
(*
 Moments.m is a Mathematica package which contains the analytical
 results for the polarization functions \Pi^v and \Pi^s as defined in 
 Section 2 of the paper K.G. Chetyrkin, M. Steinhauser: "Heavy-light
 current correlators at order $\alpha_s^2$ in QCD and HQET".
 In the low-energy limit terms up to order z^7 are included for the 
 one- and two-loop expressions and for the scalar three-loop correlator.
 In the vector case the three-loop results are contained up to order z^6.
 In the high-energy region the results are complete up to order 1/z^7.
 The following variables are used
 z   = q^2/M^2, where M is the on-shell quark mass
 api = \alpha_s/\pi
 mu  = \mu
 cf  = (N_c^2-1)/2/Nc
 ca  = N_c
 tr  = 1/2
 nl  = # massless quarks
 nh  = 1 (massive quark)
 More information on the defined functions can be obtained via 
 the Mathematica commands "?PiV*" and "?PiS*".  
 Example: the coefficient of order z^4 contributing to \Pi^{(2),s}_{FA}
 is obtained via: Coefficient[ PiSsma , ca*cf*api^2*z^4 ]
*)

(* ************************************************************ *)

BeginPackage["Moments`"];

PiVsma::usage = "corresponds to \Pi^v for z->0";
PiSsma::usage = "corresponds to \Pi^s for z->0";
PiVlar::usage = "corresponds to \Pi^v for z->infinity";
PiSlar::usage = "corresponds to \Pi^s for z->infinity";

Print["Moments loaded"];

z2 = Zeta[2];
z3 = Zeta[3];
z4 = Zeta[4];
z5 = Zeta[5];
lmm = Log[mu^2/M^2];
S2 = 4/9/Sqrt[3]*Im[PolyLog[2,Exp[I*Pi/3]]];
D3 = 6*Zeta[3]-15/4*Zeta[4]-6*cl2pi3^2;
cl2pi3 = Im[PolyLog[2,Exp[I*Pi/3]]];

  PiVsma := (
(3*(z/2 + (25*api*cf*z)/48 + (147835*api^2*ca*cf*z)/82944 + 
   (649*api^2*cf^2*z)/41472 + (api^2*ca*cf*D3*z)/8 - (api^2*cf^2*D3*z)/4 + 
   (275*api^2*ca*cf*lmm*z)/576 + (735*api^2*ca*cf*S2*z)/128 - 
   (735*api^2*cf^2*S2*z)/64 + (665*api^2*cf*nh*tr*z)/1728 - 
   (25*api^2*cf*lmm*nh*tr*z)/144 - (871*api^2*cf*nl*tr*z)/1728 - 
   (25*api^2*cf*lmm*nl*tr*z)/144 + (417*api^2*cf*nh*S2*tr*z)/16 + 
   (2*z^2)/15 + (5*api*cf*z^2)/18 + (112693*api^2*ca*cf*z^2)/129600 + 
   (15229*api^2*cf^2*z^2)/51840 + (api^2*ca*cf*D3*z^2)/30 - 
   (api^2*cf^2*D3*z^2)/15 + (55*api^2*ca*cf*lmm*z^2)/216 + 
   (6187*api^2*ca*cf*S2*z^2)/1600 - (6187*api^2*cf^2*S2*z^2)/800 + 
   (9661*api^2*cf*nh*tr*z^2)/16200 - (5*api^2*cf*lmm*nh*tr*z^2)/54 - 
   (1373*api^2*cf*nl*tr*z^2)/6480 - (5*api^2*cf*lmm*nl*tr*z^2)/54 + 
   (1719*api^2*cf*nh*S2*tr*z^2)/50 + z^3/18 + (503*api*cf*z^3)/3240 + 
   (11769743*api^2*ca*cf*z^3)/23328000 + (5303639*api^2*cf^2*z^3)/23328000 + 
   (api^2*ca*cf*D3*z^3)/72 - (api^2*cf^2*D3*z^3)/36 + 
   (5533*api^2*ca*cf*lmm*z^3)/38880 + (26869*api^2*ca*cf*S2*z^3)/324000 - 
   (26869*api^2*cf^2*S2*z^3)/162000 + (440741*api^2*cf*nh*tr*z^3)/1166400 - 
   (503*api^2*cf*lmm*nh*tr*z^3)/9720 - (25771*api^2*cf*nl*tr*z^3)/233280 - 
   (503*api^2*cf*lmm*nl*tr*z^3)/9720 + (1400461*api^2*cf*nh*S2*tr*z^3)/
    32400 + z^4/35 + (1199*api*cf*z^4)/12600 + (39697543*api^2*ca*cf*z^4)/
    114307200 + (7315733*api^2*cf^2*z^4)/65318400 + 
   (api^2*ca*cf*D3*z^4)/140 - (api^2*cf^2*D3*z^4)/70 + 
   (13189*api^2*ca*cf*lmm*z^4)/151200 + (31433*api^2*ca*cf*S2*z^4)/70560 - 
   (31433*api^2*cf^2*S2*z^4)/35280 + (52709*api^2*cf*nh*tr*z^4)/4762800 - 
   (1199*api^2*cf*lmm*nh*tr*z^4)/37800 - (43117*api^2*cf*nl*tr*z^4)/680400 - 
   (1199*api^2*cf*lmm*nl*tr*z^4)/37800 + (13738391*api^2*cf*nh*S2*tr*z^4)/
    264600 + z^5/60 + (37883*api*cf*z^5)/604800 + 
   (16737914551*api^2*ca*cf*z^5)/68279500800 + (2245278797*api^2*cf^2*z^5)/
    34139750400 + (api^2*ca*cf*D3*z^5)/240 - (api^2*cf^2*D3*z^5)/120 + 
   (416713*api^2*ca*cf*lmm*z^5)/7257600 - (552604783*api^2*ca*cf*S2*z^5)/
    711244800 + (552604783*api^2*cf^2*S2*z^5)/355622400 - 
   (8545133*api^2*cf*nh*tr*z^5)/20321280 - (37883*api^2*cf*lmm*nh*tr*z^5)/
    1814400 - (112051*api^2*cf*nl*tr*z^5)/2903040 - 
   (37883*api^2*cf*lmm*nl*tr*z^5)/1814400 + (128030963*api^2*cf*nh*S2*tr*z^5)/
    2116800 + (2*z^6)/189 + (23029*api*cf*z^6)/529200 + 
   (10342199087*api^2*ca*cf*z^6)/53331167232 + (23465474813*api^2*cf^2*z^6)/
    1904684544000 + (api^2*ca*cf*D3*z^6)/378 - (api^2*cf^2*D3*z^6)/189 + 
   (253319*api^2*ca*cf*lmm*z^6)/6350400 - (1448186461*api^2*ca*cf*S2*z^6)/
    5290790400 + (1448186461*api^2*cf^2*S2*z^6)/2645395200 - 
   (147478621319*api^2*cf*nh*tr*z^6)/166659897600 - 
   (23029*api^2*cf*lmm*nh*tr*z^6)/1587600 - (718927*api^2*cf*nl*tr*z^6)/
    29393280 - (23029*api^2*cf*lmm*nl*tr*z^6)/1587600 + 
   (15959744567*api^2*cf*nh*S2*tr*z^6)/231472080 + z^7/140 + 
   (222433*api*cf*z^7)/7056000 + (api*cf*z*z2)/2 + 
   (6757*api^2*ca*cf*z*z2)/10368 + (80579*api^2*cf^2*z*z2)/25920 + 
   (11*api^2*ca*cf*lmm*z*z2)/24 + api^2*cf*nh*tr*z*z2 - 
   (api^2*cf*lmm*nh*tr*z*z2)/6 - (125*api^2*cf*nl*tr*z*z2)/216 - 
   (api^2*cf*lmm*nl*tr*z*z2)/6 + (2*api*cf*z^2*z2)/15 + 
   (66997*api^2*ca*cf*z^2*z2)/324000 + (54089*api^2*cf^2*z^2*z2)/40500 + 
   (11*api^2*ca*cf*lmm*z^2*z2)/90 + (8*api^2*cf*nh*tr*z^2*z2)/15 - 
   (2*api^2*cf*lmm*nh*tr*z^2*z2)/45 - (367*api^2*cf*nl*tr*z^2*z2)/1350 - 
   (2*api^2*cf*lmm*nl*tr*z^2*z2)/45 + (api*cf*z^3*z2)/18 + 
   (4573*api^2*ca*cf*z^3*z2)/54000 + (1637813*api^2*cf^2*z^3*z2)/2268000 + 
   (11*api^2*ca*cf*lmm*z^3*z2)/216 + (api^2*cf*nh*tr*z^3*z2)/3 - 
   (api^2*cf*lmm*nh*tr*z^3*z2)/54 - (11*api^2*cf*nl*tr*z^3*z2)/72 - 
   (api^2*cf*lmm*nl*tr*z^3*z2)/54 + (api*cf*z^4*z2)/35 + 
   (144869*api^2*ca*cf*z^4*z2)/3472875 + (455767*api^2*cf^2*z^4*z2)/1029000 + 
   (11*api^2*ca*cf*lmm*z^4*z2)/420 + (8*api^2*cf*nh*tr*z^4*z2)/35 - 
   (api^2*cf*lmm*nh*tr*z^4*z2)/105 - (12857*api^2*cf*nl*tr*z^4*z2)/132300 - 
   (api^2*cf*lmm*nl*tr*z^4*z2)/105 + (api*cf*z^5*z2)/60 + 
   (16650583*api^2*ca*cf*z^5*z2)/711244800 + (523855033*api^2*cf^2*z^5*z2)/
    1778112000 + (11*api^2*ca*cf*lmm*z^5*z2)/720 + 
   (api^2*cf*nh*tr*z^5*z2)/6 - (api^2*cf*lmm*nh*tr*z^5*z2)/180 - 
   (10133*api^2*cf*nl*tr*z^5*z2)/151200 - (api^2*cf*lmm*nl*tr*z^5*z2)/180 + 
   (2*api*cf*z^6*z2)/189 + (69820073*api^2*ca*cf*z^6*z2)/4800902400 + 
   (82974271*api^2*cf^2*z^6*z2)/400075200 + (11*api^2*ca*cf*lmm*z^6*z2)/
    1134 + (8*api^2*cf*nh*tr*z^6*z2)/63 - (2*api^2*cf*lmm*nh*tr*z^6*z2)/567 - 
   (34933*api^2*cf*nl*tr*z^6*z2)/714420 - (2*api^2*cf*lmm*nl*tr*z^6*z2)/567 + 
   (api*cf*z^7*z2)/140 + (api^2*cf^2*z*z2^2)/2 + (2*api^2*cf^2*z^2*z2^2)/15 + 
   (api^2*cf^2*z^3*z2^2)/18 + (api^2*cf^2*z^4*z2^2)/35 + 
   (api^2*cf^2*z^5*z2^2)/60 + (2*api^2*cf^2*z^6*z2^2)/189 - 
   (1741*api^2*ca*cf*z*z3)/864 + (395*api^2*cf^2*z*z3)/144 - 
   (194*api^2*cf*nh*tr*z*z3)/27 + (api^2*cf*nl*tr*z*z3)/3 - 
   (3251*api^2*ca*cf*z^2*z3)/2700 + (5341*api^2*cf^2*z^2*z3)/2700 - 
   (1168*api^2*cf*nh*tr*z^2*z3)/135 + (4*api^2*cf*nl*tr*z^2*z3)/45 - 
   (307*api^2*ca*cf*z^3*z3)/1200 + (859*api^2*cf^2*z^3*z3)/2700 - 
   (4102*api^2*cf*nh*tr*z^3*z3)/405 + (api^2*cf*nl*tr*z^3*z3)/27 - 
   (57599*api^2*ca*cf*z^4*z3)/198450 + (189263*api^2*cf^2*z^4*z3)/396900 - 
   (3644*api^2*cf*nh*tr*z^4*z3)/315 + (2*api^2*cf*nl*tr*z^4*z3)/105 + 
   (8483*api^2*ca*cf*z^5*z3)/604800 - (7625*api^2*cf^2*z^5*z3)/84672 - 
   (1363*api^2*cf*nh*tr*z^5*z3)/105 + (api^2*cf*nl*tr*z^5*z3)/90 - 
   (1511*api^2*ca*cf*z^6*z3)/19440 + (36641*api^2*cf^2*z^6*z3)/317520 - 
   (24452*api^2*cf*nh*tr*z^6*z3)/1701 + (4*api^2*cf*nl*tr*z^6*z3)/567 - 
   (3*api^2*ca*cf*z*z4)/8 - (5*api^2*cf^2*z*z4)/2 - (api^2*ca*cf*z^2*z4)/10 - 
   (2*api^2*cf^2*z^2*z4)/3 - (api^2*ca*cf*z^3*z4)/24 - 
   (5*api^2*cf^2*z^3*z4)/18 - (3*api^2*ca*cf*z^4*z4)/140 - 
   (api^2*cf^2*z^4*z4)/7 - (api^2*ca*cf*z^5*z4)/80 - (api^2*cf^2*z^5*z4)/12 - 
   (api^2*ca*cf*z^6*z4)/126 - (10*api^2*cf^2*z^6*z4)/189 + 
   (3*api^2*ca*cf*z*z2*Log[2])/2 - 3*api^2*cf^2*z*z2*Log[2] + 
   (4*api^2*ca*cf*z^2*z2*Log[2])/5 - (8*api^2*cf^2*z^2*z2*Log[2])/5 + 
   (api^2*ca*cf*z^3*z2*Log[2])/2 - api^2*cf^2*z^3*z2*Log[2] + 
   (12*api^2*ca*cf*z^4*z2*Log[2])/35 - (24*api^2*cf^2*z^4*z2*Log[2])/35 + 
   (api^2*ca*cf*z^5*z2*Log[2])/4 - (api^2*cf^2*z^5*z2*Log[2])/2 + 
   (4*api^2*ca*cf*z^6*z2*Log[2])/21 - (8*api^2*cf^2*z^6*z2*Log[2])/21))/
 (16*Pi^2)
	     );

  PiSsma := (
(3*((2*z)/3 + (api*cf*z)/12 + (175*api^2*ca*cf*z)/1728 + 
   (103*api^2*cf^2*z)/384 + (33*api^2*cf*nh*tr*z)/16 - 
   (5*api^2*cf*nl*tr*z)/48 + z^2/6 + (19*api*cf*z^2)/48 + 
   (953*api^2*ca*cf*z^2)/1024 + (23477*api^2*cf^2*z^2)/69120 + 
   (2101*api^2*cf*nh*tr*z^2)/2880 - (143*api^2*cf*nl*tr*z^2)/576 + z^3/15 + 
   (17*api*cf*z^3)/72 + (33307*api^2*ca*cf*z^3)/64800 + 
   (65329*api^2*cf^2*z^3)/103680 + (7837*api^2*cf*nh*tr*z^3)/64800 - 
   (2083*api^2*cf*nl*tr*z^3)/12960 + z^4/30 + (31*api*cf*z^4)/216 + 
   (3961231*api^2*ca*cf*z^4)/10886400 + (4524487*api^2*cf^2*z^4)/10886400 - 
   (1179673*api^2*cf*nh*tr*z^4)/2721600 - (7759*api^2*cf*nl*tr*z^4)/77760 + 
   (2*z^5)/105 + (7001*api*cf*z^5)/75600 + (31355501*api^2*ca*cf*z^5)/
    152409600 + (33815837*api^2*cf^2*z^5)/87091200 - 
   (37456457*api^2*cf*nh*tr*z^5)/38102400 - (346519*api^2*cf*nl*tr*z^5)/
    5443200 + z^6/84 + (38113*api*cf*z^6)/604800 + 
   (4739201353*api^2*ca*cf*z^6)/29262643200 + (3685964659*api^2*cf^2*z^6)/
    14631321600 - (4201269473*api^2*cf*nh*tr*z^6)/2743372800 - 
   (608813*api^2*cf*nl*tr*z^6)/14515200 + z^7/126 + 
   (18961*api*cf*z^7)/423360 + (108189401963*api^2*ca*cf*z^7)/1111065984000 + 
   (10307800934177*api^2*cf^2*z^7)/44442639360000 - 
   (1154471458391*api^2*cf*nh*tr*z^7)/555532992000 - 
   (27828673*api^2*cf*nl*tr*z^7)/979776000 + (2*api*cf*z*z2)/3 + 
   (277*api^2*ca*cf*z*z2)/216 + (121*api^2*cf^2*z*z2)/144 - 
   (api^2*cf*nl*tr*z*z2)/6 + (api*cf*z^2*z2)/6 + (1723*api^2*ca*cf*z^2*z2)/
    5760 + (59623*api^2*cf^2*z^2*z2)/43200 + (api^2*cf*nh*tr*z^2*z2)/3 - 
   (73*api^2*cf*nl*tr*z^2*z2)/360 + (api*cf*z^3*z2)/15 + 
   (1153*api^2*ca*cf*z^3*z2)/12000 + (92717*api^2*cf^2*z^3*z2)/108000 + 
   (4*api^2*cf*nh*tr*z^3*z2)/15 - (119*api^2*cf*nl*tr*z^3*z2)/900 + 
   (api*cf*z^4*z2)/30 + (313*api^2*ca*cf*z^4*z2)/8400 + 
   (2892733*api^2*cf^2*z^4*z2)/5292000 + (api^2*cf*nh*tr*z^4*z2)/5 - 
   (1123*api^2*cf*nl*tr*z^4*z2)/12600 + (2*api*cf*z^5*z2)/105 + 
   (243241*api^2*ca*cf*z^5*z2)/14817600 + (27193603*api^2*cf^2*z^5*z2)/
    74088000 + (16*api^2*cf*nh*tr*z^5*z2)/105 - (2791*api^2*cf*nl*tr*z^5*z2)/
    44100 + (api*cf*z^6*z2)/84 + (272033*api^2*ca*cf*z^6*z2)/33868800 + 
   (91843391*api^2*cf^2*z^6*z2)/355622400 + (5*api^2*cf*nh*tr*z^6*z2)/42 - 
   (9941*api^2*cf*nl*tr*z^6*z2)/211680 + (api*cf*z^7*z2)/126 + 
   (28543*api^2*ca*cf*z^7*z2)/6531840 + (100704841*api^2*cf^2*z^7*z2)/
    533433600 + (2*api^2*cf*nh*tr*z^7*z2)/21 - (34387*api^2*cf*nl*tr*z^7*z2)/
    952560 - (9*api^2*ca*cf*z*z4)/8 - (5*api^2*cf^2*z*z4)/12 - 
   (9*api^2*ca*cf*z^2*z4)/32 - (5*api^2*cf^2*z^2*z4)/48 - 
   (9*api^2*ca*cf*z^3*z4)/80 - (api^2*cf^2*z^3*z4)/24 - 
   (9*api^2*ca*cf*z^4*z4)/160 - (api^2*cf^2*z^4*z4)/48 - 
   (9*api^2*ca*cf*z^5*z4)/280 - (api^2*cf^2*z^5*z4)/84 - 
   (9*api^2*ca*cf*z^6*z4)/448 - (5*api^2*cf^2*z^6*z4)/672 - 
   (3*api^2*ca*cf*z^7*z4)/224 - (5*api^2*cf^2*z^7*z4)/1008 - 
   (7*Sqrt[3]*api^2*ca*cf*z*Im[PolyLog[2, E^((I/3)*Pi)]])/4 + 
   (7*Sqrt[3]*api^2*cf^2*z*Im[PolyLog[2, E^((I/3)*Pi)]])/2 + 
   7*Sqrt[3]*api^2*cf*nh*tr*z*Im[PolyLog[2, E^((I/3)*Pi)]] + 
   (283*Sqrt[3]*api^2*ca*cf*z^2*Im[PolyLog[2, E^((I/3)*Pi)]])/160 - 
   (283*Sqrt[3]*api^2*cf^2*z^2*Im[PolyLog[2, E^((I/3)*Pi)]])/80 + 
   (479*api^2*cf*nh*tr*z^2*Im[PolyLog[2, E^((I/3)*Pi)]])/(20*Sqrt[3]) - 
   (1049*api^2*ca*cf*z^3*Im[PolyLog[2, E^((I/3)*Pi)]])/(3600*Sqrt[3]) + 
   (1049*api^2*cf^2*z^3*Im[PolyLog[2, E^((I/3)*Pi)]])/(1800*Sqrt[3]) + 
   (12473*api^2*cf*nh*tr*z^3*Im[PolyLog[2, E^((I/3)*Pi)]])/(450*Sqrt[3]) + 
   (324853*api^2*ca*cf*z^4*Im[PolyLog[2, E^((I/3)*Pi)]])/(170100*Sqrt[3]) - 
   (324853*api^2*cf^2*z^4*Im[PolyLog[2, E^((I/3)*Pi)]])/(85050*Sqrt[3]) + 
   (5363167*api^2*cf*nh*tr*z^4*Im[PolyLog[2, E^((I/3)*Pi)]])/
    (170100*Sqrt[3]) - (442717*api^2*ca*cf*z^5*Im[PolyLog[2, E^((I/3)*Pi)]])/
    (3175200*Sqrt[3]) + (442717*api^2*cf^2*z^5*Im[PolyLog[2, E^((I/3)*Pi)]])/
    (1587600*Sqrt[3]) + (21024149*api^2*cf*nh*tr*z^5*
     Im[PolyLog[2, E^((I/3)*Pi)]])/(595350*Sqrt[3]) + 
   (219606437*api^2*ca*cf*z^6*Im[PolyLog[2, E^((I/3)*Pi)]])/
    (228614400*Sqrt[3]) - (219606437*api^2*cf^2*z^6*
     Im[PolyLog[2, E^((I/3)*Pi)]])/(114307200*Sqrt[3]) + 
   (334931357*api^2*cf*nh*tr*z^6*Im[PolyLog[2, E^((I/3)*Pi)]])/
    (8573040*Sqrt[3]) - (2861558023*api^2*ca*cf*z^7*
     Im[PolyLog[2, E^((I/3)*Pi)]])/(27776649600*Sqrt[3]) + 
   (2861558023*api^2*cf^2*z^7*Im[PolyLog[2, E^((I/3)*Pi)]])/
    (13888324800*Sqrt[3]) + (14859593107*api^2*cf*nh*tr*z^7*
     Im[PolyLog[2, E^((I/3)*Pi)]])/(347208120*Sqrt[3]) - 
   api^2*ca*cf*z*Im[PolyLog[2, E^((I/3)*Pi)]]^2 + 
   2*api^2*cf^2*z*Im[PolyLog[2, E^((I/3)*Pi)]]^2 - 
   (api^2*ca*cf*z^2*Im[PolyLog[2, E^((I/3)*Pi)]]^2)/4 + 
   (api^2*cf^2*z^2*Im[PolyLog[2, E^((I/3)*Pi)]]^2)/2 - 
   (api^2*ca*cf*z^3*Im[PolyLog[2, E^((I/3)*Pi)]]^2)/10 + 
   (api^2*cf^2*z^3*Im[PolyLog[2, E^((I/3)*Pi)]]^2)/5 - 
   (api^2*ca*cf*z^4*Im[PolyLog[2, E^((I/3)*Pi)]]^2)/20 + 
   (api^2*cf^2*z^4*Im[PolyLog[2, E^((I/3)*Pi)]]^2)/10 - 
   (api^2*ca*cf*z^5*Im[PolyLog[2, E^((I/3)*Pi)]]^2)/35 + 
   (2*api^2*cf^2*z^5*Im[PolyLog[2, E^((I/3)*Pi)]]^2)/35 - 
   (api^2*ca*cf*z^6*Im[PolyLog[2, E^((I/3)*Pi)]]^2)/56 + 
   (api^2*cf^2*z^6*Im[PolyLog[2, E^((I/3)*Pi)]]^2)/28 - 
   (api^2*ca*cf*z^7*Im[PolyLog[2, E^((I/3)*Pi)]]^2)/84 + 
   (api^2*cf^2*z^7*Im[PolyLog[2, E^((I/3)*Pi)]]^2)/42 + 
   (api^2*ca*cf*z^2*z2*Log[2])/2 - api^2*cf^2*z^2*z2*Log[2] + 
   (2*api^2*ca*cf*z^3*z2*Log[2])/5 - (4*api^2*cf^2*z^3*z2*Log[2])/5 + 
   (3*api^2*ca*cf*z^4*z2*Log[2])/10 - (3*api^2*cf^2*z^4*z2*Log[2])/5 + 
   (8*api^2*ca*cf*z^5*z2*Log[2])/35 - (16*api^2*cf^2*z^5*z2*Log[2])/35 + 
   (5*api^2*ca*cf*z^6*z2*Log[2])/28 - (5*api^2*cf^2*z^6*z2*Log[2])/14 + 
   (api^2*ca*cf*z^7*z2*Log[2])/7 - (2*api^2*cf^2*z^7*z2*Log[2])/7 + 
   (8*api^2*ca*cf*z*Zeta[3])/3 - (85*api^2*cf^2*z*Zeta[3])/12 - 
   (104*api^2*cf*nh*tr*z*Zeta[3])/9 + (4*api^2*cf*nl*tr*z*Zeta[3])/9 - 
   (3857*api^2*ca*cf*z^2*Zeta[3])/1440 + (3461*api^2*cf^2*z^2*Zeta[3])/720 - 
   (38*api^2*cf*nh*tr*z^2*Zeta[3])/3 + (api^2*cf*nl*tr*z^2*Zeta[3])/9 + 
   (31*api^2*ca*cf*z^3*Zeta[3])/225 - (923*api^2*cf^2*z^3*Zeta[3])/1800 - 
   (628*api^2*cf*nh*tr*z^3*Zeta[3])/45 + (2*api^2*cf*nl*tr*z^3*Zeta[3])/45 - 
   (24761*api^2*ca*cf*z^4*Zeta[3])/25200 + (967*api^2*cf^2*z^4*Zeta[3])/525 - 
   (2062*api^2*cf*nh*tr*z^4*Zeta[3])/135 + (api^2*cf*nl*tr*z^4*Zeta[3])/45 + 
   (359*api^2*ca*cf*z^5*Zeta[3])/7350 - (599*api^2*cf^2*z^5*Zeta[3])/3528 - 
   (15688*api^2*cf*nh*tr*z^5*Zeta[3])/945 + (4*api^2*cf*nl*tr*z^5*Zeta[3])/
    315 - (143663*api^2*ca*cf*z^6*Zeta[3])/282240 + 
   (137203*api^2*cf^2*z^6*Zeta[3])/141120 - (3389*api^2*cf*nh*tr*z^6*Zeta[3])/
    189 + (api^2*cf*nl*tr*z^6*Zeta[3])/126 + (4439*api^2*ca*cf*z^7*Zeta[3])/
    158760 - (18371*api^2*cf^2*z^7*Zeta[3])/211680 - 
   (10922*api^2*cf*nh*tr*z^7*Zeta[3])/567 + (api^2*cf*nl*tr*z^7*Zeta[3])/
    189))/(16*Pi^2)
    );

  PiVlar := (
(3*(16/9 + (25*api*cf)/18 + (18433*api^2*ca*cf)/2592 + (71*api^2*cf^2)/576 - 
   (1141*api^2*cf*nh*tr)/216 - (589*api^2*cf*nl*tr)/216 + 1/(42*z^7) + 
   (322099*api*cf)/(7408800*z^7) - (104055061483*api^2*ca*cf)/
    (2286144000*z^7) + (44535682588013*api^2*cf^2)/(490092120000*z^7) - 
   (912529125371*api^2*cf*nh*tr)/(11668860000*z^7) + 
   (245309459*api^2*cf*nl*tr)/(2333772000*z^7) + 2/(45*z^6) + 
   (3833*api*cf)/(81000*z^6) - (120018929*api^2*ca*cf)/(9720000*z^6) + 
   (700685473*api^2*cf^2)/(29160000*z^6) - (337954307*api^2*cf*nh*tr)/
    (14580000*z^6) + (3236209*api^2*cf*nl*tr)/(14580000*z^6) + 1/(10*z^5) - 
   (1747*api*cf)/(36000*z^5) - (69281173*api^2*ca*cf)/(14580000*z^5) + 
   (804239879*api^2*cf^2)/(116640000*z^5) - (3922271*api^2*cf*nh*tr)/
    (1215000*z^5) + (233149*api^2*cf*nl*tr)/(405000*z^5) + 1/(3*z^4) - 
   (31*api*cf)/(16*z^4) + (1658717*api^2*ca*cf)/(186624*z^4) - 
   (1760405*api^2*cf^2)/(93312*z^4) - (3191*api^2*cf*nh*tr)/(7776*z^4) + 
   (15455*api^2*cf*nl*tr)/(7776*z^4) - 5/(9*z^3) + (28*api*cf)/(27*z^3) + 
   (108761*api^2*ca*cf)/(23328*z^3) - (16883*api^2*cf^2)/(2916*z^3) + 
   (2129*api^2*cf*nh*tr)/(5832*z^3) - (11491*api^2*cf*nl*tr)/(5832*z^3) - 
   2/z^2 + (2*api*cf)/z^2 + (1561*api^2*ca*cf)/(144*z^2) - 
   (31*api^2*cf^2)/(24*z^2) - (551*api^2*cf*nh*tr)/(36*z^2) - 
   (131*api^2*cf*nl*tr)/(36*z^2) + z^(-1) - (23*api*cf)/(4*z) - 
   (4015*api^2*ca*cf)/(288*z) + (3859*api^2*cf^2)/(288*z) - 
   (95*api^2*cf*nh*tr)/(9*z) + (89*api^2*cf*nl*tr)/(18*z) + (4*api*cf*z2)/9 + 
   (1985*api^2*ca*cf*z2)/648 - (713*api^2*cf^2*z2)/216 - 
   (8*api^2*cf*nh*tr*z2)/3 + (2*api^2*cf*nl*tr*z2)/9 + 
   (api^2*ca*cf*z2)/(6*z^7) - (5*api^2*cf^2*z2)/(8*z^7) - 
   (api^2*cf*nh*tr*z2)/(3*z^7) + (api^2*cf*nl*tr*z2)/(6*z^7) + 
   (4*api^2*ca*cf*z2)/(15*z^6) - (api^2*cf^2*z2)/z^6 - 
   (8*api^2*cf*nh*tr*z2)/(15*z^6) + (4*api^2*cf*nl*tr*z2)/(15*z^6) + 
   (api^2*ca*cf*z2)/(2*z^5) - (15*api^2*cf^2*z2)/(8*z^5) - 
   (api^2*cf*nh*tr*z2)/z^5 + (api^2*cf*nl*tr*z2)/(2*z^5) + 
   (4*api^2*ca*cf*z2)/(3*z^4) - (5*api^2*cf^2*z2)/z^4 - 
   (8*api^2*cf*nh*tr*z2)/(3*z^4) + (4*api^2*cf*nl*tr*z2)/(3*z^4) - 
   (api^2*ca*cf*z2)/z^3 + (15*api^2*cf^2*z2)/(4*z^3) + 
   (2*api^2*cf*nh*tr*z2)/z^3 - (api^2*cf*nl*tr*z2)/z^3 - 
   (4*api^2*ca*cf*z2)/z^2 + (15*api^2*cf^2*z2)/z^2 + 
   (8*api^2*cf*nh*tr*z2)/z^2 - (4*api^2*cf*nl*tr*z2)/z^2 - (api*cf*z2)/z - 
   (97*api^2*ca*cf*z2)/(24*z) + (155*api^2*cf^2*z2)/(72*z) + 
   (2*api^2*cf*nh*tr*z2)/z + (api^2*cf*nl*tr*z2)/(6*z) - 
   (41*api^2*ca*cf*z4)/6 + (107*api^2*cf^2*z4)/9 - 
   (25*api^2*ca*cf*z4)/(6*z^3) + (25*api^2*cf^2*z4)/(3*z^3) + 
   (427*api^2*ca*cf*z4)/(32*z) - (363*api^2*cf^2*z4)/(16*z) - 
   (11*api^2*ca*cf*Im[PolyLog[2, E^((I/3)*Pi)]])/(4*Sqrt[3]) + 
   (11*api^2*cf^2*Im[PolyLog[2, E^((I/3)*Pi)]])/(2*Sqrt[3]) - 
   (16*api^2*cf*nh*tr*Im[PolyLog[2, E^((I/3)*Pi)]])/Sqrt[3] + 
   (39*Sqrt[3]*api^2*ca*cf*Im[PolyLog[2, E^((I/3)*Pi)]])/(8*z) - 
   (39*Sqrt[3]*api^2*cf^2*Im[PolyLog[2, E^((I/3)*Pi)]])/(4*z) + 
   (9*Sqrt[3]*api^2*cf*nh*tr*Im[PolyLog[2, E^((I/3)*Pi)]])/z + 
   (4*api^2*ca*cf*Im[PolyLog[2, E^((I/3)*Pi)]]^2)/3 - 
   (8*api^2*cf^2*Im[PolyLog[2, E^((I/3)*Pi)]]^2)/3 + 
   (3*api^2*ca*cf*Im[PolyLog[2, E^((I/3)*Pi)]]^2)/(4*z) - 
   (3*api^2*cf^2*Im[PolyLog[2, E^((I/3)*Pi)]]^2)/(2*z) - 
   4*api^2*ca*cf*z2*Log[2] + 8*api^2*cf^2*z2*Log[2] - 
   (api^2*ca*cf*z2*Log[2])/(2*z^7) + (api^2*cf^2*z2*Log[2])/z^7 - 
   (4*api^2*ca*cf*z2*Log[2])/(5*z^6) + (8*api^2*cf^2*z2*Log[2])/(5*z^6) - 
   (3*api^2*ca*cf*z2*Log[2])/(2*z^5) + (3*api^2*cf^2*z2*Log[2])/z^5 - 
   (4*api^2*ca*cf*z2*Log[2])/z^4 + (8*api^2*cf^2*z2*Log[2])/z^4 + 
   (3*api^2*ca*cf*z2*Log[2])/z^3 - (6*api^2*cf^2*z2*Log[2])/z^3 + 
   (12*api^2*ca*cf*z2*Log[2])/z^2 - (24*api^2*cf^2*z2*Log[2])/z^2 + 
   (3*api^2*ca*cf*z2*Log[2])/z - (6*api^2*cf^2*z2*Log[2])/z - 
   (8*api^2*ca*cf*z2*Log[2]^2)/3 + (16*api^2*cf^2*z2*Log[2]^2)/3 - 
   (4*api^2*ca*cf*z2*Log[2]^2)/(3*z^3) + (8*api^2*cf^2*z2*Log[2]^2)/(3*z^3) + 
   (4*api^2*ca*cf*z2*Log[2]^2)/z - (8*api^2*cf^2*z2*Log[2]^2)/z + 
   (4*api^2*ca*cf*Log[2]^4)/9 - (8*api^2*cf^2*Log[2]^4)/9 + 
   (2*api^2*ca*cf*Log[2]^4)/(9*z^3) - (4*api^2*cf^2*Log[2]^4)/(9*z^3) - 
   (2*api^2*ca*cf*Log[2]^4)/(3*z) + (4*api^2*cf^2*Log[2]^4)/(3*z) - 
   (4*Log[-z])/3 - api*cf*Log[-z] - (41*api^2*ca*cf*Log[-z])/8 + 
   (api^2*cf^2*Log[-z])/8 + (11*api^2*cf*nh*tr*Log[-z])/6 + 
   (11*api^2*cf*nl*tr*Log[-z])/6 - (148*api*cf*Log[-z])/(2205*z^7) - 
   (11463009101*api^2*ca*cf*Log[-z])/(740880000*z^7) + 
   (7266775483*api^2*cf^2*Log[-z])/(243101250*z^7) - 
   (1750009337*api^2*cf*nh*tr*Log[-z])/(37044000*z^7) + 
   (3920897*api^2*cf*nl*tr*Log[-z])/(22226400*z^7) - 
   (7*api*cf*Log[-z])/(50*z^6) + (13535191*api^2*ca*cf*Log[-z])/
    (4860000*z^6) - (36020231*api^2*cf^2*Log[-z])/(4860000*z^6) - 
   (824581*api^2*cf*nh*tr*Log[-z])/(243000*z^6) + 
   (19067*api^2*cf*nl*tr*Log[-z])/(60750*z^6) - 
   (28*api*cf*Log[-z])/(75*z^5) + (10253071*api^2*ca*cf*Log[-z])/
    (3888000*z^5) - (27867253*api^2*cf^2*Log[-z])/(3240000*z^5) + 
   (136549*api^2*cf*nh*tr*Log[-z])/(108000*z^5) + 
   (199679*api^2*cf*nl*tr*Log[-z])/(324000*z^5) - 
   (31*api*cf*Log[-z])/(18*z^4) + (11267*api^2*ca*cf*Log[-z])/(7776*z^4) - 
   (757*api^2*cf^2*Log[-z])/(1944*z^4) - (1177*api^2*cf*nh*tr*Log[-z])/
    (432*z^4) + (1625*api^2*cf*nl*tr*Log[-z])/(1296*z^4) - 
   (2*Log[-z])/(3*z^3) + (52*api*cf*Log[-z])/(27*z^3) + 
   (22153*api^2*ca*cf*Log[-z])/(3888*z^3) - (4337*api^2*cf^2*Log[-z])/
    (648*z^3) - (1111*api^2*cf*nh*tr*Log[-z])/(972*z^3) - 
   (2183*api^2*cf*nl*tr*Log[-z])/(972*z^3) + (3*api*cf*Log[-z])/z^2 + 
   (91*api^2*ca*cf*Log[-z])/(12*z^2) - (21*api^2*cf^2*Log[-z])/(8*z^2) - 
   (34*api^2*cf*nh*tr*Log[-z])/(3*z^2) - (8*api^2*cf*nl*tr*Log[-z])/(3*z^2) + 
   (2*Log[-z])/z - (3*api*cf*Log[-z])/(2*z) + (11*api^2*ca*cf*Log[-z])/
    (6*z) + (121*api^2*cf^2*Log[-z])/(16*z) + (11*api^2*cf*nh*tr*Log[-z])/
    (6*z) - (7*api^2*cf*nl*tr*Log[-z])/(6*z) - (2*api^2*ca*cf*z2*Log[-z])/
    z^3 + (15*api^2*cf^2*z2*Log[-z])/(2*z^3) + (4*api^2*cf*nh*tr*z2*Log[-z])/
    z^3 - (2*api^2*cf*nl*tr*z2*Log[-z])/z^3 + (2*api^2*ca*cf*z2*Log[-z])/z - 
   (15*api^2*cf^2*z2*Log[-z])/(2*z) - (4*api^2*cf*nh*tr*z2*Log[-z])/z + 
   (2*api^2*cf*nl*tr*z2*Log[-z])/z + (6*api^2*ca*cf*z2*Log[2]*Log[-z])/z^3 - 
   (12*api^2*cf^2*z2*Log[2]*Log[-z])/z^3 - (6*api^2*ca*cf*z2*Log[2]*Log[-z])/
    z + (12*api^2*cf^2*z2*Log[2]*Log[-z])/z + (11*api^2*ca*cf*Log[-z]^2)/24 - 
   (api^2*cf*nh*tr*Log[-z]^2)/6 - (api^2*cf*nl*tr*Log[-z]^2)/6 - 
   (api*cf*Log[-z]^2)/(84*z^7) + (2877743137*api^2*ca*cf*Log[-z]^2)/
    (127008000*z^7) - (20158677919*api^2*cf^2*Log[-z]^2)/(444528000*z^7) + 
   (2488393*api^2*cf*nh*tr*Log[-z]^2)/(58800*z^7) + 
   (247*api^2*cf*nl*tr*Log[-z]^2)/(7056*z^7) - (api*cf*Log[-z]^2)/(45*z^6) + 
   (40111*api^2*ca*cf*Log[-z]^2)/(5400*z^6) - (4796371*api^2*cf^2*Log[-z]^2)/
    (324000*z^6) + (2939*api^2*cf*nh*tr*Log[-z]^2)/(225*z^6) + 
   (41*api^2*cf*nl*tr*Log[-z]^2)/(900*z^6) - (api*cf*Log[-z]^2)/(20*z^5) + 
   (43999*api^2*ca*cf*Log[-z]^2)/(25920*z^5) - (617069*api^2*cf^2*Log[-z]^2)/
    (216000*z^5) + (6679*api^2*cf*nh*tr*Log[-z]^2)/(3600*z^5) + 
   (497*api^2*cf*nl*tr*Log[-z]^2)/(10800*z^5) - (api*cf*Log[-z]^2)/(6*z^4) - 
   (1789*api^2*ca*cf*Log[-z]^2)/(1296*z^4) + (19855*api^2*cf^2*Log[-z]^2)/
    (2592*z^4) - (31*api^2*cf*nh*tr*Log[-z]^2)/(24*z^4) - 
   (23*api^2*cf*nl*tr*Log[-z]^2)/(216*z^4) + (10*api*cf*Log[-z]^2)/(9*z^3) + 
   (3409*api^2*ca*cf*Log[-z]^2)/(1296*z^3) - (85*api^2*cf^2*Log[-z]^2)/
    (24*z^3) + (173*api^2*cf*nh*tr*Log[-z]^2)/(108*z^3) - 
   (299*api^2*cf*nl*tr*Log[-z]^2)/(324*z^3) - (9*api^2*cf^2*Log[-z]^2)/
    (2*z^2) - (api^2*cf*nh*tr*Log[-z]^2)/z^2 - (3*api*cf*Log[-z]^2)/(2*z) - 
   (19*api^2*ca*cf*Log[-z]^2)/(6*z) + (15*api^2*cf^2*Log[-z]^2)/(16*z) + 
   (5*api^2*cf*nh*tr*Log[-z]^2)/(6*z) + (5*api^2*cf*nl*tr*Log[-z]^2)/(6*z) - 
   (1072571*api^2*ca*cf*Log[-z]^3)/(453600*z^7) + 
   (3780751*api^2*cf^2*Log[-z]^3)/(793800*z^7) - 
   (1033*api^2*cf*nh*tr*Log[-z]^3)/(315*z^7) - (api^2*cf*nl*tr*Log[-z]^3)/
    (378*z^7) - (2767*api^2*ca*cf*Log[-z]^3)/(1800*z^6) + 
   (25433*api^2*cf^2*Log[-z]^3)/(8100*z^6) - (1024*api^2*cf*nh*tr*Log[-z]^3)/
    (405*z^6) - (2*api^2*cf*nl*tr*Log[-z]^3)/(405*z^6) - 
   (331*api^2*ca*cf*Log[-z]^3)/(360*z^5) + (64663*api^2*cf^2*Log[-z]^3)/
    (32400*z^5) - (233*api^2*cf*nh*tr*Log[-z]^3)/(135*z^5) - 
   (api^2*cf*nl*tr*Log[-z]^3)/(90*z^5) - (491*api^2*ca*cf*Log[-z]^3)/
    (648*z^4) + (1345*api^2*cf^2*Log[-z]^3)/(648*z^4) - 
   (22*api^2*cf*nh*tr*Log[-z]^3)/(27*z^4) - (api^2*cf*nl*tr*Log[-z]^3)/
    (27*z^4) - (143*api^2*ca*cf*Log[-z]^3)/(648*z^3) - 
   (445*api^2*cf^2*Log[-z]^3)/(324*z^3) + (5*api^2*cf*nh*tr*Log[-z]^3)/
    (18*z^3) + (13*api^2*cf*nl*tr*Log[-z]^3)/(162*z^3) + 
   (11*api^2*ca*cf*Log[-z]^3)/(24*z) + (3*api^2*cf^2*Log[-z]^3)/(4*z) - 
   (api^2*cf*nh*tr*Log[-z]^3)/(6*z) - (api^2*cf*nl*tr*Log[-z]^3)/(6*z) + 
   (32*api^2*ca*cf*PolyLog[4, 1/2])/3 - (64*api^2*cf^2*PolyLog[4, 1/2])/3 + 
   (16*api^2*ca*cf*PolyLog[4, 1/2])/(3*z^3) - (32*api^2*cf^2*PolyLog[4, 1/2])/
    (3*z^3) - (16*api^2*ca*cf*PolyLog[4, 1/2])/z + 
   (32*api^2*cf^2*PolyLog[4, 1/2])/z - 4*api*cf*Zeta[3] - 
   (17*api^2*ca*cf*Zeta[3])/2 - (158*api^2*cf^2*Zeta[3])/9 + 
   (410*api^2*cf*nh*tr*Zeta[3])/27 + (122*api^2*cf*nl*tr*Zeta[3])/27 - 
   (2742577*api^2*ca*cf*Zeta[3])/(352800*z^7) + (2673157*api^2*cf^2*Zeta[3])/
    (176400*z^7) - (5078*api^2*cf*nh*tr*Zeta[3])/(315*z^7) + 
   (api^2*cf*nl*tr*Zeta[3])/(21*z^7) - (5837*api^2*ca*cf*Zeta[3])/(900*z^6) + 
   (10987*api^2*cf^2*Zeta[3])/(900*z^6) - (1568*api^2*cf*nh*tr*Zeta[3])/
    (135*z^6) + (4*api^2*cf*nl*tr*Zeta[3])/(45*z^6) - 
   (20327*api^2*ca*cf*Zeta[3])/(10800*z^5) + (1306*api^2*cf^2*Zeta[3])/
    (675*z^5) - (34*api^2*cf*nh*tr*Zeta[3])/(5*z^5) + 
   (api^2*cf*nl*tr*Zeta[3])/(5*z^5) - (80*api^2*ca*cf*Zeta[3])/(9*z^4) + 
   (373*api^2*cf^2*Zeta[3])/(36*z^4) - (4*api^2*cf*nh*tr*Zeta[3])/(3*z^4) + 
   (2*api^2*cf*nl*tr*Zeta[3])/(3*z^4) - (2*api*cf*Zeta[3])/z^3 + 
   (293*api^2*ca*cf*Zeta[3])/(72*z^3) - (47*api^2*cf^2*Zeta[3])/(6*z^3) - 
   (32*api^2*cf*nh*tr*Zeta[3])/(27*z^3) + (2*api^2*cf*nl*tr*Zeta[3])/z^3 + 
   (52*api^2*ca*cf*Zeta[3])/(3*z^2) + (68*api^2*cf^2*Zeta[3])/(3*z^2) + 
   (22*api^2*cf*nh*tr*Zeta[3])/(3*z^2) - (2*api^2*cf*nl*tr*Zeta[3])/(3*z^2) + 
   (6*api*cf*Zeta[3])/z + (12*api^2*ca*cf*Zeta[3])/z + 
   (491*api^2*cf^2*Zeta[3])/(12*z) - (20*api^2*cf*nh*tr*Zeta[3])/(3*z) - 
   (22*api^2*cf*nl*tr*Zeta[3])/(3*z) + (11*api^2*ca*cf*Log[-z]*Zeta[3])/3 - 
   (4*api^2*cf*nh*tr*Log[-z]*Zeta[3])/3 - (4*api^2*cf*nl*tr*Log[-z]*Zeta[3])/
    3 - (api^2*ca*cf*Log[-z]*Zeta[3])/(14*z^7) + (api^2*cf^2*Log[-z]*Zeta[3])/
    (14*z^7) - (2*api^2*ca*cf*Log[-z]*Zeta[3])/(15*z^6) + 
   (2*api^2*cf^2*Log[-z]*Zeta[3])/(15*z^6) - (3*api^2*ca*cf*Log[-z]*Zeta[3])/
    (10*z^5) + (3*api^2*cf^2*Log[-z]*Zeta[3])/(10*z^5) - 
   (api^2*ca*cf*Log[-z]*Zeta[3])/z^4 + (api^2*cf^2*Log[-z]*Zeta[3])/z^4 - 
   (13*api^2*ca*cf*Log[-z]*Zeta[3])/(4*z^3) + 
   (101*api^2*cf^2*Log[-z]*Zeta[3])/(6*z^3) - 
   (2*api^2*cf*nh*tr*Log[-z]*Zeta[3])/(3*z^3) - 
   (2*api^2*cf*nl*tr*Log[-z]*Zeta[3])/(3*z^3) + 
   (8*api^2*cf*nh*tr*Log[-z]*Zeta[3])/z^2 - (25*api^2*ca*cf*Log[-z]*Zeta[3])/
    (4*z) - (15*api^2*cf^2*Log[-z]*Zeta[3])/(2*z) + 
   (2*api^2*cf*nh*tr*Log[-z]*Zeta[3])/z + (2*api^2*cf*nl*tr*Log[-z]*Zeta[3])/
    z - (5*api^2*ca*cf*Zeta[5])/3 + 10*api^2*cf^2*Zeta[5] - 
   (5*api^2*ca*cf*Zeta[5])/(2*z^3) + (5*api^2*cf^2*Zeta[5])/(3*z^3) - 
   (20*api^2*ca*cf*Zeta[5])/z^2 - (80*api^2*cf^2*Zeta[5])/(3*z^2) - 
   (65*api^2*ca*cf*Zeta[5])/(6*z) - (85*api^2*cf^2*Zeta[5])/(3*z)))/(16*Pi^2)
    );

  PiSlar := (
(3*(3 + (19*api*cf)/4 + (4783*api^2*ca*cf)/288 + (1961*api^2*cf^2)/288 - 
   (46*api^2*cf*nh*tr)/9 - (95*api^2*cf*nl*tr)/18 + 2/(105*z^7) + 
   (532267*api*cf)/(9261000*z^7) - (471073727*api^2*ca*cf)/(92610000*z^7) + 
   (339666207683*api^2*cf^2)/(32672808000*z^7) - (74992868899*api^2*cf*nh*tr)/
    (1296540000*z^7) + (218460799*api^2*cf*nl*tr)/(3889620000*z^7) + 
   1/(30*z^6) + (10243*api*cf)/(108000*z^6) + (16344943*api^2*ca*cf)/
    (5184000*z^6) - (2411369*api^2*cf^2)/(405000*z^6) - 
   (29545141*api^2*cf*nh*tr)/(1620000*z^6) + (54839*api^2*cf*nl*tr)/
    (540000*z^6) + 1/(15*z^5) + (3521*api*cf)/(18000*z^5) - 
   (15978853*api^2*ca*cf)/(4320000*z^5) + (175044221*api^2*cf^2)/
    (19440000*z^5) - (34816841*api^2*cf*nh*tr)/(4860000*z^5) + 
   (1217977*api^2*cf*nl*tr)/(4860000*z^5) + 1/(6*z^4) + 
   (263*api*cf)/(288*z^4) + (420179*api^2*ca*cf)/(15552*z^4) - 
   (1271839*api^2*cf^2)/(20736*z^4) - (34093*api^2*cf*nh*tr)/(3888*z^4) + 
   (6755*api^2*cf*nl*tr)/(3888*z^4) + 2/(3*z^3) - (107*api*cf)/(18*z^3) - 
   (16153*api^2*ca*cf)/(972*z^3) + (137243*api^2*cf^2)/(3888*z^3) + 
   (3685*api^2*cf*nh*tr)/(486*z^3) - (191*api^2*cf*nl*tr)/(486*z^3) - 3/z^2 + 
   (8*api*cf)/z^2 + (5239*api^2*ca*cf)/(288*z^2) - (237*api^2*cf^2)/(8*z^2) + 
   (1639*api^2*cf*nh*tr)/(72*z^2) - (341*api^2*cf*nl*tr)/(72*z^2) - 
   (7*api*cf)/z - (821*api^2*ca*cf)/(72*z) + (3*api^2*cf^2)/(8*z) - 
   (191*api^2*cf*nh*tr)/(18*z) + (61*api^2*cf*nl*tr)/(18*z) + api*cf*z2 + 
   (193*api^2*ca*cf*z2)/24 - (1235*api^2*cf^2*z2)/72 - 10*api^2*cf*nh*tr*z2 + 
   (23*api^2*cf*nl*tr*z2)/6 + (16*api^2*ca*cf*z2)/(105*z^7) - 
   (4*api^2*cf^2*z2)/(7*z^7) - (32*api^2*cf*nh*tr*z2)/(105*z^7) + 
   (16*api^2*cf*nl*tr*z2)/(105*z^7) + (7*api^2*ca*cf*z2)/(30*z^6) - 
   (7*api^2*cf^2*z2)/(8*z^6) - (7*api^2*cf*nh*tr*z2)/(15*z^6) + 
   (7*api^2*cf*nl*tr*z2)/(30*z^6) + (2*api^2*ca*cf*z2)/(5*z^5) - 
   (3*api^2*cf^2*z2)/(2*z^5) - (4*api^2*cf*nh*tr*z2)/(5*z^5) + 
   (2*api^2*cf*nl*tr*z2)/(5*z^5) + (5*api^2*ca*cf*z2)/(6*z^4) - 
   (25*api^2*cf^2*z2)/(8*z^4) - (5*api^2*cf*nh*tr*z2)/(3*z^4) + 
   (5*api^2*cf*nl*tr*z2)/(6*z^4) + (8*api^2*ca*cf*z2)/(3*z^3) - 
   (10*api^2*cf^2*z2)/z^3 - (16*api^2*cf*nh*tr*z2)/(3*z^3) + 
   (8*api^2*cf*nl*tr*z2)/(3*z^3) - (7*api^2*ca*cf*z2)/z^2 + 
   (105*api^2*cf^2*z2)/(4*z^2) + (14*api^2*cf*nh*tr*z2)/z^2 - 
   (7*api^2*cf*nl*tr*z2)/z^2 - (4*api^2*ca*cf*z2)/z + (15*api^2*cf^2*z2)/z + 
   (8*api^2*cf*nh*tr*z2)/z - (4*api^2*cf*nl*tr*z2)/z - 
   (427*api^2*ca*cf*z4)/32 + (363*api^2*cf^2*z4)/16 - 
   (25*api^2*ca*cf*z4)/(2*z^2) + (25*api^2*cf^2*z4)/z^2 + 
   (25*api^2*ca*cf*z4)/z - (50*api^2*cf^2*z4)/z - 
   (39*Sqrt[3]*api^2*ca*cf*Im[PolyLog[2, E^((I/3)*Pi)]])/8 + 
   (39*Sqrt[3]*api^2*cf^2*Im[PolyLog[2, E^((I/3)*Pi)]])/4 - 
   9*Sqrt[3]*api^2*cf*nh*tr*Im[PolyLog[2, E^((I/3)*Pi)]] - 
   (3*api^2*ca*cf*Im[PolyLog[2, E^((I/3)*Pi)]]^2)/4 + 
   (3*api^2*cf^2*Im[PolyLog[2, E^((I/3)*Pi)]]^2)/2 - 
   15*api^2*ca*cf*z2*Log[2] + 30*api^2*cf^2*z2*Log[2] - 
   (16*api^2*ca*cf*z2*Log[2])/(35*z^7) + (32*api^2*cf^2*z2*Log[2])/(35*z^7) - 
   (7*api^2*ca*cf*z2*Log[2])/(10*z^6) + (7*api^2*cf^2*z2*Log[2])/(5*z^6) - 
   (6*api^2*ca*cf*z2*Log[2])/(5*z^5) + (12*api^2*cf^2*z2*Log[2])/(5*z^5) - 
   (5*api^2*ca*cf*z2*Log[2])/(2*z^4) + (5*api^2*cf^2*z2*Log[2])/z^4 - 
   (8*api^2*ca*cf*z2*Log[2])/z^3 + (16*api^2*cf^2*z2*Log[2])/z^3 + 
   (21*api^2*ca*cf*z2*Log[2])/z^2 - (42*api^2*cf^2*z2*Log[2])/z^2 + 
   (12*api^2*ca*cf*z2*Log[2])/z - (24*api^2*cf^2*z2*Log[2])/z - 
   4*api^2*ca*cf*z2*Log[2]^2 + 8*api^2*cf^2*z2*Log[2]^2 - 
   (4*api^2*ca*cf*z2*Log[2]^2)/z^2 + (8*api^2*cf^2*z2*Log[2]^2)/z^2 + 
   (8*api^2*ca*cf*z2*Log[2]^2)/z - (16*api^2*cf^2*z2*Log[2]^2)/z + 
   (2*api^2*ca*cf*Log[2]^4)/3 - (4*api^2*cf^2*Log[2]^4)/3 + 
   (2*api^2*ca*cf*Log[2]^4)/(3*z^2) - (4*api^2*cf^2*Log[2]^4)/(3*z^2) - 
   (4*api^2*ca*cf*Log[2]^4)/(3*z) + (8*api^2*cf^2*Log[2]^4)/(3*z) - 
   2*Log[-z] - (9*api*cf*Log[-z])/2 - (49*api^2*ca*cf*Log[-z])/3 - 
   (109*api^2*cf^2*Log[-z])/16 + (13*api^2*cf*nh*tr*Log[-z])/6 + 
   (31*api^2*cf*nl*tr*Log[-z])/6 - (743*api*cf*Log[-z])/(22050*z^7) + 
   (3758939963*api^2*ca*cf*Log[-z])/(277830000*z^7) - 
   (215940050209*api^2*cf^2*Log[-z])/(7779240000*z^7) - 
   (378496261*api^2*cf*nh*tr*Log[-z])/(6945750*z^7) + 
   (160228*api^2*cf*nl*tr*Log[-z])/(1157625*z^7) - 
   (13*api*cf*Log[-z])/(225*z^6) + (10567931*api^2*ca*cf*Log[-z])/
    (1296000*z^6) - (5650789*api^2*cf^2*Log[-z])/(324000*z^6) - 
   (3698791*api^2*cf*nh*tr*Log[-z])/(324000*z^6) + 
   (26531*api^2*cf*nl*tr*Log[-z])/(108000*z^6) - 
   (47*api*cf*Log[-z])/(450*z^5) + (650497*api^2*ca*cf*Log[-z])/
    (324000*z^5) - (17774837*api^2*cf^2*Log[-z])/(3240000*z^5) - 
   (752611*api^2*cf*nh*tr*Log[-z])/(162000*z^5) + 
   (85273*api^2*cf*nl*tr*Log[-z])/(162000*z^5) - (api*cf*Log[-z])/(9*z^4) + 
   (42247*api^2*ca*cf*Log[-z])/(10368*z^4) - (139555*api^2*cf^2*Log[-z])/
    (5184*z^4) - (8347*api^2*cf*nh*tr*Log[-z])/(2592*z^4) + 
   (4981*api^2*cf*nl*tr*Log[-z])/(2592*z^4) - (64*api*cf*Log[-z])/(9*z^3) - 
   (9395*api^2*ca*cf*Log[-z])/(648*z^3) + (2351*api^2*cf^2*Log[-z])/
    (54*z^3) + (913*api^2*cf*nh*tr*Log[-z])/(81*z^3) + 
   (59*api^2*cf*nl*tr*Log[-z])/(81*z^3) - (2*Log[-z])/z^2 + 
   (12*api*cf*Log[-z])/z^2 + (405*api^2*ca*cf*Log[-z])/(16*z^2) - 
   (299*api^2*cf^2*Log[-z])/(8*z^2) - (3*api^2*cf*nh*tr*Log[-z])/(4*z^2) - 
   (27*api^2*cf*nl*tr*Log[-z])/(4*z^2) + (4*Log[-z])/z + 
   (77*api^2*ca*cf*Log[-z])/(12*z) + (21*api^2*cf^2*Log[-z])/z - 
   (7*api^2*cf*nh*tr*Log[-z])/(3*z) - (7*api^2*cf*nl*tr*Log[-z])/(3*z) - 
   2*api^2*ca*cf*z2*Log[-z] + (15*api^2*cf^2*z2*Log[-z])/2 + 
   4*api^2*cf*nh*tr*z2*Log[-z] - 2*api^2*cf*nl*tr*z2*Log[-z] - 
   (6*api^2*ca*cf*z2*Log[-z])/z^2 + (45*api^2*cf^2*z2*Log[-z])/(2*z^2) + 
   (12*api^2*cf*nh*tr*z2*Log[-z])/z^2 - (6*api^2*cf*nl*tr*z2*Log[-z])/z^2 + 
   (8*api^2*ca*cf*z2*Log[-z])/z - (30*api^2*cf^2*z2*Log[-z])/z - 
   (16*api^2*cf*nh*tr*z2*Log[-z])/z + (8*api^2*cf*nl*tr*z2*Log[-z])/z + 
   6*api^2*ca*cf*z2*Log[2]*Log[-z] - 12*api^2*cf^2*z2*Log[2]*Log[-z] + 
   (18*api^2*ca*cf*z2*Log[2]*Log[-z])/z^2 - (36*api^2*cf^2*z2*Log[2]*Log[-z])/
    z^2 - (24*api^2*ca*cf*z2*Log[2]*Log[-z])/z + 
   (48*api^2*cf^2*z2*Log[2]*Log[-z])/z + (3*api*cf*Log[-z]^2)/2 + 
   (71*api^2*ca*cf*Log[-z]^2)/12 + (57*api^2*cf^2*Log[-z]^2)/16 - 
   (11*api^2*cf*nh*tr*Log[-z]^2)/6 - (11*api^2*cf*nl*tr*Log[-z]^2)/6 - 
   (api*cf*Log[-z]^2)/(105*z^7) - (6917*api^2*ca*cf*Log[-z]^2)/(22050*z^7) + 
   (18459061*api^2*cf^2*Log[-z]^2)/(37044000*z^7) + 
   (491947*api^2*cf*nh*tr*Log[-z]^2)/(14700*z^7) + 
   (5693*api^2*cf*nl*tr*Log[-z]^2)/(132300*z^7) - 
   (api*cf*Log[-z]^2)/(60*z^6) + (1979*api^2*ca*cf*Log[-z]^2)/(11520*z^6) - 
   (78107*api^2*cf^2*Log[-z]^2)/(144000*z^6) + 
   (34153*api^2*cf*nh*tr*Log[-z]^2)/(3600*z^6) + 
   (719*api^2*cf*nl*tr*Log[-z]^2)/(10800*z^6) - (api*cf*Log[-z]^2)/(30*z^5) - 
   (47*api^2*ca*cf*Log[-z]^2)/(160*z^5) + (63049*api^2*cf^2*Log[-z]^2)/
    (216000*z^5) + (3683*api^2*cf*nh*tr*Log[-z]^2)/(1800*z^5) + 
   (649*api^2*cf*nl*tr*Log[-z]^2)/(5400*z^5) - (api*cf*Log[-z]^2)/(12*z^4) - 
   (6847*api^2*ca*cf*Log[-z]^2)/(1728*z^4) + (2719*api^2*cf^2*Log[-z]^2)/
    (1728*z^4) + (217*api^2*cf*nh*tr*Log[-z]^2)/(144*z^4) + 
   (143*api^2*cf*nl*tr*Log[-z]^2)/(432*z^4) - (4*api*cf*Log[-z]^2)/(3*z^3) + 
   (209*api^2*ca*cf*Log[-z]^2)/(108*z^3) + (24*api^2*cf^2*Log[-z]^2)/z^3 + 
   (31*api^2*cf*nh*tr*Log[-z]^2)/(9*z^3) - (34*api^2*cf*nl*tr*Log[-z]^2)/
    (27*z^3) + (6*api*cf*Log[-z]^2)/z^2 + (509*api^2*ca*cf*Log[-z]^2)/
    (48*z^2) - (201*api^2*cf^2*Log[-z]^2)/(8*z^2) - 
   (13*api^2*cf*nh*tr*Log[-z]^2)/(12*z^2) - (31*api^2*cf*nl*tr*Log[-z]^2)/
    (12*z^2) - (6*api*cf*Log[-z]^2)/z - (185*api^2*ca*cf*Log[-z]^2)/(12*z) - 
   (3*api^2*cf^2*Log[-z]^2)/(4*z) + (13*api^2*cf*nh*tr*Log[-z]^2)/(3*z) + 
   (13*api^2*cf*nl*tr*Log[-z]^2)/(3*z) - (11*api^2*ca*cf*Log[-z]^3)/24 - 
   (3*api^2*cf^2*Log[-z]^3)/4 + (api^2*cf*nh*tr*Log[-z]^3)/6 + 
   (api^2*cf*nl*tr*Log[-z]^3)/6 - (12451*api^2*ca*cf*Log[-z]^3)/(18900*z^7) + 
   (17681*api^2*cf^2*Log[-z]^3)/(13230*z^7) - (1964*api^2*cf*nh*tr*Log[-z]^3)/
    (945*z^7) - (2*api^2*cf*nl*tr*Log[-z]^3)/(945*z^7) - 
   (2833*api^2*ca*cf*Log[-z]^3)/(4320*z^6) + (7247*api^2*cf^2*Log[-z]^3)/
    (5400*z^6) - (191*api^2*cf*nh*tr*Log[-z]^3)/(135*z^6) - 
   (api^2*cf*nl*tr*Log[-z]^3)/(270*z^6) - (427*api^2*ca*cf*Log[-z]^3)/
    (1080*z^5) + (757*api^2*cf^2*Log[-z]^3)/(900*z^5) - 
   (34*api^2*cf*nh*tr*Log[-z]^3)/(45*z^5) - (api^2*cf*nl*tr*Log[-z]^3)/
    (135*z^5) - (193*api^2*ca*cf*Log[-z]^3)/(216*z^4) + 
   (575*api^2*cf^2*Log[-z]^3)/(432*z^4) - (api^2*cf*nh*tr*Log[-z]^3)/
    (9*z^4) - (api^2*cf*nl*tr*Log[-z]^3)/(54*z^4) + 
   (31*api^2*ca*cf*Log[-z]^3)/(27*z^3) + (112*api^2*cf^2*Log[-z]^3)/
    (27*z^3) - (8*api^2*cf*nl*tr*Log[-z]^3)/(27*z^3) - 
   (55*api^2*ca*cf*Log[-z]^3)/(24*z^2) - (39*api^2*cf^2*Log[-z]^3)/(4*z^2) + 
   (5*api^2*cf*nh*tr*Log[-z]^3)/(6*z^2) + (5*api^2*cf*nl*tr*Log[-z]^3)/
    (6*z^2) + (11*api^2*ca*cf*Log[-z]^3)/(6*z) + (6*api^2*cf^2*Log[-z]^3)/z - 
   (2*api^2*cf*nh*tr*Log[-z]^3)/(3*z) - (2*api^2*cf*nl*tr*Log[-z]^3)/(3*z) + 
   16*api^2*ca*cf*PolyLog[4, 1/2] - 32*api^2*cf^2*PolyLog[4, 1/2] + 
   (16*api^2*ca*cf*PolyLog[4, 1/2])/z^2 - (32*api^2*cf^2*PolyLog[4, 1/2])/
    z^2 - (32*api^2*ca*cf*PolyLog[4, 1/2])/z + 
   (64*api^2*cf^2*PolyLog[4, 1/2])/z - 6*api*cf*Zeta[3] - 
   (5*api^2*ca*cf*Zeta[3])/2 - (631*api^2*cf^2*Zeta[3])/12 + 
   (64*api^2*cf*nh*tr*Zeta[3])/3 + 6*api^2*cf*nl*tr*Zeta[3] - 
   (591*api^2*ca*cf*Zeta[3])/(490*z^7) + (1261*api^2*cf^2*Zeta[3])/
    (588*z^7) - (312*api^2*cf*nh*tr*Zeta[3])/(35*z^7) + 
   (4*api^2*cf*nl*tr*Zeta[3])/(105*z^7) - (3939*api^2*ca*cf*Zeta[3])/
    (800*z^6) + (11261*api^2*cf^2*Zeta[3])/(1200*z^6) - 
   (74*api^2*cf*nh*tr*Zeta[3])/(15*z^6) + (api^2*cf*nl*tr*Zeta[3])/(15*z^6) + 
   (118*api^2*ca*cf*Zeta[3])/(75*z^5) - (809*api^2*cf^2*Zeta[3])/(200*z^5) - 
   (44*api^2*cf*nh*tr*Zeta[3])/(45*z^5) + (2*api^2*cf*nl*tr*Zeta[3])/
    (15*z^5) - (725*api^2*ca*cf*Zeta[3])/(48*z^4) + 
   (113*api^2*cf^2*Zeta[3])/(4*z^4) + (26*api^2*cf*nh*tr*Zeta[3])/(9*z^4) + 
   (api^2*cf*nl*tr*Zeta[3])/(3*z^4) + (8*api^2*ca*cf*Zeta[3])/z^3 - 
   (41*api^2*cf^2*Zeta[3])/z^3 + (14*api^2*cf*nh*tr*Zeta[3])/(9*z^3) + 
   (10*api^2*cf*nl*tr*Zeta[3])/(3*z^3) - (6*api*cf*Zeta[3])/z^2 + 
   (17*api^2*ca*cf*Zeta[3])/(24*z^2) + (51*api^2*cf^2*Zeta[3])/(2*z^2) - 
   (20*api^2*cf*nh*tr*Zeta[3])/(3*z^2) - (2*api^2*cf*nl*tr*Zeta[3])/(3*z^2) + 
   (12*api*cf*Zeta[3])/z + (41*api^2*ca*cf*Zeta[3])/(6*z) + 
   (137*api^2*cf^2*Zeta[3])/(2*z) + (46*api^2*cf*nh*tr*Zeta[3])/(3*z) - 
   (26*api^2*cf*nl*tr*Zeta[3])/(3*z) + (25*api^2*ca*cf*Log[-z]*Zeta[3])/4 + 
   (15*api^2*cf^2*Log[-z]*Zeta[3])/2 - 2*api^2*cf*nh*tr*Log[-z]*Zeta[3] - 
   2*api^2*cf*nl*tr*Log[-z]*Zeta[3] - (2*api^2*ca*cf*Log[-z]*Zeta[3])/
    (35*z^7) + (2*api^2*cf^2*Log[-z]*Zeta[3])/(35*z^7) - 
   (api^2*ca*cf*Log[-z]*Zeta[3])/(10*z^6) + (api^2*cf^2*Log[-z]*Zeta[3])/
    (10*z^6) - (api^2*ca*cf*Log[-z]*Zeta[3])/(5*z^5) + 
   (api^2*cf^2*Log[-z]*Zeta[3])/(5*z^5) - (api^2*ca*cf*Log[-z]*Zeta[3])/
    (2*z^4) + (api^2*cf^2*Log[-z]*Zeta[3])/(2*z^4) - 
   (8*api^2*ca*cf*Log[-z]*Zeta[3])/z^3 + (8*api^2*cf^2*Log[-z]*Zeta[3])/z^3 + 
   (25*api^2*ca*cf*Log[-z]*Zeta[3])/(4*z^2) + (69*api^2*cf^2*Log[-z]*Zeta[3])/
    (2*z^2) - (2*api^2*cf*nh*tr*Log[-z]*Zeta[3])/z^2 - 
   (2*api^2*cf*nl*tr*Log[-z]*Zeta[3])/z^2 - (11*api^2*ca*cf*Log[-z]*Zeta[3])/
    z - (36*api^2*cf^2*Log[-z]*Zeta[3])/z + 
   (4*api^2*cf*nh*tr*Log[-z]*Zeta[3])/z + (4*api^2*cf*nl*tr*Log[-z]*Zeta[3])/
    z - (5*api^2*ca*cf*Zeta[5])/2 + 15*api^2*cf^2*Zeta[5] - 
   (15*api^2*ca*cf*Zeta[5])/(2*z^2) + (5*api^2*cf^2*Zeta[5])/z^2 + 
   (5*api^2*ca*cf*Zeta[5])/z - (50*api^2*cf^2*Zeta[5])/z))/(16*Pi^2)
    );

EndPackage[];

(* ************************************************************ *)

