Table 1: Conditions on the value of the parameters 𝑔 and πœ‡ for the quasipolynomial solutions in the case of Ξ” 2 = 0 with different values of 𝑀 π‘Ž 2 and 𝑙 .

𝑛 𝑙 𝑀 π‘Ž 2 Conditions 𝐸 𝑀 π‘Ž 2 𝑛 , 𝑙 ≑ 𝐸 𝑀 π‘Ž 2 𝑛 , 𝑙 ( πœ‡ , 𝑔 )

1 −1 1 / 2 πœ‡ = 1 / 3 ( βˆ’ 3 βˆ’ 1 5 𝐴 βˆ’ 1 / 3 βˆ’ 𝐴 1 / 3 √ ) , 𝐴 = 3 ( 3 6 βˆ’ 9 6 1 ) 𝐸 1 / 2 1 , βˆ’ 1 = βˆ’ 𝑀 ( 3 / 2 + 2 / 3 𝐴 1 / 3 + 1 0 𝐴 βˆ’ 1 / 3 )
𝑔 = 1 / 9 𝐴 βˆ’ 2 / 3 ( 1 5 + 6 𝐴 1 / 3 + 𝐴 2 / 3 ) ( 1 5 + 9 𝐴 1 / 3 + 𝐴 2 / 3 )
1 πœ‡ = 1 / 3 ( βˆ’ 5 βˆ’ 1 9 𝐴 βˆ’ 1 / 3 βˆ’ 𝐴 1 / 3 √ ) , 𝐴 = 1 6 1 βˆ’ 3 2 1 1 8 𝐸 1 1 , βˆ’ 1 = βˆ’ 𝑀 ( 1 7 / 6 + 2 / 3 𝐴 1 / 3 + 3 8 / 3 𝐴 βˆ’ 1 / 3 )
𝑔 = 1 / 9 𝐴 βˆ’ 2 / 3 ( 1 9 + 8 𝐴 1 / 3 + 𝐴 2 / 3 ) ( 1 9 + 1 1 𝐴 1 / 3 + 𝐴 2 / 3 )
3 / 2 πœ‡ = 1 / 3 ( βˆ’ 7 βˆ’ 2 5 𝐴 βˆ’ 1 / 3 βˆ’ 𝐴 1 / 3 √ ) , 𝐴 = 1 9 9 βˆ’ 1 8 7 4 𝐸 3 / 2 1 , βˆ’ 1 = βˆ’ 𝑀 ( 2 5 / 6 + 2 / 3 𝐴 1 / 3 + 5 0 / 3 𝐴 βˆ’ 1 / 3 )
𝑔 = 1 / 9 𝐴 βˆ’ 2 / 3 ( 2 5 + 1 0 𝐴 1 / 3 + 𝐴 2 / 3 ) ( 2 5 + 1 3 𝐴 1 / 3 + 𝐴 2 / 3 )
2 πœ‡ = 1 / 3 ( βˆ’ 9 βˆ’ 3 3 𝐴 βˆ’ 1 / 3 βˆ’ 𝐴 1 / 3 √ ) , 𝐴 = 3 ( 7 2 βˆ’ 1 1 9 1 ) 𝐸 2 1 , βˆ’ 1 = βˆ’ 𝑀 ( 1 1 / 2 + 2 / 3 𝐴 1 / 3 + 2 2 𝐴 βˆ’ 1 / 3 )
𝑔 = 1 / 9 𝐴 βˆ’ 2 / 3 ( 3 3 + 1 2 𝐴 1 / 3 + 𝐴 2 / 3 ) ( 3 3 + 1 5 𝐴 1 / 3 + 𝐴 2 / 3 )
0 1 / 2 πœ‡ = 0 𝐸 1 / 2 1 , 0 = 3 / 2 𝑀
𝑔 = 2
√ πœ‡ = βˆ’ 1 / 2 ( 7 + 1 7 ) 𝐸 1 / 2 1 , 0 √ = βˆ’ 1 / 2 ( 1 1 + 2 1 7 ) 𝑀
√ 𝑔 = 2 9 + 5 1 7
√ πœ‡ = βˆ’ 1 / 2 ( 7 βˆ’ 1 7 ) 𝐸 1 / 2 1 , 0 √ = βˆ’ 1 / 2 ( 1 1 βˆ’ 2 1 7 ) 𝑀
√ 𝑔 = 2 9 βˆ’ 5 1 7
1 πœ‡ = βˆ’ 3 + 𝐡 𝐸 1 1 , 0 = βˆ’ ( 9 / 2 βˆ’ 2 𝐡 ) 𝑀
𝑔 = ( βˆ’ 4 + 𝐡 ) ( βˆ’ 5 + 𝐡 )
𝐡 = 1 / 3 β„œ ( 𝐴 1 / 3 + 3 3 𝐴 βˆ’ 1 / 3 √ ) , 𝐴 = βˆ’ 1 0 8 + 3 𝑖 2 6 9 7
πœ‡ = βˆ’ 3 βˆ’ 𝐡 , 𝐸 1 1 , 0 = βˆ’ ( 9 / 2 + 2 𝐡 ) 𝑀
𝑔 = ( 5 + 𝐡 ) ( 4 + 𝐡 )
√ 𝐡 = β„œ ( ( 1 1 ( 1 + 𝑖 3 ) 𝐴 βˆ’ 1 / 3 √ / 2 ) + ( ( 1 βˆ’ 𝑖 3 ) 𝐴 1 / 3 √ / 6 ) ) , 𝐴 = βˆ’ 1 0 8 + 3 𝑖 2 6 9 7
πœ‡ = βˆ’ 3 βˆ’ 𝐡 , 𝐸 1 1 , 0 = βˆ’ ( 9 / 2 + 2 𝐡 ) 𝑀
𝑔 = ( 5 + 𝐡 ) ( 4 + 𝐡 )
√ 𝐡 = β„œ ( 1 1 ( 1 βˆ’ 𝑖 3 ) 𝐴 βˆ’ 1 / 3 √ / 2 + ( ( 1 + 𝑖 3 ) 𝐴 1 / 3 √ / 6 ) ) , 𝐴 = βˆ’ 1 0 8 + 3 𝑖 2 6 9 7