To reduce the file sizes only the upper half plane roots are included in the following files. For each non-real root there is a corresponding complex conjugate root implied.
Root counts include upper and lower half planes 
16000x16000 or 25000x25000 (Use Save Link As)
Named counts are for upper half plane only 
20000x20000
Dust names are preliminary and may be changed in the future.
These files contain (x y size name); size is the distance between a root R and bulb R(1/2).
I hope to reach complete root coverage up to period 24. As you might expect the search gets more difficult with each period increase.
I had to break the larger files into parts because I was having trouble uploading them. The size shown is for each part.
| Period | Total Roots | Found (Named) | Data File |
|---|---|---|---|
| 1 | 1 | Complete (1) | MRoots_1.txt |
| 2 | 1 | Complete (1) | MRoots_2.txt |
| 3 | 3 | Complete (1) | MRoots_3.txt |
| 4 | 6 | Complete (2) | MRoots_4.txt (2 KB) |
| 5 | 15 | Complete (2) | MRoots_5.txt (3 KB) |
| 6 | 27 | Complete (3) | MRoots_6.txt (4 KB) |
| 7 | 63 | Complete (3) | MRoots_7.txt (9 KB) |
| 8 | 120 | Complete (5) | MRoots_8.txt (16 KB) |
| 9 | 252 | Complete (5) | MRoots_9.txt (31 KB) |
| 10 | 495 | Complete (6) | MRoots_10.txt (60 KB) |
| 11 | 1,023 | Complete (5) | MRoots_11.txt (122 KB) |
| 12 | 2,010 | Complete (11) | MRoots_12.txt (237 KB) |
| 13 | 4,095 | Complete (6) | MRoots_13.txt (479 KB) |
| 14 | 8,127 | Complete (9) | MRoots_14.txt (945 KB) |
| 15 | 16,365 | Complete (12) | MRoots_15.txt (1,893 KB) |
| 16 | 32,640 | Complete (14) | MRoots_16.txt (3,761 KB) |
| 17 | 65,535 | Complete (8) | MRoots_17.txt (7,523 KB) |
| 18 | 130,788 | Complete (19) | MRoots_18.txt (14,967 KB) |
| 19 | 262,143 | Complete (9) | MRoots_19.txt (29,912 KB) |
| 20 | 523,770 | Complete (22) | MRoots_20.txt (59,619 KB) |
| 21 | 1,048,509 | Complete (18) |
MRoots_21-Part_1.txt (90,661 KB) MRoots_21-Part_2.txt (28,409 KB) |
| 22 | 2,096,127 | 2,096,117 (15) |
MRoots_22-Part_1.txt (95,581 KB) MRoots_22-Part_2.txt (85,249 KB) MRoots_22-Part_3.txt (56,720 KB) |
| 23 | 4,194,303 | 4,111,852 (11) |
MRoots_23-Part_1.txt (104,849 KB) MRoots_23-Part_2.txt (85,249 KB) MRoots_23-Part_3.txt (85,249 KB) MRoots_23-Part_4.txt (85,249 KB) MRoots_23-Part_5.txt (85,249 KB) MRoots_23-Part_6.txt (19,479 KB) |
| 24 | 8,386,440 | 5,068,236 (39) |
MRoots_24-Part_1.txt (119,265 KB) MRoots_24-Part_2.txt (85,876 KB) MRoots_24-Part_3.txt (85,249 KB) MRoots_24-Part_4.txt (85,249 KB) MRoots_24-Part_5.txt (85,249 KB) MRoots_24-Part_6.txt (85,249 KB) MRoots_24-Part_7.txt (37,901 KB) |
| 25 | 16,777,200 | 153,384 (18) | MRoots_25.txt (16,678 KB) |
| 26 | 33,550,335 | 174,717 (18) | MRoots_26.txt (19,008 KB) |
| 27 | 67,108,608 | 196,688 (25) | MRoots_27.txt (21,360 KB) |
| 28 | 134,209,530 | 222,661 (33) | MRoots_28.txt (24,193 KB) |
| 29 | 268,435,455 | 245,160 (14) | MRoots_29.txt (26,603 KB) |
| 30 | 536,854,005 | 268,570 (52) | MRoots_30.txt (29,163 KB) |
| 31 | 1,073,741,823 | 127,927 (15) | MRoots_31.txt (13,872 KB) |
| 32 | 2,147,450,880 | 135,335 (41) | MRoots_32.txt (14,696 KB) |
| 33 | 4,294,966,269 | 145,215 (30) | MRoots_33.txt (15,748 KB) |
| 34 | 8,589,869,055 | 149,748 (24) | MRoots_34.txt (16,249 KB) |
| 35 | 17,179,869,105 | 159,745 (36) | MRoots_35.txt (17,321 KB) |
| 36 | 34,359,605,280 | 164,725 (79) | MRoots_36.txt (17,869 KB) |
| 37 | 68,719,476,735 | 174,793 (18) | MRoots_37.txt (18,949 KB) |
| 38 | 137,438,691,327 | 177,703 (27) | MRoots_38.txt (19,274 KB) |
| 39 | 274,877,902,845 | 187,393 (36) | MRoots_39.txt (20,317 KB) |
| 40 | 549,755,289,480 | 189,743 (78) | MRoots_40.txt (20,581 KB) |
| 41 | 1,099,511,627,775 | 200,345 (20) | MRoots_41.txt (21,719 KB) |
| 42 | 2,199,022,198,821 | 199,303 (78) | MRoots_42.txt (21,613 KB) |
| 43 | 4,398,046,511,103 | 212,039 (21) | MRoots_43.txt (22,987 KB) |
| 44 | 8,796,090,925,050 | 211,545 (55) | MRoots_44.txt (22,939 KB) |
| 45 | 17,592,186,027,780 | 219,846 (76) | MRoots_45.txt (23,834 KB) |
| 46 | 35,184,367,894,527 | 221,119 (33) | MRoots_46.txt (23,974 KB) |
| 47 | 70,368,744,177,663 | 231,951 (23) | MRoots_47.txt (25,144 KB) |
| 48 | 140,737,479,934,080 | 226,380 (135) | MRoots_48.txt (24,551 KB) |
| 49 | 281,474,976,710,592 | 241,185 (39) | MRoots_49.txt (26,146 KB) |
| 50 | 562,949,936,643,600 | 237,786 (70) | MRoots_50.txt (25,780 KB) |
| 51 | 1,125,899,906,777,085 | 245,923 (48) | MRoots_51.txt (26,659 KB) |
| 52 | 2,251,799,780,130,810 | 244,041 (66) | MRoots_52.txt (26,460 KB) |
| 53 | 4,503,599,627,370,495 | 256,014 (26) | MRoots_53.txt (27,753 KB) |
| 54 | 9,007,199,187,501,312 | 248,876 (115) | MRoots_54.txt (26,982 KB) |
| 55 | 18,014,398,509,480,945 | 261,367 (60) | MRoots_55.txt (28,334 KB) |
| 56 | 36,028,796,884,746,120 | 255,213 (117) | MRoots_56.txt (27,675 KB) |
| 57 | 72,057,594,037,665,789 | 264,817 (54) | MRoots_57.txt (28,708 KB) |
| 58 | 144,115,187,807,420,415 | 264,150 (42) | MRoots_58.txt (28,638 KB) |
| 59 | 288,230,376,151,711,743 | 273,627 (29) | MRoots_59.txt (29,662 KB) |
| 60 | 576,460,751,766,026,790 | 258,438 (228) | MRoots_60.txt (28,022 KB) |
| 61 | 1,152,921,504,606,846,975 | 277,620 (30) | MRoots_61.txt (30,095 KB) |
| 62 | 2,305,843,008,139,952,127 | 272,862 (45) | MRoots_62.txt (29,580 KB) |
| 63 | 4,611,686,018,426,339,076 | 275,278 (114) | MRoots_63.txt (29,842 KB) |
| 64 | 9,223,372,034,707,292,160 | 273,329 (122) | MRoots_64.txt (29,634 KB) |
| 65 | 18,446,744,073,709,547,505 | 284,134 (72) | MRoots_65.txt (30,802 KB) |
| 66 | 36,893,488,143,122,039,781 | 274,274 (130) | MRoots_66.txt (29,735 KB) |
| 67 | 73,786,976,294,838,206,463 | 288,113 (33) | MRoots_67.txt (31,232 KB) |
| 68 | 147,573,952,581,086,478,330 | 280,596 (88) | MRoots_68.txt (30,421 KB) |
| 69 | 295,147,905,179,348,631,549 | 287,726 (66) | MRoots_69.txt (31,191 KB) |
| 70 | 590,295,810,341,525,773,905 | 280,412 (156) | MRoots_70.txt (30,400 KB) |
| 71 | 1,180,591,620,717,411,303,423 | 294,328 (35) | MRoots_71.txt (31,906 KB) |
| 72 | 2,361,183,241,400,454,481,920 | 276,617 (311) | MRoots_72.txt (29,994 KB) |
| 73 | 4,722,366,482,869,645,213,695 | 295,191 (36) | MRoots_73.txt (32,000 KB) |
| 74 | 9,444,732,965,670,570,950,655 | 290,880 (54) | MRoots_74.txt (31,533 KB) |
| 75 | 18,889,465,931,478,564,061,200 | 1,452 (140) | MRoots_75.txt (160 KB) |
| 76 | 37,778,931,862,819,722,756,090 | 1,982 (99) | MRoots_76.txt (217 KB) |
| 77 | 75,557,863,725,914,323,418,049 | 1,284 (90) | MRoots_77.txt (141 KB) |
| 78 | 151,115,727,451,553,735,380,965 | 1,850 (156) | MRoots_78.txt (204 KB) |
| 79 | 302,231,454,903,657,293,676,543 | 1,198 (39) | MRoots_79.txt (131 KB) |
| 80 | 604,462,909,806,764,831,506,560 | 1,826 (270) | MRoots_80.txt (204 KB) |
| 81 | 1,208,925,819,614,629,107,597,312 | 1,736 (125) | MRoots_81.txt (191 KB) |
| 82 | 2,417,851,639,228,158,837,784,575 | 1,130 (60) | MRoots_82.txt (124 KB) |
| 83 | 4,835,703,278,458,516,698,824,703 | 1,128 (41) | MRoots_83.txt (124 KB) |
| 84 | 9,671,406,556,914,834,240,182,310 | 2,959 (342) | MRoots_84.txt (328 KB) |
| 85 | 19,342,813,113,834,066,795,233,265 | 2,136 (96) | MRoots_85.txt (234 KB) |
| 86 | 38,685,626,227,663,735,544,086,527 | 1,242 (63) | MRoots_86.txt (136 KB) |
| 87 | 77,371,252,455,336,266,912,759,805 | 1,224 (84) | MRoots_87.txt (135 KB) |
| 88 | 154,742,504,910,663,738,269,368,200 | 2,032 (195) | MRoots_88.txt (225 KB) |
| 89 | 309,485,009,821,345,068,724,781,055 | 1,172 (44) | MRoots_89.txt (128 KB) |
| 90 | 618,970,019,642,672,544,726,532,380 | 2,394 (404) | MRoots_90.txt (268 KB) |
| 91 | 1,237,940,039,285,380,274,899,120,065 | 1,234 (108) | MRoots_91.txt (136 KB) |
| 92 | 2,475,880,078,570,725,365,426,159,610 | 1,734 (121) | MRoots_92.txt (191 KB) |
| >144 | - | 0 | MRoots_More.txt |
Searching is performed using a quadtree subdivision of the grid which increases search resolution in areas of higher root density. Within a search area first a map of the function magnitude is made at moderate resolution, then points of local minimum are refined using 768 bit fixed point math. The final root is saved to 384 bits (good for the 96 digit tables). Root searching is done at twice the precision of the desired result due to multiplying very small numbers and accumulation of rounding errors. As roots are added the quadtree is subdivided further and the search continues. Only the upper half plane is searched due to symmetry.
Quadtree depth was purposely limited on higher periods to reduce run time since the number of roots becomes unmanageable.
Quadtree
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