File: 2adic.m

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sagemath-database-cremona-elliptic-curves 20221013-1
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// This magma script takes a filename in the format of
// Cremona's elliptic curve tables (a text file - not a gzipped text file)
// as a command line argument filename

// Each line of the output has 8 columns. 
// N class # [a1,a2,a3,a4,a6] index level matrix list (possibly empty) label

// For example
// 11 a 1 [0,-1,1,-10,-20] 1 1 [] X1
// 15 a 1 [1,1,1,-10,-10] 96 8 [[5,4,2,3],[1,0,0,5],[1,4,0,5],[1,0,4,5]] X187d
// 27 a 1 [0,0,1,0,-7] inf inf [] CM

// The index is the index of the 2-adic image in GL_2(Z_2)

// The level is the smallest 2^r so that the 2-adic image contains
// all matrices congruent to I mod 2^r.

// The matrix list is a list of generators of the image in GL_2(Z/2^r Z).
// The 2-adic image is conjugate (in GL_2(Z_2)) 
// to the inverse image in GL_2(Z_2) of the subgroup generated by the list
// of matrices.
// NOTE: These matrices act on the right! That is, we represent elements
// of E[2^r] as row vectors v, and the action of M in GL_2(Z_2) on these row
// vectors is by v -> v*M.

// The label is something like "X1" or "X7" or "X441" or "X243p". These are 
// the names we've given to the modular curves that parametrize these entries. 
// They all have the form Xn for some positive integer n, or Xnm, where n is a 
// positive integer and m is a lowercase letter. If there is no letter, the 
// 2-adic image contains -I. If there is a letter, the 2-adic image does not 
// contain -I. For each label, there is a human-readable website about that 
// image. The URL is something like http://users.wfu.edu/rouseja/2adic/X441.html

// A function field in one variable - used for maps to the j-line
F<t> := FunctionField(Rationals());
// A polynomial ring - used for computing preimages of maps to the j-line
R<x> := PolynomialRing(Rationals());
// A polynomial ring in 3 variables - used for constructing maps from
// E -> P^1
PPP<a,b,c> := PolynomialRing(Rationals(),3);

// An abbreviated collection of data about the 727 subgroups we consider
// The three things in the tuples are (i) the index, (ii) the level
// (for techical reasons, we consider GL_2(Z_2) to have level 2), and
// (iii) the genus of the corresponding modular curve.

subdata := [ <1, 2, 0>, <2, 2, 0>, <2, 4, 0>, <2, 8, 0>, <2, 8, 0>, <3, 2, 0>, 
<4, 4, 0>, <6, 2, 0>, <6, 4, 0>, <6, 4, 0>, <6, 4, 0>, <6, 4, 0>, <6, 4, 0>, <6,
8, 0>, <6, 8, 0>, <6, 8, 0>, <6, 8, 0>, <6, 8, 0>, <6, 8, 0>, <8, 4, 0>, <8, 4, 
0>, <8, 8, 0>, <12, 4, 0>, <12, 4, 0>, <12, 4, 0>, <12, 4, 0>, <12, 4, 0>, <12, 
8, 0>, <12, 8, 0>, <12, 8, 0>, <12, 8, 0>, <12, 8, 0>, <12, 8, 0>, <12, 8, 0>, 
<12, 8, 0>, <12, 8, 0>, <12, 8, 0>, <12, 8, 0>, <12, 8, 0>, <12, 8, 0>, <12, 8, 
0>, <12, 8, 0>, <12, 8, 0>, <12, 8, 0>, <12, 8, 0>, <12, 8, 0>, <12, 8, 0>, <12,
8, 0>, <12, 8, 0>, <12, 8, 0>, <12, 8, 1>, <12, 8, 1>, <12, 8, 1>, <12, 8, 1>, 
<16, 8, 0>, <16, 16, 0>, <16, 16, 0>, <24, 4, 0>, <24, 4, 0>, <24, 4, 0>, <24, 
8, 0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 0>, 
<24, 8, 0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 
0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 0>, <24,
8, 0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 0>, 
<24, 8, 0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 
0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 0>, <24, 8, 0>, <24,
8, 0>, <24, 8, 0>, <24, 16, 0>, <24, 16, 0>, <24, 16, 0>, <24, 16, 0>, <24, 16, 
0>, <24, 16, 0>, <24, 16, 0>, <24, 16, 0>, <24, 16, 0>, <24, 16, 0>, <24, 16, 
0>, <24, 16, 0>, <24, 16, 0>, <24, 16, 0>, <24, 16, 0>, <24, 16, 0>, <24, 16, 
0>, <24, 16, 0>, <24, 16, 0>, <24, 16, 0>, <24, 16, 0>, <24, 16, 0>, <24, 8, 1>,
<24, 8, 1>, <24, 8, 1>, <24, 8, 1>, <24, 8, 1>, <24, 8, 1>, <24, 8, 1>, <24, 8, 
1>, <24, 8, 1>, <24, 8, 1>, <24, 8, 1>, <24, 8, 1>, <24, 8, 1>, <24, 8, 1>, <24,
8, 1>, <24, 8, 1>, <24, 8, 1>, <24, 8, 1>, <24, 8, 1>, <24, 8, 1>, <24, 8, 1>, 
<24, 8, 1>, <24, 8, 1>, <24, 8, 1>, <24, 16, 1>, <24, 16, 1>, <24, 16, 1>, <24, 
16, 1>, <24, 16, 1>, <24, 16, 1>, <24, 16, 1>, <24, 16, 1>, <24, 16, 1>, <24, 
16, 1>, <24, 16, 1>, <24, 16, 1>, <24, 16, 1>, <24, 16, 1>, <24, 16, 1>, <24, 
16, 1>, <24, 16, 1>, <24, 16, 1>, <24, 16, 1>, <24, 16, 1>, <24, 16, 2>, <24, 
16, 2>, <24, 16, 2>, <24, 16, 2>, <24, 16, 2>, <24, 16, 2>, <24, 16, 2>, <24, 
16, 2>, <32, 32, 0>, <32, 32, 0>, <32, 8, 1>, <32, 8, 1>, <48, 8, 0>, <48, 8, 
0>, <48, 8, 0>, <48, 8, 0>, <48, 8, 0>, <48, 8, 0>, <48, 8, 0>, <48, 8, 0>, <48,
8, 0>, <48, 8, 0>, <48, 8, 0>, <48, 8, 0>, <48, 8, 0>, <48, 8, 0>, <48, 8, 0>, 
<48, 8, 0>, <48, 8, 0>, <48, 8, 0>, <48, 8, 0>, <48, 8, 0>, <48, 8, 0>, <48, 8, 
0>, <48, 8, 0>, <48, 8, 0>, <48, 8, 0>, <48, 8, 0>, <48, 16, 0>, <48, 16, 0>, 
<48, 16, 0>, <48, 16, 0>, <48, 16, 0>, <48, 16, 0>, <48, 16, 0>, <48, 16, 0>, 
<48, 16, 0>, <48, 16, 0>, <48, 16, 0>, <48, 16, 0>, <48, 16, 0>, <48, 16, 0>, 
<48, 16, 0>, <48, 16, 0>, <48, 16, 0>, <48, 16, 0>, <48, 16, 0>, <48, 16, 0>, 
<48, 16, 0>, <48, 16, 0>, <48, 16, 0>, <48, 16, 0>, <48, 16, 0>, <48, 16, 0>, 
<48, 16, 0>, <48, 16, 0>, <48, 16, 0>, <48, 16, 0>, <48, 16, 0>, <48, 32, 0>, 
<48, 32, 0>, <48, 32, 0>, <48, 32, 0>, <48, 32, 0>, <48, 32, 0>, <48, 8, 1>, 
<48, 8, 1>, <48, 8, 1>, <48, 8, 1>, <48, 8, 1>, <48, 8, 1>, <48, 8, 1>, <48, 8, 
1>, <48, 8, 1>, <48, 8, 1>, <48, 8, 1>, <48, 8, 1>, <48, 8, 1>, <48, 8, 1>, <48,
8, 1>, <48, 8, 1>, <48, 8, 1>, <48, 8, 1>, <48, 8, 1>, <48, 8, 1>, <48, 8, 1>, 
<48, 8, 1>, <48, 8, 1>, <48, 8, 1>, <48, 8, 1>, <48, 8, 1>, <48, 8, 1>, <48, 8, 
1>, <48, 8, 1>, <48, 8, 1>, <48, 8, 1>, <48, 8, 1>, <48, 8, 1>, <48, 8, 1>, <48,
8, 1>, <48, 8, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 
1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 
1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 
1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 
1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 
1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 
1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 
1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 
1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 
1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 
1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 
1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 1>, <48, 16, 
1>, <48, 16, 1>, <48, 16, 1>, <48, 32, 1>, <48, 32, 1>, <48, 32, 1>, <48, 32, 
1>, <48, 8, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>,
<48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, 
<48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, 
<48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, 
<48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, 
<48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, 
<48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, 
<48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, <48, 16, 2>, 
<48, 32, 2>, <48, 32, 2>, <48, 32, 2>, <48, 32, 2>, <48, 16, 3>, <48, 16, 3>, 
<48, 16, 3>, <48, 16, 3>, <48, 16, 3>, <48, 16, 3>, <48, 16, 3>, <48, 16, 3>, 
<48, 16, 3>, <48, 16, 3>, <48, 16, 3>, <48, 16, 3>, <48, 16, 3>, <48, 16, 3>, 
<48, 16, 3>, <48, 16, 3>, <48, 16, 3>, <48, 16, 3>, <48, 32, 3>, <48, 32, 3>, 
<48, 32, 3>, <48, 32, 3>, <48, 32, 3>, <48, 32, 3>, <48, 32, 3>, <48, 32, 3>, 
<48, 32, 3>, <48, 32, 3>, <48, 32, 3>, <48, 32, 3>, <64, 16, 1>, <64, 16, 1>, 
<64, 16, 2>, <96, 8, 1>, <96, 8, 1>, <96, 8, 1>, <96, 8, 1>, <96, 8, 1>, <96, 8,
1>, <96, 8, 1>, <96, 8, 1>, <96, 8, 1>, <96, 8, 1>, <96, 8, 1>, <96, 8, 1>, <96,
8, 1>, <96, 8, 1>, <96, 8, 1>, <96, 8, 1>, <96, 8, 1>, <96, 8, 1>, <96, 8, 1>, 
<96, 8, 1>, <96, 8, 1>, <96, 8, 1>, <96, 8, 1>, <96, 8, 1>, <96, 16, 1>, <96, 
16, 1>, <96, 16, 1>, <96, 16, 1>, <96, 16, 1>, <96, 16, 1>, <96, 16, 1>, <96, 
16, 1>, <96, 16, 1>, <96, 16, 1>, <96, 16, 1>, <96, 16, 1>, <96, 16, 1>, <96, 
16, 1>, <96, 16, 1>, <96, 16, 1>, <96, 16, 1>, <96, 16, 1>, <96, 16, 1>, <96, 
16, 1>, <96, 16, 1>, <96, 16, 1>, <96, 32, 1>, <96, 32, 1>, <96, 32, 1>, <96, 
32, 1>, <96, 32, 1>, <96, 32, 1>, <96, 32, 1>, <96, 32, 1>, <96, 32, 1>, <96, 
32, 1>, <96, 32, 1>, <96, 32, 1>, <96, 16, 2>, <96, 16, 2>, <96, 16, 2>, <96, 
16, 2>, <96, 16, 2>, <96, 16, 2>, <96, 16, 2>, <96, 16, 2>, <96, 16, 2>, <96, 
16, 2>, <96, 16, 2>, <96, 16, 2>, <96, 16, 2>, <96, 16, 2>, <96, 16, 2>, <96, 
16, 2>, <96, 16, 2>, <96, 16, 2>, <96, 16, 2>, <96, 16, 2>, <96, 32, 2>, <96, 
32, 2>, <96, 32, 2>, <96, 32, 2>, <96, 32, 2>, <96, 32, 2>, <96, 32, 2>, <96, 
32, 2>, <96, 32, 2>, <96, 32, 2>, <96, 32, 2>, <96, 32, 2>, <96, 32, 2>, <96, 
32, 2>, <96, 32, 2>, <96, 32, 2>, <96, 8, 3>, <96, 8, 3>, <96, 8, 3>, <96, 8, 
3>, <96, 8, 3>, <96, 8, 3>, <96, 8, 3>, <96, 8, 3>, <96, 16, 3>, <96, 16, 3>, 
<96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, 
<96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, 
<96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, 
<96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, 
<96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, 
<96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, 
<96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, 
<96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, 
<96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, 
<96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, 
<96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, 
<96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 16, 3>, <96, 32, 3>, <96, 32, 3>, 
<96, 32, 3>, <96, 32, 3>, <96, 32, 3>, <96, 32, 3>, <96, 32, 3>, <96, 32, 3>, 
<96, 32, 3>, <96, 32, 3>, <96, 32, 3>, <96, 32, 3>, <96, 32, 3>, <96, 32, 3>, 
<96, 32, 3>, <96, 32, 3>, <96, 32, 3>, <96, 32, 3>, <96, 32, 3>, <96, 32, 3>, 
<96, 32, 3>, <96, 32, 3>, <96, 32, 3>, <96, 32, 3>, <96, 32, 3>, <96, 32, 3>, 
<96, 32, 3>, <96, 32, 3>, <96, 32, 3>, <96, 32, 3>, <96, 32, 3>, <96, 32, 3>, 
<96, 32, 3>, <96, 32, 3>, <96, 32, 3>, <96, 32, 3>, <96, 32, 3>, <96, 32, 3>, 
<96, 32, 3>, <96, 32, 3>, <96, 32, 3>, <96, 32, 3>, <96, 32, 3>, <96, 32, 3>, 
<96, 32, 3>, <96, 32, 3>, <96, 64, 3>, <96, 64, 3>, <96, 64, 3>, <96, 64, 3>, 
<96, 64, 3>, <96, 64, 3>, <96, 64, 3>, <96, 64, 3>, <96, 16, 5>, <96, 16, 5>, 
<96, 32, 5>, <96, 32, 5>, <96, 32, 5>, <96, 32, 5>, <96, 32, 5>, <96, 32, 5>, 
<96, 32, 5>, <96, 32, 5>, <96, 32, 5>, <96, 32, 5>, <96, 32, 5>, <96, 32, 5>, 
<96, 32, 5>, <96, 32, 5>, <96, 32, 5>, <96, 32, 5>, <96, 32, 5>, <96, 32, 5>, 
<96, 32, 5>, <96, 32, 5>, <96, 32, 5>, <96, 32, 5>, <96, 32, 5>, <96, 32, 5>, 
<96, 64, 5>, <96, 64, 5>, <96, 64, 5>, <96, 64, 5>, <96, 64, 5>, <96, 64, 5>, 
<96, 64, 5>, <96, 64, 5>, <96, 32, 7>, <96, 32, 7>, <96, 32, 7>, <96, 32, 7>, 
<96, 32, 7>, <96, 32, 7>, <96, 32, 7>, <96, 32, 7>, <96, 32, 7>, <96, 32, 7>, 
<96, 32, 7>, <96, 32, 7>, <96, 32, 7>, <96, 32, 7>, <128, 32, 5>, <128, 32, 5>, 
<192, 64, 5>, <192, 64, 5>, <192, 64, 5>, <192, 64, 5>, <192, 64, 5>, <192, 64, 
5>, <192, 64, 5>, <192, 64, 5> ];

// Data about the 1006 subgroups that can occur as a 2-adic image and
// don't contain -I. Each of these is an index 2 subgroup of one of the
// subgroups referenced in the first list.

finesubdata := [ <2, 4, 4, "X2a">, <2, 4, 8, "X2b">, <3, 4, 4, "X3a">,
<3, 4, 8, "X3b">, <8, 12, 8, "X8a">, <8, 12, 4, "X8b">, <8, 12, 8,
"X8c">, <8, 12, 4, "X8d">, <9, 12, 8, "X9a">, <9, 12, 8, "X9b">, <9,
12, 8, "X9c">, <9, 12, 8, "X9d">, <10, 12, 8, "X10a">, <10, 12, 4,
"X10b">, <10, 12, 8, "X10c">, <10, 12, 4, "X10d">, <13, 12, 8,
"X13a">, <13, 12, 8, "X13b">, <13, 12, 8, "X13c">, <13, 12, 8,
"X13d">, <13, 12, 8, "X13e">, <13, 12, 4, "X13f">, <13, 12, 8,
"X13g">, <13, 12, 4, "X13h">, <20, 16, 8, "X20a">, <20, 16, 4,
"X20b">, <24, 24, 8, "X24a">, <24, 24, 8, "X24b">, <24, 24, 8,
"X24c">, <24, 24, 4, "X24d">, <24, 24, 4, "X24e">, <24, 24, 8,
"X24f">, <24, 24, 8, "X24g">, <24, 24, 8, "X24h">, <25, 24, 8,
"X25a">, <25, 24, 8, "X25b">, <25, 24, 8, "X25c">, <25, 24, 8,
"X25d">, <25, 24, 8, "X25e">, <25, 24, 8, "X25f">, <25, 24, 8,
"X25g">, <25, 24, 4, "X25h">, <25, 24, 4, "X25i">, <25, 24, 8,
"X25j">, <25, 24, 8, "X25k">, <25, 24, 8, "X25l">, <25, 24, 8,
"X25m">, <25, 24, 4, "X25n">, <27, 24, 8, "X27a">, <27, 24, 8,
"X27b">, <27, 24, 8, "X27c">, <27, 24, 8, "X27d">, <27, 24, 8,
"X27e">, <27, 24, 4, "X27f">, <27, 24, 8, "X27g">, <27, 24, 4,
"X27h">, <32, 24, 16, "X32a">, <32, 24, 16, "X32b">, <32, 24, 8,
"X32c">, <32, 24, 8, "X32d">, <32, 24, 8, "X32e">, <32, 24, 8,
"X32f">, <32, 24, 16, "X32g">, <32, 24, 16, "X32h">, <32, 24, 8,
"X32i">, <32, 24, 8, "X32j">, <32, 24, 8, "X32k">, <32, 24, 8,
"X32l">, <33, 24, 8, "X33a">, <33, 24, 8, "X33b">, <33, 24, 8,
"X33c">, <33, 24, 8, "X33d">, <33, 24, 8, "X33e">, <33, 24, 8,
"X33f">, <33, 24, 8, "X33g">, <33, 24, 8, "X33h">, <34, 24, 8,
"X34a">, <34, 24, 8, "X34b">, <34, 24, 8, "X34c">, <34, 24, 8,
"X34d">, <34, 24, 8, "X34e">, <34, 24, 8, "X34f">, <34, 24, 8,
"X34g">, <34, 24, 8, "X34h">, <36, 24, 8, "X36a">, <36, 24, 16,
"X36b">, <36, 24, 8, "X36c">, <36, 24, 16, "X36d">, <36, 24, 8,
"X36e">, <36, 24, 8, "X36f">, <36, 24, 16, "X36g">, <36, 24, 8,
"X36h">, <36, 24, 8, "X36i">, <36, 24, 16, "X36j">, <36, 24, 8,
"X36k">, <36, 24, 8, "X36l">, <36, 24, 16, "X36m">, <36, 24, 8,
"X36n">, <36, 24, 8, "X36o">, <36, 24, 16, "X36p">, <36, 24, 8,
"X36q">, <36, 24, 16, "X36r">, <36, 24, 8, "X36s">, <36, 24, 16,
"X36t">, <37, 24, 16, "X37a">, <37, 24, 8, "X37b">, <37, 24, 16,
"X37c">, <37, 24, 8, "X37d">, <38, 24, 8, "X38a">, <38, 24, 8,
"X38b">, <38, 24, 8, "X38c">, <38, 24, 8, "X38d">, <40, 24, 16,
"X40a">, <40, 24, 16, "X40b">, <40, 24, 16, "X40c">, <40, 24, 16,
"X40d">, <42, 24, 16, "X42a">, <42, 24, 8, "X42b">, <42, 24, 16,
"X42c">, <42, 24, 8, "X42d">, <44, 24, 8, "X44a">, <44, 24, 8,
"X44b">, <44, 24, 8, "X44c">, <44, 24, 8, "X44d">, <46, 24, 8,
"X46a">, <46, 24, 8, "X46b">, <46, 24, 8, "X46c">, <46, 24, 8,
"X46d">, <48, 24, 8, "X48a">, <48, 24, 8, "X48b">, <48, 24, 8,
"X48c">, <48, 24, 8, "X48d">, <57, 32, 32, "X57a">, <57, 32, 32,
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<207, 96, 32, "X207f">, <207, 96, 16, "X207g">, <207, 96, 16,
"X207h">, <207, 96, 16, "X207i">, <207, 96, 16, "X207j">, <207, 96,
16, "X207k">, <207, 96, 16, "X207l">, <207, 96, 16, "X207m">, <207,
96, 16, "X207n">, <208, 96, 16, "X208a">, <208, 96, 16, "X208b">,
<208, 96, 16, "X208c">, <208, 96, 16, "X208d">, <208, 96, 16,
"X208e">, <208, 96, 16, "X208f">, <208, 96, 16, "X208g">, <208, 96,
16, "X208h">, <208, 96, 16, "X208i">, <208, 96, 16, "X208j">, <208,
96, 16, "X208k">, <208, 96, 16, "X208l">, <209, 96, 16, "X209a">,
<209, 96, 16, "X209b">, <209, 96, 16, "X209c">, <209, 96, 16,
"X209d">, <210, 96, 16, "X210a">, <210, 96, 16, "X210b">, <210, 96,
16, "X210c">, <210, 96, 16, "X210d">, <211, 96, 16, "X211a">, <211,
96, 32, "X211b">, <211, 96, 16, "X211c">, <211, 96, 32, "X211d">,
<211, 96, 16, "X211e">, <211, 96, 32, "X211f">, <211, 96, 16,
"X211g">, <211, 96, 32, "X211h">, <211, 96, 32, "X211i">, <211, 96,
16, "X211j">, <211, 96, 32, "X211k">, <211, 96, 32, "X211l">, <211,
96, 16, "X211m">, <211, 96, 32, "X211n">, <211, 96, 16, "X211o">,
<211, 96, 16, "X211p">, <211, 96, 16, "X211q">, <211, 96, 16,
"X211r">, <211, 96, 16, "X211s">, <211, 96, 16, "X211t">, <212, 96,
32, "X212a">, <212, 96, 32, "X212b">, <212, 96, 32, "X212c">, <212,
96, 32, "X212d">, <212, 96, 16, "X212e">, <212, 96, 16, "X212f">,
<212, 96, 16, "X212g">, <212, 96, 16, "X212h">, <212, 96, 16,
"X212i">, <212, 96, 16, "X212j">, <212, 96, 16, "X212k">, <212, 96,
16, "X212l">, <213, 96, 32, "X213a">, <213, 96, 32, "X213b">, <213,
96, 32, "X213c">, <213, 96, 32, "X213d">, <213, 96, 16, "X213e">,
<213, 96, 16, "X213f">, <213, 96, 16, "X213g">, <213, 96, 16,
"X213h">, <213, 96, 16, "X213i">, <213, 96, 16, "X213j">, <213, 96,
16, "X213k">, <213, 96, 16, "X213l">, <214, 96, 16, "X214a">, <214,
96, 16, "X214b">, <214, 96, 16, "X214c">, <214, 96, 16, "X214d">,
<215, 96, 16, "X215a">, <215, 96, 16, "X215b">, <215, 96, 16,
"X215c">, <215, 96, 16, "X215d">, <215, 96, 16, "X215e">, <215, 96,
16, "X215f">, <215, 96, 16, "X215g">, <215, 96, 16, "X215h">, <215,
96, 16, "X215i">, <215, 96, 16, "X215j">, <215, 96, 16, "X215k">,
<215, 96, 16, "X215l">, <217, 96, 16, "X217a">, <217, 96, 16,
"X217b">, <217, 96, 16, "X217c">, <217, 96, 16, "X217d">, <217, 96,
16, "X217e">, <217, 96, 16, "X217f">, <217, 96, 16, "X217g">, <217,
96, 16, "X217h">, <219, 96, 16, "X219a">, <219, 96, 16, "X219b">,
<219, 96, 16, "X219c">, <219, 96, 16, "X219d">, <219, 96, 16,
"X219e">, <219, 96, 16, "X219f">, <219, 96, 16, "X219g">, <219, 96,
16, "X219h">, <221, 96, 16, "X221a">, <221, 96, 16, "X221b">, <221,
96, 16, "X221c">, <221, 96, 16, "X221d">, <222, 96, 16, "X222a">,
<222, 96, 16, "X222b">, <222, 96, 16, "X222c">, <222, 96, 16,
"X222d">, <223, 96, 16, "X223a">, <223, 96, 16, "X223b">, <223, 96,
16, "X223c">, <223, 96, 16, "X223d">, <223, 96, 16, "X223e">, <223,
96, 16, "X223f">, <223, 96, 16, "X223g">, <223, 96, 16, "X223h">,
<225, 96, 32, "X225a">, <225, 96, 32, "X225b">, <225, 96, 32,
"X225c">, <225, 96, 32, "X225d">, <225, 96, 16, "X225e">, <225, 96,
16, "X225f">, <225, 96, 16, "X225g">, <225, 96, 16, "X225h">, <225,
96, 16, "X225i">, <225, 96, 16, "X225j">, <225, 96, 16, "X225k">,
<225, 96, 16, "X225l">, <226, 96, 16, "X226a">, <226, 96, 16,
"X226b">, <226, 96, 16, "X226c">, <226, 96, 16, "X226d">, <226, 96,
16, "X226e">, <226, 96, 16, "X226f">, <226, 96, 16, "X226g">, <226,
96, 16, "X226h">, <227, 96, 32, "X227a">, <227, 96, 32, "X227b">,
<227, 96, 32, "X227c">, <227, 96, 32, "X227d">, <227, 96, 16,
"X227e">, <227, 96, 16, "X227f">, <227, 96, 16, "X227g">, <227, 96,
16, "X227h">, <227, 96, 16, "X227i">, <227, 96, 16, "X227j">, <227,
96, 16, "X227k">, <227, 96, 16, "X227l">, <228, 96, 16, "X228a">,
<228, 96, 16, "X228b">, <228, 96, 16, "X228c">, <228, 96, 16,
"X228d">, <228, 96, 16, "X228e">, <228, 96, 16, "X228f">, <228, 96,
16, "X228g">, <228, 96, 16, "X228h">, <229, 96, 16, "X229a">, <229,
96, 16, "X229b">, <229, 96, 16, "X229c">, <229, 96, 16, "X229d">,
<229, 96, 16, "X229e">, <229, 96, 16, "X229f">, <229, 96, 16,
"X229g">, <229, 96, 16, "X229h">, <230, 96, 16, "X230a">, <230, 96,
16, "X230b">, <230, 96, 16, "X230c">, <230, 96, 16, "X230d">, <230,
96, 16, "X230e">, <230, 96, 16, "X230f">, <230, 96, 16, "X230g">,
<230, 96, 16, "X230h">, <231, 96, 16, "X231a">, <231, 96, 16,
"X231b">, <231, 96, 16, "X231c">, <231, 96, 16, "X231d">, <233, 96,
16, "X233a">, <233, 96, 16, "X233b">, <233, 96, 16, "X233c">, <233,
96, 16, "X233d">, <233, 96, 16, "X233e">, <233, 96, 16, "X233f">,
<233, 96, 16, "X233g">, <233, 96, 16, "X233h">, <234, 96, 16,
"X234a">, <234, 96, 16, "X234b">, <234, 96, 16, "X234c">, <234, 96,
16, "X234d">, <234, 96, 16, "X234e">, <234, 96, 16, "X234f">, <234,
96, 16, "X234g">, <234, 96, 16, "X234h">, <235, 96, 16, "X235a">,
<235, 96, 32, "X235b">, <235, 96, 16, "X235c">, <235, 96, 32,
"X235d">, <235, 96, 16, "X235e">, <235, 96, 16, "X235f">, <235, 96,
16, "X235g">, <235, 96, 32, "X235h">, <235, 96, 16, "X235i">, <235,
96, 32, "X235j">, <235, 96, 16, "X235k">, <235, 96, 16, "X235l">,
<235, 96, 16, "X235m">, <235, 96, 32, "X235n">, <235, 96, 16,
"X235o">, <235, 96, 32, "X235p">, <235, 96, 16, "X235q">, <235, 96,
16, "X235r">, <235, 96, 32, "X235s">, <235, 96, 32, "X235t">, <236,
96, 16, "X236a">, <236, 96, 16, "X236b">, <236, 96, 16, "X236c">,
<236, 96, 16, "X236d">, <236, 96, 16, "X236e">, <236, 96, 16,
"X236f">, <236, 96, 16, "X236g">, <236, 96, 16, "X236h">, <238, 96,
32, "X238a">, <238, 96, 32, "X238b">, <238, 96, 32, "X238c">, <238,
96, 32, "X238d">, <239, 96, 32, "X239a">, <239, 96, 32, "X239b">,
<239, 96, 32, "X239c">, <239, 96, 32, "X239d">, <240, 96, 32,
"X240a">, <240, 96, 32, "X240b">, <240, 96, 32, "X240c">, <240, 96,
32, "X240d">, <240, 96, 32, "X240e">, <240, 96, 32, "X240f">, <240,
96, 32, "X240g">, <240, 96, 32, "X240h">, <240, 96, 32, "X240i">,
<240, 96, 32, "X240j">, <240, 96, 32, "X240k">, <240, 96, 32,
"X240l">, <240, 96, 32, "X240m">, <240, 96, 32, "X240n">, <240, 96,
32, "X240o">, <240, 96, 32, "X240p">, <241, 96, 32, "X241a">, <241,
96, 32, "X241b">, <241, 96, 32, "X241c">, <241, 96, 32, "X241d">,
<241, 96, 32, "X241e">, <241, 96, 32, "X241f">, <241, 96, 32,
"X241g">, <241, 96, 32, "X241h">, <242, 96, 32, "X242a">, <242, 96,
32, "X242b">, <242, 96, 32, "X242c">, <242, 96, 32, "X242d">, <242,
96, 32, "X242e">, <242, 96, 32, "X242f">, <242, 96, 32, "X242g">,
<242, 96, 32, "X242h">, <243, 96, 32, "X243a">, <243, 96, 32,
"X243b">, <243, 96, 32, "X243c">, <243, 96, 32, "X243d">, <243, 96,
32, "X243e">, <243, 96, 32, "X243f">, <243, 96, 32, "X243g">, <243,
96, 32, "X243h">, <243, 96, 32, "X243i">, <243, 96, 32, "X243j">,
<243, 96, 32, "X243k">, <243, 96, 32, "X243l">, <243, 96, 32,
"X243m">, <243, 96, 32, "X243n">, <243, 96, 32, "X243o">, <243, 96,
32, "X243p"> ]; 
// Lists of generating matrices.  
genlists := [ "[]",
"[[0,1,1,1]]", "[[3,3,0,1],[0,1,3,1]]", "[[7,7,0,1],[5,0,1,1]]",
"[[5,5,0,1],[0,1,1,1]]", "[[1,1,0,1]]", "[[2,1,3,1],[3,1,2,1]]", "[]",
"[[1,1,0,1],[3,0,2,1]]", "[[1,0,2,1],[3,3,0,1],[1,2,0,1]]",
"[[1,0,2,3],[1,2,0,1],[3,1,2,1]]", "[[1,0,0,3],[1,1,2,3]]",
"[[3,0,0,1],[1,1,0,1],[3,0,0,3]]", "[[1,0,2,5],[1,0,0,7],[1,1,6,7]]",
"[[1,1,0,1],[7,0,2,1],[5,0,2,1]]", "[[1,1,0,1],[7,0,0,1],[5,0,2,1]]",
"[[1,0,2,1],[1,0,0,7],[1,1,0,5]]", "[[1,0,2,5],[1,0,6,7],[1,1,6,7]]",
"[[1,0,2,1],[1,0,0,3],[1,1,0,5]]", "[[3,3,0,1],[1,1,3,0]]",
"[[1,1,3,0],[1,2,2,3]]", "[[2,3,1,7],[1,7,6,7]]",
"[[1,0,2,3],[1,1,2,3]]", "[[3,0,0,1],[3,2,2,3],[3,0,0,3]]",
"[[3,0,0,1],[3,0,0,3],[1,2,0,1]]", "[[1,1,0,3],[1,2,2,3]]",
"[[3,3,0,1],[3,0,0,3],[1,2,0,1]]",
"[[1,0,0,5],[1,2,0,1],[1,3,4,3],[1,3,6,7]]",
"[[1,2,4,1],[1,2,0,1],[1,0,6,3],[1,3,6,7]]",
"[[3,6,0,1],[3,0,0,7],[3,0,0,3],[3,3,2,1]]",
"[[1,1,2,1],[1,3,6,7],[1,0,0,7]]",
"[[7,0,0,1],[7,7,4,3],[5,0,0,1],[3,0,0,3]]",
"[[7,0,0,1],[7,7,4,3],[3,0,0,3],[7,0,4,3]]",
"[[5,0,4,3],[7,7,4,3],[3,0,0,3],[7,0,4,3]]",
"[[1,2,0,1],[1,3,4,3],[1,3,6,7],[1,0,4,5]]",
"[[1,1,0,1],[7,0,0,7],[7,0,0,1],[5,0,0,1],[3,0,0,3]]",
"[[1,0,6,7],[1,1,0,5],[3,0,0,3]]",
"[[1,0,6,7],[3,0,6,7],[3,0,0,3],[3,6,6,7]]",
"[[1,1,2,7],[1,3,0,7],[1,3,2,7],[1,0,4,1]]",
"[[1,2,0,1],[1,3,6,7],[1,0,0,7]]",
"[[1,2,4,1],[1,2,0,1],[1,1,2,7],[1,2,2,3]]",
"[[7,7,0,1],[1,2,0,1],[5,0,2,1]]",
"[[1,2,0,1],[1,3,2,3],[5,0,0,1],[7,5,0,1]]",
"[[3,0,0,5],[1,1,0,5],[3,0,0,3],[1,0,4,1]]",
"[[1,2,0,1],[5,0,4,1],[7,5,2,1],[7,5,0,1]]",
"[[3,0,0,5],[3,0,6,7],[3,0,0,3],[3,6,6,7]]",
"[[1,2,4,1],[1,0,0,5],[1,3,4,3],[1,3,2,3]]",
"[[1,1,0,5],[3,0,0,1],[3,0,0,3],[1,0,4,1]]",
"[[1,1,2,7],[1,0,2,3],[1,3,2,7],[1,0,4,1]]",
"[[1,2,4,1],[1,3,4,3],[1,3,6,7],[1,0,4,5]]",
"[[5,0,0,5],[1,3,6,7],[5,5,2,5],[1,1,2,5]]",
"[[1,2,0,3],[1,0,0,7],[1,1,6,3]]",
"[[1,2,4,1],[1,3,4,3],[1,0,4,5],[1,3,2,3]]",
"[[1,2,4,1],[1,0,0,5],[1,3,4,3],[1,3,6,7]]",
"[[7,5,7,2],[6,7,5,7],[3,2,7,5]]", "[[13,11,1,6],[7,3,0,1]]",
"[[1,7,1,2],[15,11,0,1]]", "[[3,0,0,3],[3,0,2,1]]",
"[[3,0,0,3],[1,2,2,3]]", "[[3,3,0,1],[3,0,0,3]]",
"[[1,0,0,5],[1,2,6,7],[3,6,2,7],[3,0,0,3]]",
"[[3,6,0,7],[7,0,0,7],[7,0,0,1],[7,0,4,7],[3,0,0,3]]",
"[[1,2,2,7],[1,3,2,7],[1,1,6,3]]",
"[[5,0,0,1],[3,0,0,3],[7,7,2,1],[3,3,0,1]]",
"[[5,5,2,3],[7,7,2,1],[3,3,0,1]]",
"[[3,0,0,5],[1,4,0,1],[3,0,0,3],[3,6,6,3]]",
"[[1,4,0,5],[3,0,0,5],[3,0,0,3],[3,6,6,3]]",
"[[1,0,0,5],[1,0,2,3],[1,1,6,7]]",
"[[1,1,2,7],[1,0,2,3],[1,4,0,1],[1,1,6,7]]",
"[[1,1,0,7],[1,0,6,3],[1,2,4,5]]", "[[1,1,0,7],[1,0,2,3],[1,2,0,5]]",
"[[3,6,0,1],[1,1,6,7],[1,1,6,3]]",
"[[1,0,4,5],[1,2,2,3],[1,5,4,7],[1,4,0,1]]",
"[[1,2,2,3],[5,0,0,1],[3,3,0,1]]",
"[[7,0,0,7],[5,5,0,1],[3,0,0,1],[3,0,0,3]]",
"[[1,1,2,7],[1,0,6,3],[5,0,0,5],[1,1,6,3]]",
"[[1,2,0,1],[1,3,0,7],[1,1,2,7]]",
"[[7,0,0,7],[7,0,0,1],[5,5,0,1],[3,0,0,3]]",
"[[3,0,0,5],[3,3,4,3],[3,0,0,3]]", "[[1,0,6,7],[1,1,2,7],[1,0,2,7]]",
"[[1,2,0,1],[1,3,6,7],[1,0,2,7]]", "[[1,2,0,1],[1,0,6,7],[1,3,0,3]]",
"[[7,7,0,1],[7,6,2,1],[1,0,4,1]]",
"[[3,3,0,3],[7,0,0,7],[5,0,0,1],[5,0,0,3]]",
"[[3,3,0,3],[7,0,0,7],[7,0,0,1],[7,0,0,3]]",
"[[3,3,0,3],[7,0,0,7],[7,0,0,3],[5,0,0,3]]",
"[[7,6,4,7],[7,0,0,7],[7,0,0,1],[7,0,0,3],[3,0,4,7]]",
"[[3,1,6,7],[3,0,0,7],[1,1,6,3]]", "[[3,1,6,7],[1,1,6,7],[1,1,6,3]]",
"[[1,3,6,7],[1,1,4,3],[1,2,0,5]]", "[[1,3,0,7],[1,1,2,7],[1,2,0,5]]",
"[[1,2,0,1],[7,0,0,7],[5,0,0,1],[3,0,0,3],[3,3,0,1]]",
"[[3,6,0,1],[3,0,0,7],[1,1,6,3]]",
"[[1,2,0,1],[3,0,0,3],[7,0,4,3],[5,5,4,3]]",
"[[7,7,0,1],[3,0,4,3],[3,1,0,1],[3,0,0,3]]",
"[[1,2,0,1],[7,0,0,7],[7,0,0,1],[7,0,0,3],[5,0,0,1]]",
"[[1,3,0,7],[1,3,2,7],[1,1,6,3]]",
"[[7,6,4,7],[7,0,0,7],[5,0,0,1],[7,0,4,3],[1,0,4,7]]",
"[[7,6,4,7],[7,0,0,7],[7,0,0,1],[5,0,0,1],[7,0,4,3]]",
"[[1,2,0,1],[7,0,0,7],[3,0,4,7],[7,0,4,3],[1,0,4,7]]",
"[[7,6,4,7],[7,0,0,7],[7,0,0,3],[3,0,4,7],[1,0,4,7]]",
"[[1,1,0,1],[7,0,0,7],[7,0,0,1],[5,0,0,1]]",
"[[1,0,0,5],[3,15,2,1],[3,12,0,3],[1,6,0,3]]",
"[[3,9,14,7],[3,0,0,7],[3,3,2,1],[1,5,6,3]]",
"[[13,10,0,1],[13,13,2,3],[15,13,0,1],[1,0,4,1]]",
"[[13,10,0,1],[13,13,2,3],[5,10,2,3],[1,0,4,1]]",
"[[5,15,2,3],[13,13,2,3],[5,10,2,3],[1,0,4,1]]",
"[[3,0,0,11],[1,1,10,5],[3,0,14,7]]",
"[[1,2,0,1],[1,3,0,7],[1,3,14,7],[1,0,4,5]]",
"[[1,2,0,1],[1,3,14,7],[1,0,4,5],[1,0,6,11]]",
"[[1,2,0,1],[1,3,0,7],[1,3,10,7],[1,0,4,13]]",
"[[1,2,0,1],[1,3,10,7],[1,0,4,13],[1,3,12,15]]",
"[[1,3,12,3],[1,1,12,7],[1,0,4,5],[1,3,14,7]]",
"[[1,3,12,3],[1,3,0,3],[1,0,2,3],[1,2,0,13]]",
"[[3,6,0,7],[1,2,0,7],[3,0,0,3],[3,9,12,7]]",
"[[1,0,0,5],[3,0,0,5],[3,0,0,3],[3,9,12,7]]",
"[[1,1,0,1],[3,0,8,7],[7,0,0,7],[1,0,8,7],[3,0,0,3]]",
"[[1,1,0,1],[7,0,0,7],[7,0,0,1],[5,0,0,1],[3,0,0,3]]",
"[[3,3,0,3],[3,0,8,3],[7,0,0,7],[7,0,0,1],[5,0,0,1]]",
"[[3,3,0,3],[3,0,8,3],[7,0,0,7],[5,0,0,1],[5,0,0,3]]",
"[[3,3,0,3],[3,0,8,3],[7,0,0,7],[7,0,0,1],[7,0,0,3]]",
"[[3,3,0,3],[3,0,8,3],[7,0,0,7],[7,0,0,3],[5,0,0,3]]",
"[[11,0,0,3],[13,13,0,1],[5,0,6,3]]",
"[[5,15,2,3],[13,13,2,3],[15,13,0,1],[1,0,4,1]]",
"[[1,2,4,1],[1,1,0,7],[1,3,6,7]]", "[[3,1,6,3],[3,0,0,3],[1,1,6,3]]",
"[[5,0,0,5],[1,1,2,3],[5,0,0,1],[3,3,0,1]]",
"[[1,2,2,7],[1,1,6,3],[1,2,0,5]]",
"[[7,6,4,7],[7,0,0,7],[3,0,4,7],[7,0,4,3],[1,0,4,7]]",
"[[1,3,0,7],[1,0,6,3],[1,2,4,5]]", "[[1,2,4,1],[1,1,2,7],[1,0,2,7]]",
"[[1,2,6,7],[1,4,0,5],[3,0,0,3],[3,6,6,7]]",
"[[1,2,4,1],[1,0,6,3],[1,1,6,3]]",
"[[3,6,4,3],[1,1,4,7],[3,0,4,7],[3,0,0,3]]",
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"[[5,10,8,1],[11,11,8,1],[9,9,2,7]]",
"[[3,12,12,3],[7,0,0,7],[3,0,10,13],[3,0,12,15],[3,0,0,3]]",
"[[5,5,2,3],[13,10,8,1],[15,13,8,1]]",
"[[5,5,2,3],[5,10,0,1],[3,3,8,1]]",
"[[5,10,8,1],[9,9,2,7],[3,3,8,1]]",
"[[5,5,2,3],[13,10,8,1],[7,5,8,1]]",
"[[13,10,0,1],[15,13,0,1],[9,9,2,7]]",
"[[9,0,0,1],[11,0,0,3],[7,0,0,7],[13,10,8,1],[3,9,8,1]]",
"[[5,15,0,7],[11,0,0,3],[7,0,0,7],[7,0,8,7],[15,15,0,1]]",
"[[1,3,10,15],[1,3,14,7],[1,1,0,15]]",
"[[1,3,10,15],[1,3,14,15],[1,6,2,3]]",
"[[1,6,2,11],[1,1,12,7],[1,7,10,15]]",
"[[1,15,10,15],[1,6,2,11],[1,11,14,15],[1,8,0,1]]",
"[[1,5,0,7],[1,0,0,9],[1,6,14,7],[1,4,0,1]]",
"[[5,5,0,3],[1,4,0,1],[1,1,6,3],[11,12,0,3]]",
"[[1,8,0,9],[3,0,0,13],[1,2,2,1],[3,0,0,3]]",
"[[1,8,0,9],[3,6,10,5],[3,0,0,13],[3,0,0,3]]",
"[[7,12,12,3],[7,0,0,7],[3,0,14,5],[3,12,0,11],[7,12,0,7]]",
"[[7,0,0,7],[5,0,0,1],[3,0,0,3],[3,3,0,1]]",
"[[7,0,0,15],[1,2,12,9],[5,0,4,7],[1,0,12,15],[1,0,4,15]]",
"[[7,0,0,15],[1,2,12,9],[1,0,12,15],[1,0,4,15],[5,0,0,1]]",
"[[7,0,0,15],[1,2,12,9],[5,0,4,7],[1,0,4,15],[1,0,8,9]]",
"[[1,4,12,7],[7,0,0,15],[1,6,4,1],[1,4,0,1],[5,0,0,1]]",
"[[9,0,12,7],[9,0,4,7],[9,0,4,3],[15,0,0,7],[1,2,12,1]]",
"[[9,0,8,1],[9,0,4,7],[9,0,4,3],[15,0,0,7],[1,2,12,1]]",
"[[7,0,0,3],[9,0,12,7],[9,0,4,7],[15,0,0,7],[1,2,12,1]]",
"[[1,4,12,7],[7,0,0,3],[15,0,0,7],[1,4,0,1],[9,6,4,1]]",
"[[3,6,0,7],[7,0,0,7],[7,0,0,1],[3,0,0,3]]",
"[[7,0,0,7],[1,0,8,7],[5,10,8,1],[3,0,0,3]]",
"[[3,0,12,7],[3,12,12,3],[7,0,0,7],[1,0,4,13],[1,0,2,11]]",
"[[13,10,0,1],[9,9,2,7],[7,5,0,1]]",
"[[11,2,0,1],[15,30,0,1],[1,1,6,3]]",
"[[7,0,0,7],[5,5,0,1],[3,0,0,1],[3,0,0,3]]",
"[[25,18,2,7],[25,25,2,7],[1,0,8,1],[29,26,0,1]]",
"[[25,18,2,7],[25,25,2,7],[1,0,8,1],[25,11,2,7]]",
"[[7,0,0,7],[3,0,16,1],[3,0,0,3],[5,5,16,1]]",
"[[7,0,0,7],[7,0,0,1],[5,5,0,1],[3,0,0,3]]",
"[[7,0,0,7],[7,0,16,1],[3,0,0,3],[5,5,16,1]]",
"[[1,1,28,15],[3,3,12,11],[3,15,12,3],[3,0,0,3]]",
"[[3,6,0,1],[7,0,0,7],[1,0,24,7],[7,0,0,3],[5,20,24,7]]",
"[[7,0,0,7],[1,0,24,7],[1,4,24,3],[5,0,0,1],[3,6,24,7]]",
"[[23,19,4,1],[25,4,0,1],[15,9,2,1],[21,0,4,1]]",
"[[7,0,0,7],[5,0,16,1],[7,14,16,1],[7,0,16,1],[7,0,16,3]]",
"[[29,26,0,1],[9,9,2,7],[29,29,2,3],[5,10,2,3]]",
"[[7,14,0,1],[7,0,0,1],[7,0,0,7],[7,0,0,3],[5,0,0,1]]",
"[[21,10,2,3],[19,19,2,1],[19,19,0,1]]",
"[[15,28,0,1],[3,3,12,3],[9,4,0,1],[3,0,0,3]]",
"[[1,2,20,5],[1,6,20,29],[1,2,30,15],[1,5,28,15]]",
"[[29,0,4,1],[31,27,0,1],[13,7,2,3],[1,4,0,1]]",
"[[1,2,20,5],[1,6,20,29],[1,0,10,31],[1,5,28,15]]",
"[[21,20,2,3],[15,13,0,1],[1,4,0,1],[31,30,2,1]]",
"[[5,10,16,1],[7,0,0,7],[5,0,16,1],[3,3,16,1],[3,0,0,3]]",
"[[21,20,2,3],[1,4,0,1],[31,30,2,1],[5,3,2,3]]",
"[[7,0,0,7],[5,10,0,1],[5,0,0,1],[3,0,0,3],[3,3,0,1]]",
"[[7,0,0,15],[1,2,0,1],[7,21,24,7],[7,21,0,1],[5,0,0,1]]",
"[[27,27,4,1],[21,21,2,3],[5,0,2,3]]",
"[[25,18,2,7],[1,0,8,1],[13,26,0,1],[7,7,2,1]]",
"[[7,0,0,15],[1,2,0,1],[7,7,0,9],[7,7,24,15],[5,10,0,9]]",
"[[7,28,0,3],[7,6,0,1],[5,15,2,1]]",
"[[7,0,0,15],[1,2,0,1],[7,7,0,9],[7,7,24,15],[5,0,0,1]]",
"[[3,21,6,3],[7,6,0,1],[5,15,2,1]]",
"[[7,20,0,3],[5,3,2,1],[7,7,2,1]]", "[[5,3,2,1],[7,7,2,1],[1,5,6,3]]",
"[[7,0,0,15],[1,2,0,1],[7,21,0,1],[7,7,24,15],[5,10,0,9]]",
"[[29,0,4,1],[31,27,0,1],[1,4,0,1],[31,31,2,1]]",
"[[25,0,8,1],[9,9,4,3],[15,13,2,1],[29,23,4,3]]",
"[[1,0,20,21],[1,1,30,31],[1,5,28,31],[1,4,0,1]]",
"[[11,2,0,1],[3,9,6,3],[9,9,6,3]]",
"[[3,6,0,1],[5,25,6,3],[15,26,0,1]]",
"[[1,0,20,5],[1,1,10,15],[1,5,28,7],[1,4,20,13]]",
"[[7,10,0,1],[3,6,0,1],[5,25,6,3]]",
"[[9,18,0,1],[9,0,0,7],[3,9,24,7],[11,11,24,3],[15,0,0,7]]",
"[[5,10,4,1],[31,31,0,1],[25,18,2,3]]",
"[[25,0,2,3],[21,21,2,3],[21,10,0,1]]",
"[[9,18,0,1],[3,9,24,7],[11,11,8,5],[11,11,24,3],[15,0,0,7]]",
"[[9,18,0,1],[11,11,8,5],[15,30,0,3],[11,11,24,3],[15,0,0,7]]",
"[[9,18,0,1],[9,0,0,7],[15,30,0,3],[11,11,24,3],[15,0,0,7]]",
"[[1,0,0,5],[5,10,0,5],[7,0,0,7],[3,9,0,1],[3,0,16,5]]",
"[[1,1,0,1],[7,0,0,7],[3,0,0,5],[5,0,0,1],[3,0,32,3]]",
"[[7,0,0,7],[3,0,16,1],[5,0,0,5],[7,14,16,1],[5,5,16,1]]",
"[[1,1,0,1],[1,0,0,5],[7,0,0,7],[3,0,0,5],[3,0,32,3]]",
"[[7,0,0,7],[5,0,0,5],[3,9,0,1],[5,0,0,1],[7,14,16,1]]",
"[[1,1,0,1],[7,0,0,7],[5,0,0,5],[1,0,32,7],[3,0,32,7]]",
"[[1,1,0,1],[7,0,0,1],[7,0,0,7],[5,0,0,5],[5,0,0,1]]",
"[[7,21,0,5],[5,10,0,5],[7,0,0,7],[5,0,0,1],[3,0,16,5]]",
"[[7,0,0,7],[7,0,6,9],[3,12,0,3],[7,12,0,15],[3,12,12,15]]",
"[[11,0,0,3],[7,0,0,7],[13,10,8,1],[3,9,8,1],[15,0,8,7]]",
"[[21,30,4,1],[9,4,0,1],[29,0,2,3],[15,11,4,1]]",
"[[21,30,4,1],[9,4,0,1],[15,30,2,1],[15,11,4,1]]",
"[[19,19,4,1],[9,9,4,3],[15,13,2,1],[29,23,4,3]]",
"[[25,0,8,1],[13,7,2,3],[29,29,2,3],[5,10,2,3]]",
"[[1,7,30,15],[1,5,28,7],[1,1,28,31],[1,0,20,29]]",
"[[25,0,8,1],[23,5,0,1],[13,13,2,3],[11,11,0,1]]",
"[[21,21,2,3],[17,0,8,1],[15,13,8,1],[13,26,8,1]]",
"[[1,6,18,27],[1,5,28,7],[1,1,28,31],[1,0,20,29]]",
"[[9,18,2,7],[15,13,4,1],[17,0,8,1],[29,26,8,1]]",
"[[3,6,0,1],[7,0,0,7],[1,0,24,7],[1,4,24,3],[5,0,0,1]]",
"[[7,0,0,7],[1,0,24,7],[7,0,0,3],[5,20,24,7],[3,6,24,7]]",
"[[15,13,4,1],[17,0,8,1],[29,26,2,3],[29,26,8,1]]",
"[[1,3,4,9],[1,7,4,1],[3,3,20,5],[3,0,0,3]]",
"[[7,10,0,1],[9,31,4,1],[15,30,0,1],[3,0,0,3]]",
"[[21,20,2,3],[15,13,0,1],[13,0,2,3],[31,30,2,1]]",
"[[29,0,4,1],[31,27,0,1],[13,7,2,3],[5,3,2,3]]",
"[[1,2,18,11],[1,3,10,15],[1,0,20,21],[1,7,26,7]]",
"[[21,20,2,3],[13,0,2,3],[31,30,2,1],[5,3,2,3]]",
"[[23,5,0,1],[21,21,2,3],[17,0,8,1],[13,26,8,1]]",
"[[1,5,0,31],[1,0,20,21],[1,1,30,31],[1,4,20,21]]",
"[[1,0,20,21],[1,1,30,31],[1,4,20,21],[1,5,28,31]]",
"[[23,19,4,1],[13,0,4,1],[25,4,0,1],[13,13,2,3]]",
"[[23,19,4,1],[13,0,4,1],[15,15,2,1],[25,4,0,1]]",
"[[19,19,4,1],[9,18,2,7],[9,9,4,3],[29,23,4,3]]",
"[[7,21,0,5],[1,0,0,5],[5,10,0,5],[7,0,0,7],[3,0,16,5]]",
"[[3,3,0,3],[1,0,0,5],[7,0,0,7],[3,0,0,5],[3,0,32,3]]",
"[[3,3,0,3],[7,0,0,7],[3,0,0,5],[5,0,0,1],[3,0,32,3]]",
"[[7,7,32,7],[7,0,0,7],[5,0,0,5],[1,0,32,7],[3,0,32,7]]",
"[[7,7,32,7],[7,0,0,7],[5,0,0,5],[1,0,32,7],[5,0,0,1]]",
"[[5,10,0,5],[7,0,0,7],[3,9,0,1],[5,0,0,1],[3,0,16,5]]",
"[[7,0,0,7],[5,0,0,5],[5,0,0,1],[7,14,16,1],[5,5,16,1]]",
"[[7,0,0,7],[3,0,16,1],[5,0,0,5],[3,9,0,1],[7,14,16,1]]",
"[[3,6,0,1],[13,1,6,3],[15,13,6,3]]",
"[[19,19,0,1],[27,27,4,1],[21,21,2,3]]",
"[[25,0,8,1],[9,9,4,3],[15,13,2,1],[21,10,0,1]]",
"[[3,21,6,3],[7,31,2,1],[5,15,2,1]]",
"[[7,14,0,1],[11,2,0,1],[1,1,6,3]]",
"[[1,13,6,3],[3,1,6,3],[7,31,2,1]]",
"[[3,9,6,3],[9,9,6,3],[7,17,6,3]]",
"[[7,2,0,1],[7,31,2,1],[1,5,6,3]]",
"[[1,1,30,15],[1,0,20,5],[1,5,28,7],[1,4,20,13]]",
"[[13,7,2,3],[9,9,2,7],[29,29,2,3],[5,10,2,3]]",
"[[23,19,4,1],[31,27,0,1],[25,4,0,1],[15,9,2,1]]",
"[[7,28,0,3],[7,31,2,1],[5,15,2,1]]",
"[[25,0,2,3],[1,2,2,3],[21,21,2,3]]",
"[[13,1,6,3],[15,13,6,3],[11,13,6,3]]", "[[4,1,17,4],[2,3,17,23]]",
"[[4,1,1,4],[2,3,1,7]]",
"[[7,0,0,15],[1,0,40,7],[15,0,0,15],[1,0,16,13],[3,3,48,11]]",
"[[15,0,40,13],[9,0,16,5],[13,13,0,1],[15,0,0,15],[1,0,16,5]]",
"[[1,1,0,1],[7,0,0,15],[1,0,0,7],[5,0,0,1],[1,0,32,9]]",
"[[1,1,0,1],[7,0,0,15],[1,0,0,7],[3,0,0,7],[1,0,32,9]]",
"[[7,7,0,7],[7,0,0,15],[1,0,0,7],[5,0,0,1],[1,0,32,9]]",
"[[7,7,0,7],[7,0,0,15],[1,0,0,7],[3,0,0,7],[1,0,32,9]]",
"[[7,0,0,15],[1,0,40,7],[15,0,0,15],[1,0,16,13],[13,13,16,13]]",
"[[15,0,40,13],[9,0,16,5],[15,0,0,15],[1,0,16,5],[13,13,16,13]]"];
finegenlists := [ "[[1,1,1,2],[1,0,2,3]]", "[[1,1,3,0],[1,0,6,7]]",
"[[2,3,3,1],[1,0,3,3]]", "[[0,1,3,1],[1,0,3,3]]",
"[[1,2,2,5],[1,0,0,7],[3,6,0,5],[1,2,0,5]]",
"[[1,0,0,3],[3,2,0,1],[1,2,2,1]]",
"[[1,0,2,1],[1,0,0,7],[3,6,0,5],[1,2,0,5]]",
"[[1,0,0,3],[1,0,2,1],[3,2,0,1]]", "[[1,0,6,3],[1,0,2,7],[1,1,2,5]]",
"[[1,0,0,5],[1,0,6,3],[1,1,2,5]]", "[[1,1,0,1],[7,0,2,1],[1,0,6,3]]",
"[[1,1,0,1],[1,0,6,3],[5,0,0,1]]", "[[1,0,2,1],[3,3,6,3],[3,0,6,7]]",
"[[3,0,2,3],[3,3,2,3]]", "[[1,0,2,5],[1,1,0,3],[3,3,0,5]]",
"[[1,1,0,3],[1,0,2,1]]", "[[1,1,4,5],[1,0,4,5],[1,0,0,3],[3,0,4,1]]",
"[[1,0,0,5],[1,1,4,5],[1,0,0,3],[3,0,4,1]]",
"[[1,1,0,1],[5,0,4,1],[1,0,0,3],[3,0,4,1]]",
"[[1,1,0,1],[1,0,0,5],[1,0,0,3],[3,0,4,1]]",
"[[5,5,0,1],[1,0,0,3],[3,3,0,1],[1,0,4,1]]", "[[1,0,0,3],[3,3,0,1]]",
"[[1,1,0,3],[5,5,0,1],[3,0,0,1],[1,0,4,1]]", "[[3,0,0,1],[1,1,0,3]]",
"[[1,1,3,0],[1,0,3,7]]", "[[1,0,3,3],[3,3,1,0]]",
"[[1,2,6,3],[3,6,2,3],[1,0,0,3],[3,6,6,7]]",
"[[1,0,0,5],[1,2,6,3],[3,6,2,3],[1,0,0,3]]",
"[[1,2,6,3],[1,0,0,3],[3,6,6,7],[1,0,4,1]]", "[[1,0,0,3],[1,2,2,3]]",
"[[1,0,0,3],[3,2,2,3]]", "[[3,0,0,5],[1,0,0,3],[3,0,4,1],[3,6,6,3]]",
"[[1,0,0,5],[1,0,0,3],[3,0,4,1],[3,6,6,3]]",
"[[3,0,0,5],[1,0,0,3],[1,0,4,1],[3,6,6,3]]",
"[[1,0,0,5],[1,2,0,1],[1,0,0,3],[3,0,0,1],[1,0,4,1]]",
"[[1,0,0,5],[1,2,0,1],[5,0,4,1],[7,0,0,1],[5,0,0,3]]",
"[[1,2,0,1],[5,0,4,1],[7,0,0,1],[5,0,0,5],[1,0,0,3]]",
"[[5,0,4,1],[7,0,0,1],[5,0,0,5],[1,0,0,3],[1,2,0,5]]",
"[[1,2,0,1],[7,0,0,1],[5,0,0,5],[1,0,0,3],[1,0,4,1]]",
"[[7,0,0,1],[5,0,0,5],[1,0,0,3],[1,2,0,5],[1,0,4,1]]",
"[[1,2,0,1],[5,0,0,5],[3,0,0,1],[5,0,0,3],[1,0,4,1]]",
"[[1,0,0,3],[1,2,0,1]]", "[[1,0,0,3],[3,2,0,1]]",
"[[1,2,0,1],[3,0,0,5],[3,0,4,1],[5,0,0,1],[3,0,0,3]]",
"[[3,0,0,5],[3,0,4,1],[5,0,0,1],[1,2,0,5],[3,0,0,3]]",
"[[1,0,0,5],[1,2,0,1],[1,0,0,3],[3,0,4,1],[5,0,0,1]]",
"[[3,6,0,1],[1,0,0,5],[1,0,0,3],[3,0,4,1],[5,0,0,1]]",
"[[3,0,0,1],[1,2,0,1]]", "[[3,3,4,5],[1,2,4,1],[1,0,4,5],[3,0,4,3]]",
"[[3,3,4,5],[1,2,4,1],[1,0,0,5],[3,0,4,3]]",
"[[5,0,4,1],[1,2,0,1],[7,7,4,1],[3,0,4,3]]",
"[[3,3,4,5],[1,0,0,5],[1,2,0,1],[3,0,4,3]]",
"[[3,6,0,3],[3,1,0,1],[5,2,0,1],[1,0,4,1]]", "[[3,1,0,1],[3,2,0,3]]",
"[[7,7,0,1],[1,1,0,3],[1,2,0,1],[1,0,4,1]]", "[[1,1,0,3],[1,2,0,1]]",
"[[3,9,4,1],[3,3,12,7],[1,3,4,5],[3,9,12,3]]",
"[[3,9,4,1],[1,0,0,5],[3,3,12,7],[1,3,4,5]]",
"[[3,3,4,1],[3,3,4,3],[5,5,4,1]]", "[[3,3,4,3],[5,0,0,3],[5,5,4,1]]",
"[[3,3,4,1],[5,0,0,1],[5,5,4,1]]", "[[1,0,0,5],[1,1,4,5],[1,0,0,7]]",
"[[1,2,0,7],[3,6,0,3],[1,2,0,5],[3,9,12,7]]",
"[[1,0,0,5],[1,2,0,7],[3,6,0,3],[3,9,12,7]]",
"[[1,0,0,5],[3,3,4,7],[1,0,0,7]]", "[[7,0,0,1],[7,0,0,3],[7,7,4,3]]",
"[[3,3,4,7],[1,0,0,7],[3,0,0,7]]", "[[7,0,0,1],[7,7,4,3],[5,0,0,1]]",
"[[3,3,4,1],[5,5,4,1],[7,0,4,3]]", "[[5,0,0,3],[5,5,4,1],[7,0,4,3]]",
"[[3,3,4,1],[5,5,0,1],[5,5,4,1]]", "[[5,5,0,1],[5,0,0,3],[5,5,4,1]]",
"[[1,1,0,3],[7,7,0,3],[7,7,4,3]]", "[[7,7,0,3],[7,7,4,3],[5,0,0,3]]",
"[[5,5,0,1],[7,7,4,3],[5,0,0,3]]", "[[7,0,0,1],[5,5,0,1],[7,7,4,3]]",
"[[3,3,4,5],[1,1,4,5],[3,3,0,5]]", "[[1,1,4,5],[1,0,0,3],[3,3,0,5]]",
"[[3,3,4,5],[1,1,4,5],[1,0,4,7]]", "[[1,1,4,5],[1,0,0,3],[1,0,4,7]]",
"[[3,3,4,7],[1,0,0,3],[1,0,4,7]]", "[[3,0,4,5],[3,3,4,7],[3,0,0,1]]",
"[[3,0,4,5],[3,3,4,7],[1,0,0,3]]", "[[3,3,4,7],[3,0,0,1],[1,0,4,7]]",
"[[1,1,0,1],[7,0,0,1],[5,0,0,1],[3,0,0,3]]",
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"[[3,6,6,11],[1,2,14,7],[1,4,0,1]]",
"[[3,12,0,3],[1,4,0,15],[1,2,2,9]]",
"[[1,0,0,15],[1,4,0,1],[1,2,2,9]]",
"[[1,0,8,5],[7,14,8,1],[7,0,8,1],[5,0,8,7]]",
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"[[3,0,8,1],[5,0,8,5],[5,5,8,3]]", "[[7,7,0,1],[3,0,8,1],[5,0,8,5]]",
"[[5,0,8,5],[5,5,8,3],[1,0,0,3]]", "[[7,7,0,1],[5,0,8,5],[1,0,0,3]]",
"[[7,7,0,3],[3,0,8,3],[7,0,0,5]]", "[[7,7,0,1],[3,0,8,3],[7,0,0,5]]",
"[[7,7,0,1],[3,0,8,3],[1,0,0,3]]", "[[1,1,0,7],[3,0,8,3],[1,0,0,3]]",
"[[1,0,8,5],[5,5,8,7],[7,0,8,5]]", "[[5,5,8,7],[1,0,0,7],[7,0,8,5]]",
"[[5,5,0,5],[1,0,8,5],[7,0,8,5]]", "[[5,5,0,5],[1,0,0,7],[7,0,8,5]]",
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"[[5,5,0,5],[1,0,0,7],[1,0,8,3]]", "[[5,5,0,5],[7,0,0,1],[1,0,8,3]]",
"[[9,9,12,3],[5,10,0,1],[13,10,4,1]]",
"[[15,14,0,3],[9,9,12,3],[7,14,12,3]]",
"[[3,0,12,3],[15,15,0,1],[5,10,0,1]]",
"[[15,14,0,3],[3,0,12,3],[3,9,0,1]]",
"[[1,1,12,3],[13,7,12,3],[1,0,4,1]]",
"[[7,7,0,1],[13,7,12,3],[1,0,4,1]]",
"[[7,7,0,1],[3,0,12,3],[3,9,0,1]]",
"[[7,7,0,1],[3,0,12,3],[9,11,0,3]]",
"[[1,1,8,7],[3,0,8,7],[7,0,8,1]]", "[[1,1,8,7],[7,0,8,1],[3,0,0,1]]",
"[[1,1,0,1],[3,0,8,7],[7,0,8,1]]", "[[1,1,0,1],[7,0,8,1],[3,0,0,1]]",
"[[1,1,0,1],[1,0,8,7],[3,0,0,1]]", "[[7,7,0,7],[1,0,8,7],[5,0,0,7]]",
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"[[1,3,4,1],[11,11,12,3],[15,0,0,1]]",
"[[11,11,12,3],[1,2,0,1],[7,7,4,1]]",
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"[[3,6,0,3],[9,9,4,1],[13,0,0,3]]",
"[[3,6,0,3],[9,9,4,1],[15,0,0,1]]",
"[[1,2,0,1],[9,9,4,1],[13,0,0,3]]",
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"[[5,0,16,3],[7,7,16,1],[5,0,0,1],[7,0,16,7]]",
"[[7,7,0,1],[5,0,16,1],[5,0,16,3],[7,0,16,7]]",
"[[7,7,0,1],[5,0,16,3],[5,0,0,1],[7,0,16,7]]",
"[[7,7,0,1],[5,0,0,1],[5,0,0,3]]", "[[1,1,0,7],[3,0,0,5],[3,0,0,7]]",
"[[1,1,0,7],[3,0,0,5],[5,0,0,1]]", "[[7,7,0,1],[3,0,0,5],[3,0,0,7]]",
"[[7,7,0,1],[3,0,0,5],[5,0,0,1]]", "[[1,1,0,7],[3,0,0,7],[5,0,0,3]]",
"[[1,1,0,7],[5,0,0,1],[5,0,0,3]]", "[[7,7,0,1],[3,0,0,7],[5,0,0,3]]",
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"[[7,7,0,1],[5,5,0,5],[3,0,8,1]]", "[[1,1,0,7],[5,5,0,5],[3,0,8,1]]",
"[[3,0,8,7],[5,5,8,7],[5,0,8,7]]", "[[5,5,8,7],[1,0,0,7],[5,0,8,7]]",
"[[7,7,0,7],[3,0,8,7],[5,0,8,7]]", "[[7,7,0,7],[1,0,0,7],[5,0,8,7]]",
"[[7,7,0,1],[1,1,0,1],[3,0,8,1]]", "[[1,1,0,1],[3,0,8,1],[1,0,0,7]]",
"[[7,7,0,7],[3,0,8,1],[1,0,0,7]]", "[[7,7,0,7],[3,0,8,1],[7,0,0,1]]",
"[[3,3,4,13],[3,9,4,5],[3,0,12,15]]",
"[[3,3,4,13],[3,6,0,3],[3,0,12,15]]",
"[[3,3,4,13],[3,3,0,13],[3,9,4,5]]",
"[[3,3,4,13],[3,6,0,3],[3,3,0,13]]",
"[[5,0,8,5],[5,5,8,1],[5,0,8,3]]", "[[7,0,0,1],[5,0,8,5],[5,5,8,1]]",
"[[7,7,0,3],[5,0,8,5],[5,0,8,3]]", "[[7,7,0,3],[7,0,0,1],[5,0,8,5]]",
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"[[3,0,8,3],[1,1,0,5],[3,3,0,1]]", "[[7,7,0,3],[3,0,8,3],[5,5,0,7]]",
"[[7,7,0,7],[1,0,0,7],[3,0,0,7],[1,0,0,9]]",
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"[[7,7,0,7],[1,0,0,7],[5,0,0,1],[1,0,0,9]]",
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"[[1,1,0,1],[1,0,0,7],[5,0,0,1],[1,0,0,9]]",
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"[[1,0,0,15],[7,0,0,7],[3,0,0,15],[7,7,0,15]]",
"[[5,0,16,1],[1,0,0,15],[7,0,0,7],[3,0,0,15],[7,7,0,15]]",
"[[1,0,0,15],[7,0,0,7],[5,0,0,1],[7,7,0,15]]",
"[[7,0,0,1],[7,0,0,7],[3,0,0,15],[7,7,0,15]]",
"[[5,0,16,1],[7,0,0,1],[7,0,0,7],[3,0,0,15],[7,7,0,15]]",
"[[7,0,0,1],[7,0,0,7],[7,0,16,15],[5,0,0,1],[7,7,0,15]]",
"[[1,0,8,5],[7,0,8,1],[3,3,8,7]]", "[[1,0,8,5],[7,0,8,1],[3,3,0,1]]",
"[[7,0,8,1],[1,0,0,3],[3,3,8,7]]", "[[7,0,8,1],[1,0,0,3],[3,3,0,1]]",
"[[3,3,0,3],[1,0,8,7],[7,0,0,5]]", "[[1,0,8,7],[3,3,0,1],[7,0,0,5]]",
"[[1,0,8,7],[1,0,0,3],[3,3,0,1]]", "[[5,5,0,7],[1,0,8,7],[1,0,0,3]]",
"[[21,0,2,1],[21,21,2,1]]", "[[31,31,0,1],[21,21,2,1]]",
"[[31,29,0,1],[17,19,2,1]]", "[[31,31,0,1],[17,19,2,1]]",
"[[15,15,6,3],[31,0,2,1]]", "[[15,15,6,3],[29,29,0,1]]",
"[[29,29,2,1],[29,29,0,1]]", "[[29,29,2,1],[15,15,0,3]]",
"[[1,0,16,7],[3,0,16,1],[3,0,16,3],[7,7,16,1]]",
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"[[1,1,0,1],[5,0,0,1],[5,0,0,3],[7,0,16,1]]",
"[[7,7,0,7],[3,0,0,7],[5,0,0,3],[7,0,16,1]]",
"[[7,7,0,7],[5,0,0,1],[5,0,0,3],[7,0,16,1]]",
"[[1,1,0,1],[3,0,0,7],[5,0,0,3],[7,0,16,1]]",
"[[3,9,28,7],[3,9,20,5],[1,7,4,1]]",
"[[3,9,28,7],[1,7,4,1],[3,0,0,1]]",
"[[5,20,0,1],[7,21,12,3],[7,21,4,1]]",
"[[3,0,0,1],[5,20,0,1],[7,21,12,3]]",
"[[5,15,4,1],[3,0,0,1],[5,20,0,1]]",
"[[3,12,0,7],[1,3,20,5],[1,0,0,3]]",
"[[3,12,0,7],[1,3,20,5],[3,0,0,1]]",
"[[1,4,0,5],[1,3,20,5],[1,0,0,3]]", "[[3,9,4,1],[1,3,4,1],[1,0,0,7]]",
"[[3,9,4,1],[1,0,0,5],[1,0,0,7]]", "[[1,3,12,3],[1,3,4,1],[3,0,0,5]]",
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"[[1,1,0,1],[3,0,16,3],[5,0,0,7],[5,0,0,3]]"]; 
// The nth entry in this list is the set of all m so that the subgroup 
// H_m is a maximal subgroup of H_n.  
subdatamaxsub := [ [ 2, 3, 4, 5, 6, 7 ], [ 8, 21 ],
[ 10, 20 ], [ 19, 22 ], [ 17 ], [ 8, 9, 10, 11, 12, 13, 14, 15, 16,
17, 18, 19 ], [ 20, 21, 22, 26, 55 ], [ 24, 25, 38, 46 ], [ 24, 37 ],
[ 27, 42 ], [ 23, 24, 26, 27, 28, 29, 35, 39, 41, 43, 45, 47, 49, 50,
53, 54 ], [ 25, 30, 31, 40, 51, 52 ], [ 25, 27, 32, 33, 34, 36, 44, 48
], [ 38, 44 ], [ 41, 46 ], [ 29, 38, 40, 42 ], [ 37, 40, 41, 44 ], [
37, 42, 46, 48 ], [ 29, 48 ], [ 60, 180 ], [ 59 ], [ 56, 57, 83, 179
], [ 58, 60, 64, 65, 68, 69, 76, 80, 127, 136, 146, 148 ], [ 58, 59,
61, 66, 67, 132, 141 ], [ 58, 62, 87, 96, 98, 99, 100, 101, 129, 142
], [ 59, 60, 73, 74, 83, 139, 140 ], [ 60, 92, 94, 95, 134, 135 ], [
67, 68, 81, 90, 128, 146 ], [ 76, 77, 83, 125, 133 ], [ 72, 88, 89,
93, 103, 104, 126, 142, 162, 163, 164, 167, 172, 174 ], [ 129, 145 ],
[ 79, 96, 115, 116, 157, 158 ], [ 78, 100 ], [ 75, 79, 94, 100 ], [
61, 63, 65, 82, 147, 148 ], [ 75, 78, 84, 85, 86, 92, 96, 102, 117,
118, 119, 120, 121, 122, 159, 168 ], [ 123 ], [ 62, 66 ], [ 63, 66,
80, 83, 90, 91, 95, 97, 105, 106, 107, 124, 128, 143, 144, 147, 160,
161, 165, 166 ], [ 126, 145 ], [ 80, 81, 82, 131, 138 ], [ 108 ], [
64, 67, 71, 74, 77, 82, 91, 92, 127, 137, 139, 144 ], [ 78, 79 ], [
61, 69, 70, 73, 77, 81, 94, 97, 109, 110, 111, 112, 130, 136, 140,
143, 149, 150, 151, 153 ], [ 62 ], [ 63, 64, 68, 70, 74, 97, 132, 133,
135, 138 ], [ 75 ], [ 70, 71, 76, 95, 130, 137 ], [ 65, 69, 71, 73,
90, 91, 113, 114, 125, 131, 134, 141, 152, 154, 155, 156, 170, 171 ],
[ 142, 145, 169, 173, 175, 176 ], [ 126, 129 ], [ 128, 133, 134, 136,
137, 138, 140, 141, 144, 148 ], [ 125, 127, 130, 131, 132, 135, 139,
143, 146, 147 ], [ 179, 180, 253, 441 ], [ 177, 178, 402, 439 ], [
370, 440 ], [ 183, 186, 187, 189, 248, 249, 251, 255, 357 ], [], [
277, 278 ], [ 209, 210, 251, 254, 392, 393 ], [ 198, 200, 203, 204,
246, 247 ], [ 254, 263, 302, 307 ], [ 191, 196, 255, 257, 263, 278 ],
[ 251, 261, 317, 318 ], [ 214, 254, 256, 395, 398 ], [ 255, 256 ], [
255, 264 ], [ 250, 251, 252, 258, 262, 277, 319, 320, 321, 322, 323,
324 ], [ 257, 260, 325, 326 ], [ 258, 259, 327, 328 ], [ 266, 273 ], [
253, 267, 276, 277, 348, 349, 350, 351 ], [ 275, 278 ], [ 197, 199,
217, 329, 330 ], [ 257, 258 ], [ 216, 257, 258, 275, 276, 373, 391 ],
[ 201, 202, 233, 234, 331, 332 ], [ 226, 333, 334, 368, 369 ], [ 224,
261, 262, 263, 264, 366, 400 ], [ 218, 220, 262, 264, 363, 364 ], [
261, 263 ], [ 232, 237, 275, 276, 370, 402 ], [ 195, 199, 201, 206,
227, 228, 336, 346 ], [ 192, 199, 202, 205, 211, 219, 225, 236, 335,
339, 341, 344 ], [ 184, 197, 201, 205, 212, 229, 337, 345 ], [ 181,
182, 183, 184, 185, 186, 198, 204, 269, 270, 273, 274 ], [ 266, 271 ],
[ 245, 265, 292, 294, 297, 299 ], [ 256, 262, 280, 281, 282, 283, 284,
285 ], [ 256, 259, 261, 276, 286, 287, 288, 289, 290, 291, 300, 352 ],
[ 195, 205, 207, 259, 278, 305, 306, 371 ], [ 244, 265, 293, 295, 296,
298 ], [ 231, 260, 277, 376, 378 ], [ 221, 222, 259, 260, 379, 381 ],
[ 184, 185, 192, 193, 194, 206, 208, 215, 246, 249, 313, 314, 315,
316, 386, 404 ], [ 254, 260, 264, 275, 301, 303, 304, 308, 309, 310,
311, 312, 377, 380 ], [ 181, 187, 188, 189, 193, 194, 200, 204, 244,
269, 272, 279 ], [ 182, 186, 187, 190, 194, 198, 203, 206, 268, 270,
271, 272 ], [ 181, 182, 188, 190, 247, 248 ], [ 183, 185, 188, 189,
190, 192, 200, 203, 245, 268, 274, 279 ], [ 193, 195, 197, 202, 213,
223, 230, 235, 338, 340, 342, 347 ], [ 296, 297, 298, 299 ], [ 292,
293, 294, 295 ], [ 214, 221, 224, 232, 282, 288, 301, 302, 388, 389,
390, 394 ], [ 221, 237, 286, 304, 359, 360 ], [ 214, 222, 224, 237,
281, 287, 307, 308, 362, 372, 374, 399 ], [ 238 ], [ 209, 220, 311,
320, 382, 401 ], [ 209, 216, 218, 231, 312, 321, 325, 349, 367, 383,
387, 397 ], [ 210, 218, 309, 322, 375, 384 ], [ 210, 216, 220, 231,
310, 323, 326, 351, 361, 385, 396, 403 ], [ 284, 290, 317, 324, 328,
348 ], [ 280, 291, 318, 319, 327, 350 ], [ 314, 334 ], [ 241, 242,
316, 333, 407, 408 ], [ 219, 223, 228, 229, 230, 236, 306, 315, 330,
332 ], [ 211, 212, 213, 225, 227, 235, 240, 243, 305, 313, 329, 331,
353, 354, 355, 356, 405, 406 ], [ 213, 215, 219, 233, 338, 344 ], [
207, 215, 217, 227, 229, 234, 235, 236, 336, 340, 341, 345 ], [ 208,
223, 225, 234, 339, 342 ], [ 207, 208, 211, 212, 217, 228, 230, 233,
335, 337, 346, 347 ], [ 239 ], [ 222, 232, 289, 303, 358, 365 ], [
258, 276, 414, 426 ], [ 265, 266, 419, 420 ], [ 255, 258, 261, 278 ],
[ 256, 264, 372, 390 ], [ 246, 248, 268, 269, 270, 279 ], [ 258, 260,
396, 397 ], [ 261, 262, 416, 418 ], [ 254, 255 ], [ 257, 275 ], [ 259,
277, 411, 412 ], [ 260, 278 ], [ 251, 257, 264, 277, 382, 383, 384,
385 ], [ 257, 259 ], [ 263, 264 ], [ 276, 278 ], [ 275, 277, 387, 403
], [ 251, 256, 413, 425 ], [ 244, 245, 247, 249, 271, 272, 273, 274,
409, 410, 423, 424 ], [ 254, 260, 262, 276, 358, 360, 361, 362, 367,
375, 389, 401, 415, 417 ], [ 256, 259, 263, 275, 359, 365, 374, 388 ],
[ 343, 421, 422 ], [ 255, 262 ], [ 254, 261, 394, 399 ], [ 251, 263 ],
[ 311, 322, 325, 351, 363, 367, 378, 385, 391, 392 ], [ 312, 323, 364,
373, 376, 384, 392, 397, 401, 403 ], [ 310, 321, 363, 373, 375, 378,
382, 387, 393, 396 ], [ 290, 319, 411, 414, 416, 425 ], [ 309, 320,
326, 349, 361, 364, 376, 383, 391, 393 ], [ 280, 317, 327, 348, 412,
413, 414, 416 ], [ 284, 318, 328, 350, 411, 418, 425, 426 ], [ 291,
324, 412, 413, 418, 426 ], [ 316, 334, 434, 435, 436, 437 ], [ 314,
333 ], [ 306, 315, 329, 331, 341, 342, 344, 345, 346, 347 ], [ 282,
286, 303, 307, 362, 366, 370, 381, 388, 398 ], [ 287, 301, 360, 365,
370, 372, 379, 394, 398, 400 ], [ 292, 296, 410, 419 ], [ 293, 299,
420, 423 ], [ 294, 298, 410, 420 ], [ 288, 308, 358, 359, 381, 390,
395, 399, 400, 402 ], [ 281, 289, 302, 304, 366, 374, 379, 389, 395,
402 ], [ 295, 297, 419, 423 ], [ 305, 313, 330, 332, 335, 336, 337,
338, 339, 340, 427, 428, 429, 430, 431, 432, 433, 438 ], [], [], [],
[], [], [], [], [], [ 719 ], [ 718 ], [ 439, 440, 538 ], [ 537 ], [
448, 450, 455, 459 ], [ 446, 448, 459, 463 ], [ 446, 447, 450, 452,
454, 458 ], [ 452, 464 ], [ 442, 452, 456, 458, 485, 486 ], [ 446,
452, 459, 460 ], [ 449, 454, 457, 459, 460, 465 ], [ 449, 450, 455,
462 ], [ 449, 450, 458, 465, 500, 501, 502, 503 ], [ 446, 449, 462,
463 ], [ 443, 445, 447, 461 ], [ 451, 458, 482, 483, 504, 505, 506,
519 ], [ 456, 465, 470, 475, 507, 508, 509, 510 ], [ 451, 460, 464,
465, 468, 469 ], [ 445, 453, 479, 487 ], [ 443, 444, 457, 461 ], [
467, 481 ], [ 442, 448, 463, 464 ], [ 466, 477 ], [ 451, 455, 456, 462
], [], [ 471, 472, 473, 474 ], [ 442, 451, 462, 463 ], [ 448, 455,
456, 464 ], [ 444, 453, 476, 478 ], [ 442, 460 ], [ 476, 478, 479,
487, 521, 527, 529, 531 ], [ 468, 475, 482, 486 ], [], [], [ 472, 477,
478, 482, 489, 490, 511, 512, 513, 514, 522, 528, 530, 532 ], [ 478,
481, 493, 498 ], [ 470, 472, 491, 492 ], [], [ 469, 470, 483, 485 ], [
520, 533 ], [ 466, 467, 477, 481 ], [], [ 473, 483 ], [], [], [], [
474, 475 ], [ 525, 526 ], [ 471, 482, 495, 497 ], [], [ 477, 479, 488,
494 ], [ 466, 487 ], [ 467, 476 ], [ 467, 473, 475, 487 ], [], [], [
472, 473 ], [ 471, 474 ], [ 470, 471, 479, 481, 496, 499, 515, 516,
517, 518, 523, 524, 534, 535 ], [ 466, 474, 476, 483 ], [], [], [], [
488, 489, 491, 493, 496, 497 ], [], [], [ 490, 492, 494, 495, 498, 499
], [ 455, 465, 604, 605, 606, 607 ], [ 458, 462, 608, 609, 610, 611 ],
[ 442, 451, 456, 464, 612, 613 ], [ 448, 455, 462, 463 ], [ 446, 449,
450, 459, 540, 541 ], [ 452, 458, 460, 465, 536, 541, 586, 614 ], [
537, 539, 540, 542, 570, 575, 577, 578 ], [ 454, 536, 540, 602, 670 ],
[ 536, 539, 542, 543, 568, 569, 576, 581 ], [ 537, 538, 596, 597 ],
[], [ 447, 457, 541 ], [ 600, 601 ], [ 443, 599 ], [ 542 ], [ 453,
544, 592, 593, 671 ], [], [ 545 ], [ 480, 539, 546 ], [ 461, 547 ],
[], [], [], [ 538, 543, 594, 595 ], [ 442, 446, 449, 451 ], [ 450,
456, 459, 464 ], [ 442, 446, 459, 464 ], [ 460, 463 ], [ 448, 460,
462, 465 ], [ 448, 452 ], [ 452, 455, 458, 463 ], [], [ 484, 538, 598
], [ 537, 543 ], [ 444, 445, 603 ], [ 449, 450, 451, 456 ], [ 579, 583
], [ 583, 584, 641, 680, 683 ], [ 579, 580 ], [ 546, 580, 583, 600 ],
[ 580, 584, 650, 674, 695, 706 ], [ 546, 579, 584, 601 ], [ 590, 591
], [ 588, 589 ], [ 587, 615, 618, 619, 678, 690 ], [ 582, 585 ], [
582, 587, 588, 590 ], [ 585, 589, 591, 615, 628, 675, 677, 713 ], [
643, 645, 707, 715 ], [ 571, 572, 573, 574 ], [ 646, 647, 709, 711 ],
[ 563, 564, 565, 566 ], [ 653, 655, 704, 717 ], [ 555, 556, 557, 558
], [ 616, 652, 708, 710 ], [ 548, 549, 550, 551 ], [ 544, 545, 582,
588, 591, 598, 600, 615 ], [], [], [], [], [ 478, 479, 544, 603, 636,
638 ], [ 476, 487, 592, 603 ], [ 630 ], [ 632, 634, 672, 673 ], [],
[], [], [ 635, 637, 686, 689 ], [ 470, 482, 586, 612, 627, 629 ], [
468, 485, 612, 614 ], [ 475, 483, 613, 614 ], [ 469, 486, 586, 613,
624, 625, 681, 682 ], [ 640, 705 ], [], [ 576, 577, 578, 581 ], [ 575,
581 ], [ 570, 576 ], [ 569, 577 ], [ 568, 578, 649, 651, 691, 692 ], [
568, 569, 570, 575, 654, 693, 694, 712 ], [ 657 ], [], [ 658, 716 ],
[], [ 477, 481, 617, 620 ], [ 466, 467 ], [ 471, 472, 621, 622 ], [
473, 474 ], [ 684, 685 ], [ 623, 631 ], [ 466, 473, 478, 482, 560,
561, 562, 567, 656, 659, 660, 661 ], [ 466, 479 ], [ 467, 478 ], [
470, 473 ], [ 474, 482 ], [ 467, 470, 474, 479, 552, 553, 554, 559,
639, 642, 644, 648 ], [ 471, 476, 477, 483 ], [ 471, 475 ], [], [ 472,
483 ], [ 476, 481 ], [ 477, 487 ], [ 472, 475, 481, 487 ], [ 594, 596
], [ 594, 597, 633, 687, 688 ], [ 595, 597, 626, 676, 679, 714 ], [
595, 596 ], [ 545, 585, 587, 589, 590, 592, 598, 601 ], [ 492, 493,
494, 497, 617, 621, 627, 636 ], [ 490, 496, 617, 621, 629, 638, 663,
665, 667, 668, 697, 698, 699, 700 ], [ 488, 491, 495, 498, 620, 622,
629, 638, 662, 664, 666, 669, 696, 701, 702, 703 ], [ 489, 499, 620,
622, 627, 636 ], [], [], [], [], [], [], [], [], [], [], [], [], [],
[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [],
[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [],
[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [],
[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [],
[], [ 718, 719 ], [], [], [], [], [], [], [], [], [], [], [], [], [],
[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [],
[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [],
[], [], [], [ 720, 721, 726, 727 ], [], [], [], [], [], [ 722, 723,
724, 725 ], [], [], [], [], [], [], [], [], [], [], [], [], [], [],
[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [],
[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [],
[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [],
[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [],
[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [],
[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [],
[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [],
[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [],
[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [],
[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [],
[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [],
[], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [],
[], [], [], [], [], [], [], [], [], [], [], [], [] ]; 
// The list of n so that X_n has genus zero and has rational points.  
genzeropoints :=
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37,
38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 55, 56, 57, 58,
60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77,
78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95,
96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110,
111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124,
177, 178, 181, 183, 185, 187, 188, 189, 190, 191, 192, 193, 194, 195,
196, 197, 199, 200, 202, 203, 204, 205, 207, 208, 209, 210, 211, 212,
213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226,
227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240,
241, 242, 243 ]; 
// The list of n so that X_n is an elliptic curve with positive rank.  
rankoneell := [ 150, 153, 155, 156, 165, 166,
167, 281, 284, 288, 289, 291, 295, 297, 302, 304, 308, 309, 312, 318,
320, 323, 324, 326, 328, 349, 350 ]; 
// The hard-coded list of which j-invariants lift to X_n for which the 
// genus of X_n > 1.
genustwoorhigher := [
<441,-18234932071051198464000/48661191875666868481>,
<441,-35817550197738955933474532061609984000/2301619141096101839813550846721>,
<556,78608>, <558,68769820673/16>, <563,2048>, <566,16974593/256>,
<619,-631595585199146625/218340105584896>,
<649,777228872334890625/60523872256>]; 
// Maps for X_n to the j-line for n in genzeropoints 
jmaps := [ <1, t>, <2, t^2 + 1728>, <3, -t^2 +
1728>, <4, -2*t^2 + 1728>, <5, 8*t^2 + 1728>, <6, t^3/(t + 16)>, <7,
(32*t - 4)/t^4>, <8, (64*t^6 + 576*t^4 + 1728*t^2 + 1728)/(t^4 - 2*t^2
+ 1)>, <9, (t^6 + 144*t^4 + 6912*t^2 + 110592)/(t^2 + 64)>, <10,
(1728*t^6 - 1728*t^4 + 576*t^2 - 64)/(t^6 + 2*t^4 + t^2)>, <11, (t^6 -
48*t^4 + 768*t^2 - 4096)/t^2>, <12, (t^6 + 48*t^4 + 768*t^2 +
4096)/t^2>, <13, (t^6 - 144*t^4 + 6912*t^2 - 110592)/(t^2 - 64)>, <14,
(4*t^6 + 96*t^4 + 768*t^2 + 2048)/t^2>, <15, (64*t^6 + 1152*t^4 +
6912*t^2 + 13824)/(t^2 + 8)>, <16, (4*t^6 - 288*t^4 + 6912*t^2 -
55296)/(t^2 - 32)>, <17, (1728*t^6 + 3456*t^4 + 2304*t^2 + 512)/(t^6 -
4*t^4 + 4*t^2)>, <18, (64*t^6 - 384*t^4 + 768*t^2 - 512)/t^2>, <19,
(1728*t^6 - 3456*t^4 + 2304*t^2 - 512)/(t^6 + 4*t^4 + 4*t^2)>, <20,
(-4*t^8 + 32*t^7 + 80*t^6 - 288*t^5 - 504*t^4 + 864*t^3 + 1296*t^2 -
864*t - 1188)/(t^4 + 4*t^3 + 6*t^2 + 4*t + 1)>, <22, (1728*t^8 -
1617408*t^6 - 35831808*t^5 - 360930816*t^4 - 2006581248*t^3 -
6352680960*t^2 - 10749542400*t - 7558272000)/(t^8 - 72*t^6 + 1944*t^4
- 23328*t^2 + 104976)>, <23, (-64*t^12 + 384*t^10 - 192*t^8 - 1792*t^6
+ 576*t^4 + 3456*t^2 + 1728)/(t^8 - 4*t^6 + 6*t^4 - 4*t^2 + 1)>, <24,
(256*t^12 + 768*t^10 + 1536*t^8 + 1792*t^6 + 1536*t^4 + 768*t^2 +
256)/(t^8 + 2*t^6 + t^4)>, <25, (256*t^12 - 768*t^10 + 1536*t^8 -
1792*t^6 + 1536*t^4 - 768*t^2 + 256)/(t^8 - 2*t^6 + t^4)>, <26,
(-64*t^12 - 384*t^10 - 192*t^8 + 1792*t^6 + 576*t^4 - 3456*t^2 +
1728)/(t^8 + 4*t^6 + 6*t^4 + 4*t^2 + 1)>, <27, (-64*t^12 + 672*t^10 -
2364*t^8 + 2828*t^6 - 591/4*t^4 + 21/8*t^2 - 1/64)/(t^10 + t^8 +
3/8*t^6 + 1/16*t^4 + 1/256*t^2)>, <28, (16*t^12 + 384*t^10 + 3648*t^8
+ 17408*t^6 + 43776*t^4 + 55296*t^2 + 27648)/(t^4 + 8*t^2 + 16)>, <29,
(1728*t^12 - 34560*t^10 + 251136*t^8 - 788480*t^6 + 1004544*t^4 -
552960*t^2 + 110592)/(t^12 + 4*t^10 - 4*t^8 - 32*t^6 - 16*t^4 + 64*t^2
+ 64)>, <30, (t^12 + 48*t^8 + 768*t^4 + 4096)/t^4>, <31, (1024*t^12 +
768*t^8 + 192*t^4 + 16)/t^8>, <32, (t^12 + 48*t^10 + 816*t^8 +
5632*t^6 + 13056*t^4 + 12288*t^2 + 4096)/(t^4 + 16*t^2)>, <33,
(16*t^12 + 384*t^10 + 3264*t^8 + 11264*t^6 + 13056*t^4 + 6144*t^2 +
1024)/(t^4 + 8*t^2)>, <34, (4096*t^12 - 24576*t^10 + 52224*t^8 -
45056*t^6 + 13056*t^4 - 1536*t^2 + 64)/(t^4 - 2*t^2)>, <35, (t^12 +
48*t^10 + 912*t^8 + 8704*t^6 + 43776*t^4 + 110592*t^2 + 110592)/(t^4 +
16*t^2 + 64)>, <36, (t^12 - 48*t^10 + 816*t^8 - 5632*t^6 + 13056*t^4 -
12288*t^2 + 4096)/(t^4 - 16*t^2)>, <37, (10976*t^12 + 28224*t^11 +
37128*t^10 + 32616*t^9 + 42297/2*t^8 + 10602*t^7 + 16807/4*t^6 +
5301/4*t^5 + 42297/128*t^4 + 4077/64*t^3 + 4641/512*t^2 + 441/512*t +
343/8192)/(t^12 + 5*t^11 + 11*t^10 + 113/8*t^9 + 759/64*t^8 +
221/32*t^7 + 23/8*t^6 + 221/256*t^5 + 759/4096*t^4 + 113/4096*t^3 +
11/4096*t^2 + 5/32768*t + 1/262144)>, <38, (64*t^12 - 384*t^10 +
1536*t^8 - 3584*t^6 + 6144*t^4 - 6144*t^2 + 4096)/(t^8 - 4*t^6 +
4*t^4)>, <39, (-t^12 + 48*t^10 - 192*t^8 - 14336*t^6 + 36864*t^4 +
1769472*t^2 + 7077888)/(t^8 - 32*t^6 + 384*t^4 - 2048*t^2 + 4096)>,
<40, (8000*t^12 + 9600*t^11 + 5040*t^10 + 2672*t^9 + 1587*t^8 +
636*t^7 + 413/2*t^6 + 159/2*t^5 + 1587/64*t^4 + 167/32*t^3 +
315/256*t^2 + 75/256*t + 125/4096)/(t^12 + 4*t^11 + 25/4*t^10 +
9/2*t^9 + 63/64*t^8 - 5/8*t^7 - 57/128*t^6 - 5/64*t^5 + 63/4096*t^4 +
9/1024*t^3 + 25/16384*t^2 + 1/8192*t + 1/262144)>, <41, (1728*t^12 +
34560*t^10 + 251136*t^8 + 788480*t^6 + 1004544*t^4 + 552960*t^2 +
110592)/(t^12 - 4*t^10 - 4*t^8 + 32*t^6 - 16*t^4 - 64*t^2 + 64)>, <42,
(128*t^12 - 3072*t^11 + 303104*t^9 + 417792*t^8 - 11403264*t^7 -
58720256*t^6 - 91226112*t^5 + 26738688*t^4 + 155189248*t^3 -
100663296*t + 33554432)/(t^12 + 16*t^11 + 112*t^10 + 384*t^9 + 192*t^8
- 4096*t^7 - 18432*t^6 - 32768*t^5 + 12288*t^4 + 196608*t^3 +
458752*t^2 + 524288*t + 262144)>, <43, (16*t^12 - 384*t^10 + 3648*t^8
- 17408*t^6 + 43776*t^4 - 55296*t^2 + 27648)/(t^4 - 8*t^2 + 16)>, <44,
(8*t^12 + 672*t^10 + 18912*t^8 + 180992*t^6 + 75648*t^4 + 10752*t^2 +
512)/(t^10 - 8*t^8 + 24*t^6 - 32*t^4 + 16*t^2)>, <45, (t^12 - 48*t^10
+ 912*t^8 - 8704*t^6 + 43776*t^4 - 110592*t^2 + 110592)/(t^4 - 16*t^2
+ 64)>, <46, (64*t^12 + 384*t^10 + 1536*t^8 + 3584*t^6 + 6144*t^4 +
6144*t^2 + 4096)/(t^8 + 4*t^6 + 4*t^4)>, <47, (-1024*t^12 + 768*t^8 -
192*t^4 + 16)/t^8>, <48, (-8*t^12 + 672*t^10 - 18912*t^8 + 180992*t^6
- 75648*t^4 + 10752*t^2 - 512)/(t^10 + 8*t^8 + 24*t^6 + 32*t^4 +
16*t^2)>, <49, (-t^12 - 48*t^10 - 192*t^8 + 14336*t^6 + 36864*t^4 -
1769472*t^2 + 7077888)/(t^8 + 32*t^6 + 384*t^4 + 2048*t^2 + 4096)>,
<50, (t^12 - 48*t^8 + 768*t^4 - 4096)/t^4>, <55, (-16384*t^13 +
8192*t^12 + 49152*t^11 - 73728*t^10 - 12288*t^9 + 116736*t^8 -
106496*t^7 + 4096*t^6 + 70656*t^5 - 70144*t^4 + 35840*t^3 - 10752*t^2
+ 1792*t - 128)/(t^16 - 4*t^14 + 7*t^12 - 7*t^10 + 35/8*t^8 - 7/4*t^6
+ 7/16*t^4 - 1/16*t^2 + 1/256)>, <56, (1728*t^16 - 1555200*t^14 -
35831808*t^13 - 403621056*t^12 - 2812796928*t^11 - 13331905344*t^10 -
45094330368*t^9 - 111483619704*t^8 - 202924486656*t^7 -
269971083216*t^6 - 256316120064*t^5 - 165509859276*t^4 -
66119763456*t^3 - 12914016300*t^2 + 1162261467/4)/(t^16 - 36*t^14 +
567*t^12 - 5103*t^10 + 229635/8*t^8 - 413343/4*t^6 + 3720087/16*t^4 -
4782969/16*t^2 + 43046721/256)>, <57, (-29000000*t^16 - 145280000*t^15
- 391283200*t^14 - 750631936*t^13 - 1117246208*t^12 - 1337748480*t^11
- 1309789696*t^10 - 1052867584*t^9 - 693335936*t^8 - 370770944*t^7 -
158256640*t^6 - 52466688*t^5 - 12899072*t^4 - 2180096*t^3 - 229888*t^2
- 13312*t - 320)/(t^16 - 16*t^15 + 104*t^14 - 336*t^13 + 476*t^12 +
112*t^11 - 1064*t^10 + 432*t^9 + 1222*t^8 - 432*t^7 - 1064*t^6 -
112*t^5 + 476*t^4 + 336*t^3 + 104*t^2 + 16*t + 1)>, <58, (16*t^24 +
672*t^20 + 9456*t^16 + 45248*t^12 + 9456*t^8 + 672*t^4 + 16)/(t^20 -
4*t^16 + 6*t^12 - 4*t^8 + t^4)>, <60, (-64*t^24 + 672*t^20 - 2364*t^16
+ 2828*t^12 - 591/4*t^8 + 21/8*t^4 - 1/64)/(t^20 + t^16 + 3/8*t^12 +
1/16*t^8 + 1/256*t^4)>, <61, (256*t^24 + 768*t^20 + 1536*t^16 +
1792*t^12 + 1536*t^8 + 768*t^4 + 256)/(t^16 + 2*t^12 + t^8)>, <62,
(4*t^24 + 672*t^20 + 37824*t^16 + 723968*t^12 + 605184*t^8 +
172032*t^4 + 16384)/(t^20 - 16*t^16 + 96*t^12 - 256*t^8 + 256*t^4)>,
<63, (1728*t^24 + 69120*t^22 + 1046016*t^20 + 7690240*t^18 +
32560128*t^16 + 104448000*t^14 + 234307584*t^12 + 417792000*t^10 +
520962048*t^8 + 492175360*t^6 + 267780096*t^4 + 70778880*t^2 +
7077888)/(t^24 - 8*t^22 + 8*t^20 + 96*t^18 - 272*t^16 - 256*t^14 +
1792*t^12 - 1024*t^10 - 4352*t^8 + 6144*t^6 + 2048*t^4 - 8192*t^2 +
4096)>, <64, (-64*t^24 + 192*t^22 + 504*t^20 - 1316*t^18 - 7407/4*t^16
+ 4899/2*t^14 + 50233/16*t^12 + 4899/32*t^10 - 7407/1024*t^8 -
329/1024*t^6 + 63/8192*t^4 + 3/16384*t^2 - 1/262144)/(t^20 - 2*t^18 +
7/4*t^16 - 7/8*t^14 + 35/128*t^12 - 7/128*t^10 + 7/1024*t^8 -
1/2048*t^6 + 1/65536*t^4)>, <65, (t^24 + 24*t^22 + 216*t^20 + 992*t^18
+ 3312*t^16 + 9984*t^14 + 19712*t^12 + 39936*t^10 + 52992*t^8 +
63488*t^6 + 55296*t^4 + 24576*t^2 + 4096)/(t^16 + 8*t^14 + 24*t^12 +
32*t^10 + 16*t^8)>, <66, (1728*t^24 + 82944*t^23 + 2101248*t^22 +
36495360*t^21 + 479453184*t^20 + 5008195584*t^19 + 42797891584*t^18 +
304316153856*t^17 + 1818588610560*t^16 + 9183889981440*t^15 +
39287173152768*t^14 + 142449234149376*t^13 + 437705016082432*t^12 +
1139593873195008*t^11 + 2514379081777152*t^10 + 4702151670497280*t^9 +
7448938948853760*t^8 + 9971831729553408*t^7 + 11219210491396096*t^6 +
10502947385376768*t^5 + 8043889629855744*t^4 + 4898324301742080*t^3 +
2256197860196352*t^2 + 712483534798848*t + 118747255799808)/(t^24 +
48*t^23 + 1024*t^22 + 12672*t^21 + 98176*t^20 + 457728*t^19 +
819200*t^18 - 4595712*t^17 - 40374272*t^16 - 133300224*t^15 -
90177536*t^14 + 1072693248*t^13 + 4899995648*t^12 + 8581545984*t^11 -
5771362304*t^10 - 68249714688*t^9 - 165373018112*t^8 -
150592290816*t^7 + 214748364800*t^6 + 959925190656*t^5 +
1647119958016*t^4 + 1700807049216*t^3 + 1099511627776*t^2 +
412316860416*t + 68719476736)>, <67, (16*t^24 + 192*t^20 + 1536*t^16 +
7168*t^12 + 24576*t^8 + 49152*t^4 + 65536)/(t^16 + 8*t^12 + 16*t^8)>,
<68, (1728*t^24 + 8640*t^22 + 16344*t^20 + 15020*t^18 + 31797/4*t^16 +
6375/2*t^14 + 14301/16*t^12 + 6375/32*t^10 + 31797/1024*t^8 +
3755/1024*t^6 + 2043/8192*t^4 + 135/16384*t^2 + 27/262144)/(t^24 -
t^22 + 1/8*t^20 + 3/16*t^18 - 17/256*t^16 - 1/128*t^14 + 7/1024*t^12 -
1/2048*t^10 - 17/65536*t^8 + 3/65536*t^6 + 1/524288*t^4 -
1/1048576*t^2 + 1/16777216)>, <69, (t^24 - 24*t^22 + 216*t^20 -
992*t^18 + 3312*t^16 - 9984*t^14 + 19712*t^12 - 39936*t^10 + 52992*t^8
- 63488*t^6 + 55296*t^4 - 24576*t^2 + 4096)/(t^16 - 8*t^14 + 24*t^12 -
32*t^10 + 16*t^8)>, <70, (1728*t^24 - 69120*t^22 + 1046016*t^20 -
7690240*t^18 + 32560128*t^16 - 104448000*t^14 + 234307584*t^12 -
417792000*t^10 + 520962048*t^8 - 492175360*t^6 + 267780096*t^4 -
70778880*t^2 + 7077888)/(t^24 + 8*t^22 + 8*t^20 - 96*t^18 - 272*t^16 +
256*t^14 + 1792*t^12 + 1024*t^10 - 4352*t^8 - 6144*t^6 + 2048*t^4 +
8192*t^2 + 4096)>, <71, (-t^24 - 24*t^22 + 504*t^20 + 10528*t^18 -
118512*t^16 - 1254144*t^14 + 12859648*t^12 - 5016576*t^10 -
1896192*t^8 + 673792*t^6 + 129024*t^4 - 24576*t^2 - 4096)/(t^20 +
16*t^18 + 112*t^16 + 448*t^14 + 1120*t^12 + 1792*t^10 + 1792*t^8 +
1024*t^6 + 256*t^4)>, <73, (1048576*t^21 + 56623104*t^20 +
1447034880*t^19 + 23177723904*t^18 + 260013293568*t^17 +
2164059537408*t^16 + 13818520403968*t^15 + 69095286374400*t^14 +
273881474531328*t^13 + 866290608635904*t^12 + 2191051796250624*t^11 +
4422098327961600*t^10 + 7075082446831616*t^9 + 8863987865223168*t^8 +
8520115603636224*t^7 + 6075901255090176*t^6 + 3034652092661760*t^5 +
949978046398464*t^4 + 140737488355328*t^3)/(t^24 + 64*t^23 + 1952*t^22
+ 37888*t^21 + 526976*t^20 + 5603328*t^19 + 47417344*t^18 +
328040448*t^17 + 1890185216*t^16 + 9190768640*t^15 + 38055182336*t^14
+ 134985285632*t^13 + 411573420032*t^12 + 1079882285056*t^11 +
2435531669504*t^10 + 4705673543680*t^9 + 7742198644736*t^8 +
10749229400064*t^7 + 12430172225536*t^6 + 11751030521856*t^5 +
8841190178816*t^4 + 5085241278464*t^3 + 2095944040448*t^2 +
549755813888*t + 68719476736)>, <74, (1728*t^24 - 8640*t^22 +
16344*t^20 - 15020*t^18 + 31797/4*t^16 - 6375/2*t^14 + 14301/16*t^12 -
6375/32*t^10 + 31797/1024*t^8 - 3755/1024*t^6 + 2043/8192*t^4 -
135/16384*t^2 + 27/262144)/(t^24 + t^22 + 1/8*t^20 - 3/16*t^18 -
17/256*t^16 + 1/128*t^14 + 7/1024*t^12 + 1/2048*t^10 - 17/65536*t^8 -
3/65536*t^6 + 1/524288*t^4 + 1/1048576*t^2 + 1/16777216)>, <75,
(-32*t^24 + 720*t^22 - 5601*t^20 + 66105/4*t^18 - 1522671/128*t^16 +
491085/128*t^14 - 1330727/2048*t^12 + 491085/8192*t^10 -
1522671/524288*t^8 + 66105/1048576*t^6 - 5601/16777216*t^4 +
45/67108864*t^2 - 1/2147483648)/(t^22 + 3/4*t^20 + 13/64*t^18 +
1/64*t^16 - 7/2048*t^14 - 7/8192*t^12 - 7/131072*t^10 + 1/262144*t^8 +
13/16777216*t^6 + 3/67108864*t^4 + 1/1073741824*t^2)>, <76,
(-8000/81*t^24 + 179200/27*t^23 - 3834880/27*t^22 + 67981312/81*t^21 +
50563072/27*t^20 + 186368000/9*t^19 - 1972748288/81*t^18 -
770244608/9*t^17 - 14969749504/27*t^16 + 172490752/81*t^15 +
47361556480/27*t^14 + 67366813696/27*t^13 + 121558269952/27*t^12 -
269467254784/27*t^11 + 757784903680/27*t^10 - 11039408128/81*t^9 -
3832255873024/27*t^8 + 788730478592/9*t^7 - 8080376987648/81*t^6 -
3053453312000/9*t^5 + 3313701486592/27*t^4 - 17820893052928/81*t^3 -
4021163130880/27*t^2 - 751619276800/27*t - 134217728000/81)/(t^24 +
16/3*t^23 - 16*t^22 + 3136/27*t^21 + 88096/81*t^20 - 159488/81*t^19 +
324352/81*t^18 + 2001920/27*t^17 - 6807808/81*t^16 + 7856128/81*t^15 +
49061888/27*t^14 - 76840960/81*t^13 + 314687488/81*t^12 +
307363840/81*t^11 + 784990208/27*t^10 - 502792192/81*t^9 -
1742798848/81*t^8 - 2049966080/27*t^7 + 1328545792/81*t^6 +
2613051392/81*t^5 + 5773459456/81*t^4 - 822083584/27*t^3 -
16777216*t^2 - 67108864/3*t + 16777216)>, <77, (1728*t^24 - 44928*t^22
+ 452448*t^20 - 2229344*t^18 + 5699796*t^16 - 7773168*t^14 +
5537396*t^12 - 1943292*t^10 + 1424949/4*t^8 - 69667/2*t^6 +
14139/8*t^4 - 351/8*t^2 + 27/64)/(t^24 - 2*t^22 - 15/2*t^20 + 3/2*t^18
+ 367/16*t^16 + 127/4*t^14 + 343/16*t^12 + 127/16*t^10 + 367/256*t^8 +
3/128*t^6 - 15/512*t^4 - 1/512*t^2 + 1/4096)>, <78, (2*t^24 + 720*t^22
+ 89616*t^20 + 4230720*t^18 + 48725472*t^16 + 251435520*t^14 +
681332224*t^12 + 1005742080*t^10 + 779607552*t^8 + 270766080*t^6 +
22941696*t^4 + 737280*t^2 + 8192)/(t^22 - 12*t^20 + 52*t^18 - 64*t^16
- 224*t^14 + 896*t^12 - 896*t^10 - 1024*t^8 + 3328*t^6 - 3072*t^4 +
1024*t^2)>, <79, (287496*t^24 + 3763584*t^23 + 22486464*t^22 +
79315200*t^21 + 177265728*t^20 + 250366464*t^19 + 239213312*t^18 +
381164544*t^17 + 1273038720*t^16 + 3023400960*t^15 + 4274632704*t^14 +
3569393664*t^13 + 2847586304*t^12 + 7138787328*t^11 + 17098530816*t^10
+ 24187207680*t^9 + 20368619520*t^8 + 12197265408*t^7 +
15309651968*t^6 + 32046907392*t^5 + 45380026368*t^4 + 40609382400*t^3
+ 23026139136*t^2 + 7707820032*t + 1177583616)/(t^24 + 36*t^23 +
596*t^22 + 6008*t^21 + 41112*t^20 + 201136*t^19 + 718608*t^18 +
1861536*t^17 + 3293680*t^16 + 2994816*t^15 - 2621824*t^14 -
15142144*t^13 - 28713728*t^12 - 30284288*t^11 - 10487296*t^10 +
23958528*t^9 + 52698880*t^8 + 59569152*t^7 + 45990912*t^6 +
25745408*t^5 + 10524672*t^4 + 3076096*t^3 + 610304*t^2 + 73728*t +
4096)>, <80, (1728*t^24 + 6048*t^22 + 6678*t^20 + 3913/2*t^18 -
16971/64*t^16 + 9597/64*t^14 - 13811/1024*t^12 + 9597/4096*t^10 -
16971/262144*t^8 + 3913/524288*t^6 + 3339/8388608*t^4 +
189/33554432*t^2 + 27/1073741824)/(t^24 - 5/2*t^22 + 65/32*t^20 -
49/128*t^18 - 785/4096*t^16 + 155/4096*t^14 + 839/65536*t^12 +
155/262144*t^10 - 785/16777216*t^8 - 49/33554432*t^6 +
65/536870912*t^4 - 5/2147483648*t^2 + 1/68719476736)>, <81, (1728*t^24
+ 179712*t^22 + 7239168*t^20 + 142678016*t^18 + 1459147776*t^16 +
7959724032*t^14 + 22681174016*t^12 + 31838896128*t^10 +
23346364416*t^8 + 9131393024*t^6 + 1853227008*t^4 + 184025088*t^2 +
7077888)/(t^24 + 8*t^22 - 120*t^20 - 96*t^18 + 5872*t^16 - 32512*t^14
+ 87808*t^12 - 130048*t^10 + 93952*t^8 - 6144*t^6 - 30720*t^4 +
8192*t^2 + 4096)>, <82, (2744000/9*t^24 + 13798400/3*t^23 +
103882240/3*t^22 + 1577867264/9*t^21 + 2032693760/3*t^20 +
2144727040*t^19 + 52258654208/9*t^18 + 13821583360*t^17 +
88310225920/3*t^16 + 510427824128/9*t^15 + 298660904960/3*t^14 +
479920455680/3*t^13 + 708001906688/3*t^12 + 959840911360/3*t^11 +
1194643619840/3*t^10 + 4083422593024/9*t^9 + 1412963614720/3*t^8 +
442290667520*t^7 + 3344553869312/9*t^6 + 274525061120*t^5 +
520369602560/3*t^4 + 807868039168/9*t^3 + 106375413760/3*t^2 +
28259123200/3*t + 11239424000/9)/(t^24 + 112/3*t^23 + 5848/9*t^22 +
63200/9*t^21 + 53000*t^20 + 2684096/9*t^19 + 11752928/9*t^18 +
13771136/3*t^17 + 119420528/9*t^16 + 289231360/9*t^15 +
595180288/9*t^14 + 1050446848/9*t^13 + 177612544*t^12 +
2100893696/9*t^11 + 2380721152/9*t^10 + 2313850880/9*t^9 +
1910728448/9*t^8 + 440676352/3*t^7 + 752187392/9*t^6 + 343564288/9*t^5
+ 13568000*t^4 + 32358400/9*t^3 + 5988352/9*t^2 + 229376/3*t + 4096)>,
<83, (1728*t^24 - 6048*t^22 + 6678*t^20 - 3913/2*t^18 - 16971/64*t^16
- 9597/64*t^14 - 13811/1024*t^12 - 9597/4096*t^10 - 16971/262144*t^8 -
3913/524288*t^6 + 3339/8388608*t^4 - 189/33554432*t^2 +
27/1073741824)/(t^24 + 5/2*t^22 + 65/32*t^20 + 49/128*t^18 -
785/4096*t^16 - 155/4096*t^14 + 839/65536*t^12 - 155/262144*t^10 -
785/16777216*t^8 + 49/33554432*t^6 + 65/536870912*t^4 +
5/2147483648*t^2 + 1/68719476736)>, <84, (-16*t^24 - 192*t^22 -
288*t^20 + 4160*t^18 + 13584*t^16 - 24960*t^14 - 128960*t^12 -
9600*t^10 + 382224*t^8 + 324160*t^6 - 37152*t^4 + 1344*t^2 - 16)/(t^20
+ 10*t^18 + 44*t^16 + 112*t^14 + 182*t^12 + 196*t^10 + 140*t^8 +
64*t^6 + 17*t^4 + 2*t^2)>, <85, (-4*t^24 + 96*t^22 - 288*t^20 -
8320*t^18 + 54336*t^16 + 199680*t^14 - 2063360*t^12 + 307200*t^10 +
24462336*t^8 - 41492480*t^6 - 9510912*t^4 - 688128*t^2 - 16384)/(t^20
- 20*t^18 + 176*t^16 - 896*t^14 + 2912*t^12 - 6272*t^10 + 8960*t^8 -
8192*t^6 + 4352*t^4 - 1024*t^2)>, <86, (-4*t^24 - 96*t^22 - 288*t^20 +
8320*t^18 + 54336*t^16 - 199680*t^14 - 2063360*t^12 - 307200*t^10 +
24462336*t^8 + 41492480*t^6 - 9510912*t^4 + 688128*t^2 - 16384)/(t^20
+ 20*t^18 + 176*t^16 + 896*t^14 + 2912*t^12 + 6272*t^10 + 8960*t^8 +
8192*t^6 + 4352*t^4 + 1024*t^2)>, <87, (4096*t^24 + 24576*t^22 +
64512*t^20 + 97280*t^18 + 93696*t^16 + 61440*t^14 + 29120*t^12 +
10560*t^10 + 2976*t^8 + 640*t^6 + 108*t^4 + 12*t^2 + 1)/(t^16 + 4*t^14
+ 13/2*t^12 + 11/2*t^10 + 41/16*t^8 + 5/8*t^6 + 1/16*t^4)>, <89, (t^24
- 24*t^22 + 1032*t^20 - 3072*t^19 - 9440*t^18 + 46080*t^17 +
217584*t^16 - 1867776*t^15 + 4066560*t^14 + 2605056*t^13 -
9840896*t^12 - 164069376*t^11 + 1131869184*t^10 - 3816325120*t^9 +
8412270336*t^8 - 13212057600*t^7 + 15286355968*t^6 - 13151502336*t^5 +
8350402560*t^4 - 3814457344*t^3 + 1189453824*t^2 - 227278848*t +
20123648)/(t^20 - 4*t^19 - 10*t^18 + 60*t^17 + 17*t^16 - 384*t^15 +
208*t^14 + 1344*t^13 - 1456*t^12 - 2688*t^11 + 4480*t^10 + 2688*t^9 -
7840*t^8 + 7936*t^6 - 3072*t^5 - 4096*t^4 + 3072*t^3 + 512*t^2 -
1024*t + 256)>, <90, (54000*t^24 + 1209600*t^23 + 13438080*t^22 +
98303488*t^21 + 531513216*t^20 + 2262789120*t^19 + 7893379584*t^18 +
23178921984*t^17 + 58389979392*t^16 + 127869853696*t^15 +
245678837760*t^14 + 416626950144*t^13 + 625734291456*t^12 +
833253900288*t^11 + 982715351040*t^10 + 1022958829568*t^9 +
934239670272*t^8 + 741725503488*t^7 + 505176293376*t^6 +
289637007360*t^5 + 136067383296*t^4 + 50331385856*t^3 +
13760593920*t^2 + 2477260800*t + 221184000)/(t^24 + 40*t^23 + 752*t^22
+ 8848*t^21 + 73208*t^20 + 453792*t^19 + 2192320*t^18 + 8477760*t^17 +
26738672*t^16 + 69711104*t^15 + 151659008*t^14 + 277058048*t^13 +
426557696*t^12 + 554116096*t^11 + 606636032*t^10 + 557688832*t^9 +
427818752*t^8 + 271288320*t^7 + 140308480*t^6 + 58085376*t^5 +
18741248*t^4 + 4530176*t^3 + 770048*t^2 + 81920*t + 4096)>, <91,
(-t^24 + 24*t^22 + 504*t^20 - 10528*t^18 - 118512*t^16 + 1254144*t^14
+ 12859648*t^12 + 5016576*t^10 - 1896192*t^8 - 673792*t^6 + 129024*t^4
+ 24576*t^2 - 4096)/(t^20 - 16*t^18 + 112*t^16 - 448*t^14 + 1120*t^12
- 1792*t^10 + 1792*t^8 - 1024*t^6 + 256*t^4)>, <92, (-4*t^24 +
720*t^22 - 44808*t^20 + 1057680*t^18 - 6090684*t^16 + 15714720*t^14 -
21291632*t^12 + 15714720*t^10 - 6090684*t^8 + 1057680*t^6 - 44808*t^4
+ 720*t^2 - 4)/(t^22 + 6*t^20 + 13*t^18 + 8*t^16 - 14*t^14 - 28*t^12 -
14*t^10 + 8*t^8 + 13*t^6 + 6*t^4 + t^2)>, <93, (t^24 - 24*t^22 +
312*t^20 + 192*t^19 - 2240*t^18 - 2880*t^17 + 9504*t^16 + 24576*t^15 -
70656*t^13 - 106496*t^12 + 24576*t^11 + 466944*t^10 + 1269760*t^9 +
2221056*t^8 + 2949120*t^7 + 3186688*t^6 + 2850816*t^5 + 2088960*t^4 +
1245184*t^3 + 589824*t^2 + 196608*t + 32768)/(t^16 + 8*t^15 + 20*t^14
- 8*t^13 - 130*t^12 - 200*t^11 + 108*t^10 + 648*t^9 + 577*t^8 -
384*t^7 - 1128*t^6 - 704*t^5 + 248*t^4 + 640*t^3 + 416*t^2 + 128*t +
16)>, <94, (1728*t^24 + 82944*t^23 + 1548288*t^22 + 12165120*t^21 -
9363456*t^20 - 919535616*t^19 - 6316097536*t^18 - 3336044544*t^17 +
178531860480*t^16 + 972784926720*t^15 + 946033655808*t^14 -
10871031988224*t^13 - 52593015390208*t^12 - 86968255905792*t^11 +
60546153971712*t^10 + 498065882480640*t^9 + 731266500526080*t^8 -
109315507617792*t^7 - 1655727072477184*t^6 - 1928405956165632*t^5 -
157092723818496*t^4 + 1632774767247360*t^3 + 1662461581197312*t^2 +
712483534798848*t + 118747255799808)/(t^24 + 48*t^23 + 1088*t^22 +
15488*t^21 + 154752*t^20 + 1143808*t^19 + 6377472*t^18 + 26468352*t^17
+ 75231232*t^16 + 90046464*t^15 - 408420352*t^14 - 3064987648*t^13 -
10964959232*t^12 - 24519901184*t^11 - 26138902528*t^10 +
46103789568*t^9 + 308147126272*t^8 + 867314958336*t^7 +
1671816019968*t^6 + 2398739234816*t^5 + 2596307730432*t^4 +
2078764171264*t^3 + 1168231104512*t^2 + 412316860416*t +
68719476736)>, <95, (-t^24 + 672*t^20 - 151296*t^16 + 11583488*t^12 -
38731776*t^8 + 44040192*t^4 - 16777216)/(t^20 + 64*t^16 + 1536*t^12 +
16384*t^8 + 65536*t^4)>, <96, (256*t^24 - 768*t^20 + 1536*t^16 -
1792*t^12 + 1536*t^8 - 768*t^4 + 256)/(t^16 - 2*t^12 + t^8)>, <97,
(1728*t^24 + 34560*t^23 + 256320*t^22 + 866240*t^21 + 1388376*t^20 +
1219920*t^19 + 320580*t^18 - 374220*t^17 - 1529163/4*t^16 - 51850*t^15
+ 182565/2*t^14 + 52275/2*t^13 - 279891/16*t^12 - 52275/8*t^11 +
182565/32*t^10 + 25925/32*t^9 - 1529163/1024*t^8 + 93555/256*t^7 +
80145/1024*t^6 - 76245/1024*t^5 + 173547/8192*t^4 - 13535/4096*t^3 +
4005/16384*t^2 - 135/16384*t + 27/262144)/(t^24 - 4*t^23 - t^22 +
23*t^21 - 143/8*t^20 - 195/4*t^19 + 1027/16*t^18 + 693/16*t^17 -
23185/256*t^16 - 301/32*t^15 + 7807/128*t^14 - 757/128*t^13 -
20521/1024*t^12 + 757/512*t^11 + 7807/2048*t^10 + 301/2048*t^9 -
23185/65536*t^8 - 693/16384*t^7 + 1027/65536*t^6 + 195/65536*t^5 -
143/524288*t^4 - 23/262144*t^3 - 1/1048576*t^2 + 1/1048576*t +
1/16777216)>, <98, (256*t^24 - 3072*t^22 + 16128*t^20 - 48640*t^18 +
93696*t^16 - 122880*t^14 + 116480*t^12 - 84480*t^10 + 47616*t^8 -
20480*t^6 + 6912*t^4 - 1536*t^2 + 256)/(t^16 - 8*t^14 + 26*t^12 -
44*t^10 + 41*t^8 - 20*t^6 + 4*t^4)>, <99, (256*t^24 + 3072*t^22 +
16128*t^20 + 48640*t^18 + 93696*t^16 + 122880*t^14 + 116480*t^12 +
84480*t^10 + 47616*t^8 + 20480*t^6 + 6912*t^4 + 1536*t^2 + 256)/(t^16
+ 8*t^14 + 26*t^12 + 44*t^10 + 41*t^8 + 20*t^6 + 4*t^4)>, <100,
(16*t^24 - 192*t^20 + 1536*t^16 - 7168*t^12 + 24576*t^8 - 49152*t^4 +
65536)/(t^16 - 8*t^12 + 16*t^8)>, <101, (1048576*t^24 - 1572864*t^22 +
1032192*t^20 - 389120*t^18 + 93696*t^16 - 15360*t^14 + 1820*t^12 -
165*t^10 + 93/8*t^8 - 5/8*t^6 + 27/1024*t^4 - 3/4096*t^2 +
1/65536)/(t^16 - t^14 + 13/32*t^12 - 11/128*t^10 + 41/4096*t^8 -
5/8192*t^6 + 1/65536*t^4)>, <102, (t^24 - 48*t^22 + 96*t^21 + 768*t^20
- 3264*t^19 - 736*t^18 + 30528*t^17 - 70608*t^16 + 8192*t^15 +
268800*t^14 - 574464*t^13 + 359424*t^12 + 694272*t^11 - 1944576*t^10 +
2091008*t^9 - 539904*t^8 - 1769472*t^7 + 3231744*t^6 - 3121152*t^5 +
2015232*t^4 - 901120*t^3 + 270336*t^2 - 49152*t + 4096)/(t^16 - 8*t^15
+ 12*t^14 + 104*t^13 - 650*t^12 + 1864*t^11 - 3332*t^10 + 4024*t^9 -
3359*t^8 + 1920*t^7 - 720*t^6 + 160*t^5 - 16*t^4)>, <103, (t^24 +
48*t^16 + 768*t^8 + 4096)/t^8>, <104, (256*t^24 + 768*t^16 + 768*t^8 +
256)/t^16>, <105, (-t^24 + 48*t^22 - 1008*t^20 + 12160*t^18 -
92352*t^16 + 448512*t^14 - 1304576*t^12 + 1622016*t^10 + 2002944*t^8 -
7929856*t^6 + 589824*t^4 + 14155776*t^2 + 7077888)/(t^16 - 32*t^14 +
416*t^12 - 2816*t^10 + 10624*t^8 - 22528*t^6 + 26624*t^4 - 16384*t^2 +
4096)>, <106, (-t^24 - 48*t^22 - 1008*t^20 - 12160*t^18 - 92352*t^16 -
448512*t^14 - 1304576*t^12 - 1622016*t^10 + 2002944*t^8 + 7929856*t^6
+ 589824*t^4 - 14155776*t^2 + 7077888)/(t^16 + 32*t^14 + 416*t^12 +
2816*t^10 + 10624*t^8 + 22528*t^6 + 26624*t^4 + 16384*t^2 + 4096)>,
<107, (-4096*t^24 + 24576*t^22 - 64512*t^20 + 97280*t^18 - 92352*t^16
+ 56064*t^14 - 20384*t^12 + 3168*t^10 + 489*t^8 - 242*t^6 + 9/4*t^4 +
27/4*t^2 + 27/64)/(t^16 - 4*t^14 + 13/2*t^12 - 11/2*t^10 + 83/32*t^8 -
11/16*t^6 + 13/128*t^4 - 1/128*t^2 + 1/4096)>, <108, (128*t^24 -
3072*t^23 - 6144*t^22 + 370688*t^21 + 1428480*t^20 - 14954496*t^19 -
136880128*t^18 - 391667712*t^17 + 33847296*t^16 + 3072098304*t^15 +
7585726464*t^14 + 3154182144*t^13 - 20746436608*t^12 -
47894102016*t^11 - 36310351872*t^10 + 27654356992*t^9 +
96373014528*t^8 + 114034999296*t^7 + 80912842752*t^6 + 37677957120*t^5
+ 11639980032*t^4 + 2324692992*t^3 + 283115520*t^2 + 18874368*t +
524288)/(t^24 + 16*t^23 + 104*t^22 + 256*t^21 - 872*t^20 - 10048*t^19
- 41504*t^18 - 84736*t^17 + 35056*t^16 + 952832*t^15 + 4054272*t^14 +
11264000*t^13 + 23835904*t^12 + 40491008*t^11 + 56503296*t^10 +
65413120*t^9 + 62951168*t^8 + 50155520*t^7 + 32753664*t^6 +
17235968*t^5 + 7116800*t^4 + 2211840*t^3 + 483328*t^2 + 65536*t +
4096)>, <109, (256*t^24 + 6144*t^22 + 64512*t^20 + 389120*t^18 +
1489152*t^16 + 3772416*t^14 + 6416384*t^12 + 7299072*t^10 +
5450496*t^8 + 2578432*t^6 + 728064*t^4 + 110592*t^2 + 6912)/(t^8 +
8*t^6 + 20*t^4 + 16*t^2 + 4)>, <110, (16777216*t^24 - 100663296*t^22 +
264241152*t^20 - 398458880*t^18 + 381222912*t^16 - 241434624*t^14 +
102662144*t^12 - 29196288*t^10 + 5450496*t^8 - 644608*t^6 + 45504*t^4
- 1728*t^2 + 27)/(t^8 - 2*t^6 + 5/4*t^4 - 1/4*t^2 + 1/64)>, <111,
(t^24 + 48*t^22 + 1008*t^20 + 12160*t^18 + 93072*t^16 + 471552*t^14 +
1604096*t^12 + 3649536*t^10 + 5450496*t^8 + 5156864*t^6 + 2912256*t^4
+ 884736*t^2 + 110592)/(t^8 + 16*t^6 + 80*t^4 + 128*t^2 + 64)>, <112,
(t^24 - 48*t^22 + 1008*t^20 - 12160*t^18 + 93072*t^16 - 471552*t^14 +
1604096*t^12 - 3649536*t^10 + 5450496*t^8 - 5156864*t^6 + 2912256*t^4
- 884736*t^2 + 110592)/(t^8 - 16*t^6 + 80*t^4 - 128*t^2 + 64)>, <113,
(t^24 - 48*t^16 + 768*t^8 - 4096)/t^8>, <114, (-256*t^24 + 768*t^16 -
768*t^8 + 256)/t^16>, <115, (64*t^24 + 768*t^20 + 3264*t^16 +
5632*t^12 + 3264*t^8 + 768*t^4 + 64)/(t^20 + 1/4*t^16)>, <116, (t^24 +
48*t^20 + 816*t^16 + 5632*t^12 + 13056*t^8 + 12288*t^4 + 4096)/(t^8 +
16*t^4)>, <117, (-64*t^24 + 768*t^20 - 3264*t^16 + 5632*t^12 -
3264*t^8 + 768*t^4 - 64)/(t^20 - 1/4*t^16)>, <118, (t^24 - 48*t^20 +
816*t^16 - 5632*t^12 + 13056*t^8 - 12288*t^4 + 4096)/(t^8 - 16*t^4)>,
<119, (t^24 + 48*t^22 + 1008*t^20 + 12160*t^18 + 92976*t^16 +
468480*t^14 + 1564160*t^12 + 3379200*t^10 + 4436736*t^8 + 3092480*t^6
+ 847872*t^4 + 98304*t^2 + 4096)/(t^8 + 16*t^6 + 80*t^4 + 128*t^2)>,
<120, (t^24 - 48*t^22 + 1008*t^20 - 12160*t^18 + 92976*t^16 -
468480*t^14 + 1564160*t^12 - 3379200*t^10 + 4436736*t^8 - 3092480*t^6
+ 847872*t^4 - 98304*t^2 + 4096)/(t^8 - 16*t^6 + 80*t^4 - 128*t^2)>,
<121, (256*t^24 + 6144*t^22 + 64512*t^20 + 389120*t^18 + 1487616*t^16
+ 3747840*t^14 + 6256640*t^12 + 6758400*t^10 + 4436736*t^8 +
1546240*t^6 + 211968*t^4 + 12288*t^2 + 256)/(t^8 + 8*t^6 + 20*t^4 +
16*t^2)>, <122, (16777216*t^24 - 100663296*t^22 + 264241152*t^20 -
398458880*t^18 + 380829696*t^16 - 239861760*t^14 + 100106240*t^12 -
27033600*t^10 + 4436736*t^8 - 386560*t^6 + 13248*t^4 - 192*t^2 +
1)/(t^8 - 2*t^6 + 5/4*t^4 - 1/4*t^2)>, <123, (10976*t^24 + 225792*t^23
+ 2338560*t^22 + 16484352*t^21 + 89505024*t^20 + 398039040*t^19 +
1497732096*t^18 + 4861280256*t^17 + 13780333056*t^16 +
34365390848*t^15 + 75629912064*t^14 + 146900189184*t^13 +
251211505664*t^12 + 376173428736*t^11 + 488976187392*t^10 +
545478672384*t^9 + 515466534912*t^8 + 406934126592*t^7 +
264375566336*t^6 + 138869735424*t^5 + 57616957440*t^4 +
18244698112*t^3 + 4167303168*t^2 + 616562688*t + 44957696)/(t^24 +
40*t^23 + 720*t^22 + 7760*t^21 + 56280*t^20 + 292768*t^19 +
1135808*t^18 + 3364160*t^17 + 7690480*t^16 + 13533440*t^15 +
17918464*t^14 + 16654848*t^13 + 8342784*t^12 - 2616320*t^11 -
8898560*t^10 - 7313408*t^9 - 1732864*t^8 + 1918976*t^7 + 1871872*t^6 +
430080*t^5 - 272384*t^4 - 188416*t^3 - 16384*t^2 + 16384*t + 4096)>,
<124, (-16*t^24 - 384*t^22 - 4032*t^20 - 24320*t^18 - 92352*t^16 -
224256*t^14 - 326144*t^12 - 202752*t^10 + 125184*t^8 + 247808*t^6 +
9216*t^4 - 110592*t^2 + 27648)/(t^16 + 16*t^14 + 104*t^12 + 352*t^10 +
664*t^8 + 704*t^6 + 416*t^4 + 128*t^2 + 16)>, <177, (1728*t^32 -
2709504*t^30 - 84934656*t^29 - 1352226816*t^28 - 14061404160*t^27 -
106521436160*t^26 - 625093902336*t^25 - 2956496744448*t^24 -
11585489731584*t^23 - 38383832104960*t^22 - 109169998823424*t^21 -
269665139326976*t^20 - 583591532691456*t^19 - 1113600197525504*t^18 -
1881802071343104*t^17 - 2823229083713536*t^16 - 3763604142686208*t^15
- 4454400790102016*t^14 - 4668732261531648*t^13 -
4314642229231616*t^12 - 3493439962349568*t^11 - 2456565254717440*t^10
- 1482942685642752*t^9 - 756863166578688*t^8 - 320048077996032*t^7 -
109077950627840*t^6 - 28797755719680*t^5 - 5538721038336*t^4 -
695784701952*t^3 - 44392513536*t^2 + 113246208)/(t^32 - 32*t^30 +
480*t^28 - 4480*t^26 + 29120*t^24 - 139776*t^22 + 512512*t^20 -
1464320*t^18 + 3294720*t^16 - 5857280*t^14 + 8200192*t^12 -
8945664*t^10 + 7454720*t^8 - 4587520*t^6 + 1966080*t^4 - 524288*t^2 +
65536)>, <178, (-23203748160*t^32 - 323005077504*t^31 -
2109977904128*t^30 - 8730811103232*t^29 - 26019722769920*t^28 -
59999818741760*t^27 - 111843664415744*t^26 - 173180712704000*t^25 -
226410818257664*t^24 - 252066767304704*t^23 - 239468220351488*t^22 -
193174781794304*t^21 - 130364955851264*t^20 - 71126597801984*t^19 -
28718444276736*t^18 - 5836526286848*t^17 + 2483144366208*t^16 +
3341506279424*t^15 + 1973119915008*t^14 + 763889752064*t^13 +
181814003200*t^12 + 5951166464*t^11 - 18634081280*t^10 -
10189539328*t^9 - 3149742848*t^8 - 306915328*t^7 - 62606336*t^6 +
101316608*t^5 - 1914368*t^4 + 8189952*t^3 - 1295360*t^2 + 153600*t -
72000)/(t^32 - 32*t^31 + 464*t^30 - 4000*t^29 + 22520*t^28 -
84896*t^27 + 206192*t^26 - 261664*t^25 - 81380*t^24 + 871520*t^23 -
1024816*t^22 - 704288*t^21 + 2465736*t^20 - 379680*t^19 - 3359760*t^18
+ 1376864*t^17 + 3607622*t^16 - 1376864*t^15 - 3359760*t^14 +
379680*t^13 + 2465736*t^12 + 704288*t^11 - 1024816*t^10 - 871520*t^9 -
81380*t^8 + 261664*t^7 + 206192*t^6 + 84896*t^5 + 22520*t^4 + 4000*t^3
+ 464*t^2 + 32*t + 1)>, <181, (4096*t^48 + 12288*t^46 + 14592*t^44 +
8512*t^42 + 3042*t^40 + 1545*t^38 + 14421/16*t^36 + 14751/64*t^34 +
171375/4096*t^32 + 70855/2048*t^30 + 235833/32768*t^28 -
79071/131072*t^26 + 3134807/4194304*t^24 - 79071/8388608*t^22 +
235833/134217728*t^20 + 70855/536870912*t^18 + 171375/68719476736*t^16
+ 14751/68719476736*t^14 + 14421/1099511627776*t^12 +
1545/4398046511104*t^10 + 1521/140737488355328*t^8 +
133/281474976710656*t^6 + 57/4503599627370496*t^4 +
3/18014398509481984*t^2 + 1/1152921504606846976)/(t^40 + 2*t^38 +
11/8*t^36 + 11/32*t^34 - 9/1024*t^32 - 39/2048*t^30 - 83/32768*t^28 +
27/131072*t^26 + 611/8388608*t^24 + 27/8388608*t^22 -
83/134217728*t^20 - 39/536870912*t^18 - 9/17179869184*t^16 +
11/34359738368*t^14 + 11/549755813888*t^12 + 1/2199023255552*t^10 +
1/281474976710656*t^8)>, <183, (16*t^48 + 672*t^40 + 9456*t^32 +
45248*t^24 + 9456*t^16 + 672*t^8 + 16)/(t^40 - 4*t^32 + 6*t^24 -
4*t^16 + t^8)>, <185, (16*t^48 + 720*t^44 + 11202*t^40 + 66105*t^36 +
1522671/16*t^32 + 491085/8*t^28 + 1330727/64*t^24 + 491085/128*t^20 +
1522671/4096*t^16 + 66105/4096*t^12 + 5601/32768*t^8 + 45/65536*t^4 +
1/1048576)/(t^44 - 3/2*t^40 + 13/16*t^36 - 1/8*t^32 - 7/128*t^28 +
7/256*t^24 - 7/2048*t^20 - 1/2048*t^16 + 13/65536*t^12 - 3/131072*t^8
+ 1/1048576*t^4)>, <187, (t^48 + 672*t^40 + 151296*t^32 +
11583488*t^24 + 38731776*t^16 + 44040192*t^8 + 16777216)/(t^40 -
64*t^32 + 1536*t^24 - 16384*t^16 + 65536*t^8)>, <188, (1/16*t^48 -
3*t^46 + 57*t^44 - 532*t^42 + 3042*t^40 - 24720*t^38 + 230736*t^36 -
944064*t^34 + 2742000*t^32 - 36277760*t^30 + 120746496*t^28 +
161937408*t^26 + 3210042368*t^24 + 647749632*t^22 + 1931943936*t^20 -
2321776640*t^18 + 701952000*t^16 - 966721536*t^14 + 945094656*t^12 -
405012480*t^10 + 199360512*t^8 - 139460608*t^6 + 59768832*t^4 -
12582912*t^2 + 1048576)/(t^40 - 32*t^38 + 352*t^36 - 1408*t^34 -
576*t^32 + 19968*t^30 - 42496*t^28 - 55296*t^26 + 312832*t^24 -
221184*t^22 - 679936*t^20 + 1277952*t^18 - 147456*t^16 - 1441792*t^14
+ 1441792*t^12 - 524288*t^10 + 65536*t^8)>, <189, (1/16*t^48 + 6*t^47
+ 276*t^46 + 8096*t^45 + 170688*t^44 + 2779392*t^43 + 36945664*t^42 +
421094400*t^41 + 4291398144*t^40 + 40195432448*t^39 +
349573398528*t^38 + 2824413511680*t^37 + 21238134865920*t^36 +
149572228743168*t^35 + 992610068987904*t^34 + 6211554303279104*t^33 +
36515979671371776*t^32 + 201026073608060928*t^31 +
1036249899261231104*t^30 + 5002031704131502080*t^29 +
22504629095513456640*t^28 + 93335740953009324032*t^27 +
351739640868526620672*t^26 + 1188716198729625894912*t^25 +
3571314952099434856448*t^24 + 9509729589837007159296*t^23 +
22511337015585703723008*t^22 + 47787899367940773904384*t^21 +
92178960775223118397440*t^20 + 163906574880981060157440*t^19 +
271646693591936166526976*t^18 + 421582232319292191277056*t^17 +
612636478398213302255616*t^16 + 833700705934744288755712*t^15 +
1065806945995837874896896*t^14 + 1284815661683475486867456*t^13 +
1459473514834619919237120*t^12 + 1552737748869902594211840*t^11 +
1537440065770838569254912*t^10 + 1414251051521943311220736*t^9 +
1207921192638552383422464*t^8 + 948220291463901295411200*t^7 +
665553914493422194917376*t^6 + 400552600816529203789824*t^5 +
196789865778333496639488*t^4 + 74672420010376264941568*t^3 +
20365205457375344984064*t^2 + 3541774862152233910272*t +
295147905179352825856)/(t^44 + 88*t^43 + 3704*t^42 + 99232*t^41 +
1898512*t^40 + 27566336*t^39 + 314791424*t^38 + 2886103040*t^37 +
21439795200*t^36 + 128638779392*t^35 + 609187790848*t^34 +
2115903684608*t^33 + 3916317851648*t^32 - 9702918324224*t^31 -
123082958176256*t^30 - 601728273612800*t^29 - 1826583388094464*t^28 -
2765498571816960*t^27 + 5288360750874624*t^26 + 51904453212635136*t^25
+ 190593985733984256*t^24 + 415235625701081088*t^23 +
338455088055975936*t^22 - 1415935268770283520*t^21 -
7481685557634924544*t^20 - 19717432069744230400*t^19 -
32265458988156452864*t^18 - 20348494569483010048*t^17 +
65704910521754451968*t^16 + 283991785214914330624*t^15 +
654110409703662026752*t^14 + 1104998700971997528064*t^13 +
1473331507471004467200*t^12 + 1586651925719831019520*t^11 +
1384467324048659972096*t^10 + 969904222949764759552*t^9 +
534383620984900943872*t^8 + 223450599111614529536*t^7 +
66725332079121268736*t^6 + 12682136550675316736*t^5 +
1152921504606846976*t^4)>, <190, (35152/9*t^48 + 346112*t^47 +
46418944/3*t^46 + 466157568*t^45 + 31983038464/3*t^44 +
197491163136*t^43 + 27762190385152/9*t^42 + 41719090380800*t^41 +
497622888087552*t^40 + 5303924948992000*t^39 +
153000248229232640/3*t^38 + 445529346581463040*t^37 +
10663191014426017792/3*t^36 + 25994298999995105280*t^35 +
174730763424732545024*t^34 + 1081459484909237174272*t^33 +
18508815280513614872576/3*t^32 + 32457234672745374023680*t^31 +
1417139570048807859126272/9*t^30 + 704173369159326766202880*t^29 +
8703838431108607963561984/3*t^28 + 11005426800090388713439232*t^27 +
115230418755305266453938176/3*t^26 + 123273769211818885332860928*t^25
+ 3273175754410138154018275328/9*t^24 +
986190153694551082662887424*t^23 + 7374746800339537053052043264/3*t^22
+ 5634778521646279021280886784*t^21 +
35650922213820858218749886464/3*t^20 +
23074352960612819474935971840*t^19 +
371494635450874687422797447168/9*t^18 +
68067754608417306624508559360*t^17 +
310526391865277507658020028416/3*t^16 +
145151034988568099743927894016*t^15 +
187615728628584809606231883776*t^14 +
223289328174848962675353845760*t^13 +
732768906847372970050466086912/3*t^12 +
244932348540881044048990699520*t^11 +
672902207922622566375159234560/3*t^10 +
186615268936573814092857344000*t^9 +
140068390835133076255499354112*t^8 + 93943039946603462035662438400*t^7
+ 500119161094237256108965101568/9*t^6 +
28461476118664173959975534592*t^5 +
36873932827813540031170084864/3*t^4 + 4299544677459428659842514944*t^3
+ 3425113520559422194912854016/3*t^2 + 204308463514872330525343744*t +
166000626605833768551841792/9)/(t^48 + 352/3*t^47 + 59776/9*t^46 +
724736/3*t^45 + 57089792/9*t^44 + 384133120/3*t^43 +
18588737536/9*t^42 + 27310080000*t^41 + 903358996480/3*t^40 +
8398010187776/3*t^39 + 198642338627584/9*t^38 + 442988531548160/3*t^37
+ 7493267477233664/9*t^36 + 3879404455329792*t^35 +
14203982142504960*t^34 + 104041100343246848/3*t^33 +
34709814290415616/9*t^32 - 1535482291504021504/3*t^31 -
9803533929980887040/3*t^30 - 38316960061591650304/3*t^29 -
297529548253897424896/9*t^28 - 111465409023142002688/3*t^27 +
435317943005289119744/3*t^26 + 1062498912435955564544*t^25 +
33784939610809965740032/9*t^24 + 8499991299487644516352*t^23 +
27860348352338503663616/3*t^22 - 57070289419848705376256/3*t^21 -
1218681029647963852374016/9*t^20 - 1255570147298235197161472/3*t^19 -
2569937598540909652213760/3*t^18 - 3220139758592241705156608/3*t^17 +
582334051670189519405056/9*t^16 + 13964160106690612081721344/3*t^15 +
15251409693756703679447040*t^14 + 33323830527196299068964864*t^13 +
514933420078384182884040704/9*t^12 +
243535520704308665468846080/3*t^11 +
873638244358585142776692736/9*t^10 + 295478715252512677672517632/3*t^9
+ 254272952495569575482490880/3*t^8 + 61496833055729217699840000*t^7 +
334864925761670207896551424/9*t^6 + 55359416834965312781680640/3*t^5 +
65820048890331935635668992/9*t^4 + 6684509756501982799986688/3*t^3 +
4410690295000248629592064/9*t^2 + 207784125246264389402624/3*t +
4722366482869645213696)>, <191, (1/4096*t^48 + 3/128*t^47 + 69/64*t^46
+ 509/16*t^45 + 10881/16*t^44 + 22551/2*t^43 + 151531*t^42 +
1702500*t^41 + 16362594*t^40 + 136928160*t^39 + 1012048320*t^38 +
6686135040*t^37 + 39899200768*t^36 + 217118115840*t^35 +
1086919446528*t^34 + 5046787096576*t^33 + 21895340027904*t^32 +
89321503457280*t^31 + 344373171060736*t^30 + 1259536876830720*t^29 +
4381918642569216*t^28 + 14528669942808576*t^27 +
45976791646470144*t^26 + 139030745258655744*t^25 +
402058899508690944*t^24 + 1112245962069245952*t^23 +
2942514665374089216*t^22 + 7438679010717990912*t^21 +
17948338759963508736*t^20 + 41272504379989032960*t^19 +
90275360554545577984*t^18 + 187320769618441666560*t^17 +
367342849041591435264*t^16 + 677368297802147299328*t^15 +
1167070869056045187072*t^14 + 1865030413803879137280*t^13 +
2741852198961569333248*t^12 + 3675741610680275435520*t^11 +
4451035582844664545280*t^10 + 4817731330879122309120*t^9 +
4605660765075919601664*t^8 + 3833689182799134720000*t^7 +
2729739820540314517504*t^6 + 1624970803149312884736*t^5 +
784058680726693871616*t^4 + 293418522922442555392*t^3 +
79551583817872441344*t^2 + 13835058055282163712*t +
1152921504606846976)/(t^40 + 64*t^39 + 1984*t^38 + 39936*t^37 +
589824*t^36 + 6840320*t^35 + 65032192*t^34 + 522027008*t^33 +
3613900800*t^32 + 21917597696*t^31 + 117836611584*t^30 +
566688219136*t^29 + 2454439591936*t^28 + 9623444652032*t^27 +
34284391890944*t^26 + 111262604197888*t^25 + 329402617430016*t^24 +
890100833583104*t^23 + 2194201081020416*t^22 + 4927203661840384*t^21 +
10053384568569856*t^20 + 18569239564648448*t^19 +
30890160707076096*t^18 + 45964533843361792*t^17 +
60631194324172800*t^16 + 70065278968397824*t^15 +
69827784456798208*t^14 + 58757901388349440*t^13 +
40532396646334464*t^12 + 21955048183431168*t^11 +
8725724278030336*t^10 + 2251799813685248*t^9 + 281474976710656*t^8)>,
<192, (1/4*t^48 + 696*t^46 + 654672*t^44 + 216040576*t^42 +
7561461888*t^40 + 45109340160*t^38 - 718836854784*t^36 -
1660941139968*t^34 + 32778430955520*t^32 - 276829437952000*t^30 +
2464198674087936*t^28 - 13354455546200064*t^26 +
53409700854628352*t^24 - 213671288739201024*t^22 +
630834860566511616*t^20 - 1133893377851392000*t^18 +
2148167251100958720*t^16 - 1741623016783085568*t^14 -
12060081181471801344*t^12 + 12108946295708712960*t^10 +
32476231518910414848*t^8 + 14846195336464039936*t^6 +
719819476379369472*t^4 + 12244161486913536*t^2 + 70368744177664)/(t^46
- 184*t^44 + 14704*t^42 - 662784*t^40 + 18203392*t^38 - 302012416*t^36
+ 2631094272*t^34 - 2874933248*t^32 - 150561226752*t^30 +
957929750528*t^28 + 1659893710848*t^26 - 26620442181632*t^24 +
26558299373568*t^22 + 245230016135168*t^20 - 616698784776192*t^18 -
188411625340928*t^16 + 2758902307356672*t^14 - 5066927537913856*t^12 +
4886435832266752*t^10 - 2846635604312064*t^8 + 1010451185926144*t^6 -
202310139510784*t^4 + 17592186044416*t^2)>, <193, (256*t^48 -
1536*t^46 + 3648*t^44 - 4256*t^42 + 3042*t^40 - 3090*t^38 +
14421/4*t^36 - 14751/8*t^34 + 171375/256*t^32 - 70855/64*t^30 +
235833/512*t^28 + 79071/1024*t^26 + 3134807/16384*t^24 +
79071/16384*t^22 + 235833/131072*t^20 - 70855/262144*t^18 +
171375/16777216*t^16 - 14751/8388608*t^14 + 14421/67108864*t^12 -
1545/134217728*t^10 + 1521/2147483648*t^8 - 133/2147483648*t^6 +
57/17179869184*t^4 - 3/34359738368*t^2 + 1/1099511627776)/(t^40 -
4*t^38 + 11/2*t^36 - 11/4*t^34 - 9/64*t^32 + 39/64*t^30 - 83/512*t^28
- 27/1024*t^26 + 611/32768*t^24 - 27/16384*t^22 - 83/131072*t^20 +
39/262144*t^18 - 9/4194304*t^16 - 11/4194304*t^14 + 11/33554432*t^12 -
1/67108864*t^10 + 1/4294967296*t^8)>, <194, (256*t^48 + 1536*t^46 +
3648*t^44 + 4256*t^42 + 3042*t^40 + 3090*t^38 + 14421/4*t^36 +
14751/8*t^34 + 171375/256*t^32 + 70855/64*t^30 + 235833/512*t^28 -
79071/1024*t^26 + 3134807/16384*t^24 - 79071/16384*t^22 +
235833/131072*t^20 + 70855/262144*t^18 + 171375/16777216*t^16 +
14751/8388608*t^14 + 14421/67108864*t^12 + 1545/134217728*t^10 +
1521/2147483648*t^8 + 133/2147483648*t^6 + 57/17179869184*t^4 +
3/34359738368*t^2 + 1/1099511627776)/(t^40 + 4*t^38 + 11/2*t^36 +
11/4*t^34 - 9/64*t^32 - 39/64*t^30 - 83/512*t^28 + 27/1024*t^26 +
611/32768*t^24 + 27/16384*t^22 - 83/131072*t^20 - 39/262144*t^18 -
9/4194304*t^16 + 11/4194304*t^14 + 11/33554432*t^12 + 1/67108864*t^10
+ 1/4294967296*t^8)>, <195, (-16*t^48 + 720*t^44 - 11202*t^40 +
66105*t^36 - 1522671/16*t^32 + 491085/8*t^28 - 1330727/64*t^24 +
491085/128*t^20 - 1522671/4096*t^16 + 66105/4096*t^12 - 5601/32768*t^8
+ 45/65536*t^4 - 1/1048576)/(t^44 + 3/2*t^40 + 13/16*t^36 + 1/8*t^32 -
7/128*t^28 - 7/256*t^24 - 7/2048*t^20 + 1/2048*t^16 + 13/65536*t^12 +
3/131072*t^8 + 1/1048576*t^4)>, <196, (-64*t^48 - 768*t^47 - 4416*t^46
- 16288*t^45 - 42804*t^44 - 83004*t^43 - 116971*t^42 - 212145/2*t^41 -
597537/32*t^40 + 2077515/16*t^39 + 16909305/64*t^38 +
37534965/128*t^37 + 188594087/1024*t^36 - 3179985/1024*t^35 -
657818793/4096*t^34 - 1755322159/8192*t^33 - 43901835759/262144*t^32 -
2532744975/32768*t^31 - 155342417/131072*t^30 + 9466285455/262144*t^29
+ 84988212627/2097152*t^28 + 61782097509/2097152*t^27 +
139192761153/8388608*t^26 + 128342978907/16777216*t^25 +
791625177369/268435456*t^24 + 128342978907/134217728*t^23 +
139192761153/536870912*t^22 + 61782097509/1073741824*t^21 +
84988212627/8589934592*t^20 + 9466285455/8589934592*t^19 -
155342417/34359738368*t^18 - 2532744975/68719476736*t^17 -
43901835759/4398046511104*t^16 - 1755322159/1099511627776*t^15 -
657818793/4398046511104*t^14 - 3179985/8796093022208*t^13 +
188594087/70368744177664*t^12 + 37534965/70368744177664*t^11 +
16909305/281474976710656*t^10 + 2077515/562949953421312*t^9 -
597537/9007199254740992*t^8 - 212145/4503599627370496*t^7 -
116971/18014398509481984*t^6 - 20751/36028797018963968*t^5 -
10701/288230376151711744*t^4 - 509/288230376151711744*t^3 -
69/1152921504606846976*t^2 - 3/2305843009213693952*t -
1/73786976294838206464)/(t^44 + 10*t^43 + 48*t^42 + 593/4*t^41 +
10669/32*t^40 + 18745/32*t^39 + 6735/8*t^38 + 261677/256*t^37 +
4397069/4096*t^36 + 508181/512*t^35 + 419267/512*t^34 +
2495337/4096*t^33 + 13502607/32768*t^32 + 8357861/32768*t^31 +
4758817/32768*t^30 + 20021681/262144*t^29 + 312225785/8388608*t^28 +
70670939/4194304*t^27 + 14886599/2097152*t^26 + 93504671/33554432*t^25
+ 273840151/268435456*t^24 + 93504671/268435456*t^23 +
14886599/134217728*t^22 + 70670939/2147483648*t^21 +
312225785/34359738368*t^20 + 20021681/8589934592*t^19 +
4758817/8589934592*t^18 + 8357861/68719476736*t^17 +
13502607/549755813888*t^16 + 2495337/549755813888*t^15 +
419267/549755813888*t^14 + 508181/4398046511104*t^13 +
4397069/281474976710656*t^12 + 261677/140737488355328*t^11 +
6735/35184372088832*t^10 + 18745/1125899906842624*t^9 +
10669/9007199254740992*t^8 + 593/9007199254740992*t^7 +
3/1125899906842624*t^6 + 5/72057594037927936*t^5 +
1/1152921504606846976*t^4)>, <197, (207646/6561*t^48 -
8341184/2187*t^47 + 290250944/2187*t^46 - 2371351808/6561*t^45 -
70659705728/2187*t^44 - 250785983488/2187*t^43 +
2369739971584/6561*t^42 - 6284946108416/2187*t^41 -
16727206700032/729*t^40 + 171162607304704/6561*t^39 -
186777349898240/2187*t^38 - 897267962937344/729*t^37 +
1017155880189952/729*t^36 - 9730939109507072/2187*t^35 -
57476450516992000/2187*t^34 + 591540222312841216/6561*t^33 -
125864743239811072/729*t^32 + 107591313204969472/2187*t^31 +
12838542402696249344/6561*t^30 - 6642977368124162048/2187*t^29 +
30732166651235532800/2187*t^28 + 12065016641537179648/6561*t^27 -
51779599482795065344/2187*t^26 + 81124937002299424768/2187*t^25 -
2397048714010386497536/6561*t^24 - 324499748009197699072/2187*t^23 -
828473591724721045504/2187*t^22 - 772161065058379497472/6561*t^21 +
7867434662716296396800/2187*t^20 + 6802408824959141937152/2187*t^19 +
52586669681443837313024/6561*t^18 - 1762776075550219829248/2187*t^17 -
8248671812964258414592/729*t^16 - 155068720037977447727104/6561*t^15 -
60268426577305403392000/2187*t^14 + 40814516830761950117888/2187*t^13
+ 17065043907616945733632/729*t^12 + 60214633696319259017216/729*t^11
- 50137663090405607997440/2187*t^10 -
183784450167948596740096/6561*t^9 - 71842805730069522153472/729*t^8 +
107974551971076761452544/2187*t^7 + 162847290847635989069824/6561*t^6
+ 68935526232073984540672/2187*t^5 - 77691168063166431100928/2187*t^4
+ 10429315545774562476032/6561*t^3 + 5106148606415369928704/2187*t^2 +
586958643034824114176/2187*t + 58447153014060875776/6561)/(t^48 +
40/3*t^47 + 544/9*t^46 - 7136/27*t^45 - 398528/81*t^44 -
6137216/243*t^43 - 10789376/729*t^42 + 1289818624/2187*t^41 +
24867701248/6561*t^40 + 63383455744/6561*t^39 - 91577491456/6561*t^38
- 1412684210176/6561*t^37 - 5783158636544/6561*t^36 -
431520907264/243*t^35 + 3353702170624/6561*t^34 +
111670095118336/6561*t^33 + 54439576010752/729*t^32 +
460330602856448/2187*t^31 + 1163342588674048/2187*t^30 +
6877045594259456/6561*t^29 + 15658048160792576/6561*t^28 +
22243325633363968/6561*t^27 + 2189051482341376/243*t^26 +
11111933818175488/2187*t^25 + 215647207435534336/6561*t^24 -
44447735272701952/2187*t^23 + 35024823717462016/243*t^22 -
1423572840535293952/6561*t^21 + 4008460329162899456/6561*t^20 -
7042094688521682944/6561*t^19 + 4765051243208900608/2187*t^18 -
7542056597200044032/2187*t^17 + 3567752053440643072/729*t^16 -
29273645414701072384/6561*t^15 + 3516611607264231424/6561*t^14 +
1809929867421024256/243*t^13 - 97025301607564181504/6561*t^12 +
94803632535648600064/6561*t^11 - 24582645678327463936/6561*t^10 -
68057467381985837056/6561*t^9 + 106805963586858385408/6561*t^8 -
22158915231406882816/2187*t^7 - 741440273027956736/729*t^6 +
1686985088543227904/243*t^5 - 438186169994313728/81*t^4 +
31384459903238144/27*t^3 + 9570149208162304/9*t^2 -
2814749767106560/3*t + 281474976710656)>, <199, (-1/2*t^48 + 696*t^46
- 327336*t^44 + 54010144*t^42 - 945182736*t^40 + 2819333760*t^38 +
22463651712*t^36 - 25952205312*t^34 - 256081491840*t^32 -
1081364992000*t^30 - 4812888035328*t^28 - 13041460494336*t^26 -
26078955495424*t^24 - 52165841977344*t^22 - 77006208565248*t^20 -
69207359488000*t^18 - 65556861911040*t^16 - 26575058239488*t^14 +
92011117412352*t^12 + 46191964323840*t^10 - 61943495786496*t^8 +
14158435188736*t^6 - 343236673536*t^4 + 2919235584*t^2 -
8388608)/(t^46 + 92*t^44 + 3676*t^42 + 82848*t^40 + 1137712*t^38 +
9437888*t^36 + 41110848*t^34 + 22460416*t^32 - 588129792*t^30 -
1870956544*t^28 + 1620989952*t^26 + 12998262784*t^24 + 6483959808*t^22
- 29935304704*t^20 - 37640306688*t^18 + 5749866496*t^16 +
42097508352*t^14 + 38657589248*t^12 + 18640273408*t^10 +
5429526528*t^8 + 963641344*t^6 + 96468992*t^4 + 4194304*t^2)>, <200,
(4*t^48 - 48*t^46 + 948*t^44 - 7732*t^42 + 144801/2*t^40 - 403665*t^38
+ 8282361/4*t^36 - 29311551/4*t^34 + 1105382895/64*t^32 -
223280215/8*t^30 + 1020068493/32*t^28 - 835340889/32*t^26 +
3942356327/256*t^24 - 835340889/128*t^22 + 1020068493/512*t^20 -
223280215/512*t^18 + 1105382895/16384*t^16 - 29311551/4096*t^14 +
8282361/16384*t^12 - 403665/16384*t^10 + 144801/131072*t^8 -
1933/65536*t^6 + 237/262144*t^4 - 3/262144*t^2 + 1/4194304)/(t^44 -
10*t^42 + 63/2*t^40 - 29/2*t^38 - 1299/16*t^36 + 119/2*t^34 +
909/8*t^32 - 301/8*t^30 - 9719/128*t^28 + 381/64*t^26 + 6669/256*t^24
+ 381/256*t^22 - 9719/2048*t^20 - 301/512*t^18 + 909/2048*t^16 +
119/2048*t^14 - 1299/65536*t^12 - 29/32768*t^10 + 63/131072*t^8 -
5/131072*t^6 + 1/1048576*t^4)>, <202, (2*t^48 + 696*t^46 + 81834*t^44
+ 3375634*t^42 + 59073921/4*t^40 + 22026045/2*t^38 - 175497279/8*t^36
- 50687901/8*t^34 + 2000636655/128*t^32 - 264005125/16*t^30 +
1175021493/64*t^28 - 795987579/64*t^26 + 3183466247/512*t^24 -
795987579/256*t^22 + 1175021493/1024*t^20 - 264005125/1024*t^18 +
2000636655/32768*t^16 - 50687901/8192*t^14 - 175497279/32768*t^12 +
22026045/32768*t^10 + 59073921/262144*t^8 + 1687817/131072*t^6 +
40917/524288*t^4 + 87/524288*t^2 + 1/8388608)/(t^46 - 23*t^44 +
919/4*t^42 - 2589/2*t^40 + 71107/16*t^38 - 147467/16*t^36 +
642357/64*t^34 - 10967/8*t^32 - 1148691/128*t^30 + 913553/128*t^28 +
791499/512*t^26 - 793351/256*t^24 + 791499/2048*t^22 +
913553/2048*t^20 - 1148691/8192*t^18 - 10967/2048*t^16 +
642357/65536*t^14 - 147467/65536*t^12 + 71107/262144*t^10 -
2589/131072*t^8 + 919/1048576*t^6 - 23/1048576*t^4 + 1/4194304*t^2)>,
<203, (64*t^48 + 192*t^46 + 948*t^44 + 1933*t^42 + 144801/32*t^40 +
403665/64*t^38 + 8282361/1024*t^36 + 29311551/4096*t^34 +
1105382895/262144*t^32 + 223280215/131072*t^30 +
1020068493/2097152*t^28 + 835340889/8388608*t^26 +
3942356327/268435456*t^24 + 835340889/536870912*t^22 +
1020068493/8589934592*t^20 + 223280215/34359738368*t^18 +
1105382895/4398046511104*t^16 + 29311551/4398046511104*t^14 +
8282361/70368744177664*t^12 + 403665/281474976710656*t^10 +
144801/9007199254740992*t^8 + 1933/18014398509481984*t^6 +
237/288230376151711744*t^4 + 3/1152921504606846976*t^2 +
1/73786976294838206464)/(t^44 + 5/2*t^42 + 63/32*t^40 + 29/128*t^38 -
1299/4096*t^36 - 119/2048*t^34 + 909/32768*t^32 + 301/131072*t^30 -
9719/8388608*t^28 - 381/16777216*t^26 + 6669/268435456*t^24 -
381/1073741824*t^22 - 9719/34359738368*t^20 + 301/34359738368*t^18 +
909/549755813888*t^16 - 119/2199023255552*t^14 -
1299/281474976710656*t^12 + 29/562949953421312*t^10 +
63/9007199254740992*t^8 + 5/36028797018963968*t^6 +
1/1152921504606846976*t^4)>, <204, (1556068/81*t^48 + 19781248/27*t^47
+ 385841792/27*t^46 + 14763951616/81*t^45 + 45949447936/27*t^44 +
334196074496/27*t^43 + 5945358026752/81*t^42 + 9855902359552/27*t^41 +
13976321951744/9*t^40 + 462910369595392/81*t^39 +
498430267064320/27*t^38 + 474534262734848/9*t^37 +
1209738445520896/9*t^36 + 8346214052921344/27*t^35 +
17428565755166720/27*t^34 + 98220515962912768/81*t^33 +
2084344786845696*t^32 + 84555054727561216/27*t^31 +
343618851587489792/81*t^30 + 145212682478288896/27*t^29 +
199732493916569600/27*t^28 + 597146982053576704/81*t^27 +
562602464528826368/27*t^26 + 183000203844911104/27*t^25 +
9718801131269783552/81*t^24 - 732000815379644416/27*t^23 +
9001639432461221888/27*t^22 - 38217406851428909056/81*t^21 +
51131518442641817600/27*t^20 - 148697786857767829504/27*t^19 +
1407462816102358188032/81*t^18 - 1385350016656362962944/27*t^17 +
136599619950719533056*t^16 - 25747918936581804654592/81*t^15 +
18275175765289698590720/27*t^14 - 35006558987024204824576/27*t^13 +
20296043204008304705536/9*t^12 - 31845455301213182492672/9*t^11 +
133796356023612520529920/27*t^10 - 497046224597870348075008/81*t^9 +
60027845701107370164224/9*t^8 - 169323113227380292845568/27*t^7 +
408561892606574929641472/81*t^6 - 91863117466361579700224/27*t^5 +
50521952295519923470336/27*t^4 - 64932545894857062744064/81*t^3 +
6787800588574861033472/27*t^2 - 1391981580026927644672/27*t +
437994204060197060608/81)/(t^48 - 16/3*t^47 - 96*t^46 + 8384/27*t^45 +
360256/81*t^44 + 13568/81*t^43 - 10435072/81*t^42 - 32914432/81*t^41 +
150462976/81*t^40 + 1009168384/81*t^39 + 624680960/81*t^38 -
12445171712/81*t^37 - 15975006208/27*t^36 + 2605907968/81*t^35 +
399232860160/81*t^34 + 1554796773376/81*t^33 + 1578545119232/81*t^32 -
5660949348352/81*t^31 - 30820177805312/81*t^30 -
99820433833984/81*t^29 - 1061687394304/81*t^28 - 7972499488768/9*t^27
+ 604673211891712/27*t^26 + 207366255542272/27*t^25 +
3665872497410048/27*t^24 - 829465022169088/27*t^23 +
9674771390267392/27*t^22 + 510239967281152/9*t^21 -
271791972941824/81*t^20 + 102216124245999616/81*t^19 -
126239448290557952/81*t^18 + 92748994123399168/81*t^17 +
103451532933988352/81*t^16 - 407580645359878144/81*t^15 +
418625995575132160/81*t^14 - 10929970213814272/81*t^13 -
268016129752956928/27*t^12 + 835181335877255168/81*t^11 +
167686518352117760/81*t^10 - 1083586301359292416/81*t^9 +
646233561178832896/81*t^8 + 565465636025663488/81*t^7 -
717092687542484992/81*t^6 - 3729543441416192/81*t^5 +
396105660976070656/81*t^4 - 36873221949095936/27*t^3 -
1688849860263936*t^2 + 1125899906842624/3*t + 281474976710656)>, <205,
(-4*t^48 + 720*t^44 - 44808*t^40 + 1057680*t^36 - 6090684*t^32 +
15714720*t^28 - 21291632*t^24 + 15714720*t^20 - 6090684*t^16 +
1057680*t^12 - 44808*t^8 + 720*t^4 - 4)/(t^44 + 6*t^40 + 13*t^36 +
8*t^32 - 14*t^28 - 28*t^24 - 14*t^20 + 8*t^16 + 13*t^12 + 6*t^8 +
t^4)>, <207, (-1/4*t^48 - 24*t^47 - 384*t^46 + 33856*t^45 +
1520448*t^44 + 7890432*t^43 - 879763456*t^42 - 24722903040*t^41 -
182706702336*t^40 + 4373903147008*t^39 + 145113654755328*t^38 +
2143959031480320*t^37 + 19625725978214400*t^36 +
110810322979258368*t^35 + 248374802497142784*t^34 -
1767275892473593856*t^33 - 20719039110482755584*t^32 -
96728221313591672832*t^31 - 150385089013681750016*t^30 +
960613058197774663680*t^29 + 7483241880019355566080*t^28 +
22713167653110632415232*t^27 + 10250232346133598830592*t^26 -
200181316734135878811648*t^25 - 879374520083920864673792*t^24 -
1601450533873087030493184*t^23 + 656014870152550325157888*t^22 +
11629141838392643796598784*t^21 + 30651358740559280398663680*t^20 +
31477368691024680179466240*t^19 - 39422548774402588676194304*t^18 -
202853782784241403862974464*t^17 - 347607794469017054707974144*t^16 -
237199755036978067347079168*t^15 + 266690413468921847680598016*t^14 +
951853426510223953788665856*t^13 + 1348669619787015303620198400*t^12 +
1178653942293991535054684160*t^11 + 638216603010220689155162112*t^10 +
153893035804842723331014656*t^9 - 51427364784906358191292416*t^8 -
55671028459230451382353920*t^7 - 15848409490463119013576704*t^6 +
1137131091679751599816704*t^5 + 1752957195836471270965248*t^4 +
312266483679755289755648*t^3 - 28334198897217871282176*t^2 -
14167099448608935641088*t - 1180591620717411303424)/(t^46 + 92*t^45 +
4148*t^44 + 122144*t^43 + 2640576*t^42 + 44656640*t^41 +
614579712*t^40 + 7067844608*t^39 + 69195886592*t^38 +
584389443584*t^37 + 4297081896960*t^36 + 27674980777984*t^35 +
156558882504704*t^34 + 777383359545344*t^33 + 3369004735397888*t^32 +
12563428551950336*t^31 + 39009211358642176*t^30 +
92240558445035520*t^29 + 109062204002664448*t^28 -
363777565619388416*t^27 - 3156028403170148352*t^26 -
13685448882480218112*t^25 - 43832546488905367552*t^24 -
109483591059841744896*t^23 - 201985817802889494528*t^22 -
186254113597126868992*t^21 + 446718787594913579008*t^20 +
3022538619126923919360*t^19 + 10226030702399894585344*t^18 +
26347419314579751043072*t^17 + 56522520150793212919808*t^16 +
104338628303183184658432*t^15 + 168103820064002561540096*t^14 +
237726274717739833622528*t^13 + 295293219450829469122560*t^12 +
321271494185077379694592*t^11 + 304326727608693652717568*t^10 +
248677674553916948217856*t^9 + 172988810122041671811072*t^8 +
100557813631809193246720*t^7 + 47568388358573899382784*t^6 +
17602805532337339629568*t^5 + 4782318401109201256448*t^4 +
848550227390639374336*t^3 + 73786976294838206464*t^2)>, <208,
(256*t^48 - 768*t^40 + 1536*t^32 - 1792*t^24 + 1536*t^16 - 768*t^8 +
256)/(t^32 - 2*t^24 + t^16)>, <209, (256*t^48 + 768*t^40 + 1536*t^32 +
1792*t^24 + 1536*t^16 + 768*t^8 + 256)/(t^32 + 2*t^24 + t^16)>, <210,
(t^48 + 48*t^40 + 1536*t^32 + 28672*t^24 + 393216*t^16 + 3145728*t^8 +
16777216)/(t^32 + 32*t^24 + 256*t^16)>, <211, (1/2*t^48 + 720*t^47 +
358512*t^46 + 67752000*t^45 + 3144241824*t^44 + 68431392000*t^43 +
848234961152*t^42 + 6547282191360*t^41 + 32628889518336*t^40 +
100882727055360*t^39 + 141061071360000*t^38 - 296892514713600*t^37 -
2301932208119808*t^36 - 6760806901678080*t^35 - 9692203365236736*t^34
+ 6621434000179200*t^33 + 67596846666055680*t^32 +
166310378251223040*t^31 + 214788884282736640*t^30 -
81128372054261760*t^29 - 1146989381186224128*t^28 -
1844274706513920000*t^27 - 1624814538580819968*t^26 -
1595614543101296640*t^25 + 16956476338758221824*t^24 +
6382458172405186560*t^23 - 25997032617293119488*t^22 +
118033581216890880000*t^21 - 293629281583673376768*t^20 +
83075452983564042240*t^19 + 879775270022089277440*t^18 -
2724829237268038287360*t^17 + 4430026943106625044480*t^16 -
1735769194542976204800*t^15 - 10163011835906475687936*t^14 +
28356879430935977656320*t^13 - 38620013872982972694528*t^12 +
19924119392532981350400*t^11 + 37865793014370140160000*t^10 -
108322003358516395376640*t^9 + 140140013386050312339456*t^8 -
112481451558297655050240*t^7 + 58290262679546727759872*t^6 -
18810277802224386048000*t^5 + 3457130446027619303424*t^4 -
297976447220318208000*t^3 + 6307009803155668992*t^2 -
50665495807918080*t + 140737488355328)/(t^47 - 48*t^46 + 916*t^45 -
7552*t^44 - 4080*t^43 + 604928*t^42 - 4292800*t^41 - 1216512*t^40 +
168931072*t^39 - 752128000*t^38 - 1207997440*t^37 + 19944996864*t^36 -
42148532224*t^35 - 158236344320*t^34 + 839134396416*t^33 -
350018863104*t^32 - 4874311172096*t^31 + 8519724040192*t^30 +
5636914413568*t^29 - 25109234450432*t^28 + 60715345903616*t^27 -
92765958438912*t^26 - 409268633206784*t^25 + 819491034365952*t^24 +
1637074532827136*t^23 - 1484255335022592*t^22 - 3885782137831424*t^21
- 6427964019310592*t^20 - 5772200359493632*t^19 +
34896789668626432*t^18 + 79860714243620864*t^17 -
22938836212383744*t^16 - 219974047214075904*t^15 -
165922832981688320*t^14 + 176783757301252096*t^13 +
334621520506650624*t^12 + 81067335913308160*t^11 -
201897822650368000*t^10 - 181388357379555328*t^9 -
5224879255191552*t^8 + 73749742433075200*t^7 + 41570335622955008*t^6 +
1121501860331520*t^5 - 8303511812964352*t^4 - 4028610604171264*t^3 -
844424930131968*t^2 - 70368744177664*t)>, <212, (-16*t^48 + 720*t^46 -
11205*t^44 + 264915/4*t^42 - 12405441/128*t^40 + 18096975/256*t^38 -
134396145/4096*t^36 + 182388465/16384*t^34 - 3121334511/1048576*t^32 +
341726265/524288*t^30 - 1006800165/8388608*t^28 +
631378215/33554432*t^26 - 2722943687/1073741824*t^24 +
631378215/2147483648*t^22 - 1006800165/34359738368*t^20 +
341726265/137438953472*t^18 - 3121334511/17592186044416*t^16 +
182388465/17592186044416*t^14 - 134396145/281474976710656*t^12 +
18096975/1125899906842624*t^10 - 12405441/36028797018963968*t^8 +
264915/72057594037927936*t^6 - 11205/1152921504606846976*t^4 +
45/4611686018427387904*t^2 - 1/295147905179352825856)/(t^46 + 3/2*t^44
+ 63/64*t^42 + 23/64*t^40 + 299/4096*t^38 + 39/8192*t^36 -
427/262144*t^34 - 35/65536*t^32 - 579/8388608*t^30 - 21/16777216*t^28
+ 611/536870912*t^26 + 117/536870912*t^24 + 611/34359738368*t^22 -
21/68719476736*t^20 - 579/2199023255552*t^18 - 35/1099511627776*t^16 -
427/281474976710656*t^14 + 39/562949953421312*t^12 +
299/18014398509481984*t^10 + 23/18014398509481984*t^8 +
63/1152921504606846976*t^6 + 3/2305843009213693952*t^4 +
1/73786976294838206464*t^2)>, <213, (t^48 + 24*t^46 + 228*t^44 +
1064*t^42 + 2322*t^40 + 840*t^38 - 5676*t^36 - 8712*t^34 + 1455*t^32 +
16240*t^30 + 14664*t^28 - 9456*t^26 - 21892*t^24 - 9456*t^22 +
14664*t^20 + 16240*t^18 + 1455*t^16 - 8712*t^14 - 5676*t^12 + 840*t^10
+ 2322*t^8 + 1064*t^6 + 228*t^4 + 24*t^2 + 1)/(t^32 + 8*t^30 + 12*t^28
- 8*t^26 - 26*t^24 - 8*t^22 + 12*t^20 + 8*t^18 + t^16)>, <214,
(1728*t^48 + 82944*t^47 + 2101248*t^46 + 36882432*t^45 +
496677888*t^44 + 5401718784*t^43 + 48880599040*t^42 +
374844973056*t^41 + 2463974184960*t^40 + 13980094152704*t^39 +
68734672109568*t^38 + 293400532451328*t^37 + 1088356500783104*t^36 +
3512936831975424*t^35 + 9900677217386496*t^34 + 24561181098901504*t^33
+ 54458357736357888*t^32 + 110498240078020608*t^31 +
210861290223042560*t^30 + 385828625763532800*t^29 +
678032230536708096*t^28 + 1131897098608836608*t^27 +
1781422056680718336*t^26 + 2658835509899427840*t^25 +
3818404670952439808*t^24 + 5317671019798855680*t^23 +
7125688226722873344*t^22 + 9055176788870692864*t^21 +
10848515688587329536*t^20 + 12346516024433049600*t^19 +
13495122574274723840*t^18 + 14143774729986637824*t^17 +
13941339580507619328*t^16 + 12575324722637570048*t^15 +
10138293470603771904*t^14 + 7194494631885668352*t^13 +
4457908227207593984*t^12 + 2403537161841278976*t^11 +
1126148867843162112*t^10 + 458099725195804672*t^9 +
161479012185538560*t^8 + 49131680308396032*t^7 + 12813755754741760*t^6
+ 2832056337825792*t^5 + 520804513087488*t^4 + 77348066033664*t^3 +
8813272891392*t^2 + 695784701952*t + 28991029248)/(t^48 + 48*t^47 +
1024*t^46 + 12512*t^45 + 91056*t^44 + 314688*t^43 - 880640*t^42 -
17552256*t^41 - 101767136*t^40 - 254255872*t^39 + 534986752*t^38 +
7699157504*t^37 + 33937231616*t^36 + 70155340800*t^35 -
71809302528*t^34 - 1139521587200*t^33 - 4650240250112*t^32 -
10913849548800*t^31 - 10381067550720*t^30 + 36062748262400*t^29 +
223002849140736*t^28 + 707251574964224*t^27 + 1653912291508224*t^26 +
3101952067829760*t^25 + 4806986446258176*t^24 + 6203904135659520*t^23
+ 6615649166032896*t^22 + 5658012599713792*t^21 +
3568045586251776*t^20 + 1154007944396800*t^19 - 664388323246080*t^18 -
1396972742246400*t^17 - 1190461504028672*t^16 - 583435052646400*t^15 -
73532725788672*t^14 + 143678137958400*t^13 + 139006900699136*t^12 +
63071498272768*t^11 + 8765222944768*t^10 - 8331456413696*t^9 -
6669411024896*t^8 - 2300609298432*t^7 - 230854492160*t^6 +
164987142144*t^5 + 95479136256*t^4 + 26239565824*t^3 + 4294967296*t^2
+ 402653184*t + 16777216)>, <215, (t^48 - 48*t^40 + 1536*t^32 -
28672*t^24 + 393216*t^16 - 3145728*t^8 + 16777216)/(t^32 - 32*t^24 +
256*t^16)>, <216, (1728*t^48 - 50112*t^46 + 583452*t^44 - 3529457*t^42
+ 390356571/32*t^40 - 1637898693/64*t^38 + 34767617387/1024*t^36 -
120539684859/4096*t^34 + 4511025549621/262144*t^32 -
913794639123/131072*t^30 + 4183447451367/2097152*t^28 -
3423154237197/8388608*t^26 + 16125200248573/268435456*t^24 -
3423154237197/536870912*t^22 + 4183447451367/8589934592*t^20 -
913794639123/34359738368*t^18 + 4511025549621/4398046511104*t^16 -
120539684859/4398046511104*t^14 + 34767617387/70368744177664*t^12 -
1637898693/281474976710656*t^10 + 390356571/9007199254740992*t^8 -
3529457/18014398509481984*t^6 + 145863/288230376151711744*t^4 -
783/1152921504606846976*t^2 + 27/73786976294838206464)/(t^48 - 5*t^46
+ 37/16*t^44 + 581/64*t^42 + 12097/2048*t^40 + 5289/4096*t^38 -
16943/65536*t^36 - 59561/262144*t^34 - 936721/16777216*t^32 -
27697/8388608*t^30 + 233605/134217728*t^28 + 316689/536870912*t^26 +
1652807/17179869184*t^24 + 316689/34359738368*t^22 +
233605/549755813888*t^20 - 27697/2199023255552*t^18 -
936721/281474976710656*t^16 - 59561/281474976710656*t^14 -
16943/4503599627370496*t^12 + 5289/18014398509481984*t^10 +
12097/576460752303423488*t^8 + 581/1152921504606846976*t^6 +
37/18446744073709551616*t^4 - 5/73786976294838206464*t^2 +
1/4722366482869645213696)>, <217, (-1/2*t^48 + 744*t^46 - 390696*t^44
+ 82703456*t^42 - 5836712976*t^40 + 208938610560*t^38 -
4467109918848*t^36 + 61759756288512*t^34 - 577063358855040*t^32 +
3742383726039040*t^30 - 17139292581285888*t^28 +
56086505494265856*t^26 - 132075245931126784*t^24 +
224346021977063424*t^22 - 274228681300574208*t^20 +
239512558466498560*t^18 - 147728219866890240*t^16 +
63241990439436288*t^14 - 18297282227601408*t^12 +
3423250195415040*t^10 - 382514821595136*t^8 + 21680214769664*t^6 -
409674448896*t^4 + 3120562176*t^2 - 8388608)/(t^46 + 4*t^44 - 164*t^42
- 1696*t^40 + 48*t^38 + 101184*t^36 + 822592*t^34 + 3344384*t^32 +
7002624*t^30 + 739328*t^28 - 41134080*t^26 - 125026304*t^24 -
164536320*t^22 + 11829248*t^20 + 448167936*t^18 + 856162304*t^16 +
842334208*t^14 + 414449664*t^12 + 786432*t^10 - 111149056*t^8 -
42991616*t^6 + 4194304*t^4 + 4194304*t^2)>, <218, (1728*t^48 +
50112*t^46 + 583452*t^44 + 3529457*t^42 + 390356571/32*t^40 +
1637898693/64*t^38 + 34767617387/1024*t^36 + 120539684859/4096*t^34 +
4511025549621/262144*t^32 + 913794639123/131072*t^30 +
4183447451367/2097152*t^28 + 3423154237197/8388608*t^26 +
16125200248573/268435456*t^24 + 3423154237197/536870912*t^22 +
4183447451367/8589934592*t^20 + 913794639123/34359738368*t^18 +
4511025549621/4398046511104*t^16 + 120539684859/4398046511104*t^14 +
34767617387/70368744177664*t^12 + 1637898693/281474976710656*t^10 +
390356571/9007199254740992*t^8 + 3529457/18014398509481984*t^6 +
145863/288230376151711744*t^4 + 783/1152921504606846976*t^2 +
27/73786976294838206464)/(t^48 + 5*t^46 + 37/16*t^44 - 581/64*t^42 +
12097/2048*t^40 - 5289/4096*t^38 - 16943/65536*t^36 +
59561/262144*t^34 - 936721/16777216*t^32 + 27697/8388608*t^30 +
233605/134217728*t^28 - 316689/536870912*t^26 +
1652807/17179869184*t^24 - 316689/34359738368*t^22 +
233605/549755813888*t^20 + 27697/2199023255552*t^18 -
936721/281474976710656*t^16 + 59561/281474976710656*t^14 -
16943/4503599627370496*t^12 - 5289/18014398509481984*t^10 +
12097/576460752303423488*t^8 - 581/1152921504606846976*t^6 +
37/18446744073709551616*t^4 + 5/73786976294838206464*t^2 +
1/4722366482869645213696)>, <219, (28756228/3*t^48 + 73902016*t^47 +
281705888*t^46 + 2897439808/3*t^45 + 3169096816*t^44 + 8673109952*t^43
+ 66414953248/3*t^42 + 53332609216*t^41 + 116262573912*t^40 +
732850865344/3*t^39 + 477988726240*t^38 + 872443052352*t^37 +
1553725783728*t^36 + 2527336257088*t^35 + 3983785870880*t^34 +
17903726640064/3*t^33 + 8137719659412*t^32 + 11251785561472*t^31 +
40386845682368/3*t^30 + 16056927660928*t^29 + 18619840183520*t^28 +
46671368714368/3*t^27 + 22234737701312*t^26 + 6637697341312*t^25 +
70777801907312/3*t^24 - 6637697341312*t^23 + 22234737701312*t^22 -
46671368714368/3*t^21 + 18619840183520*t^20 - 16056927660928*t^19 +
40386845682368/3*t^18 - 11251785561472*t^17 + 8137719659412*t^16 -
17903726640064/3*t^15 + 3983785870880*t^14 - 2527336257088*t^13 +
1553725783728*t^12 - 872443052352*t^11 + 477988726240*t^10 -
732850865344/3*t^9 + 116262573912*t^8 - 53332609216*t^7 +
66414953248/3*t^6 - 8673109952*t^5 + 3169096816*t^4 - 2897439808/3*t^3
+ 281705888*t^2 - 73902016*t + 28756228/3)/(t^48 - 88/3*t^47 +
1144/3*t^46 - 8504/3*t^45 + 38044/3*t^44 - 89560/3*t^43 - 18424/3*t^42
+ 301912*t^41 - 1038782*t^40 + 4598488/3*t^39 + 1501864/3*t^38 -
7065240*t^37 + 15438436*t^36 - 53412328/3*t^35 + 8935240*t^34 +
22126520/3*t^33 - 62868019/3*t^32 + 62271376/3*t^31 - 11142352/3*t^30
- 42475312/3*t^29 + 42928184/3*t^28 - 16297072/3*t^27 - 1521680*t^26 +
37718096/3*t^25 - 21428524/3*t^24 - 37718096/3*t^23 - 1521680*t^22 +
16297072/3*t^21 + 42928184/3*t^20 + 42475312/3*t^19 - 11142352/3*t^18
- 62271376/3*t^17 - 62868019/3*t^16 - 22126520/3*t^15 + 8935240*t^14 +
53412328/3*t^13 + 15438436*t^12 + 7065240*t^11 + 1501864/3*t^10 -
4598488/3*t^9 - 1038782*t^8 - 301912*t^7 - 18424/3*t^6 + 89560/3*t^5 +
38044/3*t^4 + 8504/3*t^3 + 1144/3*t^2 + 88/3*t + 1)>, <220,
(98611128000/289*t^48 + 1954805529600/289*t^47 +
19029301885440/289*t^46 + 120904714202112/289*t^45 +
563444118796032/289*t^44 + 2053520127507456/289*t^43 +
6095380896138752/289*t^42 + 15149404360559616/289*t^41 +
32163231653465472/289*t^40 + 59213193863496704/289*t^39 +
95647517938957824/289*t^38 + 136843130578818048/289*t^37 +
174757877046582016/289*t^36 + 200489288314954752/289*t^35 +
207707352293736960/289*t^34 + 11475286897955840/17*t^33 +
166629379497487680/289*t^32 + 129669586982983680/289*t^31 +
92251755809809408/289*t^30 + 60030879032162304/289*t^29 +
36394937464892928/289*t^28 + 19900852857952256/289*t^27 +
11854325560433664/289*t^26 + 4104201001433088/289*t^25 +
6251534073019648/289*t^24 - 4104201001433088/289*t^23 +
11854325560433664/289*t^22 - 19900852857952256/289*t^21 +
36394937464892928/289*t^20 - 60030879032162304/289*t^19 +
92251755809809408/289*t^18 - 129669586982983680/289*t^17 +
166629379497487680/289*t^16 - 11475286897955840/17*t^15 +
207707352293736960/289*t^14 - 200489288314954752/289*t^13 +
174757877046582016/289*t^12 - 136843130578818048/289*t^11 +
95647517938957824/289*t^10 - 59213193863496704/289*t^9 +
32163231653465472/289*t^8 - 15149404360559616/289*t^7 +
6095380896138752/289*t^6 - 2053520127507456/289*t^5 +
563444118796032/289*t^4 - 120904714202112/289*t^3 +
19029301885440/289*t^2 - 1954805529600/289*t + 98611128000/289)/(t^48
- 432/17*t^47 + 79160/289*t^46 - 452976/289*t^45 + 1326292/289*t^44 -
863408/289*t^43 - 5551672/289*t^42 + 6944272/289*t^41 +
50943810/289*t^40 - 169921616/289*t^39 + 90106216/289*t^38 +
328131952/289*t^37 - 152324476/289*t^36 - 1351993552/289*t^35 +
2185549720/289*t^34 - 123736976/17*t^33 + 5622566863/289*t^32 -
6739796192/289*t^31 - 5847056208/289*t^30 + 12004746144/289*t^29 +
2202060968/289*t^28 + 1711281440/289*t^27 - 12390842544/289*t^26 -
16787141472/289*t^25 + 21334898588/289*t^24 + 16787141472/289*t^23 -
12390842544/289*t^22 - 1711281440/289*t^21 + 2202060968/289*t^20 -
12004746144/289*t^19 - 5847056208/289*t^18 + 6739796192/289*t^17 +
5622566863/289*t^16 + 123736976/17*t^15 + 2185549720/289*t^14 +
1351993552/289*t^13 - 152324476/289*t^12 - 328131952/289*t^11 +
90106216/289*t^10 + 169921616/289*t^9 + 50943810/289*t^8 -
6944272/289*t^7 - 5551672/289*t^6 + 863408/289*t^5 + 1326292/289*t^4 +
452976/289*t^3 + 79160/289*t^2 + 432/17*t + 1)>, <221, (-t^48 +
672*t^40 - 151296*t^32 + 11583488*t^24 - 38731776*t^16 + 44040192*t^8
- 16777216)/(t^40 + 64*t^32 + 1536*t^24 + 16384*t^16 + 65536*t^8)>,
<222, (-16*t^48 + 672*t^40 - 9456*t^32 + 45248*t^24 - 9456*t^16 +
672*t^8 - 16)/(t^40 + 4*t^32 + 6*t^24 + 4*t^16 + t^8)>, <223,
(16777216*t^48 + 50331648*t^46 + 59768832*t^44 + 34865152*t^42 +
9510912*t^40 + 430080*t^38 - 363264*t^36 - 69696*t^34 + 1455*t^32 +
2030*t^30 + 1833/8*t^28 - 591/32*t^26 - 5473/1024*t^24 - 591/2048*t^22
+ 1833/32768*t^20 + 1015/131072*t^18 + 1455/16777216*t^16 -
1089/16777216*t^14 - 1419/268435456*t^12 + 105/1073741824*t^10 +
1161/34359738368*t^8 + 133/68719476736*t^6 + 57/1099511627776*t^4 +
3/4398046511104*t^2 + 1/281474976710656)/(t^32 + t^30 + 3/16*t^28 -
1/64*t^26 - 13/2048*t^24 - 1/4096*t^22 + 3/65536*t^20 + 1/262144*t^18
+ 1/16777216*t^16)>, <224, (1728*t^48 + 4752*t^46 + 11943/4*t^44 -
61417/64*t^42 - 3222309/8192*t^40 + 25070307/65536*t^38 -
556005173/4194304*t^36 + 1898188701/67108864*t^34 -
70087185099/17179869184*t^32 + 14269181637/34359738368*t^30 -
65471314233/2199023255552*t^28 + 53495774043/35184372088832*t^26 -
251655132547/4503599627370496*t^24 +
53495774043/36028797018963968*t^22 -
65471314233/2305843009213693952*t^20 +
14269181637/36893488147419103232*t^18 -
70087185099/18889465931478580854784*t^16 +
1898188701/75557863725914323419136*t^14 -
556005173/4835703278458516698824704*t^12 +
25070307/77371252455336267181195264*t^10 -
3222309/9903520314283042199192993792*t^8 -
61417/79228162514264337593543950336*t^6 +
11943/5070602400912917605986812821504*t^4 +
297/81129638414606681695789005144064*t^2 +
27/20769187434139310514121985316880384)/(t^48 - 13/4*t^46 +
1029/256*t^44 - 9331/4096*t^42 + 276929/524288*t^40 -
54127/4194304*t^38 - 1397711/268435456*t^36 + 812463/4294967296*t^34 +
27177199/1099511627776*t^32 - 1370009/2199023255552*t^30 -
9730203/140737488355328*t^28 + 1257657/2251799813685248*t^26 +
29945799/288230376151711744*t^24 + 1257657/2305843009213693952*t^22 -
9730203/147573952589676412928*t^20 -
1370009/2361183241434822606848*t^18 +
27177199/1208925819614629174706176*t^16 +
812463/4835703278458516698824704*t^14 -
1397711/309485009821345068724781056*t^12 -
54127/4951760157141521099596496896*t^10 +
276929/633825300114114700748351602688*t^8 -
9331/5070602400912917605986812821504*t^6 +
1029/324518553658426726783156020576256*t^4 -
13/5192296858534827628530496329220096*t^2 +
1/1329227995784915872903807060280344576)>, <225, (16*t^48 + 720*t^46 +
11205*t^44 + 264915/4*t^42 + 12405441/128*t^40 + 18096975/256*t^38 +
134396145/4096*t^36 + 182388465/16384*t^34 + 3121334511/1048576*t^32 +
341726265/524288*t^30 + 1006800165/8388608*t^28 +
631378215/33554432*t^26 + 2722943687/1073741824*t^24 +
631378215/2147483648*t^22 + 1006800165/34359738368*t^20 +
341726265/137438953472*t^18 + 3121334511/17592186044416*t^16 +
182388465/17592186044416*t^14 + 134396145/281474976710656*t^12 +
18096975/1125899906842624*t^10 + 12405441/36028797018963968*t^8 +
264915/72057594037927936*t^6 + 11205/1152921504606846976*t^4 +
45/4611686018427387904*t^2 + 1/295147905179352825856)/(t^46 - 3/2*t^44
+ 63/64*t^42 - 23/64*t^40 + 299/4096*t^38 - 39/8192*t^36 -
427/262144*t^34 + 35/65536*t^32 - 579/8388608*t^30 + 21/16777216*t^28
+ 611/536870912*t^26 - 117/536870912*t^24 + 611/34359738368*t^22 +
21/68719476736*t^20 - 579/2199023255552*t^18 + 35/1099511627776*t^16 -
427/281474976710656*t^14 - 39/562949953421312*t^12 +
299/18014398509481984*t^10 - 23/18014398509481984*t^8 +
63/1152921504606846976*t^6 - 3/2305843009213693952*t^4 +
1/73786976294838206464*t^2)>, <226, (287496*t^48 + 7527168*t^47 +
83673216*t^46 + 468163584*t^45 + 843290496*t^44 - 5687350272*t^43 -
38264757760*t^42 - 13513187328*t^41 + 871050481920*t^40 +
4862111223808*t^39 + 10123744352256*t^38 - 16325717213184*t^37 -
157673884116992*t^36 - 266851153723392*t^35 + 1380037527232512*t^34 +
10583702274572288*t^33 + 35225743045195776*t^32 +
61687139063955456*t^31 + 4322106343751680*t^30 -
239102320603299840*t^29 - 55428289519484928*t^28 +
4635419581605216256*t^27 + 28025334119030587392*t^26 +
105595237336476549120*t^25 + 305800453004913934336*t^24 +
730936706693301534720*t^23 + 1491813748814593916928*t^22 +
2649331951816511848448*t^21 + 4140576535677634609152*t^20 +
5734808613393876910080*t^19 + 7068704286616185733120*t^18 +
7771718366065745461248*t^17 + 7628083260805520818176*t^16 +
6681712766276627070976*t^15 + 5215979254174709710848*t^14 +
3620187882343265992704*t^13 + 2226404076148372799488*t^12 +
1207821326489235750912*t^11 + 574670692576231686144*t^10 +
238052595149469384704*t^9 + 85062639886050263040*t^8 +
25911041453293830144*t^7 + 6626239613511925760*t^6 +
1394023581502930944*t^5 + 234615730178359296*t^4 +
30330153879994368*t^3 + 2824030654562304*t^2 + 168379897872384*t +
4823382491136)/(t^48 + 72*t^47 + 2408*t^46 + 49520*t^45 + 697264*t^44
+ 7056096*t^43 + 51954336*t^42 + 269091904*t^41 + 820559904*t^40 -
388558976*t^39 - 21314538624*t^38 - 138961653504*t^37 -
534024704256*t^36 - 1197199166976*t^35 - 70070051328*t^34 +
12715812568064*t^33 + 65558903189248*t^32 + 213825795182592*t^31 +
524195693498368*t^30 + 1010773929648128*t^29 + 1539444624809984*t^28 +
1795505037295616*t^27 + 1435630168719360*t^26 + 405174100328448*t^25 -
846370904621056*t^24 - 1572944668065792*t^23 - 1319520693190656*t^22 -
359030186704896*t^21 + 525838155382784*t^20 + 748624701292544*t^19 +
381923295494144*t^18 - 68895981961216*t^17 - 232583301496832*t^16 -
134581618999296*t^15 + 2357711077376*t^14 + 47868235743232*t^13 +
25175369187328*t^12 - 761578651648*t^11 - 6503199145984*t^10 -
2506830643200*t^9 + 287764905984*t^8 + 505354911744*t^7 +
115251085312*t^6 - 26893877248*t^5 - 17800626176*t^4 - 1979711488*t^3
+ 637534208*t^2 + 201326592*t + 16777216)>, <227, (-8*t^48 + 720*t^46
- 22410*t^44 + 264915*t^42 - 12405441/16*t^40 + 18096975/16*t^38 -
134396145/128*t^36 + 182388465/256*t^34 - 3121334511/8192*t^32 +
341726265/2048*t^30 - 1006800165/16384*t^28 + 631378215/32768*t^26 -
2722943687/524288*t^24 + 631378215/524288*t^22 -
1006800165/4194304*t^20 + 341726265/8388608*t^18 -
3121334511/536870912*t^16 + 182388465/268435456*t^14 -
134396145/2147483648*t^12 + 18096975/4294967296*t^10 -
12405441/68719476736*t^8 + 264915/68719476736*t^6 -
11205/549755813888*t^4 + 45/1099511627776*t^2 -
1/35184372088832)/(t^46 + 3*t^44 + 63/16*t^42 + 23/8*t^40 +
299/256*t^38 + 39/256*t^36 - 427/4096*t^34 - 35/512*t^32 -
579/32768*t^30 - 21/32768*t^28 + 611/524288*t^26 + 117/262144*t^24 +
611/8388608*t^22 - 21/8388608*t^20 - 579/134217728*t^18 -
35/33554432*t^16 - 427/4294967296*t^14 + 39/4294967296*t^12 +
299/68719476736*t^10 + 23/34359738368*t^8 + 63/1099511627776*t^6 +
3/1099511627776*t^4 + 1/17592186044416*t^2)>, <228, (2048/3*t^48 +
98304*t^47 + 6619136*t^46 + 277610496*t^45 + 8143241216*t^44 +
177588928512*t^43 + 8946018418688/3*t^42 + 39280579706880*t^41 +
407718208733184*t^40 + 3287298846228480*t^39 + 19491843368550400*t^38
+ 68592565821112320*t^37 - 82995613020454912*t^36 -
3258181303350067200*t^35 - 26164394155334172672*t^34 -
123189167396021600256*t^33 - 288827323932376825856*t^32 +
684671096803672719360*t^31 + 31435412545303748804608/3*t^30 +
55177834661569395425280*t^29 + 168245063855472247832576*t^28 +
182916771235392236027904*t^27 - 1139976168827486361092096*t^26 -
8022124604092084056489984*t^25 - 85361921211841519737110528/3*t^24 -
64176996832736672451919872*t^23 - 72958474804959127109894144*t^22 +
93653386872520824846286848*t^21 + 689131781552014327122231296*t^20 +
1808067286190305949295575040*t^19 +
8240604786276105926635159552/3*t^18 +
1435859360004015850751262720*t^17 - 4845718400315455400780496896*t^16
- 16534170162105695425284538368*t^15 -
28093804304203453894364233728*t^14 -
27987564284654387726804582400*t^13 - 5703415098149210017320927232*t^12
+ 37709161849651814495063900160*t^11 +
85726033722038725557983641600*t^10 +
115661545772890968422728335360*t^9 +
114762473307683348149073608704*t^8 + 88452002065400917496420106240*t^7
+ 161157140867411482677704916992/3*t^6 +
25593261832696603285823422464*t^5 + 9388517915127210170768162816*t^4 +
2560504885943784592027680768*t^3 + 488406031124310186581295104*t^2 +
58028439341502200385896448*t + 9671406556917033397649408/3)/(t^48 +
320/3*t^47 + 5568*t^46 + 568832/3*t^45 + 14210816/3*t^44 +
92549120*t^43 + 4415565824/3*t^42 + 58733461504/3*t^41 +
222059700224*t^40 + 6535186743296/3*t^39 + 56032159858688/3*t^38 +
423097859571712/3*t^37 + 942785294237696*t^36 +
16787827572342784/3*t^35 + 88516659949600768/3*t^34 +
137825576093220864*t^33 + 566068561101979648*t^32 +
6032094497783939072/3*t^31 + 17854479321373081600/3*t^30 +
39724631409557504000/3*t^29 + 38026363828474740736/3*t^28 -
201982184191837601792/3*t^27 - 506670606740984168448*t^26 -
6384296640410439122944/3*t^25 - 6761453125853761241088*t^24 -
51074373123283512983552/3*t^23 - 32426918831422986780672*t^22 -
103414878306220852117504/3*t^21 + 155755986241432538054656/3*t^20 +
1301696722028380291072000/3*t^19 + 4680444627222025102950400/3*t^18 +
12650219040216583392722944/3*t^17 + 9497054520417110582099968*t^16 +
18498635683523220568276992*t^15 + 95044039908672076704120832/3*t^14 +
144206340788198662763184128/3*t^13 + 64787712094410265126240256*t^12 +
232600508143117261661536256/3*t^11 +
246432045176124356062871552/3*t^10 + 229936442046128678892470272/3*t^9
+ 62504248948925652946386944*t^8 + 132255997671796885780692992/3*t^7 +
79543762398385188494114816/3*t^6 + 13337733835054954200432640*t^5 +
16383955364411054716092416/3*t^4 + 5246549162468175832416256/3*t^3 +
410845884009659133591552*t^2 + 188894659314785808547840/3*t +
4722366482869645213696)>, <229, (-4*t^48 - 48*t^46 + 492*t^44 +
6668*t^42 - 36801/2*t^40 - 313665*t^38 + 396879/4*t^36 +
21425409/4*t^34 + 315735825/64*t^32 - 164014135/8*t^30 -
154003173/32*t^28 + 1226937111/32*t^26 - 8134644167/256*t^24 +
1226937111/128*t^22 - 154003173/512*t^20 - 164014135/512*t^18 +
315735825/16384*t^16 + 21425409/4096*t^14 + 396879/16384*t^12 -
313665/16384*t^10 - 36801/131072*t^8 + 1667/65536*t^6 + 123/262144*t^4
- 3/262144*t^2 - 1/4194304)/(t^44 + 10*t^42 + 87/2*t^40 + 221/2*t^38 +
2925/16*t^36 + 409/2*t^34 + 1205/8*t^32 + 477/8*t^30 - 1079/128*t^28 -
1885/64*t^26 - 5291/256*t^24 - 1885/256*t^22 - 1079/2048*t^20 +
477/512*t^18 + 1205/2048*t^16 + 409/2048*t^14 + 2925/65536*t^12 +
221/32768*t^10 + 87/131072*t^8 + 5/131072*t^6 + 1/1048576*t^4)>, <230,
(256*t^48 - 3072*t^46 + 14592*t^44 - 34048*t^42 + 37152*t^40 -
6720*t^38 - 22704*t^36 + 17424*t^34 + 1455*t^32 - 8120*t^30 +
3666*t^28 + 1182*t^26 - 5473/4*t^24 + 591/2*t^22 + 1833/8*t^20 -
1015/8*t^18 + 1455/256*t^16 + 1089/64*t^14 - 1419/256*t^12 -
105/256*t^10 + 1161/2048*t^8 - 133/1024*t^6 + 57/4096*t^4 - 3/4096*t^2
+ 1/65536)/(t^32 - 4*t^30 + 3*t^28 + t^26 - 13/8*t^24 + 1/4*t^22 +
3/16*t^20 - 1/16*t^18 + 1/256*t^16)>, <231, (1728*t^48 + 82944*t^47 +
1548288*t^46 + 11446272*t^45 - 41352192*t^44 - 1483739136*t^43 -
10697605120*t^42 - 3652952064*t^41 + 460075161600*t^40 +
3246081163264*t^39 + 6154897195008*t^38 - 47136833175552*t^37 -
389618214158336*t^36 - 1171068561063936*t^35 + 27707413364736*t^34 +
13766742092939264*t^33 + 53681798635143168*t^32 +
79928267521916928*t^31 - 115541902308147200*t^30 -
872839532799590400*t^29 - 2042310222562197504*t^28 -
1857858114412347392*t^27 + 3039113154580709376*t^26 +
14263446339248455680*t^25 + 26635840237761200128*t^24 +
28526892678496911360*t^23 + 12156452618322837504*t^22 -
14862864915298779136*t^21 - 32676963560995160064*t^20 -
27930865049586892800*t^19 - 7394681747721420800*t^18 +
10230818242805366784*t^17 + 13742540450596651008*t^16 +
7048571951584903168*t^15 + 28372391285489664*t^14 -
2398348413058940928*t^13 - 1595876205192544256*t^12 -
386144937374121984*t^11 + 100841835643011072*t^10 +
106367587557834752*t^9 + 30151485790617600*t^8 - 478799732932608*t^7 -
2804312996577280*t^6 - 777906624135168*t^5 - 43360916078592*t^4 +
24004572217344*t^3 + 6493990551552*t^2 + 695784701952*t +
28991029248)/(t^48 + 48*t^47 + 1088*t^46 + 15456*t^45 + 153328*t^44 +
1111616*t^43 + 5888768*t^42 + 20954240*t^41 + 26793504*t^40 -
248824576*t^39 - 2312692736*t^38 - 11607459328*t^37 - 40531873024*t^36
- 94111745024*t^35 - 62327926784*t^34 + 701978540032*t^33 +
4593616645888*t^32 + 18475556003840*t^31 + 58484604960768*t^30 +
156318117642240*t^29 + 363790825545728*t^28 + 749266964217856*t^27 +
1378652968058880*t^26 + 2278801771659264*t^25 + 3393647108538368*t^24
+ 4557603543318528*t^23 + 5514611872235520*t^22 +
5994135713742848*t^21 + 5820653208731648*t^20 + 5002179764551680*t^19
+ 3743014717489152*t^18 + 2364871168491520*t^17 +
1175965861347328*t^16 + 359413012496384*t^15 - 63823797026816*t^14 -
192740853809152*t^13 - 166018551906304*t^12 - 95088306814976*t^11 -
37891157786624*t^10 - 8153483706368*t^9 + 1755939078144*t^8 +
2746514145280*t^7 + 1543705198592*t^6 + 582806929408*t^5 +
160776060928*t^4 + 32413581312*t^3 + 4563402752*t^2 + 402653184*t +
16777216)>, <232, (-1481544000/83521*t^48 - 61382707200/83521*t^47 -
1195562833920/83521*t^46 - 15089082015744/83521*t^45 -
140621913427968/83521*t^44 - 1026816783187968/83521*t^43 -
6101318034685952/83521*t^42 - 30333922288730112/83521*t^41 -
128507963368439808/83521*t^40 - 473041394843779072/83521*t^39 -
1529606774431678464/83521*t^38 - 4388365077017788416/83521*t^37 -
11228242040637620224/83521*t^36 - 25618014970771931136/83521*t^35 -
52917696544175554560/83521*t^34 - 5817924155688878080/4913*t^33 -
169589457952985579520/83521*t^32 - 267006559262154424320/83521*t^31 -
403481828367467020288/83521*t^30 - 577250702549506326528/83521*t^29 -
566860353404909125632/83521*t^28 - 727386411321228525568/83521*t^27 +
480905330990090551296/83521*t^26 + 283592204392819851264/83521*t^25 +
6577186323848178434048/83521*t^24 - 1134368817571279405056/83521*t^23
+ 7694485295841448820736/83521*t^22 +
46552730324558625636352/83521*t^21 -
145116250471656736161792/83521*t^20 +
591104719410694478364672/83521*t^19 -
1652661568993144915099648/83521*t^18 +
4374635466951138088058880/83521*t^17 -
11114214716406862939422720/83521*t^16 +
1525133909868905255403520/4913*t^15 -
55488226571505426298306560/83521*t^14 +
107449742663968593851449344/83521*t^13 -
188378642016058132224016384/83521*t^12 +
294498195135936288390119424/83521*t^11 -
410600691995256749329219584/83521*t^10 +
507924330127063535822307328/83521*t^9 -
551937499943014973904519168/83521*t^8 +
521132816758005201641668608/83521*t^7 -
419279382743538519530012672/83521*t^6 +
282249248177679691564449792/83521*t^5 -
154615428934160847804039168/83521*t^4 +
66362484515105010798821376/83521*t^3 -
21032563802109867951390720/83521*t^2 +
4319424019889254091980800/83521*t -
417017562895812132864000/83521)/(t^48 - 96/17*t^47 - 25376/289*t^46 +
1095808/4913*t^45 + 409007424/83521*t^44 - 8332800/83521*t^43 -
690941440/4913*t^42 - 29139548160/83521*t^41 + 163814408704/83521*t^40
+ 924817842176/83521*t^39 + 693122473984/83521*t^38 -
11660372770816/83521*t^37 - 47533578502144/83521*t^36 -
26816031621120/83521*t^35 + 474786608578560/83521*t^34 +
90455928209408/4913*t^33 + 2213499320074240/83521*t^32 -
7948603024736256/83521*t^31 - 33031736984076288/83521*t^30 -
89128697117802496/83521*t^29 - 6530648726568960/83521*t^28 -
3611196624207872/4913*t^27 + 1802160242927075328/83521*t^26 +
18556615850459136/4913*t^25 + 11773728664275910656/83521*t^24 -
74226463401836544/4913*t^23 + 28834563886833205248/83521*t^22 +
231116583949303808/4913*t^21 - 1671846074001653760/83521*t^20 +
91267785848629755904/83521*t^19 - 135297994686776475648/83521*t^18 +
130229911957278818304/83521*t^17 + 145063891440385392640/83521*t^16 -
23712478844527050752/4913*t^15 + 497849842876872130560/83521*t^14 +
112474588692590100480/83521*t^13 - 797481113783426351104/83521*t^12 +
782514370465994113024/83521*t^11 + 186058647367743176704/83521*t^10 -
993015596725802369024/83521*t^9 + 703577527997257744384/83521*t^8 +
500613625469667901440/83521*t^7 - 47481134212018339840/4913*t^6 +
2290502622982963200/83521*t^5 + 449708418534708609024/83521*t^4 -
4819414551239852032/4913*t^3 - 446419313063100416/289*t^2 +
6755399441055744/17*t + 281474976710656)>, <233, (8*t^48 + 744*t^46 +
48837/2*t^44 + 2584483/8*t^42 + 364794561/256*t^40 +
1632332895/512*t^38 + 34899296241/8192*t^36 + 120624524001/32768*t^34
+ 4508307491055/2097152*t^32 + 913667901865/1048576*t^30 +
4184397602853/16777216*t^28 + 3423248626359/67108864*t^26 +
16122466544327/2147483648*t^24 + 3423248626359/4294967296*t^22 +
4184397602853/68719476736*t^20 + 913667901865/274877906944*t^18 +
4508307491055/35184372088832*t^16 + 120624524001/35184372088832*t^14 +
34899296241/562949953421312*t^12 + 1632332895/2251799813685248*t^10 +
364794561/72057594037927936*t^8 + 2584483/144115188075855872*t^6 +
48837/2305843009213693952*t^4 + 93/9223372036854775808*t^2 +
1/590295810358705651712)/(t^46 - 1/4*t^44 - 41/64*t^42 + 53/128*t^40 +
3/4096*t^38 - 1581/16384*t^36 + 12853/262144*t^34 - 1633/131072*t^32 +
13677/8388608*t^30 - 361/33554432*t^28 - 20085/536870912*t^26 +
7631/1073741824*t^24 - 20085/34359738368*t^22 - 361/137438953472*t^20
+ 13677/2199023255552*t^18 - 1633/2199023255552*t^16 +
12853/281474976710656*t^14 - 1581/1125899906842624*t^12 +
3/18014398509481984*t^10 + 53/36028797018963968*t^8 -
41/1152921504606846976*t^6 - 1/4611686018427387904*t^4 +
1/73786976294838206464*t^2)>, <234, (3065617154/9*t^48 +
40754362304/3*t^47 + 793377123136/3*t^46 + 30221912338688/9*t^45 +
93882494288768/3*t^44 + 684506046757888/3*t^43 +
12192930612601856/9*t^42 + 20201175942311936/3*t^41 +
28586228335567872*t^40 + 947220235131600896/9*t^39 +
1020199464513290240/3*t^38 + 973368291887611904*t^37 +
2486462218810195968*t^36 + 17109299548974743552/3*t^35 +
35420529001985474560/3*t^34 + 199457653690496712704/9*t^33 +
37877272358136184832*t^32 + 177487709287605075968/3*t^31 +
761857055777678688256/9*t^30 + 333964348407569973248/3*t^29 +
397921109630160732160/3*t^28 + 1316953433661287432192/9*t^27 +
400100454589240705024/3*t^26 + 328736393512104230912/3*t^25 +
1075179884621936459776/9*t^24 - 1314945574048416923648/3*t^23 +
6401607273427851280384/3*t^22 - 84285019754322395660288/9*t^21 +
101867804065321147432960/3*t^20 - 341979492769351652605952/3*t^19 +
3120566500465371907096576/9*t^18 - 2907958628968121564659712/3*t^17 +
2482324921262813009149952*t^16 - 52286627169041570255077376/9*t^15 +
37141116618785920972226560/3*t^14 - 71761603535462962779127808/3*t^13
+ 41715913720817920757465088*t^12 - 65321640322198050550317056*t^11 +
273857708467580883634749440/3*t^10 -
1017069982999914026111074304/9*t^9 + 122776915817252523828314112*t^8 -
347053560051886991001780224/3*t^7 + 837891811576355471822422016/9*t^6
- 188155589423320050561974272/3*t^5 +
103224894115114327073619968/3*t^4 - 132917376120057687600791552/9*t^3
+ 13957237953592053597208576/3*t^2 - 2867833295094009200377856/3*t +
862894517025937528193024/9)/(t^48 - 152/3*t^47 + 9760/9*t^46 -
109472/9*t^45 + 590144/9*t^44 + 168832/9*t^43 - 7345664/3*t^42 +
114873856/9*t^41 - 34388480/3*t^40 - 674084864/9*t^39 -
1213112320/9*t^38 + 12858400768/9*t^37 + 22557933568/3*t^36 -
575279693824/9*t^35 + 942628536320/9*t^34 + 455228391424/9*t^33 +
7143393001472/9*t^32 - 39637260173312/9*t^31 + 1902993473536/9*t^30 +
70765445644288/3*t^29 - 242265909886976/9*t^28 +
265481105702912/9*t^27 - 11892026245120*t^26 - 1882769982488576/3*t^25
+ 4819629696352256/9*t^24 + 7531079929954304/3*t^23 -
190272419921920*t^22 - 16990790764986368/9*t^21 -
62020072931065856/9*t^20 - 72463816339750912/3*t^19 +
7794661267603456/9*t^18 + 649416870679543808/9*t^17 +
468149403744468992/9*t^16 - 119335391441453056/9*t^15 +
988417660100280320/9*t^14 + 2412897920924778496/9*t^13 +
378459323983986688/3*t^12 - 862912668397207552/9*t^11 -
325642358798417920/9*t^10 + 723793111402151936/9*t^9 -
147697396959150080/3*t^8 - 1973517818741653504/9*t^7 -
504790186358472704/3*t^6 - 46408186785169408/9*t^5 +
648870190062239744/9*t^4 + 481462947663577088/9*t^3 +
171699735793500160/9*t^2 + 10696049115004928/3*t + 281474976710656)>,
<235, (t^48 - 24*t^46 + 228*t^44 - 1064*t^42 + 2322*t^40 - 840*t^38 -
5676*t^36 + 8712*t^34 + 1455*t^32 - 16240*t^30 + 14664*t^28 +
9456*t^26 - 21892*t^24 + 9456*t^22 + 14664*t^20 - 16240*t^18 +
1455*t^16 + 8712*t^14 - 5676*t^12 - 840*t^10 + 2322*t^8 - 1064*t^6 +
228*t^4 - 24*t^2 + 1)/(t^32 - 8*t^30 + 12*t^28 + 8*t^26 - 26*t^24 +
8*t^22 + 12*t^20 - 8*t^18 + t^16)>, <236, (-4*t^48 + 48*t^46 +
492*t^44 - 6668*t^42 - 36801/2*t^40 + 313665*t^38 + 396879/4*t^36 -
21425409/4*t^34 + 315735825/64*t^32 + 164014135/8*t^30 -
154003173/32*t^28 - 1226937111/32*t^26 - 8134644167/256*t^24 -
1226937111/128*t^22 - 154003173/512*t^20 + 164014135/512*t^18 +
315735825/16384*t^16 - 21425409/4096*t^14 + 396879/16384*t^12 +
313665/16384*t^10 - 36801/131072*t^8 - 1667/65536*t^6 + 123/262144*t^4
+ 3/262144*t^2 - 1/4194304)/(t^44 - 10*t^42 + 87/2*t^40 - 221/2*t^38 +
2925/16*t^36 - 409/2*t^34 + 1205/8*t^32 - 477/8*t^30 - 1079/128*t^28 +
1885/64*t^26 - 5291/256*t^24 + 1885/256*t^22 - 1079/2048*t^20 -
477/512*t^18 + 1205/2048*t^16 - 409/2048*t^14 + 2925/65536*t^12 -
221/32768*t^10 + 87/131072*t^8 - 5/131072*t^6 + 1/1048576*t^4)>, <237,
(1728*t^48 - 304128*t^46 + 12229632*t^44 + 251564032*t^42 -
6599288832*t^40 - 410751909888*t^38 - 9109588754432*t^36 -
124399694708736*t^34 - 1148308440662016*t^32 - 7481160702099456*t^30 -
34325824396591104*t^28 - 112188769525825536*t^26 -
263879532265603072*t^24 - 448755078103302144*t^22 -
549213190345457664*t^20 - 478794284934365184*t^18 -
293966960809476096*t^16 - 127385287381745664*t^14 -
37312875538153472*t^12 - 6729759291604992*t^10 - 432490992893952*t^8 +
65946001604608*t^6 + 12823698604032*t^4 - 1275605286912*t^2 +
28991029248)/(t^48 + 208*t^46 + 16464*t^44 + 597184*t^42 +
8861728*t^40 + 13856512*t^38 - 357814016*t^36 - 831962112*t^34 +
6957362944*t^32 + 11223113728*t^30 - 79709822976*t^28 -
41210904576*t^26 + 490631970816*t^24 - 164843618304*t^22 -
1275357167616*t^20 + 718279278592*t^18 + 1781084913664*t^16 -
851929202688*t^14 - 1465606209536*t^12 + 227025092608*t^10 +
580762206208*t^8 + 156548202496*t^6 + 17263755264*t^4 + 872415232*t^2
+ 16777216)>, <238, (128*t^48 - 6144*t^47 + 99072*t^46 - 495104*t^45 -
1521504*t^44 + 13826688*t^43 + 7616464*t^42 - 147260640*t^41 -
12706623*t^40 + 838349080*t^39 + 2857281*t^38 - 2824627026*t^37 +
66310513/8*t^36 + 12057817251/2*t^35 - 41813889/16*t^34 -
68328698097/8*t^33 - 1348732689/512*t^32 + 132638686977/16*t^31 +
64512695/128*t^30 - 360681559155/64*t^29 + 478507941/1024*t^28 +
697321363337/256*t^27 - 45010455/2048*t^26 - 967427479395/1024*t^25 -
1357387577/32768*t^24 + 967427479395/4096*t^23 - 45010455/32768*t^22 -
697321363337/16384*t^21 + 478507941/262144*t^20 +
360681559155/65536*t^19 + 64512695/524288*t^18 -
132638686977/262144*t^17 - 1348732689/33554432*t^16 +
68328698097/2097152*t^15 - 41813889/16777216*t^14 -
12057817251/8388608*t^13 + 66310513/134217728*t^12 +
1412313513/33554432*t^11 + 2857281/268435456*t^10 -
104793635/134217728*t^9 - 12706623/4294967296*t^8 +
4601895/536870912*t^7 + 476029/4294967296*t^6 - 108021/2147483648*t^5
- 47547/34359738368*t^4 + 967/8589934592*t^3 + 387/68719476736*t^2 +
3/34359738368*t + 1/2199023255552)/(t^48 - 8*t^47 + 6*t^46 + 38*t^45 +
69/4*t^44 + 167/2*t^43 + 253/8*t^42 - 13/8*t^41 + 5313/128*t^40 -
4255/32*t^39 + 5313/128*t^38 - 18915/128*t^37 + 33649/1024*t^36 -
33055/512*t^35 + 43263/2048*t^34 + 9477/2048*t^33 + 735471/65536*t^32
+ 85931/4096*t^31 + 81719/16384*t^30 + 197935/16384*t^29 +
245157/131072*t^28 + 231043/65536*t^27 + 156009/262144*t^26 +
105183/262144*t^25 + 676039/4194304*t^24 - 105183/1048576*t^23 +
156009/4194304*t^22 - 231043/4194304*t^21 + 245157/33554432*t^20 -
197935/16777216*t^19 + 81719/67108864*t^18 - 85931/67108864*t^17 +
735471/4294967296*t^16 - 9477/536870912*t^15 + 43263/2147483648*t^14 +
33055/2147483648*t^13 + 33649/17179869184*t^12 + 18915/8589934592*t^11
+ 5313/34359738368*t^10 + 4255/34359738368*t^9 + 5313/549755813888*t^8
+ 13/137438953472*t^7 + 253/549755813888*t^6 - 167/549755813888*t^5 +
69/4398046511104*t^4 - 19/2199023255552*t^3 + 3/8796093022208*t^2 +
1/8796093022208*t + 1/281474976710656)>, <239, (10976*t^48 +
602112*t^47 + 16353792*t^46 + 289933312*t^45 + 3740723712*t^44 +
37180637184*t^43 + 294649243648*t^42 + 1905230831616*t^41 +
10230984465408*t^40 + 46380313542656*t^39 + 180879749996544*t^38 +
621913202196480*t^37 + 1943263213527040*t^36 + 5684125326901248*t^35 +
15831960537759744*t^34 + 41960564183400448*t^33 +
104907804437323776*t^32 + 246878828022988800*t^31 +
551684842123952128*t^30 + 1183767035290583040*t^29 +
2442781973368012800*t^28 + 4803960642631368704*t^27 +
8922081089855422464*t^26 + 15649436532014579712*t^25 +
26108519091058245632*t^24 + 41562764783338389504*t^23 +
62534919245197737984*t^22 + 87160098345086615552*t^21 +
110152570235869200384*t^20 + 124253588313939640320*t^19 +
124073665913438601216*t^18 + 109484930661013782528*t^17 +
85636710120057470976*t^16 + 59735254821584764928*t^15 +
37427697037917290496*t^14 + 21200631002396884992*t^13 +
10904500494068088832*t^12 + 5104042899381682176*t^11 +
2175630045219913728*t^10 + 844213466880278528*t^9 +
297506070388015104*t^8 + 94682833213194240*t^7 + 26968595183435776*t^6
+ 6792823638589440*t^5 + 1485640461975552*t^4 + 272232207089664*t^3 +
38918846152704*t^2 + 3788161155072*t + 184146722816)/(t^48 + 16*t^47 -
96*t^46 - 3808*t^45 - 22736*t^44 + 176064*t^43 + 3299968*t^42 +
16105344*t^41 - 48149472*t^40 - 1144594688*t^39 - 7284023808*t^38 -
17991217664*t^37 + 82225391360*t^36 + 1142703629312*t^35 +
7012844812288*t^34 + 30416424454144*t^33 + 103293219499776*t^32 +
285589534580736*t^31 + 652728353832960*t^30 + 1233268689551360*t^29 +
1893026451054592*t^28 + 2238541400473600*t^27 + 1694340189585408*t^26
- 131452987834368*t^25 - 2928541823287296*t^24 - 5462878698209280*t^23
- 6097464857985024*t^22 - 3941577921921024*t^21 + 225792649199616*t^20
+ 4207653476106240*t^19 + 5846790535380992*t^18 +
4550747472527360*t^17 + 1578295924555776*t^16 - 1092531898023936*t^15
- 2221245011591168*t^14 - 1874693135007744*t^13 - 908929996423168*t^12
- 111241418768384*t^11 + 237160787607552*t^10 + 254222025097216*t^9 +
154624394788864*t^8 + 67171996663808*t^7 + 21956510351360*t^6 +
5440482050048*t^5 + 1006951727104*t^4 + 134553272320*t^3 +
12213813248*t^2 + 671088640*t + 16777216)>, <240, (t^48 - 48*t^40 +
816*t^32 - 5632*t^24 + 13056*t^16 - 12288*t^8 + 4096)/(t^16 -
16*t^8)>, <241, (16*t^48 + 768*t^40 + 13056*t^32 + 90112*t^24 +
208896*t^16 + 196608*t^8 + 65536)/(t^40 + t^32)>, <242, (t^48 +
48*t^40 + 816*t^32 + 5632*t^24 + 13056*t^16 + 12288*t^8 + 4096)/(t^16
+ 16*t^8)>, <243, (-16*t^48 + 768*t^40 - 13056*t^32 + 90112*t^24 -
208896*t^16 + 196608*t^8 - 65536)/(t^40 - t^32)> ]; 
// Models of the rank one elliptic curves X_n. These all have good reduction 
// away from 2, and there really aren't so many elliptic curves like that.
rankoneellmodels := [ <150, [ 0, 1, 0, -13, -21 ]>, <153, [ 0, 1, 0,
-3, 1 ]>, <155, [ 0, 0, 0, -2, 0 ]>, <156, [ 0, 0, 0, 8, 0 ]>, <165, [
0, 1, 0, -13, -21 ]>, <166, [ 0, 1, 0, -3, 1 ]>, <167, [ 0, 1, 0, 1, 1
]>, <281, [ 0, 1, 0, -13, -21 ]>, <284, [ 0, 0, 0, 8, 0 ]>, <288, [ 0,
1, 0, -3, 1 ]>, <289, [ 0, 1, 0, -13, -21 ]>, <291, [ 0, 0, 0, -2, 0
]>, <295, [ 0, 1, 0, -9, 7 ]>, <297, [ 0, 1, 0, -9, 7 ]>, <302, [ 0,
1, 0, -13, -21 ]>, <304, [ 0, 1, 0, -13, -21 ]>, <308, [ 0, 1, 0, -3,
1 ]>, <309, [ 0, 1, 0, -13, -21 ]>, <312, [ 0, 1, 0, -3, 1 ]>, <318, [
0, 0, 0, 8, 0 ]>, <320, [ 0, 1, 0, -13, -21 ]>, <323, [ 0, 1, 0, -3, 1
]>, <324, [ 0, 0, 0, -2, 0 ]>, <326, [ 0, 1, 0, -13, -21 ]>, <328, [
0, 0, 0, 8, 0 ]>, <349, [ 0, 1, 0, -13, -21 ]>, <350, [ 0, 0, 0, 8, 0
]> ]; 
// Maps from X_n -> X_m where X_n is an elliptic curve of positive rank 
// and X_m has genus zero.  
rankoneellmaps := <<150, [ a
- c, -c ]>, <153, [ 4*a + 4*c, -2*c ]>, <155, [ 4*a, -2*c ]>, <156, [
a, c ]>, <165, [ a - c, -c ]>, <166, [ 4*a + 4*c, -2*c ]>, <167, [ 4*a
+ 4*c, 2*c ]>, <281, [ -3*a*c + b*c - 5*c^2, 2*a*c + 4*c^2 ]>, <284, [
-3*a*c + b*c, 2*a*c - 2*c^2 ]>, <288, [ a - c, c ]>, <289, [ a + 3*c,
2*c ]>, <291, [ a, c ]>, <295, [ a + c, -2*c ]>, <297, [ a + c, 2*c
]>, <302, [ a*c + b*c + 3*c^2, 2*a*c + 4*c^2 ]>, <304, [ 4*a + 4*c,
-16*c ]>, <308, [ -3/16*a*c + 1/8*b*c + 1/8*c^2, 1/2*a*c - 5/8*c^2 ]>,
<309, [ 4*a + 4*c, 16*c ]>, <312, [ 4*a, -8*c ]>, <318, [ a, -2*c ]>,
<320, [ a + 3*c, 2*c ]>, <323, [ a - c, c ]>, <324, [ a, c ]>, <326, [
a*c + b*c + 3*c^2, 2*a*c + 4*c^2 ]>, <328, [ a, -2*c ]>, <349, [
-1/8*a*c - 1/4*c^2, 3/64*a*c - 1/64*b*c + 5/64*c^2 ]>, <350, [ -24*a*c
+ 8*b*c, 8*a*c - 8*c^2 ]>>; 
// If -I is not contained in a subgroup H, the corresponding modular curve 
// is a family E_t over P^1. Each curve is represented as 
// E_t : y^2 = x^3 + A(t) x + B(t), and an elliptic E corresponds to a point 
// on the modular curve if and only if E_t is isomorphic to E for some t 
// (including t = infinity, by the way).  
// This list takes up most of the file 

eqf := [ [ 0, 0, 0, -27*t^6 - 139968*t^4 - 241864704*t^2 - 139314069504, 
54*t^9 +
373248*t^7 + 967458816*t^5 + 1114512556032*t^3 + 481469424205824*t ],
[ 0, 0, 0, -108*t^6 - 559872*t^4 - 967458816*t^2 - 557256278016,
432*t^9 + 2985984*t^7 + 7739670528*t^5 + 8916100448256*t^3 +
3851755393646592*t ], [ 0, 0, 0, -108*t^6 + 559872*t^4 - 967458816*t^2
+ 557256278016, 432*t^9 - 2985984*t^7 + 7739670528*t^5 -
8916100448256*t^3 + 3851755393646592*t ], [ 0, 0, 0, -27*t^6 +
139968*t^4 - 241864704*t^2 + 139314069504, 54*t^9 - 373248*t^7 +
967458816*t^5 - 1114512556032*t^3 + 481469424205824*t ], [ 0, 0, 0,
-27*t^6 - 27*t^4 + 135*t^2 - 81, 54*t^9 - 648*t^7 + 1620*t^5 -
1512*t^3 + 486*t ], [ 0, 0, 0, -108*t^6 - 108*t^4 + 540*t^2 - 324,
432*t^9 - 5184*t^7 + 12960*t^5 - 12096*t^3 + 3888*t ], [ 0, 0, 0,
-27*t^2 - 81, 54*t^3 - 486*t ], [ 0, 0, 0, -108*t^2 - 324, 432*t^3 -
3888*t ], [ 0, 0, 0, -27*t^6 - 4752*t^4 - 276480*t^2 - 5308416, 54*t^9
+ 14256*t^7 + 1410048*t^5 + 61931520*t^3 + 1019215872*t ], [ 0, 0, 0,
-108*t^6 - 19008*t^4 - 1105920*t^2 - 21233664, 432*t^9 + 114048*t^7 +
11280384*t^5 + 495452160*t^3 + 8153726976*t ], [ 0, 0, 0, -27*t^2 -
1296, 54*t^3 + 3888*t ], [ 0, 0, 0, -108*t^2 - 5184, 432*t^3 + 31104*t
], [ 0, 0, 0, 324*t^4 - 108*t^2, 3888*t^5 + 432*t^3 ], [ 0, 0, 0,
81*t^8 + 135*t^6 + 27*t^4 - 27*t^2, 486*t^11 + 1512*t^9 + 1620*t^7 +
648*t^5 + 54*t^3 ], [ 0, 0, 0, 324*t^8 + 540*t^6 + 108*t^4 - 108*t^2,
3888*t^11 + 12096*t^9 + 12960*t^7 + 5184*t^5 + 432*t^3 ], [ 0, 0, 0,
81*t^4 - 27*t^2, 486*t^5 + 54*t^3 ], [ 0, 0, 0, -108*t^6 + 19008*t^4 -
1105920*t^2 + 21233664, 432*t^9 - 114048*t^7 + 11280384*t^5 -
495452160*t^3 + 8153726976*t ], [ 0, 0, 0, -27*t^6 + 4752*t^4 -
276480*t^2 + 5308416, 54*t^9 - 14256*t^7 + 1410048*t^5 - 61931520*t^3
+ 1019215872*t ], [ 0, 0, 0, -108*t^2 + 5184, 432*t^3 - 31104*t ], [
0, 0, 0, -27*t^2 + 1296, 54*t^3 - 3888*t ], [ 0, 0, 0, -108*t^4 +
1728*t^3 - 1728*t^2 - 82944*t + 331776, 432*t^6 - 10368*t^5 +
51840*t^4 + 525312*t^3 - 5971968*t^2 + 15925248*t ], [ 0, 0, 0,
-27*t^4 + 432*t^3 - 432*t^2 - 20736*t + 82944, -54*t^6 + 1296*t^5 -
6480*t^4 - 65664*t^3 + 746496*t^2 - 1990656*t ], [ 0, 0, 0, -108*t^4 +
1728*t^3 - 1728*t^2 - 82944*t + 331776, -432*t^6 + 10368*t^5 -
51840*t^4 - 525312*t^3 + 5971968*t^2 - 15925248*t ], [ 0, 0, 0,
-27*t^4 + 432*t^3 - 432*t^2 - 20736*t + 82944, 54*t^6 - 1296*t^5 +
6480*t^4 + 65664*t^3 - 746496*t^2 + 1990656*t ], [ 0, 0, 0, -108*t^8 +
2592*t^7 - 16848*t^6 - 9504*t^5 + 240408*t^4 + 318816*t^3 - 422928*t^2
- 940896*t - 431244, 432*t^12 - 15552*t^11 + 194400*t^10 - 782784*t^9
- 2010096*t^8 + 13779072*t^7 + 38574144*t^6 - 69579648*t^5 -
514588464*t^4 - 1123581888*t^3 - 1256096160*t^2 - 724489920*t -
170772624 ], [ 0, 0, 0, -27*t^8 + 648*t^7 - 4212*t^6 - 2376*t^5 +
60102*t^4 + 79704*t^3 - 105732*t^2 - 235224*t - 107811, 54*t^12 -
1944*t^11 + 24300*t^10 - 97848*t^9 - 251262*t^8 + 1722384*t^7 +
4821768*t^6 - 8697456*t^5 - 64323558*t^4 - 140447736*t^3 -
157012020*t^2 - 90561240*t - 21346578 ], [ 0, 0, 0, -108*t^10 -
324*t^8 - 432*t^6 - 324*t^4 - 108*t^2, 432*t^15 + 1944*t^13 +
2592*t^11 - 2592*t^7 - 1944*t^5 - 432*t^3 ], [ 0, 0, 0, -27*t^6 -
27*t^4 - 27*t^2, 54*t^9 + 81*t^7 - 81*t^5 - 54*t^3 ], [ 0, 0, 0,
-108*t^4 - 108*t^2 - 108, 432*t^6 + 648*t^4 - 648*t^2 - 432 ], [ 0, 0,
0, -27*t^8 - 81*t^6 - 108*t^4 - 81*t^2 - 27, 54*t^12 + 243*t^10 +
324*t^8 - 324*t^4 - 243*t^2 - 54 ], [ 0, 0, 0, -27*t^4 - 27*t^2 - 27,
54*t^6 + 81*t^4 - 81*t^2 - 54 ], [ 0, 0, 0, -108*t^6 - 108*t^4 -
108*t^2, 432*t^9 + 648*t^7 - 648*t^5 - 432*t^3 ], [ 0, 0, 0, -27*t^10
- 81*t^8 - 108*t^6 - 81*t^4 - 27*t^2, 54*t^15 + 243*t^13 + 324*t^11 -
324*t^7 - 243*t^5 - 54*t^3 ], [ 0, 0, 0, -108*t^8 - 324*t^6 - 432*t^4
- 324*t^2 - 108, 432*t^12 + 1944*t^10 + 2592*t^8 - 2592*t^4 - 1944*t^2
- 432 ], [ 0, 0, 0, -108*t^6 + 216*t^5 - 216*t^3 + 216*t - 108,
432*t^9 - 1296*t^8 + 648*t^7 + 1512*t^6 - 2592*t^5 + 2592*t^4 -
1512*t^3 - 648*t^2 + 1296*t - 432 ], [ 0, 0, 0, -108*t^6 - 216*t^5 +
216*t^3 - 216*t - 108, 432*t^9 + 1296*t^8 + 648*t^7 - 1512*t^6 -
2592*t^5 - 2592*t^4 - 1512*t^3 + 648*t^2 + 1296*t + 432 ], [ 0, 0, 0,
-108*t^6 + 108*t^4 - 108*t^2, 432*t^9 - 648*t^7 - 648*t^5 + 432*t^3 ],
[ 0, 0, 0, -108*t^10 + 324*t^8 - 432*t^6 + 324*t^4 - 108*t^2, 432*t^15
- 1944*t^13 + 2592*t^11 - 2592*t^7 + 1944*t^5 - 432*t^3 ], [ 0, 0, 0,
-108*t^4 + 108*t^2 - 108, 432*t^6 - 648*t^4 - 648*t^2 + 432 ], [ 0, 0,
0, -108*t^8 + 324*t^6 - 432*t^4 + 324*t^2 - 108, 432*t^12 - 1944*t^10
+ 2592*t^8 - 2592*t^4 + 1944*t^2 - 432 ], [ 0, 0, 0, -108*t^4 +
108*t^2 - 108, -432*t^6 + 648*t^4 + 648*t^2 - 432 ], [ 0, 0, 0,
-27*t^4 + 27*t^2 - 27, -54*t^6 + 81*t^4 + 81*t^2 - 54 ], [ 0, 0, 0,
-27*t^8 + 81*t^6 - 108*t^4 + 81*t^2 - 27, 54*t^12 - 243*t^10 + 324*t^8
- 324*t^4 + 243*t^2 - 54 ], [ 0, 0, 0, -27*t^6 + 54*t^5 - 54*t^3 +
54*t - 27, 54*t^9 - 162*t^8 + 81*t^7 + 189*t^6 - 324*t^5 + 324*t^4 -
189*t^3 - 81*t^2 + 162*t - 54 ], [ 0, 0, 0, -27*t^6 - 54*t^5 + 54*t^3
- 54*t - 27, 54*t^9 + 162*t^8 + 81*t^7 - 189*t^6 - 324*t^5 - 324*t^4 -
189*t^3 + 81*t^2 + 162*t + 54 ], [ 0, 0, 0, -27*t^6 + 27*t^4 - 27*t^2,
54*t^9 - 81*t^7 - 81*t^5 + 54*t^3 ], [ 0, 0, 0, -27*t^10 + 81*t^8 -
108*t^6 + 81*t^4 - 27*t^2, 54*t^15 - 243*t^13 + 324*t^11 - 324*t^7 +
243*t^5 - 54*t^3 ], [ 0, 0, 0, -27*t^4 + 27*t^2 - 27, 54*t^6 - 81*t^4
- 81*t^2 + 54 ], [ 0, 0, 0, -27648*t^10 + 82944*t^8 + 44928*t^6 +
5184*t^4 - 108*t^2, 1769472*t^15 + 15925248*t^13 + 7630848*t^11 -
476928*t^7 - 62208*t^5 - 432*t^3 ], [ 0, 0, 0, -6912*t^10 + 20736*t^8
+ 11232*t^6 + 1296*t^4 - 27*t^2, 221184*t^15 + 1990656*t^13 +
953856*t^11 - 59616*t^7 - 7776*t^5 - 54*t^3 ], [ 0, 0, 0, -27648*t^8 +
82944*t^6 + 44928*t^4 + 5184*t^2 - 108, 1769472*t^12 + 15925248*t^10 +
7630848*t^8 - 476928*t^4 - 62208*t^2 - 432 ], [ 0, 0, 0, -6912*t^8 +
20736*t^6 + 11232*t^4 + 1296*t^2 - 27, 221184*t^12 + 1990656*t^10 +
953856*t^8 - 59616*t^4 - 7776*t^2 - 54 ], [ 0, 0, 0, -1728*t^6 +
6048*t^4 - 108*t^2, 27648*t^9 + 228096*t^7 - 57024*t^5 - 432*t^3 ], [
0, 0, 0, -432*t^6 + 1512*t^4 - 27*t^2, 3456*t^9 + 28512*t^7 - 7128*t^5
- 54*t^3 ], [ 0, 0, 0, -1728*t^4 + 6048*t^2 - 108, 27648*t^6 +
228096*t^4 - 57024*t^2 - 432 ], [ 0, 0, 0, -432*t^4 + 1512*t^2 - 27,
3456*t^6 + 28512*t^4 - 7128*t^2 - 54 ], [ 0, 0, 0, -108*t^10 -
5184*t^8 - 84672*t^6 - 497664*t^4 - 442368*t^2, 432*t^15 + 31104*t^13
+ 881280*t^11 + 12192768*t^9 + 80953344*t^7 + 191102976*t^5 -
113246208*t^3 ], [ 0, 0, 0, -27*t^10 - 1296*t^8 - 21168*t^6 -
124416*t^4 - 110592*t^2, 54*t^15 + 3888*t^13 + 110160*t^11 +
1524096*t^9 + 10119168*t^7 + 23887872*t^5 - 14155776*t^3 ], [ 0, 0, 0,
-108*t^8 - 5184*t^6 - 84672*t^4 - 497664*t^2 - 442368, 432*t^12 +
31104*t^10 + 881280*t^8 + 12192768*t^6 + 80953344*t^4 + 191102976*t^2
- 113246208 ], [ 0, 0, 0, -108*t^8 - 5184*t^6 - 84672*t^4 - 497664*t^2
- 442368, -432*t^12 - 31104*t^10 - 881280*t^8 - 12192768*t^6 -
80953344*t^4 - 191102976*t^2 + 113246208 ], [ 0, 0, 0, -27*t^8 -
1296*t^6 - 21168*t^4 - 124416*t^2 - 110592, 54*t^12 + 3888*t^10 +
110160*t^8 + 1524096*t^6 + 10119168*t^4 + 23887872*t^2 - 14155776 ], [
0, 0, 0, -27*t^8 - 1296*t^6 - 21168*t^4 - 124416*t^2 - 110592,
-54*t^12 - 3888*t^10 - 110160*t^8 - 1524096*t^6 - 10119168*t^4 -
23887872*t^2 + 14155776 ], [ 0, 0, 0, -108*t^6 - 1728*t^4 - 1728*t^2,
432*t^9 + 10368*t^7 + 51840*t^5 - 27648*t^3 ], [ 0, 0, 0, -27*t^6 -
432*t^4 - 432*t^2, 54*t^9 + 1296*t^7 + 6480*t^5 - 3456*t^3 ], [ 0, 0,
0, -27*t^4 - 432*t^2 - 432, -54*t^6 - 1296*t^4 - 6480*t^2 + 3456 ], [
0, 0, 0, -108*t^4 - 1728*t^2 - 1728, 432*t^6 + 10368*t^4 + 51840*t^2 -
27648 ], [ 0, 0, 0, -108*t^4 - 1728*t^2 - 1728, -432*t^6 - 10368*t^4 -
51840*t^2 + 27648 ], [ 0, 0, 0, -27*t^4 - 432*t^2 - 432, 54*t^6 +
1296*t^4 + 6480*t^2 - 3456 ], [ 0, 0, 0, -108*t^8 - 2592*t^6 -
21168*t^4 - 62208*t^2 - 27648, 432*t^12 + 15552*t^10 + 220320*t^8 +
1524096*t^6 + 5059584*t^4 + 5971968*t^2 - 1769472 ], [ 0, 0, 0,
-108*t^8 - 2592*t^6 - 21168*t^4 - 62208*t^2 - 27648, -432*t^12 -
15552*t^10 - 220320*t^8 - 1524096*t^6 - 5059584*t^4 - 5971968*t^2 +
1769472 ], [ 0, 0, 0, -27*t^8 - 648*t^6 - 5292*t^4 - 15552*t^2 - 6912,
54*t^12 + 1944*t^10 + 27540*t^8 + 190512*t^6 + 632448*t^4 + 746496*t^2
- 221184 ], [ 0, 0, 0, -27*t^8 - 648*t^6 - 5292*t^4 - 15552*t^2 -
6912, -54*t^12 - 1944*t^10 - 27540*t^8 - 190512*t^6 - 632448*t^4 -
746496*t^2 + 221184 ], [ 0, 0, 0, -27*t^4 - 216*t^2 - 108, 54*t^6 +
648*t^4 + 1620*t^2 - 432 ], [ 0, 0, 0, -27*t^4 - 216*t^2 - 108,
-54*t^6 - 648*t^4 - 1620*t^2 + 432 ], [ 0, 0, 0, -108*t^4 - 864*t^2 -
432, -432*t^6 - 5184*t^4 - 12960*t^2 + 3456 ], [ 0, 0, 0, -108*t^4 -
864*t^2 - 432, 432*t^6 + 5184*t^4 + 12960*t^2 - 3456 ], [ 0, 0, 0,
-432*t^8 + 2592*t^6 - 5292*t^4 + 3888*t^2 - 432, 3456*t^12 -
31104*t^10 + 110160*t^8 - 190512*t^6 + 158112*t^4 - 46656*t^2 - 3456
], [ 0, 0, 0, -108*t^8 + 648*t^6 - 1323*t^4 + 972*t^2 - 108, 432*t^12
- 3888*t^10 + 13770*t^8 - 23814*t^6 + 19764*t^4 - 5832*t^2 - 432 ], [
0, 0, 0, -108*t^8 + 648*t^6 - 1323*t^4 + 972*t^2 - 108, -432*t^12 +
3888*t^10 - 13770*t^8 + 23814*t^6 - 19764*t^4 + 5832*t^2 + 432 ], [ 0,
0, 0, -432*t^8 + 2592*t^6 - 5292*t^4 + 3888*t^2 - 432, -3456*t^12 +
31104*t^10 - 110160*t^8 + 190512*t^6 - 158112*t^4 + 46656*t^2 + 3456
], [ 0, 0, 0, -432*t^4 + 864*t^2 - 108, -3456*t^6 + 10368*t^4 -
6480*t^2 - 432 ], [ 0, 0, 0, -432*t^4 + 864*t^2 - 108, 3456*t^6 -
10368*t^4 + 6480*t^2 + 432 ], [ 0, 0, 0, -108*t^4 + 216*t^2 - 27,
432*t^6 - 1296*t^4 + 810*t^2 + 54 ], [ 0, 0, 0, -108*t^4 + 216*t^2 -
27, -432*t^6 + 1296*t^4 - 810*t^2 - 54 ], [ 0, 0, 0, -27*t^8 + 216*t^7
- 3456*t^5 + 6480*t^4 + 3456*t^3 - 6912*t^2, 54*t^12 - 648*t^11 +
1296*t^10 + 12096*t^9 - 55728*t^8 + 5184*t^7 + 314496*t^6 - 456192*t^5
+ 165888*t^4 - 221184*t^3 ], [ 0, 0, 0, -27*t^6 - 216*t^5 + 3456*t^3 +
6480*t^2 - 3456*t - 6912, 54*t^9 + 648*t^8 + 1296*t^7 - 12096*t^6 -
55728*t^5 - 5184*t^4 + 314496*t^3 + 456192*t^2 + 165888*t + 221184 ],
[ 0, 0, 0, -108*t^8 + 5184*t^6 - 84672*t^4 + 497664*t^2 - 442368,
-432*t^12 + 31104*t^10 - 881280*t^8 + 12192768*t^6 - 80953344*t^4 +
191102976*t^2 + 113246208 ], [ 0, 0, 0, -108*t^10 + 5184*t^8 -
84672*t^6 + 497664*t^4 - 442368*t^2, 432*t^15 - 31104*t^13 +
881280*t^11 - 12192768*t^9 + 80953344*t^7 - 191102976*t^5 -
113246208*t^3 ], [ 0, 0, 0, -108*t^8 + 5184*t^6 - 84672*t^4 +
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20218601092939776*t^15 + 20376359402471424*t^14 -
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46633056240402432*t^11 - 38816436952498176*t^10 +
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22394880*t^9 + 48176640*t^8 - 89579520*t^7 + 86040576*t^6 -
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50730624*t^21 - 316540224*t^20 - 838688256*t^19 - 733404672*t^18 +
2414168064*t^17 + 12561246720*t^16 + 20149420032*t^15 +
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13741068386304*t^5 - 20744780120064*t^4 + 13298728697856*t^3 -
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7042781675520*t^11 - 3100030009344*t^10 + 17584871178240*t^9 -
7741057794048*t^8 - 12937246801920*t^7 + 11547942322176*t^6 +
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36288*t^26 + 108864*t^25 + 46656*t^24 + 155844*t^23 + 48600*t^22 +
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1302912*t^12 - 642816*t^11 + 695952*t^10 + 379296*t^9 + 193104*t^8 +
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6048*t^12 - 2592*t^11 - 6804*t^10 + 11664*t^9 - 1296*t^8 + 1296*t^7 +
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2592*t^38 - 25056*t^36 - 34992*t^35 + 41472*t^34 + 96768*t^33 +
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451008*t^27 + 290304*t^26 + 870912*t^25 + 373248*t^24 + 1246752*t^23 +
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202176*t^11 + 124416*t^10 - 96768*t^9 + 41472*t^8 + 34992*t^7 -
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+ 23814*t^24 - 27540*t^16 + 15552*t^8 - 3456 ], [ 0, 0, 0, -108*t^32 +
1944*t^24 - 5292*t^16 + 5184*t^8 - 1728, 432*t^48 + 11664*t^40 -
79056*t^32 + 190512*t^24 - 220320*t^16 + 124416*t^8 - 27648 ], [ 0, 0,
0, -27*t^16 + 432*t^8 - 432, -54*t^24 - 1620*t^16 + 5184*t^8 - 3456 ],
[ 0, 0, 0, -108*t^16 + 1728*t^8 - 1728, -432*t^24 - 12960*t^16 +
41472*t^8 - 27648 ], [ 0, 0, 0, -27*t^24 + 54*t^20 + 405*t^16 -
864*t^12 + 864*t^4 - 432, 54*t^36 - 162*t^32 + 1782*t^28 - 4914*t^24 -
324*t^20 + 13932*t^16 - 12096*t^12 - 5184*t^8 + 10368*t^4 - 3456 ], [
0, 0, 0, -108*t^24 + 216*t^20 + 1620*t^16 - 3456*t^12 + 3456*t^4 -
1728, 432*t^36 - 1296*t^32 + 14256*t^28 - 39312*t^24 - 2592*t^20 +
111456*t^16 - 96768*t^12 - 41472*t^8 + 82944*t^4 - 27648 ], [ 0, 0, 0,
-27*t^24 - 54*t^20 + 405*t^16 + 864*t^12 - 864*t^4 - 432, -54*t^36 -
162*t^32 - 1782*t^28 - 4914*t^24 + 324*t^20 + 13932*t^16 + 12096*t^12
- 5184*t^8 - 10368*t^4 - 3456 ], [ 0, 0, 0, -108*t^24 - 216*t^20 +
1620*t^16 + 3456*t^12 - 3456*t^4 - 1728, -432*t^36 - 1296*t^32 -
14256*t^28 - 39312*t^24 + 2592*t^20 + 111456*t^16 + 96768*t^12 -
41472*t^8 - 82944*t^4 - 27648 ], [ 0, 0, 0, -27*t^24 - 54*t^20 +
405*t^16 + 864*t^12 - 864*t^4 - 432, 54*t^36 + 162*t^32 + 1782*t^28 +
4914*t^24 - 324*t^20 - 13932*t^16 - 12096*t^12 + 5184*t^8 + 10368*t^4
+ 3456 ], [ 0, 0, 0, -108*t^24 + 216*t^20 + 1620*t^16 - 3456*t^12 +
3456*t^4 - 1728, -432*t^36 + 1296*t^32 - 14256*t^28 + 39312*t^24 +
2592*t^20 - 111456*t^16 + 96768*t^12 + 41472*t^8 - 82944*t^4 + 27648
], [ 0, 0, 0, -27*t^24 + 54*t^20 + 405*t^16 - 864*t^12 + 864*t^4 -
432, -54*t^36 + 162*t^32 - 1782*t^28 + 4914*t^24 + 324*t^20 -
13932*t^16 + 12096*t^12 + 5184*t^8 - 10368*t^4 + 3456 ], [ 0, 0, 0,
-108*t^24 - 216*t^20 + 1620*t^16 + 3456*t^12 - 3456*t^4 - 1728,
432*t^36 + 1296*t^32 + 14256*t^28 + 39312*t^24 - 2592*t^20 -
111456*t^16 - 96768*t^12 + 41472*t^8 + 82944*t^4 + 27648 ] ]; 
// For each subgroup X_n a model was constructed using a covering X_n -> X_m.
// The nth entry in this list is m.  
coverlist := [ 0, 1, 1, 1, 1, 1,
1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 11, 8, 8, 11, 10, 11,
11, 12, 12, 13, 13, 13, 11, 13, 9, 8, 11, 12, 11, 10, 11, 13, 11, 8,
11, 13, 11, 11, 12, 12, 11, 11, 7, 22, 22, 23, 24, 23, 24, 25, 35, 23,
23, 24, 24, 23, 23, 45, 43, 30, 26, 26, 34, 23, 29, 33, 32, 23, 28,
35, 26, 36, 36, 36, 25, 30, 30, 28, 39, 27, 30, 27, 27, 25, 39, 25,
25, 25, 25, 36, 30, 30, 39, 39, 39, 42, 45, 45, 45, 45, 50, 50, 32,
32, 36, 36, 36, 36, 36, 36, 37, 39, 29, 30, 23, 28, 25, 45, 41, 24,
29, 27, 27, 23, 43, 41, 26, 26, 24, 25, 39, 39, 31, 23, 35, 23, 45,
45, 45, 50, 45, 50, 50, 50, 32, 32, 36, 39, 39, 30, 30, 30, 39, 39,
30, 36, 51, 50, 50, 30, 51, 30, 51, 51, 56, 56, 55, 55, 87, 87, 58,
86, 87, 58, 58, 98, 58, 99, 64, 85, 96, 96, 84, 64, 75, 62, 75, 62,
78, 78, 62, 62, 85, 84, 92, 96, 61, 61, 85, 86, 102, 66, 96, 77, 75,
81, 85, 81, 95, 95, 102, 80, 85, 79, 84, 84, 86, 102, 94, 83, 78, 78,
102, 85, 83, 108, 123, 118, 116, 116, 118, 93, 89, 62, 62, 58, 58, 69,
58, 69, 73, 61, 58, 66, 64, 69, 71, 70, 65, 69, 63, 68, 89, 72, 73,
99, 87, 87, 88, 98, 72, 87, 74, 73, 60, 60, 98, 90, 90, 90, 90, 90,
90, 91, 91, 91, 91, 91, 91, 89, 93, 89, 93, 93, 89, 93, 89, 91, 97,
63, 97, 97, 92, 92, 63, 97, 97, 97, 97, 97, 96, 96, 96, 96, 65, 65,
69, 69, 69, 69, 69, 69, 70, 70, 71, 71, 75, 75, 78, 78, 79, 79, 85,
84, 86, 102, 85, 102, 85, 102, 145, 85, 86, 84, 102, 73, 73, 73, 73,
91, 118, 118, 118, 118, 58, 124, 106, 106, 112, 107, 81, 81, 124, 80,
110, 79, 79, 83, 92, 107, 77, 107, 111, 94, 97, 94, 95, 97, 95, 109,
110, 111, 112, 96, 110, 105, 105, 105, 77, 61, 61, 105, 66, 112, 110,
66, 107, 80, 109, 83, 112, 96, 118, 118, 116, 116, 142, 142, 134, 134,
141, 125, 143, 131, 143, 131, 126, 126, 145, 145, 142, 142, 141, 125,
168, 168, 168, 168, 168, 168, 168, 157, 157, 157, 157, 168, 179, 179,
55, 185, 191, 196, 191, 182, 183, 181, 187, 181, 192, 183, 195, 183,
181, 185, 187, 183, 181, 186, 191, 188, 182, 184, 187, 199, 197, 194,
194, 193, 202, 202, 202, 202, 193, 205, 199, 205, 195, 262, 197, 192,
192, 276, 185, 185, 195, 227, 211, 211, 213, 213, 212, 227, 225, 235,
225, 212, 235, 189, 189, 189, 189, 192, 192, 192, 193, 193, 193, 193,
211, 211, 211, 211, 235, 235, 235, 235, 192, 216, 207, 211, 235, 235,
224, 224, 207, 211, 207, 211, 207, 211, 216, 235, 235, 249, 250, 253,
250, 248, 248, 250, 252, 259, 261, 262, 263, 299, 299, 299, 299, 340,
340, 340, 297, 297, 297, 297, 340, 335, 335, 335, 295, 295, 295, 295,
335, 252, 252, 250, 293, 293, 293, 293, 250, 252, 250, 250, 280, 282,
252, 289, 280, 281, 289, 249, 288, 287, 287, 286, 286, 259, 259, 267,
267, 253, 253, 276, 257, 256, 256, 251, 278, 244, 244, 244, 244, 245,
245, 245, 245, 246, 246, 249, 288, 298, 329, 288, 288, 329, 331, 331,
334, 316, 316, 350, 313, 291, 313, 307, 334, 308, 349, 308, 312, 305,
312, 305, 340, 317, 281, 340, 292, 340, 292, 294, 294, 340, 323, 284,
323, 298, 296, 324, 296, 335, 325, 327, 335, 335, 335, 355, 354, 355,
354, 355, 354, 354, 355, 251, 259, 308, 308, 284, 291, 350, 291, 288,
350, 281, 316, 316, 281, 333, 333, 312, 349, 349, 312, 288, 323, 323,
324, 324, 284, 355, 354, 354, 354, 354, 355, 355, 355, 296, 317, 284,
292, 298, 294, 298, 294, 324, 291, 350, 292, 327, 296, 439, 439, 490,
490, 496, 496, 496, 496, 490, 490 ];

function make_2adic_string(E);

if HasComplexMultiplication(E) then
  outstr := "inf inf [] CM";
else

done1 := false;
curgp := 1;
// Make a list of subgroups, and all the choices for the invariants
invarlist := [];
jval := jInvariant(E);
//printf "j-invariant is %o.\n",jval;
P1 := ProjectiveSpace(Rationals(),1);
Append(~invarlist,<1,[P1![jval,1]]>);

while done1 eq false do
  // For each maximal subgroup G of curgp, test to see if the points on X_curgp
  // lift to points on X_G.
  testmore := false;
  moregps := [];
  //printf "Current group is %o.\n",curgp;
  for ind in subdatamaxsub[curgp] do
    //printf "Working on X_%o.\n",ind;
    if subdata[ind][3] eq 0 then
      if ind in genzeropoints then
        jind := Index(genzeropoints,ind);
        jfunc := jmaps[jind][2];
        num := R!Numerator(jfunc);
        denom := R!Denominator(jfunc);
        poly := num - jval*denom;
        rtlist := Roots(poly);
        p1points := [ P1![ rtlist[i][1],1] : i in [1..#rtlist]];
        if Degree(num) eq Degree(denom) then
          if LeadingCoefficient(num)/LeadingCoefficient(denom) eq jval then
            Append(~p1points, P1![1,0]);
          end if;
        end if;
        if #p1points ge 1 then
          //printf "Point on X_%o lifts to a point on X_%o!\n",curgp,ind;
          testmore := true;
          Append(~invarlist,<ind,p1points>);
          Append(~moregps,ind);
        end if;                   
      end if;
    end if;
    if subdata[ind][3] eq 1 then
      if ind in rankoneell then
        // Is the cover of this group in the invarlist?
        ind2 := Index([ invarlist[i][1] : i in [1..#invarlist]],coverlist[ind]);
        if (ind2 ne 0) then
          p1points := invarlist[ind2][2];
        else
          coverind := coverlist[ind];
          jind := Index(genzeropoints,coverind);
          jfunc := jmaps[jind][2];
          num := R!Numerator(jfunc);
          denom := R!Denominator(jfunc);
          poly := num - jval*denom;
          rtlist := Roots(poly);
          p1points := [ P1![ rtlist[i][1],1] : i in [1..#rtlist]];
          if Degree(num) eq Degree(denom) then
            if LeadingCoefficient(num)/LeadingCoefficient(denom) eq jval then
              Append(~p1points, P1![1,0]);
            end if;
          end if;
        end if;
        r1ind := Index(rankoneell,ind); 
        EE<a,b,c> := EllipticCurve(rankoneellmodels[r1ind][2]);
        ellmap := map<EE -> P1 | rankoneellmaps[r1ind][2]>;
        ptset := { Codomain(ellmap)!Eltseq(p1points[i]) : i in [1..#p1points]};
        //printf "Computing preimage of map from X%o to X%o.\n",ind,coverind;
        //printf "Point set is %o.\n",ptset;
        addinvarlist := <>;
        for p in ptset do
          preims := RationalPoints(p@@ellmap);
          //printf "The preimages of %o are %o.\n",p,preims;
          for p2 in preims do
            //printf "The image of %o is %o.\n",p2,ellmap(p2);
            if ellmap(p2) eq p then
              Append(~addinvarlist,p2);
            end if;
          end for;
        end for;
        if #addinvarlist gt 0 then
          //printf "Point on X_%o lifts to a point on X_%o!\n",curgp,ind;
          testmore := true;
          Append(~moregps,ind);
        end if;                 
      end if;       
    end if;
    if subdata[ind][3] ge 2 then
      ind2 := Index( [ genustwoorhigher[i][2] : i in [1..#genustwoorhigher]],jval);
      if (ind2 ne 0) then
        if ind eq genustwoorhigher[ind2][1] then
          //printf "Point on X_%o lifts to a point on X_%o!\n",curgp,ind;
          testmore := true; 
          Append(~moregps,ind);       
        end if;
      end if;
    end if;
  end for;
  if #moregps gt 0 then
    curgp := moregps[#moregps];
  end if;
  if testmore eq false then
    done1 := true;
    minusonegp := curgp;
  end if;
end while;
//printf "The image for the subgroup containing -I is X%o.\n",minusonegp;
finesubs := [ i : i in [1..#finesubdata] | finesubdata[i][1] eq minusonegp];
index := subdata[minusonegp][1];
level := subdata[minusonegp][2];
subname := "X" cat IntegerToString(minusonegp);
gens := genlists[minusonegp];
if (minusonegp eq 1) then
  // For technical reasons our subgroup data had 
  // the level of GL_2(Z_2) as 2.
  // We fix that now.
  level := 1;
end if;

foundtimes := 0;
for n in [1..#finesubs] do
  foundhere := false;
  // If we get here, the genus of X_minusonegp is zero.
  ind := Index([ invarlist[i][1] : i in [1..#invarlist]],minusonegp);
  tvals1 := invarlist[ind][2];
  tvals2 := [];
  infinitetval := [];
  for m in [1..#tvals1] do
    if tvals1[m][2] eq 0 then
      // Point at infinity.
      Append(~infinitetval,true);
      Append(~tvals2,0);
    else
      Append(~tvals2,Rationals()!tvals1[m][1]);
      Append(~infinitetval,false);
    end if;
  end for;
  ainvars := eqf[finesubs[n]];
  A := ainvars[4];
  B := ainvars[5];
  for m in [1..#tvals2] do
    if infinitetval[m] eq false then
      Aspec := Evaluate(A,tvals2[m]);
      Bspec := Evaluate(B,tvals2[m]);
      E2 := EllipticCurve([0,0,0,Aspec,Bspec]);
      chk := IsIsomorphic(E,E2);
      if (chk eq true) then
        foundhere := true;
      end if;
    else
      // We do this when E might be isomorphic to E_t
      // when t = (1:0).
      degA := Degree(Numerator(A));
      degB := Degree(Numerator(B));
      powt := Max(Ceiling(degA/4),Ceiling(degB/6));
      A2 := Evaluate(A,1/t)*t^(4*powt);
      B2 := Evaluate(B,1/t)*t^(6*powt);
      Aspec := Evaluate(A2,0);
      Bspec := Evaluate(B2,0);
      //printf "Curve is y^2 = x^3 + %ox + %o.\n",Aspec,Bspec;
      if (-64*Aspec^3 - 432*Bspec^2) ne 0 then
        E2 := EllipticCurve([0,0,0,Aspec,Bspec]);
        chk := IsIsomorphic(E,E2);
        if (chk eq true) then
          foundhere := true;
        end if;
      end if;
    end if;
  end for;
  if foundhere eq true then
    foundtimes := foundtimes + 1;
    subname := finesubdata[finesubs[n]][4];
    //printf "The image should be %o.\n",subname;
    index := finesubdata[finesubs[n]][2];
    level := finesubdata[finesubs[n]][3];
    gens := finegenlists[finesubs[n]];
  end if;
end for;
if foundtimes gt 1 then
  printf "Error! The elliptic curve was found multiple times!\n";
  printf "Something is haywire!\n";
  printf "The curve is %o.\n",E;
  bad := 0;
  bad2 := 1/bad;
end if;
// The index of the 2-adic image is stored in index
// The smallest 2^r so that every matrix congruent to I (mod 2^r)
// is level.
// The name of the modular curve is subname
outstr := IntegerToString(index) cat " " cat IntegerToString(level) cat " " cat gens cat " " cat subname;
// End the non-CM case
end if;
return outstr;
end function;

procedure make_2adic_file(curvefile);

// (Nicolas) Form the output file name from the input one
// Assuming the input file is called allcurves.XXX
// The output file will be called 2adic.XXX

outputfilename := "2adic" cat Substring(curvefile,Position(curvefile,"."),#curvefile);
SetColumns(0);

FP := Open(curvefile,"r");
Rewind(FP);
done := false;
while (done eq false) do
 A := Gets(FP);
 if IsEof(A) then
  done := true;
 else
  startind := Position(A,"[");
  endind := Position(A,"]");
  prefix := Substring(A,1,endind) cat " ";
  ainvars := eval Substring(A,startind,endind-startind+1);
  Eline := prefix cat make_2adic_string(EllipticCurve(ainvars));
  PrintFile(outputfilename, Eline);
//print Eline;
  // End the case when we haven't gotten to the end of the file
 end if;
// End the while loop
end while;

end procedure;

if (assigned filename) then
  printf "Processing curves in %o...", filename;
  make_2adic_file(filename);
  printf ".finished\n";
  quit;
else
  if (assigned ainvs) then
  E := EllipticCurve(eval ainvs);
  res := make_2adic_string(E);
  print res ;
  quit;
else
  printf "This magma script may be called with filename as an argument.\n";
  printf "Something like:\n";
  printf "magma -b filename:=allcurves.00000-09999 2adic.m";
  printf "which will then process all curves, writing the output file 2adic.00000-09999";
  printf "";
  printf "Otherwise run make_2adic_file(filename) to process a file, or use the function make_2adic_string(E) on a single elliptic curve.";
end if;
end if;