];
221apmod_k16p19[288,10] = [x, [0,0,5,1,3,3,1,4,1,2,13,4,0,10,10,6,6,15,14,11,13,3,15,18,11]];
222apmod_k16p19[288,11] = [x, [0,0,13,7,17,10,7,2,2,18,11,4,4,18,1,3,17,14,4,17,17,15,6,10,8]];
223apmod_k16p19[288,12] = [x, [0,0,13,12,2,10,7,17,17,18,8,4,4,1,18,3,2,14,15,2,17,4,13,10,8]];
224apmod_k16p19[288,13] = [x, [0,0,18,9,12,15,3,4,12,3,12,11,1,14,6,4,11,16,9,10,15,10,6,2,14]];
225apmod_k16p19[288,14] = [x, [0,0,18,10,7,15,3,15,7,3,7,11,1,5,13,4,8,16,10,9,15,9,13,2,14]];
226apmod_k16p19[288,15] = [x, [0,0,1,9,7,15,16,4,7,16,12,11,18,14,13,15,8,16,9,9,15,10,13,17,14]];
227apmod_k16p19[288,16] = [x, [0,0,1,10,12,15,16,15,12,16,7,11,18,5,6,15,11,16,10,10,15,9,6,17,14]];
228apmod_k16p19[288,17] = [x^2+5*x+17, [0,0,4*x+1,14,7,x,3*x+13,9*x+8,4*x+17,15*x+17,18*x+13,14*x+1,15*x+1,17*x+4,18*x+13,5*x+9,8*x+1,9*x+7,3*x+6,17*x+2,4*x+3,12*x+16,16*x+6,17*x+9,16*x+13]];
229apmod_k16p19[288,18] = [x^2+5*x+17, [0,0,4*x+1,5,12,x,3*x+13,10*x+11,15*x+2,15*x+17,x+6,14*x+1,15*x+1,2*x+15,x+6,5*x+9,11*x+18,9*x+7,16*x+13,2*x+17,4*x+3,7*x+3,3*x+13,17*x+9,16*x+13]];
230apmod_k16p19[288,19] = [x^2+12*x+2, [0,0,18*x+9,x,8*x+17,x+10,x+6,18*x+2,2*x+2,6*x+11,12*x+10,17*x,17*x+10,10*x+2,14*x+9,14*x+18,14*x+5,13*x+13,11*x+2,2*x+15,14*x+14,2*x+12,18*x+17,5*x+17,5*x+13]];
231apmod_k16p19[288,20] = [x^2+7*x+2, [0,0,x+9,x,8*x+2,18*x+10,18*x+6,18*x+17,2*x+17,13*x+11,12*x+9,2*x,2*x+10,10*x+17,14*x+10,5*x+18,14*x+14,6*x+13,11*x+17,2*x+4,5*x+14,2*x+7,18*x+2,14*x+17,14*x+13]];
232apmod_k16p19[288,21] = [x^2+2*x+12, [0,0,6*x+15,x,11*x+14,x+3,2*x+5,12*x+12,10*x+8,16*x+1,2*x+9,9*x+18,8*x+1,12*x+7,6*x+9,x+7,12*x+12,6*x+10,13*x+11,x+15,17*x+12,11*x+2,14*x+7,6*x+3,7*x+17]];
233apmod_k16p19[288,22] = [x^2+17*x+12, [0,0,13*x+15,x,11*x+5,18*x+3,17*x+5,12*x+7,10*x+11,3*x+1,2*x+10,10*x+18,11*x+1,12*x+12,6*x+10,18*x+7,12*x+7,13*x+10,13*x+8,x+4,2*x+12,11*x+17,14*x+12,13*x+3,12*x+17]];
234apmod_k16p19[288,23] = [x^3+5*x^2+14*x+4, [0,0,7*x^2+14*x+16,x,15*x^2+17*x+8,3*x^2+7*x+11,17*x+6,7*x^2+11*x+13,x^2+17*x+7,8*x^2+13*x+16,2*x^2+14*x+16,16*x^2+9*x+15,5*x^2+16*x+18,11*x^2+16*x+4,18*x+3,4*x^2+13*x+15,15*x^2+14*x+12,9*x^2+16*x+12,18*x^2+3*x+18,3*x^2+14*x+16,15*x^2+8*x+11,14*x^2+10*x+8,3*x^2+5*x+4,12*x^2+6*x+12,18*x^2+15*x+14]];
235apmod_k16p19[288,24] = [x^3+14*x^2+14*x+15, [0,0,7*x^2+5*x+16,x,4*x^2+17*x+11,3*x^2+12*x+11,2*x+6,12*x^2+11*x+6,18*x^2+17*x+12,8*x^2+6*x+16,17*x^2+14*x+3,16*x^2+10*x+15,5*x^2+3*x+18,8*x^2+16*x+15,18*x+16,4*x^2+6*x+15,4*x^2+14*x+7,9*x^2+3*x+12,x^2+3*x+1,16*x^2+14*x+3,15*x^2+11*x+11,5*x^2+10*x+11,16*x^2+5*x+15,12*x^2+13*x+12,18*x^2+4*x+14]];
236apmod_k16p19[288,25] = [x^3+7*x+4, [0,0,15*x^2+15*x+4,x,10*x^2+5*x+9,10*x^2+18*x+18,18*x^2+10*x+3,4*x^2+8*x+11,14*x^2+12*x+4,8*x^2+10*x,10*x^2+2*x+13,4*x^2+12*x+7,5*x^2+x,4*x^2+13*x+15,13*x^2+6*x+3,12*x^2+10*x+3,18*x+10,4*x^2+8,13*x^2+14*x+7,6*x^2+12*x+18,8*x^2+2*x+4,15*x^2+15*x+17,9*x^2+2*x+7,15*x^2+13*x+16,16*x^2+4*x+9]];
237apmod_k16p19[288,26] = [x^3+7*x+15, [0,0,15*x^2+4*x+4,x,9*x^2+5*x+10,10*x^2+x+18,18*x^2+9*x+3,15*x^2+8*x+8,5*x^2+12*x+15,8*x^2+9*x,9*x^2+2*x+6,4*x^2+7*x+7,5*x^2+18*x,15*x^2+13*x+4,6*x^2+6*x+16,12*x^2+9*x+3,18*x+9,4*x^2+8,6*x^2+14*x+12,13*x^2+12*x+1,8*x^2+17*x+4,4*x^2+15*x+2,10*x^2+2*x+12,15*x^2+6*x+16,16*x^2+15*x+9]];
238apmod_k16p19[288,27] = [x^3+5*x+7, [0,0,17*x^2+x,x,14*x^2+15*x+11,17*x^2+2*x+5,2*x+4,10*x^2+8*x+7,9*x^2+11*x+3,10*x^2+9*x+15,4*x^2+6*x+13,3*x^2+5,17*x^2+9*x+4,15*x^2+18*x+6,9*x^2+2*x+16,5*x^2+18*x,11*x^2+6*x+3,14*x^2+4*x+17,18*x^2+15*x+9,3*x^2+3*x+14,12*x^2+17*x+2,13*x^2+14*x+1,13*x^2+10*x+16,13*x^2+17*x+13,x^2+18*x+15]];
239apmod_k16p19[288,28] = [x^3+5*x+12, [0,0,17*x^2+18*x,x,5*x^2+15*x+8,17*x^2+17*x+5,17*x+4,9*x^2+8*x+12,10*x^2+11*x+16,10*x^2+10*x+15,15*x^2+6*x+6,3*x^2+5,17*x^2+10*x+4,4*x^2+18*x+13,10*x^2+2*x+3,5*x^2+x,8*x^2+6*x+16,14*x^2+15*x+17,x^2+15*x+10,16*x^2+3*x+5,12*x^2+2*x+2,6*x^2+14*x+18,6*x^2+10*x+3,13*x^2+2*x+13,x^2+x+15]];
240apmod_k16p19[288,29] = [x^8+13*x^6+6*x^4+2*x^2+18, [0,0,17*x^7+3*x^3+14*x,16*x^7+6*x^5+9*x^3+x,16*x^6+16*x^4+8*x^2,14*x^6+10*x^4+18*x^2+2,x,x^7+x^5+12*x^3+2*x,12*x^6+18*x^4+9*x^2+10,4*x^7+x^5,2*x^7+16*x^5+10*x^3+16*x,17*x^6+9*x^4+16*x^2+11,17*x^7+10*x^5+17*x^3+3*x,6*x^7+14*x^5+18*x^3,14*x^6+17*x^4+7*x^2+16,14*x^7+5*x^5+17*x^3+13*x,18*x^6+14*x^4+5*x^2+9,15*x^6+17*x^4+8*x^2+9,15*x^7+13*x^5+7*x^3+13*x,17*x^6+8*x^4+8*x^2+11,7*x^6+9*x^4+14*x^2+3,11*x^7+9*x^5+7*x^3+11*x,5*x^6+5*x^4+14*x^2+18,6*x^7+9*x^5+11*x^3+5*x,3*x^6+x^4+10*x^2+11]];
241apmod_k16p19[288,30] = [x^8+13*x^6+6*x^4+2*x^2+18, [0,0,17*x^7+3*x^3+14*x,3*x^7+13*x^5+10*x^3+18*x,3*x^6+3*x^4+11*x^2,14*x^6+10*x^4+18*x^2+2,x,18*x^7+18*x^5+7*x^3+17*x,7*x^6+x^4+10*x^2+9,4*x^7+x^5,17*x^7+3*x^5+9*x^3+3*x,17*x^6+9*x^4+16*x^2+11,17*x^7+10*x^5+17*x^3+3*x,13*x^7+5*x^5+x^3,5*x^6+2*x^4+12*x^2+3,14*x^7+5*x^5+17*x^3+13*x,x^6+5*x^4+14*x^2+10,15*x^6+17*x^4+8*x^2+9,4*x^7+6*x^5+12*x^3+6*x,2*x^6+11*x^4+11*x^2+8,7*x^6+9*x^4+14*x^2+3,8*x^7+10*x^5+12*x^3+8*x,14*x^6+14*x^4+5*x^2+1,6*x^7+9*x^5+11*x^3+5*x,3*x^6+x^4+10*x^2+11]];
242apmod_k16p19[288,31] = [x, [0,0,17,10,1,7,7,16,0,2,18,8,13,1,7,8,13,4,3,11,4,11,17,5,14]];
243apmod_k16p19[288,32] = [x, [0,0,17,9,18,7,7,3,0,2,1,8,13,18,12,8,6,4,16,8,4,8,2,5,14]];
244apmod_k16p19[288,33] = [x, [0,0,17,8,18,16,3,13,8,7,18,6,9,6,8,2,10,14,8,13,0,9,7,4,13]];
245apmod_k16p19[288,34] = [x, [0,0,17,11,1,16,3,6,11,7,1,6,9,13,11,2,9,14,11,6,0,10,12,4,13]];
246apmod_k16p19[288,35] = [x^2+9, [0,0,0,x,3*x,18,15,7*x,2*x,2,5*x,8,11,x,7*x,8,13*x,17,7*x,18*x,16,4*x,15*x,4,11]];
247apmod_k16p19[288,36] = [x, [0,0,0,0,0,4,16,0,0,15,0,13,9,0,0,15,0,5,0,0,0,0,0,4,9]];
248apmod_k16p19[288,37] = [x, [0,0,0,0,0,4,3,0,0,4,0,13,10,0,0,4,0,5,0,0,0,0,0,15,9]];
249apmod_k16p19[288,38] = [x, [0,0,16,0,0,15,0,0,0,15,0,13,10,0,0,15,0,5,0,0,0,0,0,15,10]];
250apmod_k16p19[288,39] = [x, [0,0,16,8,1,10,11,8,15,8,11,15,14,6,6,8,12,10,14,9,6,0,6,18,1]];
251apmod_k16p19[288,40] = [x, [0,0,16,11,18,10,11,11,4,8,8,15,14,13,13,8,7,10,5,10,6,0,13,18,1]];
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