Part 1: X-basis computations (ranks mod P1 = mod P2 asserted)
  phi = [1, 2, 3, 0, 4]  cycle type [4, 1] : H_A=[1, 5, 4, 4, 5] H_B=[1, 5, 21, 85, 331] H_K=[1, 5, 21, 89, 376]  H_A(t)H_B(-t)=[1, 0, 0, 4, -25]  first failure weight: 3
  phi = [1, 2, 3, 4, 5, 6, 7, 0]  cycle type [8] : H_A=[1, 8, 4, 1] H_B=[1, 8, 60, 435] H_K=[1, 8, 60, 449]  H_A(t)H_B(-t)=[1, 0, 0, 14]  first failure weight: 3
  phi = [1, 2, 0, 4, 3]  cycle type [3, 2] : H_A=[1, 5, 4, 4, 5] H_B=[1, 5, 21, 89, 361] H_K=[1, 5, 21, 89, 376]  H_A(t)H_B(-t)=[1, 0, 0, 0, -15]  first failure weight: 4
  phi = [1, 2, 3, 4, 5, 0]  cycle type [6] : H_A=[1, 6, 3, 1, 1] H_B=[1, 6, 33, 173, 883] H_K=[1, 6, 33, 181, 992]  H_A(t)H_B(-t)=[1, 0, 0, 8, -61]  first failure weight: 3
  phi = [1, 2, 0, 3]  cycle type [3, 1] : H_A=[1, 4, 4, 4, 5] H_B=[1, 4, 12, 36, 98] H_K=[1, 4, 12, 36, 107]  H_A(t)H_B(-t)=[1, 0, 0, 0, -9]  first failure weight: 4
  phi = [1, 0, 3, 2]  cycle type [2, 2] : H_A=[1, 4, 4, 4, 5] H_B=[1, 4, 12, 36, 104] H_K=[1, 4, 12, 36, 107]  H_A(t)H_B(-t)=[1, 0, 0, 0, -3]  first failure weight: 4
  phi = [1, 2, 3, 4, 0]  cycle type [5] : H_A=[1, 5, 3, 1, 1] H_B=[1, 5, 22, 96, 407] H_K=[1, 5, 22, 96, 418]  H_A(t)H_B(-t)=[1, 0, 0, 0, -11]  first failure weight: 4

Part 2: cyclic racks Z/m (eigenbasis blocks mod p)
  prime p = 880803841 (p = 1 mod 840)
  Z/2: H_A=[1, 2, 1, 1, 1, 1, 1, 1] H_B=[1, 2, 3, 5, 8, 13, 21, 34] H_K=[1, 2, 3, 5, 8, 13, 21, 34]
        H_A(t)H_B(-t)=[1, 0, 0, 0, 0, 0, 0, 0] ; first n with B_n != K_n: None ; first Euler failure weight: None
  Z/3: H_A=[1, 3, 2, 1, 1, 1, 1] H_B=[1, 3, 7, 16, 33, 64, 113] H_K=[1, 3, 7, 16, 36, 81, 182]
        H_A(t)H_B(-t)=[1, 0, 0, 0, -3, 8, -24] ; first n with B_n != K_n: 4 ; first Euler failure weight: 4
  Z/4: H_A=[1, 4, 2, 1, 1, 1] H_B=[1, 4, 14, 47, 152, 489] H_K=[1, 4, 14, 49, 171, 597]
        H_A(t)H_B(-t)=[1, 0, 0, 2, -11, 36] ; first n with B_n != K_n: 3 ; first Euler failure weight: 3
  Z/5: H_A=[1, 5, 3, 1, 1, 1, 1] H_B=[1, 5, 22, 96, 407, 1706, 7036] H_K=[1, 5, 22, 96, 418, 1820, 7924]
        H_A(t)H_B(-t)=[1, 0, 0, 0, -11, 59, -351] ; first n with B_n != K_n: 4 ; first Euler failure weight: 4
  Z/6: H_A=[1, 6, 3, 1, 1, 1] H_B=[1, 6, 33, 173, 883, 4437] H_K=[1, 6, 33, 181, 992, 5437]
        H_A(t)H_B(-t)=[1, 0, 0, 8, -61, 370] ; first n with B_n != K_n: 3 ; first Euler failure weight: 3
  Z/7: H_A=[1, 7, 4, 1, 1, 1] H_B=[1, 7, 45, 286, 1788, 11092] H_K=[1, 7, 45, 288, 1842, 11781]
        H_A(t)H_B(-t)=[1, 0, 0, 2, -40, 319] ; first n with B_n != K_n: 3 ; first Euler failure weight: 3
  Z/8: H_A=[1, 8, 4, 1, 1, 1] H_B=[1, 8, 60, 435, 3109, 21883] H_K=[1, 8, 60, 449, 3359, 25129]
        H_A(t)H_B(-t)=[1, 0, 0, 14, -138, 1302] ; first n with B_n != K_n: 3 ; first Euler failure weight: 3
