bel4 = -11*a - 102*a^2 - (2857*a^3)/2 - (149753*a^4)/6 + (2*a*nf)/3 + 
     (38*a^2*nf)/3 + (5033*a^3*nf)/18 + (1078361*a^4*nf)/162 - 
     (325*a^3*nf^2)/54 - (50065*a^4*nf^2)/162 - (1093*a^4*nf^3)/729 - 
     3564*a^4*z3 + (6508*a^4*nf*z3)/27 - (6472*a^4*nf^2*z3)/81
 
gml4 = -4*a - (202*a^2)/3 - 1249*a^3 - (4603055*a^4)/162 + (20*a^2*nf)/9 + 
     (2216*a^3*nf)/27 + (91723*a^4*nf)/27 + (140*a^3*nf^2)/81 - 
     (5242*a^4*nf^2)/243 + (332*a^4*nf^3)/243 - (135680*a^4*z3)/27 + 
     (160*a^3*nf*z3)/3 + (34192*a^4*nf*z3)/9 - (800*a^4*nf^2*z3)/9 - 
     (64*a^4*nf^3*z3)/27 - 880*a^4*nf*z4 + (160*a^4*nf^2*z4)/3 + 
     8800*a^4*z5 - (18400*a^4*nf*z5)/9
 
gamma3l4 = (13*a)/2 + (531*a^2)/8 + (29895*a^3)/32 + (10596127*a^4)/768 - 
     (2*a*nf)/3 - (61*a^2*nf)/6 - (8155*a^3*nf)/36 - (23350603*a^4*nf)/5184 + 
     (215*a^3*nf^2)/27 + (43033*a^4*nf^2)/162 + (4427*a^4*nf^3)/1458 - 
     (3*a*xil)/2 - (99*a^2*xil)/8 - (4509*a^3*xil)/32 - 
     (2174765*a^4*xil)/768 + 9*a^3*nf*xil + (10879*a^4*nf*xil)/36 + 
     (1229*a^4*nf^2*xil)/216 - (9*a^2*xil^2)/4 - (891*a^3*xil^2)/32 - 
     (100575*a^4*xil^2)/256 + (1161*a^4*nf*xil^2)/64 - (189*a^3*xil^3)/32 - 
     (25299*a^4*xil^3)/256 - (1215*a^4*xil^4)/64 - (243*a^3*z3)/16 - 
     (1012023*a^4*z3)/256 + 33*a^3*nf*z3 + (387649*a^4*nf*z3)/216 + 
     (2017*a^4*nf^2*z3)/81 - (8*a^4*nf^3*z3)/3 - (81*a^3*xil*z3)/4 - 
     (247725*a^4*xil*z3)/128 + 156*a^4*nf*xil*z3 - 6*a^4*nf^2*xil*z3 - 
     (81*a^3*xil^2*z3)/16 - (18117*a^4*xil^2*z3)/64 + (9*a^4*nf*xil^2*z3)/2 - 
     (2619*a^4*xil^3*z3)/128 + (459*a^4*xil^4*z3)/256 + (8019*a^4*z4)/32 - 
     (8955*a^4*nf*z4)/16 + 33*a^4*nf^2*z4 + (16443*a^4*xil*z4)/64 + 
     (45*a^4*nf*xil*z4)/4 + (405*a^4*xil^2*z4)/8 - (27*a^4*nf*xil^2*z4)/16 + 
     (243*a^4*xil^3*z4)/64 + (40905*a^4*z5)/4 - (3355*a^4*nf*z5)/2 + 
     (170235*a^4*xil*z5)/128 - (4455*a^4*xil^2*z5)/128 - 
     (4995*a^4*xil^3*z5)/128 - (945*a^4*xil^4*z5)/128
 
gamma3ghl4 = (9*a)/4 + (285*a^2)/16 + (15817*a^3)/64 + (2857419*a^4)/512 - 
     (5*a^2*nf)/4 - (637*a^3*nf)/24 - (1239661*a^4*nf)/1152 - 
     (35*a^3*nf^2)/36 + (586*a^4*nf^2)/27 - (83*a^4*nf^3)/108 - (3*a*xil)/4 + 
     (9*a^2*xil)/16 - (459*a^3*xil)/32 - (368231*a^4*xil)/1536 + 
     (63*a^3*nf*xil)/16 + (11107*a^4*nf*xil)/288 + (779*a^4*nf^2*xil)/432 - 
     (81*a^3*xil^2)/32 - (17613*a^4*xil^2)/512 + (651*a^4*nf*xil^2)/128 - 
     (81*a^3*xil^3)/64 - (4185*a^4*xil^3)/512 - (81*a^4*xil^4)/32 + 
     (243*a^3*z3)/32 + (1924407*a^4*z3)/512 - (33*a^3*nf*z3)/2 - 
     (48857*a^4*nf*z3)/48 + (55*a^4*nf^2*z3)/2 + (4*a^4*nf^3*z3)/3 + 
     (81*a^3*xil*z3)/8 + (75573*a^4*xil*z3)/256 + (39*a^4*nf*xil*z3)/8 - 
     3*a^4*nf^2*xil*z3 + (81*a^3*xil^2*z3)/32 + (4131*a^4*xil^2*z3)/128 + 
     (27*a^4*nf*xil^2*z3)/8 - (9045*a^4*xil^3*z3)/256 + 
     (3213*a^4*xil^4*z3)/512 - (8019*a^4*z4)/64 + (8955*a^4*nf*z4)/32 - 
     (33*a^4*nf^2*z4)/2 - (17901*a^4*xil*z4)/128 + (153*a^4*nf*xil*z4)/8 - 
     (81*a^4*xil^2*z4)/2 + (27*a^4*nf*xil^2*z4)/32 - (729*a^4*xil^3*z4)/128 - 
     (40905*a^4*z5)/8 + (3355*a^4*nf*z5)/4 + (12015*a^4*xil*z5)/256 + 
     (21465*a^4*xil^2*z5)/256 + (17145*a^4*xil^3*z5)/256 - 
     (945*a^4*xil^4*z5)/256
 
gamma1ccgl4 = (-3*a*xil)/2 - (45*a^2*xil)/8 - (5427*a^3*xil)/64 - 
     (635749*a^4*xil)/384 + (135*a^3*nf*xil)/16 + (54623*a^4*nf*xil)/288 + 
     (251*a^4*nf^2*xil)/54 - (9*a^2*xil^2)/8 - (1053*a^3*xil^2)/64 - 
     (29547*a^4*xil^2)/128 + (453*a^4*nf*xil^2)/32 - (135*a^3*xil^3)/32 - 
     (7371*a^4*xil^3)/128 - (1539*a^4*xil^4)/128 - (21519*a^4*xil*z3)/32 + 
     (663*a^4*nf*xil*z3)/8 - 6*a^4*nf^2*xil*z3 - (6993*a^4*xil^2*z3)/64 + 
     (45*a^4*nf*xil^2*z3)/8 - (729*a^4*xil^3*z3)/16 + (459*a^4*xil^4*z3)/64 - 
     (729*a^4*xil*z4)/64 + (99*a^4*nf*xil*z4)/4 - (243*a^4*xil^2*z4)/16 - 
     (243*a^4*xil^3*z4)/64 + (91125*a^4*xil*z5)/128 + 
     (8505*a^4*xil^2*z5)/128 + (6075*a^4*xil^3*z5)/128 - 
     (945*a^4*xil^4*z5)/128
 
gamma1qqgl4 = (-9*a)/4 - (1927*a^2)/48 - (474017*a^3)/576 - 
     (771454523*a^4)/41472 + (31*a^2*nf)/12 + (6311*a^3*nf)/72 + 
     (31906133*a^4*nf)/10368 + (25*a^3*nf^2)/108 - (5611*a^4*nf^2)/81 + 
     (187*a^4*nf^3)/972 - (25*a*xil)/12 - (227*a^2*xil)/16 - 
     (10821*a^3*xil)/64 - (45822149*a^4*xil)/13824 + 13*a^3*nf*xil + 
     (61363*a^4*nf*xil)/162 + (28277*a^4*nf^2*xil)/3888 - (17*a^2*xil^2)/8 - 
     (1827*a^3*xil^2)/64 - (204047*a^4*xil^2)/512 + (6971*a^4*nf*xil^2)/384 - 
     (429*a^3*xil^3)/64 - (53907*a^4*xil^3)/512 - (2583*a^4*xil^4)/128 + 
     (1021*a^3*z3)/32 - (83436775*a^4*z3)/41472 + (33*a^3*nf*z3)/2 + 
     (476369*a^4*nf*z3)/432 - (815*a^4*nf^2*z3)/18 - (4*a^4*nf^3*z3)/3 - 
     (153*a^3*xil*z3)/8 - (527501*a^4*xil*z3)/256 + (548*a^4*nf*xil*z3)/3 - 
     (25*a^4*nf^2*xil*z3)/3 - (225*a^3*xil^2*z3)/32 - 
     (46213*a^4*xil^2*z3)/128 + (37*a^4*nf*xil^2*z3)/4 - 
     (7707*a^4*xil^3*z3)/256 + (1483*a^4*xil^4*z3)/512 - (33693*a^4*z4)/64 - 
     (7691*a^4*nf*z4)/32 + (33*a^4*nf^2*z4)/2 + (30411*a^4*xil*z4)/128 + 
     (173*a^4*nf*xil*z4)/8 + (1017*a^4*xil^2*z4)/16 - 
     (75*a^4*nf*xil^2*z4)/32 + (675*a^4*xil^3*z4)/128 + 
     (7388135*a^4*z5)/1296 - (9425*a^4*nf*z5)/12 + (405755*a^4*xil*z5)/256 + 
     (19385*a^4*xil^2*z5)/256 - (4995*a^4*xil^3*z5)/256 - 
     (1825*a^4*xil^4*z5)/256

 
gammaggl4Landau = (35*a)/4 + (1347*a^2)/16 + (75607*a^3)/64 + 
     (29764511*a^4)/1536 - (2*a*nf)/3 - (137*a^2*nf)/12 - (18221*a^3*nf)/72 - 
     (57858155*a^4*nf)/10368 + (755*a^3*nf^2)/108 + (46549*a^4*nf^2)/162 + 
     (6613*a^4*nf^3)/2916 - (243*a^3*z3)/32 - (99639*a^4*z3)/512 + 
     (33*a^3*nf*z3)/2 + (335585*a^4*nf*z3)/432 + (8489*a^4*nf^2*z3)/162 - 
     (4*a^4*nf^3*z3)/3 + (8019*a^4*z4)/64 - (8955*a^4*nf*z4)/32 + 
     (33*a^4*nf^2*z4)/2 + (40905*a^4*z5)/8 - (3355*a^4*nf*z5)/4

 
