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Line 565: Line 545:
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Line 821: Line 825:
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Line 925: Line 909:
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Line 941: Line 925:
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Line 1,009: Line 1,001:
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Line 1,245: Line 1,241:
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| 1.847
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Line 1,421: Line 1,405:
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| [-10 -5 7 2 1 -2⟩
| [11 -10 0 7 0 -4⟩
| 2.335
| 0.121
|-
|-
| [[65625/65536]]
| [[1714374025/1712848896]]
| [-16 1 5 1⟩
| [-19 -3 2 4 -2 4⟩
| 2.349
| 1.541
|-
|-
| [[46200375/46137344]]
| [[1714871048/1714374025]]
| [-22 7 3 0 -1 2⟩
| [3 0 -2 -4 8 -4⟩
| 2.364
| 0.502
|-
|-
| [[478515625/477854091]]
| [[1722499009/1719926784]]
| [0 -2 10 2 -1 -6⟩
| [-18 -8 0 6 4⟩
| 2.395
| 2.587
|-
|-
| [[221484375/221176384]]
| [[1722499009/1721868840]]
| [-6 4 8 1 -2 -4⟩
| [-3 -16 -1 6 4⟩
| 2.409
| 0.633
|-
|-
| [[386683451/386144720]]
| [[1775239375/1773674496]]
| [-4 0 -1 4 5 -6⟩
| [-13 -9 4 5 -1 2⟩
| 2.414
| 1.527
|-
|-
| [[922640625/921350144]]
| [[1779441125/1776722688]]
| [-12 10 6 0 -3 -2⟩
| [-8 -5 3 6 2 -4⟩
| 2.423
| 2.647
|-
|-
| [[1530966437/1528823808]]
| [[1801088541/1799512000]]
| [-21 -6 0 7 1 2⟩
| [-6 7 -3 7 -3 -2⟩
| 2.425
| 1.516
|-
|-
| [[3660938127/3655808000]]
| [[1815912315/1814078464]]
| [-10 6 -3 3 4 -4⟩
| [-10 2 1 9 -6⟩
| 2.428
| 1.749
|-
|-
| [[3360173089/3355443200]]
| [[1838265625/1836660096]]
| [-27 0 -2 6 0 4⟩
| [-7 -15 6 6⟩
| 2.439
| 1.513
|-
|-
| [[680440475/679477248]]
| [[1845703125/1842700288]]
| [-23 -4 2 0 5 2⟩
| [-13 3 10 1 -3 -2⟩
| 2.452
| 2.819
|-
|-
| [[3763454409/3758096384]]
| [[1929229929/1927561216]]
| [-29 2 0 -1 4 4⟩
| [-14 2 0 -6 8⟩
| 2.467
| 1.498
|-
|-
| [[102942875/102795264]]
| [[1953045675/1949302784]]
| [-11 -3 3 7 -1 -2⟩
| [-20 13 2 2 -1 -2⟩
| 2.484
| 3.321
|-
|-
| [[816903549/815730721]]
| [[1977326743/1974136320]]
| [0 9 0 3 2 -8⟩
| [-9 -3 -1 11 0 -4⟩
| 2.487
| 2.796
|-
|-
| [[15882615/15859712]]
| [[1977326743/1975897638]]
| [-17 3 1 6 -2⟩
| [-1 -12 0 11 -1 -2⟩
| 2.498
| 1.252
|-
|-
| [[4159375/4153344]]
| [[1977326743/1976535000]]
| [-13 -1 5 0 3 -2⟩
| [-3 -3 -4 11 -4⟩
| 2.512
| 0.693
|-
|-
| [[3675375/3670016]]
| [[2091059712/2090808005]]
| [-19 5 3 -1 2⟩
| [9 5 -1 5 -4 -4⟩
| 2.526
| 0.208
|-
|-
| [[1646581365/1644167168]]
| [[2122043913/2119936000]]
| [-25 11 1 -2 1 2⟩
| [-11 13 -3 -2 3 -2⟩
| 2.540
| 1.721
|-
|-
| [[38671875/38614472]]
| [[2129600000/2128622769]]
| [-3 2 8 0 1 -6⟩
| [9 -2 5 -2 3 -6⟩
| 2.572
| 0.795
|-
|-
| [[102515625/102362624]]
| [[2152024875/2147483648]]
| [-9 8 6 -1 0 -4⟩
| [-31 3 3 3 1 2⟩
| 2.586
| 3.657
|-
|-
| [[1722499009/1719926784]]
| [[2152446615/2147483648]]
| [-18 -8 0 6 4⟩
| [-31 5 1 0 6⟩
| 2.587
| 3.996
|-
|-
| [[2989355625/2984869888]]
| [[2152828125/2147483648]]
| [-15 14 4 -2 -1 -2⟩
| [-31 9 6 1⟩
| 2.600
| 4.303
|-
|-
| [[3780549773/3774873600]]
| [[2159925625/2157969408]]
| [-24 -2 -2 5 3 2⟩
| [-21 -1 4 -3 2 4⟩
| 2.601
| 1.569
|-
|-
| [[3293331899/3288334336]]
| [[2197265625/2194398752]]
| [-26 0 0 -2 7 2⟩
| [-5 2 12 -4 0 -4⟩
| 2.629
| 2.260
|-
|-
| [[1779441125/1776722688]]
| [[2204627139/2202927104]]
| [-8 -5 3 6 2 -4⟩
| [-17 4 0 -5 5 2⟩
| 2.647
| 1.336
|-
|-
| [[2773155/2768896]]
| [[2343775203/2339717120]]
| [-14 1 1 5 1 -2⟩
| [-14 3 -1 2 6 -4⟩
| 2.661
| 3.000
|-
|-
| [[5250987/5242880]]
| [[2357947691/2354946048]]
| [-20 7 -1 4⟩
| [-13 -5 0 -1 9 -2⟩
| 2.675
| 2.205
|-
|-
| [[543547125/542703616]]
| [[2373046875/2370734366]]
| [-16 3 3 -2 5 -2⟩
| [-1 5 10 -3 -2 -4⟩
| 2.689
| 1.688
|-
|-
| [[1440894015/1438646272]]
| [[2435896375/2432711736]]
| [-22 9 1 -3 4⟩
| [-3 -2 3 -1 7 -6⟩
| 2.703
| 2.265
|-
|-
| [[850854375/849518384]]
| [[2450000000/2447192163]]
| [-4 4 4 5 -1 -6⟩
| [7 -1 8 2 0 -8⟩
| 2.720
| 1.985
|-
|-
| [[3544416225/3538822144]]
| [[2495390625/2494357888]]
| [-10 10 2 4 -2 -4⟩
| [-7 3 7 1 -7 2⟩
| 2.735
| 0.717
|-
|-
| [[95703125/95551488]]
| [[2516421875/2514778812]]
| [-17 -6 9 2⟩
| [-2 -12 6 -1 5 -2⟩
| 2.745
| 1.131
|-
|-
| [[92421875/92274688]]
| [[2519337249/2517630976]]
| [-23 0 7 1 -1 2⟩
| [-20 6 0 -4 2 4⟩
| 2.759
| 1.173
|-
|-
| [[4253517961/4246732800]]
| [[2542277241/2537553920]]
| [-21 -4 -2 4 6⟩
| [-22 2 -1 10 -2⟩
| 2.764
| 3.219
|-
|-
| [[1977326743/1974136320]]
| [[2573571875/2569273344]]
| [-9 -3 -1 11 0 -4⟩
| [-18 -4 5 7 -2⟩
| 2.796
| 2.894
|-
|-
| [[1845703125/1842700288]]
| [[2573571875/2572306572]]
| [-13 3 10 1 -3 -2⟩
| [-2 -1 5 7 -8⟩
| 2.819
| 0.851
|-
|-
| [[175765205/175478784]]
| [[2662250409/2662000000]]
| [-11 -1 1 4 4 -4⟩
| [-7 8 -6 4 -3 2⟩
| 2.823
| 0.163
|-
|-
| [[110937519/110755840]]
| [[2690514981/2684354560]]
| [-17 5 -1 3 3 -2⟩
| [-29 3 -1 7 2⟩
| 2.838
| 3.969
|-
|-
| [[1050304563/1048576000]]
| [[2706784157/2704000000]]
| [-23 11 -3 2 2⟩
| [-10 0 -6 5 5 -2⟩
| 2.852
| 1.782
|-
| [[1634180625/1631461442]]
| [-1 2 4 4 2 -8⟩
| 2.883
|-
|-
| [[2573571875/2569273344]]
| [[2841733125/2835349504]]
| [-18 -4 5 7 -2⟩
| [-24 10 4 1 1 -2⟩
| 2.894
| 3.893
|-
|-
| [[618866325/617831552]]
| [[2929687500/2927131207]]
| [-7 8 2 3 1 -6⟩
| [2 1 12 -1 -4 -4⟩
| 2.897
| 1.511
|-
|-
| [[234365481/233971712]]
| [[2977309629/2974400000]]
| [-13 14 0 2 0 -4⟩
| [-9 11 -5 5 -1 -2⟩
| 2.911
| 1.693
|-
|-
| [[9453125/9437184]]
| [[2989355625/2984869888]]
| [-20 -2 7 0 2⟩
| [-15 14 4 -2 -1 -2⟩
| 2.922
| 2.600
|-
|-
| [[470559375/469762048]]
| [[3228504075/3224725504]]
| [-26 4 5 -1 1 2⟩
| [-11 17 2 -1 -3 -2⟩
| 2.936
| 2.027
|-
| [[29296875/29246464]]
| [-10 1 10 0 0 -4⟩
| 2.981
|-
| [[854296875/852819968]]
| [-16 7 8 -1 -1 -2⟩
| 2.996
|-
| [[2343775203/2339717120]]
| [-14 3 -1 2 6 -4⟩
| 3.000
|-
|-
| [[3268642167/3262922884]]
| [[3268642167/3262922884]]
Line 1,633: Line 1,601:
| 3.032
| 3.032
|-
|-
| [[4044184375/4037050368]]
| [[3293331899/3288334336]]
| [-15 -6 5 6 1 -2⟩
| [-26 0 0 -2 7 2⟩
| 3.057
| 2.629
|-
|-
| [[2100875/2097152]]
| [[3293331899/3292047360]]
| [-21 0 3 5⟩
| [-11 -8 -1 -2 7 2⟩
| 3.071
| 0.675
|-
|-
| [[1479028005/1476395008]]
| [[3293331899/3292800000]]
| [-27 6 1 4 -1 2⟩
| [-10 -1 -5 -3 7 2⟩
| 3.085
| 0.280
|-
|-
| [[411778125/411041792]]
| [[3294172000/3293331899]]
| [-23 2 5 -2 4⟩
| [5 0 3 7 -7 -2⟩
| 3.099
| 0.442
|-
|-
| [[2542277241/2537553920]]
| [[3349609375/3345292808]]
| [-22 2 -1 10 -2⟩
| [-3 0 10 3 -4 -4⟩
| 3.219
| 2.232
|-
|-
| [[399466375/398721024]]
| [[3360173089/3355443200]]
| [-18 -2 3 4 3 -2⟩
| [-27 0 -2 6 0 4⟩
| 3.233
| 2.439
|-
|-
| [[16808715/16777216]]
| [[3360173089/3359232000]]
| [-24 4 1 3 2⟩
| [-12 -8 -3 6 0 4⟩
| 3.247
| 0.485
|-
|-
| [[1238015625/1235663104]]
| [[3402639576/3402202375]]
| [-8 1 6 4 1 -6⟩
| [3 11 -3 4 -5 -2⟩
| 3.293
| 0.222
|-
|-
| [[468838125/467943424]]
| [[3410254925/3406261248]]
| [-14 7 4 3 0 -4⟩
| [-10 -9 2 1 7 -2⟩
| 3.307
| 2.029
|-
|-
| [[1953045675/1949302784]]
| [[3465028125/3461742592]]
| [-20 13 2 2 -1 -2⟩
| [-17 8 5 -4 -1 2⟩
| 3.321
| 1.642
|-
|-
| [[3630859375/3623878656]]
| [[3486784401/3483855232]]
| [-27 -3 9 0 1 2⟩
| [-7 20 0 0 -5 -2⟩
| 3.332
| 1.455
|-
|-
| [[443889677/443023360]]
| [[3487704605/3486784401]]
| [-19 0 -1 9 1 -2⟩
| [0 -20 1 8 2⟩
| 3.382
| 0.457
|-
|-
| [[244140625/243662848]]
| [[3514671875/3511517184]]
| [-17 0 12 0 -1 -2⟩
| [-15 -7 6 -2 3 2⟩
| 3.391
| 1.555
|-
|-
| [[4202539929/4194304000]]
| [[3520000000/3518743761]]
| [-25 6 -3 8⟩
| [12 -6 7 0 1 -6⟩
| 3.396
| 0.618
|-
|-
| [[355117455/354418688]]
| [[3522990625/3518743761]]
| [-21 2 1 2 5 -2⟩
| [0 -6 5 1 5 -6⟩
| 3.410
| 2.088
|-
|-
| [[672417207/671088640]]
| [[3544416225/3538822144]]
| [-27 8 -1 1 4⟩
| [-10 10 2 4 -2 -4⟩
| 3.424
| 2.735
|-
| [[3630859375/3623878656]]
| [-27 -3 9 0 1 2⟩
| 3.332
|-
| [[3660938127/3655808000]]
| [-10 6 -3 3 4 -4⟩
| 2.428
|-
| [[3742230375/3739918336]]
| [-13 11 3 -3 -3 2⟩
| 1.070
|-
|-
| [[3751087725/3743547392]]
| [[3751087725/3743547392]]
Line 1,701: Line 1,681:
| 3.484
| 3.484
|-
|-
| [[1420541793/1417674752]]
| [[3763454409/3758096384]]
| [-23 17 0 0 1 -2⟩
| [-29 2 0 -1 4 4⟩
| 3.498
| 2.467
|-
|-
| [[907878125/905969664]]
| [[3764768000/3763454409]]
| [-25 -3 5 4 2⟩
| [8 -2 3 6 -4 -4⟩
| 3.643
| 0.604
|-
|-
| [[2152024875/2147483648]]
| [[3780549773/3774873600]]
| [-31 3 3 3 1 2⟩
| [-24 -2 -2 5 3 2⟩
| 3.657
| 2.601
|-
|-
| [[937890625/935886848]]
| [[3780549773/3779136000]]
| [-15 0 8 4 0 -4⟩
| [-9 -10 -3 5 3 2⟩
| 3.703
| 0.648
|-
|-
| [[3906984375/3898605568]]
| [[3906984375/3898605568]]
Line 1,721: Line 1,701:
| 3.717
| 3.717
|-
|-
| [[201768035/201326592]]
| [[3955078125/3954653486]]
| [-26 -1 1 9⟩
| [-1 4 11 -11⟩
| 3.792
| 0.186
|-
|-
| [[269028375/268435456]]
| [[4000989993/4000000000]]
| [-28 1 3 2 4⟩
| [-11 1 -9 2 5 2⟩
| 3.820
| 0.428
|-
|-
| [[2841733125/2835349504]]
| [[4041608805/4040447488]]
| [-24 10 4 1 1 -2⟩
| [-9 14 1 -2 -5 2⟩
| 3.893
| 0.498
|-
| [[4044184375/4037050368]]
| [-15 -6 5 6 1 -2⟩
| 3.057
|-
| [[4078653605/4076863488]]
| [-24 -5 1 0 0 8⟩
| 0.760
|-
| [[4079910912/4078653605]]
| [15 1 -1 3 2 -8⟩
| 0.534
|-
| [[4081676544/4078653605]]
| [8 2 -1 0 6 -8⟩
| 1.283
|-
| [[4202539929/4194304000]]
| [-25 6 -3 8⟩
| 3.396
|-
|-
| [[1076168025/1073741824]]
| [[4226622444/4223457875]]
| [-30 16 2⟩
| [2 8 -3 -1 5 -6⟩
| 3.907
| 1.297
|-
|-
| [[2690514981/2684354560]]
| [[4227952113/4225000000]]
| [-29 3 -1 7 2⟩
| [-6 3 -8 6 3 -2⟩
| 3.969
| 1.209
|-
|-
| [[2152446615/2147483648]]
| [[4253517961/4246732800]]
| [-31 5 1 0 6⟩
| [-21 -4 -2 4 6⟩
| 3.996
| 2.764
|-
|-
| [[2152828125/2147483648]]
| [[4253517961/4251528000]]
| [-31 9 6 1⟩
| [-6 -12 -3 4 6⟩
| 4.303
| 0.810
|}
|}

Revision as of 23:46, 8 November 2025

← 683edo 684edo 685edo →
Prime factorization 22 × 32 × 19
Step size 1.75439 ¢ 
Fifth 400\684 (701.754 ¢) (→ 100\171)
Semitones (A1:m2) 64:52 (112.3 ¢ : 91.23 ¢)
Consistency limit 17
Distinct consistency limit 17

684 equal divisions of the octave (abbreviated 684edo or 684ed2), also called 684-tone equal temperament (684tet) or 684 equal temperament (684et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 684 equal parts of about 1.75 ¢ each. Each step represents a frequency ratio of 21/684, or the 684th root of 2.

Theory

684edo divides the steps of 171edo into four. It is consistent to the 17-odd-limit, tempering out 2401/2400, 3025/3024, 4225/4224, 4375/4374, 9801/9800, 10648/10647, 32805/32768, 41503/41472, 43923/43904, 50193/50176, 59535/59488, and 65625/65536 in the 13-limit; 1089/1088, 1225/1224, 1701/1700, 2025/2023, 2058/2057, 2500/2499, 8624/8619, and 14875/14872 in the 17-limit.

Prime harmonics

Approximation of prime harmonics in 684edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.201 -0.349 -0.405 -0.441 -0.177 +0.308 +0.733 -0.204 +0.247 +0.578
Relative (%) +0.0 -11.4 -19.9 -23.1 -25.1 -10.1 +17.5 +41.8 -11.6 +14.1 +33.0
Steps
(reduced) 		684
(0) 		1084
(400) 		1588
(220) 		1920
(552) 		2366
(314) 		2531
(479) 		2796
(60) 		2906
(170) 		3094
(358) 		3323
(587) 		3389
(653)

Subsets and supersets

Since 684 factors into 22 × 32 × 19, 684edo has subset edos 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, and 342.

Approximation to JI

Zeta peak index

Tuning Strength Octave (cents) Integer limit
ZPI Steps
per 8ve 		Step size
(cents) 		Height Integral Gap Size Stretch Consistent Distinct
Tempered Pure
5818zpi 683.938935 1.754543 14.267321 7.268914 1.773752 20.109967 1200.107141 0.107141 18 18

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.3.5.7.11.13 2401/2400, 3025/3024, 4225/4224, 4375/4374, 32805/32768 [⟨684 1084 1588 1920 2366 2531]] +0.0994 0.0558 3.18
2.3.5.7.11.13.17 1089/1088, 1225/1224, 1701/1700, 2025/2023, 4225/4224, 13013/13005 [⟨684 1084 1588 1920 2366 2531 2796]] +0.0744 0.0800 4.56
  • 684et is the first equal temperament past 494 with a lower 13-limit absolute error. The next equal temperament that is better tuned is 764.

Rank-2 temperaments

Note: 11-limit temperaments supported by 342et are not shown.

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
ratio* 		Temperaments
18 271\684
(5\684) 		475.44
(8.77) 		1053/800
(1287/1280) 		Semihemiennealimmal
38 151\684
(7\684) 		264.91
(12.28) 		500/429
(144/143) 		Semihemienneadecal

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct

Scales

  • Diamond15: 64 4 5 6 7 8 10 12 16 9 11 13 15 18 7 15 18 10 11 25 22 8 7 11 20 11 7 8 22 25 11 10 18 15 7 18 15 13 11 9 16 12 10 8 7 6 5 4 64

Commas of the 2.3.5.7.11.13 subgroup tempered out in 684edo patent val

Commas with numerator <= 2^32:

Ratio Monzo Cents
2401/2400 [-5 -1 -2 4⟩ 0.721
3025/3024 [-4 -3 2 -1 2⟩ 0.572
4225/4224 [-7 -1 2 0 -1 2⟩ 0.410
4375/4374 [-1 -7 4 1⟩ 0.396
9801/9800 [-3 4 -2 -2 2⟩ 0.177
10648/10647 [3 -2 0 -1 3 -2⟩ 0.163
32805/32768 [-15 8 1⟩ 1.954
41503/41472 [-9 -4 0 3 2⟩ 1.294
43923/43904 [-7 1 0 -3 4⟩ 0.749
50193/50176 [-10 3 0 -2 1 2⟩ 0.586
59535/59488 [-5 5 1 2 -1 -2⟩ 1.367
65625/65536 [-16 1 5 1⟩ 2.349
78125/78078 [-1 -1 7 -1 -1 -2⟩ 1.042
85750/85683 [1 -1 3 3 0 -4⟩ 1.353
86625/86528 [-9 2 3 1 1 -2⟩ 1.940
91125/91091 [0 6 3 -2 -1 -2⟩ 0.646
102487/102400 [-12 0 -2 1 4⟩ 1.470
105644/105625 [2 0 -4 4 1 -2⟩ 0.311
114345/114244 [-2 3 1 1 2 -4⟩ 1.530
117649/117612 [-2 -5 0 6 -2⟩ 0.545
123201/123200 [-6 6 -2 -1 -1 2⟩ 0.014
142884/142805 [2 6 -1 2 0 -4⟩ 0.957
151263/151250 [-1 2 -4 5 -2⟩ 0.149
160083/160000 [-8 3 -4 2 2⟩ 0.898
200000/199927 [6 0 5 -1 0 -4⟩ 0.632
216513/216320 [-8 9 -1 0 1 -2⟩ 1.544
225000/224939 [3 2 5 0 -3 -2⟩ 0.469
234375/234256 [-4 1 7 0 -4⟩ 0.879
250047/250000 [-4 6 -6 3⟩ 0.325
369754/369603 [1 -7 0 5 1 -2⟩ 0.707
405769/405504 [-12 -2 0 4 -1 2⟩ 1.131
420175/419904 [-6 -8 2 5⟩ 1.117
456533/456300 [-2 -3 -2 3 3 -2⟩ 0.884
496125/495616 [-12 4 3 2 -2⟩ 1.777
703125/702464 [-11 2 7 -3⟩ 1.628
759375/758912 [-7 5 5 -2 -2⟩ 1.056
819819/819200 [-15 2 -2 2 1 2⟩ 1.308
820125/819896 [-3 8 3 -1 -4⟩ 0.483
900375/899756 [-2 1 3 4 -3 -2⟩ 1.191
928125/927472 [-4 3 5 -3 1 -2⟩ 1.218
1071875/1070784 [-6 -2 5 3 -1 -2⟩ 1.763
1161875/1161216 [-11 -4 4 -1 1 2⟩ 0.982
1240029/1239040 [-11 11 -1 1 -2⟩ 1.381
1399680/1399489 [7 7 1 -2 0 -4⟩ 0.236
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2573571875/2572306572 [-2 -1 5 7 -8⟩ 0.851
2662250409/2662000000 [-7 8 -6 4 -3 2⟩ 0.163
2690514981/2684354560 [-29 3 -1 7 2⟩ 3.969
2706784157/2704000000 [-10 0 -6 5 5 -2⟩ 1.782
2841733125/2835349504 [-24 10 4 1 1 -2⟩ 3.893
2929687500/2927131207 [2 1 12 -1 -4 -4⟩ 1.511
2977309629/2974400000 [-9 11 -5 5 -1 -2⟩ 1.693
2989355625/2984869888 [-15 14 4 -2 -1 -2⟩ 2.600
3228504075/3224725504 [-11 17 2 -1 -3 -2⟩ 2.027
3268642167/3262922884 [-2 4 0 9 0 -8⟩ 3.032
3293331899/3288334336 [-26 0 0 -2 7 2⟩ 2.629
3293331899/3292047360 [-11 -8 -1 -2 7 2⟩ 0.675
3293331899/3292800000 [-10 -1 -5 -3 7 2⟩ 0.280
3294172000/3293331899 [5 0 3 7 -7 -2⟩ 0.442
3349609375/3345292808 [-3 0 10 3 -4 -4⟩ 2.232
3360173089/3355443200 [-27 0 -2 6 0 4⟩ 2.439
3360173089/3359232000 [-12 -8 -3 6 0 4⟩ 0.485
3402639576/3402202375 [3 11 -3 4 -5 -2⟩ 0.222
3410254925/3406261248 [-10 -9 2 1 7 -2⟩ 2.029
3465028125/3461742592 [-17 8 5 -4 -1 2⟩ 1.642
3486784401/3483855232 [-7 20 0 0 -5 -2⟩ 1.455
3487704605/3486784401 [0 -20 1 8 2⟩ 0.457
3514671875/3511517184 [-15 -7 6 -2 3 2⟩ 1.555
3520000000/3518743761 [12 -6 7 0 1 -6⟩ 0.618
3522990625/3518743761 [0 -6 5 1 5 -6⟩ 2.088
3544416225/3538822144 [-10 10 2 4 -2 -4⟩ 2.735
3630859375/3623878656 [-27 -3 9 0 1 2⟩ 3.332
3660938127/3655808000 [-10 6 -3 3 4 -4⟩ 2.428
3742230375/3739918336 [-13 11 3 -3 -3 2⟩ 1.070
3751087725/3743547392 [-17 11 2 1 2 -4⟩ 3.484
3763454409/3758096384 [-29 2 0 -1 4 4⟩ 2.467
3764768000/3763454409 [8 -2 3 6 -4 -4⟩ 0.604
3780549773/3774873600 [-24 -2 -2 5 3 2⟩ 2.601
3780549773/3779136000 [-9 -10 -3 5 3 2⟩ 0.648
3906984375/3898605568 [-21 6 6 3 -1 -2⟩ 3.717
3955078125/3954653486 [-1 4 11 -11⟩ 0.186
4000989993/4000000000 [-11 1 -9 2 5 2⟩ 0.428
4041608805/4040447488 [-9 14 1 -2 -5 2⟩ 0.498
4044184375/4037050368 [-15 -6 5 6 1 -2⟩ 3.057
4078653605/4076863488 [-24 -5 1 0 0 8⟩ 0.760
4079910912/4078653605 [15 1 -1 3 2 -8⟩ 0.534
4081676544/4078653605 [8 2 -1 0 6 -8⟩ 1.283
4202539929/4194304000 [-25 6 -3 8⟩ 3.396
4226622444/4223457875 [2 8 -3 -1 5 -6⟩ 1.297
4227952113/4225000000 [-6 3 -8 6 3 -2⟩ 1.209
4253517961/4246732800 [-21 -4 -2 4 6⟩ 2.764
4253517961/4251528000 [-6 -12 -3 4 6⟩ 0.810
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