Gamma(1/2) = pi^(1/2)
Gamma(1/3) = 2^(4/9) * 3^(-1/12) * pi^(2/3) * h3^(1/3)
Gamma(2/3) = 2^(5/9) * 3^(-5/12) * pi^(1/3) * h3^(-1/3)
Gamma(1/4) = 2^(1/2) * pi^(3/4) * h1^(1/2)
Gamma(3/4) = pi^(1/4) * h1^(-1/2)
Gamma(1/6) = 2^(5/9) * 3^(1/3) * pi^(5/6) * h3^(2/3)
Gamma(5/6) = 2^(4/9) * 3^(-1/3) * pi^(1/6) * h3^(-2/3)
Gamma(1/8) = 2^(11/8) * pi^(7/8) * h1^(1/4) * h2^(1/2)
Gamma(3/8) = 2^(7/8) * alpha^(-1/2) * pi^(5/8) * h1^(-1/4) * h2^(1/2)
Gamma(5/8) = 2^(-1/8) * pi^(3/8) * h1^(1/4) * h2^(-1/2)
Gamma(7/8) = 2^(-5/8) * alpha^(1/2) * pi^(1/8) * h1^(-1/4) * h2^(-1/2)
Gamma(1/12) = 2^(17/18) * 3^(7/24) * beta^(1/4) * pi^(11/12) * h1^(1/2) * h3^(1/3)
Gamma(5/12) = 2^(5/9) * 3^(-1/24) * beta^(-1/4) * pi^(7/12) * h1^(1/2) * h3^(-1/3)
Gamma(7/12) = 2^(4/9) * 3^(1/24) * beta^(-1/4) * pi^(5/12) * h1^(-1/2) * h3^(1/3)
Gamma(11/12) = 2^(1/18) * 3^(-7/24) * beta^(1/4) * pi^(1/12) * h1^(-1/2) * h3^(-1/3)
Gamma(1/24) = 2^(121/72) * 3^(25/48) * alpha^(1/2) * beta^(-1/8) * pi^(23/24) * h1^(1/4) * h3^(1/6) * h6^(1/2)
Gamma(5/24) = 2^(95/72) * 3^(5/48) * beta^(-3/8) * pi^(19/24) * h1^(1/4) * h3^(-1/6) * h6^(1/2)
Gamma(7/24) = 2^(85/72) * 3^(7/48) * alpha^(1/2) * beta^(-3/8) * a23^(-1/2) * pi^(17/24) * h1^(-1/4) * h3^(1/6) * h6^(1/2)
Gamma(11/24) = 2^(59/72) * 3^(11/48) * beta^(-1/8) * a23^(-1/2) * pi^(13/24) * h1^(-1/4) * h3^(-1/6) * h6^(1/2)
Gamma(13/24) = 2^(13/72) * 3^(-11/48) * alpha^(-1/2) * beta^(3/8) * pi^(11/24) * h1^(1/4) * h3^(1/6) * h6^(-1/2)
Gamma(17/24) = 2^(-13/72) * 3^(-7/48) * beta^(1/8) * pi^(7/24) * h1^(1/4) * h3^(-1/6) * h6^(-1/2)
Gamma(19/24) = 2^(-23/72) * 3^(-5/48) * alpha^(-1/2) * beta^(1/8) * a23^(1/2) * pi^(5/24) * h1^(-1/4) * h3^(1/6) * h6^(-1/2)
Gamma(23/24) = 2^(-49/72) * 3^(-25/48) * beta^(3/8) * a23^(1/2) * pi^(1/24) * h1^(-1/4) * h3^(-1/6) * h6^(-1/2)
alpha = 1 + sqrt(2)
beta = 2 + sqrt(3)
a23 = sqrt(2) + sqrt(3)
h1 ~= 1.18034059901609622605
h2 ~= 1.04760137722700737130
h3 ~= 1.01740879759595600867
h6 ~= 1.00182067173235443475
Gamma(1/5) = g15
Gamma(2/5) = g25
Gamma(3/5) = 2 * 5^(-1/4) * phi^(-1/2) * pi * g25^-1
Gamma(4/5) = 2 * 5^(-1/4) * phi^(1/2) * pi * g15^-1
Gamma(1/10) = 2^(-1/5) * 5^(1/4) * phi^(1/2) * pi^(-1/2) * g15 * g25
Gamma(3/10) = 2^(2/5) * phi^-1 * pi^(1/2) * g15 * g25^-1
Gamma(7/10) = 2^(3/5) * pi^(1/2) * g15^-1 * g25
Gamma(9/10) = 2^(6/5) * 5^(-1/4) * phi^(1/2) * pi^(3/2) * g15^-1 * g25^-1
Gamma(1/15) = 2^(2/9) * 3^(29/60) * 5^(7/24) * phi^(-1/4) * ay1^(1/4) * ay2^(1/4) * pi^(5/6) * h3^(1/6) * h15^(1/2) * g15^(1/2) * g25^(-1/2)
Gamma(2/15) = 2^(-2/9) * 3^(13/60) * 5^(1/3) * phi^(-1/2) * ay1^(1/4) * ay2^(-1/4) * pi^(1/6) * h3^(-1/6) * h15^(1/2) * g15^(1/2) * g25^(1/2)
Gamma(4/15) = 2^(2/9) * 3^(11/60) * 5^(7/24) * phi^(1/4) * ay1^(-1/4) * ay2^(-1/4) * pi^(5/6) * h3^(1/6) * h15^(1/2) * g15^(-1/2) * g25^(1/2)
Gamma(7/15) = 2^(2/9) * 3^(-7/60) * 5^(-1/12) * ay1^(-1/4) * ay2^(1/4) * pi^(-1/6) * h3^(1/6) * h15^(-1/2) * g15^(1/2) * g25^(1/2)
Gamma(8/15) = 2^(7/9) * 3^(7/60) * 5^(1/12) * phi^(-1/2) * ay1^(-1/4) * ay2^(1/4) * pi^(7/6) * h3^(-1/6) * h15^(1/2) * g15^(-1/2) * g25^(-1/2)
Gamma(11/15) = 2^(7/9) * 3^(-11/60) * 5^(-7/24) * phi^(1/4) * ay1^(-1/4) * ay2^(-1/4) * pi^(1/6) * h3^(-1/6) * h15^(-1/2) * g15^(1/2) * g25^(-1/2)
Gamma(13/15) = 2^(11/9) * 3^(-13/60) * 5^(-1/3) * ay1^(1/4) * ay2^(-1/4) * pi^(5/6) * h3^(1/6) * h15^(-1/2) * g15^(-1/2) * g25^(-1/2)
Gamma(14/15) = 2^(7/9) * 3^(-29/60) * 5^(-7/24) * phi^(3/4) * ay1^(1/4) * ay2^(1/4) * pi^(1/6) * h3^(-1/6) * h15^(-1/2) * g15^(-1/2) * g25^(1/2)
Gamma(1/20) = 2^(3/5) * 5^(7/16) * phi^(-1/8) * ax1^(1/4) * ax2^(1/4) * pi^(1/4) * h5^(1/2) * g15^(1/2) * g25^(1/2)
Gamma(3/20) = 2^(4/5) * 5^(3/16) * phi^(-7/8) * ax1^(1/4) * ax2^(-1/4) * pi^(3/4) * h5^(1/2) * g15^(1/2) * g25^(-1/2)
Gamma(7/20) = 2^(7/10) * 5^(3/16) * phi^(-3/8) * ax1^(-1/4) * ax2^(1/4) * pi^(3/4) * h5^(1/2) * g15^(-1/2) * g25^(1/2)
Gamma(9/20) = 2^(9/10) * 5^(3/16) * phi^(-1/8) * ax1^(-1/4) * ax2^(-1/4) * pi^(5/4) * h5^(1/2) * g15^(-1/2) * g25^(-1/2)
Gamma(11/20) = 2^(1/10) * 5^(-3/16) * phi^(5/8) * ax1^(-1/4) * ax2^(-1/4) * pi^(-1/4) * h5^(-1/2) * g15^(1/2) * g25^(1/2)
Gamma(13/20) = 2^(3/10) * 5^(-3/16) * phi^(-1/8) * ax1^(-1/4) * ax2^(1/4) * pi^(1/4) * h5^(-1/2) * g15^(1/2) * g25^(-1/2)
Gamma(17/20) = 2^(1/5) * 5^(-3/16) * phi^(3/8) * ax1^(1/4) * ax2^(-1/4) * pi^(1/4) * h5^(-1/2) * g15^(-1/2) * g25^(1/2)
Gamma(19/20) = 2^(2/5) * 5^(-7/16) * phi^(5/8) * ax1^(1/4) * ax2^(1/4) * pi^(3/4) * h5^(-1/2) * g15^(-1/2) * g25^(-1/2)
Gamma(1/30) = 2^(17/45) * 3^(11/30) * 5^(5/24) * phi^(1/4) * ay1^(1/2) * pi^(1/6) * h3^(1/3) * g15
Gamma(7/30) = 2^(-1/45) * 3^(1/15) * 5^(5/24) * phi^(-1/4) * ay2^(1/2) * pi^(1/6) * h3^(1/3) * g25
Gamma(11/30) = 2^(-8/45) * 3^(1/30) * 5^(1/24) * phi^(1/4) * ay1^(-1/2) * pi^(-1/6) * h3^(-1/3) * g15
Gamma(13/30) = 2^(26/45) * 3^(4/15) * 5^(-1/24) * phi^(-3/4) * ay2^(-1/2) * pi^(7/6) * h3^(1/3) * g25^-1
Gamma(17/30) = 2^(19/45) * 3^(-4/15) * 5^(1/24) * phi^(-1/4) * ay2^(-1/2) * pi^(-1/6) * h3^(-1/3) * g25
Gamma(19/30) = 2^(53/45) * 3^(-1/30) * 5^(-1/24) * phi^(3/4) * ay1^(-1/2) * pi^(7/6) * h3^(1/3) * g15^-1
Gamma(23/30) = 2^(46/45) * 3^(-1/15) * 5^(-5/24) * phi^(-3/4) * ay2^(1/2) * pi^(5/6) * h3^(-1/3) * g25^-1
Gamma(29/30) = 2^(28/45) * 3^(-11/30) * 5^(-5/24) * phi^(3/4) * ay1^(1/2) * pi^(5/6) * h3^(-1/3) * g15^-1
phi = 1/2 + 1/2 * sqrt(5)
ax1 = 5^(1/4) * phi^(1/2) + phi
ax2 = 5^(1/4) * phi^(-1/2) + phi^-1
ay1 = 1/2 * 3^(1/2) * 5^(1/4) * phi^(1/2) + 1/2 * phi^2
ay2 = 1/2 * 3^(1/2) * 5^(1/4) * phi^(-1/2) + 1/2 * phi^-2
h5 ~= 1.00356129430166810582
h15 ~= 1.00002079004130484823
g15 ~= 4.59084371199880305320
g25 ~= 2.21815954375768822306