8 Appendix: The classical Adams spectral sequence in the range \(122 \le t-s \le 127, s \le 25\)
We provide a brief overview of Lin’s computer program for computing Adams differentials and extensions. The program’s functionality for propagating differentials and extensions relies on the following data:
The Adams \(E_2\)-pages of a collection of CW spectra.
Maps between these \(E_2\)-pages.
Adams \(d_2\)-differentials for certain CW spectra.
There are three manually added differentials: \(d_5 h_0^{24}h_6=h_0^2P^6d_0\) and
\(d_6 h_0^{55}h_7=h_0^2x_{126,60}\) in the Adams spectral sequence of \(S^0\) (from the image of \(J\)), and \(d_3 v_2^{16}=\beta ^5g\) in the Adams spectral sequence of \(\mathit{tmf}\), derived from power operations (Bruner–Rognes [ ).
Detailed descriptions of these data are available in [ . Lin’s program extends these results by computing additional Adams differentials using tools such as the Leibniz rule, naturality, the Generalized Leibniz Rule, and the Generalized Mahowald Trick. All computed differentials and extensions are accessible via interactive plots [ .
Moreover, the proofs provided in [ offer more information than the interactive plots. These proofs include numerous disproofs of potential differentials, even for cases where the differentials remain unresolved. For example, consider
The spectral sequence plot for \(S^0\) shows that \(x_{126,21}\) survives to the \(E_4\)-page, but the value of \(d_4(x_{126,21})\) undetermined. By analyzing the proofs in [ , we observe that many potential values for \(d_4(x_{126,21})\) have been ruled out. Consequently, we conclude:
Tables 2–12 present results from Lin’s program for the classical Adams spectral sequence of the sphere in the range \(122 \le t-s \le 127, s \le 25\).
|
\(s\) |
Elements |
\(d_r\) |
value |
|
25 |
\(e_0g^3\Delta h_1g\) |
\(d_{2}^{-1}\) |
\(g^2\Delta ^2m\) |
|
\(d_0^3g[B_4]\) |
\(d_{4}\) |
\(d_0^4x_{65,13}\) |
|
|
24 |
\(d_0g\Delta ^2g^2\) |
\(d_{2}\) |
\(d_0e_0g^3\Delta h_2^2\) |
|
23 |
\(Ph_1x_{113,18,2}\) |
\(d_{3}^{-1}\) |
\(x_{123,20}\) |
|
\(h_0^2d_0x_{108,17}\) |
\(d_{3}\) |
\(d_0^4Mg\) |
|
|
22 |
\(e_0g^2Mg\) |
\(d_{3}^{-1}\) |
\(h_0^2h_3x_{116,16}\) |
|
\(x_{122,22}\) |
\(d_{3}\) |
\(h_0^2d_0x_{107,19}\) |
|
|
\(h_0d_0x_{108,17}\) |
\(d_{2}\) |
\(h_0^2d_0x_{107,18}\) |
|
|
21 |
\(h_0^2d_0e_0x_{91,11}\) |
Permanent |
|
|
\(d_0x_{108,17}\) |
\(d_{2}\) |
\(d_0e_0\Delta h_2^2[B_4]+h_0d_0x_{107,18}\) |
|
|
20 |
\(h_0^4x_{122,16}\) |
\(d_{2}^{-1}\) |
\(h_0h_3x_{116,16}\) |
|
\(g^3(C_0+h_0^6h_5^2)\) |
\(d_{3}\) |
\(g^3\Delta h_2^2n\) |
|
|
\(h_0d_0e_0x_{91,11}\) |
\(d_{2}\) |
\(h_0^6x_{121,16}\) |
|
|
19 |
\(h_0^3x_{122,16}\) |
\(d_{2}^{-1}\) |
\(h_3x_{116,16}\) |
|
\(d_0e_0x_{91,11}\) |
\(d_{2}\) |
\(h_0d_0^2x_{93,12}\) |
|
|
18 |
\(h_0^2x_{122,16}\) |
\(d_{3}^{-1}\) |
\(h_0^2x_{123,13,2}\) |
|
\(h_1x_{121,17}\) |
\(d_{7}^{-1}\) |
\(x_{123,11,2}+x_{123,11}+h_0h_6[B_4]\) |
|
|
\(d_0x_{108,14}\) |
\(d_{3}\) |
\(h_0d_0^2x_{93,12}+h_0^5x_{121,16}\) |
|
|
17 |
\(h_0x_{122,16}\) |
\(d_{3}^{-1}\) |
\(h_0x_{123,13,2}\) |
|
\(g^3[H_1]\) |
\(d_{3}^{-1}\) |
\(\Delta h_2^2x_{93,8}\) |
|
|
16 |
\(x_{122,16}+h_0x_{122,15,2}\) |
\(d_{3}^{-1}\) |
\(x_{123,13,2}\) |
|
\(\Delta h_2^2x_{92,10}\) |
\(d_{3}^{-1}\) |
\(x_{123,13}\) |
|
|
\(h_0x_{122,15,2}\) |
Permanent |
||
|
15 |
\(x_{122,15}\) |
\(d_{3}\) |
\(g^3A\) |
|
\(x_{122,15,2}\) |
\(d_{2}\) |
\(h_0^2h_4x_{106,14}\) |
|
|
14 |
\(h_0x_{122,13}\) |
\(d_{3}^{-1}\) |
\(x_{123,11,2}\) |
|
13 |
\(h_0^2h_6Md_0\) |
\(d_{2}^{-1}\) |
\(x_{123,11}\) |
|
\(h_1^2x_{120,11}\) |
Permanent |
||
|
\(x_{122,13}\) |
\(d_{3}\) |
\(h_0h_4x_{106,14}\) |
|
|
12 |
\(h_0h_6Md_0\) |
\(d_{2}^{-1}\) |
\(x_{123,10}\) |
|
\(h_0x_{122,11}\) |
\(d_{3}^{-1}\) |
\(h_0x_{123,8}\) |
|
|
\(h_5x_{91,11}\) |
Permanent |
||
|
11 |
\(x_{122,11}+h_6Md_0\) |
\(d_{3}^{-1}\) |
\(x_{123,8}\) |
|
\(h_6Md_0\) |
Permanent |
||
|
9-10 |
|||
|
8 |
\(h_1x_{121,7}\) |
\(d_{6}\) |
\(?\) |
|
0-7 |
|||
|
\(s\) |
Elements |
\(d_r\) |
value |
|
25 |
|||
|
24 |
\(h_1Ph_1x_{113,18,2}\) |
\(d_{2}^{-1}\) |
\(x_{124,22}\) |
|
\(d_0^2\Delta h_2^2Mg\) |
\(d_{2}^{-1}\) |
\(d_0x_{110,18}\) |
|
|
\(d_0M\! Px_{56,10}\) |
\(d_{4}\) |
\(M\! Px_{69,18}\) |
|
|
23 |
\(g^2\Delta ^2m\) |
\(d_{2}\) |
\(e_0g^3\Delta h_1g\) |
|
21-22 |
|||
|
20 |
\(x_{123,20}\) |
\(d_{3}\) |
\(Ph_1x_{113,18,2}\) |
|
19 |
\(e_0g^2x_{66,7}+h_0^6x_{123,13,2}\) |
\(d_{2}^{-1}\) |
\(x_{124,17}\) |
|
\(h_0^6x_{123,13,2}\) |
\(d_{2}^{-1}\) |
\(h_0^3x_{124,14,2}\) |
|
|
\(h_0e_0x_{106,14}+h_0^2h_3x_{116,16}\) |
\(d_{3}^{-1}\) |
\(e_0x_{107,12}\) |
|
|
\(h_0^2h_3x_{116,16}\) |
\(d_{3}\) |
\(e_0g^2Mg\) |
|
|
18 |
\(h_0^5x_{123,13,2}\) |
\(d_{2}^{-1}\) |
\(h_0^2x_{124,14,2}\) |
|
\(e_0x_{106,14}+h_0h_3x_{116,16}\) |
Permanent |
||
|
\(h_0h_3x_{116,16}\) |
\(d_{2}\) |
\(h_0^4x_{122,16}\) |
|
|
17 |
\(h_0^2x_{123,15}+h_0^4x_{123,13,2}\) |
\(d_{2}^{-1}\) |
\(h_0x_{124,14}\) |
|
\(h_0^4x_{123,13,2}\) |
\(d_{2}^{-1}\) |
\(h_0x_{124,14,2}+h_0x_{124,14}\) |
|
|
\(d_0x_{109,13}\) |
Permanent |
||
|
\(h_3x_{116,16}\) |
\(d_{2}\) |
\(h_0^3x_{122,16}\) |
|
|
16 |
\(h_0x_{123,15}+h_0^3x_{123,13,2}\) |
\(d_{2}^{-1}\) |
\(x_{124,14}\) |
|
\(h_0^3x_{123,13,2}\) |
\(d_{2}^{-1}\) |
\(x_{124,14,2}+x_{124,14}\) |
|
|
\(h_1x_{122,15,2}\) |
\(d_{3}^{-1}\) |
\(h_4x_{109,12}\) |
|
|
15 |
\(x_{123,15}\) |
\(d_{4}^{-1}\) |
\(x_{124,11,2}+x_{124,11}\) |
|
\(h_4x_{108,14}\) |
\(d_{5}^{-1}\) |
\(h_0x_{124,9}\) |
|
|
\(h_0^2x_{123,13,2}\) |
\(d_{3}\) |
\(h_0^2x_{122,16}\) |
|
|
14 |
\(h_0^3x_{123,11}\) |
\(d_{2}^{-1}\) |
\(h_0x_{124,11}\) |
|
\(h_0x_{123,13,2}\) |
\(d_{3}\) |
\(h_0x_{122,16}\) |
|
|
\(\Delta h_2^2x_{93,8}\) |
\(d_{3}\) |
\(g^3[H_1]\) |
|
|
13 |
\(h_0^2x_{123,11}\) |
\(d_{2}^{-1}\) |
\(x_{124,11}\) |
|
\(x_{123,13,2}\) |
\(d_{3}\) |
\(x_{122,16}+h_0x_{122,15,2}\) |
|
|
\(x_{123,13}\) |
\(d_{3}\) |
\(\Delta h_2^2x_{92,10}\) |
|
|
12 |
\(h_0x_{123,11}+h_0^2h_6[B_4]\) |
\(d_{3}^{-1}\) |
\(x_{124,9,2}+h_0x_{124,8}\) |
|
\(x_{123,12}\) |
\(d_{3}^{-1}\) |
\(x_{124,9}+h_0x_{124,8}\) |
|
|
\(h_0^2h_6[B_4]\) |
\(d_{5}^{-1}\) |
\(h_6A\) |
|
|
11 |
\(h_0^2x_{123,9}\) |
\(d_{2}^{-1}\) |
\(x_{124,9}\) |
|
\(h_5x_{92,10}\) |
\(d_{5}^{-1}\) |
\(x_{124,6}\) |
|
|
\(x_{123,11,2}+x_{123,11}+h_0h_6[B_4]\) |
\(d_{7}\) |
\(h_1x_{121,17}\) |
|
|
\(x_{123,11}+h_0h_6[B_4]\) |
\(d_{3}\) |
\(h_0x_{122,13}\) |
|
|
\(h_0h_6[B_4]\) |
\(d_{2}\) |
\(h_0^2h_6Md_0\) |
|
|
10 |
\(h_0x_{123,9}\) |
\(d_{2}^{-1}\) |
\(x_{124,8}\) |
|
\(x_{123,10}+h_6[B_4]\) |
\(d_{3}^{-1}\) |
\(x_{124,7}\) |
|
|
\(h_6[B_4]\) |
\(d_{2}\) |
\(h_0h_6Md_0\) |
|
|
9 |
\(x_{123,9}+h_0x_{123,8}\) |
\(d_{12}\) |
\(?\) |
|
\(h_0x_{123,8}\) |
\(d_{3}\) |
\(h_0x_{122,11}+h_0h_6Md_0\) |
|
|
8 |
\(x_{123,8}\) |
\(d_{3}\) |
\(x_{122,11}+h_6Md_0\) |
|
0-7 |
|||
|
\(s\) |
Elements |
\(d_r\) |
value |
|
25 |
\(h_0^{11}x_{124,14,2}\) |
\(d_{2}^{-1}\) |
\(h_0^9x_{125,14}\) |
|
\(ix_{101,18}\) |
\(d_{2}\) |
\(d_0^2\Delta h_2^2x_{65,13}+h_0Pd_0x_{101,18}\) |
|
|
\(d_0e_0\Delta ^3h_1g\) |
\(d_{2}\) |
\(d_0^2g^3m\) |
|
|
24 |
\(h_0^{10}x_{124,14,2}\) |
\(d_{2}^{-1}\) |
\(h_0^8x_{125,14}\) |
|
\(h_0^2d_0x_{110,18}\) |
\(d_{2}^{-1}\) |
\(h_0e_0x_{108,17}\) |
|
|
23 |
\(h_0^9x_{124,14,2}\) |
\(d_{2}^{-1}\) |
\(h_0^7x_{125,14}\) |
|
\(d_0g\Delta h_2^2[B_4]+h_0d_0x_{110,18}\) |
\(d_{2}^{-1}\) |
\(e_0x_{108,17}\) |
|
|
\(h_0d_0x_{110,18}\) |
\(d_{3}^{-1}\) |
\(x_{125,20}\) |
|
|
\(d_0x_{110,19}\) |
Permanent |
||
|
22 |
\(h_0^8x_{124,14,2}\) |
\(d_{2}^{-1}\) |
\(h_0^6x_{125,14}\) |
|
\(g^2\Delta ^2t\) |
\(d_{3}^{-1}\) |
\(gx_{105,15}\) |
|
|
\(x_{124,22}\) |
\(d_{2}\) |
\(h_1Ph_1x_{113,18,2}\) |
|
|
\(d_0x_{110,18}\) |
\(d_{2}\) |
\(d_0^2\Delta h_2^2Mg\) |
|
|
21 |
\(h_0^7x_{124,14,2}\) |
\(d_{2}^{-1}\) |
\(h_0^5x_{125,14}\) |
|
\(h_0d_0^2[\Delta \Delta _1g]\) |
\(d_{2}^{-1}\) |
\(d_0gx_{91,11}\) |
|
|
20 |
\(h_0^6x_{124,14,2}\) |
\(d_{2}^{-1}\) |
\(h_0^4x_{125,14}\) |
|
\(d_0^2[\Delta \Delta _1g]\) |
\(d_{5}^{-1}\) |
\(h_1x_{124,14}\) |
|
|
19 |
\(h_0^5x_{124,14,2}\) |
\(d_{2}^{-1}\) |
\(h_0^3x_{125,14}\) |
|
\(d_0x_{110,15}\) |
Permanent |
||
|
18 |
\(h_0x_{124,17}+h_0^4x_{124,14,2}\) |
\(d_{2}^{-1}\) |
\(x_{125,16}\) |
|
\(h_0^4x_{124,14,2}\) |
\(d_{2}^{-1}\) |
\(h_0^2x_{125,14}\) |
|
|
17 |
\(h_0^3x_{124,14}\) |
\(d_{2}^{-1}\) |
\(x_{125,15}\) |
|
\(h_0^2x_{124,15}\) |
\(d_{2}^{-1}\) |
\(h_0x_{125,14}\) |
|
|
\(x_{124,17}\) |
\(d_{2}\) |
\(e_0g^2x_{66,7}+h_0^6x_{123,13,2}\) |
|
|
\(h_0^3x_{124,14,2}\) |
\(d_{2}\) |
\(h_0^6x_{123,13,2}\) |
|
|
16 |
\(h_0x_{124,15}\) |
\(d_{2}^{-1}\) |
\(x_{125,14}\) |
|
\(h_1x_{123,15}\) |
\(d_{3}^{-1}\) |
\(h_3x_{118,12}\) |
|
|
\(h_0^2x_{124,14}\) |
Permanent |
||
|
\(e_0x_{107,12}\) |
\(d_{3}\) |
\(e_0g^2x_{66,7}+h_0e_0x_{106,14}+h_0^2h_3x_{116,16}\) |
|
|
\(h_0^2x_{124,14,2}\) |
\(d_{2}\) |
\(h_0^5x_{123,13,2}\) |
|
|
15 |
\(x_{124,15}\) |
\(d_{4}^{-1}\) |
\(h_6x_{62,10}\) |
|
\(h_3^2x_{110,13}+h_0x_{124,14}\) |
Permanent |
||
|
\(h_0x_{124,14}\) |
\(d_{2}\) |
\(h_0^2x_{123,15}+h_0^4x_{123,13,2}\) |
|
|
\(h_0x_{124,14,2}\) |
\(d_{2}\) |
\(h_0^2x_{123,15}\) |
|
|
14 |
\(h_1x_{123,13}\) |
\(d_{2}^{-1}\) |
\(x_{125,12}\) |
|
\(h_1x_{123,13,2}\) |
\(d_{2}^{-1}\) |
\(x_{125,12,2}\) |
|
|
\(\Delta h_2^2x_{94,8}\) |
Permanent |
||
|
\(x_{124,14}\) |
\(d_{2}\) |
\(h_0x_{123,15}+h_0^3x_{123,13,2}\) |
|
|
\(x_{124,14,2}\) |
\(d_{2}\) |
\(h_0x_{123,15}\) |
|
|
13 |
\(h_0^5x_{124,8}\) |
\(d_{2}^{-1}\) |
\(h_0^3x_{125,8}\) |
|
\([H_1](\Delta e_1+C_0+h_0^6h_5^2)\) |
\(d_{3}^{-1}\) |
\(x_{125,10,2}\) |
|
|
\(e_0\Delta h_6g\) |
Permanent |
||
|
\(h_4x_{109,12}\) |
\(d_{3}\) |
\(h_1x_{122,15,2}\) |
|
12 |
\(h_0x_{124,11,2}+h_0x_{124,11}\) |
\(d_{2}^{-1}\) |
\(x_{125,10}\) |
|
\(h_0^2x_{124,10,2}+h_0^4x_{124,8}\) |
\(d_{2}^{-1}\) |
\(h_0x_{125,9,2}\) |
|
|
\(h_0^4x_{124,8}\) |
\(d_{2}^{-1}\) |
\(h_0^2x_{125,8}\) |
|
|
\(h_1x_{123,11,2}\) |
\(d_{3}^{-1}\) |
\(x_{125,9}\) |
|
|
\(h_0x_{124,11}\) |
\(d_{2}\) |
\(h_0^3x_{123,11}\) |
|
|
11 |
\(h_0x_{124,10,2}+h_0^3x_{124,8}\) |
\(d_{2}^{-1}\) |
\(x_{125,9,2}\) |
|
\(h_0^3x_{124,8}\) |
\(d_{2}^{-1}\) |
\(h_0x_{125,8}\) |
|
|
\(x_{124,11,3}\) |
\(d_{3}^{-1}\) |
\(x_{125,8,2}\) |
|
|
\(x_{124,11,2}+x_{124,11}\) |
\(d_{4}\) |
\(x_{123,15}\) |
|
|
\(x_{124,11}\) |
\(d_{2}\) |
\(h_0^2x_{123,11}\) |
|
|
10 |
\(h_1x_{123,9}+h_0^2x_{124,8}\) |
\(d_{2}^{-1}\) |
\(x_{125,8}\) |
|
\(x_{124,10,2}+h_0x_{124,9}\) |
\(d_{4}^{-1}\) |
\(h_6[H_1]\) |
|
|
\(x_{124,10}+h_0^2x_{124,8}\) |
\(d_{4}^{-1}\) |
\(h_6[H_1]+h_0x_{125,5}\) |
|
|
\(h_0^2x_{124,8}\) |
Permanent |
||
|
\(h_0x_{124,9}\) |
\(d_{5}\) |
\(h_4x_{108,14}\) |
|
|
9 |
\(x_{124,9,2}+h_0x_{124,8}\) |
\(d_{3}\) |
\(h_0x_{123,11}+h_0^2h_6[B_4]\) |
|
\(x_{124,9}+h_0x_{124,8}\) |
\(d_{3}\) |
\(x_{123,12}\) |
|
|
\(h_0x_{124,8}\) |
\(d_{2}\) |
\(h_0^2x_{123,9}\) |
|
|
8 |
\(x_{124,8}\) |
\(d_{2}\) |
\(h_0x_{123,9}\) |
|
7 |
\(h_0x_{124,6}\) |
\(d_{2}^{-1}\) |
\(x_{125,5}\) |
|
\(h_6A\) |
\(d_{5}\) |
\(h_0^2h_6[B_4]\) |
|
|
\(x_{124,7}\) |
\(d_{3}\) |
\(x_{123,10}+h_6[B_4]\) |
|
|
6 |
\(x_{124,6}\) |
\(d_{5}\) |
\(h_5x_{92,10}\) |
|
0-5 |
|||
|
\(s\) |
Elements |
\(d_r\) |
value |
|
25 |
\(d_0^2e_0g[B_4]\) |
\(d_{4}^{-1}\) |
\(h_1x_{125,20}\) |
|
\(x_{125,25,2}+x_{125,25}+g^4\Delta h_1g\) |
\(d_{4}^{-1}\) |
\(x_{126,21}+\text{possibly }h_1x_{125,20}\) |
|
|
\(g^4\Delta h_1g\) |
Permanent |
||
|
\(x_{125,25}\) |
\(d_{2}\) |
\(h_0x_{124,26}\) |
|
|
24 |
\(e_0g\Delta ^2g^2\) |
\(d_{2}\) |
\(d_0g^4\Delta h_2^2\) |
|
23 |
\(h_0^2e_0x_{108,17}\) |
\(d_{3}\) |
\(d_0^3e_0Mg\) |
|
\(h_0^9x_{125,14}\) |
\(d_{2}\) |
\(h_0^{11}x_{124,14,2}\) |
|
|
22 |
\(g^3Mg\) |
\(d_{4}^{-1}\) |
\(x_{126,18}\) |
|
\(ix_{102,15}+h_0^8x_{125,14}\) |
\(d_{4}^{-1}\) |
\(gx_{106,14}+e_0x_{109,14,2}\) |
|
|
\(h_0^8x_{125,14}\) |
\(d_{2}\) |
\(h_0^{10}x_{124,14,2}\) |
|
|
\(h_0e_0x_{108,17}\) |
\(d_{2}\) |
\(h_0^2d_0x_{110,18}\) |
|
|
21 |
\(x_{125,21}\) |
\(d_{4}^{-1}\) |
\(d_0x_{112,13}\) |
|
\(h_0^7x_{125,14}\) |
\(d_{2}\) |
\(h_0^9x_{124,14,2}\) |
|
|
\(e_0x_{108,17}\) |
\(d_{2}\) |
\(d_0g\Delta h_2^2[B_4]+h_0d_0x_{110,18}\) |
|
|
20 |
\(h_0d_0gx_{91,11}\) |
\(d_{2}^{-1}\) |
\(x_{126,18,2}\) |
|
\(x_{125,20}\) |
\(d_{3}\) |
\(d_0g\Delta h_2^2[B_4]\) |
|
|
\(h_0^6x_{125,14}\) |
\(d_{2}\) |
\(h_0^8x_{124,14,2}\) |
|
19 |
\(gx_{105,15}\) |
\(d_{3}\) |
\(g^2\Delta ^2t\) |
|
\(h_0^5x_{125,14}\) |
\(d_{2}\) |
\(h_0^7x_{124,14,2}\) |
|
|
\(d_0gx_{91,11}\) |
\(d_{2}\) |
\(h_0d_0^2[\Delta \Delta _1g]\) |
|
|
18 |
\(d_0^2x_{97,10}\) |
\(d_{5}^{-1}\) |
\(h_1x_{125,12,2}\) |
|
\(h_0^4x_{125,14}\) |
\(d_{2}\) |
\(h_0^6x_{124,14,2}\) |
|
|
17 |
\(h_0^2Q_2x_{68,8}\) |
\(d_{2}^{-1}\) |
\(h_0D_2x_{68,8}\) |
|
\(h_0^3x_{125,14}\) |
\(d_{2}\) |
\(h_0^5x_{124,14,2}\) |
|
|
16 |
\(h_0Q_2x_{68,8}\) |
\(d_{2}^{-1}\) |
\(D_2x_{68,8}\) |
|
\(h_1x_{124,15}\) |
\(d_{4}^{-1}\) |
\(h_0^2x_{126,10}\) |
|
|
\(x_{125,16}\) |
\(d_{2}\) |
\(h_0x_{124,17}+h_0^4x_{124,14,2}\) |
|
|
\(h_0^2x_{125,14}\) |
\(d_{2}\) |
\(h_0^4x_{124,14,2}\) |
|
|
15 |
\(h_0^3x_{125,12}\) |
\(d_{2}^{-1}\) |
\(h_0h_3x_{119,11}\) |
|
\(Q_2x_{68,8}\) |
\(d_{4}^{-1}\) |
\(h_1x_{125,10}\) |
|
|
\(h_1x_{124,14}\) |
\(d_{5}\) |
\(d_0^2[\Delta \Delta _1g]\) |
|
|
\(x_{125,15}\) |
\(d_{2}\) |
\(h_0^3x_{124,14}\) |
|
|
\(h_0x_{125,14}\) |
\(d_{2}\) |
\(h_0^2x_{124,15}\) |
|
|
14 |
\(h_0^2x_{125,12}\) |
\(d_{2}^{-1}\) |
\(h_3x_{119,11}\) |
|
\(h_1h_4x_{109,12}\) |
Permanent |
||
|
\(x_{125,14}\) |
\(d_{2}\) |
\(h_0x_{124,15}\) |
|
|
13 |
\(h_0^4x_{125,9,2}\) |
\(d_{2}^{-1}\) |
\(x_{126,11}\) |
|
\(h_0^5x_{125,8}\) |
\(d_{2}^{-1}\) |
\(h_0x_{126,10}\) |
|
|
\(nx_{94,8}\) |
\(d_{4}^{-1}\) |
\(h_1x_{125,8}\) |
|
|
\(h_0x_{125,12}\) |
\(d_{4}^{-1}\) |
\(h_1x_{125,8,2}\) |
|
|
\(h_3x_{118,12}\) |
\(d_{3}\) |
\(h_1x_{123,15}\) |
|
|
12 |
\(h_0h_6x_{62,10}\) |
\(d_{2}^{-1}\) |
\(x_{126,10}\) |
|
\(h_0^3x_{125,9,2}+h_0^4x_{125,8}\) |
\(d_{3}^{-1}\) |
\(x_{126,9}\) |
|
|
\(h_0^4x_{125,8}\) |
\(d_{3}^{-1}\) |
\(x_{126,9}+h_0x_{126,8,3}\) |
|
|
\(x_{125,12}\) |
\(d_{2}\) |
\(h_1x_{123,13}\) |
|
|
\(x_{125,12,2}\) |
\(d_{2}\) |
\(h_1x_{123,13,2}\) |
|
|
11 |
\(h_1x_{124,10,2}\) |
\(d_{3}^{-1}\) |
\(x_{126,8}\) |
|
\(h_1x_{124,10}\) |
\(d_{3}^{-1}\) |
\(x_{126,8,2}\) |
|
|
\(h_0^2x_{125,9,2}\) |
\(d_{5}\) |
\(?\) |
|
|
\(h_6x_{62,10}\) |
\(d_{4}\) |
\(x_{124,15}\) |
|
|
\(h_0^3x_{125,8}\) |
\(d_{2}\) |
\(h_0^5x_{124,8}\) |
|
|
10 |
\(h_0x_{125,9}\) |
\(d_{2}^{-1}\) |
\(x_{126,8,3}\) |
|
\(x_{125,10,2}\) |
\(d_{3}\) |
\([H_1](\Delta e_1+C_0+h_0^6h_5^2)\) |
|
|
\(x_{125,10}\) |
\(d_{2}\) |
\(h_0x_{124,11,2}+h_0x_{124,11}\) |
|
|
\(h_0x_{125,9,2}\) |
\(d_{2}\) |
\(h_0^2x_{124,10,2}+h_0^4x_{124,8}\) |
|
|
\(h_0^2x_{125,8}\) |
\(d_{2}\) |
\(h_0^4x_{124,8}\) |
|
|
9 |
\(h_6(\Delta e_1+C_0+h_0^6h_5^2)\) |
Permanent |
|
|
\(h_5x_{94,8}\) |
\(d_{7}\) |
\(?\) |
|
|
\(x_{125,9}\) |
\(d_{3}\) |
\(h_1x_{123,11,2}\) |
|
|
\(x_{125,9,2}\) |
\(d_{2}\) |
\(h_0x_{124,10,2}+h_0^3x_{124,8}\) |
|
|
\(h_0x_{125,8}\) |
\(d_{2}\) |
\(h_0^3x_{124,8}\) |
|
|
8 |
\(x_{125,8,2}\) |
\(d_{3}\) |
\(x_{124,11,3}\) |
|
\(x_{125,8}\) |
\(d_{2}\) |
\(h_1x_{123,9}+h_0^2x_{124,8}\) |
|
|
7 |
\(h_0^2x_{125,5}\) |
\(d_{3}^{-1}\) |
\(x_{126,4}\) |
|
6 |
\(h_6[H_1]\) |
\(d_{4}\) |
\(x_{124,10,2}+h_0x_{124,9}\) |
|
\(h_0x_{125,5}\) |
\(d_{4}\) |
\(x_{124,10,2}+x_{124,10}+h_0x_{124,9}+h_0^2x_{124,8}\) |
|
|
5 |
\(x_{125,5}\) |
\(d_{2}\) |
\(h_0x_{124,6}\) |
|
0-4 |
|||
|
\(s\) |
Elements |
\(d_r\) |
value |
|
25 |
\(h_0^7x_{126,18}\) |
\(d_{3}^{-1}\) |
\(h_0^{21}h_7\) |
|
24 |
\(d_0e_0\Delta h_2^2Mg\) |
\(d_{2}^{-1}\) |
\(d_0x_{113,18}\) |
|
\(h_0^6x_{126,18}\) |
\(d_{3}^{-1}\) |
\(h_0^{20}h_7\) |
|
|
\(g^4\Delta h_2c_1\) |
\(d_{3}^{-1}\) |
\(g^3C^{\prime \prime }\) |
|
|
\(d_0Pd_0M^2\) |
\(d_{4}^{-1}\) |
\(d_0e_0[\Delta \Delta _1g]\) |
|
|
23 |
\(h_0^5x_{126,18}\) |
\(d_{3}^{-1}\) |
\(h_0^{19}h_7\) |
|
\(x_{126,23}\) |
\(d_{4}^{-1}\) |
\(e_0x_{110,15}\) |
|
|
22 |
\(h_0x_{126,21}+h_0^4x_{126,18}\) |
\(d_{3}^{-1}\) |
\(h_1x_{126,18,2}\) |
|
\(h_0^4x_{126,18}\) |
\(d_{3}^{-1}\) |
\(h_0^{18}h_7\) |
|
|
21 |
\(h_0^3x_{126,18}\) |
\(d_{3}^{-1}\) |
\(h_0^{17}h_7\) |
|
\(h_1x_{125,20}\) |
\(d_{4}\) |
\(d_0^2e_0g[B_4]\) |
|
|
\(x_{126,21}\) |
\(d_{4}\) |
\(x_{125,25,2}+x_{125,25}+g^4\Delta h_1g+\text{possibly }d_0^2e_0gB_4\) |
|
|
20 |
\(h_0^2x_{126,18}\) |
\(d_{3}^{-1}\) |
\(h_0^{16}h_7\) |
|
\(d_0x_{112,16}\) |
\(d_{5}^{-1}\) |
\(x_{127,15}\) |
|
|
19 |
\(h_0x_{126,18}\) |
\(d_{3}^{-1}\) |
\(h_0^{15}h_7\) |
|
\(g^3x_{66,7}\) |
\(d_{3}^{-1}\) |
\(gx_{107,12}\) |
|
|
18 |
\(x_{126,18}+e_0x_{109,14,2}\) |
\(d_{7}\) |
\(?\) |
|
\(e_0x_{109,14,2}\) |
\(d_{4}\) |
\(g^3Mg\) |
|
|
\(gx_{106,14}\) |
\(d_{4}\) |
\(ix_{102,15}+g^3Mg+h_0^8x_{125,14}\) |
|
|
\(x_{126,18,2}\) |
\(d_{2}\) |
\(h_0d_0gx_{91,11}\) |
|
|
17 |
\(h_0^{15}h_6^2\) |
\(d_{2}^{-1}\) |
\(h_0^{14}h_7\) |
|
\(h_1^2x_{124,15}\) |
\(d_{2}^{-1}\) |
\(h_6x_{64,14}\) |
|
|
\(x_{126,17}\) |
\(d_{8}\) |
\(?\) |
|
|
\(d_0x_{112,13}\) |
\(d_{4}\) |
\(x_{125,21}\) |
|
|
16 |
\(h_0^{14}h_6^2\) |
\(d_{2}^{-1}\) |
\(h_0^{13}h_7\) |
|
\(h_0^2D_2x_{68,8}\) |
\(d_{3}^{-1}\) |
\(x_{127,13}\) |
|
|
\(h_1^2x_{124,14}\) |
\(d_{6}^{-1}\) |
\(h_2x_{124,9}+h_0^2x_{127,8}\) |
|
|
15 |
\(h_0^{13}h_6^2\) |
\(d_{2}^{-1}\) |
\(h_0^{12}h_7\) |
|
\(h_0D_2x_{68,8}\) |
\(d_{2}\) |
\(h_0^2Q_2x_{68,8}\) |
|
|
14 |
\(h_0^{12}h_6^2\) |
\(d_{2}^{-1}\) |
\(h_0^{11}h_7\) |
|
\(x_{126,14}\) |
\(d_{4}^{-1}\) |
\(h_0^2x_{127,8}\) |
|
|
\(h_1h_3x_{118,12}\) |
\(d_{5}^{-1}\) |
\(h_1x_{126,8,2}\) |
|
|
\(D_2x_{68,8}\) |
\(d_{2}\) |
\(h_0Q_2x_{68,8}\) |
|
|
13 |
\(h_0^{11}h_6^2\) |
\(d_{2}^{-1}\) |
\(h_0^{10}h_7\) |
|
\(h_1x_{125,12,2}\) |
\(d_{5}\) |
\(d_0^2x_{97,10}\) |
|
|
\(h_0h_3x_{119,11}\) |
\(d_{2}\) |
\(h_0^3x_{125,12}\) |
|
|
12 |
\(d_1x_{94,8}\) |
\(d_{2}^{-1}\) |
\(x_{127,10}\) |
|
\(h_0x_{126,11}\) |
\(d_{2}^{-1}\) |
\(h_3x_{120,9}\) |
|
|
\(h_0^{10}h_6^2\) |
\(d_{2}^{-1}\) |
\(h_0^9h_7\) |
|
|
\(h_0^2x_{126,10}\) |
\(d_{4}\) |
\(h_1x_{124,15}\) |
|
|
\(h_3x_{119,11}\) |
\(d_{2}\) |
\(h_0^2x_{125,12}\) |
|
|
11 |
\(h_0^2x_{126,9}\) |
\(d_{2}^{-1}\) |
\(h_0x_{127,8}\) |
|
\(h_0^9h_6^2\) |
\(d_{2}^{-1}\) |
\(h_0^8h_7\) |
|
|
\(h_1x_{125,10,2}+h_1x_{125,10}\) |
Permanent |
||
|
\(h_1x_{125,10}\) |
\(d_{4}\) |
\(Q_2x_{68,8}\) |
|
|
\(x_{126,11}\) |
\(d_{2}\) |
\(h_0^4x_{125,9,2}\) |
|
|
\(h_0x_{126,10}\) |
\(d_{2}\) |
\(h_0^5x_{125,8}\) |
|
10 |
\(h_0x_{126,9}\) |
\(d_{2}^{-1}\) |
\(x_{127,8}\) |
|
\(h_0^2x_{126,8}\) |
\(d_{2}^{-1}\) |
\(h_0x_{127,7}\) |
|
|
\(h_0^8h_6^2\) |
\(d_{2}^{-1}\) |
\(h_0^7h_7\) |
|
|
\(h_0^2x_{126,8,3}\) |
Permanent |
||
|
\(x_{126,10}\) |
\(d_{2}\) |
\(h_0h_6x_{62,10}\) |
|
|
9 |
\(h_0x_{126,8}\) |
\(d_{2}^{-1}\) |
\(x_{127,7}\) |
|
\(h_0^7h_6^2\) |
\(d_{2}^{-1}\) |
\(h_0^6h_7\) |
|
|
\(h_1x_{125,8}\) |
\(d_{4}\) |
\(nx_{94,8}\) |
|
|
\(h_1x_{125,8,2}\) |
\(d_{4}\) |
\(h_0x_{125,12}\) |
|
|
\(x_{126,9}\) |
\(d_{3}\) |
\(h_0^3x_{125,9,2}+h_0^4x_{125,8}\) |
|
|
\(h_0x_{126,8,3}\) |
\(d_{3}\) |
\(h_0^3x_{125,9,2}\) |
|
|
8 |
\(h_0^6h_6^2\) |
\(d_{2}^{-1}\) |
\(h_0^5h_7\) |
|
\(h_6(C^{\prime }+X_2)\) |
\(d_{17}\) |
\(?\) |
|
|
\(x_{126,8,4}+x_{126,8}\) |
\(d_{6}\) |
\(?\) |
|
|
\(x_{126,8}\) |
\(d_{3}\) |
\(h_1x_{124,10,2}\) |
|
|
\(x_{126,8,2}\) |
\(d_{3}\) |
\(h_1x_{124,10}\) |
|
|
\(x_{126,8,3}\) |
\(d_{2}\) |
\(h_0x_{125,9}\) |
|
|
7 |
\(h_0^5h_6^2\) |
\(d_{2}^{-1}\) |
\(h_0^4h_7\) |
|
\(h_1h_6[H_1]\) |
\(d_{18}\) |
\(?\) |
|
|
6 |
\(h_0^4h_6^2\) |
\(d_{2}^{-1}\) |
\(h_0^3h_7\) |
|
\(x_{126,6}\) |
\(d_{3}\) |
\(h_5x_{94,8} +\text{possibly }h_6(\Delta e_1 + C_0 + h_0^6h_5^2)\) |
|
|
5 |
\(h_0^3h_6^2\) |
\(d_{2}^{-1}\) |
\(h_0^2h_7\) |
|
4 |
\(h_0^2h_6^2\) |
\(d_{2}^{-1}\) |
\(h_0h_7\) |
|
\(x_{126,4}\) |
\(d_{3}\) |
\(h_0^2x_{125,5}\) |
|
|
3 |
\(h_0h_6^2\) |
\(d_{2}^{-1}\) |
\(h_7\) |
|
2 |
\(h_6^2\) |
\(d_{7}\) |
\(?\) |
|
0-1 |
|||
|
\(s\) |
Elements |
\(d_r\) |
value |
|
25 |
\(h_0^{24}h_7\) |
\(d_{3}\) |
\(h_0^{10}x_{126,18}\) |
|
\(ix_{104,18}\) |
\(d_{2}\) |
\(d_0^3x_{84,15,2}+h_0d_0x_{112,22}\) |
|
|
\(d_0g\Delta ^3h_1g\) |
\(d_{2}\) |
\(d_0e_0g^3m\) |
|
|
24 |
\(h_0^2d_0x_{113,18}\) |
\(d_{2}^{-1}\) |
\(h_0gx_{108,17}\) |
|
\(h_1x_{126,23}\) |
\(d_{3}^{-1}\) |
\(x_{128,21}\) |
|
|
\(h_0^{23}h_7\) |
\(d_{3}\) |
\(h_0^9x_{126,18}\) |
|
|
23 |
\(e_0g\Delta h_2^2[B_4]+h_0d_0x_{113,18}\) |
\(d_{2}^{-1}\) |
\(gx_{108,17}\) |
|
\(h_0d_0x_{113,18}\) |
\(d_{4}\) |
\(d_0^3x_{84,15,2}\) |
|
|
\(h_0^{22}h_7\) |
\(d_{3}\) |
\(h_0^8x_{126,18}\) |
|
|
\(d_0Pd_0x_{91,11}\) |
\(d_{3}\) |
\(h_1x_{125,25}\) |
|
|
22 |
\(d_0x_{113,18,2}\) |
\(d_{4}^{-1}\) |
\(d_0e_0x_{97,10}\) |
|
\(h_0^{21}h_7\) |
\(d_{3}\) |
\(h_0^7x_{126,18}\) |
|
|
\(d_0x_{113,18}\) |
\(d_{2}\) |
\(d_0e_0\Delta h_2^2Mg\) |
|
|
21 |
\(h_0^6x_{127,15}\) |
\(d_{2}^{-1}\) |
\(h_0^5x_{128,14}\) |
|
\(x_{127,21}+g^3C^{\prime \prime }\) |
Permanent |
||
|
\(h_0^{20}h_7\) |
\(d_{3}\) |
\(h_0^6x_{126,18}\) |
|
|
\(g^3C^{\prime \prime }\) |
\(d_{3}\) |
\(g^4\Delta h_2c_1\) |
|
20 |
\(h_0^5x_{127,15}\) |
\(d_{2}^{-1}\) |
\(h_0^4x_{128,14}\) |
|
\(d_0e_0[\Delta \Delta _1g]\) |
\(d_{4}\) |
\(d_0Pd_0M^2\) |
|
|
\(h_0^{19}h_7\) |
\(d_{3}\) |
\(h_0^5x_{126,18}\) |
|
|
19 |
\(h_0^4x_{127,15}\) |
\(d_{2}^{-1}\) |
\(h_0^3x_{128,14}\) |
|
\(h_1x_{126,18}\) |
Permanent |
||
|
\(e_0x_{110,15}\) |
\(d_{4}\) |
\(x_{126,23}\) |
|
|
\(h_1x_{126,18,2}\) |
\(d_{3}\) |
\(h_0x_{126,21}+h_0^4x_{126,18}\) |
|
|
\(h_0^{18}h_7\) |
\(d_{3}\) |
\(h_0^4x_{126,18}\) |
|
|
18 |
\(h_0^3x_{127,15}\) |
\(d_{2}^{-1}\) |
\(h_0^2x_{128,14}\) |
|
\(h_0^3h_6x_{64,14}\) |
\(d_{2}^{-1}\) |
\(h_0^2h_6x_{65,13}\) |
|
|
\(g^2\Delta h_1H_1\) |
\(d_{3}^{-1}\) |
\(gx_{108,11}\) |
|
|
\(h_1x_{126,17}\) |
Permanent |
||
|
\(h_0^{17}h_7\) |
\(d_{3}\) |
\(h_0^3x_{126,18}\) |
|
|
17 |
\(h_0^2h_2x_{124,14}\) |
\(d_{2}^{-1}\) |
\(x_{128,15}\) |
|
\(h_0^2x_{127,15}\) |
\(d_{2}^{-1}\) |
\(x_{128,15}+h_0x_{128,14}\) |
|
|
\(h_0^2h_6x_{64,14}\) |
\(d_{2}^{-1}\) |
\(h_0h_6x_{65,13}\) |
|
|
\(gx_{107,13}\) |
\(d_{4}^{-1}\) |
\(h_0h_3x_{121,11}\) |
|
|
\(h_0^{16}h_7\) |
\(d_{3}\) |
\(h_0^2x_{126,18}\) |
|
|
16 |
\(h_0x_{127,15}+h_0h_2x_{124,14}\) |
\(d_{2}^{-1}\) |
\(x_{128,14}\) |
|
\(h_0h_6x_{64,14}\) |
\(d_{2}^{-1}\) |
\(h_6x_{65,13}\) |
|
|
\(h_0h_2x_{124,14}\) |
Permanent |
||
|
\(x_{127,16}\) |
Permanent |
||
|
\(h_0^{15}h_7\) |
\(d_{3}\) |
\(h_0x_{126,18}\) |
|
|
\(gx_{107,12}\) |
\(d_{3}\) |
\(g^3x_{66,7}\) |
|
|
15 |
\(h_1x_{126,14}\) |
\(d_{2}^{-1}\) |
\(x_{128,13,2}\) |
|
\(h_2x_{124,14}\) |
Permanent |
||
|
\(x_{127,15}\) |
\(d_{5}\) |
\(d_0x_{112,16}\) |
|
|
\(h_0^{14}h_7\) |
\(d_{2}\) |
\(h_0^{15}h_6^2\) |
|
|
\(h_6x_{64,14}\) |
\(d_{2}\) |
\(h_1^2x_{124,15}\) |
|
|
14 |
\(h_0g\Delta h_6g\) |
\(d_{2}^{-1}\) |
\(x_{128,12,2}\) |
|
\(h_0h_3x_{120,12}\) |
\(d_{2}^{-1}\) |
\(h_3x_{121,11}\) |
|
|
\(h_0^{13}h_7\) |
\(d_{2}\) |
\(h_0^{14}h_6^2\) |
|
|
13 |
\(h_0^3x_{127,10}\) |
\(d_{2}^{-1}\) |
\(h_0x_{128,10}\) |
|
\(g\Delta h_6g\) |
\(d_{3}^{-1}\) |
\(x_{128,10,2}\) |
|
|
\(h_3x_{120,12}\) |
\(d_{4}^{-1}\) |
\(h_2x_{125,8,2}\) |
|
|
\(x_{127,13}\) |
\(d_{3}\) |
\(h_0^2D_2x_{68,8}\) |
|
|
\(h_0^{12}h_7\) |
\(d_{2}\) |
\(h_0^{13}h_6^2\) |
|
|
12 |
\(h_0^2x_{127,10}\) |
\(d_{2}^{-1}\) |
\(x_{128,10}\) |
|
\(h_1x_{126,11}\) |
\(d_{3}^{-1}\) |
\(h_1x_{127,8}\) |
|
|
\(h_0^{11}h_7\) |
\(d_{2}\) |
\(h_0^{12}h_6^2\) |
|
|
11 |
\(h_0h_3x_{120,9}\) |
\(d_{3}^{-1}\) |
\(h_3D_2h_6\) |
|
\(h_0h_2x_{124,9}\) |
Permanent |
||
|
\(h_0x_{127,10}\) |
Permanent |
||
|
\(h_0^{10}h_7\) |
\(d_{2}\) |
\(h_0^{11}h_6^2\) |
|
|
10 |
\(h_1^2x_{125,8}\) |
Permanent |
|
|
\(h_2x_{124,9}+h_0^2x_{127,8}\) |
\(d_{6}\) |
\(h_1^2x_{124,14}\) |
|
|
\(h_0^2x_{127,8}\) |
\(d_{4}\) |
\(x_{126,14}\) |
|
|
\(x_{127,10}\) |
\(d_{2}\) |
\(d_1x_{94,8}\) |
|
|
\(h_3x_{120,9}\) |
\(d_{2}\) |
\(h_0x_{126,11}\) |
|
|
\(h_0^9h_7\) |
\(d_{2}\) |
\(h_0^{10}h_6^2\) |
|
9 |
\(h_0^2x_{127,7}\) |
\(d_{2}^{-1}\) |
\(h_0x_{128,6}\) |
|
\(h_1x_{126,8}\) |
Permanent |
||
|
\(h_1x_{126,8,2}\) |
\(d_{5}\) |
\(h_1h_3x_{118,12}\) |
|
|
\(h_0x_{127,8}\) |
\(d_{2}\) |
\(h_0^2x_{126,9}\) |
|
|
\(h_0^8h_7\) |
\(d_{2}\) |
\(h_0^9h_6^2\) |
|
|
8 |
\(h_0x_{127,7,2}+h_0x_{127,7}+h_0^2x_{127,6}\) |
\(d_{2}^{-1}\) |
\(x_{128,6}\) |
|
\(h_0^2x_{127,6}\) |
\(d_{2}^{-1}\) |
\(h_0x_{128,5}\) |
|
|
\(h_2h_6A\) |
Permanent |
||
|
\(h_2x_{124,7}\) |
\(d_{9}\) |
\(?\) |
|
|
\(x_{127,8}\) |
\(d_{2}\) |
\(h_0x_{126,9}\) |
|
|
\(h_0x_{127,7}\) |
\(d_{2}\) |
\(h_0^2x_{126,8}\) |
|
|
\(h_0^7h_7\) |
\(d_{2}\) |
\(h_0^8h_6^2\) |
|
|
7 |
\(h_0x_{127,6}\) |
\(d_{2}^{-1}\) |
\(x_{128,5}\) |
|
\(h_1x_{126,6}\) |
\(d_{10}\) |
\(?\) |
|
|
\(x_{127,7,2}+x_{127,7}\) |
\(d_{3}\) |
\(?\) |
|
|
\(x_{127,7}\) |
\(d_{2}\) |
\(h_0x_{126,8}\) |
|
|
\(h_0^6h_7\) |
\(d_{2}\) |
\(h_0^7h_6^2\) |
|
|
6 |
\(x_{127,6}\) |
\(d_{4}\) |
\(?\) |
|
\(h_0^5h_7\) |
\(d_{2}\) |
\(h_0^6h_6^2\) |
|
|
5 |
\(h_0^4h_7\) |
\(d_{2}\) |
\(h_0^5h_6^2\) |
|
4 |
\(h_0^3h_7\) |
\(d_{2}\) |
\(h_0^4h_6^2\) |
|
3 |
\(h_1h_6^2\) |
\(d_{14}\) |
\(?\) |
|
\(h_0^2h_7\) |
\(d_{2}\) |
\(h_0^3h_6^2\) |
|
|
2 |
\(h_0h_7\) |
\(d_{2}\) |
\(h_0^2h_6^2\) |
|
1 |
\(h_7\) |
\(d_{2}\) |
\(h_0h_6^2\) |
|
0 |
|||