 pure Helium
 
 
                             X     0.0000000000000000E+00
                             Y     1.0000000000000000E+00
                             Z     0.0000000000000000E+00
                          abar     4.0000000000000000E+00
                          zbar     2.0000000000000000E+00
                        logRho    -2.0000000000000000E+00
                          logT     6.0000000000000000E+00
                            T6     1.0000000000000000E+00
 
                             P      6.2100730711604395E+11
                             E      1.1185928203373142E+14
                             S      8.9350156636595654E+08
                       grad_ad      3.9338991045951843E-01
                        chiRho      9.9219799041748047E-01
                          chiT      1.0236392021179199E+00
                            Cp      1.6286430400000000E+08
                            Cv      9.7281376000000000E+07
                       dE_dRho     -1.4678233605734400E+14
                        gamma1      1.6610966920852661E+00
                        gamma3      1.6534556150436401E+00
                           eta     -7.3977394104003906E+00
 
 
                             X     0.0000000000000000E+00
                             Y     1.0000000000000000E+00
                             Z     0.0000000000000000E+00
                          abar     4.0000000000000000E+00
                          zbar     2.0000000000000000E+00
                        logRho    -1.0000000000000000E+00
                          logT     4.0000000000000000E+00
                            T6     1.0000000000000000E-02
 
                             P      2.3440638624672375E+10
                             E      3.2446068870892108E+11
                             S      2.8977776589581698E+08
                       grad_ad      3.9197054505348206E-01
                        chiRho      1.1192462444305420E+00
                          chiT      9.4195151329040527E-01
                            Cp      5.0467376000000000E+07
                            Cv      3.1885068000000000E+07
                       dE_dRho      1.3606760448000000E+11
                        gamma1      1.7666745185852051E+00
                        gamma3      1.6924794912338257E+00
                           eta     -2.0000000000000000E+01
 
 
                             X     0.0000000000000000E+00
                             Y     1.0000000000000000E+00
                             Z     0.0000000000000000E+00
                          abar     4.0000000000000000E+00
                          zbar     2.0000000000000000E+00
                        logRho    -1.0000000000000000E+00
                          logT     5.0000000000000000E+00
                            T6     9.9999999999999992E-02
 
                             P      3.2384020035350269E+11
                             E      9.4473259902115410E+12
                             S      4.7301064357999790E+08
                       grad_ad      2.5815799832344055E-01
                        chiRho      8.8670599460601807E-01
                          chiT      1.4448368549346924E+00
                            Cp      2.0440185600000000E+08
                            Cv      1.2816164000000000E+08
                       dE_dRho     -1.4402725085184000E+13
                        gamma1      1.4141864776611328E+00
                        gamma3      1.3650779724121094E+00
                           eta     -2.2140123844146729E+00
 
 
                             X     0.0000000000000000E+00
                             Y     1.0000000000000000E+00
                             Z     0.0000000000000000E+00
                          abar     4.0000000000000000E+00
                          zbar     2.0000000000000000E+00
                        logRho     2.0000000000000000E+00
                          logT     8.3010299956639813E+00
                            T6     2.0000000000000000E+02
 
                             P      5.2823694083955118E+18
                             E      1.4026771991051990E+17
                             S      1.6268307636635504E+09
                       grad_ad      2.5150709749449457E-01
                        chiRho      2.3616326439497445E-01
                          chiT      3.2915889092097750E+00
                            Cp      1.4636652945569447E+10
                            Cv      2.5195831109306946E+09
                       dE_dRho     -1.2105019150628148E+15
                        gamma1      1.3719093942351319E+00
                        gamma3      1.3450449497695083E+00
                           eta     -6.1787961578113144E+00
 
 pure Hydrogen
 
 
                             X     1.0000000000000000E+00
                             Y     0.0000000000000000E+00
                             Z     0.0000000000000000E+00
                          abar     1.0000000000000000E+00
                          zbar     1.0000000000000000E+00
                        logRho    -2.0000000000000000E+00
                          logT     6.0000000000000000E+00
                            T6     1.0000000000000000E+00
 
                             P      1.6452734663338088E+12
                             E      2.6126892325534116E+14
                             S      2.3899988359041357E+09
                       grad_ad      3.9710110425949097E-01
                        chiRho      9.9636244773864746E-01
                          chiT      1.0110590457916260E+00
                            Cp      4.2043520000000000E+08
                            Cv      2.5163355200000000E+08
                       dE_dRho     -1.8194823643136000E+14
                        gamma1      1.6647443771362305E+00
                        gamma3      1.6610684394836426E+00
                           eta     -6.7136716842651367E+00
 
 
                             X     1.0000000000000000E+00
                             Y     0.0000000000000000E+00
                             Z     0.0000000000000000E+00
                          abar     1.0000000000000000E+00
                          zbar     1.0000000000000000E+00
                        logRho    -1.0000000000000000E+00
                          logT     4.0000000000000000E+00
                            T6     1.0000000000000000E-02
 
                             P      6.9084038809327866E+10
                             E      1.8861596843913438E+12
                             S      9.1014643157590842E+08
                       grad_ad      2.2741113603115082E-01
                        chiRho      1.2436978816986084E+00
                          chiT      1.1782004833221436E+00
                            Cp      2.8870048000000000E+08
                            Cv      2.1159318400000000E+08
                       dE_dRho     -1.2310866821120000E+12
                        gamma1      1.6915541887283325E+00
                        gamma3      1.3846744298934937E+00
                           eta     -1.6593854904174805E+01
 
 
                             X     1.0000000000000000E+00
                             Y     0.0000000000000000E+00
                             Z     0.0000000000000000E+00
                          abar     1.0000000000000000E+00
                          zbar     1.0000000000000000E+00
                        logRho    -1.0000000000000000E+00
                          logT     5.0000000000000000E+00
                            T6     9.9999999999999992E-02
 
                             P      1.2385344803642195E+12
                             E      2.4388395852735816E+13
                             S      1.4600493430798335E+09
                       grad_ad      3.6117446422576904E-01
                        chiRho      9.6642440557479858E-01
                          chiT      1.2770934104919434E+00
                            Cp      4.5314678400000000E+08
                            Cv      2.4412793600000000E+08
                       dE_dRho     -3.4315169693696000E+13
                        gamma1      1.7938622236251831E+00
                        gamma3      1.6479052305221558E+00
                           eta     -1.2132427692413330E+00
 
 
                             X     1.0000000000000000E+00
                             Y     0.0000000000000000E+00
                             Z     0.0000000000000000E+00
                          abar     1.0000000000000000E+00
                          zbar     1.0000000000000000E+00
                        logRho     2.0000000000000000E+00
                          logT     8.3010299956639813E+00
                            T6     2.0000000000000000E+02
 
                             P      7.3618741187337236E+18
                             E      1.7196947611641840E+17
                             S      3.0137710342560482E+09
                       grad_ad      2.5713263652572865E-01
                        chiRho      4.5204384664932784E-01
                          chiT      2.6440943671058568E+00
                            Cp      8.3733178570005798E+09
                            Cv      2.6804417622223277E+09
                       dE_dRho     -1.2103615769952510E+15
                        gamma1      1.4121205193273270E+00
                        gamma3      1.3631022722267168E+00
                           eta     -5.4849390367623219E+00
 
 mixed Z with H&He 3:1 ratio
 
 
                             X     7.2750000000000004E-01
                             Y     2.4249999999999994E-01
                             Z     2.9999999999999999E-02
                          abar     1.2658784082055623E+00
                          zbar     1.0934024750875544E+00
                        logRho    -2.0000000000000000E+00
                          logT     6.0000000000000000E+00
                            T6     1.0000000000000000E+00
 
                             P      1.3599429384033818E+12
                             E      2.2040688629184988E+14
                             S      2.0014924245463562E+09
                       grad_ad      3.9377415047914455E-01
                        chiRho      9.9553470463041549E-01
                          chiT      1.0149606920267393E+00
                            Cp      3.5189557680104476E+08
                            Cv      2.1125497591070700E+08
                       dE_dRho     -2.0358549671664428E+14
                        gamma1      1.6583047951681502E+00
                        gamma3      1.6530025661871037E+00
                           eta     -6.8617377347129489E+00
 
 
                             X     7.2750000000000004E-01
                             Y     2.4249999999999994E-01
                             Z     2.9999999999999999E-02
                          abar     1.2658784082055623E+00
                          zbar     1.0934024750875544E+00
                        logRho    -1.0000000000000000E+00
                          logT     4.0000000000000000E+00
                            T6     1.0000000000000000E-02
 
                             P      5.5658388354025940E+10
                             E      1.4847640694276655E+12
                             S      7.6549681256073642E+08
                       grad_ad      2.3704281398588495E-01
                        chiRho      1.1951386616419621E+00
                          chiT      1.1870475423792810E+00
                            Cp      2.3134218424290419E+08
                            Cv      1.6582793916244623E+08
                       dE_dRho     -1.0368110920710155E+12
                        gamma1      1.6762462791427384E+00
                        gamma3      1.3973178157854269E+00
                           eta     -1.8503436817406442E+01
 
 
                             X     7.2750000000000004E-01
                             Y     2.4249999999999994E-01
                             Z     2.9999999999999999E-02
                          abar     1.2658784082055623E+00
                          zbar     1.0934024750875544E+00
                        logRho    -1.0000000000000000E+00
                          logT     5.0000000000000000E+00
                            T6     9.9999999999999992E-02
 
                             P      9.8609566711459644E+11
                             E      2.0334640729000492E+13
                             S      1.2180980793278699E+09
                       grad_ad      3.5162713325653011E-01
                        chiRho      9.4783529761836660E-01
                          chiT      1.2891698943128718E+00
                            Cp      3.8122994651209366E+08
                            Cv      2.0847088771310151E+08
                       dE_dRho     -2.8507471498139891E+13
                        gamma1      1.7336596086676865E+00
                        gamma3      1.6094760760386118E+00
                           eta     -1.3851459676497320E+00
 
 
                             X     7.2750000000000004E-01
                             Y     2.4249999999999994E-01
                             Z     2.9999999999999999E-02
                          abar     1.2658784082055623E+00
                          zbar     1.0934024750875544E+00
                        logRho     2.0000000000000000E+00
                          logT     8.3010299956639813E+00
                            T6     2.0000000000000000E+02
 
                             P      6.7857460510208225E+18
                             E      1.6318907006851594E+17
                             S      2.6488760220794072E+09
                       grad_ad      2.5540384895898804E-01
                        chiRho      4.0547888444541047E-01
                          chiT      2.7837493952657129E+00
                            Cp      9.1201516918163090E+09
                            Cv      2.6359034139180717E+09
                       dE_dRho     -1.2104070414935080E+15
                        gamma1      1.4029455383092959E+00
                        gamma3      1.3583176903640335E+00
                           eta     -5.6315681957006101E+00
 
 solar
 
 
                             X     6.9999999999999996E-01
                             Y     2.8000000000000003E-01
                             Z     2.0000000000000000E-02
                          abar     1.2966353410255222E+00
                          zbar     1.1021400398716941E+00
                        logRho    -2.0000000000000000E+00
                          logT     6.0000000000000000E+00
                            T6     1.0000000000000000E+00
 
                             P      1.3340338837905352E+12
                             E      2.1637192635845825E+14
                             S      1.9656824218299994E+09
                       grad_ad      3.9461383223533619E-01
                        chiRho      9.9556837975978840E-01
                          chiT      1.0144154280424116E+00
                            Cp      3.4427980399999994E+08
                            Cv      2.0646320799999994E+08
                       dE_dRho     -1.9240351432703997E+14
                        gamma1      1.6601236313581462E+00
                        gamma3      1.6551114022731777E+00
                           eta     -6.8766261339187622E+00
 
 
                             X     6.9999999999999996E-01
                             Y     2.8000000000000003E-01
                             Z     2.0000000000000000E-02
                          abar     1.2966353410255222E+00
                          zbar     1.1021400398716941E+00
                        logRho    -1.0000000000000000E+00
                          logT     4.0000000000000000E+00
                            T6     1.0000000000000000E-02
 
                             P      5.4349169194705391E+10
                             E      1.4432344794897551E+12
                             S      7.4976387301004088E+08
                       grad_ad      2.3836515285074711E-01
                        chiRho      1.1904707849025724E+00
                          chiT      1.1866070181131363E+00
                            Cp      2.2529105600000000E+08
                            Cv      1.6110462699999997E+08
                       dE_dRho     -1.0104528076799999E+12
                        gamma1      1.6752448827028275E+00
                        gamma3      1.3992966562509535E+00
                           eta     -1.8663280725479122E+01
 
 
                             X     6.9999999999999996E-01
                             Y     2.8000000000000003E-01
                             Z     2.0000000000000000E-02
                          abar     1.2966353410255222E+00
                          zbar     1.1021400398716941E+00
                        logRho    -1.0000000000000000E+00
                          logT     5.0000000000000000E+00
                            T6     9.9999999999999992E-02
 
                             P      9.6136638084116040E+11
                             E      1.9942384666711414E+13
                             S      1.1939397354527369E+09
                       grad_ad      3.5011287778615946E-01
                        chiRho      9.4570557028055180E-01
                          chiT      1.2902790755033491E+00
                            Cp      3.7445821599999994E+08
                            Cv      2.0534408599999997E+08
                       dE_dRho     -2.7901927096319992E+13
                        gamma1      1.7248613089323044E+00
                        gamma3      1.6037879586219783E+00
                           eta     -1.4041102230548856E+00
 
 
                             X     6.9999999999999996E-01
                             Y     2.8000000000000003E-01
                             Z     2.0000000000000000E-02
                          abar     1.2966353410255222E+00
                          zbar     1.1021400398716941E+00
                        logRho     2.0000000000000000E+00
                          logT     8.3010299956639813E+00
                            T6     2.0000000000000000E+02
 
                             P      6.7316945747436165E+18
                             E      1.6236433178368397E+17
                             S      2.6147592264309516E+09
                       grad_ad      2.5524608970074869E-01
                        chiRho      4.0070135790575212E-01
                          chiT      2.7980779675300593E+00
                            Cp      9.2081907596452732E+09
                            Cv      2.6317151007345228E+09
                       dE_dRho     -1.2104111698988132E+15
                        gamma1      1.4020265872302209E+00
                        gamma3      1.3578618040469994E+00
                           eta     -5.6476423717687982E+00
 
 
 
                     tolerance  1.0000000000000000E-04
 
                 actual logRho -7.0000000000000000E+00
                  guess logRho -7.3010299956639813E+00
                  found logRho -6.9952481230145711E+00
                   wanted logS  9.4724733362637039E+00
                      got logS  9.4724735109301879E+00
 
 
                   actual logT  4.7999999999999998E+00
                    guess logT  5.1010299956639811E+00
                    found logT  4.7975097076588566E+00
                   wanted logS  9.4724733362637039E+00
                      got logS  9.4724741321934278E+00
 
 
 test_theta_e
           eta           theta_e
        -10.00      9.999839E-01
         -5.00      9.976295E-01
          0.00      7.905652E-01
          5.00      2.796166E-01
         10.00      1.475121E-01
         15.00      9.926693E-02
         20.00      7.469115E-02
         25.00      5.984195E-02
         30.00      4.990856E-02
         35.00      4.279957E-02
         40.00      3.746143E-02
         45.00      3.330625E-02
         50.00      2.998026E-02
         55.00      2.725789E-02
         60.00      2.498858E-02
         65.00      2.306794E-02
         70.00      2.142138E-02
         75.00      1.999415E-02
 
 test1_eosPT
                                    logT    8.1499996185299999E+00
                                 logPgas    1.8410894721399998E+01
                                       T    1.4125363038967422E+08
                                    Pgas    2.5756966991208591E+18
                                       Z    2.0000000000000000E-02
                                       X    6.9999999999999996E-01
                                    abar    1.2966353410255222E+00
                                    zbar    1.1021400398716941E+00
 
 
                                     rho    1.3515258756660802E+02
                                  logRho    2.1308243649081575E+00
 
                      dlnRho_dlnPgas_c_T    9.9931627910651533E-01
                      dlnRho_dlnT_c_Pgas   -9.9844013999056491E-01
                                       P    3.5796885867451453E+18
                                       E    5.1305442181905472E+16
                                       S    1.9053041406129000E+09
                                 grad_ad    2.7841803207863691E-01
                                  chiRho    7.2002077646485219E-01
                                    chiT    1.8406989871884920E+00
                                      Cp    1.7212390894021988E+09
                                      Cv    8.3913331650196075E+08
                                 dE_dRho   -1.6466236307100875E+14
                                   dS_dT    5.9406106652111461E+00
                                 dS_dRho   -2.5523321367534483E+06
                                      mu    6.1626183498984533E-01
                                lnfree_e   -1.6240205421155127E-01
                                  gamma1    1.4769165968940747E+00
                                  gamma3    1.4112002198032760E+00
                                     eta   -4.8050537645586200E+00
 
