\[\tiny{ 0 = { p_{1y}^{(j)}}^{2}{ a_z^{(i)}}^{2}{t}^{4}+{ p_{1y}^{(j)}}^{2}{ b_z^{(i)}}^{2}{t}^ {2}+{ a_z^{(i)}}^{2}{t}^{4}{ p_{2y}^{(j)}}^{2}+{ b_z^{(i)}}^{2}{t}^{2}{ p_{2y}^{(j)}}^{2}+{ a_z^{(i)}}^{2}{t}^{4}{ p_{2x}^{(j)}}^{2}+{ b_z^{(i)}}^{2}{t}^{2}{ p_{2x}^{(j)}}^{2}+{ p_{1x}^{(j)}}^{2}{ a_z^{(i)}}^{2}{t}^{4}+{ p_{1x}^{(j)}}^{2}{ b_z^{(i)}}^{2}{t}^{2}+{ a_x^{(i)}}^{2}{t}^{4}{ p_{2y}^{(j)}}^{2}+\\ { b_x^{(i)}}^{2 }{t}^{2}{ p_{2y}^{(j)}}^{2}+{ p_{1x}^{(j)}}^{2}{ a_y^{(i)}}^{2}{t}^{4}+{ p_{1x}^{(j)} }^{2}{ b_y^{(i)}}^{2}{t}^{2}+{ a_y^{(i)}}^{2}{t}^{4}{ p_{2x}^{(j)}}^{2}+{ b_y^{(i)}}^{2}{t}^{2}{ p_{2x}^{(j)}}^{2}+{ p_{1y}^{(j)}}^{2}{ a_x^{(i)}}^{2}{t}^{ 4}+{ p_{1y}^{(j)}}^{2}{ b_x^{(i)}}^{2}{t}^{2}+4\, p_{1y}^{(j)}\, c_z^{(i)}\,h p_{2y}^{(j)}+4\, c_z^{(i)}\, p_{2x}^{(j)}\, p_{1x}^{(j)}\,h+\\ 2\, c_x^{(i)}\, p_{2y}^{(j)}\, p_{1x}^{(j)}\, c_y^{(i)}-2\, c_x^{(i)}\, p_{2y}^{(j)}\, c_y^{(i)}\, p_{2x}^{(j)}+2\, p_{1x}^{(j)}\, p_{2y}^{(j)}\, c_y^{(i)}\, p_{2x}^{(j)}-2\, p_{1y}^{(j)}\, c_x^{(i)}\, p_{1x}^{(j)}\, c_y^{(i)}+2\, p_{1y}^{(j)}\, c_x^{(i)}\, p_{1x}^{(j)}\, p_{2y}^{(j)}+2\, p_{1y}^{(j)}\, c_x^{(i)}\, c_y^{(i)}\, p_{2x}^{(j)}+\\ 2\, p_{1y}^{(j)}\, p_{2x}^{(j)}\, c_x^{(i)} \, p_{2y}^{(j)}+2\, p_{1y}^{(j)}\, p_{2x}^{(j)}\, p_{1x}^{(j)}\, c_y^{(i)}-2\, p_{1y}^{(j)} \, p_{2x}^{(j)}\, p_{1x}^{(j)}\, p_{2y}^{(j)}-2\,{ p_{1y}^{(j)}}^{2} c_x^{(i)}\, p_{2x}^{(j)} -2\, p_{1y}^{(j)}\,{ c_x^{(i)}}^{2} p_{2y}^{(j)}-2\, p_{1y}^{(j)}\,{ p_{2x}^{(j)}}^{2} c_y^{(i)}-2\, c_x^{(i)}\,{ p_{2y}^{(j)}}^{2} p_{1x}^{(j)}-\\ 2\,{ p_{1x}^{(j)}}^{2} c_y^{(i)}\, p_{2y}^{(j)}-2\, p_{1x}^{(j)}\,{ c_y^{(i)}}^{2} p_{2x}^{(j)}-2\,{ p_{1y}^{(j)}}^{2 } c_z^{(i)}\,h-2\, p_{1y}^{(j)}\,{ c_z^{(i)}}^{2} p_{2y}^{(j)}-2\, p_{1y}^{(j)}\,{h}^{ 2} p_{2y}^{(j)}-2\, c_z^{(i)}\,{ p_{2y}^{(j)}}^{2}h+{ p_{1y}^{(j)}}^{2}{ c_x^{(i)}}^{2 }+{ p_{1y}^{(j)}}^{2}{ p_{2x}^{(j)}}^{2}+{ c_x^{(i)}}^{2}{ p_{2y}^{(j)}}^{2}+\\ { p_{1x}^{(j)}}^{2}{ c_y^{(i)}}^{2}+{ p_{1x}^{(j)}}^{2}{ p_{2y}^{(j)}}^{2}+{ c_y^{(i)}}^{2}{ p_{2x}^{(j)}}^{2}+{ p_{1y}^{(j)}}^{2}{ c_z^{(i)}}^{2}+{ p_{1y}^{(j)}}^{2}{h}^{2}+{ c_z^{(i)}}^{2}{ p_{2y}^{(j)}}^{2}+{h}^{2}{ p_{2y}^{(j)}}^{2}+{ c_z^{(i)}}^{2}{ p_{2x}^{(j)}}^{2}+{h}^{2}{ p_{2x}^{(j)}}^{2}+{ p_{1x}^{(j)}}^{2}{ c_z^{(i)}}^{2}+{ p_{1x}^{(j)}}^{2}{h}^{2}-\\ 2\, c_z^{(i)}\,{ p_{2x}^{(j)}}^{2}h-2\,{ c_z^{(i)}}^{2} p_{2x}^{(j)}\, p_{1x}^{(j)}-2\,{h}^{2} p_{2x}^{(j)}\, p_{1x}^{(j)}-2\,{ p_{1x}^{(j)}}^{2} c_z^{(i)}\,h+2\,{ p_{1y}^{(j)}}^{2} a_z^{(i)}\,{t}^{3} b_z^{(i)}-2\, p_{1y}^{(j)}\,{ a_z^{(i)}}^{2}{t}^{4} p_{2y}^{(j)}+2\,{ p_{1y}^{(j)}}^{2} a_z^{(i)}\,{t}^{2} c_z^{(i)}-2\,{ p_{1y}^{(j)}}^{2} a_z^{(i)}\,{t}^{2}h-\\ 2\, p_{1y}^{(j)}\,{ b_z^{(i)}}^{2}{ t}^{2} p_{2y}^{(j)}+2\,{ p_{1y}^{(j)}}^{2} b_z^{(i)}\,t c_z^{(i)}-2\,{ p_{1y}^{(j)}}^{ 2} b_z^{(i)}\,th+2\, a_z^{(i)}\,{t}^{3}{ p_{2y}^{(j)}}^{2} b_z^{(i)}+2\, a_z^{(i)} \,{t}^{2}{ p_{2y}^{(j)}}^{2} c_z^{(i)}-2\, a_z^{(i)}\,{t}^{2}{ p_{2y}^{(j)}}^{2}h+ 2\, b_z^{(i)}\,t{ p_{2y}^{(j)}}^{2} c_z^{(i)}-2\, b_z^{(i)}\,t{ p_{2y}^{(j)}}^{2}h+\\ 2 \, a_z^{(i)}\,{t}^{3}{ p_{2x}^{(j)}}^{2} b_z^{(i)}-2\,{ a_z^{(i)}}^{2}{t}^{4} p_{2x}^{(j)}\, p_{1x}^{(j)}+2\, a_z^{(i)}\,{t}^{2}{ p_{2x}^{(j)}}^{2} c_z^{(i)}-2\, a_z^{(i)}\,{t}^{2}{ p_{2x}^{(j)}}^{2}h-2\,{ b_z^{(i)}}^{2}{t}^{2} p_{2x}^{(j)}\, p_{1x}^{(j)}+2\, b_z^{(i)}\,t{ p_{2x}^{(j)}}^{2} c_z^{(i)}-2\, b_z^{(i)}\,t{ p_{2x}^{(j)} }^{2}h+2\,{ p_{1x}^{(j)}}^{2} a_z^{(i)}\,{t}^{3} b_z^{(i)}+\\ 2\,{ p_{1x}^{(j)}}^{2} a_z^{(i)}\,{t}^{2} c_z^{(i)}-2\,{ p_{1x}^{(j)}}^{2} a_z^{(i)}\,{t}^{2}h+2\,{ p_{1x}^{(j)}}^{2} b_z^{(i)}\,t c_z^{(i)}-2\,{ p_{1x}^{(j)}}^{2} b_z^{(i)}\,th-2\, a_y^{(i)}\,{t}^{2}{ p_{2x}^{(j)}}^{2} p_{1y}^{(j)}+2\, a_y^{(i)}\,{t}^{2}{ p_{2x}^{(j)} }^{2} c_y^{(i)}-2\, b_y^{(i)}\,t{ p_{2x}^{(j)}}^{2} p_{1y}^{(j)}+2\, b_y^{(i)}\,t { p_{2x}^{(j)}}^{2} c_y^{(i)}+\\ 2\,{ p_{1y}^{(j)}}^{2} a_x^{(i)}\,{t}^{3} b_x^{(i)}+2 \,{ p_{1y}^{(j)}}^{2} a_x^{(i)}\,{t}^{2} c_x^{(i)}-2\,{ p_{1y}^{(j)}}^{2} a_x^{(i)} \,{t}^{2} p_{2x}^{(j)}+2\,{ p_{1y}^{(j)}}^{2} b_x^{(i)}\,t c_x^{(i)}-2\,{ p_{1y}^{(j)} }^{2} b_x^{(i)}\,t p_{2x}^{(j)}+2\, a_x^{(i)}\,{t}^{3}{ p_{2y}^{(j)}}^{2} b_x^{(i)}- 2\,{ a_x^{(i)}}^{2}{t}^{4} p_{2y}^{(j)}\, p_{1y}^{(j)}+\\ 2\, a_x^{(i)}\,{t}^{2}{ p_{2y}^{(j)}}^{2} c_x^{(i)}-2\, a_x^{(i)}\,{t}^{2}{ p_{2y}^{(j)}}^{2} p_{1x}^{(j)}-2\, { b_x^{(i)}}^{2}{t}^{2} p_{2y}^{(j)}\, p_{1y}^{(j)}+2\, b_x^{(i)}\,t{ p_{2y}^{(j)}}^{2 } c_x^{(i)}-2\, b_x^{(i)}\,t{ p_{2y}^{(j)}}^{2} p_{1x}^{(j)}+2\,{ p_{1x}^{(j)}}^{2} a_y^{(i)}\,{t}^{3} b_y^{(i)}-2\, p_{1x}^{(j)}\,{ a_y^{(i)}}^{2}{t}^{4} p_{2x}^{(j)} +\\ 2\,{ p_{1x}^{(j)}}^{2} a_y^{(i)}\,{t}^{2} c_y^{(i)}-2\,{ p_{1x}^{(j)}}^{2} a_y^{(i)} \,{t}^{2} p_{2y}^{(j)}-2\, p_{1x}^{(j)}\,{ b_y^{(i)}}^{2}{t}^{2} p_{2x}^{(j)}+2\,{ p_{1x}^{(j)}}^{2} b_y^{(i)}\,t c_y^{(i)}-2\,{ p_{1x}^{(j)}}^{2} b_y^{(i)}\,t p_{2y}^{(j)}+2\, a_y^{(i)}\,{t}^{3}{ p_{2x}^{(j)}}^{2} b_y^{(i)}-{R}^{2} \left( -2\, p_{1y}^{(j)}\, p_{2y}^{(j)}+{ p_{2y}^{(j)}}^{2}+{ p_{1y}^{(j)}}^{2}-\\ 2\, p_{1x}^{(j)}\, p_{2x}^{(j)}+{ p_{1x}^{(j)}}^{2}+{ p_{2x}^{(j)}}^{2} \right) +2\, a_y^{(i)}\,{t}^{4} p_{2x}^{(j)}\, p_{1y}^{(j)}\, a_x^{(i)}+2\, a_y^{(i)}\,{t}^{3} p_{2x}^{(j)}\, p_{1y}^{(j)} \, b_x^{(i)}+2\, a_y^{(i)}\,{t}^{2} p_{2x}^{(j)}\, p_{1y}^{(j)}\, c_x^{(i)}-2\, a_y^{(i)}\,{t}^{2} p_{2x}^{(j)}\, c_x^{(i)}\, p_{2y}^{(j)}+\\ 2\, a_y^{(i)}\,{t}^{2} p_{2x}^{(j)}\, p_{1x}^{(j)}\, p_{2y}^{(j)}+2\, b_y^{(i)}\,{t}^{3} p_{2x}^{(j)}\, p_{1y}^{(j)}\, a_x^{(i)}+2\, b_y^{(i)}\,{t}^{2} p_{2x}^{(j)}\, p_{1y}^{(j)}\, b_x^{(i)}+2\, b_y^{(i)}\,t p_{2x}^{(j)}\, p_{1y}^{(j)}\, c_x^{(i)}-2\, b_y^{(i)}\,t p_{2x}^{(j)}\, c_x^{(i)}\, p_{2y}^{(j)}+2\, b_y^{(i)}\,t p_{2x}^{(j)}\, p_{1x}^{(j)}\, p_{2y}^{(j)}-\\ 2\, p_{1y}^{(j)}\, a_x^{(i)}\,{t}^{2} p_{1x}^{(j)}\, c_y^{(i)}+2\, p_{1y}^{(j)}\, a_x^{(i)} \,{t}^{2} p_{1x}^{(j)}\, p_{2y}^{(j)}+2\, p_{1y}^{(j)}\, a_x^{(i)}\,{t}^{2} c_y^{(i)} \, p_{2x}^{(j)}-2\, p_{1y}^{(j)}\, b_x^{(i)}\,t p_{1x}^{(j)}\, c_y^{(i)}+2\, p_{1y}^{(j)} \, b_x^{(i)}\,t p_{1x}^{(j)}\, p_{2y}^{(j)}+2\, p_{1y}^{(j)}\, b_x^{(i)}\,t c_y^{(i)}\, p_{2x}^{(j)}+\\ 2\, a_x^{(i)}\,{t}^{4} p_{2y}^{(j)}\, p_{1x}^{(j)}\, a_y^{(i)}+2\, a_x^{(i)} \,{t}^{3} p_{2y}^{(j)}\, p_{1x}^{(j)}\, b_y^{(i)}-2\, a_x^{(i)}\,{t}^{4} p_{2y}^{(j)} \, a_y^{(i)}\, p_{2x}^{(j)}-2\, a_x^{(i)}\,{t}^{3} p_{2y}^{(j)}\, b_y^{(i)}\, p_{2x}^{(j)}-4\, a_x^{(i)}\,{t}^{3} p_{2y}^{(j)}\, p_{1y}^{(j)}\, b_x^{(i)}-4\, a_x^{(i)}\,{ t}^{2} p_{2y}^{(j)}\, p_{1y}^{(j)}\, c_x^{(i)}+\\ 2\, a_x^{(i)}\,{t}^{2} p_{2y}^{(j)}\, p_{1y}^{(j)}\, p_{2x}^{(j)}+2\, a_x^{(i)}\,{t}^{2} p_{2y}^{(j)}\, p_{1x}^{(j)}\, c_y^{(i)} -2\, a_x^{(i)}\,{t}^{2} p_{2y}^{(j)}\, c_y^{(i)}\, p_{2x}^{(j)}+2\, b_x^{(i)}\,{t}^{ 3} p_{2y}^{(j)}\, p_{1x}^{(j)}\, a_y^{(i)}+2\, b_x^{(i)}\,{t}^{2} p_{2y}^{(j)}\, p_{1x}^{(j)}\, b_y^{(i)}-2\, b_x^{(i)}\,{t}^{3} p_{2y}^{(j)}\, a_y^{(i)}\, p_{2x}^{(j)}-\\ 2\, b_x^{(i)}\,{t}^{2} p_{2y}^{(j)}\, b_y^{(i)}\, p_{2x}^{(j)}-4\, b_x^{(i)}\,t p_{2y}^{(j)}\, p_{1y}^{(j)}\, c_x^{(i)}+2\, b_x^{(i)}\,t p_{2y}^{(j)}\, p_{1y}^{(j)}\, p_{2x}^{(j)} +2\, b_x^{(i)}\,t p_{2y}^{(j)}\, p_{1x}^{(j)}\, c_y^{(i)}-2\, b_x^{(i)}\,t p_{2y}^{(j)} \, c_y^{(i)}\, p_{2x}^{(j)}-4\, p_{1x}^{(j)}\, a_y^{(i)}\,{t}^{3} b_y^{(i)}\, p_{2x}^{(j)}-\\ 2\, p_{1x}^{(j)}\, a_y^{(i)}\,{t}^{4} p_{1y}^{(j)}\, a_x^{(i)}-2\, p_{1x}^{(j)}\, a_y^{(i)}\,{t}^{3} p_{1y}^{(j)}\, b_x^{(i)}-2\, p_{1x}^{(j)}\, a_y^{(i)}\,{t}^{2} p_{1y}^{(j)}\, c_x^{(i)}+2\, p_{1x}^{(j)}\, a_y^{(i)}\,{t}^{2} p_{1y}^{(j)}\, p_{2x}^{(j)} +2\, p_{1x}^{(j)}\, a_y^{(i)}\,{t}^{2} c_x^{(i)}\, p_{2y}^{(j)}-4\, p_{1x}^{(j)}\, a_y^{(i)}\,{t}^{2} c_y^{(i)}\, p_{2x}^{(j)}-\\ 2\, p_{1x}^{(j)}\, b_y^{(i)}\,{t}^{3} p_{1y}^{(j)}\, a_x^{(i)}-2\, p_{1x}^{(j)}\, b_y^{(i)}\,{t}^{2} p_{1y}^{(j)}\, b_x^{(i)} -2\, p_{1x}^{(j)}\, b_y^{(i)}\,t p_{1y}^{(j)}\, c_x^{(i)}+2\, p_{1x}^{(j)}\, b_y^{(i)} \,t p_{1y}^{(j)}\, p_{2x}^{(j)}+2\, p_{1x}^{(j)}\, b_y^{(i)}\,t c_x^{(i)}\, p_{2y}^{(j)}- 4\, p_{1x}^{(j)}\, b_y^{(i)}\,t c_y^{(i)}\, p_{2x}^{(j)}-\\ 4\, p_{1y}^{(j)}\, a_z^{(i)}\, {t}^{3} b_z^{(i)}\, p_{2y}^{(j)}-4\, p_{1y}^{(j)}\, a_z^{(i)}\,{t}^{2} c_z^{(i)}\, p_{2y}^{(j)}+4\, p_{1y}^{(j)}\, a_z^{(i)}\,{t}^{2}h p_{2y}^{(j)}-4\, p_{1y}^{(j)}\, b_z^{(i)}\,t c_z^{(i)}\, p_{2y}^{(j)}+4\, p_{1y}^{(j)}\, b_z^{(i)}\,th p_{2y}^{(j)}-4\, a_z^{(i)}\,{t}^{3} p_{2x}^{(j)}\, p_{1x}^{(j)}\, b_z^{(i)}-\\ 4\, a_z^{(i)}\,{t}^{2} p_{2x}^{(j)}\, p_{1x}^{(j)}\, c_z^{(i)}+4\, a_z^{(i)}\,{t}^{2} p_{2x}^{(j)}\, p_{1x}^{(j)}\,h- 4\, b_z^{(i)}\,t p_{2x}^{(j)}\, p_{1x}^{(j)}\, c_z^{(i)}+4\, b_z^{(i)}\,t p_{2x}^{(j)}\, p_{1x}^{(j)}\,h } \notag\]