Code and Computations

Here are the SageMath worksheets used to establish the tables below:
Abelian Surfaces
Abelian Threefolds
Abelian Fourfolds




n < 1,000 where 2 is a common index divisors with dim A = 2
a3 a2 p-rank non-monogenic n
-3 5 2 3, 19, 31, 57, 61, 93, 171, 183, 589, 981
-2 2 0 5, 7, 9, 13, 15, 21, 35, 37, 39, 45, 51, 61, 63, 65, 85, 91, 105, 109, 111, 117, 119, 133, 135, 153, 171, 185, 189, 195, 205, 219, 221, 241, 247, 255, 259, 273, 285, 305, 315, 325, 327, 333, 351, 357, 365, 377, 399, 455, 481, 485, 511, 513, 533, 545, 555, 565, 585, 595, 657, 663, 665, 673, 679, 703, 723, 741, 763, 765, 771, 777, 793, 819, 855, 873, 945, 949, 981, 999
-2 3 2 7, 47
-1 -1 2 5, 9, 11, 15, 23, 37, 43, 45, 67, 111, 127, 135, 151, 185, 203, 301, 333, 555, 999
-1 0 1 47
-1 1 2 3, 9, 103, 127
-1 3 2 5, 15, 59
0 -3 2 3, 5, 9, 11, 15, 23, 29, 33, 37, 45, 53, 87, 111, 135, 137, 185, 203, 233, 281, 301, 333, 555, 999
0 -2 0 3, 5, 7, 9, 11, 13, 15, 19, 21, 27, 33, 35, 39, 43, 45, 51, 57, 63, 65, 67, 73, 77, 81, 85, 91, 93, 99, 105, 109, 111, 117, 119, 129, 133, 135, 151, 153, 171, 185, 189, 195, 201, 217, 219, 221, 231, 241, 247, 255, 259, 273, 279, 285, 301, 315, 327, 331, 333, 337, 341, 351, 357, 365, 381, 387, 399, 441, 453, 455, 481, 485, 511, 513, 545, 555, 585, 595, 603, 627, 651, 657, 663, 665, 673, 679, 683, 693, 703, 723, 741, 763, 765, 771, 777, 819, 855, 873, 889, 903, 921, 945, 949, 981, 993, 999
0 -1 2 3, 17, 19, 23, 31, 57, 61, 93, 171, 183, 229, 589, 981
0 1 2 3, 9, 17, 19, 23, 47, 57, 61, 69, 93, 171, 183, 229, 981
0 2 0 3, 5, 7, 9, 13, 15, 19, 21, 27, 31, 35, 39, 45, 49, 51, 57, 63, 65, 73, 77, 85, 89, 91, 93, 99, 105, 109, 111, 117, 119, 127, 133, 135, 151, 153, 161, 171, 185, 189, 195, 217, 219, 221, 231, 241, 247, 255, 259, 273, 279, 285, 301, 315, 327, 331, 333, 337, 341, 351, 357, 365, 381, 387, 399, 441, 453, 455, 481, 485, 511, 513, 545, 553, 555, 585, 595, 623, 631, 651, 657, 663, 665, 673, 679, 693, 703, 721, 723, 741, 763, 765, 771, 777, 819, 855, 873, 889, 903, 945, 949, 981, 993, 999
1 -1 2 5, 7, 9, 11, 15, 37, 43, 45, 67, 79, 111, 135, 185, 203, 301, 333, 555, 999
1 0 1 47
1 1 2 3, 9
1 3 2 5, 15, 59
2 2 0 5, 7, 9, 13, 15, 21, 35, 37, 39, 45, 51, 61, 63, 65, 85, 91, 105, 109, 111, 117, 119, 133, 135, 153, 171, 185, 189, 195, 205, 219, 221, 241, 247, 255, 259, 273, 285, 305, 315, 325, 327, 333, 351, 357, 365, 377, 399, 455, 481, 485, 511, 513, 533, 545, 555, 565, 585, 595, 657, 663, 665, 673, 679, 703, 723, 741, 763, 765, 771, 777, 793, 819, 855, 873, 945, 949, 981, 999
2 3 2 7, 47
3 5 2 3, 19, 31, 57, 61, 93, 171, 183, 589, 981





n < 500 where 3 is a common index divisors with dim A = 2
a3 a2 p-rank non-monogenic n
-4 8 2 2, 4, 5, 8, 10, 16, 17, 20, 32, 34, 40, 68, 73, 82, 88, 136, 140, 146, 164, 170, 194, 238, 272, 280, 328, 340, 365, 388, 451, 476, 485
-3 5 2 2, 4, 29, 488
-3 7 2 2, 4, 10, 19, 20, 40, 44, 80
-2 1 2 2, 4, 13, 19, 20, 38, 40, 76, 86, 136, 140, 170, 194, 238, 272, 280, 340, 388, 476, 485
-2 2 2 2, 4, 8, 10, 14, 28, 29, 58, 82, 164, 205, 410
-2 4 2 2, 4, 8, 23
-2 5 2 2, 4, 23
-1 -2 2 2, 4, 5, 8, 10, 13, 16, 20, 31, 37, 40, 62, 74, 80, 124, 140, 148, 160, 185, 224, 280, 296, 370
-1 -1 2 2, 4, 23
-1 1 2 2, 4, 5, 80, 82, 100, 164, 200, 205, 328, 400, 410
-1 2 2 2, 4, 8, 16
-1 3 1 2, 4, 5, 17
-1 5 2 2, 4, 29, 31, 62, 124
0 -5 2 2, 4, 5, 8, 10, 16, 20, 25, 37, 40, 74, 80, 115, 140, 148, 160, 185, 224, 265, 280, 296, 335, 370
0 -4 2 2, 4, 7, 8, 14, 16, 28, 32, 56, 82, 164, 205, 328, 410
0 -2 2 2, 4, 8, 11, 17, 20, 22, 34, 68, 82, 136, 140, 164, 170, 194, 238, 272, 280, 340, 388, 433, 451, 476, 485
0 -1 2 2, 4, 8, 11, 13, 16, 26, 29, 32, 52, 103, 104, 208, 416
0 0 0 2, 4, 5, 8, 10, 13, 14, 16, 20, 25, 26, 28, 29, 32, 34, 35, 40, 41, 50, 52, 56, 58, 61, 64, 65, 68, 70, 73, 80, 82, 85, 88, 91, 100, 104, 110, 112, 121, 122, 130, 136, 140, 145, 146, 160, 164, 170, 176, 182, 193, 200, 205, 208, 220, 224, 242, 244, 260, 265, 272, 275, 280, 287, 290, 292, 305, 320, 328, 340, 364, 365, 386, 400, 410, 416, 440, 455, 464, 484, 488
0 1 2 2, 4, 8, 11, 13, 16, 26, 29, 32, 44, 52, 88, 104, 208, 416
0 3 0 2, 4, 7, 8, 13, 14, 16, 20, 26, 28, 35, 37, 40, 52, 56, 65, 70, 73, 74, 76, 80, 91, 104, 112, 121, 130, 133, 140, 143, 146, 148, 152, 160, 164, 182, 205, 208, 224, 242, 247, 259, 260, 266, 280, 286, 287, 292, 296, 328, 364, 365, 410, 416, 427, 433, 455, 481, 484, 488, 494
0 4 2 2, 4, 7, 8, 14, 16, 23, 28, 32, 56, 82, 164, 205, 328, 410
1 -2 2 2, 4, 5, 8, 10, 16, 20, 31, 37, 40, 62, 74, 80, 124, 140, 148, 160, 181, 185, 224, 280, 296, 370
1 -1 2 2, 4, 23
1 1 2 2, 4, 5, 80, 82, 100, 164, 200, 205, 328, 400, 410
1 2 2 2, 4, 8, 16
1 3 1 2, 4, 5, 17
1 5 2 2, 4, 29, 31, 62, 124
2 1 2 2, 4, 11, 19, 20, 38, 40, 76, 86, 136, 140, 170, 194, 238, 272, 280, 340, 388, 476, 485
2 2 2 2, 4, 8, 10, 14, 28, 29, 58, 82, 164, 205, 410
2 4 2 2, 4, 8, 23
2 5 2 2, 4, 23
3 5 2 2, 4, 29, 488
3 7 2 2, 4, 10, 11, 19, 20, 22, 40, 44, 80
4 8 2 2, 4, 5, 8, 10, 16, 17, 20, 32, 34, 40, 68, 73, 82, 88, 136, 140, 146, 164, 170, 194, 238, 272, 280, 328, 340, 365, 388, 451, 476, 485





n < 500 where 5 is a common index divisors with dim A = 2
a3 a2 p-rank non-monogenic n
-6 17 2 7, 12, 14, 21, 28, 42, 56, 84, 168, 217, 252, 434
-5 13 2 8
-5 15 0 11, 22, 24, 33, 44, 66, 71, 88, 124, 132, 142, 181, 213, 264, 284, 341, 362, 426, 429, 451, 492
-4 8 2 2, 4, 8, 16, 42, 56, 84, 168, 377
-4 9 2 4, 8
-4 11 2 8, 13, 26, 39, 48, 52, 72, 78, 104, 117, 122, 144, 156, 208, 234, 296, 312, 468, 481
-4 12 2 2, 4, 8, 16
-3 4 2 3, 6, 9, 12, 18, 27, 31, 36, 54, 72, 93, 186, 279, 333, 444
-3 5 1 4, 8
-3 7 2 3
-3 8 2 12, 13, 19, 26, 38, 39, 42, 52, 56, 78, 84, 91, 104, 156, 168, 182, 228, 234, 247, 273, 312, 342, 364, 468, 494
-3 9 2 4, 8
-3 11 2
-2 -1 2 13, 26, 39, 52, 72, 78, 104, 117, 156, 234, 312, 468, 481
-2 0 1 2, 4, 19
-2 1 2 72
-2 3 2 17
-2 4 2 2, 4, 6, 12, 24
-2 5 1
-2 6 2 2, 4, 19
-2 8 2 2, 4, 11
-2 9 2
-1 -5 1 19
-1 -4 2 7, 14, 28, 42, 56, 63, 72, 84, 126, 154, 168, 252
-1 -3 2 8, 24, 48
-1 -1 2 19, 22, 44, 88
-1 0 1
-1 1 2 8
-1 2 2 8, 48
-1 3 2 7, 24
-1 5 1 8
-1 6 2 8
-1 7 2
-1 9 2 8, 24, 48
0 -9 2 7, 8, 14, 16, 17, 28, 42, 48, 51, 56, 63, 72, 84, 96, 112, 122, 126, 144, 168, 224, 252, 288, 336
0 -8 2 2, 3, 4, 8, 16, 17, 32, 34, 39, 41, 48, 52, 68, 78, 82, 104, 136, 156, 208, 272, 312
0 -7 2 4, 8, 12, 13, 16, 19, 24, 26, 38, 39, 42, 48, 52, 56, 76, 78, 84, 91, 96, 104, 112, 152, 156, 168, 182, 208, 224, 228, 234, 247, 273, 304, 312, 336, 342, 364, 416, 456, 468, 494
0 -5 0 3, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 31, 36, 39, 42, 48, 52, 54, 56, 62, 63, 72, 78, 84, 91, 93, 104, 112, 117, 122, 124, 126, 144, 156, 168, 182, 183, 186, 189, 208, 217, 228, 234, 248, 252, 266, 273, 279, 312, 336, 342, 364, 366, 372, 378, 399, 403, 427, 434, 456, 468, 496
0 -4 2 2, 4, 8, 9, 11, 16, 18, 22, 72, 136, 272, 341, 342
0 -3 2 4, 8, 48, 72, 144
0 -2 2 2, 3, 4, 7, 11, 14, 21, 22, 42, 84
0 -1 2 8, 12, 16, 24, 48, 96, 296, 333, 444
0 0 0 2, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 41, 42, 48, 52, 56, 62, 63, 72, 78, 82, 84, 91, 93, 96, 104, 112, 117, 124, 126, 136, 144, 156, 168, 182, 186, 192, 204, 208, 217, 221, 234, 248, 252, 272, 273, 279, 312, 313, 336, 364, 372, 403, 408, 416, 426, 429, 434, 442, 451, 468, 481, 492, 496
0 2 2 2, 4, 7, 14, 21, 22, 42, 84, 217
0 3 2 8, 19, 29, 38, 48, 72, 144
0 4 2 2, 3, 4, 8, 9, 16, 18, 19, 22, 27, 57, 72, 136, 171, 272, 342
0 5 0 4, 7, 8, 9, 12, 14, 18, 19, 21, 24, 28, 31, 36, 38, 39, 42, 48, 52, 56, 62, 63, 72, 76, 78, 84, 91, 93, 104, 112, 117, 124, 126, 142, 144, 156, 168, 181, 182, 186, 208, 217, 228, 234, 248, 252, 266, 273, 279, 284, 312, 336, 341, 342, 362, 364, 372, 378, 399, 403, 434, 456, 468, 496
0 7 2 3, 6, 8, 11, 12, 13, 16, 18, 24, 26, 39, 42, 48, 52, 56, 78, 84, 91, 96, 104, 112, 156, 168, 182, 208, 224, 228, 234, 247, 273, 304, 312, 336, 342, 364, 416, 456, 468, 494
0 8 2 2, 4, 8, 16, 17, 32, 34, 39, 41, 48, 52, 68, 78, 82, 104, 136, 156, 208, 272, 312
1 -5 1 19
1 -4 2 7, 11, 14, 28, 42, 56, 63, 72, 84, 126, 154, 168, 252
1 -3 2 4, 8, 24, 48
1 -1 2 19, 22, 44, 88
1 0 1
1 1 2 4, 8
1 2 2 8, 48
1 3 2 7, 24
1 5 1 4, 8
1 6 2 8
1 7 2 11, 22
1 9 2 4, 8, 24, 48
2 -1 2 13, 26, 39, 52, 72, 78, 104, 117, 156, 234, 312, 468, 481
2 0 1 2, 4, 19
2 1 2 31, 72
2 3 2 17
2 4 2 2, 4, 6, 12, 24
2 5 1
2 6 2 2, 4, 19
2 8 2 2, 4
2 9 2
3 4 2 3, 6, 9, 12, 18, 27, 36, 54, 72, 93, 186, 279, 333, 444
3 5 1 8
3 7 2 3
3 8 2 12, 13, 19, 26, 38, 39, 42, 52, 56, 78, 84, 91, 104, 156, 168, 182, 228, 234, 247, 273, 312, 342, 364, 468, 494
3 9 2 8
3 11 2
4 8 2 2, 4, 8, 16, 42, 56, 84, 168, 377
4 9 2 4, 8
4 11 2 8, 13, 26, 39, 48, 52, 72, 78, 104, 109, 117, 122, 144, 156, 208, 234, 296, 312, 468, 481
4 12 2 2, 4, 8, 16, 31
5 13 2 4, 8
5 15 0 11, 22, 24, 33, 44, 66, 71, 88, 124, 132, 142, 181, 213, 264, 284, 341, 362, 426, 429, 451, 492
6 17 2 7, 12, 14, 21, 28, 42, 56, 84, 168, 217, 252, 434





n < 500 where 7 is a common index divisors with dim A = 2
a3 a2 p-rank non-monogenic n
-7 25 2 12
-6 18 2 6, 12, 24
-6 20 2 9, 11, 18
-6 21 1 51
-5 13 2 3, 6, 12, 18
-5 15 2 5, 40, 50, 100, 200
-5 16 2 3
-5 17 2
-5 19 2 3, 6, 12, 18
-4 8 2 8, 13, 26, 39, 78, 104, 156, 312
-4 10 2 34, 68, 136
-4 11 2 12, 24
-4 12 2 8
-4 13 2 4, 31, 279, 372
-4 15 2
-4 16 2 8, 279
-3 2 2 4, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 73, 80, 90, 120, 144, 146, 180, 219, 240, 292, 360, 365, 438
-3 3 2 11, 22, 44, 88
-3 5 2
-3 6 2 4, 80, 90, 120, 144, 180, 240, 360
-3 7 1 15
-3 8 2 12
-3 9 2 5, 15
-3 11 2 9
-3 12 2 10, 19, 20, 38, 90, 120, 180, 360
-3 13 2 29
-3 15 2
-2 -3 2 10, 20, 31, 209, 341, 418
-2 -2 2 3
-2 0 1 34, 68, 136
-2 1 2 3
-2 2 2 10, 15, 30, 34, 68, 95, 114, 136, 190, 228, 285, 380
-2 3 2 11
-2 4 2 3, 5, 10, 20, 40
-2 5 2 12
-2 7 1 3, 10, 20
-2 8 2 9, 18
-2 9 2 5
-2 10 2 3
-2 12 2 10
-2 13 2 3
-1 -8 2
-1 -7 1 9, 40
-1 -5 2 12, 37
-1 -4 2 12
-1 -3 2 11, 22, 44, 88
-1 -2 2 4
-1 -1 2
-1 0 1
-1 1 2 12
-1 3 2 40
-1 4 2
-1 5 2
-1 6 2 4
-1 7 1 12, 13
-1 9 2
-1 10 2 4
-1 11 2 9
-1 13 2 12, 40, 60, 120
0 -13 2 12, 13, 24, 26, 37, 39, 52, 74, 78, 80, 104, 120, 130, 156, 195, 208, 240, 260, 312, 390
0 -12 2 6, 8, 11, 12, 19, 24, 34, 38, 48, 51, 68, 90, 95, 102, 113, 114, 120, 136, 152, 171, 180, 190, 204, 209, 226, 228, 272, 285, 342, 360, 380, 408, 456
0 -10 2 5, 10, 15, 20, 29, 30, 40, 50, 55, 110, 275, 290
0 -9 2 16, 96, 144, 288
0 -8 2 8, 16, 32, 80, 120, 240
0 -7 0 4, 8, 9, 12, 16, 18, 19, 24, 36, 38, 43, 48, 57, 72, 76, 80, 86, 90, 95, 96, 100, 104, 114, 117, 120, 129, 130, 144, 150, 152, 156, 160, 171, 172, 180, 181, 190, 195, 200, 208, 215, 225, 228, 234, 240, 247, 258, 260, 285, 288, 300, 304, 312, 325, 342, 344, 360, 362, 380, 382, 387, 390, 400, 416, 430, 450, 456, 468, 473, 475, 480, 494
0 -6 2 6, 11, 12, 24, 117, 156, 234, 468
0 -5 2 5, 6, 10, 12, 15, 20, 24, 30, 40, 55, 60, 73, 80, 85, 120, 146, 219, 240, 275, 292, 365, 438
0 -4 2 8
0 -3 2 4, 80, 90, 120, 144, 180, 240, 360
0 -1 2 11, 12, 16, 24, 32, 48, 96, 192
0 0 0 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 25, 26, 30, 32, 40, 48, 50, 60, 64, 65, 75, 80, 86, 90, 95, 96, 100, 104, 114, 117, 120, 125, 129, 130, 144, 150, 152, 156, 160, 171, 172, 180, 181, 190, 192, 195, 200, 208, 215, 225, 228, 234, 240, 247, 250, 258, 260, 281, 285, 288, 300, 304, 312, 320, 325, 340, 342, 344, 360, 362, 380, 384, 387, 390, 400, 408, 416, 425, 430, 450, 456, 468, 475, 480, 494
0 1 2 4, 6, 8, 12, 16, 24, 32, 36, 48, 72, 96, 144, 192
0 2 2 9, 13, 18, 26, 37, 39, 78, 90, 117, 130, 156, 180, 195, 234, 260, 390, 468
0 3 2 80, 90, 120, 144, 180, 240, 360
0 4 2 8
0 6 2 6, 12, 24, 117, 156, 234, 468
0 7 0 6, 9, 12, 16, 18, 19, 24, 27, 36, 37, 38, 43, 48, 54, 57, 72, 74, 76, 80, 86, 90, 95, 96, 100, 104, 111, 114, 117, 120, 129, 130, 144, 150, 152, 156, 160, 171, 172, 180, 181, 190, 195, 200, 208, 215, 222, 225, 228, 234, 240, 247, 258, 260, 279, 285, 288, 300, 304, 312, 325, 333, 342, 344, 360, 362, 380, 387, 390, 400, 416, 430, 450, 456, 468, 475, 480, 494
0 8 2 8, 16, 29, 32, 80, 120, 240
0 9 2 4, 8, 16, 29, 96, 144, 248, 288
0 11 2 9, 12, 13, 18, 24, 26, 36, 37, 39, 52, 72, 74, 78, 104, 117, 144, 156, 208, 234, 312, 468
0 12 2 6, 8, 12, 19, 24, 34, 38, 48, 51, 68, 90, 95, 102, 114, 120, 136, 152, 171, 180, 190, 204, 226, 228, 272, 285, 342, 360, 380, 408, 456
1 -8 2 3
1 -7 1 9, 40
1 -5 2 3, 6, 12, 18, 37
1 -4 2 12
1 -3 2 11, 22, 44, 88
1 -2 2 3, 4
1 -1 2
1 0 1
1 1 2 3, 6, 12, 18
1 3 2 40
1 4 2 3
1 5 2
1 6 2 4
1 7 1 3, 6, 12, 13, 18
1 9 2
1 10 2 3, 4
1 11 2 9
1 13 2 3, 6, 12, 18, 19, 40, 60, 120
2 -3 2 10, 19, 20, 209, 341, 418
2 -2 2
2 0 1 34, 68, 136
2 1 2
2 2 2 10, 15, 30, 34, 68, 95, 114, 136, 190, 228, 285, 380
2 3 2 11
2 4 2 5, 10, 20, 40
2 5 2 12
2 7 1 10, 20
2 8 2 9, 18
2 9 2 5
2 10 2
2 12 2 10
2 13 2
3 2 2 4, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 73, 80, 90, 120, 144, 146, 180, 219, 240, 292, 360, 365, 438
3 3 2 11, 22, 44, 88
3 5 2
3 6 2 4, 80, 90, 120, 144, 180, 240, 360
3 7 1 15
3 8 2 12
3 9 2 5, 15
3 11 2 9
3 12 2 10, 20, 38, 90, 120, 180, 360
3 13 2 29
3 15 2
4 8 2 8, 13, 26, 39, 78, 104, 156, 312
4 10 2 3, 34, 68, 136
4 11 2 12, 24
4 12 2 8
4 13 2 3, 4, 279, 372
4 15 2
4 16 2 3, 8, 279
5 13 2 12
5 15 2 5, 40, 50, 100, 200
5 16 2
5 17 2
5 19 2 12
6 18 2 6, 12, 24
6 20 2 9, 11, 18
6 21 1 51
7 25 2 3, 6, 12, 18





n < 200 where 11 is a common index divisors with dim A = 2
a3 a2 p-rank non-monogenic n
-11 51 2 10, 20, 120
-10 44 1
-10 45 2 85
-9 37 2 15
-9 38 2 18, 24, 26, 36, 39, 52, 72, 76, 78, 104, 117, 156
-9 39 2
-9 41 2 5, 10, 20
-8 31 2 16
-8 32 2 8, 16
-8 33 1 8, 16
-8 35 2
-8 36 2 8
-7 24 2 28
-7 25 2 7
-7 26 2
-7 27 2 120
-7 29 2
-7 30 2
-7 31 2
-7 33 1
-6 17 2 15, 20, 30, 60
-6 18 2 12, 51, 68, 102, 122, 136
-6 19 2 6
-6 20 2
-6 21 2
-6 23 2
-6 24 2 12
-6 25 2 6, 9, 18, 36, 57, 114, 171
-6 26 2
-6 28 2 111
-6 29 2
-5 11 1 5
-5 12 2
-5 13 2 10, 20
-5 14 2 20, 40
-5 15 2 91
-5 17 2
-5 18 2
-5 19 2
-5 20 2
-5 21 2 5
-5 23 2 10, 20
-5 24 2 20
-5 25 2 15
-5 27 2 120
-4 4 2 8, 12, 24, 48
-4 5 2
-4 6 2 5
-4 7 2 20, 40
-4 8 2 8, 68, 136
-4 9 2
-4 11 1 5
-4 12 2 8, 26, 65, 130
-4 13 2
-4 14 2
-4 15 2 74
-4 16 2 5, 8, 12, 24, 48
-4 18 2
-4 19 2
-4 20 2 8
-4 21 2 5, 19, 76
-4 23 2
-4 24 2 8
-3 -3 2
-3 -2 2 6, 9, 12, 18, 24, 26, 36, 39, 52, 72, 78, 104, 108, 117, 156
-3 -1 2
-3 0 1
-3 1 2
-3 2 2 24
-3 3 2
-3 5 2
-3 6 2
-3 7 2 9
-3 8 2
-3 9 2
-3 10 2 6, 12, 24
-3 11 1 39
-3 13 2
-3 14 2 24, 74, 148
-3 15 2
-3 16 2 6, 9, 18, 36
-3 17 2
-3 19 2
-3 20 2
-3 21 2 51
-3 23 2
-2 -9 2
-2 -8 2 12
-2 -7 2 26, 52, 74
-2 -6 2
-2 -5 2
-2 -4 2
-2 -3 2
-2 -1 2
-2 0 1
-2 1 2 28
-2 2 2 37, 68, 74, 136
-2 3 2
-2 4 2 12
-2 5 2
-2 6 2 26
-2 8 2
-2 9 2
-2 10 2 12
-2 11 1
-2 12 2
-2 13 2
-2 15 2 28
-2 16 2 12
-2 17 2
-2 18 2
-2 20 2
-2 21 2
-1 -16 2
-1 -15 2
-1 -14 2
-1 -13 2
-1 -12 2 183
-1 -11 1
-1 -10 2 26, 52, 104
-1 -9 2 10, 20, 120
-1 -7 2
-1 -6 2 26, 52, 104
-1 -5 2
-1 -4 2
-1 -3 2
-1 -2 2
-1 -1 2
-1 0 1
-1 1 2 10, 20
-1 3 2
-1 4 2
-1 5 2
-1 6 2
-1 7 2 65
-1 8 2
-1 9 2
-1 11 1 10, 20
-1 12 2 20, 183
-1 13 2
-1 14 2
-1 15 2
-1 17 2
-1 18 2 76
-1 19 2
-1 21 2 10, 20, 120
0 -21 2 20, 26, 40, 51, 52, 65, 104, 130
0 -20 2 8, 9, 10, 18, 20, 40, 57, 68, 80, 85, 136, 170, 171
0 -19 2 5, 10, 15, 20, 24, 30, 40, 60, 74, 120, 148, 185
0 -18 2 12, 26, 91, 182
0 -17 2 6, 7, 14, 16, 21, 24, 28, 42, 48, 56, 63, 84, 112, 126, 168
0 -16 2 8, 15, 16, 18, 30, 45, 90
0 -15 2 8, 15, 16
0 -13 2 24, 26, 39, 52, 78, 104, 156
0 -12 2 8, 12, 24, 48
0 -11 0 6, 9, 12, 15, 18, 19, 20, 21, 24, 28, 30, 35, 36, 37, 38, 40, 42, 45, 56, 57, 60, 63, 70, 72, 74, 76, 84, 90, 95, 105, 108, 111, 114, 120, 126, 133, 140, 148, 152, 168, 171, 180, 185, 190
0 -10 2 7, 10, 20, 21, 40, 42
0 -9 2 5, 10, 16, 20, 40, 80
0 -8 2 8, 16, 19, 26, 38, 39, 57, 78, 114, 171
0 -7 2 8, 16, 18, 24, 36, 48, 72, 144
0 -6 2 12
0 -5 2 6, 24, 26, 39, 52, 78, 104, 156
0 -4 2 5, 8, 15, 21, 30, 35, 42, 68, 70, 95, 105, 136
0 -2 2 9, 18, 43
0 -1 2 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 199
0 0 0 8, 10, 12, 15, 16, 20, 24, 26, 30, 40, 48, 60, 61, 80, 96, 120, 122, 160, 183
0 1 2 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 72, 80, 90, 120, 180
0 2 2 18
0 3 2 28, 51, 56
0 4 2 7, 8, 15, 21, 30, 35, 42, 63, 68, 70, 105, 136
0 5 2 24, 26, 39, 52, 76, 78, 104, 156
0 7 2 6, 9, 16, 18, 24, 36, 43, 48, 72, 144
0 8 2 8, 16, 19, 26, 38, 39, 57, 78, 114
0 9 2 8, 16, 20, 40, 80
0 10 2 10, 20, 21, 40, 42
0 11 0 5, 7, 10, 14, 15, 18, 19, 20, 21, 24, 28, 30, 35, 36, 37, 38, 40, 42, 45, 56, 57, 60, 63, 70, 72, 74, 76, 84, 90, 95, 105, 111, 114, 120, 126, 133, 140, 148, 152, 168, 171, 180, 185, 190
0 12 2 8, 12, 24, 48
0 14 2 15, 30, 68, 136
0 15 2 15, 16
0 16 2 5, 8, 9, 15, 16, 18, 30, 45, 90, 135
0 17 2 8, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168
0 19 2 6, 15, 20, 24, 30, 40, 60, 120
0 20 2 8, 10, 18, 20, 40, 68, 80, 85, 136, 170
1 -16 2
1 -15 2
1 -14 2 5
1 -13 2
1 -12 2 183
1 -11 1
1 -10 2 26, 52, 104
1 -9 2 5, 10, 20, 120
1 -7 2
1 -6 2 26, 52, 104
1 -5 2
1 -4 2 5
1 -3 2
1 -2 2
1 -1 2 19
1 0 1
1 1 2 5, 10, 20
1 3 2
1 4 2
1 5 2
1 6 2 5
1 7 2 65
1 8 2
1 9 2
1 11 1 5, 10, 20
1 12 2 20, 183
1 13 2
1 14 2
1 15 2
1 17 2
1 18 2 19, 76
1 19 2
1 21 2 5, 10, 20, 120
2 -9 2
2 -8 2 12
2 -7 2 19, 26, 52, 74
2 -6 2
2 -5 2
2 -4 2
2 -3 2
2 -1 2
2 0 1
2 1 2 28
2 2 2 37, 68, 74, 136
2 3 2
2 4 2 12
2 5 2
2 6 2 26
2 8 2
2 9 2
2 10 2 12
2 11 1
2 12 2 19
2 13 2
2 15 2 28
2 16 2 12
2 17 2
2 18 2 35
2 20 2
2 21 2
3 -3 2
3 -2 2 6, 9, 12, 18, 24, 26, 36, 39, 52, 72, 78, 104, 108, 117, 156
3 -1 2
3 0 1
3 1 2
3 2 2 24
3 3 2
3 5 2
3 6 2
3 7 2 9
3 8 2
3 9 2
3 10 2 6, 12, 24
3 11 1 39
3 13 2
3 14 2 24, 74, 148
3 15 2
3 16 2 6, 9, 18, 36
3 17 2 38
3 19 2
3 20 2
3 21 2 51
3 23 2
4 4 2 8, 12, 24, 48
4 5 2
4 6 2
4 7 2 20, 40
4 8 2 8, 68, 136
4 9 2
4 11 1
4 12 2 8, 26, 65, 130
4 13 2
4 14 2
4 15 2 74
4 16 2 8, 12, 24, 48
4 18 2
4 19 2
4 20 2 8, 95
4 21 2 76
4 23 2
4 24 2 8
5 11 1 5
5 12 2
5 13 2 10, 20
5 14 2 20, 40
5 15 2 91
5 17 2
5 18 2
5 19 2
5 20 2
5 21 2 5
5 23 2 10, 20
5 24 2 20
5 25 2 15
5 27 2 19, 120
6 17 2 15, 20, 30, 60
6 18 2 12, 51, 68, 102, 122, 136
6 19 2 6
6 20 2
6 21 2 5
6 23 2
6 24 2 12
6 25 2 6, 9, 18, 19, 36, 57, 114, 171
6 26 2 5
6 28 2 111
6 29 2
7 24 2 28
7 25 2 7
7 26 2
7 27 2 120
7 29 2
7 30 2
7 31 2
7 33 1
8 31 2 16
8 32 2 8, 16
8 33 1 8, 16
8 35 2
8 36 2 8
9 37 2 15
9 38 2 18, 24, 26, 36, 39, 52, 72, 76, 78, 104, 117, 156
9 39 2
9 41 2 10, 20
10 44 1
10 45 2 85
11 51 2 5, 10, 20, 120





n < 200 where 13 is a common index divisors with dim A = 2
a3 a2 p-rank non-monogenic n
-11 55 2 6, 12
-10 48 2 11
-10 49 2
-9 39 1
-9 41 2
-9 42 2
-9 43 2
-9 45 2 11, 22, 44, 88, 176
-8 32 2 8, 16, 157
-8 34 2
-8 35 2 24
-8 36 2 8
-8 37 2 11, 33, 165
-8 39 1
-8 40 2 8, 16, 56, 112
-7 25 2 4, 12, 24
-7 27 2
-7 28 2 7
-7 29 2 4, 7, 11, 21, 22, 44, 88, 176
-7 30 2
-7 31 2 12
-7 33 2 4
-7 34 2 28, 56
-7 35 2 7
-7 37 2 4, 12, 24
-6 18 2 12
-6 20 2
-6 21 2 15
-6 22 2
-6 23 2 20, 30, 36, 45, 60, 90, 180
-6 24 2 12
-6 25 2 6
-6 27 2
-6 28 2 30
-6 29 2 23
-6 30 2 12
-6 32 2
-6 33 2 20
-5 11 2
-5 13 1 6, 12, 24
-5 14 2 23, 24, 36, 72
-5 15 2 5
-5 16 2
-5 17 2
-5 18 2
-5 19 2 6, 7, 12
-5 21 2
-5 22 2
-5 23 2
-5 24 2
-5 25 2 5, 6, 12, 24, 150
-5 27 2
-5 28 2
-5 29 2
-5 31 2 6, 12
-4 3 2 20, 40
-4 4 2 8
-4 6 2 10, 20
-4 7 2 11, 33
-4 8 2 8, 30, 56, 61, 112, 122, 183
-4 9 2
-4 10 2
-4 11 2 24
-4 12 2 8, 56, 112
-4 13 1 20, 40
-4 15 2
-4 16 2 8, 10, 20, 40, 80
-4 17 2 24
-4 18 2 11, 154
-4 19 2
-4 20 2 8
-4 22 2 56
-4 23 2 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180
-4 24 2 8, 23
-4 25 2
-4 27 2
-4 28 2 8
-3 -4 2 17, 34, 36, 51, 68, 102, 153
-3 -3 2 4, 140
-3 -1 2
-3 0 1
-3 1 2 4
-3 2 2 24
-3 3 2
-3 4 2 6, 11
-3 5 2 4
-3 6 2
-3 7 2
-3 9 2 4, 17, 51
-3 10 2 6, 24
-3 11 2
-3 12 2
-3 13 1 4, 17, 51
-3 14 2 24, 36, 72
-3 15 2 11, 22, 44
-3 17 2 4
-3 18 2
-3 19 2
-3 20 2
-3 21 2 4
-3 23 2
-3 24 2
-3 25 2 4
-3 27 2
-2 -11 2
-2 -10 2 11
-2 -8 2
-2 -7 2
-2 -6 2
-2 -5 2
-2 -4 2
-2 -3 2
-2 -2 2 7
-2 -1 2 36
-2 0 1
-2 1 2 11, 33
-2 3 2
-2 4 2
-2 5 2 7, 14, 21, 28, 29, 42, 84
-2 6 2
-2 7 2
-2 8 2
-2 9 2
-2 10 2
-2 12 2 7, 11
-2 13 1
-2 14 2
-2 15 2
-2 16 2 56
-2 17 2 36
-2 19 2 7, 14, 28
-2 20 2
-2 21 2 53
-2 22 2
-2 24 2
-2 25 2
-1 -18 2 11
-1 -17 2 12
-1 -15 2
-1 -14 2
-1 -13 1
-1 -12 2 20, 114
-1 -11 2 12, 24, 29
-1 -10 2 24
-1 -9 2
-1 -8 2
-1 -7 2 11, 22, 44, 45, 88, 176
-1 -6 2
-1 -5 2 12
-1 -3 2
-1 -2 2 20, 40
-1 -1 2
-1 0 1
-1 1 2 12, 24
-1 2 2 24, 36, 72
-1 3 2 53
-1 4 2 11, 33
-1 5 2
-1 7 2 12
-1 8 2 20, 30, 60
-1 9 2
-1 10 2
-1 11 2
-1 12 2
-1 13 1 12, 24
-1 15 2 11, 22, 44
-1 16 2
-1 17 2
-1 18 2 20, 29, 40
-1 19 2 12
-1 21 2
-1 22 2
-1 23 2
-1 25 2 12, 24
0 -25 2 5, 20, 24, 29, 30, 40, 48, 60, 80, 120
0 -24 2 8, 12, 16, 24, 48, 51, 56, 68, 84, 96, 102, 112, 119, 136, 168
0 -22 2 21, 42, 63, 126
0 -21 2 7, 21
0 -20 2 5, 7, 8, 10, 20, 21, 30, 35, 40, 42, 70, 80, 105
0 -19 2 11, 24, 29
0 -18 2 12, 56, 84, 168
0 -17 2 6, 17, 24, 34, 48, 51, 68, 102, 119, 136, 187
0 -16 2 8, 11, 16
0 -15 2 5, 8, 15, 20, 28, 35, 40, 56, 70, 80, 112, 140
0 -14 2 7, 9, 14, 28, 56
0 -13 0 7, 14, 21, 24, 28, 36, 42, 56, 61, 63, 72, 84, 122, 126, 133, 157, 168, 183
0 -12 2 8, 12, 24
0 -11 2 6, 12, 24
0 -9 2
0 -8 2 8, 11, 16, 21, 42
0 -7 2 7, 8, 24, 48, 119
0 -6 2 7, 12
0 -5 2 5, 6, 9, 11, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180
0 -4 2 8, 56, 112
0 -3 2
0 -2 2
0 -1 2 21, 24, 28, 42, 48, 56, 84, 112, 168
0 0 0 5, 7, 8, 10, 12, 14, 15, 16, 17, 20, 21, 24, 28, 30, 34, 35, 40, 42, 48, 51, 56, 60, 68, 70, 80, 84, 85, 96, 102, 105, 112, 119, 120, 136, 140, 160, 168, 170
0 2 2 29
0 3 2 11
0 4 2 8, 9, 29, 56, 112
0 5 2 5, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180
0 6 2 11, 12
0 7 2 6, 7, 24, 48, 119
0 8 2 7, 8, 16, 21, 42
0 9 2 8
0 11 2 24
0 12 2 8, 12, 24
0 13 0 6, 9, 12, 18, 21, 24, 28, 36, 42, 56, 61, 63, 72, 84, 108, 122, 126, 157, 168, 183
0 14 2 7, 11, 14, 28, 56
0 15 2 5, 7, 14, 15, 20, 28, 35, 40, 56, 70, 80, 112, 133, 140
0 16 2 8, 16
0 18 2 12, 56, 84, 168
0 19 2 6, 24
0 20 2 5, 8, 10, 20, 21, 30, 35, 40, 42, 70, 80, 105
0 21 2 7, 21
0 23 2 24, 36, 48, 72, 144
0 24 2 8, 12, 16, 24, 48, 51, 56, 68, 84, 96, 102, 112, 119, 136, 168
1 -18 2 11
1 -17 2 6, 12
1 -15 2 4
1 -14 2
1 -13 1
1 -12 2 20, 114
1 -11 2 4, 6, 12, 24, 29
1 -10 2 24
1 -9 2
1 -8 2
1 -7 2 4, 11, 22, 44, 45, 88, 176
1 -6 2
1 -5 2 6, 12
1 -3 2 4
1 -2 2 20, 40
1 -1 2
1 0 1
1 1 2 4, 6, 12, 24
1 2 2 24, 36, 72
1 3 2
1 4 2 11, 33
1 5 2 4
1 7 2 6, 12
1 8 2 20, 30, 60
1 9 2 4
1 10 2
1 11 2
1 12 2
1 13 1 4, 6, 12, 24
1 15 2 11, 22, 44
1 16 2 103
1 17 2 4
1 18 2 20, 29, 40
1 19 2 6, 12
1 21 2 4
1 22 2
1 23 2
1 25 2 4, 6, 12, 24
2 -11 2
2 -10 2 11
2 -8 2
2 -7 2
2 -6 2
2 -5 2
2 -4 2
2 -3 2
2 -2 2 7
2 -1 2 36
2 0 1 23
2 1 2 11, 33
2 3 2
2 4 2
2 5 2 7, 14, 21, 28, 29, 42, 84
2 6 2
2 7 2
2 8 2
2 9 2
2 10 2
2 12 2 7, 11
2 13 1
2 14 2
2 15 2
2 16 2 56
2 17 2 36
2 19 2 7, 14, 28
2 20 2
2 21 2
2 22 2
2 24 2
2 25 2
3 -4 2 17, 34, 36, 51, 68, 102, 153
3 -3 2 140
3 -1 2
3 0 1 53
3 1 2
3 2 2 24
3 3 2
3 4 2 6, 11
3 5 2
3 6 2
3 7 2
3 9 2 17, 51
3 10 2 6, 24
3 11 2
3 12 2
3 13 1 17, 51
3 14 2 24, 36, 72
3 15 2 11, 22, 44
3 17 2
3 18 2
3 19 2
3 20 2
3 21 2
3 23 2
3 24 2
3 25 2
3 27 2
4 3 2 20, 40
4 4 2 8
4 6 2 10, 20
4 7 2 11, 33
4 8 2 8, 30, 56, 61, 112, 122, 183
4 9 2
4 10 2
4 11 2 24
4 12 2 8, 56, 112
4 13 1 20, 40
4 15 2
4 16 2 8, 10, 20, 40, 80
4 17 2 24
4 18 2 11, 154
4 19 2
4 20 2 8
4 22 2 56
4 23 2 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180
4 24 2 8
4 25 2
4 27 2
4 28 2 8
5 11 2
5 13 1 4, 12, 24
5 14 2 24, 36, 72
5 15 2 5
5 16 2
5 17 2 4
5 18 2
5 19 2 7, 12
5 21 2 4
5 22 2
5 23 2
5 24 2
5 25 2 4, 5, 12, 24, 150
5 27 2
5 28 2
5 29 2 4
5 31 2 12
6 18 2 12
6 20 2
6 21 2 15
6 22 2
6 23 2 20, 30, 36, 45, 60, 61, 90, 180
6 24 2 12
6 25 2 6
6 27 2
6 28 2 30
6 29 2
6 30 2 12
6 32 2
6 33 2 20
7 25 2 6, 12, 24
7 27 2
7 28 2 7
7 29 2 7, 11, 21, 22, 44, 88, 176
7 30 2
7 31 2 6, 12
7 33 2
7 34 2 28, 56
7 35 2 7
7 37 2 6, 12, 24
8 32 2 8, 16, 157
8 34 2
8 35 2 24
8 36 2 8
8 37 2 11, 33, 165
8 39 1
8 40 2 8, 16, 23, 56, 112
9 39 1 23
9 41 2 4
9 42 2
9 43 2
9 45 2 4, 11, 22, 44, 88, 176
10 48 2 11
10 49 2
11 55 2 12







n < 200 where 2 is a common index divisors with dim A = 3
a5 a4 a3 p-rank non-monogenic n
-4 9 -15 3 7, 11, 23, 29, 43, 71, 87, 113, 127
-3 2 1 3 7, 11, 29, 43, 71, 87, 113, 127
-3 5 -7 3
-3 6 -9 3 3, 9, 27, 153
-2 0 3 3 107, 149
-2 1 0 2 3, 5, 11, 55, 83
-2 1 1 3 3
-2 2 -2 0 3, 9
-2 2 -1 3 3
-2 3 -6 2 73
-2 3 -5 3 3, 9, 27, 59, 63
-2 3 -3 3 5, 83, 131
-2 4 -6 0 3
-2 5 -7 3 3, 7
-1 -1 2 2 3, 9
-1 -1 4 2 3, 7
-1 -1 5 3 3, 9
-1 0 -1 3 3
-1 0 0 1
-1 0 1 3 5, 15
-1 0 3 3 7, 77, 103
-1 1 -3 3 3
-1 1 -1 3 3
-1 1 0 2 3, 7
-1 2 -5 3 3, 5
-1 2 -3 3 3
-1 2 -2 1 3
-1 2 -1 3 3, 5, 7, 9, 35, 75
-1 3 -3 3 5, 25
-1 4 -3 3 3, 83, 127
0 -1 -2 2 73
0 -1 -1 3
0 -1 1 3
0 -1 2 2 73
0 0 -3 3 3, 7, 9, 13, 15, 21, 27, 29, 31, 35, 39, 45, 63, 65, 87, 91, 93, 105, 117, 123, 141, 151, 195
0 0 -2 0 3, 7, 11, 15, 23, 29, 37, 45, 67, 71, 79
0 0 -1 3 3, 5, 7, 15, 19, 21, 25, 35, 45, 63, 71, 75, 95, 97, 105, 123, 133
0 0 1 3 3, 5, 7, 15, 19, 21, 25, 35, 45, 47, 49, 63, 75, 95, 97, 105, 123, 133
0 0 2 0 3, 7, 11, 15, 23, 29, 37, 45, 67
0 0 3 3 3, 7, 9, 13, 15, 21, 27, 29, 31, 35, 39, 45, 47, 63, 65, 71, 87, 91, 93, 105, 117, 123, 141, 151, 195
0 1 -3 3 3, 9
0 1 -1 3
0 1 1 3
0 1 3 3 3, 9
0 2 -2 0
0 2 -1 3 7
0 2 1 3 7
0 2 2 0
0 3 -1 3 3, 89, 153
0 3 1 3 3, 7, 89, 153
1 -1 -5 3 3, 9
1 -1 -4 2 3, 7, 49
1 -1 -2 2 3, 9
1 0 -3 3 7, 77, 103
1 0 -1 3 5, 15
1 0 0 1
1 0 1 3 3
1 1 0 2 3, 7
1 1 1 3 3
1 1 3 3 3
1 2 1 3 3, 5, 7, 9, 35, 75
1 2 2 1 3
1 2 3 3 3
1 2 5 3 3, 5
1 3 3 3 5, 25
1 4 3 3 3, 83, 127
2 0 -3 3 107, 149
2 1 -1 3 3
2 1 0 2 3, 5, 11, 55, 83
2 2 1 3 3
2 2 2 0 3, 9
2 3 3 3 5, 83, 131
2 3 5 3 3, 9, 27, 59, 63
2 3 6 2 73
2 4 6 0 3
2 5 7 3 3, 7
3 2 -1 3 7, 11, 23, 29, 43, 71, 87, 113, 127
3 5 7 3 7
3 6 9 3 3, 9, 27, 153
4 9 15 3 7, 11, 29, 43, 71, 87, 113, 127





n < 200 where 3 is a common index divisors with dim A = 3
a5 a4 a3 p-rank non-monogenic n
-5 13 -25 3 2, 4, 5, 8, 20, 25, 40, 80
-5 15 -31 3 2, 4, 8, 14, 28, 91, 104, 182
-4 6 -7 3 2, 4, 5, 8, 40, 80
-4 7 -10 3 2, 4, 8
-4 8 -13 3 2, 4, 8
-4 9 -17 3
-4 10 -21 2 2, 4, 7, 8, 56, 79, 112
-4 10 -20 3 2, 4, 8, 16, 32
-4 10 -19 3 2, 4, 8
-4 11 -22 3 2, 4, 5, 8, 10, 13, 20
-4 12 -23 3 2, 4, 8, 13
-3 0 8 3 2, 4, 8
-3 1 5 3 2, 4, 8, 77
-3 2 1 3 2, 4, 5
-3 2 2 3 2, 4, 8, 16
-3 3 -1 3 2, 4, 8, 17
-3 4 -6 2 2, 4, 8, 16
-3 4 -5 3 2, 4, 79
-3 5 -9 2 2, 4, 8, 16, 32
-3 5 -8 3 2, 4
-3 5 -7 3 2, 4, 8
-3 5 -5 3 2, 4, 8, 16, 32, 83, 104
-3 6 -12 0 2, 4, 8
-3 6 -11 3 2, 4, 22
-3 6 -10 3 2, 4, 8, 16, 83
-3 7 -15 2 2, 4, 8, 17
-3 7 -13 3 2, 4, 8
-3 7 -11 3 2, 4, 5, 8, 25
-3 8 -17 3 2, 4, 5, 10, 20, 40
-3 8 -16 3 2, 4, 8, 28
-3 8 -14 3 2, 4, 8, 13, 16, 53
-3 8 -13 3 2, 4, 136
-3 9 -17 3 2, 4, 8, 16, 32
-3 9 -15 0 2, 4, 8
-2 -2 9 2 2, 4, 7, 8, 56, 79, 112
-2 -2 11 3 2, 4, 8, 47, 179
-2 -1 6 2 2, 4, 8
-2 -1 7 3
-2 0 2 3 2, 4, 8, 16
-2 0 3 1 2, 4, 8
-2 0 4 3 2, 4, 8, 16, 53
-2 0 5 3 2, 4, 8, 13
-2 0 7 3 2, 4, 8, 61
-2 1 -1 3 5, 11, 22, 44, 88
-2 1 0 2 2, 4, 8, 61
-2 1 1 3
-2 1 2 3 2, 4, 8, 14, 28
-2 2 -5 3 2, 4, 8, 76, 152
-2 2 -3 2 2, 4, 8
-2 2 -2 3 2, 4, 8, 16
-2 2 -1 3 2, 4, 5, 8
-2 2 1 3 2, 4, 5, 8, 10, 20, 25, 40, 55, 80
-2 3 -7 3
-2 3 -6 1 2, 4, 8, 14, 28
-2 3 -4 3 2, 4, 8, 16, 32
-2 3 -2 3 2, 4, 8
-2 3 -1 3 61, 122
-2 4 -11 3 2, 4, 8
-2 4 -10 3 2, 4, 7, 8, 14, 16, 28, 56, 112
-2 4 -9 2 2, 4, 8
-2 4 -8 3 2, 4, 8, 16
-2 4 -7 3 2, 4, 8
-2 4 -5 3 2, 4, 8
-2 4 -4 3 2, 4, 8, 16
-2 4 -3 2 2, 4, 7, 8, 56, 79, 112
-2 5 -11 3
-2 5 -10 3 2, 4, 8
-2 5 -8 3 2, 4, 8
-2 5 -6 2 2, 4, 8
-2 5 -5 3 7
-2 6 -11 3 2, 4, 5, 8, 40, 80
-2 6 -10 3 2, 4, 8, 16
-2 6 -9 1 2, 4, 8
-2 6 -7 3 2, 4, 5, 8, 13, 40, 80
-2 7 -10 3 2, 4, 8
-2 8 -11 3 2, 4, 8, 29
-1 -2 3 2 2, 4, 61, 122
-1 -2 4 3 2, 4, 8
-1 -2 6 2 2, 4, 8, 16
-1 -2 7 3 2, 4, 59
-1 -2 8 3 2, 4, 8, 28
-1 -1 1 3 2, 4, 8
-1 -1 2 3 2, 4
-1 -1 3 2 2, 4, 8
-1 -1 5 3 2, 4, 5, 8
-1 -1 7 3 2, 4, 8, 20, 40, 80
-1 -1 8 3 2, 4, 8, 16
-1 -1 9 2 2, 4, 8
-1 0 -4 3 2, 4, 8
-1 0 -3 1 2, 4, 79
-1 0 -2 3 2, 4, 5, 8, 16
-1 0 -1 3 2, 4, 53
-1 0 0 1 2, 4, 8
-1 0 1 3 2, 4, 14, 28, 56
-1 0 2 3 2, 4, 8, 16
-1 0 4 3 2, 4, 8
-1 0 5 3 2, 4, 22
-1 0 6 1 2, 4, 8, 16
-1 0 7 3 2, 4
-1 1 -7 3 2, 4, 8, 16, 32
-1 1 -5 3 2, 4, 8
-1 1 -4 3 2, 4
-1 1 -3 2 2, 4, 5, 8, 16, 32
-1 1 -2 3 2, 4, 11, 83
-1 1 -1 3 2, 4, 5, 8
-1 1 1 3 2, 4, 8, 16, 32, 104
-1 1 3 2 2, 4, 8, 13, 26, 52, 104
-1 1 4 3 2, 4, 5, 10, 20, 40, 71, 79
-1 1 5 3 2, 4, 8, 16, 32
-1 2 -10 3 2, 4, 8, 16
-1 2 -9 2 2, 4
-1 2 -7 3 2, 4, 8, 16
-1 2 -5 3 2, 4
-1 2 -4 3 2, 4, 8, 10, 20, 40, 80
-1 2 -2 3 2, 4, 8, 16, 71, 142
-1 2 -1 3 2, 4, 5, 10, 20, 40
-1 2 0 2 2, 4, 8
-1 2 2 3 2, 4, 8, 13, 16
-1 2 3 2 2, 4, 14, 28, 56
-1 3 -9 1 2, 4, 8
-1 3 -8 3 2, 4, 8, 16, 32
-1 3 -7 3 2, 4, 8, 23
-1 3 -5 3 2, 4, 5, 8
-1 3 -4 3 2, 4, 8, 16
-1 3 -3 1 2, 4, 8
-1 3 -2 3 2, 4
-1 3 -1 3 2, 4, 8
-1 3 1 3 2, 4, 8
-1 4 -8 3 2, 4, 8, 13
-1 4 -7 3 2, 4, 22
-1 4 -5 3 2, 4, 5, 10, 20, 40
-1 4 -3 2 2, 4, 61, 122
-1 4 -2 3 2, 4, 8, 16, 61, 122
-1 5 -7 3 2, 4, 5, 8, 16, 32, 53
-1 5 -5 3 2, 4, 8
-1 5 -4 3 2, 4, 181
-1 5 -3 2 2, 4, 8, 16, 32, 61
-1 6 -5 3 2, 4, 136
-1 7 -5 3 2, 4, 8
0 -2 -3 2 2, 4, 8
0 -2 -2 3 2, 4, 8, 16
0 -2 -1 3 2, 4, 8
0 -2 1 3 2, 4, 8
0 -2 2 3 2, 4, 8, 16
0 -2 3 2 2, 4, 8
0 -1 -6 2 2, 4, 8
0 -1 -5 3
0 -1 -4 3 2, 4, 8, 16, 32
0 -1 -2 3 2, 4, 8
0 -1 -1 3
0 -1 1 3
0 -1 2 3 2, 4, 8
0 -1 4 3 2, 4, 8, 16, 32
0 -1 5 3
0 -1 6 2 2, 4, 8
0 0 -9 0 2, 4, 7, 8, 13, 14, 19, 26, 28, 37, 38, 40, 52, 56, 65, 70, 73, 74, 76, 80, 91, 95, 104, 112, 122, 124, 130, 133, 140, 146, 148, 152, 182, 185, 190
0 0 -7 3 2, 4, 5, 7, 8, 10, 11, 13, 14, 17, 19, 20, 22, 25, 26, 28, 35, 38, 40, 49, 56, 70, 76, 80, 85, 91, 112, 119, 133, 140, 145, 154, 175
0 0 -6 0 2, 4, 8, 11, 13, 14, 16, 17, 19, 22, 26, 28, 34, 38, 40, 43, 44, 56, 68, 86, 112, 119, 136, 172
0 0 -5 3 2, 4, 5, 7, 8, 11, 13, 14, 17, 23, 28, 37, 40, 56, 61, 70, 74, 80, 85, 112, 124, 140, 148, 154
0 0 -4 3 2, 4, 8, 13, 14, 16, 26, 28, 32, 40, 52, 56, 65, 76, 80, 95, 104, 112, 116, 124, 130, 152, 190
0 0 -3 0 2, 4, 5, 8, 10, 13, 20, 25, 31, 35, 40, 47, 67, 80, 124, 155
0 0 -2 3 2, 4, 5, 7, 8, 10, 13, 14, 16, 17, 20, 25, 28, 34, 35, 40, 47, 50, 56, 68, 70, 80, 85, 100, 109, 136, 140, 160, 170
0 0 -1 3 2, 4, 8, 11, 13, 19, 22, 26, 38, 40, 52, 65, 76, 79, 80, 104, 122, 130, 143, 193
0 0 1 3 2, 4, 8, 11, 13, 19, 23, 26, 38, 40, 47, 52, 65, 76, 79, 80, 104, 122, 130, 143, 193
0 0 2 3 2, 4, 5, 7, 8, 10, 14, 16, 17, 20, 25, 28, 34, 35, 40, 50, 56, 68, 70, 80, 85, 100, 109, 136, 140, 160, 170
0 0 3 0 2, 4, 5, 8, 10, 13, 20, 23, 25, 26, 31, 35, 40, 67, 80, 124, 155
0 0 4 3 2, 4, 8, 11, 13, 14, 16, 26, 28, 32, 40, 47, 52, 56, 65, 76, 80, 95, 104, 112, 116, 124, 130, 152, 190
0 0 5 3 2, 4, 5, 7, 8, 11, 13, 14, 17, 22, 26, 28, 37, 40, 56, 61, 70, 74, 80, 85, 109, 112, 124, 140, 148, 154
0 0 6 0 2, 4, 8, 11, 13, 14, 16, 17, 19, 22, 26, 28, 34, 38, 40, 43, 44, 56, 68, 86, 112, 119, 136, 172
0 0 7 3 2, 4, 5, 7, 8, 10, 13, 14, 17, 19, 20, 25, 28, 35, 38, 40, 49, 56, 70, 76, 80, 85, 91, 112, 119, 133, 140, 145, 154, 175
0 0 9 0 2, 4, 7, 8, 13, 14, 19, 26, 28, 37, 38, 40, 52, 56, 65, 70, 73, 74, 76, 80, 91, 95, 104, 112, 122, 124, 130, 133, 140, 146, 148, 152, 182, 185, 190
0 1 -6 2 2, 4, 8, 14, 28, 79
0 1 -5 3 5
0 1 -4 3 2, 4, 8
0 1 -2 3 2, 4, 8
0 1 -1 3
0 1 1 3
0 1 2 3 2, 4, 8
0 1 4 3 2, 4, 8
0 1 5 3 5
0 1 6 2 2, 4, 8, 14, 28, 79
0 2 -7 3 2, 4, 8, 41, 91
0 2 -5 3 2, 4, 8
0 2 -4 3 2, 4, 8, 16, 32, 179
0 2 -3 2 2, 4, 8
0 2 -2 3 2, 4, 8, 16
0 2 -1 3 2, 4, 8
0 2 1 3 2, 4, 8
0 2 2 3 2, 4, 8, 16
0 2 3 2 2, 4, 8
0 2 4 3 2, 4, 8, 16, 32
0 2 5 3 2, 4, 8
0 2 7 3 2, 4, 8, 41, 91
0 3 -3 0 83
0 3 -2 3 2, 4, 8
0 3 -1 3 13, 26, 52, 104
0 3 1 3 13, 26, 52, 104
0 3 2 3 2, 4, 8
0 3 3 0 83
0 4 -3 2 2, 4, 8
0 4 -1 3 2, 4, 8
0 4 1 3 2, 4, 8
0 4 3 2 2, 4, 8
0 5 -2 3 2, 4, 5, 8, 10, 20, 25
0 5 -1 3
0 5 1 3
0 5 2 3 2, 4, 5, 8, 10, 20, 25
0 6 -1 3 2, 4, 8, 53
0 6 1 3 2, 4, 8, 53
1 -2 -8 3 2, 4, 8, 28
1 -2 -7 3 2, 4, 59
1 -2 -6 2 2, 4, 8, 16
1 -2 -4 3 2, 4, 8, 13
1 -2 -3 2 2, 4, 61, 122
1 -1 -9 2 2, 4, 8
1 -1 -8 3 2, 4, 8, 16
1 -1 -7 3 2, 4, 8, 20, 40, 80
1 -1 -5 3 2, 4, 5, 8
1 -1 -3 2 2, 4, 8
1 -1 -2 3 2, 4
1 -1 -1 3 2, 4, 8
1 0 -7 3 2, 4
1 0 -6 1 2, 4, 8, 16
1 0 -5 3 2, 4, 22
1 0 -4 3 2, 4, 8
1 0 -2 3 2, 4, 8, 16
1 0 -1 3 2, 4, 14, 28, 56
1 0 0 1 2, 4, 8
1 0 1 3 2, 4, 53
1 0 2 3 2, 4, 5, 8, 16
1 0 3 1 2, 4, 79
1 0 4 3 2, 4, 8
1 1 -5 3 2, 4, 8, 16, 32
1 1 -4 3 2, 4, 5, 10, 20, 40, 71, 79
1 1 -3 2 2, 4, 8, 13, 26, 52, 104
1 1 -1 3 2, 4, 8, 16, 32, 104
1 1 1 3 2, 4, 5, 8
1 1 2 3 2, 4, 11, 83
1 1 3 2 2, 4, 5, 8, 16, 32
1 1 4 3 2, 4
1 1 5 3 2, 4, 8
1 1 7 3 2, 4, 8, 16, 32
1 2 -3 2 2, 4, 14, 28, 56
1 2 -2 3 2, 4, 8, 13, 16
1 2 0 2 2, 4, 8
1 2 1 3 2, 4, 5, 10, 20, 40
1 2 2 3 2, 4, 8, 16, 71, 142
1 2 4 3 2, 4, 8, 10, 20, 40, 80
1 2 5 3 2, 4
1 2 7 3 2, 4, 8, 16
1 2 9 2 2, 4
1 2 10 3 2, 4, 8, 16
1 3 -1 3 2, 4, 8
1 3 1 3 2, 4, 8
1 3 2 3 2, 4
1 3 3 1 2, 4, 8
1 3 4 3 2, 4, 8, 16
1 3 5 3 2, 4, 5, 8
1 3 7 3 2, 4, 8, 23
1 3 8 3 2, 4, 8, 16, 32
1 3 9 1 2, 4, 8
1 4 2 3 2, 4, 8, 16, 61, 107, 122
1 4 3 2 2, 4, 61, 122
1 4 5 3 2, 4, 5, 10, 20, 40
1 4 7 3 2, 4, 22
1 4 8 3 2, 4, 8
1 5 3 2 2, 4, 8, 16, 32, 61
1 5 4 3 2, 4, 181
1 5 5 3 2, 4, 8
1 5 7 3 2, 4, 5, 8, 13, 16, 32, 53
1 6 5 3 2, 4, 136
1 7 5 3 2, 4, 8
2 -2 -11 3 2, 4, 8, 47
2 -2 -9 2 2, 4, 7, 8, 56, 79, 112
2 -1 -7 3
2 -1 -6 2 2, 4, 8
2 0 -7 3 2, 4, 8, 61
2 0 -5 3 2, 4, 8
2 0 -4 3 2, 4, 8, 16, 53
2 0 -3 1 2, 4, 8
2 0 -2 3 2, 4, 8, 16
2 1 -2 3 2, 4, 8, 14, 28
2 1 -1 3
2 1 0 2 2, 4, 8, 61
2 1 1 3 5, 11, 22, 44, 88
2 2 -1 3 2, 4, 5, 8, 10, 20, 25, 40, 55, 80
2 2 1 3 2, 4, 5, 8
2 2 2 3 2, 4, 8, 16
2 2 3 2 2, 4, 8
2 2 5 3 2, 4, 8, 76, 152
2 3 1 3 61, 122
2 3 2 3 2, 4, 8
2 3 4 3 2, 4, 8, 16, 32
2 3 6 1 2, 4, 8, 14, 28
2 3 7 3
2 4 3 2 2, 4, 7, 8, 56, 79, 112
2 4 4 3 2, 4, 8, 16
2 4 5 3 2, 4, 8
2 4 7 3 2, 4, 8
2 4 8 3 2, 4, 8, 16
2 4 9 2 2, 4, 8
2 4 10 3 2, 4, 7, 8, 14, 16, 28, 56, 112
2 4 11 3 2, 4, 8
2 5 5 3 7
2 5 6 2 2, 4, 8
2 5 8 3 2, 4, 8
2 5 10 3 2, 4, 8
2 5 11 3
2 6 7 3 2, 4, 5, 8, 40, 80
2 6 9 1 2, 4, 8
2 6 10 3 2, 4, 8, 16
2 6 11 3 2, 4, 5, 8, 40, 80
2 7 10 3 2, 4, 8
2 8 11 3 2, 4, 8, 29
3 0 -8 3 2, 4, 8
3 1 -5 3 2, 4, 8, 77
3 2 -2 3 2, 4, 8, 16
3 2 -1 3 2, 4, 5
3 3 1 3 2, 4, 8, 17
3 4 5 3 2, 4, 79
3 4 6 2 2, 4, 8, 16
3 5 5 3 2, 4, 8, 16, 32, 83, 104
3 5 7 3 2, 4, 8
3 5 8 3 2, 4
3 5 9 2 2, 4, 8, 16, 32
3 6 10 3 2, 4, 8, 16, 83
3 6 11 3 2, 4, 22
3 6 12 0 2, 4, 8
3 7 11 3 2, 4, 5, 8, 25
3 7 13 3 2, 4, 8
3 7 15 2 2, 4, 8, 17
3 8 13 3 2, 4, 136
3 8 14 3 2, 4, 8, 13, 16, 53
3 8 16 3 2, 4, 8, 28
3 8 17 3 2, 4, 5, 10, 20, 40
3 9 15 0 2, 4, 8
3 9 17 3 2, 4, 8, 16, 32
4 6 7 3 2, 4, 5, 8, 40, 80
4 7 10 3 2, 4, 8
4 8 13 3 2, 4, 8, 191
4 9 17 3
4 10 19 3 2, 4, 8
4 10 20 3 2, 4, 8, 16, 32
4 10 21 2 2, 4, 7, 8, 56, 79, 112
4 11 22 3 2, 4, 5, 8, 10, 13, 20
4 12 23 3 2, 4, 8, 13
5 13 25 3 2, 4, 5, 8, 20, 25, 40, 80
5 15 31 3 2, 4, 8, 14, 28, 91, 104, 182





n < 200 where 5 is a common index divisors with dim A = 3 and a5 = 0
a5 a4 a3 p-rank non-monogenic n
0 -4 -4 3 2, 4, 8, 16
0 -4 -3 3 3, 4, 8, 9, 16
0 -4 -2 3 2, 4, 8
0 -4 -1 3 4, 8, 16
0 -4 1 3 4, 8, 16
0 -4 2 3 2, 4, 8
0 -4 3 3 3, 4, 8, 9, 16
0 -4 4 3 2, 4, 8, 16
0 -3 -7 3
0 -3 -6 3 2, 3, 4, 9, 42, 84
0 -3 -5 2
0 -3 -4 3 2, 4, 8, 12, 16
0 -3 -3 3 3, 9, 12, 24
0 -3 -2 3 2, 4
0 -3 -1 3
0 -3 1 3
0 -3 2 3 2, 4
0 -3 3 3 3, 9, 12, 24
0 -3 4 3 2, 4, 8, 12, 16
0 -3 5 2
0 -3 6 3 2, 3, 4, 9, 42, 84
0 -3 7 3
0 -2 -13 3 4, 13
0 -2 -12 3 2, 3, 4, 6, 8, 12, 16, 18, 24, 36, 48, 72, 96
0 -2 -11 3 4, 11, 33
0 -2 -10 2 2, 4, 8
0 -2 -9 3 3, 4, 18, 24, 36, 72
0 -2 -8 3 2, 4, 8, 16, 53
0 -2 -7 3 4, 7
0 -2 -6 3 2, 3, 4, 6, 8, 12, 18, 24, 36, 48
0 -2 -5 2 4
0 -2 -3 3 3, 4, 18, 24, 36, 72
0 -2 -2 3 2, 4, 8
0 -2 -1 3 4
0 -2 1 3 4
0 -2 2 3 2, 4, 8
0 -2 3 3 3, 4, 18, 24, 36, 72
0 -2 5 2 4
0 -2 6 3 2, 3, 4, 6, 8, 12, 18, 24, 36, 48
0 -2 7 3 4, 7
0 -2 8 3 2, 4, 8, 16, 53
0 -2 9 3 3, 4, 18, 24, 36, 72
0 -2 10 2 2, 4, 8
0 -2 11 3 4, 11, 33
0 -2 12 3 2, 3, 4, 6, 8, 12, 16, 18, 24, 36, 48, 72, 96
0 -2 13 3 4, 13
0 -1 -17 3 17
0 -1 -16 3 2, 4
0 -1 -14 3 2, 4
0 -1 -13 3 13
0 -1 -12 3 2, 3, 4, 6, 9, 12, 18, 24
0 -1 -11 3 88
0 -1 -10 2 2, 4
0 -1 -9 3 3, 9
0 -1 -8 3 2, 4
0 -1 -7 3
0 -1 -6 3 2, 3, 4, 6, 9, 12, 18, 24, 78
0 -1 -5 2
0 -1 -4 3 2, 4, 22
0 -1 -3 3 3, 9
0 -1 -2 3 2, 4
0 -1 -1 3
0 -1 1 3
0 -1 2 3 2, 4
0 -1 3 3 3, 9
0 -1 4 3 2, 4, 22
0 -1 5 2
0 -1 6 3 2, 3, 4, 6, 9, 12, 18, 24, 78
0 -1 7 3
0 -1 8 3 2, 4
0 -1 9 3 3, 9
0 -1 10 2 2, 4
0 -1 11 3 88
0 -1 12 3 2, 3, 4, 6, 9, 12, 18, 24
0 -1 13 3 13
0 -1 14 3 2, 4
0 -1 16 3 2, 4
0 -1 17 3 17
0 0 -21 3 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 19, 21, 24, 28, 36, 38, 42, 48, 49, 51, 56, 57, 63, 72, 76, 84, 108, 112, 114, 119, 126, 133, 144, 147, 152, 168, 171, 189
0 0 -20 0 2, 4, 8, 12, 16, 24, 26, 42, 48, 51, 52, 56, 68, 84, 96, 102, 104, 109, 112, 119, 136, 168
0 0 -19 3 4, 7, 8, 11, 14, 16, 19, 26, 28, 29, 31, 37, 38, 44, 52, 56, 74, 76, 91, 104, 112, 133, 148, 152, 163, 182
0 0 -17 3 4, 8, 11, 13, 16, 26, 39, 52, 76, 91, 93, 104, 109, 143, 152
0 0 -16 3 2, 4, 7, 8, 11, 12, 14, 16, 22, 24, 26, 28, 31, 48, 52, 56, 71, 88, 91, 96, 104, 142, 164, 182
0 0 -15 0 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 37, 48, 72, 74, 108, 111, 144, 148
0 0 -13 3 4, 8, 9, 13, 16, 31, 39, 51, 63, 76, 91, 117, 119, 152, 153
0 0 -12 3 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 19, 21, 24, 28, 31, 36, 38, 42, 48, 51, 56, 57, 62, 63, 68, 72, 76, 84, 93, 96, 102, 114, 124, 126, 133, 136, 138, 152, 168, 171, 186, 189
0 0 -11 3 4, 8, 16, 19, 38, 61, 76, 152
0 0 -10 0 2, 4, 8, 12, 24, 26, 29, 42, 48, 51, 52, 56, 58, 68, 84, 102, 112, 119, 136, 168
0 0 -9 3 3, 4, 6, 7, 8, 9, 12, 13, 14, 16, 18, 21, 24, 26, 27, 28, 36, 38, 39, 42, 48, 52, 54, 56, 63, 72, 78, 81, 84, 91, 104, 108, 112, 117, 123, 126, 144, 156, 162, 168, 182, 189
0 0 -8 3 2, 4, 8, 11, 12, 16, 22, 24, 31, 42, 48, 56, 62, 84, 88, 93, 96, 112, 124, 134, 168, 186
0 0 -7 3 4, 7, 8, 14, 16, 19, 21, 26, 28, 29, 31, 38, 49, 51, 52, 56, 62, 76, 91, 104, 112, 119, 124, 133, 152, 161, 163, 182
0 0 -6 3 2, 3, 4, 6, 8, 9, 11, 12, 18, 19, 22, 24, 26, 31, 33, 36, 39, 42, 48, 52, 56, 57, 66, 78, 84, 112, 114, 117, 132, 156, 168, 171
0 0 -5 0 4, 7, 8, 9, 11, 14, 16, 28, 43, 51, 56, 93, 112, 153
0 0 -3 3 3, 4, 6, 8, 9, 11, 12, 16, 18, 24, 26, 31, 33, 36, 38, 39, 43, 48, 51, 52, 62, 72, 76, 78, 79, 104, 108, 117, 119, 123, 124, 129, 144, 156, 181
0 0 -2 3 2, 4, 7, 8, 12, 14, 19, 24, 28, 48, 133, 164
0 0 -1 3 4, 8, 16, 29, 31, 62, 124, 127
0 0 1 3 4, 8, 16, 29, 31, 62, 124, 127
0 0 2 3 2, 4, 7, 8, 12, 14, 24, 28, 48, 133, 164
0 0 3 3 3, 4, 6, 8, 9, 11, 12, 16, 18, 24, 26, 33, 36, 39, 43, 48, 51, 52, 72, 78, 104, 108, 117, 119, 123, 129, 144, 156, 181
0 0 5 0 4, 7, 8, 9, 11, 14, 16, 28, 43, 51, 56, 93, 112, 153, 191
0 0 6 3 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 26, 33, 36, 39, 42, 48, 52, 56, 57, 66, 78, 79, 84, 112, 114, 117, 132, 156, 168, 171
0 0 7 3 4, 7, 8, 14, 16, 19, 21, 26, 28, 29, 38, 49, 51, 52, 56, 76, 91, 104, 112, 119, 133, 152, 161, 163, 182
0 0 8 3 2, 4, 8, 11, 12, 16, 19, 22, 24, 31, 42, 48, 56, 62, 84, 88, 93, 96, 112, 124, 134, 168, 186
0 0 9 3 3, 4, 6, 7, 8, 9, 12, 13, 14, 16, 18, 21, 24, 26, 27, 28, 36, 39, 42, 44, 48, 52, 54, 56, 63, 72, 78, 81, 84, 91, 104, 108, 112, 117, 123, 126, 144, 156, 162, 168, 182, 189
0 0 10 0 2, 4, 8, 12, 24, 26, 29, 42, 48, 51, 52, 56, 58, 68, 84, 102, 112, 119, 136, 168
0 0 11 3 4, 8, 16, 61, 76, 152
0 0 12 3 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 19, 21, 24, 28, 31, 36, 38, 42, 48, 51, 56, 57, 62, 63, 68, 72, 76, 84, 93, 96, 102, 114, 124, 126, 133, 136, 138, 152, 168, 171, 186, 189
0 0 13 3 4, 8, 9, 13, 16, 19, 31, 38, 39, 51, 62, 63, 76, 91, 117, 119, 124, 152, 153
0 0 15 0 3, 4, 6, 8, 9, 12, 16, 18, 24, 31, 36, 37, 48, 62, 72, 74, 108, 111, 144, 148, 191
0 0 16 3 2, 4, 7, 8, 11, 12, 14, 16, 22, 24, 26, 28, 48, 52, 56, 71, 88, 91, 96, 104, 142, 164, 182
0 0 17 3 4, 8, 11, 13, 16, 19, 26, 38, 39, 44, 52, 76, 79, 91, 93, 104, 109, 143, 152
0 0 19 3 4, 7, 8, 11, 14, 16, 19, 26, 28, 29, 31, 37, 38, 52, 56, 62, 74, 76, 79, 91, 104, 112, 133, 148, 152, 163, 182
0 0 20 0 2, 4, 8, 12, 16, 24, 26, 42, 48, 51, 52, 56, 68, 84, 96, 102, 104, 109, 112, 119, 136, 168
0 0 21 3 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 49, 51, 56, 57, 63, 72, 76, 84, 108, 112, 114, 119, 126, 133, 144, 147, 152, 168, 171, 189
0 1 -19 3 19
0 1 -18 3 2, 3, 4, 9, 18, 27
0 1 -17 3 17
0 1 -16 3 2, 4, 8, 16
0 1 -14 3 2, 4
0 1 -12 3 2, 3, 4, 8, 12, 16
0 1 -11 3 11, 33, 88, 176
0 1 -10 2 2, 4
0 1 -9 3 3, 9, 27, 144
0 1 -7 3
0 1 -6 3 2, 3, 4, 42, 84
0 1 -5 2
0 1 -4 3 2, 4, 8, 16
0 1 -3 3 3
0 1 -2 3 2, 4
0 1 -1 3
0 1 1 3
0 1 2 3 2, 4
0 1 3 3 3
0 1 4 3 2, 4, 8, 16
0 1 5 2
0 1 6 3 2, 3, 4, 42, 84
0 1 7 3
0 1 9 3 3, 9, 27, 144
0 1 10 2 2, 4
0 1 11 3 11, 33, 88, 176
0 1 12 3 2, 3, 4, 8, 12, 16
0 1 14 3 2, 4
0 1 16 3 2, 4, 8, 16
0 1 17 3 17
0 1 18 3 2, 3, 4, 9, 18, 27
0 1 19 3 19
0 2 -17 3 4
0 2 -16 3 2, 4, 8, 16
0 2 -15 2 3, 4, 9
0 2 -14 3 2, 4, 8
0 2 -13 3 4
0 2 -11 3 4, 71
0 2 -10 2 2, 4, 8
0 2 -9 3 3, 4, 9
0 2 -8 3 2, 4, 8, 16
0 2 -7 3 4
0 2 -6 3 2, 3, 4, 8, 9, 12, 18, 24, 36, 48, 72, 144
0 2 -5 2 4
0 2 -4 3 2, 4, 8, 16
0 2 -3 3 3, 4, 9
0 2 -2 3 2, 4, 8, 134
0 2 -1 3 4
0 2 1 3 4
0 2 2 3 2, 4, 8, 134
0 2 3 3 3, 4, 9
0 2 4 3 2, 4, 8, 16
0 2 5 2 4
0 2 6 3 2, 3, 4, 8, 9, 12, 18, 24, 36, 48, 72, 144
0 2 7 3 4
0 2 8 3 2, 4, 8, 16
0 2 9 3 3, 4, 9
0 2 10 2 2, 4, 8
0 2 11 3 4
0 2 13 3 4
0 2 14 3 2, 4, 8
0 2 15 2 3, 4, 9
0 2 16 3 2, 4, 8, 16
0 2 17 3 4
0 3 -15 2 3, 9, 12
0 3 -14 3 2, 4, 7, 14, 21, 42, 84
0 3 -13 3
0 3 -12 3 2, 3, 4, 9
0 3 -10 2 2, 4
0 3 -8 3 2, 4
0 3 -7 3 7, 21
0 3 -6 3 2, 3, 4, 9
0 3 -5 2
0 3 -4 3 2, 4
0 3 -3 3 3, 9, 12
0 3 -2 3 2, 4
0 3 -1 3
0 3 1 3
0 3 2 3 2, 4
0 3 3 3 3, 9, 12
0 3 4 3 2, 4
0 3 5 2
0 3 6 3 2, 3, 4, 9
0 3 7 3 7, 21
0 3 8 3 2, 4
0 3 10 2 2, 4
0 3 12 3 2, 3, 4, 9
0 3 13 3
0 3 14 3 2, 4, 7, 14, 21, 42, 84
0 3 15 2 3, 9, 12
0 4 -13 3 4, 8, 16
0 4 -12 3 2, 3, 4, 6, 8, 12, 16, 18, 24, 36, 48, 72, 96
0 4 -11 3 4, 8, 16
0 4 -9 3 3, 4, 8, 16, 18, 24, 36, 48, 72, 144
0 4 -8 3 2, 4, 8, 16, 56, 112
0 4 -7 3 4, 8, 16
0 4 -5 2 4, 8, 16
0 4 -4 3 2, 4, 8, 16
0 4 -3 3 3, 4, 8, 16, 17, 18, 24, 36, 48, 51, 72, 144
0 4 -2 3 2, 4, 8
0 4 -1 3 4, 8, 16
0 4 1 3 4, 8, 16
0 4 2 3 2, 4, 8
0 4 3 3 3, 4, 8, 16, 17, 18, 24, 36, 48, 51, 72, 144
0 4 4 3 2, 4, 8, 16
0 4 5 2 4, 8, 16
0 4 7 3 4, 8, 16
0 4 8 3 2, 4, 8, 16, 56, 112
0 4 9 3 3, 4, 8, 16, 18, 24, 36, 48, 72, 144
0 4 11 3 4, 8, 16
0 4 12 3 2, 3, 4, 6, 8, 12, 16, 18, 24, 36, 48, 72, 96
0 4 13 3 4, 8, 16
0 5 -11 3
0 5 -10 0 2, 4
0 5 -8 3 2, 4, 8, 16, 32, 53
0 5 -7 3 7
0 5 -6 3 2, 3, 4, 6, 9, 12, 18, 24
0 5 -5 0
0 5 -4 3 2, 4, 8, 16
0 5 -2 3 2, 4, 11
0 5 -1 3 31, 62, 124
0 5 1 3 31, 62, 124
0 5 2 3 2, 4, 11
0 5 4 3 2, 4, 8, 16
0 5 5 0
0 5 6 3 2, 3, 4, 6, 9, 12, 18, 24
0 5 7 3 7
0 5 8 3 2, 4, 8, 16, 32, 53
0 5 10 0 2, 4
0 5 11 3
0 6 -9 3 3, 4, 6, 9, 12, 18, 24, 36, 72, 108
0 6 -7 3 4
0 6 -6 3 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 48
0 6 -5 2 4
0 6 -4 3 2, 4, 8, 12, 16, 24, 48, 96
0 6 -3 3 3, 4, 6, 9, 12, 18, 24, 36, 72, 108
0 6 -2 3 2, 4, 8, 12, 24, 48
0 6 -1 3 4
0 6 1 3 4
0 6 2 3 2, 4, 8, 12, 24, 48
0 6 3 3 3, 4, 6, 9, 12, 18, 24, 36, 72, 108
0 6 4 3 2, 4, 8, 12, 16, 24, 48, 96
0 6 5 2 4
0 6 6 3 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 48
0 6 7 3 4
0 6 9 3 3, 4, 6, 9, 12, 18, 24, 36, 72, 108
0 7 -6 3 2, 3, 4, 42, 84
0 7 -5 2 7
0 7 -4 3 2, 4, 43
0 7 -2 3 2, 4, 7
0 7 -1 3
0 7 1 3
0 7 2 3 2, 4, 7
0 7 4 3 2, 4, 43
0 7 5 2 7
0 7 6 3 2, 3, 4, 42, 84
0 8 -7 3 4, 8, 16
0 8 -5 2 4, 8, 16
0 8 -4 3 2, 4, 8, 16, 89
0 8 -3 3 3, 4, 8, 9, 16, 38, 76
0 8 -2 3 2, 4, 8
0 8 -1 3 4, 8, 16
0 8 1 3 4, 8, 16
0 8 2 3 2, 4, 8
0 8 3 3 3, 4, 8, 9, 16
0 8 4 3 2, 4, 8, 16, 89
0 8 5 2 4, 8, 16
0 8 7 3 4, 8, 16
0 9 -3 3 3, 9, 12, 24
0 9 -2 3 2, 4
0 9 -1 3
0 9 1 3
0 9 2 3 2, 4
0 9 3 3 3, 9, 12, 24
0 10 -3 3 3, 4, 18, 24, 36, 72
0 10 -1 3 4
0 10 1 3 4
0 10 3 3 3, 4, 18, 24, 36, 72
0 11 -2 3 2, 4
0 11 -1 3
0 11 1 3
0 11 2 3 2, 4
0 12 -1 3 4, 8, 16
0 12 1 3 4, 8, 16







n < 100 where 2 is a common index divisors with dim A = 4
a7 a6 a5 a4 p-rank non-monogenic n
-5 12 -20 29 4 5, 11, 15, 55, 99
-5 13 -25 39 4 5, 11, 15, 19, 31, 33, 55, 57, 61, 85, 93
-4 4 7 -21 4 11, 15, 19, 31, 33, 55, 57, 61, 93
-4 5 2 -11 4 13, 97
-4 6 -4 2 0 7, 89
-4 8 -12 17 4 3, 5, 47, 89, 91, 93
-4 9 -17 27 4
-4 10 -19 29 4 3, 9
-3 2 0 1 4 3, 5, 9, 11, 15, 25, 31, 33, 45, 55, 75, 93, 99
-3 2 4 -10 1
-3 2 5 -13 4
-3 2 6 -15 4 3, 9, 27
-3 3 -2 3 4
-3 3 -1 0 3
-3 3 0 -3 4 3, 9, 27
-3 3 1 -5 4 3, 15, 17, 45
-3 3 2 -7 4
-3 3 3 -11 4 3, 5, 9, 27
-3 4 -6 10 1 3, 9, 27
-3 4 -4 5 4 3
-3 4 -2 -1 4 3
-3 5 -9 15 4 3, 9, 27
-3 5 -8 13 4
-3 5 -7 9 4 3, 9
-3 5 -7 11 4 17
-3 5 -6 6 2 3, 9, 13, 27, 97
-3 5 -6 7 4 3, 9
-3 5 -5 5 4
-3 6 -12 19 4 3, 9, 27
-3 6 -11 17 4
-3 6 -10 14 1
-3 6 -10 15 4
-3 6 -9 12 3 3, 9, 27
-3 6 -8 11 4
-3 7 -13 19 4 5
-3 7 -13 21 4 3, 5
-3 7 -12 19 4 3, 9, 27
-3 7 -11 17 4 3
-3 8 -14 23 4 11, 99
-2 -1 3 -1 4 3
-2 0 -2 9 4 3
-2 0 1 1 4 3, 9, 39
-2 0 2 -2 0 3, 7, 9, 45
-2 0 3 -5 4 3, 9
-2 0 3 -4 3
-2 0 4 -7 4
-2 0 4 -6 0 3
-2 1 -3 8 3
-2 1 -2 5 4 3, 9
-2 1 -1 3 4 15
-2 1 -1 4 3
-2 1 0 1 4 15
-2 1 1 -3 4 3, 9, 11, 33
-2 1 1 -1 4 3, 9, 15
-2 1 2 -6 2
-2 1 2 -5 4 5, 25
-2 1 2 -3 4 9, 13, 47, 91, 93
-2 1 3 -9 4 3
-2 1 3 -8 3 23
-2 1 3 -7 4 9, 11, 33, 99
-2 1 4 -11 4 3, 7
-2 1 4 -10 2 3, 9
-2 2 -5 11 4 5, 7, 11, 15, 25, 31, 33, 45, 55
-2 2 -4 7 4
-2 2 -4 9 4 3
-2 2 -3 4 3
-2 2 -3 5 4 3
-2 2 -3 7 4
-2 2 -2 1 4 5, 13, 97
-2 2 -2 2 0
-2 2 -2 3 4 3
-2 2 -1 -1 4 3, 9, 15
-2 2 -1 1 4 11
-2 2 0 -4 0 3, 5, 11, 13, 15, 17, 21, 25, 29, 31, 33, 35, 37, 39, 41, 45, 51, 55, 61, 63, 65, 75, 77, 85, 91, 93, 99
-2 2 0 -3 4 3, 9
-2 2 0 -2 0
-2 2 0 -1 4 3, 11
-2 2 1 -5 4
-2 2 1 -3 4 3
-2 2 2 -6 0 3, 11
-2 2 2 -5 4
-2 2 3 -7 4 3
-2 3 -6 11 4
-2 3 -5 7 4 3, 9
-2 3 -5 8 3
-2 3 -5 9 4 3
-2 3 -4 3 4
-2 3 -4 5 4 3
-2 3 -4 6 2 17
-2 3 -4 7 4 3, 9, 17
-2 3 -3 2 3
-2 3 -3 3 4
-2 3 -3 5 4 5, 25
-2 3 -2 2 2
-2 3 -2 3 4 3, 39
-2 3 -1 0 3 11, 55
-2 3 -1 1 4 3, 9
-2 3 0 -1 4
-2 4 -8 10 0 3
-2 4 -8 11 4 3, 9
-2 4 -7 9 4
-2 4 -7 10 3 11
-2 4 -7 11 4 3, 9, 11, 33
-2 4 -7 13 4
-2 4 -6 9 4 3, 7
-2 4 -6 10 0
-2 4 -5 7 4 3, 11
-2 4 -5 9 4 3, 9, 13, 39
-2 4 -4 6 0
-2 4 -4 7 4
-2 4 -3 5 4 9
-2 5 -10 13 4 17
-2 5 -9 14 3 3
-2 5 -8 13 4 13, 97
-2 5 -7 13 4
-2 5 -6 11 4 3, 73
-2 6 -9 17 4 11
-1 -3 1 7 4 3, 9
-1 -3 2 5 4
-1 -2 0 6 1 3, 5, 11
-1 -2 0 7 4
-1 -2 1 3 4 5, 9, 11, 15, 33, 45, 55, 59, 99
-1 -2 1 4 3
-1 -2 2 1 4 3
-1 -2 2 2 1 3, 5, 9, 15, 17, 45
-1 -2 2 3 4 3, 9, 13, 39
-1 -1 -1 5 4 17
-1 -1 -1 7 4
-1 -1 0 2 2 3
-1 -1 0 3 4 3, 9, 93
-1 -1 0 5 4 3
-1 -1 1 -1 4 3, 9, 83
-1 -1 1 0 3 3
-1 -1 1 1 4
-1 -1 1 3 4 3
-1 -1 2 -3 4 3
-1 -1 2 -1 4
-1 -1 2 1 4 5
-1 -1 3 -1 4 3, 11, 15, 23, 25, 29, 31, 33, 37, 45, 55, 71, 75, 77, 93, 99
-1 0 -2 4 1 3, 9, 45
-1 0 -2 5 4 3
-1 0 -2 6 1
-1 0 -2 7 4 3, 9
-1 0 -1 1 4 3, 9
-1 0 -1 2 3
-1 0 -1 4 3 3, 9
-1 0 -1 5 4
-1 0 0 -2 1 3, 9
-1 0 0 -1 4 7, 35, 49
-1 0 0 1 4 3, 9
-1 0 0 2 1 5, 25
-1 0 0 3 4 11, 33
-1 0 1 -5 4 3, 9
-1 0 1 -4 3 3
-1 0 1 -3 4 5
-1 0 1 -2 3 3, 9, 17
-1 0 1 0 3
-1 0 1 1 4 3, 9
-1 0 2 -7 4 29
-1 0 2 -6 1 3
-1 0 2 -5 4 3, 9
-1 0 2 -4 1
-1 0 2 -3 4 3
-1 0 2 -2 1 3, 9
-1 0 2 -1 4 7
-1 0 3 -5 4 3, 7, 9, 27, 81
-1 0 3 -4 3 11
-1 1 -4 5 4 3, 9, 15
-1 1 -3 3 4 3, 63
-1 1 -3 5 4 15
-1 1 -3 7 4
-1 1 -2 0 2 7
-1 1 -2 1 4
-1 1 -2 3 4
-1 1 -2 4 2
-1 1 -2 6 2
-1 1 -2 7 4 7
-1 1 -1 -3 4 3, 9, 13, 39
-1 1 -1 -1 4 3, 9
-1 1 -1 0 3 3, 9
-1 1 -1 1 4 3
-1 1 -1 2 3 3, 9, 11
-1 1 -1 3 4 3, 9
-1 1 -1 4 3 3
-1 1 -1 5 4 3, 9, 13
-1 1 0 -5 4
-1 1 0 -2 2
-1 1 0 -1 4
-1 1 0 0 2 3
-1 1 0 1 4 11
-1 1 0 3 4 3, 31
-1 1 1 -5 4 11
-1 1 1 -3 4
-1 1 1 -2 3
-1 1 1 -1 4 3, 9, 27, 81
-1 1 1 1 4 5, 25
-1 1 2 -3 4 3, 9
-1 1 2 -2 2 3
-1 1 2 -1 4 3, 9
-1 1 3 -5 4
-1 1 3 -3 4 3
-1 1 4 -6 2 7, 9, 47
-1 1 4 -5 4
-1 2 -5 4 3
-1 2 -5 6 3 3, 19
-1 2 -4 1 4 7, 21
-1 2 -4 2 1
-1 2 -4 3 4 3
-1 2 -4 5 4
-1 2 -4 7 4
-1 2 -3 1 4
-1 2 -3 2 3 3
-1 2 -3 4 3
-1 2 -3 5 4 3
-1 2 -3 8 3 3, 5
-1 2 -2 1 4
-1 2 -2 3 4 3, 7
-1 2 -2 4 1
-1 2 -2 5 4 3, 9, 11, 33
-1 2 -2 6 1 3
-1 2 -2 7 4 5
-1 2 -1 2 3
-1 2 -1 4 3
-1 2 0 -1 4 3
-1 2 0 1 4 11
-1 2 0 2 1 3, 5
-1 2 0 3 4 3, 9
-1 2 1 1 4
-1 2 2 -1 4
-1 3 -6 5 4
-1 3 -5 5 4 3, 7
-1 3 -5 6 3 5
-1 3 -5 7 4 3, 9
-1 3 -4 5 4
-1 3 -4 6 2 3
-1 3 -4 8 2 5
-1 3 -3 5 4
-1 3 -3 7 4 3, 5, 9, 27, 81
-1 3 -3 8 3
-1 3 -3 9 4
-1 3 -2 6 2
-1 3 -2 7 4 3, 9
-1 3 -1 3 4 3
-1 3 -1 5 4 35
-1 3 1 3 4 5
-1 4 -6 9 4 3
-1 4 -5 10 3
-1 4 -4 9 4 3, 9
-1 4 -4 11 4 3, 9
-1 4 -2 9 4 11, 15, 19, 33, 55, 57, 61
-1 5 -5 13 4
0 -5 0 13 4 3, 5, 9, 11, 15, 25, 27, 31, 33, 45, 55, 59, 75, 93, 99
0 -4 0 9 4 3, 9, 11, 27, 97
0 -4 0 10 0 3, 7, 9, 47, 89
0 -3 -1 7 4 3
0 -3 0 6 2 3, 9, 27
0 -3 0 7 4 3, 5, 7, 9, 11, 15, 17, 21, 27, 33, 35, 39, 43, 45, 51, 61, 79, 85
0 -3 0 9 4 3, 5, 9, 11, 15, 27, 55, 59, 99
0 -3 1 7 4 3
0 -2 -1 3 4 3
0 -2 -1 5 4 3, 11
0 -2 0 1 4 3, 7, 9, 13, 21, 27, 47, 49, 63, 89, 91, 93
0 -2 0 2 0 3, 5, 9, 11, 15, 17, 29, 37, 45, 51, 53, 85, 87
0 -2 0 3 4 3, 5, 7, 9, 15, 25, 29, 35, 71
0 -2 0 4 0 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 25, 27, 31, 33, 35, 39, 41, 43, 45, 51, 55, 57, 61, 63, 65, 69, 71, 73, 75, 77, 85, 89, 91, 93, 99
0 -2 0 6 0 3, 9, 97
0 -2 0 7 4 3, 5, 7, 9, 17, 27, 51, 63, 85
0 -2 1 3 4 3
0 -2 1 5 4 3, 11
0 -1 -2 2 2
0 -1 -1 -1 4
0 -1 -1 0 3 3, 9, 15
0 -1 -1 1 4 5, 53
0 -1 -1 2 3
0 -1 -1 3 4 3, 9
0 -1 -1 4 3
0 -1 -1 5 4
0 -1 0 -3 4 3, 7, 9, 11, 17, 19, 21, 23, 27, 31, 47, 55, 57, 61, 69, 79, 93
0 -1 0 -2 2 3, 5, 9, 15, 45, 59, 75, 99
0 -1 0 -1 4 3, 7, 9, 11, 21, 41, 63, 83
0 -1 0 0 2 3, 9, 13, 27, 97
0 -1 0 1 4 3, 7, 9, 15, 45, 67, 83
0 -1 0 3 4 3, 5, 7, 9, 21, 27, 41, 59
0 -1 0 5 4 3, 9, 19
0 -1 0 7 4 3, 9, 15, 29, 41, 45
0 -1 1 -1 4
0 -1 1 0 3 3, 9, 15
0 -1 1 1 4 5, 53
0 -1 1 2 3
0 -1 1 3 4 3, 9
0 -1 1 4 3
0 -1 1 5 4
0 -1 2 2 2
0 0 -3 1 4 3, 9, 27
0 0 -2 -2 0 3
0 0 -2 -1 4 11
0 0 -2 0 0
0 0 -2 2 0
0 0 -2 3 4
0 0 -1 -5 4 3, 29
0 0 -1 -4 3
0 0 -1 -3 4
0 0 -1 -1 4
0 0 -1 1 4 3
0 0 -1 2 3
0 0 -1 3 4 17
0 0 -1 5 4
0 0 0 -7 4 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 31, 33, 39, 47, 51, 53, 55, 57, 61, 63, 85, 93
0 0 0 -6 0 3, 5, 9, 11, 15, 17, 23, 25, 27, 29, 33, 35, 37, 43, 45, 51, 53, 55, 65, 67, 69, 85, 87, 91, 99
0 0 0 -5 4 3, 5, 7, 9, 11, 15, 17, 21, 25, 27, 33, 35, 39, 41, 43, 45, 47, 51, 55, 61, 63, 79, 81, 85, 99
0 0 0 -3 4 3, 5, 7, 9, 13, 15, 17, 21, 27, 31, 35, 39, 41, 43, 49, 51, 63, 83, 89, 91, 93
0 0 0 -2 0 3, 5, 7, 9, 15, 17, 19, 21, 23, 25, 27, 31, 39, 45, 47, 51, 53, 57, 79, 83, 93
0 0 0 0 0 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 51, 53, 55, 57, 63, 65, 69, 73, 75, 85, 87, 89, 91, 93, 95, 97, 99
0 0 0 1 4 3, 5, 9, 11, 13, 15, 17, 23, 25, 27, 29, 31, 33, 35, 37, 39, 43, 45, 51, 53, 55, 57, 65, 75, 85, 87, 91, 95
0 0 0 2 0 3, 5, 7, 9, 13, 15, 17, 19, 21, 23, 31, 39, 47, 51, 53, 57, 93
0 0 0 3 4 3, 5, 7, 9, 13, 15, 17, 21, 25, 27, 31, 35, 39, 43, 49, 51, 59, 63, 71, 89, 91, 93, 95
0 0 0 5 4 3, 5, 7, 9, 11, 15, 17, 21, 25, 27, 29, 33, 35, 41, 43, 45, 47, 51, 55, 59, 61, 63, 71, 81, 83, 85, 99
0 0 0 6 0 3, 5, 7, 9, 11, 13, 15, 17, 23, 25, 27, 29, 33, 35, 37, 43, 45, 51, 53, 55, 65, 69, 71, 79, 85, 87, 91, 99
0 0 1 -5 4 3, 29
0 0 1 -4 3
0 0 1 -3 4
0 0 1 -1 4
0 0 1 1 4 3
0 0 1 2 3
0 0 1 3 4 17
0 0 1 5 4
0 0 2 -2 0 3
0 0 2 -1 4 11
0 0 2 0 0
0 0 2 2 0
0 0 2 3 4
0 0 3 1 4 3, 9, 27
0 1 -3 -3 4 3, 9
0 1 -3 -2 3 3, 9, 27
0 1 -3 0 3 3, 9
0 1 -3 1 4 3, 9, 27
0 1 -2 -3 4 3
0 1 -2 -1 4 3, 11, 17
0 1 -2 1 4
0 1 -2 2 2 3
0 1 -2 3 4 3
0 1 -1 -3 4 3
0 1 -1 -2 3 21
0 1 -1 -1 4 3, 11, 39
0 1 -1 0 3 3
0 1 -1 2 3 3
0 1 -1 4 3
0 1 -1 5 4 3
0 1 0 -2 2 3, 5, 9, 15, 21, 27, 45, 59, 63, 75, 99
0 1 0 -1 4 3, 7, 9, 21, 41, 63, 83
0 1 0 0 2 3, 9, 11, 13, 97
0 1 0 1 4 3, 7, 9, 15, 27, 45, 67, 83
0 1 0 3 4 3, 5, 7, 9, 41, 59
0 1 0 4 2 3, 7, 9, 27, 47, 89
0 1 0 7 4 3, 9, 15, 21, 27, 29, 41, 45, 63
0 1 1 -3 4 3
0 1 1 -2 3 21
0 1 1 -1 4 3, 11, 39
0 1 1 0 3 3
0 1 1 2 3 3
0 1 1 4 3
0 1 1 5 4 3
0 1 2 -3 4 3
0 1 2 -1 4 3, 11, 17
0 1 2 1 4
0 1 2 2 2 3
0 1 2 3 4 3
0 1 3 -3 4 3, 9
0 1 3 -2 3 3, 9, 27
0 1 3 0 3 3, 9
0 1 3 1 4 3, 9, 27
0 2 -5 -1 4 5, 11, 15, 55, 99
0 2 -4 2 0 89
0 2 -3 1 4 3, 9
0 2 -3 3 4 3, 7, 9, 27
0 2 -2 1 4
0 2 -2 2 0
0 2 -2 5 4 5
0 2 -1 1 4
0 2 -1 2 3
0 2 -1 3 4 3, 9
0 2 -1 5 4 5, 25, 65
0 2 -1 7 4 7
0 2 0 2 0 3, 5, 9, 11, 15, 17, 29, 37, 45, 51, 53, 85, 87
0 2 0 3 4 3, 5, 7, 9, 15, 25, 27, 29, 35, 71
0 2 0 4 0 3, 5, 7, 9, 11, 13, 15, 17, 21, 23, 25, 31, 33, 35, 39, 41, 43, 45, 51, 55, 57, 61, 63, 65, 69, 71, 73, 75, 77, 85, 89, 91, 93, 99
0 2 0 6 0 3, 9, 27, 97
0 2 0 7 4 3, 5, 7, 9, 17, 51, 85
0 2 1 1 4
0 2 1 2 3
0 2 1 3 4 3, 9
0 2 1 5 4 5, 25, 65
0 2 1 7 4 7
0 2 2 1 4
0 2 2 2 0
0 2 2 5 4 5
0 2 3 1 4 3, 9
0 2 3 3 4 3, 9, 27
0 2 4 2 0 89
0 2 5 -1 4 5, 11, 15, 55, 99
0 3 -2 5 4
0 3 -1 5 4
0 3 -1 8 3
0 3 0 5 4 3, 7, 9, 11, 15, 17, 23, 27, 29, 33, 37, 39, 43, 45, 51, 53, 55, 63, 67, 79, 81, 87, 91, 99
0 3 0 6 2 3, 9, 19, 27
0 3 0 7 4 3, 5, 7, 9, 11, 15, 17, 21, 27, 33, 35, 39, 43, 45, 51, 61, 79, 85
0 3 0 9 4 3, 5, 9, 11, 15, 27, 55, 59, 99
0 3 1 5 4
0 3 1 8 3
0 3 2 5 4
0 4 -1 9 4 3
0 4 0 9 4 3, 9, 97
0 4 0 10 0 3, 7, 9, 27, 47, 89
0 4 1 9 4 3
1 -3 -2 5 4
1 -3 -1 7 4 3, 9
1 -2 -2 1 4 3
1 -2 -2 2 1 3, 5, 9, 15, 17, 45
1 -2 -2 3 4 3, 9, 13, 39
1 -2 -1 3 4 5, 7, 9, 11, 15, 33, 45, 55, 59, 99
1 -2 -1 4 3
1 -2 0 6 1 3, 5, 11
1 -2 0 7 4
1 -1 -3 -1 4 3, 11, 15, 23, 25, 29, 31, 33, 37, 45, 55, 71, 75, 77, 79, 89, 93, 99
1 -1 -2 -3 4 3
1 -1 -2 -1 4
1 -1 -2 1 4 5
1 -1 -1 -1 4 3, 9, 83
1 -1 -1 0 3 3
1 -1 -1 1 4
1 -1 -1 3 4 3
1 -1 0 2 2 3
1 -1 0 3 4 3, 9, 93
1 -1 0 5 4 3
1 -1 1 5 4 17
1 -1 1 7 4
1 0 -3 -5 4 3, 9, 27, 81
1 0 -3 -4 3 11
1 0 -2 -7 4 29
1 0 -2 -6 1 3
1 0 -2 -5 4 3, 9
1 0 -2 -4 1
1 0 -2 -3 4 3
1 0 -2 -2 1 3, 9
1 0 -2 -1 4 7
1 0 -1 -5 4 3, 9
1 0 -1 -4 3 3
1 0 -1 -3 4 5
1 0 -1 -2 3 3, 9, 17
1 0 -1 0 3
1 0 -1 1 4 3, 9
1 0 0 -2 1 3, 9
1 0 0 -1 4 7, 35, 49
1 0 0 1 4 3, 9
1 0 0 2 1 5, 25
1 0 0 3 4 11, 33
1 0 1 1 4 3, 9
1 0 1 2 3
1 0 1 4 3 3, 9
1 0 1 5 4
1 0 2 4 1 3, 7, 9, 45
1 0 2 5 4 3
1 0 2 6 1
1 0 2 7 4 3, 9
1 1 -4 -6 2 7, 9, 47
1 1 -4 -5 4
1 1 -3 -5 4
1 1 -3 -3 4 3
1 1 -2 -3 4 3, 9
1 1 -2 -2 2 3
1 1 -2 -1 4 3, 9
1 1 -1 -5 4 11
1 1 -1 -3 4
1 1 -1 -2 3
1 1 -1 -1 4 3, 9, 27, 81
1 1 -1 1 4 5, 25
1 1 0 -5 4
1 1 0 -2 2
1 1 0 -1 4
1 1 0 0 2 3
1 1 0 1 4 11
1 1 0 3 4 3, 31
1 1 1 -3 4 3, 9, 13, 39
1 1 1 -1 4 3, 9
1 1 1 0 3 3, 7, 9
1 1 1 1 4 3
1 1 1 2 3 3, 9, 11
1 1 1 3 4 3, 9
1 1 1 4 3 3
1 1 1 5 4 3, 9, 13
1 1 2 0 2
1 1 2 1 4
1 1 2 3 4
1 1 2 4 2
1 1 2 6 2
1 1 2 7 4
1 1 3 3 4 3, 63
1 1 3 5 4 15
1 1 3 7 4
1 1 4 5 4 3, 9, 15
1 2 -2 -1 4
1 2 -1 1 4
1 2 0 -1 4 3
1 2 0 1 4 11
1 2 0 2 1 3, 5
1 2 0 3 4 3, 9
1 2 1 2 3
1 2 1 4 3
1 2 2 1 4
1 2 2 3 4 3
1 2 2 4 1
1 2 2 5 4 3, 9, 11, 33
1 2 2 6 1 3
1 2 2 7 4 5
1 2 3 1 4
1 2 3 2 3 3
1 2 3 4 3
1 2 3 5 4 3
1 2 3 8 3 3, 5
1 2 4 1 4 7, 21
1 2 4 2 1
1 2 4 3 4 3
1 2 4 5 4
1 2 4 7 4
1 2 5 4 3
1 2 5 6 3 3, 19
1 3 -1 3 4 5
1 3 1 3 4 3
1 3 1 5 4 35
1 3 2 6 2
1 3 2 7 4 3, 9
1 3 3 5 4
1 3 3 7 4 3, 5, 9, 27, 81
1 3 3 8 3
1 3 3 9 4
1 3 4 5 4
1 3 4 6 2 3
1 3 4 8 2 5
1 3 5 5 4 3
1 3 5 6 3 5
1 3 5 7 4 3, 9
1 3 6 5 4
1 4 2 9 4 11, 15, 19, 33, 55, 57, 61
1 4 4 9 4 3, 9
1 4 4 11 4 3, 9
1 4 5 10 3
1 4 6 9 4 3
1 5 5 13 4
2 -1 -3 -1 4 3
2 0 -4 -7 4
2 0 -4 -6 0 3
2 0 -3 -5 4 3, 9
2 0 -3 -4 3
2 0 -2 -2 0 3, 9, 45
2 0 -1 1 4 3, 9, 39
2 0 2 9 4 3
2 1 -4 -11 4 3, 7
2 1 -4 -10 2 3, 9
2 1 -3 -9 4 3
2 1 -3 -8 3 23
2 1 -3 -7 4 9, 11, 33, 99
2 1 -2 -6 2 7
2 1 -2 -5 4 5, 25
2 1 -2 -3 4 9, 13, 47, 91, 93
2 1 -1 -3 4 3, 9, 11, 33
2 1 -1 -1 4 3, 9, 15
2 1 0 1 4 15
2 1 1 3 4 15
2 1 1 4 3
2 1 2 5 4 3, 9
2 1 3 8 3
2 2 -3 -7 4 3
2 2 -2 -6 0 3, 11
2 2 -2 -5 4
2 2 -1 -5 4
2 2 -1 -3 4 3
2 2 0 -4 0 3, 5, 11, 13, 15, 17, 21, 25, 29, 31, 33, 35, 37, 39, 41, 45, 51, 55, 61, 63, 65, 75, 77, 85, 91, 93, 99
2 2 0 -3 4 3, 9
2 2 0 -2 0
2 2 0 -1 4 3, 11
2 2 1 -1 4 3, 9, 15
2 2 1 1 4 11
2 2 2 1 4 5, 13, 97
2 2 2 2 0
2 2 2 3 4 3
2 2 3 4 3
2 2 3 5 4 3
2 2 3 7 4
2 2 4 7 4
2 2 4 9 4 3
2 2 5 11 4 5, 11, 15, 25, 31, 33, 45, 55
2 3 0 -1 4
2 3 1 0 3 11, 55
2 3 1 1 4 3, 9
2 3 2 2 2
2 3 2 3 4 3, 39
2 3 3 2 3
2 3 3 3 4
2 3 3 5 4 5, 7, 25
2 3 4 3 4
2 3 4 5 4 3
2 3 4 6 2 17
2 3 4 7 4 3, 9, 17
2 3 5 7 4 3, 9
2 3 5 8 3
2 3 5 9 4 3
2 3 6 11 4
2 4 3 5 4 9
2 4 4 6 0
2 4 4 7 4
2 4 5 7 4 3, 11
2 4 5 9 4 3, 9, 13, 39
2 4 6 9 4 3
2 4 6 10 0
2 4 7 9 4
2 4 7 10 3 11
2 4 7 11 4 3, 9, 11, 33
2 4 7 13 4
2 4 8 10 0 3
2 4 8 11 4 3, 9
2 5 6 11 4 3, 73
2 5 7 13 4
2 5 8 13 4 13, 97
2 5 9 14 3 3
2 5 10 13 4 17
2 6 9 17 4 11
3 2 -6 -15 4 3, 7, 9, 27
3 2 -5 -13 4
3 2 -4 -10 1
3 2 0 1 4 3, 5, 7, 9, 11, 15, 25, 31, 33, 45, 55, 75, 93, 99
3 3 -3 -11 4 3, 5, 9, 27
3 3 -2 -7 4
3 3 -1 -5 4 3, 15, 17, 45
3 3 0 -3 4 3, 9, 27
3 3 1 0 3
3 3 2 3 4
3 4 2 -1 4 3
3 4 4 5 4 3
3 4 6 10 1 3, 9, 27
3 5 5 5 4
3 5 6 6 2 3, 9, 13, 27, 97
3 5 6 7 4 3, 9
3 5 7 9 4 3, 9
3 5 7 11 4 17
3 5 8 13 4
3 5 9 15 4 3, 9, 27
3 6 8 11 4
3 6 9 12 3 3, 9, 27
3 6 10 14 1
3 6 10 15 4
3 6 11 17 4
3 6 12 19 4 3, 9, 27
3 7 11 17 4 3
3 7 12 19 4 3, 9, 27
3 7 13 19 4 5
3 7 13 21 4 3, 5
3 8 14 23 4 11, 99
4 4 -7 -21 4 11, 15, 19, 31, 33, 55, 57, 61, 93
4 5 -2 -11 4 13, 97
4 6 4 2 0 7, 89
4 8 12 17 4 3, 5, 47, 89, 91, 93
4 9 17 27 4
4 10 19 29 4 3, 9
5 12 20 29 4 5, 11, 15, 55, 99
5 13 25 39 4 5, 11, 15, 19, 31, 33, 55, 57, 61, 85, 93