{
  "sage_version": "10.9",
  "similarities": {
    "A1*": "Gram(A1*) = Gram(A1)/4",
    "A2*": "Gram(A2*) = diag(1,-1) Gram(A2) diag(1,-1)/3",
    "D4*": {
      "squared_scale": "1/2",
      "unimodular_change": [
        [
          "1",
          "0",
          "0",
          "0"
        ],
        [
          "-1",
          "1",
          "0",
          "-1"
        ],
        [
          "0",
          "-1",
          "1",
          "1"
        ],
        [
          "0",
          "0",
          "-1",
          "1"
        ]
      ]
    },
    "E8*": "Integral Gram matrix of determinant 1 proves E8 is self-dual.",
    "D3=A3": "Equal Gram matrices after permuting the D3 basis."
  },
  "omitted_dual_moments": "Exact positive nth powers agree for A1/A1*, A2/A2*, D4/D4*.",
  "conversion": "With v=t^n, I=s/t^n and G=s/(n*t^(n+2)); conversion checked exactly for n=1..24.",
  "stored_entries_checked_exactly": 114,
  "entries_also_compared_with_source_formulas": 72
}