CoCalc Shared Fileswww / tables / ap_s2new_1-100.gp
Author: William A. Stein
1\\ ap_s2new_1-100.gp
2\\ This is a table of eigenforms for the action of
3\\ the Hecke operators on S_2^{new}(Gamma_0(N)).
4\\ William Stein ([email protected]), October, 1998.
5\\ 1<=N<=97
6\\ E=matrix(97,?,i,j,0);
7\\ E[N,ith eigenform]=[[a_2,...,a_97],  f(x)]
8\\ where the a_i are defined over Q[x]/f(x).
9
10E[11,1]=[[-2,-1,1,-2,1,4,-2,0,-1,0,7,3,-8,-6,8,-6,5,12,-7,-3,4,-10,-6,15,-7], x-1];
11E[14,1]=[[-1,-2,0,1,0,-4,6,2,0,-6,-4,2,6,8,-12,6,-6,8,-4,0,2,8,-6,-6,-10], x-1];
12E[15,1]=[[-1,-1,1,0,-4,-2,2,4,0,-2,0,-10,10,4,8,-10,-4,-2,12,-8,10,0,12,-6,2], x-1];
13E[17,1]=[[-1,0,-2,4,0,-2,1,-4,4,6,4,-2,-6,4,0,6,-12,-10,4,-4,-6,12,-4,10,2], x-1];
14E[19,1]=[[0,-2,3,-1,3,-4,-3,1,0,6,-4,2,-6,-1,-3,12,-6,-1,-4,6,-7,8,12,12,8], x-1];
15E[20,1]=[[0,-2,-1,2,0,2,-6,-4,6,6,-4,2,6,-10,-6,-6,12,2,2,-12,2,8,6,-6,2], x-1];
16E[21,1]=[[-1,1,-2,-1,4,-2,-6,4,0,-2,0,6,2,-4,0,6,12,-2,4,0,-6,-16,-12,-14,18], x-1];
17E[23,1]=[[x,-2*x-1,2*x,2*x+2,-2*x-4,3,-2*x+2,-2,1,-3,6*x+3,-2*x,-4*x-1,0,-2*x-1,4*x-2,4*x+4,-8*x-2,2*x-4,2*x+11,-4*x+9,-8*x-6,2*x-10,-4*x-8,6*x+14], x^2+x-1];
18E[24,1]=[[0,-1,-2,0,4,-2,2,-4,-8,6,8,6,-6,4,0,-2,4,-2,-4,8,10,-8,-4,-6,2], x-1];
19E[26,1]=[[-1,1,-3,-1,6,1,-3,2,0,6,-4,-7,0,-1,3,0,-6,8,14,-3,2,8,12,-6,-10], x-1];
20E[26,2]=[[1,-3,-1,1,-2,-1,-3,6,-4,2,4,3,0,-5,13,12,-10,-8,-2,-5,-10,-4,0,6,14], x-1];
21E[27,1]=[[0,0,0,-1,0,5,0,-7,0,0,-4,11,0,8,0,0,0,-1,5,0,-7,17,0,0,-19], x-1];
22E[29,1]=[[x,-x,-1,2*x+2,x+2,2*x+1,-2*x-4,6,-4*x-6,1,-5*x-2,-4,6*x+10,x+6,3*x+4,-6*x-5,4*x+6,2*x,-4*x-4,2*x-4,4,x,-4*x-2,6*x+2,-6*x-10], x^2+2*x-1];
23E[30,1]=[[-1,1,-1,-4,0,2,6,-4,0,-6,8,2,-6,-4,0,-6,0,-10,-4,0,2,8,12,18,2], x-1];
24E[31,1]=[[x,-2*x,1,2*x-3,2,-2*x,-2*x+4,-2*x+1,6*x-4,-2*x+6,1,-2,7,2*x-2,4*x-4,-4*x-4,2*x-1,10*x-8,8,-10*x+7,4*x+2,-6*x-2,-8*x-2,6*x+2,-8*x-3], x^2-x-1];
25E[32,1]=[[0,0,-2,0,0,6,2,0,0,-10,0,-2,10,0,0,14,0,-10,0,0,-6,0,0,10,18], x-1];
26E[33,1]=[[1,-1,-2,4,1,-2,-2,0,8,-6,-8,6,-2,0,8,6,-4,6,-4,0,-14,-4,12,-6,2], x-1];
27E[34,1]=[[1,-2,0,-4,6,2,-1,-4,0,0,-4,-4,6,8,0,-6,0,-4,8,0,2,8,0,-6,14], x-1];
28E[35,1]=[[x,-x-1,1,-1,x+1,x+3,-x-3,2*x-2,-2*x-2,-3*x-1,0,6,-2*x,2*x+6,3*x-1,2*x,-4,-6*x,-4*x,8,4*x-2,-x-5,4,2*x+4,-5*x-7], x^2+x-4];
29E[35,2]=[[0,1,-1,1,-3,5,3,2,-6,3,-4,2,-12,-10,9,12,0,8,-4,0,2,-1,12,-12,-1], x-1];
30E[36,1]=[[0,0,0,-4,0,2,0,8,0,0,-4,-10,0,8,0,0,0,14,-16,0,-10,-4,0,0,14], x-1];
31E[37,1]=[[-2,-3,-2,-1,-5,-2,0,0,2,6,-4,-1,-9,2,-9,1,8,-8,8,9,-1,4,-15,4,4], x-1];
32E[37,2]=[[0,1,0,-1,3,-4,6,2,6,-6,-4,1,-9,8,3,-3,12,8,-4,-15,11,-10,9,6,8], x-1];
33E[38,1]=[[1,-1,-4,3,2,-1,3,-1,-1,-5,-8,-2,-8,4,8,-1,15,2,3,2,9,-10,-6,0,-2], x-1];
34E[38,2]=[[-1,1,0,-1,-6,5,3,1,3,9,-4,2,0,8,0,-3,9,-10,5,-6,-7,-10,-6,-12,-10], x-1];
35E[39,1]=[[1,-1,2,-4,4,1,2,0,0,-10,4,-2,6,-12,0,6,12,-2,-8,0,2,8,4,-2,10], x-1];
36E[39,2]=[[x,1,-2*x-2,2*x+2,-2,-1,4*x+6,-2*x-2,-4,2,2*x-2,-4*x-6,-2*x+6,-4*x,-4*x-10,-2,4*x+6,8*x+10,2*x+6,2,-4*x+2,-8*x-8,4*x+2,2*x+14,4*x+2], x^2+2*x-1];
37E[40,1]=[[0,0,1,-4,4,-2,2,4,4,-2,-8,6,-6,-8,4,6,-4,-2,8,0,-6,0,-16,-6,-14], x-1];
38E[41,1]=[[x,-1/2*x^2-x+3/2,-x-1,1/2*x^2+x+1/2,3/2*x^2+x-9/2,-x^2+3,-2,-3/2*x^2-x+13/2,-2*x^2-2*x+8,x^2+2*x-5,2*x+6,-3*x-3,1,x^2-5,3/2*x^2-3*x-13/2,x^2+2*x-1,-2*x^2-2*x+4,-x^2+2*x+5,-3/2*x^2-x+9/2,-3/2*x^2+x+25/2,4*x^2+x-15,1/2*x^2-x+17/2,2*x^2+4*x-6,-4*x^2-2*x+12,-2*x^2-4*x+8], x^3+x^2-5*x-1];
39E[42,1]=[[1,-1,-2,-1,-4,6,2,-4,8,-2,0,-10,-6,-4,0,6,4,6,4,8,10,0,-4,-6,-14], x-1];
40E[43,1]=[[-2,-2,-4,0,3,-5,-3,-2,-1,-6,-1,0,5,-1,4,-5,-12,2,-3,2,2,-8,15,-4,7], x-1];
41E[43,2]=[[x,-x,-x+2,x-2,2*x-1,2*x+1,2*x+5,-2*x-2,-4*x+1,3*x,-3,-6*x,-2*x-1,1,6,-2*x+11,2*x-2,3*x+4,6*x+1,-2*x-6,3*x-12,-2*x+2,4*x+9,-3*x-6,-2*x-1], x^2-2];
42E[44,1]=[[0,1,-3,2,-1,-4,6,8,-3,0,5,-1,0,-10,0,-6,3,-4,-1,15,-4,2,6,-9,-7], x-1];
43E[45,1]=[[1,0,-1,0,4,-2,-2,4,0,2,0,-10,-10,4,-8,10,4,-2,12,8,10,0,-12,6,2], x-1];
44E[46,1]=[[-1,0,4,-4,2,-2,-2,-2,1,2,0,-4,6,10,0,-4,12,-8,-10,0,6,-12,14,-6,6], x-1];
45E[47,1]=[[x,x^3-x^2-6*x+4,-4*x^3+2*x^2+20*x-10,3*x^3-x^2-16*x+7,2*x^3-2*x^2-10*x+6,-4*x^3+2*x^2+22*x-8,x^3+x^2-6*x,-2*x^3+10*x-2,-2*x^3+12*x-4,-2*x^3+2*x^2+10*x-10,4*x^3-2*x^2-22*x+8,3*x^3-x^2-14*x+8,-2*x+2,-2*x^3+2*x^2+14*x-8,1,5*x^3-3*x^2-30*x+13,7*x^3-x^2-36*x+11,-7*x^3+5*x^2+38*x-23,-12*x^3+6*x^2+60*x-26,7*x^3-3*x^2-34*x+12,-2*x^2-4*x+12,7*x^3-3*x^2-34*x+20,8*x^3-4*x^2-40*x+24,5*x^3+x^2-26*x+1,-9*x^3+7*x^2+46*x-21], x^4-x^3-5*x^2+5*x-1];
46E[48,1]=[[0,1,-2,0,-4,-2,2,4,8,6,-8,6,-6,-4,0,-2,-4,-2,4,-8,10,8,4,-6,2], x-1];
47E[49,1]=[[1,0,0,0,4,0,0,0,8,2,0,-6,0,-12,0,-10,0,0,4,16,0,8,0,0,0], x-1];
48E[50,1]=[[1,-1,0,-2,-3,4,3,5,-6,0,2,-2,-3,4,-12,-6,0,2,13,12,-11,-10,9,15,-2], x-1];
49E[50,2]=[[-1,1,0,2,-3,-4,-3,5,6,0,2,2,-3,-4,12,6,0,2,-13,12,11,-10,-9,15,2], x-1];
50E[51,1]=[[x,-1,-x+1,0,-x-1,x+3,1,3*x+3,-x-5,4*x+2,-2*x-2,2*x,x-1,-3*x-3,2*x-6,-4*x+2,-2*x+2,-2*x+4,4,4*x+4,4*x-2,6*x+6,-2*x-6,2*x+4,-2*x-8], x^2+x-4];
51E[51,2]=[[0,1,3,-4,-3,-1,-1,-1,9,6,2,-4,-3,-7,-6,-6,6,8,-4,12,2,-10,-6,0,-16], x-1];
52E[52,1]=[[0,0,2,-2,-2,-1,6,-6,8,2,10,-6,-6,4,-2,6,-10,-2,10,10,2,-4,-6,-6,2], x-1];
53E[53,1]=[[-1,-3,0,-4,0,-3,-3,-5,7,-7,4,5,6,-2,-2,-1,-2,-8,-12,1,-4,-1,-1,-14,1], x-1];
54E[53,2]=[[x,-x^2-x+3,x^2-3,x^2-1,x^2+2*x-3,1,2*x-1,x+4,2*x^2-x-4,-3*x^2-4*x+4,-x^2+4*x+3,x^2+6*x-2,-2*x-4,-3*x^2-6*x+11,-2*x^2-4*x,1,4*x^2+2*x-8,3*x^2-2*x-11,3*x^2+6*x-3,-3*x^2-7*x+3,x^2+4*x+1,5*x^2+3*x-13,3*x+10,-4*x^2+4*x+10,5*x^2-12], x^3+x^2-3*x-1];
55E[54,1]=[[1,0,-3,-1,3,-4,0,2,6,-6,5,2,6,-10,-6,-9,-12,8,14,0,-7,8,3,18,-1], x-1];
56E[54,2]=[[-1,0,3,-1,-3,-4,0,2,-6,6,5,2,-6,-10,6,9,12,8,14,0,-7,8,-3,-18,-1], x-1];
57E[55,1]=[[1,0,1,0,-1,2,6,-4,4,6,-8,-2,2,4,-12,-2,4,-10,-16,8,14,8,-4,10,10], x-1];
58E[55,2]=[[x,-2*x+2,-1,-2,1,2*x-6,2*x+2,0,-2*x+2,-4*x+6,0,-4*x+2,6,-6,2*x-2,4*x+2,4*x-8,-8*x+10,6*x-2,8*x-8,2*x-6,4,-6,-8*x+6,4*x-6], x^2-2*x-1];
59E[56,1]=[[0,2,-4,1,0,0,-2,-2,8,2,4,-6,-2,8,-4,-10,6,4,-12,0,-14,-8,6,10,-2], x-1];
60E[56,2]=[[0,0,2,-1,-4,2,-6,8,0,6,8,-2,2,-4,-8,6,0,-6,-4,-8,10,16,8,-6,-6], x-1];
61E[57,1]=[[1,1,-2,0,0,6,-6,-1,4,2,8,-10,-2,-4,12,-6,-12,-2,-4,0,10,0,16,-2,10], x-1];
62E[57,2]=[[-2,1,1,3,-3,-6,3,-1,4,-10,2,8,-8,-1,3,-6,0,7,8,12,-11,0,4,10,-2], x-1];
63E[57,3]=[[-2,-1,-3,-5,1,2,-1,-1,-4,-2,-6,0,0,-1,-9,10,-8,-1,8,-12,-11,16,12,-6,-10], x-1];
64E[58,1]=[[-1,-3,-3,-2,-1,3,-4,-8,0,-1,3,-8,-2,7,11,1,-4,4,-4,-2,-12,-7,0,-6,-6], x-1];
65E[58,2]=[[1,-1,1,-2,-3,-1,8,0,4,-1,-3,8,2,-11,13,-11,0,-8,-12,2,4,15,4,-10,-2], x-1];
66E[59,1]=[[x,-1/4*x^4+5/4*x^2-1/2*x,3/4*x^4+1/2*x^3-23/4*x^2-3*x+7,-1/2*x^4-1/2*x^3+7/2*x^2+3/2*x-3,-1/2*x^4-x^3+9/2*x^2+6*x-8,-1/2*x^4-x^3+9/2*x^2+6*x-6,x^4-8*x^2+9,3/4*x^4+3/2*x^3-23/4*x^2-8*x+9,-1/2*x^4+9/2*x^2+x-8,-x^4-1/2*x^3+8*x^2+1/2*x-7,x^4+x^3-9*x^2-3*x+14,-x^4+7*x^2-2,1/4*x^4+x^3-13/4*x^2-17/2*x+6,-x^3+5*x-2,-2*x-4,1/4*x^4+x^3-13/4*x^2-9/2*x+6,1,1/2*x^4+x^3-9/2*x^2-2*x+12,-1/2*x^4-2*x^3+13/2*x^2+11*x-16,-x^4-2*x^3+8*x^2+10*x-11,1/2*x^4+2*x^3-5/2*x^2-9*x,7/4*x^4+2*x^3-51/4*x^2-21/2*x+16,1/2*x^4+3*x^3-5/2*x^2-16*x+4,-3/2*x^4-x^3+19/2*x^2+4*x-4,-3/2*x^4-2*x^3+27/2*x^2+11*x-26], x^5-9*x^3+2*x^2+16*x-8];
67E[61,1]=[[-1,-2,-3,1,-5,1,4,-4,-9,-6,0,8,5,-8,4,6,9,-1,-7,-8,-11,3,4,-4,-14], x-1];
68E[61,2]=[[x,-x^2+3,x^2-2*x-2,x^2-x-3,x+4,-2*x^2+2*x+1,-x^2+2*x+1,3*x^2-7,-x+2,-x^2+2*x+3,-x^2-4*x+3,3*x^2-9,4*x^2-4*x-7,-x^2+2*x-3,-4*x^2+6*x+6,-2*x,-x^2-3*x+13,1,-x^2-5*x+7,x^2+4*x+1,3*x^2-4*x-6,-4*x^2-x+14,4*x^2-12,4*x^2-2*x-10,-4*x^2+8*x+10], x^3-x^2-3*x+1];
69E[62,1]=[[-1,x,-2*x+2,2,x-4,-3*x+2,2*x-2,-4,0,3*x-6,1,3*x+2,-2*x+8,3*x-4,6,x+2,2*x-8,-3*x+2,8,-8*x+8,-10,-6*x+8,-5*x+8,6,6*x-4], x^2-2*x-2];
70E[62,2]=[[1,0,-2,0,0,2,-6,4,8,2,-1,10,-6,8,-8,-6,-12,-6,-12,8,10,-8,8,-6,2], x-1];
71E[63,1]=[[1,0,2,-1,-4,-2,6,4,0,2,0,6,-2,-4,0,-6,-12,-2,4,0,-6,-16,12,14,18], x-1];
72E[63,2]=[[x,0,-2*x,1,2*x,2,2*x,-4,-2*x,0,-4,2,6*x,-4,4*x,-4*x,-4*x,-10,-4,-6*x,14,8,0,-2*x,14], x^2-3];
73E[64,1]=[[0,0,2,0,0,-6,2,0,0,10,0,2,10,0,0,-14,0,10,0,0,-6,0,0,10,18], x-1];
74E[65,1]=[[-1,-2,-1,-4,2,-1,2,-6,-6,2,-10,-2,-6,10,4,2,6,2,-4,6,-6,-12,-16,2,-2], x-1];
75E[65,2]=[[x,-x+1,-1,2,x-3,1,2*x,3*x-1,x+3,-2*x-6,-3*x+5,-4,-2*x,3*x+5,6,-6*x,-7*x-3,6*x+2,-6*x-4,-x+3,-4,6*x+2,-6,4*x-6,2], x^2-3];
76E[65,3]=[[x,x+1,1,-2*x,-x+1,-1,-2*x-4,x+3,-x-1,4*x+4,3*x+9,6*x+6,-2*x-8,5*x+1,2*x,-6*x-12,3*x+9,-8,-2,-7*x-5,-6*x-6,6*x+6,-2*x-8,6,4*x+2], x^2+2*x-1];
77E[66,1]=[[1,-1,2,-4,-1,-6,2,4,4,6,0,6,-6,4,-12,2,12,-14,4,-12,-6,-4,4,10,-14], x-1];
78E[66,2]=[[1,1,-4,-2,1,4,-2,0,-6,10,-8,-2,2,4,-2,4,0,-8,-12,2,-6,10,4,10,-2], x-1];
79E[66,3]=[[-1,1,0,2,-1,-4,-6,-4,6,6,8,-10,6,8,-6,0,0,8,-4,6,2,14,-12,-6,14], x-1];
80E[67,1]=[[2,-2,2,-2,-4,2,3,7,9,-5,-10,-1,0,-2,-1,10,9,-2,1,0,-7,-8,4,7,0], x-1];
81E[67,2]=[[x,-x-3,-3,3*x+4,-2*x-3,-3*x-8,-2*x-6,3*x+5,-4*x-3,4*x+3,-1,3*x+4,-x-3,-3*x-3,x-6,-9,6,9*x+10,-1,2*x+9,-4,-9*x-17,7*x+3,2*x+3,-12*x-17], x^2+3*x+1];
82E[67,3]=[[x,x+1,-2*x+1,-x,1,x,-2*x+2,x-5,4*x+1,4*x+7,6*x+3,x+2,5*x+5,-5*x-7,-x-4,6*x+3,-6,-3*x-6,1,-14*x-7,8,-7*x-9,-3*x+5,6*x-5,6*x+3], x^2+x-1];
83E[68,1]=[[0,x,-2*x+2,-x,x-4,2*x,-1,-2*x+4,x-4,2*x-2,3*x-4,-2*x+10,-6,-6*x+8,-4*x+4,4*x+2,-2*x+8,2*x-6,4*x+4,-3*x,2,-3*x-4,2*x-8,-2*x+8,-4*x+6], x^2-2*x-2];
84E[69,1]=[[1,1,0,-2,4,-6,4,2,-1,2,4,2,2,10,0,-12,-12,-6,-10,8,-14,10,12,-16,-10], x-1];
85E[69,2]=[[x,-1,-x-1,-x+1,4,2*x,-x-5,-x+5,1,-2*x,2*x-2,-2*x,4*x-2,3*x+1,-4,x-3,4*x+4,-2*x,x+3,-8,-4*x-2,-3*x+3,4,x+1,-2*x+4], x^2-5];
86E[70,1]=[[1,0,-1,-1,4,-6,2,0,0,6,8,-10,2,4,8,-2,-8,-14,-12,-16,2,-8,8,10,2], x-1];
87E[71,1]=[[x,-x,-x^2+x+5,-2*x,2*x^2-6,-2*x^2+4,2*x^2+2*x-6,x^2+2*x-2,-4,-2*x^2+x+10,4,-x^2-2,-4*x-2,-x^2-x+7,2*x^2+2*x-4,-4*x^2+6,2*x^2-2*x-8,-4*x+4,-2*x^2+2,1,x^2+3*x+7,-x^2+3*x+3,x^2-2*x-10,-2*x^2-x+6,2*x+8], x^3+x^2-4*x-3];
88E[71,2]=[[x,-x^2+3,-x-1,2*x^2+2*x-6,-2*x^2-2*x+6,4,2*x^2+2*x-6,-x^2-x+7,2*x^2-4,x^2+2*x-5,-2*x-2,-3*x^2-x+13,2*x^2+2*x-2,-2*x^2-3*x+1,2*x^2-10,-2*x,2*x^2+2*x-14,-4*x^2-6*x+16,4*x-4,1,x+1,-2*x^2-7*x+9,-x^2-x+11,-5*x^2-2*x+21,-2*x^2-4*x+8], x^3-5*x+3];
89E[72,1]=[[0,0,2,0,-4,-2,-2,-4,8,-6,8,6,6,4,0,2,-4,-2,-4,-8,10,-8,4,6,2], x-1];
90E[73,1]=[[1,0,2,2,-2,-6,2,8,4,2,-2,-6,6,-2,6,10,-6,-14,8,0,1,-4,-14,-6,-10], x-1];
91E[73,2]=[[x,-x-3,x,-3,-x-3,3*x+5,-6*x-9,1,x-6,-4*x-3,6*x+10,-6*x-11,4*x+6,-1,-4*x-9,8*x+15,4*x,3*x+8,6*x+17,x-9,-1,3*x-5,-3*x-6,-2*x+3,-3*x-9], x^2+3*x+1];
92E[73,3]=[[x,-x+1,-x,-1,x+3,x-1,2*x-3,-7,x+6,-4*x+3,2*x+2,-2*x+5,-6,-4*x+5,9,4*x-3,0,-x-4,-6*x+5,-3*x+3,1,3*x-1,-5*x+6,6*x+3,-3*x-1], x^2-x-3];
93E[74,1]=[[1,x,-3*x-1,2*x,-x-3,3*x+2,4*x+2,-4*x-2,-3*x-2,7*x+2,x+9,-1,-x+8,2*x-2,2*x+2,-4*x-6,-2*x-8,-x+9,-5*x-7,-8*x-10,-5*x-1,9*x+6,4*x-8,-4*x-8,4*x+6], x^2+x-1];
94E[74,2]=[[-1,x,-x+1,-2*x+4,-x+1,x-2,-6,2,3*x-6,-3*x+6,-x+3,1,3*x,2*x-6,2*x-2,-6,2*x+4,5*x-9,-5*x+13,6,-x-9,7*x-14,-4*x+16,-4*x+4,-8*x+10], x^2-3*x-1];
95E[75,1]=[[1,1,0,0,-4,2,-2,4,0,-2,0,10,10,-4,-8,10,-4,-2,-12,-8,-10,0,-12,-6,-2], x-1];
96E[75,2]=[[-2,1,0,3,2,-1,-2,-5,-6,10,-3,-2,-8,-1,-2,4,-10,7,3,-8,14,0,-6,0,-17], x-1];
97E[75,3]=[[2,-1,0,-3,2,1,2,-5,6,10,-3,2,-8,1,2,-4,-10,7,-3,-8,-14,0,6,0,17], x-1];
98E[76,1]=[[0,2,-1,-3,5,-4,-3,-1,8,-2,4,10,10,1,-1,-4,6,-13,-12,2,9,8,-12,12,-8], x-1];
99E[77,1]=[[0,-3,-1,-1,-1,-4,2,-6,-5,10,1,-5,-2,-8,8,-6,3,-2,-3,1,10,6,12,-15,-5], x-1];
100E[77,2]=[[0,1,3,1,-1,-4,-6,2,3,-6,5,11,6,8,0,-6,-9,-10,5,9,2,-10,12,-3,-1], x-1];
101E[77,3]=[[1,2,-2,-1,1,4,4,0,-4,-6,10,-6,4,12,-10,-6,2,0,8,-12,-8,8,0,-6,-10], x-1];
102E[77,4]=[[-x+1,x,-2,1,-1,-x+2,x-2,-2*x+4,-2*x,-2*x+6,-x-4,2*x-6,x-10,8,x+4,2*x+2,x,x-6,-2*x+12,2*x-8,-x-2,4*x-4,6*x-4,2,-6*x+10], x^2-2*x-4];
103E[78,1]=[[-1,-1,2,4,-4,1,2,-8,0,6,-4,-2,-10,4,8,-10,4,-2,-16,-8,2,8,12,14,10], x-1];
104E[79,1]=[[-1,-1,-3,-1,-2,3,-6,4,2,-6,-10,-2,-10,4,7,8,-3,-4,8,15,2,-1,-6,-7,-19], x-1];
105E[79,2]=[[x,-x^4+x^3+3*x^2-3*x+1,x^4-4*x^2-x+3,x^4-x^3-5*x^2+3*x+3,-x^4-2*x^3+6*x^2+7*x-6,x^3+x^2-2*x-3,-2*x^3+6*x+2,-3*x^3+3*x^2+10*x-8,2*x^4+x^3-9*x^2-4*x+6,2*x^3-2*x^2-4*x+6,-x^4+2*x^3+6*x^2-5*x-6,2*x^4-2*x^3-10*x^2+4*x+8,2*x^3-6*x+6,-2*x^4+2*x^3+8*x^2-6*x-6,x^4-5*x^3-5*x^2+17*x+5,-4*x^4+16*x^2+2*x-6,x^4+x^3-5*x^2-7*x+5,-2*x^4+4*x^3+2*x^2-14*x+10,3*x^3-3*x^2-14*x+4,x^4+x^3-x^2-3*x-5,-x^3-x^2+2*x,1,2*x^4+2*x^3-10*x^2-6*x+2,-2*x^4-x^3+11*x^2+4*x-1,x^4-6*x^3+2*x^2+19*x-13], x^5-6*x^3+8*x-1];
106E[80,1]=[[0,2,-1,-2,0,2,-6,4,-6,6,4,2,6,10,6,-6,-12,2,-2,12,2,-8,-6,-6,2], x-1];
107E[80,2]=[[0,0,1,4,-4,-2,2,-4,-4,-2,8,6,-6,8,-4,6,4,-2,-8,0,-6,0,16,-6,-14], x-1];
108E[81,1]=[[x,0,-x,2,-2*x,-1,3*x,2,2*x,x,8,-7,-4*x,2,4*x,0,8*x,-7,-10,-6*x,-7,2,-8*x,-3*x,2], x^2-3];
109E[82,1]=[[-1,-2,-2,-4,-2,4,-2,6,-8,0,-8,2,-1,-12,4,-4,8,-14,-2,8,10,4,12,-14,6], x-1];
110E[82,2]=[[1,x,-2*x,-x-2,3*x,0,4*x+2,-x-4,-2*x+4,-4*x+4,2*x-4,6*x,-1,-4*x+4,-5*x-2,12,2*x-4,6,-3*x-4,x-2,-4*x-8,-3*x-6,4*x+12,-4*x-6,4*x-2], x^2-2];
111E[83,1]=[[-1,-1,-2,-3,3,-6,5,2,-4,-7,5,-11,-2,-8,0,6,5,5,-2,2,0,14,-1,0,-8], x-1];
112E[83,2]=[[x,1/2*x^4-1/2*x^3-7/2*x^2+3/2*x+4,-1/2*x^5-1/2*x^4+9/2*x^3+7/2*x^2-8*x-2,3/4*x^5-1/4*x^4-25/4*x^3+3/4*x^2+19/2*x,-1/4*x^5+1/4*x^4+5/4*x^3+1/4*x^2-4,x^3-5*x+2,1/4*x^5-3/4*x^4-7/4*x^3+17/4*x^2+7/2*x-4,3/2*x^5-1/2*x^4-23/2*x^3-1/2*x^2+16*x+4,-x^5+7*x^3+3*x^2-8*x-7,3/2*x^5-12*x^3-4*x^2+39/2*x+8,-3/4*x^5+3/4*x^4+23/4*x^3-21/4*x^2-8*x+8,-3/4*x^5+3/4*x^4+19/4*x^3-13/4*x^2-3*x+8,-x^5+9*x^3+x^2-16*x-1,1/2*x^5-1/2*x^4-9/2*x^3+3/2*x^2+10*x,-1/2*x^5+3/2*x^4+9/2*x^3-21/2*x^2-10*x+10,x^5-8*x^3+9*x,-5/4*x^5-1/4*x^4+39/4*x^3+11/4*x^2-29/2*x-4,3/2*x^5+2*x^4-14*x^3-16*x^2+55/2*x+16,-2*x^5-x^4+17*x^3+13*x^2-29*x-18,1/2*x^5+1/2*x^4-11/2*x^3-3/2*x^2+13*x-8,-1/2*x^5+5/2*x^4+7/2*x^3-31/2*x^2-5*x+12,-1/2*x^5-1/2*x^4+9/2*x^3+7/2*x^2-10*x-4,1,-x^5-x^4+9*x^3+9*x^2-20*x-14,2*x^4-2*x^3-16*x^2+10*x+22], x^6-x^5-9*x^4+7*x^3+20*x^2-12*x-8];
113E[84,1]=[[0,-1,4,-1,2,-6,-4,-4,2,-2,0,2,0,-4,12,-6,-8,6,-8,14,-2,12,-4,0,-2], x-1];
114E[84,2]=[[0,1,0,1,-6,2,0,-4,-6,6,8,2,12,-4,12,-6,0,-10,8,6,-10,-4,-12,12,-10], x-1];
115E[85,1]=[[1,2,-1,-2,2,2,1,0,6,-6,-10,2,10,4,12,-10,8,-14,8,-2,-14,-14,4,6,2], x-1];
116E[85,2]=[[x,-x-3,-1,x-1,x-3,-2*x-2,-1,-2*x-2,-x-3,-2*x-4,3*x+3,6*x+4,-6*x-4,4*x+6,-2*x-4,-4*x+2,2*x-10,4*x+6,2*x-4,-3*x-3,-2*x-4,x+5,8*x+6,4*x-4,4*x+2], x^2+2*x-1];
117E[85,3]=[[x,-x+1,1,x-1,-x+3,-4,-1,2*x+2,3*x-3,2*x,x+5,-2*x-4,2*x,-2*x-4,-4*x+6,6,2*x+6,4*x+2,-10,-5*x+3,-6*x-4,-9*x-1,2*x+12,-6*x-6,4*x+2], x^2-3];
118E[86,1]=[[-1,x,-x+1,2,0,2,x-4,-3*x-1,-x-5,x+2,3*x+2,3*x+2,3*x+3,1,-3*x-6,2*x+4,6,2,-10,4*x+2,14,3*x-1,2*x-2,2*x+4,-3*x-7], x^2+x-5];
119E[86,2]=[[1,x,-x-1,-4*x+2,4*x-4,4*x-2,-x,x+5,-3*x+3,-3*x-2,x+6,-x-2,-3*x-1,-1,7*x-2,-2*x-4,-4*x+10,-8*x+6,2,4*x-10,8*x-2,x-1,-6*x-2,-6*x+4,-5*x-3], x^2-x-1];
120E[87,1]=[[x,1,-2*x+2,-2*x-1,2*x+1,4*x-3,3,2*x-6,6*x-4,-1,-6*x,-2*x+4,2,4,-6*x+1,-2*x+10,-4*x+2,2*x-4,10*x-7,2*x-4,2*x+8,-2*x-14,-8*x-2,5,-14*x+10], x^2-x-1];
121E[87,2]=[[x,-1,-2*x^2+8,x^2-x-2,x^2-x-6,-x^2-x+6,3*x^2-x-10,2*x-2,-2*x^2+10,1,-2*x^2+10,-2*x+4,4*x^2-4*x-14,-4*x^2+4*x+12,-3*x^2+3*x+6,2*x^2+4*x-8,-2*x^2+2*x,2*x,3*x^2-3*x-10,-2*x^2-4*x+6,2*x-4,-4*x^2+2*x+14,2*x^2+2*x-12,x^2+5*x-10,2*x^2-4*x-4], x^3-2*x^2-4*x+7];
122E[88,1]=[[0,-3,-3,-2,-1,0,-6,4,1,-8,-7,-1,4,6,-8,2,-1,4,-5,3,16,2,-2,15,-7], x-1];
123E[88,2]=[[0,x,-x+2,-2*x,-1,2*x-2,2,-4,x+4,2*x-2,x-4,x-6,2*x+2,2*x-4,8,-4*x+6,-5*x,-2*x-2,-x+8,3*x-4,-2*x+2,2*x-8,2*x+4,-3*x-2,-x+14], x^2-x-4];
124E[89,1]=[[-1,-1,-1,-4,-2,2,3,-5,7,0,-9,-2,0,-7,-12,-3,4,6,12,-10,7,-6,12,-1,9], x-1];
125E[89,2]=[[1,2,-2,2,-4,2,6,-2,2,-6,6,10,-6,2,12,-6,-10,-6,12,4,10,-12,-6,1,-18], x-1];
126E[89,3]=[[x,-1/2*x^4+1/2*x^3+7/2*x^2-5/2*x-4,-x^2+4,1/2*x^4-4*x^2-x+13/2,-x^3+5*x+2,-x^4+x^3+8*x^2-5*x-11,x^4-x^3-7*x^2+4*x+4,1/2*x^3-1/2*x^2-3/2*x+9/2,x^4-3/2*x^3-13/2*x^2+17/2*x+11/2,-x^4+9*x^2-14,1/2*x^4-3/2*x^3-7/2*x^2+15/2*x+8,x^4-2*x^3-8*x^2+10*x+9,-x^4+x^3+8*x^2-3*x-11,-3/2*x^3+1/2*x^2+17/2*x-1/2,x^3-7*x-2,-x^4+7*x^2+x-8,1/2*x^4+x^3-3*x^2-8*x-1/2,-x^2+5,-x^4+9*x^2-2*x-14,-2*x^4+4*x^3+16*x^2-20*x-24,x^4-7*x^2+1,-x^4+2*x^3+8*x^2-10*x-1,1/2*x^4-4*x^2-3*x+1/2,1,-x^3-x^2+2*x+7], x^5+x^4-10*x^3-10*x^2+21*x+17];
127E[90,1]=[[1,0,-1,2,-6,-4,6,-4,0,6,-4,8,0,8,0,6,-6,2,-4,12,-10,-4,-12,-12,2], x-1];
128E[90,2]=[[-1,0,1,2,6,-4,-6,-4,0,-6,-4,8,0,8,0,-6,6,2,-4,-12,-10,-4,12,12,2], x-1];
129E[90,3]=[[1,0,1,-4,0,2,-6,-4,0,6,8,2,6,-4,0,6,0,-10,-4,0,2,8,-12,-18,2], x-1];
130E[91,1]=[[-2,0,-3,-1,-6,-1,4,5,3,-5,-3,-4,-6,-1,7,-9,8,-10,-6,-8,-13,3,15,3,7], x-1];
131E[91,2]=[[x,-x,x+3,1,-3*x,-1,-x,3*x-3,2*x-3,2*x+3,-3*x-1,-3*x-2,-2*x+6,-5,x+3,-2*x-3,4*x+6,6,6*x-6,5*x-6,3*x-5,-6*x+7,-3*x+9,x+3,-9*x-1], x^2-2];
132E[91,3]=[[x,-x^2+x+2,-x+1,-1,x^2-x-2,1,x^2+x-2,-x-1,-x^2-2*x+7,x^2+5,2*x^2-x-7,x^2+3*x-4,-2*x^2+2*x+6,-3*x^2-2*x+13,-4*x^2+x+9,-3*x^2+2*x+11,4*x^2+2*x-14,-2,4*x^2-6*x-14,-x^2+3*x,-4*x^2-x+9,-x^2+4*x-3,4*x^2-9*x-13,-2*x^2+5*x+5,-x-3], x^3-x^2-4*x+2];
133E[91,4]=[[0,-2,-3,1,0,1,-6,-7,3,-9,5,2,-6,-1,3,-9,0,-10,14,-6,11,-1,3,15,-1], x-1];
134E[92,1]=[[0,1,0,2,0,-1,-6,2,-1,-3,5,8,3,8,9,6,-12,14,8,-15,-7,-10,6,0,-10], x-1];
135E[92,2]=[[0,-3,-2,-4,2,-5,4,-2,1,-7,-3,2,-9,-8,9,2,0,-2,14,-3,-3,-6,8,12,0], x-1];
136E[93,1]=[[x,-1,-2*x-5,2*x+1,2*x,2*x+2,-4*x-8,-2*x-7,-2*x-2,2*x+4,-1,-6*x-8,6*x+9,-6*x-12,-4*x-4,8*x+12,-3,8,-12,9,2*x+4,4*x+10,-4*x-18,8*x+10,9], x^2+3*x+1];
137E[93,2]=[[x,1,-x^2-x+2,-x^2-x+4,2*x^2-6,2*x^2-4,2*x^2+2*x-6,-x^2+3*x+4,-2*x-2,-4*x^2-2*x+8,-1,2*x,x^2-3*x-6,-2*x^2-4*x+10,4*x+4,-2*x^2+2*x+2,x^2-x+6,2*x^2+6*x-6,4,x^2+7*x-6,-6*x-4,-2*x^2-2*x+8,-2*x^2-2*x+12,-6,-x^2-3*x+4], x^3-4*x+1];
138E[94,1]=[[-1,x,-1/2*x+2,-x-2,-1/2*x+4,-1/2*x-2,0,3/2*x-4,-x,3/2*x+6,-3*x,3*x+2,-x-6,3/2*x-4,1,x+2,2*x-4,3*x-2,-5/2*x-4,x+6,6,0,x,0,6], x^2-8];
139E[94,2]=[[1,0,0,0,2,-4,-2,-2,4,4,4,2,6,6,-1,2,12,2,2,8,-14,-16,-16,-10,-14], x-1];
140E[95,1]=[[x,-x^2+3,1,2*x^2-2*x-4,-2*x-2,x^2-2*x+1,-2*x^2+4*x+4,-1,2*x-2,2*x^2-8,4*x,x^2-2*x+5,2*x^2-4*x-4,-6*x^2+2*x+12,2*x^2-2*x-4,-x^2+2*x+7,-2*x^2-2,-2*x^2+6*x+2,x^2+4*x-3,-4*x^2+8,2*x^2-4,6*x^2-14,-2*x-10,6*x^2-4*x-12,-5*x^2-2*x+19], x^3-x^2-3*x+1];
141E[95,2]=[[x,-x^3+5*x-2,-1,-2*x^2-2*x+8,2*x^2+2*x-6,x^3+2*x^2-3*x-4,2*x^3-10*x+6,1,-2*x^3-2*x^2+8*x,2*x^3-10*x+6,2*x^3-2*x^2-10*x+14,x^3-3*x+2,-2*x^2+12,-2*x^2-2*x+8,2*x^2-2*x-12,-x^3+3*x-6,2*x^2+4*x-6,4*x^2+2*x-10,-3*x^3-2*x^2+15*x-4,2*x^3-2*x^2-14*x+6,-2*x^3+10*x+2,2*x^2+4*x-10,2*x^3-2*x^2-12*x+12,-2*x^3+6*x-6,-x^3+4*x^2+7*x-10], x^4+2*x^3-6*x^2-8*x+9];
142E[96,1]=[[0,-1,2,4,-4,-2,-6,4,0,2,-4,-2,2,-4,-8,10,4,6,-4,16,-6,-4,-12,10,-14], x-1];
143E[96,2]=[[0,1,2,-4,4,-2,-6,-4,0,2,4,-2,2,4,8,10,-4,6,4,-16,-6,4,12,10,-14], x-1];
144E[97,1]=[[x,-x^2-3*x-2,2*x^2+5*x-1,-x^2-3*x-3,x-1,-x-2,x^2+4*x+1,-4*x^2-6*x+7,-3*x-8,-4*x^2-14*x-5,x^2-6,6*x^2+17*x+2,x^2+x-1,3*x^2+8*x+1,4*x^2+12*x-3,-2*x^2-13*x-10,2*x^2+7*x+9,-5*x^2-8*x+7,3*x^2+13*x+7,3*x^2+11*x-3,-x^2-3*x-1,4*x^2+7*x-8,-8*x-10,-5*x^2-14*x+2,-1], x^3+4*x^2+3*x-1];
145E[97,2]=[[x,-x^2+x+2,-x+1,x^3-x^2-4*x+2,-2*x^3+4*x^2+3*x-3,-3*x^3+4*x^2+8*x-5,2*x^3-3*x^2-4*x+3,-x^3+2*x^2+3*x-4,-x^3+4*x^2-1,x^3-2*x^2+x+2,3*x^3-7*x^2-3*x+7,-3*x^3+6*x^2+6*x-9,3*x^3-7*x^2-10*x+14,-x^2+5,x^3-4*x^2-x+12,-x^3-2*x^2+8*x+3,-2*x^3+11*x+1,4*x^3-9*x^2-8*x+11,3*x^3-x^2-10*x-6,-x^3-x^2+8*x+4,3*x^3-x^2-10*x-8,-3*x^3+14*x-1,2*x^3-4*x^2+2*x+4,x^3+3*x^2-11*x-11,1], x^4-3*x^3-x^2+6*x-1];
146