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EXAMPLE
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a(2) = 11 because there are 11 cyclotomic cosets of 3 mod 100:
O(0) = {0},
O(1) = {1, 3, 9, 27, 81, 43, 29, 87, 61, 83, 49, 47, 41, 23, 69, 7, 21, 63, 89, 67},
O(2) = {2, 6, 18, 54, 62, 86, 58, 74, 22, 66, 98, 94, 82, 46, 38, 14, 42, 26, 78, 34},
O(4) = {4, 12, 36, 8, 24, 72, 16, 48, 44, 32, 96, 88, 64, 92, 76, 28, 84, 52, 56, 68},
O(5) = {5, 15, 45, 35},
O(10) = {10, 30, 90, 70},
O(11) = {11, 33, 99, 97, 91, 73, 19, 57, 71, 13, 39, 17, 51, 53, 59, 77, 31, 93, 79, 37},
O(20) = {20, 60, 80, 40},
O(25) = {25, 75},
O(50) = {50},
O(55) = {55, 65, 95, 85}.
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