Для построения коэффициентов матрицы оператора для бивекторов используем ранее полученные результаты и применим к бивекторам.
Используя ранее опеределлную функцию построения экспоненты от бикавтерниона быстроты и угла определим построение левого и правого полуоператоров как
left:makeexp(psi[x]/2,psi[y]/2,psi[z]/2, phi[x]/2,phi[y]/2,phi[z]/2); right:makeexp(-psi[x]/2,-psi[y]/2,-psi[z]/2, -phi[x]/2,-phi[y]/2,-phi[z]/2);Здесь использовалось правило сопряжения правого полуоператора при преоразовании бивекторов. Для приведения к сокращенной записи, которую может упростить система Maxima, используем ранее найденное произведение трех бикватернионов.
a7:left[8];b7:right[8]; a6:left[7];b6:right[7]; a5:left[6];b5:right[6]; a4:left[5];b4:right[5]; a3:left[4];b3:right[4]; a2:left[3];b2:right[3]; a1:left[2];b1:right[2]; a0:left[1];b0:right[1];Добавим правила упрощения, выражающие промежуточные переменные через параметры преобразования
tellsimpafter( atan2(alpha[1],alpha[0])/2, Theta); tellsimpafter( alpha[1]^2+alpha[0]^2, alpha); tellsimpafter(cos(cos(Theta)*alpha^(1/4))^2* sinh(sin(Theta)*alpha^(1/4))^2+ sin(cos(Theta)*alpha^(1/4))^2* cosh(sin(Theta)*alpha^(1/4))^2, sin(cos(Theta)*alpha^(1/4))^2+ sinh(sin(Theta)*alpha^(1/4))^2); tellsimpafter(4*sin(cos(Theta)*alpha^(1/4))^2* sinh(sin(Theta)*alpha^(1/4))^2+ 4*cos(cos(Theta)*alpha^(1/4))^2* cosh(sin(Theta)*alpha^(1/4))^2, 4*(cos(cos(Theta)*alpha^(1/4))^2+ sinh(sin(Theta)*alpha^(1/4))^2));Здесь используются вместе с введенным символом $\alpha$ замены: $$ \begin{array}{c} \alpha_0+i\alpha_1= \\ = x_5^2-x_1^2+x_6^2-x_2^2+x_7^2-x_3^2+ \\ +i(2x_1x_5+2x_2x_6+2x_3x_7) \\ \alpha=\alpha_0^2+\alpha_1^2 \\ \Theta=\mathrm{arctg}(\alpha_1/\alpha_0)/2 \end{array} $$ Далее вычислим коэффициенты оператора для бивекторов используя тригонометрические упрощения, и в полученных выражениях будем учитывать выполненные подстановки $\alpha$ и $\Theta$. Выходную матрицу формируем используя только результат в виде бивектора образующегося линейным преобразованием исходного биветора. Здесь используется тот факт, что преобразование в котором участвуют бивекторы оставляет неизменной скалярную и псевдоскалярную части и если они считаются равными 0, то и результат также равен 0. Нумерование коэффициентов произведения трех бикватернионов приводим к нумерованию индексов искомой матрицы.
A11:trigreduce(trigsimp(a7*b7+a6*b6-a5*b5- a4*b4-a3*b3-a2*b2+a1*b1+a0*b0)); A12:trigreduce(trigsimp(a0*b7-a5*b6-a6*b5+ a3*b4-a4*b3+a1*b2+a2*b1-a7*b0)); A13:trigreduce(trigsimp(-a5*b7-a0*b6-a7*b5- a2*b4+a1*b3+a4*b2+a3*b1+a6*b0)); A14:trigreduce(trigsimp(a3*b7+a2*b6-a1*b5+ a0*b4+a7*b3+a6*b2-a5*b1+a4*b0)); A15:trigreduce(trigsimp(a4*b7-a1*b6-a2*b5- a7*b4+a0*b3-a5*b2-a6*b1-a3*b0)); A16:trigreduce(trigsimp(-a1*b7-a4*b6-a3*b5+ a6*b4-a5*b3-a0*b2-a7*b1+a2*b0)); A21:trigreduce(trigsimp(-a0*b7-a5*b6-a6*b5- a3*b4+a4*b3+a1*b2+a2*b1+a7*b0)); A22:trigreduce(trigsimp(a7*b7-a6*b6+a5*b5- a4*b4-a3*b3+a2*b2-a1*b1+a0*b0)); A23:trigreduce(trigsimp(-a6*b7-a7*b6+a0*b5+ a1*b4+a2*b3+a3*b2-a4*b1-a5*b0)); A24:trigreduce(trigsimp(-a4*b7-a1*b6-a2*b5+ a7*b4-a0*b3-a5*b2-a6*b1+a3*b0)); A25:trigreduce(trigsimp(a3*b7-a2*b6+a1*b5+ a0*b4+a7*b3-a6*b2+a5*b1+a4*b0)); A26:trigreduce(trigsimp(-a2*b7-a3*b6+a4*b5- a5*b4-a6*b3-a7*b2+a0*b1-a1*b0)); A31:trigreduce(trigsimp(-a5*b7+a0*b6-a7*b5+ a2*b4+a1*b3-a4*b2+a3*b1-a6*b0)); A32:trigreduce(trigsimp(-a6*b7-a7*b6-a0*b5- a1*b4+a2*b3+a3*b2+a4*b1+a5*b0)); A33:trigreduce(trigsimp(-a7*b7+a6*b6+a5*b5- a4*b4+a3*b3-a2*b2-a1*b1+a0*b0)); A34:trigreduce(trigsimp(-a1*b7+a4*b6-a3*b5- a6*b4-a5*b3+a0*b2-a7*b1-a2*b0)); A35:trigreduce(trigsimp(-a2*b7-a3*b6-a4*b5+ a5*b4-a6*b3-a7*b2-a0*b1+a1*b0)); A36:trigreduce(trigsimp(-a3*b7+a2*b6+a1*b5+ a0*b4-a7*b3+a6*b2+a5*b1+a4*b0)); A41:trigreduce(trigsimp(-a3*b7-a2*b6+a1*b5- a0*b4-a7*b3-a6*b2+a5*b1-a4*b0)); A42:trigreduce(trigsimp(-a4*b7+a1*b6+a2*b5+ a7*b4-a0*b3+a5*b2+a6*b1+a3*b0)); A43:trigreduce(trigsimp(a1*b7+a4*b6+a3*b5- a6*b4+a5*b3+a0*b2+a7*b1-a2*b0)); A44:trigreduce(trigsimp(a7*b7+a6*b6-a5*b5- a4*b4-a3*b3-a2*b2+a1*b1+a0*b0)); A45:trigreduce(trigsimp(a0*b7-a5*b6-a6*b5+ a3*b4-a4*b3+a1*b2+a2*b1-a7*b0)); A46:trigreduce(trigsimp(-a5*b7-a0*b6-a7*b5- a2*b4+a1*b3+a4*b2+a3*b1+a6*b0)); A51:trigreduce(trigsimp(a4*b7+a1*b6+a2*b5- a7*b4+a0*b3+a5*b2+a6*b1-a3*b0)); A52:trigreduce(trigsimp(-a3*b7+a2*b6-a1*b5- a0*b4-a7*b3+a6*b2-a5*b1-a4*b0)); A53:trigreduce(trigsimp(a2*b7+a3*b6-a4*b5+ a5*b4+a6*b3+a7*b2-a0*b1+a1*b0)); A54:trigreduce(trigsimp(-a0*b7-a5*b6-a6*b5- a3*b4+a4*b3+a1*b2+a2*b1+a7*b0)); A55:trigreduce(trigsimp(a7*b7-a6*b6+a5*b5- a4*b4-a3*b3+a2*b2-a1*b1+a0*b0)); A56:trigreduce(trigsimp(-a6*b7-a7*b6+a0*b5+ a1*b4+a2*b3+a3*b2-a4*b1-a5*b0)); A61:trigreduce(trigsimp(a1*b7-a4*b6+a3*b5+ a6*b4+a5*b3-a0*b2+a7*b1+a2*b0)); A62:trigreduce(trigsimp(a2*b7+a3*b6+a4*b5- a5*b4+a6*b3+a7*b2+a0*b1-a1*b0)); A63:trigreduce(trigsimp(a3*b7-a2*b6-a1*b5- a0*b4+a7*b3-a6*b2-a5*b1-a4*b0)); A64:trigreduce(trigsimp(-a5*b7+a0*b6-a7*b5+ a2*b4+a1*b3-a4*b2+a3*b1-a6*b0)); A65:trigreduce(trigsimp(-a6*b7-a7*b6-a0*b5- a1*b4+a2*b3+a3*b2+a4*b1+a5*b0)); A66:trigreduce(trigsimp(-a7*b7+a6*b6+a5*b5- a4*b4+a3*b3-a2*b2-a1*b1+a0*b0));В результате получаем коэффициенты оператора группы Лоренца для бивекторов, к которым можем применить дополнительные правила упрощения сумм и разностей гиперболических функций в виде экспонент.
В итоге совместно с введенными обозначениями получаем коэффициенты матрицы оператора для бивекторов: $$ \begin{array}{c} \alpha_0 = x_5^2-x_1^2+x_6^2-x_2^2+x_7^2-x_3^2 \\ \alpha_1 = 2x_1x_5+2x_2x_6+2x_3x_7 \\ \alpha=\alpha_0^2+\alpha_1^2 \\ \Theta=\mathrm{arctg}(\alpha_1/\alpha_0)/2 \end{array} $$ $$ \begin{array}{c} A_{11} = (((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\psi_z\psi_z+ \\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}})\sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)- 4\sin(2\Theta))\varphi_z\psi_z+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_z\varphi_z+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\psi_y\psi_y+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-4\sin(2\Theta))\varphi_y\psi_y+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_y\varphi_y+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_x\psi_x+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+4\sin(2\Theta))\varphi_x\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\varphi_x\varphi_x+\\ (8\cos(2\cos(\Theta)\alpha^{1/4})\mathrm{ch}(2\sin(\Theta)\alpha^{1/4})+ 8)\sqrt{\alpha})/ (16\sqrt{\alpha}) \end{array} $$ $$ \begin{array}{c} A_{12} = (\sqrt{\alpha}( ((2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2\mathrm{sh}(2\sin(\Theta)\alpha^{1/4})- 2\mathrm{ch}(2\sin(\Theta)\alpha^{1/4}))\cos(2\cos(\Theta)\alpha^{1/4}-\Theta)) \sqrt{\alpha}\psi_z+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\varphi_z)+\\ \alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_x)\psi_y+\\ (((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+\\ 2\cos(2\Theta))\varphi_x)\varphi_y))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{13} = (\alpha^{3/4}((( e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_x)\psi_z+\\ (((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\varphi_x)\varphi_z)+\\ \sqrt{\alpha}(((-2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_y+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}- \Theta))\sqrt{\alpha}\varphi_y))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{14} = ((e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\psi_z\psi_z+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-4\cos(2\Theta))\varphi_z\psi_z+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_z\varphi_z+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\psi_y\psi_y+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-4\cos(2\Theta))\varphi_y\psi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_y\varphi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\psi_x\psi_x+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+4\cos(2\Theta))\varphi_x\psi_x+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\varphi_x\varphi_x-\\ 8\sin(2\cos(\Theta)\alpha^{1/4})\mathrm{sh}(2\sin(\Theta)\alpha^{1/4}) \sqrt{\alpha})/ (16\sqrt{\alpha}) \end{array} $$ $$ \begin{array}{c} A_{15} = -(\sqrt{\alpha}(( (2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_z+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\varphi_z)+\\ \alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\psi_x+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_x)\psi_y+\\ ((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+\\ 2\sin(2\Theta))\varphi_x)\varphi_y))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{16} = -(\alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\psi_x+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_x)\psi_z+\\ ((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_x)\varphi_z)+\\ \sqrt{\alpha}(((-2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_y+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\\ \Theta))\sqrt{\alpha}\varphi_y))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{21} = (\sqrt{\alpha}(((-2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_z+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\varphi_z)+\\ \alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_x)\psi_y+\\ (((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+\\ 2\cos(2\Theta))\varphi_x)\varphi_y))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{22} = (((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\psi_z\psi_z+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-4\sin(2\Theta))\varphi_z\psi_z+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_z\varphi_z+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_y\psi_y+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+4\sin(2\Theta))\varphi_y\psi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\varphi_y\varphi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\psi_x\psi_x+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-4\sin(2\Theta))\varphi_x\psi_x+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_x\varphi_x+\\ (8\cos(2\cos(\Theta)\alpha^{1/4})\mathrm{ch}(2\sin(\Theta)\alpha^{1/4})+\\ 8)\sqrt{\alpha})/ (16\sqrt{\alpha}) \end{array} $$ $$ \begin{array}{c} A_{23} = (\alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_y)\psi_z+\\ (((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\psi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\varphi_y)\varphi_z)+\\ \sqrt{\alpha}(((2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_x+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\\ \Theta))\sqrt{\alpha}\varphi_x))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{24} = -(\sqrt{\alpha}(((-2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_z+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\varphi_z)+\\ \alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\psi_x+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_x)\psi_y+\\ ((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+\\ 2\sin(2\Theta))\varphi_x)\varphi_y))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{25} = ((e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\psi_z\psi_z+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-4\cos(2\Theta))\varphi_z\psi_z+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_z\varphi_z+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\psi_y\psi_y+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+4\cos(2\Theta))\varphi_y\psi_y+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\varphi_y\varphi_y+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\psi_x\psi_x+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-4\cos(2\Theta))\varphi_x\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_x\varphi_x-\\ 8\sin(2\cos(\Theta)\alpha^{1/4})\mathrm{sh}(2\sin(\Theta)\alpha^{1/4}) \sqrt{\alpha})/ (16\sqrt{\alpha}) \end{array} $$ $$ \begin{array}{c} A_{26} = -(\alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\psi_y+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_y)\psi_z+\\ ((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_y)\varphi_z)+\\ \sqrt{\alpha}(((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_x+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\\ \Theta))\sqrt{\alpha}\varphi_x))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{31} = (\alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_x)\psi_z+\\ (((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\varphi_x)\varphi_z)+\\ \sqrt{\alpha}(((2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_y+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\\ \Theta))\sqrt{\alpha}\varphi_y))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{32} = (\alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_y)\psi_z+\\ (((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\psi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\varphi_y)\varphi_z)+\\ \sqrt{\alpha}(((-2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_x+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\\ \Theta))\sqrt{\alpha}\varphi_x))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{33} = ((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_z\psi_z+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+4\sin(2\Theta))\varphi_z\psi_z+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\varphi_z\varphi_z+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\psi_y\psi_y+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-4\sin(2\Theta))\varphi_y\psi_y+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_y\varphi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\psi_x\psi_x+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-4\sin(2\Theta))\varphi_x\psi_x+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_x\varphi_x+\\ (8\cos(2\cos(\Theta)\alpha^{1/4})\mathrm{ch}(2\sin(\Theta)\alpha^{1/4})+8) \sqrt{\alpha})/(16\sqrt{\alpha}) \end{array} $$ $$ \begin{array}{c} A_{34} = -(\alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\psi_x+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_x)\psi_z+\\ ((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_x)\varphi_z)+\\ \sqrt{\alpha}(((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_y+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\\ \Theta))\sqrt{\alpha}\varphi_y))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{35} = -(\alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\psi_y+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_y)\psi_z+\\ ((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_y)\varphi_z)+\\ \sqrt{\alpha}(((-2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_x+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\\ \Theta))\sqrt{\alpha}\varphi_x))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{36} = (((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\psi_z\psi_z+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+4\cos(2\Theta))\varphi_z\psi_z+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\varphi_z\varphi_z+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\psi_y\psi_y+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-4\cos(2\Theta))\varphi_y\psi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_y\varphi_y+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\psi_x\psi_x+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-4\cos(2\Theta))\varphi_x\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_x\varphi_x-\\ 8\sin(2\cos(\Theta)\alpha^{1/4}) \mathrm{sh}(2\sin(\Theta)\alpha^{1/4})\sqrt{\alpha})/ (16\sqrt{\alpha}) \end{array} $$ $$ \begin{array}{c} A_{41} = (((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\psi_z\psi_z+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+4\cos(2\Theta))\varphi_z\psi_z+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\varphi_z\varphi_z+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\psi_y\psi_y+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+4\cos(2\Theta))\varphi_y\psi_y+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\varphi_y\varphi_y+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\psi_x\psi_x+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-4\cos(2\Theta))\varphi_x\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_x\varphi_x+\\ 8\sin(2\cos(\Theta)\alpha^{1/4}) \mathrm{sh}(2\sin(\Theta)\alpha^{1/4})\sqrt{\alpha})/ (16\sqrt{\alpha}) \end{array} $$ $$ \begin{array}{c} A_{42} = (\sqrt{\alpha}(((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_z+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\varphi_z)+\\ \alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\psi_x+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_x)\psi_y+\\ ((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+\\ 2\sin(2\Theta))\varphi_x)\varphi_y))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{43} = (\alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\psi_x+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_x)\psi_z+\\ ((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_x)\varphi_z)+\\ \sqrt{\alpha}(((-2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_y+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\\ \Theta))\sqrt{\alpha}\varphi_y))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{44} = (((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\psi_z\psi_z+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-4\sin(2\Theta))\varphi_z\psi_z+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_z\varphi_z+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\psi_y\psi_y+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-4\sin(2\Theta))\varphi_y\psi_y+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_y\varphi_y+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_x\psi_x+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+4\sin(2\Theta))\varphi_x\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\varphi_x\varphi_x+\\ (8\cos(2\cos(\Theta)\alpha^{1/4})\mathrm{ch}(2\sin(\Theta)\alpha^{1/4})+\\ 8)\sqrt{\alpha})/ (16\sqrt{\alpha}) \end{array} $$ $$ \begin{array}{c} A_{45} = (\sqrt{\alpha}(((2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_z+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\varphi_z)+\\ \alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_x)\psi_y+\\ (((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\\ 2\Theta)+2\cos(2\Theta))\varphi_x)\varphi_y))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{46} = (\alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_x)\psi_z+\\ (((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\varphi_x)\varphi_z)+\\ \sqrt{\alpha}(((-2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_y+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\\ \Theta))\sqrt{\alpha}\varphi_y))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{51} = (\sqrt{\alpha}(((-2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_z+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\varphi_z)+\\ \alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\psi_x+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_x)\psi_y+\\ ((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-\\ 2\Theta)+2\sin(2\Theta))\varphi_x)\varphi_y))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{52} = (((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\psi_z\psi_z+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+4\cos(2\Theta))\varphi_z\psi_z+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\varphi_z\varphi_z+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\psi_y\psi_y+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-4\cos(2\Theta))\varphi_y\psi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_y\varphi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\psi_x\psi_x+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+4\cos(2\Theta))\varphi_x\psi_x+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\varphi_x\varphi_x+\\ 8\sin(2\cos(\Theta)\alpha^{1/4}) \mathrm{sh}(2\sin(\Theta)\alpha^{1/4})\sqrt{\alpha})/ (16\sqrt{\alpha}) \end{array} $$ $$ \begin{array}{c} A_{53} = (\alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\psi_y+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_y)\psi_z+\\ ((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_y)\varphi_z)+\\ \sqrt{\alpha}(((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_x+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\\ \Theta))\sqrt{\alpha}\varphi_x))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{54} = (\sqrt{\alpha}(((-2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_z+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\varphi_z)+\\ \alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_x)\psi_y+\\ (((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+\\ 2\cos(2\Theta))\varphi_x)\varphi_y))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{55} = (((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\psi_z\psi_z+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-4\sin(2\Theta))\varphi_z\psi_z+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_z\varphi_z+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_y\psi_y+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+4\sin(2\Theta))\varphi_y\psi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\varphi_y\varphi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\psi_x\psi_x+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-4\sin(2\Theta))\varphi_x\psi_x+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_x\varphi_x+\\ (8\cos(2\cos(\Theta)\alpha^{1/4})\mathrm{ch}(2\sin(\Theta)\alpha^{1/4})+\\ 8)\sqrt{\alpha})/ (16\sqrt{\alpha}) \end{array} $$ $$ \begin{array}{c} A_{56} = (\alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_y)\psi_z+\\ (((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\psi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\varphi_y)\varphi_z)+\\ \sqrt{\alpha}(((2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_x+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\\ \Theta))\sqrt{\alpha}\varphi_x))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{61} = (\alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\psi_x+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_x)\psi_z+\\ ((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_x)\varphi_z)+\\ \sqrt{\alpha}(((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_y+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\\ \Theta))\sqrt{\alpha}\varphi_y))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{62} = (\alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\psi_y+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_y)\psi_z+\\ ((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_y)\varphi_z)+\\ \sqrt{\alpha}(((-2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_x+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\\ \Theta))\sqrt{\alpha}\varphi_x))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{63} = ((e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\psi_z\psi_z+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-4\cos(2\Theta))\varphi_z\psi_z+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_z\varphi_z+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\psi_y\psi_y+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+4\cos(2\Theta))\varphi_y\psi_y+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\varphi_y\varphi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\psi_x\psi_x+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+4\cos(2\Theta))\varphi_x\psi_x+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\sin(2\Theta))\varphi_x\varphi_x+\\ 8\sin(2\cos(\Theta)\alpha^{1/4}) \mathrm{sh}(2\sin(\Theta)\alpha^{1/4})\sqrt{\alpha})/ (16\sqrt{\alpha}) \end{array} $$ $$ \begin{array}{c} A_{64} = (\alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_x)\psi_z+\\ (((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\psi_x+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\varphi_x)\varphi_z)+\\ \sqrt{\alpha}(((2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_y+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\\ \Theta))\sqrt{\alpha}\varphi_y))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{65} = (\alpha^{3/4}(((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\varphi_y)\psi_z+\\ (((-e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\sin(2\Theta))\psi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\varphi_y)\varphi_z)+\\ \sqrt{\alpha}(((-2e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-\Theta))\sqrt{\alpha}\psi_x+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-\\ \Theta))\sqrt{\alpha}\varphi_x))/(8\alpha^{5/4}) \end{array} $$ $$ \begin{array}{c} A_{66} = ((e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\psi_z\psi_z+\\ ((-2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)+4\sin(2\Theta))\varphi_z\psi_z+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\varphi_z\varphi_z+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\psi_y\psi_y+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-4\sin(2\Theta))\varphi_y\psi_y+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_y\varphi_y+\\ ((-e^{2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-e^{-2\sin(\Theta)\alpha^{1/4}}) \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)+2\cos(2\Theta))\psi_x\psi_x+\\ ((2e^{2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ (-2e^{-2\sin(\Theta)\alpha^{1/4}}) \sin(2\cos(\Theta)\alpha^{1/4}-2\Theta)-4\sin(2\Theta))\varphi_x\psi_x+\\ (e^{2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}+2\Theta)+\\ e^{-2\sin(\Theta)\alpha^{1/4}} \cos(2\cos(\Theta)\alpha^{1/4}-2\Theta)-2\cos(2\Theta))\varphi_x\varphi_x+\\ (8\cos(2\cos(\Theta)\alpha^{1/4})\mathrm{ch}(2\sin(\Theta)\alpha^{1/4})+\\ 8)\sqrt{\alpha})/ (16\sqrt{\alpha}) \end{array} $$ Функция $\mathrm{arctg}(\alpha_1/\alpha_0)$ здесь указывается символически, по правилам математики. В реальных вычислениях, разумеется, она должна быть заменена на функцию $\mathrm{atan2}(\alpha_1,\alpha_0)$, которая корректно учитывает как квадранты так и возможный нулевой параметр $\alpha_0$.
Оператор группы Лоренца
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