User:Contribution/(31-Limit Factor Gradient) x (26 Tritaves Chain) x (Infinite Octaves) Table

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Purpose

See here.

Content

For each interval, you'll find: its factorization (ignoring octaves), its just ratio, its Functional Just System notation and its cents value.

Table

Limit Boundary

~~

17-31-limit
Limit Boundary

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17-31-limit
Limit Boundary

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17-31-limit
Limit Boundary

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17-31-limit
Limit Boundary

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17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

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17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
Limit Boundary

~~

17-31-limit
3-26⋅311

4260607557632/2541865828329

ddd831

894.205549964
3-25⋅311

1065151889408/847288609443

ddd531

396.160550830
3-24⋅311

532575944704/282429536481

cdd231

1098.115551695
3-23⋅311

133143986176/94143178827

dd631

600.070552560
3-22⋅311

33285996544/31381059609

dd331

102.025553426
3-21⋅311

16642998272/10460353203

dd731

803.980554291
3-20⋅311

4160749568/3486784401

dd431

305.935555157
3-19⋅311

2080374784/1162261467

dd831

1007.890556022
3-18⋅311

520093696/387420489

dd531

509.845556887
3-17⋅311

130023424/129140163

d231

11.800557753
3-16⋅311

65011712/43046721

d631

713.755558618
3-15⋅311

16252928/14348907

d331

215.710559483
3-14⋅311

8126464/4782969

d731

917.665560349
3-13⋅311

2031616/1594323

d431

419.620561214
3-12⋅311

1015808/531441

d831

1121.575562080
3-11⋅311

253952/177147

d531

623.530562945
3-10⋅311

63488/59049

m231

125.485563810
3-9⋅311

31744/19683

m631

827.440564676
3-8⋅311

7936/6561

m331

329.395565541
3-7⋅311

3968/2187

m731

1031.350566407
3-6⋅311

992/729

P431

533.305567272
3-5⋅311

248/243

P131

35.260568137
3-4⋅311

124/81

P531

737.215569003
3-3⋅311

31/27

M231

239.170569868
3-2⋅311

31/18

M631

941.125570733
3-1⋅311

31/24

M331

443.080571599
311

31/16

M731

1145.035572464
31⋅311

93/64

A431

646.990573330
32⋅311

279/256

A131

148.945574195
33⋅311

837/512

A531

850.900575060
34⋅311

2511/2048

A231

352.855575926
35⋅311

7533/4096

A631

1054.810576791
36⋅311

22599/16384

A331

556.765577657
37⋅311

67797/65536

-cA731

58.720578522
38⋅311

203391/131072

AA431

760.675579387
39⋅311

610173/524288

AA131

262.630580253
310⋅311

1830519/1048576

AA531

964.585581118
311⋅311

5491557/4194304

AA231

466.540581984
312⋅311

16474671/8388608

AA631

1168.495582849
313⋅311

49424013/33554432

AA331

670.450583714
314⋅311

148272039/134217728

-cAA731

172.405584580
315⋅311

444816117/268435456

AAA431

874.360585445
316⋅311

1334448351/1073741824

AAA131

376.315586310
317⋅311

4003345053/2147483648

AAA531

1078.270587176
318⋅311

12010035159/8589934592

AAA231

580.225588041
319⋅311

36030105477/34359738368

-cAAA631

82.180588907
320⋅311

108090316431/68719476736

AAA331

784.135589772
321⋅311

324270949293/274877906944

-cAAA731

286.090590637
322⋅311

972812847879/549755813888

AAAA431

988.045591503
323⋅311

2918438543637/2199023255552

AAAA131

490.000592368
324⋅311

8755315630911/4398046511104

AAAA531

1191.955593234
325⋅311

26265946892733/17592186044416

AAAA231

693.910594099
326⋅311

78797840678199/70368744177664

-cAAAA631

195.865594964
3-26⋅291

3985729650688/2541865828329

dddd829

778.747171653
3-25⋅291

996432412672/847288609443

dddd529

280.702172518
3-24⋅291

498216206336/282429536481

cddd229

982.657173384
3-23⋅291

124554051584/94143178827

ddd629

484.612174249
3-22⋅291

62277025792/31381059609

cddd329

1186.567175115
3-21⋅291

15569256448/10460353203

ddd729

688.522175980
3-20⋅291

3892314112/3486784401

ddd429

190.477176845
3-19⋅291

1946157056/1162261467

ddd829

892.432177711
3-18⋅291

486539264/387420489

ddd529

394.387178576
3-17⋅291

243269632/129140163

cdd229

1096.342179442
3-16⋅291

60817408/43046721

dd629

598.297180307
3-15⋅291

15204352/14348907

dd329

100.252181172
3-14⋅291

7602176/4782969

dd729

802.207182038
3-13⋅291

1900544/1594323

dd429

304.162182903
3-12⋅291

950272/531441

dd829

1006.117183768
3-11⋅291

237568/177147

dd529

508.072184634
3-10⋅291

59392/59049

d229

10.027185499
3-9⋅291

29696/19683

d629

711.982186365
3-8⋅291

7424/6561

d329

213.937187230
3-7⋅291

3712/2187

d729

915.892188095
3-6⋅291

928/729

d429

417.847188961
3-5⋅291

464/243

d829

1119.802189826
3-4⋅291

116/81

d529

621.757190692
3-3⋅291

29/27

m229

123.712191557
3-2⋅291

29/18

m629

825.667192422
3-1⋅291

29/24

m329

327.622193288
291

29/16

m729

1029.577194153
31⋅291

87/64

P429

531.532195018
32⋅291

261/256

P129

33.487195884
33⋅291

783/512

P529

735.442196749
34⋅291

2349/2048

M229

237.397197615
35⋅291

7047/4096

M629

939.352198480
36⋅291

21141/16384

M329

441.307199345
37⋅291

63423/32768

M729

1143.262200211
38⋅291

190269/131072

A429

645.217201076
39⋅291

570807/524288

A129

147.172201942
310⋅291

1712421/1048576

A529

849.127202807
311⋅291

5137263/4194304

A229

351.082203672
312⋅291

15411789/8388608

A629

1053.037204538
313⋅291

46235367/33554432

A329

554.992205403
314⋅291

138706101/134217728

-cA729

56.947206269
315⋅291

416118303/268435456

AA429

758.902207134
316⋅291

1248354909/1073741824

AA129

260.857207999
317⋅291

3745064727/2147483648

AA529

962.812208865
318⋅291

11235194181/8589934592

AA229

464.767209730
319⋅291

33705582543/17179869184

AA629

1166.722210595
320⋅291

101116747629/68719476736

AA329

668.677211461
321⋅291

303350242887/274877906944

-cAA729

170.632212326
322⋅291

910050728661/549755813888

AAA429

872.587213192
323⋅291

2730152185983/2199023255552

AAA129

374.542214057
324⋅291

8190456557949/4398046511104

AAA529

1076.497214922
325⋅291

24571369673847/17592186044416

AAA229

578.452215788
326⋅291

73714109021541/70368744177664

-cAAA629

80.407216653
3-26⋅231

3161095929856/2541865828329

ddd523

377.444324768
3-25⋅231

1580547964928/847288609443

cdd223

1079.399325634
3-24⋅231

395136991232/282429536481

dd623

581.354326499
3-23⋅231

98784247808/94143178827

dd323

83.309327365
3-22⋅231

49392123904/31381059609

dd723

785.264328230
3-21⋅231

12348030976/10460353203

dd423

287.219329095
3-20⋅231

6174015488/3486784401

dd823

989.174329961
3-19⋅231

1543503872/1162261467

dd523

491.129330826
3-18⋅231

771751936/387420489

cd223

1193.084331691
3-17⋅231

192937984/129140163

d623

695.039332557
3-16⋅231

48234496/43046721

d323

196.994333422
3-15⋅231

24117248/14348907

d723

898.949334288
3-14⋅231

6029312/4782969

d423

400.904335153
3-13⋅231

3014656/1594323

d823

1102.859336018
3-12⋅231

753664/531441

d523

604.814336884
3-11⋅231

188416/177147

m223

106.769337749
3-10⋅231

94208/59049

m623

808.724338615
3-9⋅231

23552/19683

m323

310.679339480
3-8⋅231

11776/6561

m723

1012.634340345
3-7⋅231

2944/2187

P423

514.589341211
3-6⋅231

736/729

P123

16.544342076
3-5⋅231

368/243

P523

718.499342941
3-4⋅231

92/81

M223

220.454343807
3-3⋅231

46/27

M623

922.409344672
3-2⋅231

23/18

M323

424.364345538
3-1⋅231

23/12

M723

1126.319346403
231

23/16

A423

628.274347268
31⋅231

69/64

A123

130.229348134
32⋅231

207/128

A523

832.184348999
33⋅231

621/512

A223

334.139349865
34⋅231

1863/1024

A623

1036.094350730
35⋅231

5589/4096

A323

538.049351595
36⋅231

16767/16384

-cA723

40.004352461
37⋅231

50301/32768

AA423

741.959353326
38⋅231

150903/131072

AA123

243.914354192
39⋅231

452709/262144

AA523

945.869355057
310⋅231

1358127/1048576

AA223

447.824355922
311⋅231

4074381/2097152

AA623

1149.779356788
312⋅231

12223143/8388608

AA323

651.734357653
313⋅231

36669429/33554432

-cAA723

153.689358518
314⋅231

110008287/67108864

AAA423

855.644359384
315⋅231

330024861/268435456

AAA123

357.599360249
316⋅231

990074583/536870912

AAA523

1059.554361115
317⋅231

2970223749/2147483648

AAA223

561.509361980
318⋅231

8910671247/8589934592

-cAAA623

63.464362845
319⋅231

26732013741/17179869184

AAA323

765.419363711
320⋅231

80196041223/68719476736

-cAAA723

267.374364576
321⋅231

240588123669/137438953472

AAAA423

969.329365442
322⋅231

721764371007/549755813888

AAAA123

471.284366307
323⋅231

2165293113021/1099511627776

AAAA523

1173.239367172
324⋅231

6495879339063/4398046511104

AAAA223

675.194368038
325⋅231

19487638017189/17592186044416

-cAAAA623

177.149368903
326⋅231

58462914051567/35184372088832

AAAA323

879.104369768
3-26⋅191

2611340115968/2541865828329

dddd419

46.682993632
3-25⋅191

1305670057984/847288609443

dddd819

748.637994498
3-24⋅191

326417514496/282429536481

dddd519

250.592995363
3-23⋅191

163208757248/94143178827

cddd219

952.547996228
3-22⋅191

40802189312/31381059609

ddd619

454.502997094
3-21⋅191

20401094656/10460353203

cddd319

1156.457997959
3-20⋅191

5100273664/3486784401

ddd719

658.412998825
3-19⋅191

1275068416/1162261467

ddd419

160.367999690
3-18⋅191

637534208/387420489

ddd819

862.323000555
3-17⋅191

159383552/129140163

ddd519

364.278001421
3-16⋅191

79691776/43046721

cdd219

1066.233002286
3-15⋅191

19922944/14348907

dd619

568.188003151
3-14⋅191

4980736/4782969

dd319

70.143004017
3-13⋅191

2490368/1594323

dd719

772.098004882
3-12⋅191

622592/531441

dd419

274.053005748
3-11⋅191

311296/177147

dd819

976.008006613
3-10⋅191

77824/59049

dd519

477.963007478
3-9⋅191

38912/19683

cd219

1179.918008344
3-8⋅191

9728/6561

d619

681.873009209
3-7⋅191

2432/2187

d319

183.828010075
3-6⋅191

1216/729

d719

885.783010940
3-5⋅191

304/243

d419

387.738011805
3-4⋅191

152/81

d819

1089.693012671
3-3⋅191

38/27

d519

591.648013536
3-2⋅191

19/18

m219

93.603014402
3-1⋅191

19/12

m619

795.558015267
191

19/16

m319

297.513016132
31⋅191

57/32

m719

999.468016998
32⋅191

171/128

P419

501.423017863
33⋅191

513/512

P119

3.378018728
34⋅191

1539/1024

P519

705.333019594
35⋅191

4617/4096

M219

207.288020459
36⋅191

13851/8192

M619

909.243021325
37⋅191

41553/32768

M319

411.198022190
38⋅191

124659/65536

M719

1113.153023055
39⋅191

373977/262144

A419

615.108023921
310⋅191

1121931/1048576

A119

117.063024786
311⋅191

3365793/2097152

A519

819.018025652
312⋅191

10097379/8388608

A219

320.973026517
313⋅191

30292137/16777216

A619

1022.928027382
314⋅191

90876411/67108864

A319

524.883028248
315⋅191

272629233/268435456

-cA719

26.838029113
316⋅191

817887699/536870912

AA419

728.793029979
317⋅191

2453663097/2147483648

AA119

230.748030844
318⋅191

7360989291/4294967296

AA519

932.703031709
319⋅191

22082967873/17179869184

AA219

434.658032575
320⋅191

66248903619/34359738368

AA619

1136.613033440
321⋅191

198746710857/137438953472

AA319

638.568034305
322⋅191

596240132571/549755813888

-cAA719

140.523035171
323⋅191

1788720397713/1099511627776

AAA419

842.478036036
324⋅191

5366161193139/4398046511104

AAA119

344.433036902
325⋅191

16098483579417/8796093022208

AAA519

1046.388037767
326⋅191

48295450738251/35184372088832

AAA219

548.343038632
3-26⋅171

4672924418048/2541865828329

cdddd317

1054.125387000
3-25⋅171

1168231104512/847288609443

dddd717

556.080387866
3-24⋅171

292057776128/282429536481

dddd417

58.035388731
3-23⋅171

146028888064/94143178827

dddd817

759.990389596
3-22⋅171

36507222016/31381059609

dddd517

261.945390462
3-21⋅171

18253611008/10460353203

cddd217

963.900391327
3-20⋅171

4563402752/3486784401

ddd617

465.855392193
3-19⋅171

2281701376/1162261467

cddd317

1167.810393058
3-18⋅171

570425344/387420489

ddd717

669.765393923
3-17⋅171

142606336/129140163

ddd417

171.720394789
3-16⋅171

71303168/43046721

ddd817

873.675395654
3-15⋅171

17825792/14348907

ddd517

375.630396520
3-14⋅171

8912896/4782969

cdd217

1077.585397385
3-13⋅171

2228224/1594323

dd617

579.540398250
3-12⋅171

557056/531441

dd317

81.495399116
3-11⋅171

278528/177147

dd717

783.450399981
3-10⋅171

69632/59049

dd417

285.405400847
3-9⋅171

34816/19683

dd817

987.360401712
3-8⋅171

8704/6561

dd517

489.315402577
3-7⋅171

4352/2187

cd217

1191.270403443
3-6⋅171

1088/729

d617

693.225404308
3-5⋅171

272/243

d317

195.180405173
3-4⋅171

136/81

d717

897.135406039
3-3⋅171

34/27

d417

399.090406904
3-2⋅171

17/9

d817

1101.045407770
3-1⋅171

17/12

d517

603.000408635
171

17/16

m217

104.955409500
31⋅171

51/32

m617

806.910410366
32⋅171

153/128

m317

308.865411231
33⋅171

459/256

m717

1010.820412097
34⋅171

1377/1024

P417

512.775412962
35⋅171

4131/4096

P117

14.730413827
36⋅171

12393/8192

P517

716.685414693
37⋅171

37179/32768

M217

218.640415558
38⋅171

111537/65536

M617

920.595416424
39⋅171

334611/262144

M317

422.550417289
310⋅171

1003833/524288

M717

1124.505418154
311⋅171

3011499/2097152

A417

626.460419020
312⋅171

9034497/8388608

A117

128.415419885
313⋅171

27103491/16777216

A517

830.370420750
314⋅171

81310473/67108864

A217

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180224/177147

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29.812932845
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3-9⋅111

22528/19683

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233.722934576
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11264/6561

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935.677935442
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2816/2187

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1408/729

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1139.587937172
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352/243

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3-4⋅111

88/81

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44/27

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11/9

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11/6

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11/8

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1143.518095612
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411.727445037
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261508830075/137438953472

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1113.682445903
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784526490225/549755813888

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615.637446768
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2353579470675/2199023255552

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117.592447634
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7060738412025/4398046511104

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819.547448499
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21182215236075/17592186044416

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321.502449364
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1023.457450230
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2748779069440/2541865828329

ddd45

135.483691365
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1374389534720/847288609443

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837.438692230
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343597383680/282429536481

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339.393693096
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171798691840/94143178827

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1041.348693961
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42949672960/31381059609

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543.303694826
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10737418240/10460353203

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45.258695692
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5368709120/3486784401

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747.213696557
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1342177280/1162261467

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249.168697422
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671088640/387420489

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951.123698288
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167772160/129140163

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453.078699153
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83886080/43046721

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1155.033700019
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20971520/14348907

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656.988700884
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5242880/4782969

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158.943701749
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2621440/1594323

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860.898702615
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655360/531441

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362.853703480
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327680/177147

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1064.808704346
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81920/59049

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566.763705211
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20480/19683

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68.718706076
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10240/6561

m65

770.673706942
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2560/2187

m35

272.628707807
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1280/729

m75

974.583708673
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320/243

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476.538709538
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160/81

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1178.493710403
3-3⋅51

40/27

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680.448711269
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10/9

M25

182.403712134
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5/3

M65

884.358712999
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5/4

M35

386.313713865
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15/8

M75

1088.268714730
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45/32

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590.223715596
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135/128

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92.178716461
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405/256

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794.133717326
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1215/1024

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296.088718192
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3645/2048

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998.043719057
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10935/8192

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499.998719923
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32805/32768

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1.953720788
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98415/65536

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703.908721653
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295245/262144

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205.863722519
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885735/524288

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907.818723384
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2657205/2097152

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409.773724249
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7971615/4194304

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1111.728725115
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23914845/16777216

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613.683725980
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319.548728576
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1021.503729442
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5811307335/4294967296

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637.143736365
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3-limit
3-26

4398046511104/2541865828329

cddd2

949.169977500
3-25

1099511627776/847288609443

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451.124978365
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549755813888/282429536481

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1153.079979231
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137438953472/94143178827

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655.034980096
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34359738368/31381059609

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156.989980961
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17179869184/10460353203

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858.944981827
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4294967296/3486784401

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360.899982692
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2147483648/1162261467

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1062.854983558
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536870912/387420489

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564.809984423
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134217728/129140163

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66.764985288
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67108864/43046721

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768.719986154
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16777216/14348907

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270.674987019
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8388608/4782969

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972.629987885
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2097152/1594323

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474.584988750
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1048576/531441

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1176.539989615
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262144/177147

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678.494990481
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65536/59049

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180.449991346
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32768/19683

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882.404992212
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8192/6561

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384.359993077
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4096/2187

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1086.314993942
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1024/729

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588.269994808
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256/243

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90.224995673
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128/81

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792.179996538
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32/27

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294.134997404
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16/9

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996.089998269
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4/3

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498.044999135
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1/1

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0.000000000
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3/2

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701.955000865
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9/8

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203.910001731
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27/16

M6

905.865002596
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81/64

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407.820003462
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243/128

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1109.775004327
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729/512

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611.730005192
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2187/2048

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113.685006058
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6561/4096

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815.640006923
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19683/16384

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317.595007788
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59049/32768

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1019.550008654
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177147/131072

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521.505009519
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531441/524288

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23.460010385
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1594323/1048576

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725.415011250
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4782969/4194304

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227.370012115
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14348907/8388608

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929.325012981
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43046721/33554432

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431.280013846
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129140163/67108864

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1133.235014712
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387420489/268435456

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635.190015577
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137.145016442
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3486784401/2147483648

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839.100017308
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341.055018173
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1043.010019039
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544.965019904
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250.830022500
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~~

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5-limit
3-26⋅5-1

17592186044416/12709329141645

dddd75

562.856263635
3-25⋅5-1

4398046511104/4236443047215

dddd45

64.811264500
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2199023255552/1412147682405

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766.766265366
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549755813888/470715894135

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268.721266231
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274877906944/156905298045

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970.676267097
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68719476736/52301766015

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472.631267962
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34359738368/17433922005

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1174.586268827
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8589934592/5811307335

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676.541269693
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2147483648/1937102445

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178.496270558
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1073741824/645700815

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880.451271424
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268435456/215233605

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382.406272289
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134217728/71744535

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1084.361273154
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33554432/23914845

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586.316274020
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8388608/7971615

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88.271274885
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4194304/2657205

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790.226275751
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1048576/885735

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292.181276616
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524288/295245

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994.136277481
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131072/98415

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496.091278347
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65536/32805

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1198.046279212
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16384/10935

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700.001280077
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4096/3645

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201.956280943
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2048/1215

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903.911281808
3-4⋅5-1

512/405

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405.866282674
3-3⋅5-1

256/135

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1107.821283539
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64/45

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609.776284404
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16/15

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111.731285270
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8/5

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813.686286135
31⋅5-1

6/5

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315.641287001
32⋅5-1

9/5

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1017.596287866
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27/20

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519.551288731
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81/80

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21.506289597
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243/160

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723.461290462
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729/640

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225.416291327
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2187/1280

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927.371292193
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6561/5120

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429.326293058
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19683/10240

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1131.281293924
310⋅5-1

59049/40960

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633.236294789
311⋅5-1

177147/163840

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135.191295654
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531441/327680

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837.146296520
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1594323/1310720

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339.101297385
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4782969/2621440

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1041.056298251
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14348907/10485760

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543.011299116
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43046721/41943040

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44.966299981
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129140163/83886080

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746.921300847
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248.876301712
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1162261467/671088640

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950.831302578
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3486784401/2684354560

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452.786303443
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31381059609/21474836480

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362.561307770
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1064.516308635
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35184372088832/21182215236075

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878.497550636
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8796093022208/7060738412025

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380.452551501
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4398046511104/2353579470675

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1082.407552366
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1099511627776/784526490225

dddd75,5

584.362553232
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274877906944/261508830075

dddd45,5

86.317554097
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137438953472/87169610025

dddd85,5

788.272554963
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34359738368/29056536675

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290.227555828
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17179869184/9685512225

cddd25,5

992.182556693
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4294967296/3228504075

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494.137557559
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2147483648/1076168025

cddd35,5

1196.092558424
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536870912/358722675

ddd75,5

698.047559290
3-14⋅5-2

134217728/119574225

ddd45,5

200.002560155
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67108864/39858075

ddd85,5

901.957561020
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16777216/13286025

ddd55,5

403.912561886
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8388608/4428675

cdd25,5

1105.867562751
3-10⋅5-2

2097152/1476225

dd65,5

607.822563616
3-9⋅5-2

524288/492075

dd35,5

109.777564482
3-8⋅5-2

262144/164025

dd75,5

811.732565347
3-7⋅5-2

65536/54675

dd45,5

313.687566213
3-6⋅5-2

32768/18225

dd85,5

1015.642567078
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8192/6075

dd55,5

517.597567943
3-4⋅5-2

2048/2025

d25,5

19.552568809
3-3⋅5-2

1024/675

d65,5

721.507569674
3-2⋅5-2

256/225

d35,5

223.462570540
3-1⋅5-2

128/75

d75,5

925.417571405
5-2

32/25

d45,5

427.372572270
31⋅5-2

48/25

d85,5

1129.327573136
32⋅5-2

36/25

d55,5

631.282574001
33⋅5-2

27/25

m25,5

133.237574866
34⋅5-2

81/50

m65,5

835.192575732
35⋅5-2

243/200

m35,5

337.147576597
36⋅5-2

729/400

m75,5

1039.102577463
37⋅5-2

2187/1600

P45,5

541.057578328
38⋅5-2

6561/6400

P15,5

43.012579193
39⋅5-2

19683/12800

P55,5

744.967580059
310⋅5-2

59049/51200

M25,5

246.922580924
311⋅5-2

177147/102400

M65,5

948.877581790
312⋅5-2

531441/409600

M35,5

450.832582655
313⋅5-2

1594323/819200

M75,5

1152.787583520
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4782969/3276800

A45,5

654.742584386
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14348907/13107200

A15,5

156.697585251
316⋅5-2

43046721/26214400

A55,5

858.652586117
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129140163/104857600

A25,5

360.607586982
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387420489/209715200

A65,5

1062.562587847
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1162261467/838860800

A35,5

564.517588713
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3486784401/3355443200

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66.472589578
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10460353203/6710886400

AA45,5

768.427590443
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31381059609/26843545600

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270.382591309
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94143178827/53687091200

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972.337592174
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282429536481/214748364800

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474.292593040
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847288609443/429496729600

AA65,5

1176.247593905
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2541865828329/1717986918400

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678.202594770
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562949953421312/317733228541125

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990.228835905
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140737488355328/105911076180375

ddddd75,5,5

492.183836771
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70368744177664/35303692060125

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1194.138837636
3-23⋅5-3

17592186044416/11767897353375

ddddd85,5,5

696.093838502
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4398046511104/3922632451125

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198.048839367
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2199023255552/1307544150375

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900.003840232
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549755813888/435848050125

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401.958841098
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274877906944/145282683375

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1103.913841963
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68719476736/48427561125

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605.868842829
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17179869184/16142520375

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107.823843694
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8589934592/5380840125

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809.778844559
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2147483648/1793613375

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311.733845425
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1013.688846290
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268435456/199290375

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515.643847155
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67108864/66430125

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17.598848021
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33554432/22143375

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719.553848886
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8388608/7381125

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221.508849752
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4194304/2460375

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923.463850617
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1048576/820125

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425.418851482
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524288/273375

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1127.373852348
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131072/91125

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629.328853213
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32768/30375

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131.283854079
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16384/10125

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833.238854944
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4096/3375

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335.193855809
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2048/1125

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1037.148856675
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512/375

dd55,5,5

539.103857540
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128/125

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41.058858405
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192/125

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743.013859271
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144/125

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244.968860136
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216/125

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946.923861002
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162/125

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448.878861867
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243/125

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1150.833862732
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729/500

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652.788863598
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2187/2000

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154.743864463
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6561/4000

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856.698865329
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19683/16000

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358.653866194
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59049/32000

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1060.608867059
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177147/128000

P45,5,5

562.563867925
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64.518868790
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4782969/4096000

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268.428870521
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M65,5,5

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472.338872252
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676.248873982
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178.203874848
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382.113876579
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586.023878309
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789.933880040
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AA15,5,5

291.888880906
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1180.344071031
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319.445368416
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25.310371012
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229.220372743
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131072/76545

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931.175373608
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433.130374474
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16384/8505

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1135.085375339
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637.040376204
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138.995377070
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512/315

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840.950377935
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342.905378801
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1044.860379666
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546.815380531
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36/35

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48.770381397
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750.725382262
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81/70

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252.680383128
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243/140

M65,7

954.635383993
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729/560

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456.590384858
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2187/1120

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1158.545385724
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6561/4480

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660.500386589
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162.455387455
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864.410388320
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366.365389185
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707.712803069
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209.667803934
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911.622804800
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413.577805665
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119.442808261
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323.352809992
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1025.307810857
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303.404485312
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14348907/8028160

AA55,7,7

1005.359486178
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43046721/32112640

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507.314487043
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129140163/128450560

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9.269487909
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387420489/256901120

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711.224488774
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213.179489639
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3486784401/2055208960

AAA45,7,7

915.134490505
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99.786879292
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915.426886215
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417.381887080
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1342177280/703096443

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1119.336887946
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335544320/234365481

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621.291888811
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123.246889677
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41943040/26040609

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825.201890542
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10485760/8680203

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327.156891407
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5242880/2893401

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1029.111892273
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1310720/964467

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531.066893138
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327680/321489

P157,7

33.021894003
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163840/107163

P557,7

734.976894869
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40960/35721

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236.931895734
3-5⋅51⋅7-2

20480/11907

M657,7

938.886896600
3-4⋅51⋅7-2

5120/3969

M357,7

440.841897465
3-3⋅51⋅7-2

2560/1323

M757,7

1142.796898330
3-2⋅51⋅7-2

640/441

A457,7

644.751899196
3-1⋅51⋅7-2

160/147

A157,7

146.706900061
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80/49

A557,7

848.661900927
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60/49

A257,7

350.616901792
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90/49

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1052.571902657
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135/98

A357,7

554.526903523
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405/392

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56.481904388
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1215/784

AA457,7

758.436905254
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3645/3136

AA157,7

260.391906119
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10935/6272

AA557,7

962.346906984
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32805/25088

AA257,7

464.301907850
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98415/50176

AA657,7

1166.256908715
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295245/200704

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668.211909580
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885735/802816

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170.166910446
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79.941914773
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781.896915638
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283.851916504
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5811307335/3288334336

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985.806917369
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AAAA157,7

487.761918234
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52301766015/26306674688

AAAA557,7

1189.716919100
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156905298045/105226698752

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691.671919965
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193.626920830
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397.536922561
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1125899906842624/871859979116847

ddd57,7,7

442.692258093
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cdd27,7,7

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140737488355328/96873331012983

dd67,7,7

646.602259823
3-23⋅7-3

35184372088832/32291110337661

dd37,7,7

148.557260689
3-22⋅7-3

17592186044416/10763703445887

dd77,7,7

850.512261554
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352.467262419
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556.377264150
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137438953472/132885227727

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58.332265016
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68719476736/44295075909

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760.287265881
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262.242266746
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964.197267612
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466.152268477
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1073741824/546852789

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1168.107269343
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268435456/182284263

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873.972271939
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8388608/6751269

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375.927272804
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4194304/2250423

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1077.882273670
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1048576/750141

P47,7,7

579.837274535
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262144/250047

P17,7,7

81.792275400
3-5⋅7-3

131072/83349

P57,7,7

783.747276266
3-4⋅7-3

32768/27783

M27,7,7

285.702277131
3-3⋅7-3

16384/9261

M67,7,7

987.657277996
3-2⋅7-3

4096/3087

M37,7,7

489.612278862
3-1⋅7-3

2048/1029

M77,7,7

1191.567279727
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512/343

A47,7,7

693.522280593
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384/343

A17,7,7

195.477281458
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576/343

A57,7,7

897.432282323
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432/343

A27,7,7

399.387283189
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648/343

A67,7,7

1101.342284054
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486/343

A37,7,7

603.297284920
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729/686

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105.252285785
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2187/1372

AA47,7,7

807.207286650
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6561/5488

AA17,7,7

309.162287516
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19683/10976

AA57,7,7

1011.117288381
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59049/43904

AA27,7,7

513.072289246
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177147/175616

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15.027290112
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218.937291843
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3-26⋅11-1

35184372088832/27960524111619

ddd611

397.852035135
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17592186044416/9320174703873

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1099.807036001
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601.762036866
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1099511627776/1035574967097

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103.717037731
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549755813888/345191655699

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805.672038597
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137438953472/115063885233

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307.627039462
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1009.582040327
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13.492042058
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1123.267046385
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127.177048116
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829.132048981
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331.087049847
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1033.042050712
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32768/24057

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534.997051578
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8192/8019

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36.952052443
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738.907053308
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240.862054174
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942.817055039
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128/99

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444.772055904
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64/33

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1146.727056770
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16/11

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648.682057635
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12/11

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150.637058501
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18/11

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852.592059366
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27/22

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354.547060231
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81/44

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1056.502061097
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558.457061962
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60.412062828
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762.367063693
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264.322064558
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966.277065424
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468.232066289
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1170.187067155
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672.142068020
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174.097068885
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876.052069751
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378.007070616
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1079.962071481
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581.917072347
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387420489/369098752

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83.872073212
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287.782074943
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3-25⋅5-1⋅11-1

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dddd85,11

713.493322136
3-24⋅5-1⋅11-1

17592186044416/15533624506455

dddd55,11

215.448323001
3-23⋅5-1⋅11-1

8796093022208/5177874835485

cddd25,11

917.403323866
3-22⋅5-1⋅11-1

2199023255552/1725958278495

ddd65,11

419.358324732
3-21⋅5-1⋅11-1

1099511627776/575319426165

cddd35,11

1121.313325597
3-20⋅5-1⋅11-1

274877906944/191773142055

ddd75,11

623.268326463
3-19⋅5-1⋅11-1

68719476736/63924380685

ddd45,11

125.223327328
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34359738368/21308126895

ddd85,11

827.178328193
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8589934592/7102708965

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329.133329059
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4294967296/2367569655

cdd25,11

1031.088329924
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1073741824/789189885

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533.043330790
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268435456/263063295

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34.998331655
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134217728/87687765

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736.953332520
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33554432/29229255

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238.908333386
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16777216/9743085

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940.863334251
3-10⋅5-1⋅11-1

4194304/3247695

dd55,11

442.818335117
3-9⋅5-1⋅11-1

2097152/1082565

cd25,11

1144.773335982
3-8⋅5-1⋅11-1

524288/360855

d65,11

646.728336847
3-7⋅5-1⋅11-1

131072/120285

d35,11

148.683337713
3-6⋅5-1⋅11-1

65536/40095

d75,11

850.638338578
3-5⋅5-1⋅11-1

16384/13365

d45,11

352.593339443
3-4⋅5-1⋅11-1

8192/4455

d85,11

1054.548340309
3-3⋅5-1⋅11-1

2048/1485

d55,11

556.503341174
3-2⋅5-1⋅11-1

512/495

m25,11

58.458342040
3-1⋅5-1⋅11-1

256/165

m65,11

760.413342905
5-1⋅11-1

64/55

m35,11

262.368343770
31⋅5-1⋅11-1

96/55

m75,11

964.323344636
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524288/369603

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65536/41067

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13-limit

~~

Limit Boundary

~~

17-31-limit
13-limit

~~

Limit Boundary

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17-31-limit
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ddd531

325.639414555
3-14⋅31-1

268435456/148272039

cdd231

1027.594415420
3-13⋅31-1

67108864/49424013

dd631

529.549416286
3-12⋅31-1

16777216/16474671

dd331

31.504417151
3-11⋅31-1

8388608/5491557

dd731

733.459418016
3-10⋅31-1

2097152/1830519

dd431

235.414418882
3-9⋅31-1

1048576/610173

dd831

937.369419747
3-8⋅31-1

262144/203391

dd531

439.324420613
3-7⋅31-1

131072/67797

cd231

1141.279421478
3-6⋅31-1

32768/22599

d631

643.234422343
3-5⋅31-1

8192/7533

d331

145.189423209
3-4⋅31-1

4096/2511

d731

847.144424074
3-3⋅31-1

1024/837

d431

349.099424940
3-2⋅31-1

512/279

d831

1051.054425805
3-1⋅31-1

128/93

d531

553.009426670
31-1

32/31

m231

54.964427536
31⋅31-1

48/31

m631

756.919428401
32⋅31-1

36/31

m331

258.874429267
33⋅31-1

54/31

m731

960.829430132
34⋅31-1

81/62

P431

462.784430997
35⋅31-1

243/124

P831

1164.739431863
36⋅31-1

729/496

P531

666.694432728
37⋅31-1

2187/1984

M231

168.649433593
38⋅31-1

6561/3968

M631

870.604434459
39⋅31-1

19683/15872

M331

372.559435324
310⋅31-1

59049/31744

M731

1074.514436190
311⋅31-1

177147/126976

A431

576.469437055
312⋅31-1

531441/507904

A131

78.424437920
313⋅31-1

1594323/1015808

A531

780.379438786
314⋅31-1

4782969/4063232

A231

282.334439651
315⋅31-1

14348907/8126464

A631

984.289440517
316⋅31-1

43046721/32505856

A331

486.244441382
317⋅31-1

129140163/65011712

A731

1188.199442247
318⋅31-1

387420489/260046848

AA431

690.154443113
319⋅31-1

1162261467/1040187392

AA131

192.109443978
320⋅31-1

3486784401/2080374784

AA531

894.064444843
321⋅31-1

10460353203/8321499136

AA231

396.019445709
322⋅31-1

31381059609/16642998272

AA631

1097.974446574
323⋅31-1

94143178827/66571993088

AA331

599.929447440
324⋅31-1

282429536481/266287972352

-cAA731

101.884448305
325⋅31-1

847288609443/532575944704

AAA431

803.839449170
326⋅31-1

2541865828329/2130303778816

AAA131

305.794450036
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