Zero-based metrics
Zeta metrics corresponding to regions between zeros on the critical line (σ = 0.5). The Riemann hypothesis is the equivalent to the statement that these correspond directly to peaks.
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| Zeta integral
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| Zeta gap
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σ = 1/2
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| Absolute zeta peak
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| Absolute zeta integer
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| Real zeta peak
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| Real zeta integer
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σ = 1
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| Absolute zeta peak
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| Absolute zeta integer
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| Real zeta peak
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| Real zeta integer
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σ = 3/2
| Record type
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1
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2
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3
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5
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7
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10
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12
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19
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31
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41
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53
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72
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130
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171
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224
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270
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494
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1106
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1578
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2460
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2684
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3395
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5585
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8269
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8539
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| Absolute zeta peak
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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| Absolute zeta integer
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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| Real zeta peak
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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| Real zeta integer
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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|
★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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No-twos tritave divisions
| Record type
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1
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2
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4
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9
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13
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17
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26
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39
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88
|
114
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131
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415
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712
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800
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914
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1342
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1757
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2426
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3624
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3755
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6181
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| Absolute zeta peak
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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|
★
|
★
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★
|
★
|
★
|
★
|
★
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| Absolute zeta integer
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★
|
★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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| Real zeta peak
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
|
★
|
★
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| Real zeta integer
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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σ = 2
For σ = 2, the record lists for real zeta are identical to those for absolute zeta out to 8539edo.
| Record type
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1
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2
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3
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5
|
7
|
10
|
12
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19
|
31
|
41
|
53
|
130
|
171
|
270
|
494
|
1106
|
1578
|
2460
|
2684
|
3395
|
5585
|
6079
|
8269
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8539
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| Real zeta peak (cosine mu peak)
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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★
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|
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★
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★
|
★
|
★
|
|
★
|
★
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|
| Absolute zeta integer
|
★
|
★
|
★
|
★
|
★
|
★
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★
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|
★
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★
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★
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★
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★
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★
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★
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★
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|
★
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|
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★
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|
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★
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| Real zeta peak (cosine mu peak)
|
★
|
★
|
★
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★
|
★
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|
★
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★
|
★
|
★
|
★
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★
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★
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★
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|
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★
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★
|
★
|
★
|
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★
|
★
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| Real zeta integer (cosine mu integer)
|
★
|
★
|
|
★
|
★
|
★
|
★
|
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
|
★
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|
|
★
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|
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★
|
No-twos tritave divisions
| Record type
|
1
|
2
|
4
|
9
|
13
|
17
|
26
|
39
|
88
|
114
|
131
|
800
|
914
|
1342
|
1757
|
2426
|
3624
|
3755
|
6181
|
| Real zeta peak (cosine mu peak)
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
|
| Absolute zeta integer
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
|
★
|
★
|
★
|
★
|
|
★
|
★
|
|
★
|
|
★
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| Real zeta peak (cosine mu peak)
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
|
★
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| Real zeta integer (cosine mu integer)
|
★
|
★
|
★
|
★
|
★
|
★
|
★
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★
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★
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★
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★
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★
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★
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★
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★
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