Description of the implementation: The way I set it up was to start with the nine solutions (d,e) such that A_{si+ga}(d) is divisible by 81 (with no restriction on e of course, i.e., e congruent 0 mod 1), and then, one by one, combine with the solutions (d,e) obtained when considering the moduli m = 5, 8, 11, 13, 37, 41, 61. The list of solutions is attached in each case. The way to read these data is (except for m=81) {d(m)/2, e(m), list of solutions} where each element in has the form {d, {r, e}} where r is A_{si+ga}(d) mod m. ------------------------------------------------------------------ m = 81: The solutions d mod 4212 are d = 483, 1113, 1293, 1491, 2391, 2655, 2691, 3891, 4161. m = 5: {312, 4, {{3, {3, 1}}, {9, {2, 3}}, {21, {1, 0}}, {27, {4, 2}}, {33, {3, 1}}, {39, {3, 1}}, {45, {1, 0}}, {51, {4, 2}}, {57, {2, 3}}, {63, {4, 2}}, {69, {2, 3}}, {75, {1, 0}}, {81, {2, 3}}, {87, {3, 1}}, {93, {3, 1}}, {99, {4, 2}}, {105, {3, 1}}, {111, {3, 1}}, {117, {3, 1}}, {123, {3, 1}}, {129, {2, 3}}, {147, {2, 3}}, {153, {3, 1}}, {165, {2, 3}}, {171, {1, 0}}, {177, {4, 2}}, {183, {3, 1}}, {201, {4, 2}}, {207, {3, 1}}, {213, {2, 3}}, {219, {3, 1}}, {225, {2, 3}}, {231, {4, 2}}, {237, {2, 3}}, {255, {3, 1}}, {285, {2, 3}}, {291, {1, 0}}, {297, {1, 0}}, {303, {2, 3}}, {315, {1, 0}}, {321, {2, 3}}, {327, {4, 2}}, {333, {3, 1}}, {345, {1, 0}}, {351, {1, 0}}, {357, {3, 1}}, {369, {2, 3}}, {381, {2, 3}}, {387, {3, 1}}, {393, {2, 3}}, {399, {1, 0}}, {405, {1, 0}}, {417, {1, 0}}, {423, {1, 0}}, {429, {1, 0}}, {435, {1, 0}}, {441, {2, 3}}, {447, {4, 2}}, {453, {4, 2}}, {459, {2, 3}}, {465, {1, 0}}, {471, {4, 2}}, {477, {2, 3}}, {483, {3, 1}}, {495, {1, 0}}, {501, {4, 2}}, {507, {4, 2}}, {519, {1, 0}}, {525, {2, 3}}, {531, {1, 0}}, {537, {2, 3}}, {549, {2, 3}}, {555, {4, 2}}, {561, {4, 2}}, {567, {1, 0}}, {573, {4, 2}}, {579, {4, 2}}, {585, {4, 2}}, {591, {4, 2}}, {597, {2, 3}}, {603, {3, 1}}, {609, {3, 1}}, {615, {2, 3}}, {621, {4, 2}}}} m = 8: {10, 2, {{1, {1, 0}}, {3, {3, 1}}, {5, {1, 0}}, {7, {3, 1}}}} m = 13: {84, 3, {{3, {3, 1}}, {21, {9, 2}}, {63, {1, 0}}, {105, {3, 1}}}} m = 11: {120, 5, {{3, {3, 1}}, {15, {1, 0}}, {39, {5, 3}}, {87, {3, 1}}, {99, {1, 0}}, {111, {1, 0}}, {117, {1, 0}}, {123, {3, 1}}, {165, {4, 4}}, {177, {1, 0}}, {183, {4, 4}}, {219, {1, 0}}, {225, {4, 4}}}} m = 37: {1368, 18, {{3, {3, 1}}, {9, {7, 4}}, {21, {25, 17}}, {39, {21, 5}}, {51, {4, 7}}, {63, {4, 7}}, {69, {10, 12}}, {81, {7, 4}}, {105, {9, 2}}, {111, {28, 11}}, {117, {4, 7}}, {123, {25, 17}}, {129, {28, 11}}, {135, {28, 11}}, {141, {28, 11}}, {153, {1, 0}}, {159, {1, 0}}, {165, {11, 15}}, {183, {4, 7}}, {189, {34, 10}}, {201, {10, 12}}, {207, {9, 2}}, {225, {4, 7}}, {249, {21, 5}}, {255, {9, 2}}, {267, {36, 9}}, {297, {27, 3}}, {315, {26, 6}}, {327, {12, 8}}, {333, {25, 17}}, {345, {34, 10}}, {351, {30, 13}}, {375, {33, 16}}, {381, {11, 15}}, {405, {27, 3}}, {417, {16, 14}}, {423, {36, 9}}, {435, {28, 11}}, {447, {12, 8}}, {459, {26, 6}}, {465, {36, 9}}, {477, {3, 1}}, {483, {21, 5}}, {495, {16, 14}}, {507, {33, 16}}, {513, {33, 16}}, {519, {16, 14}}, {525, {25, 17}}, {537, {36, 9}}, {543, {26, 6}}, {555, {34, 10}}, {585, {26, 6}}, {597, {30, 13}}, {615, {11, 15}}, {627, {12, 8}}, {639, {1, 0}}, {645, {9, 2}}, {651, {34, 10}}, {657, {21, 5}}, {663, {3, 1}}, {687, {26, 6}}, {699, {10, 12}}, {711, {25, 17}}, {717, {33, 16}}, {723, {9, 2}}, {729, {12, 8}}, {753, {21, 5}}, {771, {33, 16}}, {777, {36, 9}}, {789, {25, 17}}, {801, {3, 1}}, {813, {33, 16}}, {819, {1, 0}}, {885, {36, 9}}, {897, {9, 2}}, {903, {12, 8}}, {915, {33, 16}}, {921, {3, 1}}, {939, {11, 15}}, {945, {28, 11}}, {951, {7, 4}}, {957, {34, 10}}, {975, {9, 2}}, {981, {3, 1}}, {987, {10, 12}}, {993, {3, 1}}, {999, {3, 1}}, {1005, {34, 10}}, {1023, {4, 7}}, {1047, {4, 7}}, {1053, {27, 3}}, {1059, {12, 8}}, {1083, {27, 3}}, {1089, {30, 13}}, {1095, {9, 2}}, {1107, {12, 8}}, {1113, {7, 4}}, {1119, {28, 11}}, {1125, {25, 17}}, {1131, {34, 10}}, {1137, {36, 9}}, {1143, {3, 1}}, {1155, {10, 12}}, {1161, {34, 10}}, {1167, {28, 11}}, {1179, {3, 1}}, {1191, {21, 5}}, {1203, {21, 5}}, {1251, {27, 3}}, {1269, {34, 10}}, {1311, {11, 15}}, {1317, {1, 0}}, {1335, {27, 3}}, {1341, {4, 7}}, {1365, {34, 10}}, {1383, {36, 9}}, {1401, {11, 15}}, {1407, {25, 17}}, {1419, {36, 9}}, {1431, {25, 17}}, {1443, {10, 12}}, {1455, {26, 6}}, {1461, {7, 4}}, {1467, {25, 17}}, {1485, {7, 4}}, {1497, {16, 14}}, {1503, {1, 0}}, {1515, {27, 3}}, {1545, {28, 11}}, {1563, {25, 17}}, {1569, {34, 10}}, {1581, {25, 17}}, {1599, {26, 6}}, {1611, {30, 13}}, {1617, {25, 17}}, {1629, {9, 2}}, {1635, {4, 7}}, {1647, {16, 14}}, {1653, {33, 16}}, {1659, {11, 15}}, {1665, {34, 10}}, {1671, {36, 9}}, {1683, {36, 9}}, {1695, {34, 10}}, {1713, {10, 12}}, {1719, {36, 9}}, {1725, {9, 2}}, {1737, {30, 13}}, {1743, {11, 15}}, {1755, {11, 15}}, {1773, {21, 5}}, {1779, {16, 14}}, {1785, {28, 11}}, {1791, {30, 13}}, {1821, {7, 4}}, {1827, {36, 9}}, {1833, {10, 12}}, {1875, {9, 2}}, {1881, {28, 11}}, {1887, {28, 11}}, {1899, {30, 13}}, {1905, {10, 12}}, {1929, {30, 13}}, {1935, {9, 2}}, {1947, {34, 10}}, {1959, {9, 2}}, {1965, {1, 0}}, {1989, {16, 14}}, {1995, {28, 11}}, {2001, {9, 2}}, {2007, {28, 11}}, {2025, {3, 1}}, {2031, {4, 7}}, {2043, {25, 17}}, {2067, {30, 13}}, {2079, {4, 7}}, {2091, {33, 16}}, {2097, {12, 8}}, {2103, {7, 4}}, {2121, {25, 17}}, {2139, {7, 4}}, {2151, {34, 10}}, {2163, {28, 11}}, {2169, {21, 5}}, {2193, {28, 11}}, {2205, {16, 14}}, {2217, {12, 8}}, {2229, {28, 11}}, {2241, {26, 6}}, {2259, {27, 3}}, {2271, {34, 10}}, {2283, {7, 4}}, {2289, {4, 7}}, {2295, {27, 3}}, {2301, {10, 12}}, {2313, {33, 16}}, {2325, {34, 10}}, {2331, {3, 1}}, {2337, {11, 15}}, {2355, {30, 13}}, {2361, {4, 7}}, {2367, {26, 6}}, {2373, {36, 9}}, {2391, {3, 1}}, {2397, {36, 9}}, {2403, {12, 8}}, {2421, {21, 5}}, {2427, {28, 11}}, {2433, {12, 8}}, {2445, {4, 7}}, {2469, {33, 16}}, {2511, {26, 6}}, {2529, {27, 3}}, {2535, {16, 14}}, {2559, {25, 17}}, {2565, {9, 2}}, {2583, {27, 3}}, {2595, {3, 1}}, {2601, {4, 7}}, {2607, {12, 8}}, {2625, {7, 4}}, {2631, {27, 3}}, {2643, {16, 14}}, {2649, {9, 2}}, {2661, {4, 7}}, {2673, {1, 0}}, {2679, {33, 16}}, {2685, {30, 13}}, {2691, {1, 0}}, {2709, {7, 4}}, {2721, {30, 13}}, {2727, {34, 10}}, {2733, {36, 9}}}} m = 41: {240, 8, {{3, {3, 1}}, {27, {3, 1}}, {81, {40, 4}}, {105, {14, 7}}, {129, {38, 5}}, {141, {32, 6}}, {189, {40, 4}}, {207, {14, 7}}, {261, {38, 5}}, {279, {38, 5}}, {285, {27, 3}}, {291, {32, 6}}, {297, {38, 5}}, {303, {32, 6}}, {321, {14, 7}}, {333, {27, 3}}, {369, {3, 1}}, {429, {1, 0}}, {441, {14, 7}}, {471, {38, 5}}, {477, {40, 4}}}} m = 61: {226980, 10, {{3, {3, 1}}, {165, {3, 1}}, {177, {41, 9}}, {213, {52, 7}}, {231, {34, 8}}, {249, {58, 6}}, {279, {20, 4}}, {285, {20, 4}}, {297, {3, 1}}, {381, {9, 2}}, {387, {20, 4}}, {417, {9, 2}}, {435, {58, 6}}, {459, {34, 8}}, {489, {41, 9}}, {561, {58, 6}}, {567, {58, 6}}, {585, {52, 7}}, {597, {3, 1}}, {615, {41, 9}}, {645, {3, 1}}, {657, {60, 5}}, {759, {9, 2}}, {795, {20, 4}}, {831, {60, 5}}, {843, {27, 3}}, {849, {60, 5}}, {885, {27, 3}}, {909, {1, 0}}, {933, {1, 0}}, {963, {60, 5}}, {1041, {52, 7}}, {1101, {52, 7}}, {1113, {27, 3}}, {1119, {41, 9}}, {1185, {3, 1}}, {1257, {52, 7}}, {1269, {1, 0}}, {1317, {41, 9}}, {1407, {52, 7}}, {1461, {58, 6}}, {1539, {60, 5}}, {1563, {60, 5}}, {1623, {20, 4}}, {1731, {60, 5}}, {1737, {60, 5}}, {1749, {58, 6}}, {1755, {52, 7}}, {1767, {58, 6}}, {1779, {41, 9}}, {1809, {9, 2}}, {1851, {60, 5}}, {1887, {52, 7}}, {1929, {20, 4}}, {1965, {52, 7}}, {1995, {1, 0}}, {2013, {3, 1}}, {2031, {41, 9}}, {2103, {20, 4}}, {2145, {34, 8}}, {2151, {20, 4}}, {2175, {27, 3}}, {2205, {52, 7}}, {2247, {3, 1}}, {2283, {60, 5}}, {2289, {1, 0}}, {2337, {60, 5}}, {2409, {34, 8}}, {2415, {52, 7}}, {2439, {27, 3}}, {2505, {9, 2}}, {2565, {3, 1}}, {2577, {34, 8}}, {2637, {60, 5}}, {2643, {58, 6}}, {2649, {1, 0}}, {2697, {52, 7}}, {2709, {27, 3}}, {2727, {58, 6}}, {2763, {3, 1}}, {2799, {60, 5}}, {2829, {52, 7}}, {2883, {58, 6}}, {2943, {52, 7}}, {2949, {34, 8}}, {2979, {34, 8}}, {2985, {52, 7}}, {3069, {9, 2}}, {3111, {34, 8}}, {3183, {58, 6}}, {3249, {20, 4}}, {3261, {60, 5}}, {3273, {27, 3}}, {3285, {9, 2}}, {3399, {20, 4}}, {3417, {3, 1}}, {3531, {60, 5}}, {3549, {60, 5}}, {3561, {41, 9}}, {3579, {58, 6}}, {3705, {20, 4}}, {3735, {58, 6}}, {3807, {20, 4}}, {3813, {3, 1}}, {3855, {52, 7}}, {3951, {20, 4}}, {4041, {27, 3}}, {4065, {27, 3}}, {4095, {3, 1}}, {4131, {9, 2}}, {4179, {58, 6}}, {4185, {27, 3}}, {4191, {34, 8}}, {4233, {52, 7}}, {4281, {58, 6}}, {4305, {27, 3}}, {4311, {60, 5}}, {4359, {20, 4}}, {4371, {52, 7}}, {4383, {60, 5}}, {4395, {41, 9}}, {4413, {9, 2}}, {4461, {41, 9}}, {4581, {3, 1}}, {4599, {1, 0}}, {4635, {60, 5}}, {4689, {52, 7}}, {4713, {60, 5}}, {4719, {34, 8}}, {4773, {34, 8}}, {4833, {27, 3}}, {4845, {9, 2}}, {4887, {34, 8}}, {4893, {3, 1}}, {4959, {34, 8}}, {5007, {34, 8}}, {5013, {34, 8}}, {5055, {3, 1}}, {5067, {60, 5}}, {5139, {3, 1}}, {5193, {27, 3}}, {5223, {1, 0}}, {5265, {20, 4}}, {5283, {9, 2}}, {5343, {3, 1}}, {5445, {41, 9}}, {5547, {34, 8}}, {5589, {3, 1}}, {5643, {3, 1}}, {5655, {20, 4}}, {5661, {1, 0}}, {5673, {3, 1}}, {5775, {60, 5}}, {5787, {58, 6}}, {5811, {9, 2}}, {5835, {9, 2}}, {5853, {9, 2}}, {5979, {20, 4}}, {6015, {20, 4}}, {6021, {20, 4}}, {6081, {60, 5}}, {6099, {58, 6}}, {6147, {3, 1}}, {6165, {9, 2}}, {6195, {52, 7}}, {6213, {58, 6}}, {6225, {58, 6}}, {6303, {52, 7}}, {6357, {20, 4}}, {6399, {20, 4}}, {6417, {9, 2}}, {6429, {3, 1}}, {6441, {58, 6}}, {6471, {41, 9}}, {6501, {27, 3}}, {6519, {9, 2}}, {6549, {41, 9}}, {6567, {1, 0}}, {6579, {41, 9}}, {6669, {34, 8}}, {6693, {34, 8}}, {6699, {3, 1}}, {6705, {1, 0}}, {6711, {9, 2}}, {6747, {9, 2}}, {6783, {58, 6}}, {6873, {9, 2}}, {6885, {52, 7}}, {6915, {9, 2}}, {6933, {1, 0}}, {6939, {34, 8}}, {6981, {34, 8}}, {6993, {60, 5}}, {7077, {52, 7}}, {7155, {34, 8}}, {7167, {27, 3}}, {7179, {58, 6}}, {7197, {20, 4}}, {7299, {20, 4}}, {7305, {41, 9}}, {7377, {41, 9}}, {7389, {20, 4}}, {7395, {41, 9}}, {7443, {34, 8}}, {7461, {9, 2}}, {7491, {27, 3}}, {7521, {34, 8}}, {7533, {27, 3}}, {7545, {20, 4}}, {7581, {9, 2}}, {7611, {20, 4}}, {7683, {52, 7}}, {7689, {52, 7}}, {7695, {20, 4}}, {7701, {60, 5}}, {7725, {34, 8}}, {7809, {1, 0}}, {7869, {1, 0}}, {7917, {27, 3}}, {7923, {1, 0}}, {7953, {52, 7}}, {7965, {20, 4}}, {7989, {58, 6}}, {8031, {58, 6}}, {8043, {41, 9}}, {8091, {1, 0}}, {8103, {3, 1}}, {8139, {3, 1}}, {8277, {52, 7}}, {8289, {3, 1}}, {8319, {9, 2}}, {8331, {1, 0}}, {8397, {20, 4}}, {8499, {34, 8}}, {8721, {27, 3}}, {8733, {1, 0}}, {8805, {20, 4}}, {8817, {27, 3}}, {8853, {41, 9}}, {8865, {52, 7}}, {8955, {27, 3}}, {8961, {41, 9}}, {8973, {52, 7}}, {9003, {9, 2}}, {9009, {60, 5}}, {9021, {34, 8}}, {9039, {34, 8}}, {9081, {58, 6}}, {9255, {60, 5}}, {9357, {9, 2}}, {9387, {52, 7}}, {9405, {34, 8}}, {9435, {52, 7}}, {9441, {20, 4}}, {9453, {52, 7}}, {9471, {52, 7}}, {9477, {3, 1}}, {9495, {34, 8}}, {9567, {41, 9}}, {9621, {27, 3}}, {9675, {1, 0}}, {9777, {1, 0}}, {9837, {41, 9}}, {9855, {27, 3}}, {9867, {41, 9}}, {9873, {1, 0}}, {9921, {20, 4}}, {9975, {52, 7}}, {10071, {27, 3}}, {10083, {58, 6}}, {10089, {3, 1}}, {10095, {9, 2}}, {10101, {27, 3}}, {10143, {41, 9}}, {10185, {27, 3}}, {10191, {20, 4}}, {10215, {27, 3}}, {10221, {41, 9}}, {10227, {20, 4}}, {10233, {58, 6}}, {10239, {3, 1}}, {10275, {3, 1}}, {10359, {34, 8}}, {10389, {41, 9}}, {10395, {9, 2}}, {10437, {3, 1}}, {10455, {1, 0}}, {10533, {58, 6}}, {10575, {1, 0}}, {10599, {52, 7}}, {10623, {1, 0}}, {10647, {58, 6}}, {10707, {27, 3}}, {10749, {20, 4}}, {10773, {58, 6}}, {10815, {34, 8}}, {10923, {60, 5}}, {10989, {41, 9}}, {11073, {34, 8}}, {11103, {60, 5}}, {11121, {20, 4}}, {11169, {60, 5}}, {11205, {9, 2}}, {11343, {1, 0}}, {11385, {27, 3}}, {11397, {3, 1}}, {11559, {20, 4}}, {11595, {52, 7}}, {11607, {20, 4}}, {11643, {27, 3}}, {11715, {52, 7}}, {11739, {3, 1}}, {11805, {1, 0}}, {11877, {20, 4}}, {11943, {9, 2}}, {11961, {52, 7}}, {12051, {34, 8}}, {12075, {58, 6}}, {12135, {41, 9}}, {12183, {1, 0}}, {12261, {20, 4}}, {12267, {34, 8}}, {12273, {41, 9}}, {12291, {58, 6}}, {12303, {58, 6}}, {12309, {1, 0}}, {12321, {1, 0}}, {12345, {34, 8}}, {12435, {60, 5}}, {12519, {20, 4}}, {12549, {27, 3}}, {12561, {20, 4}}, {12639, {9, 2}}, {12705, {3, 1}}, {12729, {58, 6}}, {12753, {1, 0}}, {12765, {9, 2}}, {12783, {9, 2}}, {12789, {60, 5}}, {12849, {34, 8}}, {12879, {20, 4}}, {12915, {20, 4}}, {12933, {58, 6}}, {12987, {3, 1}}, {12999, {58, 6}}, {13005, {34, 8}}, {13017, {52, 7}}, {13035, {41, 9}}, {13047, {34, 8}}, {13113, {9, 2}}, {13167, {52, 7}}, {13173, {9, 2}}, {13221, {3, 1}}, {13245, {60, 5}}, {13317, {58, 6}}, {13329, {3, 1}}, {13347, {52, 7}}, {13407, {60, 5}}, {13449, {58, 6}}, {13509, {1, 0}}, {13581, {3, 1}}, {13659, {52, 7}}, {13707, {9, 2}}, {13785, {27, 3}}, {13851, {60, 5}}, {13917, {34, 8}}, {13935, {9, 2}}, {13953, {41, 9}}, {13977, {20, 4}}, {13989, {9, 2}}, {14061, {41, 9}}, {14091, {34, 8}}, {14103, {52, 7}}, {14175, {9, 2}}, {14265, {3, 1}}, {14313, {3, 1}}, {14343, {9, 2}}, {14349, {20, 4}}, {14373, {1, 0}}, {14385, {20, 4}}, {14439, {60, 5}}, {14445, {1, 0}}, {14463, {3, 1}}, {14469, {9, 2}}, {14499, {34, 8}}, {14589, {3, 1}}, {14619, {9, 2}}, {14643, {20, 4}}, {14649, {1, 0}}, {14781, {60, 5}}, {14877, {34, 8}}, {14907, {34, 8}}, {14913, {60, 5}}, {14919, {20, 4}}, {14961, {52, 7}}, {15033, {41, 9}}, {15051, {9, 2}}, {15135, {1, 0}}, {15165, {58, 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