格目录中的条目，这是一个联合项目
Gabriele Nebe，亚琛RWTH大学(nebe@math.rwth-aachen.de)和
尼尔·J·A·斯隆(njasloane@gmail.com)

上次修改时间：2014年7月18日星期五13:24:42 CEST

索引文件|缩写

此文件的内容

名称
仪表板集成模块
格拉姆
属性
最小_形式
亲吻_编号
THETA_系列
子组订单
子组名称
子组_发电机
参考文献
最后一行

• 名称
  第42.1页
  

• 仪表板集成模块
  42
  

• 格拉姆
  42 0
  4
  -2 4
  -2 1 4
  -1 2 -1 4
  -2 1 2 -1 4
  -2 0 0 0 0 4
  -2 0 0 1 0 1 4
  -2 2 1 2 0 0 2 4
  1 -2 -2 -1 0 1 0 -1 4
  -2 0 1 -1 2 1 2 1 0 4
  -2 1 0 0 0 2 1 0 0 1 4
  -1 2 2 0 2 -1 0 1 -1 0 -1 4
  -2 0 1 -1 1 2 2 1 1 2 1 1 4
  -2 2 1 0 2 0 1 0 1 1 2 1 4
  -1 2 -1 2 0 1 0 0 -1 0 1 0 0 0 4
  -2 1 2 1 0 0 1 2 -2 1 1 0 0 1 0 4
  -2 1 2 1 0 0 1 2 -2 0 0 1 1 1 0 2 4
  -1 2 0 2 -1 0 0 1 -1 -1 1 0 0 1 1 1 1 4
  -2 2 0 1 0 2 1 1 0 0 2 1 2 1 2 0 1 1 4
  -2 0 0 0 1 1 2 0 0 2 2 0 1 1 1 1 0 0 1 4
  -2 0 1 -1 2 2 0 0 1 1 1 0 1 1 0 0 0 -1 1 1 4
  -2 1 0 2 0 2 1 1 0 0 1 0 1 0 2 1 1 1 2 1 1 5
  -2 1 2 -1 2 0 1 1 -1 2 1 1 1 2 -1 1 1 0 0 1 1 0 5
  -2 1 0 0 1 2 1 1 1 1 2 0 2 1 1 0 0 0 2 1 2 1 0 5
  -2 2 1 0 2 0 0-1 2 1 0 2 1 1 1 0 1 2 1 1 1 2 6
  1 -1 0 -1 -1 -1 0 -1 -1 0 0 -1 -1 -1 -1 0 0 0 -1 0 -1 -1 0 -1 0 5
  -1 1 0 1 1 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 1 1 -1 2 1 -2 5
  -1 2 -1 1 1 1 0 0 0 0 1 1 0 1 2 -1 -1 0 2 1 1 0 0 2 1 -2 0 6
  1 -2 1 -1 -1 -1 0 0 0 0 -1 -1 0 -1 -2 1 1 0 -2 -1 -1 0 1 -1 -2 2 -1 -3 6
  -2 2 0 1 0 2 0 1 0 0 2 0 1 2 1 1 1 2 2 0 1 2 1 1 0 0 1 1 0 6
  -1 2 2 0 0 0 -1 1 -2 -1 1 1 0 1 0 1 2 1 1 -1 0 -1 0 1 1 1 1 0 0 1 6
  -2 1 0 0 0 2 2 1 0 2 2 0 2 1 1 1 0 1 2 2 1 1 0 2 1 0 -1 2 -1 2 -1 6
  -2 2 1 0 2 0 0 0 -1 1 2 1 0 2 1 1 0 1 1 2 1 0 1 2 3 1 1 1 -1 2 1 2 6
  1 0 -1 1 0 -2 -1 -1 -1 -1 -1 0 -2 0 1 0 0 0 -1 0 -1 -1 -1 -1 0 1 -1 1 -1 -1 0 -1 0 5
  1 -1 0 -1 -1 -1 0 -1 -1 0 0 -1 -1 -1 -1 0 0 0 -1 0 -1 -1 0 -2 1 2 -3 -1 0 -2 0 0 -1 0 5
  1 -2 0 -2 1 -1 0 -2 1 0 -1 0 0 0 -2 -1 -1 -1 -2 0 0 -2 1 0 0 0 -1 0 1 -2 -2 -1 0 0 1 6
  -2 1 0 0 1 2 1 1 1 1 2 0 2 1 1 0 0 0 2 1 2 1 1 2 0 -1 2 1 -1 2 1 1 1 -1 -2 -1 5
  -2 0 1 1 0 2 2 2 0 1 0 0 2 0 0 1 2 0 1 0 1 2 0 2 0 0 1 -1 1 1 0 1 -1 -1 -1 -1 0 6
  -2 0 1 1 0 1 1 1 0 0 1 0 1 1 0 2 2 1 1 1 1 2 0 0 0 0 0 -1 0 2 0 1 0 0 0 -1 1 2 5
  -2 2 0 1 0 2 0 1 0 0 2 0 1 2 1 1 1 2 2 0 1 1 1 2 0 -1 1 2 -1 4 1 2 2 0 -2 -1 2 0 1 6
  1-1 0-1 0-1 0-1-1-1-1 0 0 0-1 0-1 0-1 0-1-2 0 0 0 0 1-1 0-1 0-1 1-2 1 0-1 5
  -2 0 2 0 2 0 2 1 -1 2 0 1 1 0 0 1 1 -1 0 2 1 0 2 1 0 0 -1 1 1 -1 -1 1 1 0 -1 1 0 2 1 -1 0 6
  

• 属性
  积分=1
  单模=1
  

• 最小_形式
  4
  

• 亲吻_编号
  44100
  

• THETA_系列
  1+44100*q^4+693504*q^5+42571200*q^6+907776000*q^7+13025848500*q^8+137700774400*q*9+O（q^10）
  

• 子组订单
  (2^4*3^2*5^3*7)^2
  

• 子组名称
  U3（5）xU3（五）
  

• 子组_发电机
  6
  42 42
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  -1 -2 2 1 -1 -1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 -1 0 0 0
  -6 1 0 0 -1 -2 -1 -2 0 -1 -1 0 0 0 -1 0 -1 -1 0 1 -1 -1 0 2 -1 0 0 -1 0 1 -1 0 -1 0 1 -1 0 0 -1 0 0 0
  -5 -2 -1 -2 -2 -3 0 -2 0 2 -1 1 -3 0 0 0 -1 1 1 -1 -1 1 0 1 -1 -1 0 0 -1 0 1 0 0 -1 0 0 1 1 0 0 0 0
  3 -2 -4 -2 1 1 1 -2 1 4 0 4 -4 -2 -1 3 2 4 1 -2 0 2 2 1 -1 -1 0 0 -2 0 2 0 1 0 0 0 1 0 0 -1 1 1
  -6 -2 4 -1 -5 -3 1 -1 0 1 -2 -2 -2 2 1 -3 -2 -1 1 -1 -1 0 -1 0 1 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 -1 0
  3 0 0 0 1 1 1-1 0 2-1 1-2 0-1 0 0 1 1 0 1 0 1 0 1 0-2 0-1 0 1 0 1 1 1 0 1 0 1 0 0 0 0 1
  -4 0 -3 1 1 -2 -2 -1 -1 -1 0 1 1 -1 0 1 -1 -1 0 1 0 -1 0 0 0 1 -1 0 0 -1 0 0 -1 -2 -1 0 0 1 0 1 0 -1
  -6 -3 5 0 -4 -5 0 -1 1 0 -1 -2 -1 2 2 -2 -2 -1 0 0 -1 0 -1 0 0 0 0 0 -1 1 0 0 -1 -1 0 0 0 1 -1 1 -1 0
  -6 -1 5 0 -4 -3 0 0 0 -1 -1 -3 0 3 1 -3 -2 -2 0 0 -1 0 -2 0 1 0 0 0 0 1 -1 0 -1 0 0 0 0 0 -1 1 -1 0
  -1 2 1 0 -2 0 0 -1 0 0 -1 -1 0 0 0 -1 0 -1 0 0 0 -1 0 0 1 -1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 -1 0
  -4 0 0 -3 -2 -1 0 2 0 0 1 -1 0 1 1 -1 -1 0 0 -1 0 1 -1 -2 0 1 1 1 0 -1 0 0 0 0 -1 1 -1 0 0 0 0 0
  -9 1 0 -5 -4 -3 0 -1 0 1 -1 -1 -3 1 -1 -2 -2 0 1 -1 -2 2 -1 0 -1 -1 2 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1
  -3 -1 2 3 -1 -2 -1 -1 -1 -1 -1 -1 1 1 1 -1 -1 -2 0 1 0 -2 -1 1 1 0 -1 0 1 1 -1 0 -1 -1 0 0 0 0 0 0 -1 -1
  0 -2 -4 0 2 0 -1 0 0 0 1 2 0 -2 0 2 1 1 0 -1 0 0 2 -1 0 1 0 0 -1 -1 1 1 0 -1 -1 0 0 0 0 0 1 0
  -5 0 -6 -3 1 -2 0 -4 0 1 -1 3 -2 -2 -2 3 0 2 0 -1 -1 1 1 1 -2 0 0 0 -1 -1 1 0 0 -1 0 -1 1 1 0 0 1 0
  -1 4 1 2 0 1 -1 1 0 -3 0 -2 4 0 0 -1 -1 -3 -1 2 1 -2 -1 0 1 0 0 -1 2 1 -1 0 -1 1 1 0 -1 -1 0 0 -1 0
  1-8 5 1-2-3 2-1 0 3-1 0-4 3 2-1 0 2 1-2 0 1 0-1 1-3 1 0 0-2-1 0 2 1-1 0 0 0
  -2 -5 7 5 -2 -3 -1 2 0 -2 0 -3 2 3 3 -3 -2 -3 0 1 0 -1 -1 -1 2 1 -1 0 0 1 0 1 -1 -1 -1 1 0 0 -1 1 -1 -1
  -9 1 1 2 -2 -4 -3 -2 0 -2 -1 -1 1 0 0 -1 -2 -3 0 2 -1 -2 -1 1 0 0 0 -1 1 1 -1 1 -2 -1 1 0 0 1 -1 1 -1 -1
  0 -2 -3 -3 -1 -1 1 -2 1 3 0 2 -3 0 0 2 1 3 0 -3 0 3 1 -1 -1 0 0 1 -2 -2 2 0 1 -1 -1 0 1 1 0 0 1 1
  -4 -2 2 -1 -1 -3 0 0 0 0 0 -1 -1 1 1 -1 -1 0 0 0 -1 1 0 0 -1 1 0 1 -1 -1 0 0 0 -1 -1 0 0 1 0 0 0 -1
  42 42
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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  0-1 5 3-2-1 0-1 1 0-1 0-1 0-1 0-1 0-1 1 1 0 0 0 2-1 0-1 0 1 0 1 0-1 0-1 0-1 0-1 0-1 0-1 0
  1 -2 6 1 -2 -1 1 2 0 0 0 -3 0 3 2 -3 -1 -1 0 0 0 0 -1 -1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 -1 0
  3 1 -2 4 4 1 -2 0 0 -2 1 1 3 -2 0 2 1 -1 -1 2 1 -2 1 1 0 1 -1 -1 0 0 0 1 -1 -1 0 0 0 0 0 0 0 -1
  -2 0 -2 2 1 -1 -1 -3 0 0 -1 2 0 -1 -1 2 0 0 0 1 0 -1 0 2 0 0 -1 -1 0 1 0 0 -1 -1 1 -1 1 0 -1 0 0 0
  -1 -2 2 -1 -2 -1 1 -1 0 2 -1 0 -3 1 0 -1 0 1 1 -1 -1 1 0 1 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0
  0 -1 -1 2 2 -1 -1 0 -1 -1 0 0 1 0 0 0 -1 -1 0 1 0 0 0 0 0 0 0 -1 0 0 1 1 -1 -1 0 0 0 0 0 1 0 0
  3 3 -6 -1 4 3 -1 1 0 -1 2 2 2 -3 -1 3 2 1 -1 0 1 0 2 -1 -1 1 0 1 0 -2 0 0 1 0 -1 0 -1 0 1 -1 1 -1
  2 -2 6 3 -1 -1 0 1 1 0 0 -2 0 1 2 -2 0 -1 0 1 0 -1 0 0 1 0 0 0 0 1 0 1 -1 0 0 1 0 0 0 0 -1 -1
  -1 -2 2 -1 -2 -1 1 -1 0 2 -1 0 -3 1 0 -1 0 1 1 -1 -1 1 0 1 0 -1 0 0 -1 1 0 0 0 0 0 0 1 0 0 0 0 0
  2 1 -4 -2 2 2 0 1 -1 0 1 1 0 -1 -1 1 1 1 0 -1 0 1 1 -1 0 0 0 0 0 -2 1 0 1 0 -1 0 0 0 1 0 1 0
  -3 2 -2 -1 -1 0 0 -3 1 1 -1 2 -1 -2 -1 2 1 1 0 0 0 -1 1 2 -1 0 0 0 0 0 -1 0 0 0 0 -1 0 0 0 -1 0 -1
  -1-1 3 4 0-2-1-1 0-1-1-1 1 0 1-1-2 0 2 0-2 0 1 0-1 0 1 1 1-1 0 0 0 0 1-1 1 1-1 1 1 1-1
  1 1 -4 -4 1 2 1 1 -1 1 1 1 -1 0 -1 1 1 2 0 -2 0 2 0 -1 -1 0 0 1 0 -2 0 -1 2 1 -1 0 0 0 1 -1 1 0
  -3 2 -2 -1 -1 0 0 -2 0 0 -1 1 0 -1 -1 1 0 0 0 0 0 -1 0 1 0 0 0 0 1 0 -1 -1 0 0 1 -1 0 0 0 0 0 0
  0 1 1 5 2 -1 -2 0 0 -3 0 -1 4 -1 1 0 -1 -3 -1 3 1 -3 0 0 1 1 -1 -1 1 1 0 1 -2 -1 0 1 -1 0 0 1 -1 -1
  0 0 1 -3 -1 0 1 3 0 0 1 -2 0 1 1 -2 -1 0 0 -1 0 2 0 -2 0 0 1 1 0 -1 1 0 1 1 -1 1 -1 0 1 0 0 0
  -3 -2 0 1 -1 -2 0 -4 0 2 -2 2 -3 0 -1 1 0 1 1 0 -1 0 0 3 -1 -1 -1 -1 -1 1 0 0 -1 -1 1 -1 2 1 -1 0 0 0
  -3 0 -3 -4 -2 0 1 -3 1 3 -1 3 -4 -1 -2 2 1 3 1 -2 -1 2 1 2 -2 -1 1 0 -1 0 0 -1 1 1 1 -1 1 0 0 -1 1 1
  4 1 0 0 2 2 0 3 0 -1 2 -1 2 0 1 0 1 0 -1 0 1 0 0 -2 0 1 0 1 0 -1 0 0 1 0 -1 1 -1 0 1 0 0 -1
  -3 1 -3 1 1 -1 -1 -3 0 0 -1 2 0 -2 -1 2 0 0 0 1 0 -1 1 2 -1 0 -1 -1 0 0 0 0 -1 -1 0 -1 0 0 0 0 1 -1
  0 0 0 0 0 0 0 -1 1 1 0 1 -1 -1 0 1 1 1 0 0 0 0 1 1 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 -1 0 0
  42 42
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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  5 1 1 0 1 3 2 2 -1 0 0 -1 1 1 0 -1 0 0 0 0 1 0 -1 0 1 -1 -1 0 1 0 0 -1 1 1 0 0 0 -1 1 0 0 0
  3 3 -4 -5 0 4 3 -2 0 4 -1 3 -4 -1 -3 2 2 4 1 -2 0 2 0 2 -1 -2 0 0 0 0 0 -2 2 2 1 -1 1 -1 1 -2 1 1
  -6 -2 -1 0 -1 -3 -1 -1 -1 0 -1 0 -1 0 0 -1 -2 -1 1 0 -1 0 0 0 0 0 0 -1 0 0 1 1 -1 -1 0 0 0 0 0 1 0 0
  5 1 -1 2 2 2 1 -2 0 1 -1 2 0 -1 -1 2 1 1 0 1 1 -1 0 2 0 -1 -1 -1 0 1 0 -1 0 0 1 -1 1 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 -1 3 4 0 -2 -1 -1 0 -1 -1 -1 1 0 1 -1 -1 -2 0 2 0 -2 0 1 1 0 -1 -1 1 1 0 1 -2 -1 0 0 0 0 0 1 -1 -1
  -6 -5 4 6 -1 -6 -3 -2 0 -2 -1 -1 1 1 2 -1 -2 -3 0 2 -1 -2 0 1 1 1 -1 -1 -1 2 0 2 -3 -3 0 0 1 1 -2 2 -1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
  -1 -1 3 4 0 -2 -1 -1 0 -1 -1 -1 1 0 1 -1 -1 -2 0 2 0 -2 0 1 1 0 -1 -1 0 1 0 1 -1 -1 0 0 0 0 0 1 -1 -1
  -5 -1 -4 -4 -1 -1 0 0 -1 1 0 1 -2 0 -1 0 -1 1 1 -2 -1 2 0 -1 -1 -1 1 0 0 -1 1 0 1 1 0 0 0 0 0 0 1 1
  -3 2 -5 -8 -2 1 2 -2 1 3 0 2 -4 -1 -2 2 2 4 0 -4 -1 3 1 0 -2 0 2 2 -1 -2 0 -1 2 1 0 -1 0 0 1 -2 1 1
  4 1 -1 -1 1 2 2 0 0 0 0 0 1 0 0 1 1 1 -1 -1 1 0 0 -1 1 0 -1 1 0 -1 0 -1 1 0 -1 0 0 0 1 0 0 0
  -3 0 -3 1 1 -2 -2 -1 0 -1 0 1 1 -2 0 1 -1 -1 0 1 0 -1 1 0 0 0 0 -1 0 0 1 1 -1 -1 0 0 0 1 0 1 0 0
  -3 -2 2 -1 -2 -1 1 0 -1 1 -1 -1 -2 2 0 -2 -1 0 1 -1 -1 1 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
  -5-4 1 2-1-4-2-1 0-1 0 0 1 1 0-1 0-1 0 0 0 1 0-1 0 0 1 0-1 0 1-1-1-2 0 1 1-1 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
  0 2 2 -1 -3 1 2 -3 1 2 -2 0 -2 1 -1 0 1 1 0 -1 0 0 -1 2 0 -1 0 0 0 1 -1 -1 0 1 1 -1 1 -1 0 -1 0 1
  2 -3 4 4 2 -1 -1 3 -1 -2 1 -2 2 1 2 -2 -1 -2 0 2 0 -1 0 -1 1 1 -1 0 0 0 0 1 -1 -1 -1 1 0 0 0 1 0 -1
  42 42
  -1 0 -1 -2 1 1 0 1 0 -1 0 0 -1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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  -4 2 0 0 -3 -2 0 -3 1 1 -1 0 0 -1 -1 0 0 -1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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  -2 -2 -2 -1 1 0 -1 2 -1 -1 1 1 0 0 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
  4 1 -1 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
  42 42
  4 2 0 1 1 1 0 -1 0 0 0 0 1 -1 -1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 0 0 0 -1 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -2 0 1 0 -1 -1 0 0 0 0 0 -1 0 1 0 -1 -1 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 2 -1 0 0 0 0 -1 1 0 0 0 1 -1 0 1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -3 -3 0 -1 0 -1 0 1 -1 0 0 0 -1 1 1 -1 -1 0 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 -4 0 0 0 0 0 2 -1 0 1 1 -1 1 1 -1 -1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -2 0 0-1-1 0 1 0 1 0 0 1-1 0 0 0-1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -2 2 0 0 -2 -1 0 -1 1 0 0 0 1 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -4 -1 -1 1 1 0 2 -1 0 1 2 -2 0 1 0 0 1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -3 -2 1 0 -2 -1 0 0 0 1 0 1 -1 1 1 -1 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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  -3 1 1 0 -2 -1 0 -1 1 0 -1 -1 0 1 0 0 -1 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 3 0 1 0 0 0 -1 1 0 0 -1 1 0 -1 0 1 -1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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  -5 -2 1 -2 -2 -1 0 1 1 0 -1 0 -2 1 2 -1 -1 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -3 -4 -1 -2 0 0 0 2 -1 0 0 1 -2 1 1 -1 -1 1 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -3 -2 0 -1 -1 -1 0 1 0 0 0 0 -1 1 1 -1 -1 0 0 -1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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  -2 -4 0 -1 0 0 0 2 -1 0 0 1 -2 1 1 -1 -1 1 1 -1 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -3 -2 1 -1 -1 -1 0 1 0 0 -1 -1 -1 1 1 -1 -1 0 1 -1 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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  -3 -3 0 -1 -1 -1 0 1 -1 0 0 0 -1 1 1 -1 -1 0 1 -1 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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  0 -2 1 1 0 -1 0 1 -1 0 0 -1 0 1 0 -1 -1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
  2 1 0 1 1 0 0 0 0 0 0 -1 1 0 -1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
  -2 -2 1 0 -1 -1 0 1 0 0 0 0 -1 1 1 -1 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
  -3 -2 1 -1 -1 -1 0 1 0 0 -1 -1 -1 1 1 -1 -1 0 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
  2 3 0 0 1 1 0 -1 1 0 -1 -1 1 -1 -1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
  3 3 0 1 1 1 0 -1 1 0 0 0 1 -1 -1 1 1 0 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
  1 -1 0 0 1 1 0 1 -1 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
  -2 -4 0 -1 0 0 0 2 -1 0 0 1 -2 1 1 -1 -1 1 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
  0 0 -1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
  0 0 -1 -1 1 1 0 1 0 0 0 0 -1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
  0 -2 1 1 0 -1 0 1 -1 0 0 -1 0 1 0 -1 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
  4 0 -2 0 3 2 0 1 -1 0 1 1 0 -1 -1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
  -3 0 -1 -2 -1 0 0 0 1 0 0 1 -1 0 1 0 0 0 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
  42 42
  -2 0 -2 -1 0 0 -1 0 0 0 0 1 0 -1 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1-1 2 1 0 0 1-1 0 0-1 0 1 0-1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 1 0 0 -1 0 0 0 0 0 -1 0 0 0 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 1 1 0 0 1 0 0 0 0 -1 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 1 0 -1 0 1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 1 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 1 -1 -1 0 0 0 0 1 0 0 0 0 -1 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 1 1 0 -2 -1 0 -1 1 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  3 -1 1 1 1 1 1 1 -1 0 1 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 1 0 0 -1 0 0 0 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 2 0-1-1 1 0 0-1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 1 0 0 0 0 1 -1 0 0 -1 0 1 0 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 2 2 0 0 0 0 -1 0 0 -1 1 1 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  4 -2 1 0 2 2 1 2 -1 0 0 0 -1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 2 1 0 0 1 0 0 0 0 -1 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  4 2 1 1 1 1 1 -1 0 0 0 -1 1 0 -1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  3 2 0 1 1 0 1 -1 0 0 0 -1 1 0 -1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 0 2 1 0 0 1 0 0 0 0 -1 0 1 0 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 0 2 1 0 0 1 0 0 0-1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  4 -1 2 1 1 1 1 1 -1 0 0 -1 0 1 0 -1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 -1 0 1 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 0 1 0 -1 -1 0 0 0 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 0 3 1 0 0 1 0 0 0 0 -2 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -2 0 -3 -1 0 0 -1 0 0 0 0 2 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 -3 3 1 0 0 1 2 -1 0 0 -1 -1 2 1 -2 -1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
  1 -2 0 1 1 0 0 1 -1 0 0 0 0 1 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
  2 0 2 1 0 0 1 0 0 0 0 -1 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
  4 -1 2 1 1 1 1 1 -1 0 0 -1 0 1 0 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
  1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
  1 0 -1 0 1 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
  0 -1 0 -1 0 0 0 1 0 0 0 0 -1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
  2 0 2 1 0 0 1 0 0 0 0 -1 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
  -1 1 0 0 -1 -1 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
  3 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
  2-3 3 1 0 1 2-1 0-1-1 2 1-2-1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
  -1 0 -3 0 1 0 -1 0 -1 0 0 1 1 -1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
  1 3 -1 0 0 0 0 -2 1 0 0 0 1 -1 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
  

• 参考文献
  对于F=Gram矩阵，构造为Q（F，1,3,10）
  （C2 x PSU（3.5））。尺寸21的S3，如所述
  C.Bachoc和G.Nebe，与Mathieu群M22相关的最小8个极端晶格，
  J.reine angew。Mathematik，494（1998），155-171
  

• 最后一行
  

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  加布里埃尔·内布