bel4 = (-11*a*nc)/3 - (34*a^2*nc^2)/3 + (40*a^4*nc^2)/3 - 
     (2857*a^3*nc^3)/54 - (150473*a^4*nc^4)/486 + (2*a*nf)/3 - 
     (187*a^3*nf)/36 + (23*a^4*nf)/(8*nc^3) - (a^3*nf)/(4*nc^2) - 
     (a^2*nf)/nc + (2341*a^4*nf)/(216*nc) + (13*a^2*nc*nf)/3 - 
     (58583*a^4*nc*nf)/1944 + (1709*a^3*nc^2*nf)/54 + 
     (485513*a^4*nc^3*nf)/1944 + (2477*a^4*nf^2)/243 + 
     (623*a^4*nf^2)/(54*nc^2) + (11*a^3*nf^2)/(18*nc) - (56*a^3*nc*nf^2)/27 - 
     (8654*a^4*nc^2*nf^2)/243 + (77*a^4*nf^3)/(243*nc) - 
     (130*a^4*nc*nf^3)/243 - 352*a^4*nc^2*z3 - (44*a^4*nc^4*z3)/9 - 
     (44*a^4*nf*z3)/(9*nc) + (548*a^4*nc*nf*z3)/9 + (20*a^4*nc^3*nf*z3)/9 + 
     (64*a^4*nf^2*z3)/9 - (244*a^4*nf^2*z3)/(9*nc^2) - (28*a^4*nc^2*nf^2*z3)/3
 
gml4 = (53*a^2)/6 - (108359*a^4)/576 + (1261*a^4)/(128*nc^4) + 
     (129*a^3)/(16*nc^3) - (3*a^2)/(8*nc^2) + (5783*a^4)/(48*nc^2) + 
     (3*a)/(2*nc) - (129*a^3)/(8*nc) - (3*a*nc)/2 + (26309*a^3*nc)/432 - 
     (203*a^2*nc^2)/24 + (21947*a^4*nc^2)/48 - (11413*a^3*nc^3)/216 - 
     (460151*a^4*nc^4)/1152 - (899*a^3*nf)/54 + (37*a^4*nf)/(6*nc^3) + 
     (23*a^3*nf)/(4*nc^2) - (5*a^2*nf)/(6*nc) + (9143*a^4*nf)/(216*nc) + 
     (5*a^2*nc*nf)/6 - (126689*a^4*nc*nf)/648 + (1177*a^3*nc^2*nf)/108 + 
     (11908*a^4*nc^3*nf)/81 + (1127*a^4*nf^2)/324 - (19*a^4*nf^2)/(27*nc^2) - 
     (35*a^3*nf^2)/(54*nc) + (35*a^3*nc*nf^2)/54 - (899*a^4*nc^2*nf^2)/324 - 
     (83*a^4*nf^3)/(162*nc) + (83*a^4*nc*nf^3)/162 + (151*a^4*z3)/2 + 
     (21*a^4*z3)/nc^4 - (89*a^4*z3)/(2*nc^2) + (221*a^4*nc^2*z3)/18 - 
     (1157*a^4*nc^4*z3)/18 - (111*a^4*nf*z3)/(2*nc^3) - (6*a^3*nf*z3)/nc^2 - 
     (59*a^4*nf*z3)/(2*nc) - (379*a^4*nc*nf*z3)/6 + 6*a^3*nc^2*nf*z3 + 
     (889*a^4*nc^3*nf*z3)/6 + (10*a^4*nf^2*z3)/nc^2 - 10*a^4*nc^2*nf^2*z3 + 
     (8*a^4*nf^3*z3)/(9*nc) - (8*a^4*nc*nf^3*z3)/9 + (33*a^4*nf*z4)/nc - 
     33*a^4*nc^3*nf*z4 - (6*a^4*nf^2*z4)/nc^2 + 6*a^4*nc^2*nf^2*z4 - 
     110*a^4*z5 + 110*a^4*nc^4*z5 - (30*a^4*nf*z5)/nc^3 + (80*a^4*nf*z5)/nc + 
     30*a^4*nc*nf*z5 - 80*a^4*nc^3*nf*z5
 
gamma3l4 = (13*a*nc)/6 + (59*a^2*nc^2)/8 - (659*a^4*nc^2)/96 + 
     (9965*a^3*nc^3)/288 + (10643575*a^4*nc^4)/62208 - (2*a*nf)/3 - 
     (31*a^3*nf)/72 - (23*a^4*nf)/(8*nc^3) + (a^3*nf)/(4*nc^2) + 
     (a^2*nf)/nc - (7121*a^4*nf)/(432*nc) - (7*a^2*nc*nf)/2 + 
     (42529*a^4*nc*nf)/3888 - (201*a^3*nc^2*nf)/8 - 
     (2610187*a^4*nc^3*nf)/15552 - (8873*a^4*nf^2)/972 - 
     (623*a^4*nf^2)/(54*nc^2) - (11*a^3*nf^2)/(18*nc) + (49*a^3*nc*nf^2)/18 + 
     (29813*a^4*nc^2*nf^2)/972 - (77*a^4*nf^3)/(243*nc) + 
     (509*a^4*nc*nf^3)/486 - (a*nc*xil)/2 - (11*a^2*nc^2*xil)/8 + 
     (9*a^4*nc^2*xil)/8 - (167*a^3*nc^3*xil)/32 - (2182541*a^4*nc^4*xil)/
      62208 - (863*a^4*nc*nf*xil)/96 + a^3*nc^2*nf*xil + 
     (94799*a^4*nc^3*nf*xil)/7776 + (1229*a^4*nc^2*nf^2*xil)/1944 - 
     (a^2*nc^2*xil^2)/4 + (9*a^4*nc^2*xil^2)/32 - (33*a^3*nc^3*xil^2)/32 - 
     (3749*a^4*nc^4*xil^2)/768 + (43*a^4*nc^3*nf*xil^2)/64 - 
     (7*a^3*nc^3*xil^3)/32 - (937*a^4*nc^4*xil^3)/768 - 
     (15*a^4*nc^4*xil^4)/64 + (989*a^4*nc^2*z3)/8 - (9*a^3*nc^3*z3)/16 - 
     (144095*a^4*nc^4*z3)/2304 + 6*a^3*nf*z3 - (245*a^4*nf*z3)/(18*nc) + 
     (289*a^4*nc*nf*z3)/9 + 3*a^3*nc^2*nf*z3 + (4541*a^4*nc^3*nf*z3)/72 - 
     (154*a^4*nf^2*z3)/9 + (244*a^4*nf^2*z3)/(9*nc^2) + 
     (13*a^4*nc^2*nf^2*z3)/3 - (8*a^4*nc*nf^3*z3)/9 - 
     (1347*a^4*nc^2*xil*z3)/32 - (3*a^3*nc^3*xil*z3)/4 - 
     (7379*a^4*nc^4*xil*z3)/384 + 7*a^4*nc*nf*xil*z3 + 5*a^4*nc^3*nf*xil*z3 - 
     (2*a^4*nc^2*nf^2*xil*z3)/3 - (9*a^4*nc^2*xil^2*z3)/2 - 
     (3*a^3*nc^3*xil^2*z3)/16 - (575*a^4*nc^4*xil^2*z3)/192 + 
     (a^4*nc^3*nf*xil^2*z3)/6 - (3*a^4*nc^2*xil^3*z3)/32 - 
     (31*a^4*nc^4*xil^3*z3)/128 - (3*a^4*nc^2*xil^4*z3)/16 + 
     (11*a^4*nc^4*xil^4*z3)/256 + (99*a^4*nc^4*z4)/32 - 33*a^4*nc*nf*z4 - 
     (273*a^4*nc^3*nf*z4)/16 + 6*a^4*nf^2*z4 + 3*a^4*nc^2*nf^2*z4 + 
     (203*a^4*nc^4*xil*z4)/64 + (3*a^4*nc*nf*xil*z4)/2 + 
     (a^4*nc^3*nf*xil*z4)/4 + (5*a^4*nc^4*xil^2*z4)/8 - 
     (a^4*nc^3*nf*xil^2*z4)/16 + (3*a^4*nc^4*xil^3*z4)/64 + 
     (30555*a^4*nc^2*z5)/128 + (12765*a^4*nc^4*z5)/128 + (30*a^4*nf*z5)/nc - 
     45*a^4*nc*nf*z5 - (115*a^4*nc^3*nf*z5)/2 + (1425*a^4*nc^2*xil*z5)/64 + 
     (1785*a^4*nc^4*xil*z5)/128 - (225*a^4*nc^2*xil^2*z5)/32 + 
     (45*a^4*nc^4*xil^2*z5)/128 - (165*a^4*nc^2*xil^3*z5)/64 - 
     (25*a^4*nc^4*xil^3*z5)/128 - (15*a^4*nc^2*xil^4*z5)/128 - 
     (5*a^4*nc^4*xil^4*z5)/64
 
gamma3ghl4 = (3*a*nc)/4 + (95*a^2*nc^2)/48 - (207*a^4*nc^2)/64 + 
     (15817*a^3*nc^3)/1728 + (319147*a^4*nc^4)/4608 + (45*a^3*nf)/16 + 
     (271*a^4*nf)/(96*nc) - (5*a^2*nc*nf)/12 + (8293*a^4*nc*nf)/864 - 
     (1409*a^3*nc^2*nf)/432 - (424639*a^4*nc^3*nf)/10368 - 
     (115*a^4*nf^2)/216 - (35*a^3*nc*nf^2)/108 + (1601*a^4*nc^2*nf^2)/648 - 
     (83*a^4*nc*nf^3)/324 - (a*nc*xil)/4 + (a^2*nc^2*xil)/16 - 
     (9*a^4*nc^2*xil)/16 - (17*a^3*nc^3*xil)/32 - (360455*a^4*nc^4*xil)/
      124416 - (425*a^4*nc*nf*xil)/192 + (7*a^3*nc^2*nf*xil)/16 + 
     (26039*a^4*nc^3*nf*xil)/15552 + (779*a^4*nc^2*nf^2*xil)/3888 - 
     (9*a^4*nc^2*xil^2)/64 - (3*a^3*nc^3*xil^2)/32 - 
     (1885*a^4*nc^4*xil^2)/4608 + (217*a^4*nc^3*nf*xil^2)/1152 - 
     (3*a^3*nc^3*xil^3)/64 - (155*a^4*nc^4*xil^3)/1536 - 
     (a^4*nc^4*xil^4)/32 + (1827*a^4*nc^2*z3)/16 + (9*a^3*nc^3*z3)/32 + 
     (155359*a^4*nc^4*z3)/4608 - 3*a^3*nf*z3 + (37*a^4*nf*z3)/(4*nc) - 
     (93*a^4*nc*nf*z3)/2 - (3*a^3*nc^2*nf*z3)/2 - (1567*a^4*nc^3*nf*z3)/48 + 
     5*a^4*nf^2*z3 + (5*a^4*nc^2*nf^2*z3)/2 + (4*a^4*nc*nf^3*z3)/9 + 
     (15*a^4*nc^2*xil*z3)/64 + (3*a^3*nc^3*xil*z3)/8 + 
     (2779*a^4*nc^4*xil*z3)/768 + (a^4*nc*nf*xil*z3)/2 + 
     (a^4*nc^3*nf*xil*z3)/8 - (a^4*nc^2*nf^2*xil*z3)/3 - 
     (27*a^4*nc^2*xil^2*z3)/32 + (3*a^3*nc^3*xil^2*z3)/32 + 
     (63*a^4*nc^4*xil^2*z3)/128 + (a^4*nc^3*nf*xil^2*z3)/8 - 
     (141*a^4*nc^2*xil^3*z3)/64 - (49*a^4*nc^4*xil^3*z3)/256 + 
     (3*a^4*nc^2*xil^4*z3)/4 - (3*a^4*nc^4*xil^4*z3)/512 - 
     (99*a^4*nc^4*z4)/64 + (33*a^4*nc*nf*z4)/2 + (273*a^4*nc^3*nf*z4)/32 - 
     3*a^4*nf^2*z4 - (3*a^4*nc^2*nf^2*z4)/2 - (221*a^4*nc^4*xil*z4)/128 + 
     (3*a^4*nc*nf*xil*z4)/4 + (5*a^4*nc^3*nf*xil*z4)/8 - 
     (a^4*nc^4*xil^2*z4)/2 + (a^4*nc^3*nf*xil^2*z4)/32 - 
     (9*a^4*nc^4*xil^3*z4)/128 - (30555*a^4*nc^2*z5)/256 - 
     (12765*a^4*nc^4*z5)/256 - (15*a^4*nf*z5)/nc + (45*a^4*nc*nf*z5)/2 + 
     (115*a^4*nc^3*nf*z5)/4 + (1455*a^4*nc^2*xil*z5)/128 - 
     (175*a^4*nc^4*xil*z5)/256 + (315*a^4*nc^2*xil^2*z5)/64 + 
     (125*a^4*nc^4*xil^2*z5)/256 + (525*a^4*nc^2*xil^3*z5)/128 + 
     (95*a^4*nc^4*xil^3*z5)/256 - (105*a^4*nc^2*xil^4*z5)/256
 
gamma1ccgl4 = -(a*nc*xil)/2 - (5*a^2*nc^2*xil)/8 - (201*a^3*nc^3*xil)/64 - 
     (635749*a^4*nc^4*xil)/31104 - (161*a^4*nc*nf*xil)/24 + 
     (15*a^3*nc^2*nf*xil)/16 + (60419*a^4*nc^3*nf*xil)/7776 + 
     (251*a^4*nc^2*nf^2*xil)/486 - (a^2*nc^2*xil^2)/8 - 
     (39*a^3*nc^3*xil^2)/64 - (3283*a^4*nc^4*xil^2)/1152 + 
     (151*a^4*nc^3*nf*xil^2)/288 - (5*a^3*nc^3*xil^3)/32 - 
     (91*a^4*nc^4*xil^3)/128 - (19*a^4*nc^4*xil^4)/128 - 
     (333*a^4*nc^2*xil*z3)/16 - (575*a^4*nc^4*xil*z3)/96 + 
     4*a^4*nc*nf*xil*z3 + (21*a^4*nc^3*nf*xil*z3)/8 - 
     (2*a^4*nc^2*nf^2*xil*z3)/3 - (99*a^4*nc^2*xil^2*z3)/32 - 
     (193*a^4*nc^4*xil^2*z3)/192 + (5*a^4*nc^3*nf*xil^2*z3)/24 - 
     (9*a^4*nc^2*xil^3*z3)/4 - (5*a^4*nc^4*xil^3*z3)/16 + 
     (21*a^4*nc^2*xil^4*z3)/32 + (a^4*nc^4*xil^4*z3)/64 - 
     (9*a^4*nc^4*xil*z4)/64 + (3*a^4*nc*nf*xil*z4)/2 + 
     (3*a^4*nc^3*nf*xil*z4)/4 - (3*a^4*nc^4*xil^2*z4)/16 - 
     (3*a^4*nc^4*xil^3*z4)/64 + (45*a^4*nc^2*xil*z5)/2 + 
     (805*a^4*nc^4*xil*z5)/128 + (45*a^4*nc^2*xil^2*z5)/32 + 
     (85*a^4*nc^4*xil^2*z5)/128 + (45*a^4*nc^2*xil^3*z5)/16 + 
     (35*a^4*nc^4*xil^3*z5)/128 - (15*a^4*nc^2*xil^4*z5)/32 - 
     (5*a^4*nc^4*xil^4*z5)/128
 
gamma1qqgl4 = (19*a^2)/8 + (26087*a^4)/576 + (1027*a^4)/(128*nc^4) + 
     (3*a^3)/(16*nc^3) + (3*a^2)/(8*nc^2) + (1025*a^4)/(48*nc^2) + 
     (67*a^3)/(8*nc) - (3*a*nc)/4 + (4169*a^3*nc)/288 - (227*a^2*nc^2)/48 + 
     (522251*a^4*nc^2)/5184 - (55627*a^3*nc^3)/1728 - 
     (10012807*a^4*nc^4)/41472 - (1445*a^3*nf)/144 + (307*a^4*nf)/(12*nc^3) - 
     (3*a^3*nf)/(8*nc^2) - (a^2*nf)/(2*nc) - (11291*a^4*nf)/(288*nc) + 
     (11*a^2*nc*nf)/12 - (7805*a^4*nc*nf)/96 + (4691*a^3*nc^2*nf)/432 + 
     (1280023*a^4*nc^3*nf)/10368 + (953*a^4*nf^2)/108 - 
     (19*a^4*nf^2)/(9*nc^2) + (5*a^3*nf^2)/(18*nc) + (5*a^3*nc*nf^2)/108 - 
     (2803*a^4*nc^2*nf^2)/324 + (35*a^4*nf^3)/(162*nc) + 
     (13*a^4*nc*nf^3)/324 + a^2*xil - (5*a^4*xil)/8 + (a*xil)/(2*nc) - 
     (3*a*nc*xil)/4 + (263*a^3*nc*xil)/64 - (27*a^2*nc^2*xil)/16 + 
     (1718771*a^4*nc^2*xil)/62208 - (215*a^3*nc^3*xil)/32 - 
     (1824113*a^4*nc^4*xil)/41472 - (17*a^3*nf*xil)/16 + 
     (767*a^4*nf*xil)/(96*nc) - (22219*a^4*nc*nf*xil)/972 + 
     (25*a^3*nc^2*nf*xil)/16 + (42691*a^4*nc^3*nf*xil)/2592 - 
     (269*a^4*nf^2*xil)/486 + (1127*a^4*nc^2*nf^2*xil)/1296 + (a^2*xil^2)/8 + 
     (39*a^3*nc*xil^2)/64 - (a^2*nc^2*xil^2)/4 + (6791*a^4*nc^2*xil^2)/2304 - 
     (9*a^3*nc^3*xil^2)/8 - (24181*a^4*nc^4*xil^2)/4608 - 
     (109*a^4*nc*nf*xil^2)/288 + (823*a^4*nc^3*nf*xil^2)/1152 + 
     (5*a^3*nc*xil^3)/32 + (149*a^4*nc^2*xil^3)/192 - 
     (17*a^3*nc^3*xil^3)/64 - (2129*a^4*nc^4*xil^3)/1536 + 
     (19*a^4*nc^2*xil^4)/128 - (17*a^4*nc^4*xil^4)/64 - (6271*a^4*z3)/64 + 
     (25*a^4*z3)/nc^4 + (6*a^4*z3)/nc^2 - (3*a^3*z3)/nc + (27*a^3*nc*z3)/16 - 
     (1031*a^4*nc^2*z3)/16 + (33*a^3*nc^3*z3)/32 - (75943*a^4*nc^4*z3)/4608 + 
     3*a^3*nf*z3 - (4*a^4*nf*z3)/nc^3 + (11*a^4*nf*z3)/(4*nc) + 
     (273*a^4*nc*nf*z3)/8 + (3*a^3*nc^2*nf*z3)/2 + (1777*a^4*nc^3*nf*z3)/48 - 
     5*a^4*nf^2*z3 + (2*a^4*nf^2*z3)/nc^2 - (9*a^4*nc^2*nf^2*z3)/2 - 
     (4*a^4*nc*nf^3*z3)/9 + (115*a^4*xil*z3)/16 + (3*a^3*nc*xil*z3)/8 - 
     (665*a^4*nc^2*xil*z3)/48 - (3*a^3*nc^3*xil*z3)/4 - 
     (6141*a^4*nc^4*xil*z3)/256 - (11*a^4*nf*xil*z3)/(2*nc) + 
     (21*a^4*nc*nf*xil*z3)/4 + (25*a^4*nc^3*nf*xil*z3)/4 + 
     (2*a^4*nf^2*xil*z3)/3 - a^4*nc^2*nf^2*xil*z3 + (11*a^4*xil^2*z3)/32 + 
     (3*a^3*nc*xil^2*z3)/16 + (5*a^4*nc^2*xil^2*z3)/12 - 
     (9*a^3*nc^3*xil^2*z3)/32 - (577*a^4*nc^4*xil^2*z3)/128 - 
     (7*a^4*nc*nf*xil^2*z3)/24 + (3*a^4*nc^3*nf*xil^2*z3)/8 - 
     (3*a^4*xil^3*z3)/16 + (7*a^4*nc^2*xil^3*z3)/16 - 
     (107*a^4*nc^4*xil^3*z3)/256 - (7*a^4*xil^4*z3)/64 + 
     (19*a^4*nc^4*xil^4*z3)/512 + (33*a^4*z4)/2 - (297*a^4*nc^2*z4)/32 - 
     (363*a^4*nc^4*z4)/64 - (3*a^4*nf*z4)/nc - (237*a^4*nc*nf*z4)/16 - 
     (231*a^4*nc^3*nf*z4)/32 + 3*a^4*nf^2*z4 + (3*a^4*nc^2*nf^2*z4)/2 - 
     (97*a^4*nc^2*xil*z4)/64 + (397*a^4*nc^4*xil*z4)/128 - 
     (3*a^4*nf*xil*z4)/(2*nc) + (7*a^4*nc*nf*xil*z4)/4 + 
     (5*a^4*nc^3*nf*xil*z4)/8 - (17*a^4*nc^2*xil^2*z4)/32 + 
     (27*a^4*nc^4*xil^2*z4)/32 + (a^4*nc*nf*xil^2*z4)/16 - 
     (3*a^4*nc^3*nf*xil^2*z4)/32 - (3*a^4*nc^2*xil^3*z4)/64 + 
     (9*a^4*nc^4*xil^3*z4)/128 + (5785*a^4*z5)/64 - (40*a^4*z5)/nc^4 - 
     (20*a^4*z5)/nc^2 + (20025*a^4*nc^2*z5)/256 + (15515*a^4*nc^4*z5)/256 - 
     (5*a^4*nf*z5)/nc - (5*a^4*nc*nf*z5)/2 - (115*a^4*nc^3*nf*z5)/4 - 
     (65*a^4*xil*z5)/8 + (945*a^4*nc^2*xil*z5)/128 + 
     (4825*a^4*nc^4*xil*z5)/256 - (35*a^4*xil^2*z5)/32 - 
     (115*a^4*nc^2*xil^2*z5)/32 + (345*a^4*nc^4*xil^2*z5)/256 - 
     (165*a^4*nc^2*xil^3*z5)/128 - (25*a^4*nc^4*xil^3*z5)/256 + 
     (5*a^4*xil^4*z5)/64 - (25*a^4*nc^2*xil^4*z5)/256 - 
     (5*a^4*nc^4*xil^4*z5)/64

 
gammaggl4Landau = (35*a*nc)/12 + (449*a^2*nc^2)/48 - (1939*a^4*nc^2)/192 + 
     (75607*a^3*nc^3)/1728 + (29904119*a^4*nc^4)/124416 - (2*a*nf)/3 + 
     (343*a^3*nf)/144 - (23*a^4*nf)/(8*nc^3) + (a^3*nf)/(4*nc^2) + 
     (a^2*nf)/nc - (11803*a^4*nf)/(864*nc) - (47*a^2*nc*nf)/12 + 
     (159695*a^4*nc*nf)/7776 - (12263*a^3*nc^2*nf)/432 - 
     (6494291*a^4*nc^3*nf)/31104 - (18781*a^4*nf^2)/1944 - 
     (623*a^4*nf^2)/(54*nc^2) - (11*a^3*nf^2)/(18*nc) + 
     (259*a^3*nc*nf^2)/108 + (64429*a^4*nc^2*nf^2)/1944 - 
     (77*a^4*nf^3)/(243*nc) + (769*a^4*nc*nf^3)/972 + (3805*a^4*nc^2*z3)/16 - 
     (9*a^3*nc^3*z3)/32 - (14759*a^4*nc^4*z3)/512 + 3*a^3*nf*z3 - 
     (157*a^4*nf*z3)/(36*nc) - (259*a^4*nc*nf*z3)/18 + (3*a^3*nc^2*nf*z3)/2 + 
     (4381*a^4*nc^3*nf*z3)/144 - (109*a^4*nf^2*z3)/9 + 
     (244*a^4*nf^2*z3)/(9*nc^2) + (41*a^4*nc^2*nf^2*z3)/6 - 
     (4*a^4*nc*nf^3*z3)/9 + (99*a^4*nc^4*z4)/64 - (33*a^4*nc*nf*z4)/2 - 
     (273*a^4*nc^3*nf*z4)/32 + 3*a^4*nf^2*z4 + (3*a^4*nc^2*nf^2*z4)/2 + 
     (30555*a^4*nc^2*z5)/256 + (12765*a^4*nc^4*z5)/256 + (15*a^4*nf*z5)/nc - 
     (45*a^4*nc*nf*z5)/2 - (115*a^4*nc^3*nf*z5)/4

 
