The format for the *.txt files containing contradictions using the 27 known representations of motivic weight <=24 (whose dimension is <=10) and Inequality (2.3.7) is

U:l:c:mask:t

U=[a,b,w_1,...,w_r] denotes the element a 1+ b \varepsilon_{C/R} + I_{w_1}+...+I_{w_r} of K_\infty (see \S 2.1),
l is the parameter of the Odlyzko function F_l (see \S 2.4.3),
mask is an integer in [1,2^26] whose binary decomposition defines the subset S'=vecextract(S,mask) of the known set S recalled below,
t=(t_1,t_2,...,t_s) is a vector of length s=|S'|+1, 
c is the quantity \beta_Q^{F_l}(t,t)/\hat{F_l}(i/4pi) (always <0, in order to reach the contradiction), where Q is the quadruple (s,(U_i),(d_i),(m_i)), with (U_i,d_i,m_i)=(S'[i][1],1,S'[i][2]) for 1 <= i <s, and (U_s,d_s,m_s)=(U,1,1) (see \S 2.4.2 for \beta_Q^F)

The list of 27 known representations of motivic weight <=24 is represented as the following length 26 vector S of [V,m], with V in K_\infty and m the number of \pi with L((\pi)_\infty)=V:
[[[1, 0], 1], [[0, 0, 11], 1], [[0, 0, 15], 1], [[0, 0, 17], 1], [[0, 0, 19], 1], [[0, 0, 21], 1], [[0, 1, 22], 1], [[0, 0, 23], 2], [[0, 0, 7, 19], 1], [[0, 0, 5, 21], 1], [[0, 0, 9, 21], 1], [[0, 0, 13, 21], 1], [[0, 0, 7, 23], 1], [[0, 0, 9, 23], 1], [[0, 0, 13, 23], 1], [[0, 0, 5, 13, 23], 1], [[0, 0, 3, 15, 23], 1], [[0, 0, 7, 15, 23], 1], [[0, 0, 5, 17, 23], 1], [[0, 0, 9, 17, 23], 1], [[0, 0, 3, 19, 23], 1], [[0, 0, 11, 19, 23], 1], [[0, 0, 3, 11, 17, 21, 23], 1], [[0, 1, 8, 16, 24], 1], [[0, 0, 4, 10, 18, 24], 1], [[0, 0, 2, 14, 20, 24], 1]]
example of masks: the mask 35=1+2+2^5 corresponds to S'=vecextract(S,35)=[[[1, 0], 1], [[0, 0, 11], 1], [[0, 0, 21], 1]].


Whenever U:*:*:*:* appears in these files, Proposition 2.2 of the paper asserts that there is no level 1 selfdual cuspidal automorphic representation pi of GL_n over Q, with n=dim U and L(pi_\infty)=U. Certain subsets of these lists are used (together with contradictions obtained with the basic inequality) to compute the masses for SO_m with m=16,17, and Sp_{2n} with 2n=14, 16 : see \S 3.3 of the paper.