CoCalc
Sharedwww / Tables / slopes_2-adic.mOpen in CoCalc
/*********************************************************************
This is a MAGMA-readable table of the 2-adic slopes of the Hecke 
operator T_2 acting on Gamma_0(N).  The syntax is:
     <N,
      [
      <k, [* slopes of T_2 on S_k(Gamma_0(N)) *]
      ...
      ]>

William Stein, February 13, 2000
***********************************************************************/


oo := Infinity();

slopes_2adic :=
[*

<1,
[ 
<2, [**]>, 
<4, [* 0 *]>, 
<6, [* 0 *]>, 
<8, [* 0 *]>, 
<10, [* 0 *]>, 
<12, [* 3, 0 *]>, 
<14, [* 0 *]>, 
<16, [* 3, 0 *]>, 
<18, [* 4, 0 *]>, 
<20, [* 3, 0 *]>, 
<22, [* 5, 0 *]>, 
<24, [* 7, 3, 0 *]>, 
<26, [* 4, 0 *]>, 
<28, [* 8, 3, 0 *]>, 
<30, [* 6, 6, 0 *]>,
<32, [* 7, 3, 0 *]>,
<34, [* 8, 4, 0 *]>,
<36, [* 9, 9, 3, 0 *]>,
<38, [* 8, 5, 0 *]>,
<40, [* 11, 7, 3, 0 *]>,
<42, [* 12, 9, 4, 0 *]>,
<44, [* 11, 8, 3, 0 *]>,
<46, [* 13, 6, 6, 0 *]>,
<48, [* 15, 12, 7, 3, 0 *]>,
<50, [* 13, 8, 4, 0 *]>,
<52, [* 16, 9, 9, 3 *]>,
<54, [* 16, 11, 9, 5 *]>,
<56, [* 16, 11, 7, 3 *]>,
<58, [* 14, 12, 10, 4 *]>,
<60, [* 19, 14, 12, 8, 3 *]>,
<62, [* 14, 14, 6, 6 *]>,
<64, [* 17, 15, 13, 7, 3 *]>,
<66, [* 18, 16, 14, 8, 4 *]>,
<68, [* 17, 17, 9, 9, 3 *]>,
<70, [* 19, 17, 13, 8, 5 *]>,
<72, [* 21, 19, 17, 11, 7, 3 *]>,
<74, [* 20, 16, 12, 9, 4 *]>,
<76, [* 22, 20, 16, 11, 8, 3 *]>,
<78, [* 22, 22, 16, 13, 6, 6 *]>,
<80, [* 23, 19, 15, 12, 7, 3 *]>,
<82, [* 24, 20, 17, 13, 8, 4 *]>,
<84, [* 25, 25, 19, 16, 9, 9, 3 *]>,
<86, [* 24, 21, 16, 10, 10, 5 *]>,
<88, [* 27, 23, 20, 16, 11, 7, 3 *]>,
<90, [* 28, 25, 21, 13, 12, 11, 4 *]>,
<92, [* 27, 24, 19, 13, 13, 8, 3 *]>,
<94, [* 29, 23, 23, 14, 14, 6, 6 *]>,
<96, [* 31, 28, 24, 16, 15, 14, 7, 3 *]>,
<98, [* 29, 25, 17, 16, 15, 8, 4 *]>,
<100, [* 32, 26, 26, 17, 17, 9, 9, 3 *]>,
<102, [* 32, 29, 22, 18, 18, 14, 8, 5 *]>,
<104, [* 32, 28, 20, 19, 18, 11, 7, 3 *]>,
<106, [* 32, 29, 23, 20, 17, 12, 9, 4 *]>,
<108, [* 35, 32, 25, 21, 21, 17, 11, 8, 3 *]>,
<110, [* 32, 27, 22, 22, 17, 13, 6, 6 *]>,
<112, [* 35, 32, 26, 23, 20, 15, 12, 7, 3 *]>,
<114, [* 36, 30, 27, 24, 21, 18, 13, 8, 4 *]>,
<116, [* 35, 30, 25, 25, 20, 16, 9, 9, 3 *]>,
<118, [* 37, 30, 27, 25, 22, 16, 11, 9, 5 *]>,
<120, [* 39, 33, 30, 27, 24, 21, 16, 11, 7, 3 *]>,
<122, [* 34, 30, 28, 26, 22, 14, 12, 10, 4 *]>,
<124, [* 40, 33, 30, 28, 25, 19, 14, 12, 8, 3 *]>,
<126, [* 36, 36, 30, 30, 24, 24, 14, 14, 6, 6 *]>,
<128, [* 37, 33, 31, 29, 25, 17, 15, 13, 7, 3 *]>,
<130, [* 38, 34, 32, 30, 26, 18, 16, 14, 8, 4 *]>,
<132, [* 39, 39, 33, 33, 27, 27, 17, 17, 9, 9, 3 *]>,
<134, [* 38, 35, 33, 30, 24, 19, 17, 13, 8, 5 *]>,
<136, [* 41, 37, 35, 33, 29, 21, 19, 17, 11, 7, 3 *]>,
<138, [* 42, 39, 36, 33, 30, 25, 20, 16, 12, 9, 4 *]>,
<140, [* 41, 38, 36, 33, 27, 22, 20, 16, 11, 8, 3 *]>,
<142, [* 43, 38, 38, 33, 29, 22, 22, 16, 13, 6, 6 *]>,
<144, [* 45, 42, 39, 36, 33, 28, 23, 19, 15, 12, 7, 3 *]>,
<146, [* 43, 40, 37, 32, 29, 24, 20, 17, 13, 8, 4 *]>,
<148, [* 46, 41, 41, 36, 32, 25, 25, 19, 16, 9, 9, 3 *]>,
<150, [* 46, 42, 42, 38, 32, 29, 24, 21, 16, 10, 10, 5 *]> 
]>,



<2,[
<2, [**]>,
<4, [**]>,
<6, [**]>,
<8, [* 3 *]>,
<10, [* 4 *]>,
<12, [* 8, 3 *]>,
<14, [* 6, 6 *]>,
<16, [* 12, 7, 3 *]>,
<18, [* 13, 8, 4 *]>,
<20, [* 16, 9, 9, 3 *]>,
<22, [* 16, 10, 10, 5 *]>,
<24, [* 20, 16, 11, 7, 3 *]>,
<26, [* 21, 12, 12, 12, 4 *]>,
<28, [* 24, 19, 13, 13, 8, 3 *]>,
<30, [* 23, 23, 14, 14, 6, 6 *]>,
<32, [* 28, 24, 15, 15, 15, 7, 3 *]>,
<34, [* 29, 25, 16, 16, 16, 8, 4 *]>,
<36, [* 32, 26, 26, 17, 17, 9, 9, 3 *]>,
<38, [* 32, 29, 18, 18, 18, 18, 8, 5 *]>,
<40, [* 36, 32, 28, 19, 19, 19, 11, 7, 3 *]>,
<42, [* 37, 32, 29, 20, 20, 20, 12, 9, 4 *]>,
<44, [* 40, 35, 32, 21, 21, 21, 21, 11, 8, 3 *]>,
<46, [* 39, 39, 32, 22, 22, 22, 22, 13, 6, 6 *]>,
<48, [* 44, 40, 35, 32, 23, 23, 23, 15, 12, 7, 3 *]>,
<50, [* 45, 41, 36, 24, 24, 24, 24, 24, 13, 8, 4 *]>,
<52, [* 48, 42, 42, 35, 25, 25, 25, 25, 16, 9, 9, 3 *]>,
<54, [* 48, 44, 42, 37, 26, 26, 26, 26, 16, 11, 9, 5 *]>,
<56, [* 52, 48, 44, 39, 27, 27, 27, 27, 27, 16, 11, 7, 3 *]>,
<58, [* 53, 47, 45, 43, 28, 28, 28, 28, 28, 14, 12, 10, 4 *]>,
<60, [* 56, 51, 47, 45, 40, 29, 29, 29, 29, 19, 14, 12, 8, 3 *]>,
<62, [* 55, 55, 47, 47, 30, 30, 30, 30, 30, 30, 14, 14, 6, 6 *]>,
<64, [* 60, 56, 50, 48, 46, 31, 31, 31, 31, 31, 17, 15, 13, 7, 3 *]>,
<66, [* 61, 57, 51, 49, 47, 32, 32, 32, 32, 32, 18, 16, 14, 8, 4 *]>,
<68, [* 64, 58, 58, 50, 50, 33, 33, 33, 33, 33, 33, 17, 17, 9, 9, 3 *]>,
<70, [* 64, 61, 56, 52, 50, 34, 34, 34, 34, 34, 34, 19, 17, 13, 8, 5 *]>,
<72, [* 68, 64, 60, 54, 52, 50, 35, 35, 35, 35, 35, 21, 19, 17, 11, 7, 3 *]>,
<74, [* 69, 64, 61, 57, 53, 36, 36, 36, 36, 36, 36, 36, 20, 16, 12, 9, 4 *]>,
<76, [* 72, 67, 64, 59, 55, 53, 37, 37, 37, 37, 37, 37, 22, 20, 16, 11, 8, 3 *]>,
<78, [* 71, 71, 64, 61, 55, 55, 38, 38, 38, 38, 38, 38, 22, 22, 16, 13, 6, 6 *]>,
<80, [* 76, 72, 67, 64, 60, 56, 39, 39, 39, 39, 39, 39, 39, 23, 19, 15, 12, 7, 3 *]>,
<82, [* 77, 73, 68, 64, 61, 57, 40, 40, 40, 40, 40, 40, 40, 24, 20, 17, 13, 8, 4 *]>,
<84, [* 80, 74, 74, 67, 64, 58, 58, 41, 41, 41, 41, 41, 41, 25, 25, 19, 16, 9, 9, 3 *]>,
<86, [* 80, 75, 75, 69, 64, 61, 42, 42, 42, 42, 42, 42, 42, 42, 24, 21, 16, 10, 10, 5 *]>,
<88, [* 84, 80, 76, 71, 67, 64, 60, 43, 43, 43, 43, 43, 43, 43, 27, 23, 20, 16, 11, 7, 3 *]>,
<90, [* 85, 78, 77, 76, 68, 64, 61, 44, 44, 44, 44, 44, 44, 44, 28, 25, 21, 13, 12, 11, 4 *]>,
<92, [* 88, 83, 78, 78, 72, 67, 64, 45, 45, 45, 45, 45, 45, 45, 45, 27, 24, 19, 13, 13, 8, 3 *]>,
<94, [* 87, 87, 79, 79, 70, 70, 64, 46, 46, 46, 46, 46, 46, 46, 46, 29, 23, 23, 14, 14, 6, 6 *]>,
<96, [* 92, 88, 81, 80, 79, 71, 67, 64, 47, 47, 47, 47, 47, 47, 47, 31, 28, 24, 16, 15, 14, 7, 3 *]>,
<98, [* 93, 89, 82, 81, 80, 72, 68, 48, 48, 48, 48, 48, 48, 48, 48, 48, 29, 25, 17, 16, 15, 8, 4 *]>,
<100, [* 96, 90, 90, 82, 82, 73, 73, 67, 49, 49, 49, 49, 49, 49, 49, 49, 32, 26, 26, 17, 17, 9, 9, 3 *]> 
]>,



<3,
[ 
<2, [**]>,
<4, [**]>,
<6, [* 1 *]>,
<8, [* 1 *]>,
<10, [* 2, 1 *]>,
<12, [* 3, 3, 1 *]>,
<14, [* 4, 2, 1 *]>,
<16, [* 3, 3, 3, 1 *]>,
<18, [* 4, 4, 4, 2, 1*]>,
<20, [* 5, 4, 3, 3, 1 *]>,
<22, [* 6, 5, 5, 4, 2, 1 *]>,
<24, [* 7, 7, 6,3, 3, 3, 1 *]>,
<26, [* 8, 7, 4, 4, 4, 2, 1 *]>,
<28, [* 8, 8, 5, 5, 5, 3, 3, 1*]>,
<30, [* 9, 6, 6, 6, 6, 6, 4, 2, 1 *]>,
<32, [* 7, 7, 7, 7, 7, 3, 3, 3, 1*]>,
<34, [* 8, 8, 8, 8, 8, 4, 4, 4, 2, 1 *]>,
<36, [* 9, 9, 9, 9, 9, 7, 5, 4,3, 3, 1 *]>,
<38, [* 10, 10, 10, 8, 8, 6, 5, 5, 4, 2, 1 *]>,
<40, [* 11, 11, 11,9, 8, 7, 7, 6, 3, 3, 3, 1 *]>,
<42, [* 12, 12, 12, 10, 9, 9, 8, 7, 4, 4, 4, 2, 1*]>,
<44, [* 13, 12, 11, 11, 10, 8, 8, 5, 5, 5, 3, 3, 1 *]>,
<46, [* 14, 13, 13,12, 11, 9, 6, 6, 6, 6, 6, 4, 2, 1 *]>,
<48, [* 15, 15, 14, 12, 12, 12, 7, 7, 7,7, 7, 3, 3, 3, 1 *]>,
<50, [* 16, 15, 13, 13, 13, 8, 8, 8, 8, 8, 4, 4, 4, 2, 1*]> 
]>,


<4,[ 
<2, [**]>,
<4, [**]>,
<6, [* oo *]>,
<8, [* oo, 3 *]>,
<10, [* oo, oo, 4 *]>,
<12, [* oo, oo, 8, 3 *]>,
<14, [* oo, oo, oo, 6, 6 *]>,
<16, [* oo, oo, oo, 12, 7, 3 *]>,
<18, [* oo, oo, oo, oo, 13, 8, 4 *]>,
<20, [* oo, oo, oo, oo, 16, 9, 9, 3 *]>,
<22, [* oo, oo, oo, oo, oo, 16, 10, 10, 5 *]>,
<24, [* oo, oo, oo, oo, oo, 20, 16, 11, 7, 3 *]>,
<26, [* oo, oo, oo, oo, oo, oo, 21, 12, 12, 12, 4 *]>,
<28, [* oo, oo, oo, oo, oo, oo, 24, 19, 13, 13, 8, 3 *]>,
<30, [* oo, oo, oo, oo, oo, oo, oo, 23, 23, 14, 14, 6, 6 *]>,
<32, [* oo, oo, oo, oo, oo, oo, oo, 28, 24, 15, 15, 15, 7, 3 *]>,
<34, [* oo, oo, oo, oo, oo, oo, oo, oo, 29, 25, 16, 16, 16, 8, 4 *]>,
<36, [* oo, oo, oo, oo, oo, oo, oo, oo, 32, 26, 26, 17, 17, 9, 9, 3 *]>,
<38, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, 32, 29, 18, 18, 18, 18, 8, 5 *]>,
<40, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, 36, 32, 28, 19, 19, 19, 11, 7, 3 *]>,
<42, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 37, 32, 29, 20, 20, 20, 12, 9, 4 *]>,
<44, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 40, 35, 32, 21, 21, 21, 21, 11, 8, 3 *]>,
<46, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 39, 39, 32, 22, 22, 22, 22, 13, 6, 6 *]>,
<48, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 44, 40, 35, 32, 23, 23, 23, 15, 12, 7, 3 *]>,
<50, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 45, 41, 36, 24, 24, 24, 24, 24, 13, 8, 4 *]>,
<52, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 48, 42, 42, 35, 25, 25, 25, 25, 16, 9, 9, 3 *]>,
<54, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 48, 44, 42, 37, 26, 26, 26, 26, 16, 11, 9, 5 *]>,
<56, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 52, 48, 44, 39, 27, 27, 27, 27, 27, 16, 11, 7, 3 *]>,
<58, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 53, 47, 45, 43, 28, 28, 28, 28, 28, 14, 12, 10, 4 *]>,
<60, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 56, 51, 47, 45, 40, 29, 29, 29, 29, 19, 14, 12, 8, 3 *]>,
<62, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 55, 55, 47, 47, 30, 30, 30, 30, 30, 30, 14, 14, 6, 6 *]>,
<64, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 60, 56, 50, 48, 46, 31, 31, 31, 31, 31, 17, 15, 13, 7, 3 *]>,
<66, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 61, 57, 51, 49, 47, 32, 32, 32, 32, 32, 18, 16, 14, 8, 4 *]>,
<68, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 64, 58, 58, 50, 50, 33, 33, 33, 33, 33, 33, 17, 17, 9, 9, 3 *]>,
<70, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 64, 61, 56, 52, 50, 34, 34, 34, 34, 34, 34, 19, 17, 13, 8, 5 *]>,
<72, [* oo, oo, oo, oo, oo, oo, oo, oo,oo, oo, oo, oo, oo, oo, oo, oo, oo, 68, 64, 60, 54, 52, 50, 35, 35, 35, 35, 35, 21, 19,17, 11, 7, 3 *]>,
<74, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 69, 64, 61, 57, 53, 36, 36, 36, 36, 36, 36, 36, 20, 16, 12, 9, 4 *]>,
<76, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 72, 67, 64, 59, 55, 53, 37, 37, 37, 37, 37, 37, 22, 20, 16, 11, 8, 3 *]>,
<78, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 71, 71, 64, 61, 55, 55, 38, 38, 38, 38, 38, 38, 22, 22, 16, 13, 6, 6 *]>,
<80, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 76, 72, 67, 64, 60, 56, 39, 39, 39, 39, 39, 39, 39, 23, 19, 15, 12, 7, 3 *]>,
<82, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 77, 73, 68, 64, 61, 57, 40, 40, 40, 40, 40, 40, 40, 24, 20, 17, 13, 8, 4 *]>,
<84, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 80, 74, 74, 67, 64, 58, 58, 41, 41, 41, 41, 41, 41, 25, 25, 19, 16, 9, 9, 3 *]>,
<86, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 80, 75, 75, 69, 64, 61, 42, 42, 42, 42, 42, 42, 42, 42, 24, 21, 16, 10, 10, 5 *]>,
<88, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 84, 80, 76, 71, 67, 64, 60, 43, 43, 43, 43, 43, 43, 43, 27, 23, 20, 16, 11, 7, 3 *]>,
<90, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 85, 78, 77, 76, 68, 64, 61, 44, 44, 44, 44, 44, 44, 44, 28, 25, 21, 13, 12, 11, 4 *]>,
<92, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 88, 83, 78, 78, 72, 67, 64, 45, 45, 45, 45, 45, 45, 45, 45, 27, 24, 19, 13, 13, 8, 3 *]>,
<94, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 87, 87, 79, 79, 70, 70, 64, 46, 46, 46, 46, 46, 46, 46, 46, 29, 23, 23, 14, 14, 6, 6 *]>,
<96, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 92, 88, 81, 80, 79, 71, 67, 64, 47, 47, 47, 47, 47, 47, 47, 31, 28, 24, 16, 15, 14, 7, 3 *]>,
<98, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 93, 89, 82, 81, 80, 72, 68, 48, 48, 48, 48, 48, 48, 48, 48, 48, 29, 25, 17, 16, 15, 8, 4 *]>,
<100, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 96, 90, 90, 82, 82, 73, 73, 67, 49, 49, 49, 49, 49, 49, 49, 49, 32, 26, 26, 17, 17, 9, 9, 3 *]> 
]>,



<5, 
[ <2, [**]>,
<4, [* 2 *]>,
<6, [* 1 *]>,
<8, [* 3/2, 3/2, 1 *]>,
<10, [* 3, 2, 1 *]>,
<12, [* 3, 3, 3/2, 3/2, 1 *]>,
<14, [* 4, 2, 2, 2, 1 *]>,
<16, [* 6, 3, 3, 3, 3/2, 3/2, 1 *]>,
<18, [* 4, 4, 4, 5/2, 5/2, 2, 1 *]>,
<20, [* 5, 5, 5, 4, 3, 3, 3/2, 3/2, 1 *]>,
<22, [* 7, 6, 5, 5, 4, 2, 2, 2, 1 *]>,
<24, [* 7, 7, 6, 11/2, 11/2, 3, 3, 3, 3/2, 3/2, 1 *]>,
<26, [* 8, 7, 6, 5, 4, 4, 4, 3, 3, 2, 1 *]>,
<28, [* 10, 8, 8, 5, 5, 5, 5, 5, 3, 3, 3/2, 3/2, 1 *]>,
<30, [* 9, 6, 6, 6, 6, 6, 6, 6, 4, 2, 2, 2, 1 *]>,
<32, [* 9, 8, 7, 7, 7, 7, 7, 6, 6, 3, 3, 3, 3/2, 3/2, 1*]>,
<34, [* 9, 8, 8, 8, 8, 8, 7, 7, 4, 4, 4, 5/2, 5/2, 2, 1 *]>,
<36, [* 9, 9, 9, 9, 9, 9, 9, 7, 5, 5, 5, 4, 3, 3, 3/2, 3/2, 1 *]>,
<38, [* 10, 10, 10, 10, 10, 8, 8, 13/2, 13/2, 6, 5, 5, 4, 2, 2, 2, 1 *]>, 
<40, [* 12, 11, 11, 11, 10, 10, 9, 8, 7, 7, 6, 11/2, 11/2, 3, 3, 3, 3/2, 3/2, 1 *]>,
<42, [* 12, 12, 12, 21/2, 21/2, 10, 9, 9, 8, 7, 6, 4, 4, 4, 4, 4, 3, 2, 1 *]>,
<44, [* 13, 13, 13, 12, 11, 11, 10, 19/2, 19/2, 8, 8, 5, 5, 5, 5, 5, 3, 3, 3/2, 3/2, 1 *]>, 
<46, [* 15, 14, 13, 13, 12, 11, 11, 11, 9, 6, 6, 6, 6, 6, 6, 6, 4, 2, 2, 2, 1 *]>, 
<48, [* 15, 15, 14, 27/2, 27/2, 12, 12, 12, 9, 7, 7, 7, 7, 7, 7, 7, 6, 3, 3, 3, 3/2, 3/2, 1 *]>, 
<50, [* 16, 15, 29/2, 29/2, 13, 13, 13, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 5/2, 5/2, 2, 1 *]>
]>,



<6, [ 
<2, [**]>,
<4, [* 1 *]>,
<6, [* 4, 2, 1 *]>,
<8, [* 6, 3, 3, 3, 1 *]>,
<10, [* 8, 7, 4, 4, 4, 2, 1 *]>,
<12, [* 10, 8, 8, 5, 5, 5, 3, 3, 1*]>,
<14, [* 12, 11, 9, 6, 6, 6, 6, 6, 4, 2, 1 *]>,
<16, [* 14, 12, 12, 12, 7, 7, 7, 7, 7, 3, 3, 3, 1 *]>,
<18, [* 16, 15, 13, 13, 13, 8, 8, 8, 8, 8, 4, 4, 4, 2, 1 *]>,
<20, [* 18, 16, 16, 15, 14, 9, 9, 9, 9, 9, 9, 9, 5, 4, 3, 3, 1 *]>,
<22, [* 20, 19, 17, 16, 16, 15, 10, 10, 10,10, 10, 10, 10, 6, 5, 5, 4, 2, 1 *]>,
<24, [* 22, 20, 20, 20, 17, 16, 16, 11, 11, 11, 11, 11, 11, 11, 7, 7, 6, 3, 3, 3, 1 *]>,
<26, [* 24, 23, 21, 21, 21, 18, 17, 12, 12, 12, 12, 12, 12, 12, 12, 12, 8, 7, 4, 4, 4, 2, 1 *]>,
<28, [* 26, 24, 24, 22, 22, 22, 19, 19, 13, 13, 13, 13, 13, 13, 13, 13, 13, 8, 8, 5, 5, 5, 3, 3, 1 *]>,
<30, [* 28, 27, 25, 23, 23, 23, 23, 23, 20, 14, 14, 14, 14, 14, 14, 14, 14, 14, 9, 6, 6, 6, 6, 6, 4, 2, 1 *]>,
<32, [* 30, 28, 28, 28, 24, 24, 24, 24, 24, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 7, 7, 7, 7, 7, 3, 3, 3, 1 *]>,
<34, [* 32, 31, 29, 29, 29, 25, 25, 25, 25, 25, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 8, 8, 8, 8, 8, 4, 4, 4, 2, 1 *]>,
<36, [* 34, 32, 32, 31, 30, 28, 26, 26, 26, 26, 26, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 9, 9, 9, 9, 9, 7, 5, 4, 3, 3, 1 *]>,
<38, [* 36, 35, 33, 32, 32, 31, 29, 29, 27, 27, 27, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 10, 10, 10, 8, 8, 6, 5, 5, 4, 2, 1 *]>, 
<40, [* 38, 36, 36, 36, 33, 32, 32, 31, 30, 28, 28, 28, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 11, 11, 11, 9, 8, 7, 7, 6, 3, 3, 3, 1 *]>, 
<42, [* 40, 39, 37, 37, 37, 34, 33, 32, 32, 31, 29, 29, 29, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 12, 12, 12, 10, 9, 9, 8, 7, 4, 4, 4, 2, 1 *]>,<44, [* 42, 40, 40, 38, 38, 38, 35, 35, 33, 32, 32, 31, 30, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 13, 12, 11, 11, 10, 8, 8, 5, 5, 5, 3, 3, 1 *]>, 
<46, [* 44, 43, 41, 39, 39, 39, 39, 39, 36, 34, 33, 32, 32, 31, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 14, 13, 13, 12, 11, 9, 6, 6, 6, 6, 6, 4, 2, 1 *]>, 
<48, [* 46, 44, 44, 44, 40, 40, 40, 40, 40, 35, 35, 35, 33, 32, 32, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 15, 15, 14, 12, 12, 12, 7, 7, 7, 7, 7, 3, 3, 3, 1 *]>, 
<50, [* 48, 47, 45, 45, 45, 41, 41, 41, 41, 41, 36, 36, 36, 34, 33, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 16, 15, 13, 13, 13, 8, 8, 8, 8, 8, 4, 4, 4, 2, 1 *]> 
]>,

<7,[ 
<2, [**]>,
<4, [* 0 *]>,
<6, [* 1, 1, 0 *]>,
<8, [* 1, 1, 0 *]>,
<10, [* 2, 2, 1, 1, 0 *]>,
<12, [* 3, 3, 3, 3, 1, 1, 0 *]>,
<14, [* 4, 4, 2, 2, 1, 1, 0 *]>,
<16, [* 3, 3, 3, 3, 3, 3, 1, 1, 0 *]>,
<18, [* 4, 4, 4, 4, 4, 4, 2, 2, 1, 1, 0 *]>,
<20, [* 5, 5, 4, 4, 3, 3, 3, 3, 1, 1, 0 *]>,
<22, [* 6, 6, 5, 5, 5, 5, 4, 4, 2, 2, 1, 1, 0 *]>,
<24, [* 7, 7, 7, 7, 6, 6, 3, 3, 3, 3, 3, 3, 1, 1, 0 *]>,
<26, [* 8, 8, 7, 7, 4, 4, 4, 4, 4, 4, 2, 2, 1, 1, 0 *]>,
<28, [* 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 1, 1, 0 *]>,
<30, [* 9, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 2, 2, 1, 1, 0 *]>,
<32, [* 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 3, 3, 3, 3, 3, 1, 1, 0 *]>,
<34, [* 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 2, 2, 1, 1, 0 *]>,
<36, [* 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 7, 5, 5, 4, 4, 3, 3, 3, 3, 1, 1, 0 *]>,
<38, [* 10, 10, 10, 10, 10, 10, 8, 8, 8, 8, 6, 6, 5, 5, 5, 5, 4, 4, 2, 2, 1, 1, 0 *]>,
<40, [* 11, 11, 11, 11, 11, 11, 9, 9, 8, 8, 7, 7, 7, 7, 6, 6, 3, 3, 3, 3, 3, 3, 1, 1, 0 *]>,
<42, [* 12, 12, 12, 12, 12, 12, 10, 10, 9, 9, 9, 9, 8, 8, 7, 7, 4, 4, 4, 4, 4, 4, 2, 2, 1, 1, 0 *]>,
<44, [* 13, 13, 12, 12, 11, 11, 11, 11, 10, 10, 8, 8, 8, 8, 5, 5, 5, 5, 5, 5, 3, 3, 3, 3, 1, 1, 0 *]>,
<46, [* 14, 14, 13, 13, 13, 13, 12, 12, 11, 11, 9, 9, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 2, 2, 1, 1, 0 *]>,
<48, [* 15, 15, 15, 15, 14, 14, 12, 12, 12, 12, 12, 12, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 3, 3, 3, 3, 3, 3, 1, 1, 0 *]>,
<50, [* 16, 16, 15, 15, 13, 13, 13, 13, 13, 13, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 2, 2, 1, 1, 0 *]> 
]>, 



<8,[ 
<2, [* *]>,
<4, [* oo *]>,
<6, [* oo, oo, oo *]>,
<8, [* oo, oo, oo, oo, 3 *]>,
<10, [* oo, oo, oo, oo, oo, oo, 4 *]>,
<12, [* oo, oo, oo, oo, oo, oo, oo, 8, 3 *]>,
<14, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, 6, 6 *]>,
<16, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 12, 7, 3 *]>,
<18, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 13, 8, 4 *]>,
<20, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 16, 9, 9, 3 *]>,
<22, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 16, 10, 10, 5 *]>,
<24, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 20, 16, 11, 7, 3 *]>,
<26, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 21, 12, 12, 12, 4 *]>,
<28, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 24, 19, 13, 13, 8, 3 *]>,
<30, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 23, 23, 14, 14, 6, 6 *]>,
<32, [* oo, oo, oo, oo, oo, oo, 
oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 28, 24, 15, 15, 15, 7, 3 *]>,
<34, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 29, 25, 16, 16, 16, 8, 4 *]>,
<36, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 32, 26, 26, 17, 17, 9, 9, 3 *]>,
<38, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 32, 29, 18, 18, 18, 18, 8, 5 *]>,
<40, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 36, 32, 28, 19, 19, 19, 11, 7, 3 *]>, 
<42, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 37, 32, 29, 20, 20, 20, 12, 9, 4 *]>,
<44, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 40, 35, 32, 21, 21, 21, 21, 11, 8, 3 *]>,
<46, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 39, 39, 32, 22, 22, 22, 22, 13, 6, 6 *]>,
<48, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 44, 40, 35, 32, 23, 23, 23, 15, 12, 7, 3 *]>,
<50, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 45, 41, 36, 24, 24, 24, 24, 24, 13, 8, 4 *]>
]>,

<16,
[
<2, [**]>,
<4, [* oo, oo, oo *]>,
<6, [* oo, oo, oo, oo, oo, oo, oo *]>,
<8, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 3 *]>,
<10, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo,  4 *]>,
<12, [* oo, oo, oo, oo, oo, oo,  oo, oo, oo, oo, oo, oo, oo, oo,  oo, oo, oo, 8, 3 *]>,
<14, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 6, 6 *]>,
<16, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 12, 7, 3 *]>,
<18, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 13, 8, 4 *]>,
<20, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 16, 9, 9, 3 *]>,
<22, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 16, 10, 10, 5 *]>,
<24, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 20, 16, 11, 7, 3 *]>,
<26, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 21, 12, 12, 12, 4 *]>,
<28, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 24, 19, 13, 13, 8, 3 *]>,
<30, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 23, 23, 14, 14, 6, 6
*]>,
<32, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 28, 24, 15, 15, 15, 7, 3 *]>,
<34, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 29, 25, 16, 16, 16, 8, 4 *]>,
<36, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 32, 26, 26, 17, 17, 9, 9, 3 *]>,
<38, [* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 32, 29, 18, 18, 18, 18, 8, 5 *]>,
<40, 
[* oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, 36, 32, 28, 19, 19, 19, 11, 7, 3 *]> 
]>

*];