well, here is the same information when the target number has a factor of 2 or 3. The ratio pair (12,4) is evidently repeated, the two cases are $1,10 \pmod {12}.$
Oh, note that multiples of $9$ are never represented primitively. That is fine, the number of representations is exactly the same as the number of representations of $M/9.$
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g0 : 9 : 1 1 3 0 0 1 auto 24
g1 : 36 : 1 3 3 0 0 0 auto 16
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M r0 r1 h(4M) %72 r0/h r1/h
3 8 4 1 N 3 8 4 3 = 3
75 48 24 6 N 3 8 4 75 = 3 * 5^2
147 48 24 6 N 3 8 4 147 = 3 * 7^2
219 96 48 12 N 3 8 4 219 = 3 * 73
291 96 48 12 N 3 8 4 291 = 3 * 97
363 96 48 12 N 3 8 4 363 = 3 * 11^2
435 96 48 12 N 3 8 4 435 = 3 * 5 * 29
507 96 48 12 N 3 8 4 507 = 3 * 13^2
579 192 96 24 N 3 8 4 579 = 3 * 193
651 192 96 24 N 3 8 4 651 = 3 * 7 * 31
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
4 12 8 1 N 4 12 8 4 = 2^2
76 72 48 6 N 4 12 8 76 = 2^2 * 19
148 48 32 4 N 4 12 8 148 = 2^2 * 37
220 96 64 8 N 4 12 8 220 = 2^2 * 5 * 11
292 96 64 8 N 4 12 8 292 = 2^2 * 73
364 144 96 12 N 4 12 8 364 = 2^2 * 7 * 13
436 144 96 12 N 4 12 8 436 = 2^2 * 109
508 120 80 10 N 4 12 8 508 = 2^2 * 127
580 192 128 16 N 4 12 8 580 = 2^2 * 5 * 29
652 72 48 6 N 4 12 8 652 = 2^2 * 163
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
6 12 4 2 N 6 6 2 6 = 2 * 3
78 24 8 4 N 6 6 2 78 = 2 * 3 * 13
150 48 16 8 N 6 6 2 150 = 2 * 3 * 5^2
222 72 24 12 N 6 6 2 222 = 2 * 3 * 37
294 72 24 12 N 6 6 2 294 = 2 * 3 * 7^2
366 72 24 12 N 6 6 2 366 = 2 * 3 * 61
438 48 16 8 N 6 6 2 438 = 2 * 3 * 73
510 96 32 16 N 6 6 2 510 = 2 * 3 * 5 * 17
582 96 32 16 N 6 6 2 582 = 2 * 3 * 97
654 168 56 28 N 6 6 2 654 = 2 * 3 * 109
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
10 24 8 2 N10 12 4 10 = 2 * 5
82 48 16 4 N10 12 4 82 = 2 * 41
154 96 32 8 N10 12 4 154 = 2 * 7 * 11
226 96 32 8 N10 12 4 226 = 2 * 113
298 72 24 6 N10 12 4 298 = 2 * 149
370 144 48 12 N10 12 4 370 = 2 * 5 * 37
442 96 32 8 N10 12 4 442 = 2 * 13 * 17
514 192 64 16 N10 12 4 514 = 2 * 257
586 216 72 18 N10 12 4 586 = 2 * 293
658 96 32 8 N10 12 4 658 = 2 * 7 * 47
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
12 12 8 2 N12 6 4 12 = 2^2 * 3
84 48 32 8 N12 6 4 84 = 2^2 * 3 * 7
156 48 32 8 N12 6 4 156 = 2^2 * 3 * 13
228 48 32 8 N12 6 4 228 = 2^2 * 3 * 19
300 72 48 12 N12 6 4 300 = 2^2 * 3 * 5^2
372 48 32 8 N12 6 4 372 = 2^2 * 3 * 31
444 96 64 16 N12 6 4 444 = 2^2 * 3 * 37
516 144 96 24 N12 6 4 516 = 2^2 * 3 * 43
588 72 48 12 N12 6 4 588 = 2^2 * 3 * 7^2
660 96 64 16 N12 6 4 660 = 2^2 * 3 * 5 * 11
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
15 24 16 2 N15 12 8 15 = 3 * 5
87 72 48 6 N15 12 8 87 = 3 * 29
159 120 80 10 N15 12 8 159 = 3 * 53
231 144 96 12 N15 12 8 231 = 3 * 7 * 11
303 120 80 10 N15 12 8 303 = 3 * 101
375 120 80 10 N15 12 8 375 = 3 * 5^3
447 168 112 14 N15 12 8 447 = 3 * 149
519 216 144 18 N15 12 8 519 = 3 * 173
591 264 176 22 N15 12 8 591 = 3 * 197
663 192 128 16 N15 12 8 663 = 3 * 13 * 17
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
16 24 16 2 N16 12 8 16 = 2^4
88 48 32 4 N16 12 8 88 = 2^3 * 11
160 96 64 8 N16 12 8 160 = 2^5 * 5
232 48 32 4 N16 12 8 232 = 2^3 * 29
304 144 96 12 N16 12 8 304 = 2^4 * 19
376 192 128 16 N16 12 8 376 = 2^3 * 47
448 96 64 8 N16 12 8 448 = 2^6 * 7
520 96 64 8 N16 12 8 520 = 2^3 * 5 * 13
592 96 64 8 N16 12 8 592 = 2^4 * 37
664 240 160 20 N16 12 8 664 = 2^3 * 83
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
21 24 8 4 N21 6 2 21 = 3 * 7
93 24 8 4 N21 6 2 93 = 3 * 31
165 48 16 8 N21 6 2 165 = 3 * 5 * 11
237 72 24 12 N21 6 2 237 = 3 * 79
309 72 24 12 N21 6 2 309 = 3 * 103
381 120 40 20 N21 6 2 381 = 3 * 127
453 72 24 12 N21 6 2 453 = 3 * 151
525 96 32 16 N21 6 2 525 = 3 * 5^2 * 7
597 72 24 12 N21 6 2 597 = 3 * 199
669 72 24 12 N21 6 2 669 = 3 * 223
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
22 24 8 2 N22 12 4 22 = 2 * 11
94 96 32 8 N22 12 4 94 = 2 * 47
166 120 40 10 N22 12 4 166 = 2 * 83
238 96 32 8 N22 12 4 238 = 2 * 7 * 17
310 96 32 8 N22 12 4 310 = 2 * 5 * 31
382 96 32 8 N22 12 4 382 = 2 * 191
454 168 56 14 N22 12 4 454 = 2 * 227
526 144 48 12 N22 12 4 526 = 2 * 263
598 96 32 8 N22 12 4 598 = 2 * 13 * 23
670 144 48 12 N22 12 4 670 = 2 * 5 * 67
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
24 24 16 4 N24 6 4 24 = 2^3 * 3
96 48 32 8 N24 6 4 96 = 2^5 * 3
168 48 32 8 N24 6 4 168 = 2^3 * 3 * 7
240 48 32 8 N24 6 4 240 = 2^4 * 3 * 5
312 48 32 8 N24 6 4 312 = 2^3 * 3 * 13
384 96 64 16 N24 6 4 384 = 2^7 * 3
456 96 64 16 N24 6 4 456 = 2^3 * 3 * 19
528 96 64 16 N24 6 4 528 = 2^4 * 3 * 11
600 96 64 16 N24 6 4 600 = 2^3 * 3 * 5^2
672 96 64 16 N24 6 4 672 = 2^5 * 3 * 7
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
28 24 16 2 N28 12 8 28 = 2^2 * 7
100 48 32 4 N28 12 8 100 = 2^2 * 5^2
172 72 48 6 N28 12 8 172 = 2^2 * 43
244 144 96 12 N28 12 8 244 = 2^2 * 61
316 120 80 10 N28 12 8 316 = 2^2 * 79
388 96 64 8 N28 12 8 388 = 2^2 * 97
460 144 96 12 N28 12 8 460 = 2^2 * 5 * 23
532 96 64 8 N28 12 8 532 = 2^2 * 7 * 19
604 168 112 14 N28 12 8 604 = 2^2 * 151
676 144 96 12 N28 12 8 676 = 2^2 * 13^2
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
30 24 8 4 N30 6 2 30 = 2 * 3 * 5
102 24 8 4 N30 6 2 102 = 2 * 3 * 17
174 72 24 12 N30 6 2 174 = 2 * 3 * 29
246 72 24 12 N30 6 2 246 = 2 * 3 * 41
318 72 24 12 N30 6 2 318 = 2 * 3 * 53
390 96 32 16 N30 6 2 390 = 2 * 3 * 5 * 13
462 48 16 8 N30 6 2 462 = 2 * 3 * 7 * 11
534 120 40 20 N30 6 2 534 = 2 * 3 * 89
606 72 24 12 N30 6 2 606 = 2 * 3 * 101
678 120 40 20 N30 6 2 678 = 2 * 3 * 113
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
33 24 8 4 N33 6 2 33 = 3 * 11
105 48 16 8 N33 6 2 105 = 3 * 5 * 7
177 24 8 4 N33 6 2 177 = 3 * 59
249 72 24 12 N33 6 2 249 = 3 * 83
321 120 40 20 N33 6 2 321 = 3 * 107
393 72 24 12 N33 6 2 393 = 3 * 131
465 96 32 16 N33 6 2 465 = 3 * 5 * 31
537 72 24 12 N33 6 2 537 = 3 * 179
609 96 32 16 N33 6 2 609 = 3 * 7 * 29
681 120 40 20 N33 6 2 681 = 3 * 227
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
34 48 16 4 N34 12 4 34 = 2 * 17
106 72 24 6 N34 12 4 106 = 2 * 53
178 96 32 8 N34 12 4 178 = 2 * 89
250 120 40 10 N34 12 4 250 = 2 * 5^3
322 96 32 8 N34 12 4 322 = 2 * 7 * 23
394 120 40 10 N34 12 4 394 = 2 * 197
466 96 32 8 N34 12 4 466 = 2 * 233
538 120 40 10 N34 12 4 538 = 2 * 269
610 144 48 12 N34 12 4 610 = 2 * 5 * 61
682 144 48 12 N34 12 4 682 = 2 * 11 * 31
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
39 48 32 4 N39 12 8 39 = 3 * 13
111 96 64 8 N39 12 8 111 = 3 * 37
183 96 64 8 N39 12 8 183 = 3 * 61
255 144 96 12 N39 12 8 255 = 3 * 5 * 17
327 144 96 12 N39 12 8 327 = 3 * 109
399 192 128 16 N39 12 8 399 = 3 * 7 * 19
471 192 128 16 N39 12 8 471 = 3 * 157
543 144 96 12 N39 12 8 543 = 3 * 181
615 240 160 20 N39 12 8 615 = 3 * 5 * 41
687 144 96 12 N39 12 8 687 = 3 * 229
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
40 48 32 4 N40 12 8 40 = 2^3 * 5
112 48 32 4 N40 12 8 112 = 2^4 * 7
184 96 64 8 N40 12 8 184 = 2^3 * 23
256 96 64 8 N40 12 8 256 = 2^8
328 96 64 8 N40 12 8 328 = 2^3 * 41
400 96 64 8 N40 12 8 400 = 2^4 * 5^2
472 144 96 12 N40 12 8 472 = 2^3 * 59
544 192 128 16 N40 12 8 544 = 2^5 * 17
616 192 128 16 N40 12 8 616 = 2^3 * 7 * 11
688 144 96 12 N40 12 8 688 = 2^4 * 43
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
42 24 8 4 N42 6 2 42 = 2 * 3 * 7
114 48 16 8 N42 6 2 114 = 2 * 3 * 19
186 72 24 12 N42 6 2 186 = 2 * 3 * 31
258 48 16 8 N42 6 2 258 = 2 * 3 * 43
330 48 16 8 N42 6 2 330 = 2 * 3 * 5 * 11
402 96 32 16 N42 6 2 402 = 2 * 3 * 67
474 120 40 20 N42 6 2 474 = 2 * 3 * 79
546 144 48 24 N42 6 2 546 = 2 * 3 * 7 * 13
618 72 24 12 N42 6 2 618 = 2 * 3 * 103
690 96 32 16 N42 6 2 690 = 2 * 3 * 5 * 23
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
46 48 16 4 N46 12 4 46 = 2 * 23
118 72 24 6 N46 12 4 118 = 2 * 59
190 48 16 4 N46 12 4 190 = 2 * 5 * 19
262 72 24 6 N46 12 4 262 = 2 * 131
334 144 48 12 N46 12 4 334 = 2 * 167
406 192 64 16 N46 12 4 406 = 2 * 7 * 29
478 96 32 8 N46 12 4 478 = 2 * 239
550 144 48 12 N46 12 4 550 = 2 * 5^2 * 11
622 144 48 12 N46 12 4 622 = 2 * 311
694 120 40 10 N46 12 4 694 = 2 * 347
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
48 24 16 4 N48 6 4 48 = 2^4 * 3
120 48 32 8 N48 6 4 120 = 2^3 * 3 * 5
192 48 32 8 N48 6 4 192 = 2^6 * 3
264 96 64 16 N48 6 4 264 = 2^3 * 3 * 11
336 96 64 16 N48 6 4 336 = 2^4 * 3 * 7
408 48 32 8 N48 6 4 408 = 2^3 * 3 * 17
480 96 64 16 N48 6 4 480 = 2^5 * 3 * 5
552 96 64 16 N48 6 4 552 = 2^3 * 3 * 23
624 96 64 16 N48 6 4 624 = 2^4 * 3 * 13
696 144 96 24 N48 6 4 696 = 2^3 * 3 * 29
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
51 48 24 6 N51 8 4 51 = 3 * 17
123 48 24 6 N51 8 4 123 = 3 * 41
195 96 48 12 N51 8 4 195 = 3 * 5 * 13
267 48 24 6 N51 8 4 267 = 3 * 89
339 144 72 18 N51 8 4 339 = 3 * 113
411 144 72 18 N51 8 4 411 = 3 * 137
483 96 48 12 N51 8 4 483 = 3 * 7 * 23
555 96 48 12 N51 8 4 555 = 3 * 5 * 37
627 96 48 12 N51 8 4 627 = 3 * 11 * 19
699 240 120 30 N51 8 4 699 = 3 * 233
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
52 48 32 4 N52 12 8 52 = 2^2 * 13
124 72 48 6 N52 12 8 124 = 2^2 * 31
196 96 64 8 N52 12 8 196 = 2^2 * 7^2
268 72 48 6 N52 12 8 268 = 2^2 * 67
340 96 64 8 N52 12 8 340 = 2^2 * 5 * 17
412 120 80 10 N52 12 8 412 = 2^2 * 103
484 144 96 12 N52 12 8 484 = 2^2 * 11^2
556 216 144 18 N52 12 8 556 = 2^2 * 139
628 144 96 12 N52 12 8 628 = 2^2 * 157
700 144 96 12 N52 12 8 700 = 2^2 * 5^2 * 7
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
57 24 8 4 N57 6 2 57 = 3 * 19
129 72 24 12 N57 6 2 129 = 3 * 43
201 72 24 12 N57 6 2 201 = 3 * 67
273 48 16 8 N57 6 2 273 = 3 * 7 * 13
345 48 16 8 N57 6 2 345 = 3 * 5 * 23
417 72 24 12 N57 6 2 417 = 3 * 139
489 120 40 20 N57 6 2 489 = 3 * 163
561 96 32 16 N57 6 2 561 = 3 * 11 * 17
633 120 40 20 N57 6 2 633 = 3 * 211
705 144 48 24 N57 6 2 705 = 3 * 5 * 47
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
58 24 8 2 N58 12 4 58 = 2 * 29
130 48 16 4 N58 12 4 130 = 2 * 5 * 13
202 72 24 6 N58 12 4 202 = 2 * 101
274 144 48 12 N58 12 4 274 = 2 * 137
346 120 40 10 N58 12 4 346 = 2 * 173
418 96 32 8 N58 12 4 418 = 2 * 11 * 19
490 144 48 12 N58 12 4 490 = 2 * 5 * 7^2
562 96 32 8 N58 12 4 562 = 2 * 281
634 168 56 14 N58 12 4 634 = 2 * 317
706 288 96 24 N58 12 4 706 = 2 * 353
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
60 24 16 4 N60 6 4 60 = 2^2 * 3 * 5
132 48 32 8 N60 6 4 132 = 2^2 * 3 * 11
204 72 48 12 N60 6 4 204 = 2^2 * 3 * 17
276 96 64 16 N60 6 4 276 = 2^2 * 3 * 23
348 72 48 12 N60 6 4 348 = 2^2 * 3 * 29
420 96 64 16 N60 6 4 420 = 2^2 * 3 * 5 * 7
492 72 48 12 N60 6 4 492 = 2^2 * 3 * 41
564 96 64 16 N60 6 4 564 = 2^2 * 3 * 47
636 120 80 20 N60 6 4 636 = 2^2 * 3 * 53
708 48 32 8 N60 6 4 708 = 2^2 * 3 * 59
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
64 48 32 4 N64 12 8 64 = 2^6
136 96 64 8 N64 12 8 136 = 2^3 * 17
208 96 64 8 N64 12 8 208 = 2^4 * 13
280 96 64 8 N64 12 8 280 = 2^3 * 5 * 7
352 96 64 8 N64 12 8 352 = 2^5 * 11
424 144 96 12 N64 12 8 424 = 2^3 * 53
496 144 96 12 N64 12 8 496 = 2^4 * 31
568 96 64 8 N64 12 8 568 = 2^3 * 71
640 192 128 16 N64 12 8 640 = 2^7 * 5
712 192 128 16 N64 12 8 712 = 2^3 * 89
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
66 48 16 8 N66 6 2 66 = 2 * 3 * 11
138 48 16 8 N66 6 2 138 = 2 * 3 * 23
210 48 16 8 N66 6 2 210 = 2 * 3 * 5 * 7
282 48 16 8 N66 6 2 282 = 2 * 3 * 47
354 96 32 16 N66 6 2 354 = 2 * 3 * 59
426 144 48 24 N66 6 2 426 = 2 * 3 * 71
498 48 16 8 N66 6 2 498 = 2 * 3 * 83
570 96 32 16 N66 6 2 570 = 2 * 3 * 5 * 19
642 96 32 16 N66 6 2 642 = 2 * 3 * 107
714 144 48 24 N66 6 2 714 = 2 * 3 * 7 * 17
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
69 48 16 8 N69 6 2 69 = 3 * 23
141 48 16 8 N69 6 2 141 = 3 * 47
213 48 16 8 N69 6 2 213 = 3 * 71
285 96 32 16 N69 6 2 285 = 3 * 5 * 19
357 48 16 8 N69 6 2 357 = 3 * 7 * 17
429 96 32 16 N69 6 2 429 = 3 * 11 * 13
501 96 32 16 N69 6 2 501 = 3 * 167
573 96 32 16 N69 6 2 573 = 3 * 191
645 96 32 16 N69 6 2 645 = 3 * 5 * 43
717 96 32 16 N69 6 2 717 = 3 * 239
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
70 48 16 4 N70 12 4 70 = 2 * 5 * 7
142 48 16 4 N70 12 4 142 = 2 * 71
214 72 24 6 N70 12 4 214 = 2 * 107
286 144 48 12 N70 12 4 286 = 2 * 11 * 13
358 72 24 6 N70 12 4 358 = 2 * 179
430 144 48 12 N70 12 4 430 = 2 * 5 * 43
502 168 56 14 N70 12 4 502 = 2 * 251
574 192 64 16 N70 12 4 574 = 2 * 7 * 41
646 192 64 16 N70 12 4 646 = 2 * 17 * 19
718 144 48 12 N70 12 4 718 = 2 * 359
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
M r0 r1 h(4M) %72 r0/h r1/h
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g0 : 9 : 1 1 3 0 0 1 auto 24
g1 : 36 : 1 3 3 0 0 0 auto 16
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