0 | 0 | 1 | 0 | 0 |

1 | $-1$ | $2y$ | 0 | 2 |

1 | 1 | $2x$ | 2 | 0 |

2 | $-2$ | $2\sqrt{6}xy$ | $2\sqrt{6}y$ | $2\sqrt{6}x$ |

2 | 0 | $\sqrt{3}(2({x}^{2}+{y}^{2})-1)$ | $4\sqrt{3}x$ | $4\sqrt{3}y$ |

2 | 2 | $\sqrt{6}({x}^{2}-{y}^{2})$ | $2\sqrt{6}x$ | $-2\sqrt{6}y$ |

3 | $-3$ | $2\sqrt{2}y(3{x}^{2}-{y}^{2})$ | $12\sqrt{2}xy$ | $6\sqrt{2}({x}^{2}-{y}^{2})$ |

3 | $-1$ | $2\sqrt{2}y[3({x}^{2}+{y}^{2})-2]$ | $12\sqrt{2}xy$ | $2\sqrt{2}(3{x}^{2}+9{y}^{2}-2)$ |

3 | 1 | $2\sqrt{2}x[3({x}^{2}+{y}^{2})-2]$ | $2\sqrt{2}(9{x}^{2}+3{y}^{2}-2)$ | $12\sqrt{2}xy$ |

3 | 3 | $2\sqrt{2}x({x}^{2}-3{y}^{2})$ | $6\sqrt{2}({x}^{2}-{y}^{2})$ | $-12\sqrt{2}xy$ |

4 | $-4$ | $4\sqrt{10}xy({x}^{2}-{y}^{2})$ | $-4\sqrt{10}y({y}^{2}-3{x}^{2})$ | $4\sqrt{10}x({x}^{2}-3{y}^{2})$ |

4 | $-2$ | $2\sqrt{10}xy[4({x}^{2}+{y}^{2})\u20133]$ | $2\sqrt{10}y(12{x}^{2}+4{y}^{2}-3)$ | $2\sqrt{10}x(4{x}^{2}+12{y}^{2}-3)$ |

4 | 0 | $\sqrt{5}[6{({x}^{2}+{y}^{2})}^{2}-6({x}^{2}+{y}^{2})+1]$ | $12\sqrt{5}x[2({x}^{2}+{y}^{2})-1]$ | $12\sqrt{5}y[2({x}^{2}+{y}^{2})\u20131]$ |

4 | 2 | $\sqrt{10}({x}^{2}-{y}^{2})[4({x}^{2}+{y}^{2})-3]$ | $2\sqrt{10}x(8{x}^{2}-3)$ | $2\sqrt{10}y(3-8{y}^{2})$ |

4 | 4 | $\sqrt{10}({x}^{4}-6{x}^{2}{y}^{2}+{y}^{4})$ | $4\sqrt{10}x({x}^{2}-3{y}^{2})$ | $-4\sqrt{10}y({y}^{2}-3{x}^{2})$ |

5 | $-5$ | $2\sqrt{3}({x}^{4}y-10{x}^{2}{y}^{3}+{y}^{5})$ | $40\sqrt{3}xy({x}^{2}-{y}^{2})$ | $10\sqrt{3}({x}^{4}-6{x}^{2}{y}^{2}+{y}^{4})$ |

5 | $-3$ | $2\sqrt{3}y(3{x}^{2}-{y}^{2})[5({x}^{2}+{y}^{2})-4]$ | $8\sqrt{3}xy(15{x}^{2}+5{y}^{2}-6)$ | $2\sqrt{3}[15{x}^{4}-6{x}^{2}(5{y}^{2}-2)-{y}^{2}(25{y}^{2}-12)]$ |

5 | $-1$ | $2\sqrt{3}y[10{({x}^{2}+{y}^{2})}^{2}-12({x}^{2}+{y}^{2})+3]$ | $16\sqrt{3}xy(5{x}^{2}+5{y}^{2}-3)$ | $2\sqrt{3}[50{x}^{4}+12{x}^{2}(5{y}^{2}\u20133)+2{y}^{2}(5{y}^{2}\u20136)+3]$ |

5 | 1 | $2\sqrt{3}x[10{({x}^{2}+{y}^{2})}^{2}\u201312({x}^{2}+{y}^{2})+3]$ | $2\sqrt{3}(50{x}^{4}+12(5{y}^{2}-3){x}^{2}+10{y}^{4}-12{y}^{2}+3)$ | $16\sqrt{3}xy[5({x}^{2}+{y}^{2})\u20133]$ |

5 | 3 | $2\sqrt{3}x({x}^{2}\u20133{y}^{2})[5({x}^{2}+{y}^{2})\u20134]$ | $2\sqrt{3}[25{x}^{4}-6{x}^{2}({y}^{2}+2)-3{y}^{2}(5{y}^{2}-4)]$ | $-8\sqrt{3}xy(5{x}^{2}+15{y}^{2}-6)$ |

5 | 5 | $2\sqrt{3}({x}^{5}-10{x}^{3}{y}^{2}+5x{y}^{4})$ | $10\sqrt{3}({x}^{4}-6{y}^{2}{x}^{2}+{y}^{4})$ | $-40\sqrt{3}xy({x}^{2}-{y}^{2})$ |

6 | $-6$ | $2\sqrt{14}xy(3{x}^{4}-10{x}^{2}{y}^{2}+3{y}^{4})$ | $6\sqrt{14}y(5{x}^{4}-10{y}^{2}{x}^{2}+{y}^{4})$ | $6\sqrt{14}x({x}^{4}\u201310{x}^{2}{y}^{3}+5{y}^{5})$ |

6 | $-4$ | $4\sqrt{14}xy({x}^{2}-{y}^{2})[6({x}^{2}+{y}^{2})-5]$ | $4\sqrt{14}y(30{x}^{4}-15{x}^{2}-6{y}^{4}+5{y}^{2}$ | $4\sqrt{14}x(30{y}^{4}-15{y}^{2}-6{x}^{4}+5{x}^{2})$ |

6 | $-2$ | $2\sqrt{14}xy[15{({x}^{2}+{y}^{2})}^{2}-20({x}^{2}+{y}^{2})+6]$ | $2\sqrt{14}y[5(5{x}^{2}+{y}^{2})(3({x}^{2}+{y}^{2})-4)+40{x}^{2}+6]$ | $2\sqrt{14}x[5({x}^{2}+5{y}^{2})(3({x}^{2}+{y}^{2})-4)+40{y}^{2}+6]$ |

6 | 0 | $\sqrt{7}[20{({x}^{2}+{y}^{2})}^{3}-30{({x}^{2}+{y}^{2})}^{2}+12({x}^{2}+{y}^{2})-1]$ | $24\sqrt{7}x[1+5({x}^{2}+{y}^{2})({x}^{2}+{y}^{2}-1)]$ | $24\sqrt{7}y[1+5({x}^{2}+{y}^{2})({x}^{2}+{y}^{2}-1)]$ |

6 | 2 | $\sqrt{14}({x}^{2}-{y}^{2})[15{({x}^{2}+{y}^{2})}^{2}-20({x}^{2}+{y}^{2})+6]$ | $2\sqrt{14}x[15({x}^{2}+{y}^{2})(3{x}^{2}-{y}^{2})-40{x}^{2}+6]$ | $2\sqrt{14}y[15({x}^{2}+{y}^{2})({x}^{2}-3{y}^{2})+40{y}^{2}-6]$ |

6 | 4 | $\sqrt{14}({x}^{4}-6{x}^{2}{y}^{2}+{y}^{4})[6({x}^{2}+{y}^{2})-5]$ | $4\sqrt{14}x(9{x}^{4}-5(6{y}^{2}+1){x}^{2}-15{y}^{2}({y}^{2}-1))$ | $4\sqrt{14}y(9{x}^{4}-5{y}^{2}(6{x}^{2}+1)-15{x}^{2}({x}^{2}-1))$ |

6 | 6 | $\sqrt{14}[{x}^{6}-15{x}^{2}{y}^{2}({x}^{2}-{y}^{2})-{y}^{6}]$ | $6\sqrt{14}x({x}^{4}-10{y}^{2}{x}^{2}+5{y}^{4})$ | $-6\sqrt{14}y(5{x}^{4}-10{x}^{2}{y}^{2}+{y}^{4})$ |